An Integrated Impedance Biosensor Array - Stacksdn968xz4219/thesis_toplevel... · AN INTEGRATED IMPEDANCE BIOSENSOR ARRAY ... helped me understand circuit design, ... 1 Introduction

AN INTEGRATED IMPEDANCE BIOSENSOR ARRAY

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF ELECTRICAL

ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Jonathan S. Daniels

March 2010

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/dn968xz4219

© 2010 by Jonathan Spencer Daniels. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

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http://purl.stanford.edu/dn968xz4219

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Thomas Lee, Primary Adviser


Thomas Kenny


Nader Pourmand

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

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Abstract

Affinity biosensors are important tools for detecting DNA, proteins, cells, and other

biomedical analytes. Although optical readout is prevalent, impedance readout is promising

for many applications due to lower cost, reduced system size, and label-free operation.

Impedance biosensors detect the binding of a target biomolecule to an immobilized probe

by quantifying changes in the the electrode-electrolyte interface impedance.

Impedance biosensors traditionally use bulky and expensive instruments to monitor

the impedance of a single electrode. We describe miniaturized and inexpensive readout

circuitry for an array of such sensors. By using a sensor array, multiple analytes can be

simultaneously detected and limitations inherent to individual sensors can be mitigated.

Reducing the size and cost of the measurement system enablesnew applications.

We present a measurement system for a 6x6 array of impedance biosensors built from

off-the-shelf components. Experimental results with DNA probe-target pairs confirm oth-

ers’ reports that changes in the interface impedance can signify binding. Other experiments

with proteins demonstrate that changes in the nonlinearityof the I-V relationship can also

indicate probe-target binding. We show that the impedance and the nonlinearity can be

quantified simultaneously by superimposing a large-amplitude tone on the impedance-

measurement tone and analyzing the resulting intermodulation tones.

We conclude by describing an integrated array of measurement circuits implemented

in 0.18 µm CMOS. Each of the 36 measurement pixels contains an impedance-measuring

circuit plus tone cancellation circuitry, which enables simultaneous nonlinearity measure-

ment. To prevent the large-amplitude excitation from saturating the amplifier output, a per-

pixel digital feedback loop injects an appropriate cancelling current at the amplifier input.

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Impedance changes of 0.2% can be detected using the integrated measurement circuit. Each

pixel occupies 0.14 mm2 and consumes 1.9 mW.

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Acknowledgement

The work presented in this dissertation would not be possible without the contributions of

many individuals, and I can only hope to mention some of the most important here.

First, I am indebted to my EE advisor and mentor, Thomas H. Lee, for agreeing to serve

as my advisor despite his busy schedule and negative indications about my aptitude.1 On

several occasions Tom had a critical insight that saved me great effort. I admire both his

intensity and his humor, not to mention his significant musical ability on the violin. Thank

you Tom!

I also owe much to my biochemical mentor, Nader Pourmand. He also took a huge

chance on me, giving me a “home” (and funding) at the StanfordGenome Technology

Center. Nader taught me many of the biologist’s tricks over the years, and I only hope the

information exchange was mutual. I may never understand whyhe would let me work on a

topic essentially of my own choosing, but I will be forever grateful for this freedom. Nader,

thank you for your faith in me!

Other Stanford professors encouraged and taught me much. Ofparticular note are

Steve Boxer, Boris Murmann, Roger Howe, John Fox, and Tom Kenny. It was from the

lips of Professor Boxer, less than a month after starting at Stanford, that I first heard

the words “impedance spectroscopy,” and his encouragementwas vital in preserving my

hope of working on an idea that had come to me the summer beforestarting graduate

school (several other professors had been much less encouraging). Boris Murmann also

helped me understand circuit design, and Roger Howe suggested pursuing the idea of

treating nonlinearity as something interesting instead ofa problem to overcome. John Fox

1The worst grade I ever received was in Tom’s class my first yearat Stanford, EE214. It was my firstcircuit design class — coming from a non-EE undergraduate curriculum — and was overwhelming, butthanks to that experience I fared much better in subsequent circuit classes.

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generously took me on as a TA for his lab electronics class during my first year at Stanford.

I enjoyed being his TA many times over my years here, and when Ireturn to teach I hope to

emulate his effective teaching style. Finally, Tom Kenny has been a mentor since my first

year at Stanford. Besides almost joining his research group, his class was perhaps the most

time-consuming and most rewarding I ever had. Our final project, the basketball-playing

robot, didn’t function until a week late, but at least we madeit work! I also appreciate

Tom for agreeing to be on my reading and orals committee despite his many other time

commitments.

I was fortunate to encounter Arjang Hassibi about one year into graduate school. Arjang

happened to be working on a very similar project to what I wanted to do, and in many ways

the rest of my graduate career was spent trying to follow in his footsteps as best I could. I

appreciate Arjang’s patient mentoring and continued friendship.

I met Erik Anderson on my first day at Stanford, as one of my roommates; we later

became labmates under Nader and close collaborators as the two EEs in the bio-heavy

research group. Erik graciously served as a source of ideas and as a tutor to fill in some

gaps in my engineering knowledge; among other things he showed me how to design PCBs,

compute noise transfer functions, and use LATEX. He has a brilliant and restless mind, which

made for some interesting conversations. Erik, thank you for all of your help and your

continued friendship.

There are a host of other people that have assisted in sundry ways, both at the Stanford

Genome Technology Center and in the Electrical Engineeringdepartment. Ron Davis, the

director of the SGTC, has always been supportive. I learned much from group members

Andy Mak, Heng Yu, Milos Karhanek, Senkei Umehara, Annika Branting, and others. The

other technical students and staff at SGTC helped tremendously, including Henrik Persson,

Amir Ali Talasaz, Vincent Tabard-Cossa, Mehdi Javanmard, Hesaam Esfandyarpour, Paul

Vavra, Michael Proctor, Les Roberts, and David Huber. Finally, thanks to the support staff

(Donna Bowe and Jenny Zhang especially) and the other students and researchers at the

Center.

Many fellow EE students assisted in large and small ways. Kelin Lee, Valentin

Abramzon, Hyunsik Park, Ross Walker, Bob Wiser, and Moon Kimall lent assistance

as I designed an integrated circuit for the first time. Keith Fife and Jim Weaver served

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as brilliant and patient tutors and friends. Other SMiRCs gave helpful input, including

already-graduated Joel Dawson. Special thanks to June Wang, Natasha Newson, and the

other EE admins and staff for their patient help.

I started a job at Intel Labs almost 18 months before finishingmy Ph.D., working as

part of a multi-disciplinary team working to develop electronic biosensors. I am indebted

to my manager Madoo Varma and all of my colleagues for their understanding and support

as I tried to finish, while also keeping abreast of my (enjoyable) work responsibilities.

Financial support came from the National Human Genome Research Institute

(HG000205/HG/NHGRI and T32 HG00044/HG/NHGRI) and the National Science

Foundation (DBI-0551990). National Semiconductor provided manufacturing for my

CMOS design.

Finally, completion of this dissertation would not have been possible without the

support and encouragement of my family. Meeting my wife Jen was the best thing that

happened to me while studying at Stanford. She has shown near-endless patience and

given invaluable encouragement. I love her and am glad to have found and married my

“twin soul.” Our daughter Hannah may have slowed down my research, but she has added

much joy to my life. My parents, siblings, and extended family have likewise provided

much-needed encouragement and support, from my earliest years to the present. Thank

you!

This dissertation was typeset using LATEX, with LYX as a front-end editor (using

something with a change tracking feature was a requirement of Tom’s, though I’m glad

in retrospect that I switched to LYX instead of using straight LATEX). Using these free tools

was a huge time-saver, and their creators deserve accolades.

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Contents

Abstract v

Acknowledgement vii

1 Introduction and Outline 1

1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Label-free Impedance Biosensors 4

2.1 Impedance Biosensors: What and Why . . . . . . . . . . . . . . . . . .. . 5

2.1.1 Definition of impedance biosensors . . . . . . . . . . . . . . . .. 5

2.1.2 Related fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.3 Why study impedance biosensors? . . . . . . . . . . . . . . . . . .8

2.1.4 Further reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.2 Affinity Biosensor Concepts . . . . . . . . . . . . . . . . . . . . . . . .. 9

2.2.1 Affinity biosensor = affinity + sensor . . . . . . . . . . . . . . .. 9

2.2.2 Probe-target binding . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.2.3 To label or not to label? . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.4 Label-free operation . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.5 Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.2.6 Limit of detection and reproducibility . . . . . . . . . . . .. . . . 15

2.2.7 Dynamic range . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2.8 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.9 Amplification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

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2.2.10 Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.11 What really limits biosensor performance? . . . . . . . .. . . . . 18

2.3 Electrochemical Impedance Concepts . . . . . . . . . . . . . . . .. . . . 19

2.3.1 Apply a voltage, measure a current . . . . . . . . . . . . . . . . .. 19

2.3.2 Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3.3 Instrumentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.3.4 Faradaic vs. non-faradaic . . . . . . . . . . . . . . . . . . . . . . .22

2.3.5 Data fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.6 Circuit models . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3.7 Constant phase element . . . . . . . . . . . . . . . . . . . . . . . . 26

2.3.8 Double-layer capacitance . . . . . . . . . . . . . . . . . . . . . . .27

2.3.8.1 Mathematical treatment . . . . . . . . . . . . . . . . . . 28

2.3.8.2 Important observations . . . . . . . . . . . . . . . . . . 31

2.3.8.3 Stern’s modification for adsorbed charge . . . . . . . . .34

2.3.8.4 Response time . . . . . . . . . . . . . . . . . . . . . . . 36

2.3.9 Scaling electrode size . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.4 Practical Issues in Impedance Biosensors . . . . . . . . . . . .. . . . . . 37

2.4.1 What causes an impedance change? . . . . . . . . . . . . . . . . . 37

2.4.2 Response curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.4.3 Differential measurement . . . . . . . . . . . . . . . . . . . . . . .43

2.4.4 Probe attachment chemistry . . . . . . . . . . . . . . . . . . . . . 43

2.4.5 DNA vs. protein biosensors . . . . . . . . . . . . . . . . . . . . . 45

2.5 Published Prior Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.5.1 Early affinity impedance biosensors . . . . . . . . . . . . . . .. . 48

2.5.2 Potentiostatic step . . . . . . . . . . . . . . . . . . . . . . . . . . 48

2.5.3 Non-faradaic studies . . . . . . . . . . . . . . . . . . . . . . . . . 50

2.5.4 Faradaic studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

2.5.5 Polymer films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.5.6 Special electrode surfaces . . . . . . . . . . . . . . . . . . . . . .54

2.5.7 Interdigitated electrodes . . . . . . . . . . . . . . . . . . . . . .. 54

2.5.8 Miniaturization efforts . . . . . . . . . . . . . . . . . . . . . . . .55

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2.6 Conclusions and Research Directions . . . . . . . . . . . . . . . .. . . . 56

3 PCB Measurement System 59

3.1 Measurement System Overview . . . . . . . . . . . . . . . . . . . . . . .59

3.2 Fabrication of Electrode Array Chip . . . . . . . . . . . . . . . . .. . . . 59

3.3 Socket for Chip Interfacing . . . . . . . . . . . . . . . . . . . . . . . .. . 61

3.4 Impedance Measurement Architecture . . . . . . . . . . . . . . . .. . . . 62

3.5 PCB Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.6 Data Acquisition and Signal Extraction . . . . . . . . . . . . . .. . . . . 66

3.7 Calibration Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.7.1 Why is calibration needed? . . . . . . . . . . . . . . . . . . . . . . 69

3.7.2 Derivation of calibration equations . . . . . . . . . . . . . .. . . . 70

3.7.3 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

3.8 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

3.9 Surface Functionalization . . . . . . . . . . . . . . . . . . . . . . . .. . . 73

3.9.1 Polyelectrolyte film deposition . . . . . . . . . . . . . . . . . .. . 73

3.9.2 Attaching DNA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

3.9.3 Attaching proteins . . . . . . . . . . . . . . . . . . . . . . . . . . 75

3.10 Other Measurement Details . . . . . . . . . . . . . . . . . . . . . . . .. . 77

3.11 Representative Impedance Data . . . . . . . . . . . . . . . . . . . .. . . . 78

4 Using Nonlinearity as a Sensed Variable 84

4.1 Early Nonlinearity Measurements . . . . . . . . . . . . . . . . . . .. . . 85

4.2 Nonlinearity of Double Layer Capacitance . . . . . . . . . . . .. . . . . . 86

4.3 Mathematics of Nonlinearity . . . . . . . . . . . . . . . . . . . . . . .. . 87

4.3.1 Nonlinear capacitors . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.3.2 Double layer “varactance” . . . . . . . . . . . . . . . . . . . . . . 89

4.4 Two-tone Approach to Nonlinearity Measurement . . . . . . .. . . . . . . 89

4.4.1 Motivation for a two-tone approach . . . . . . . . . . . . . . . .. 90

4.4.2 Mathematical explanation . . . . . . . . . . . . . . . . . . . . . . 90

4.5 Modifications to PCB Measurement System . . . . . . . . . . . . . .. . . 92

4.6 Measurement Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

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4.6.1 System characterization . . . . . . . . . . . . . . . . . . . . . . . 92

4.6.2 Biological measurements . . . . . . . . . . . . . . . . . . . . . . . 93

4.7 Implications of our observations . . . . . . . . . . . . . . . . . . .. . . . 98

4.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5 Requirements for CMOS Measurement System 100

5.1 Detection Steps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

5.1.1 Affinity capture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.1.2 Selectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.1.3 Readout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

5.2 Measurement System Architecture . . . . . . . . . . . . . . . . . . .. . . 102

5.2.1 The TIA is our focus . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.3 Requirements Related toZDUT . . . . . . . . . . . . . . . . . . . . . . . . 103

5.3.1 Electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.3.2 Multiplexing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.3.3 Frequency range . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.3.4 Excitation amplitude . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.3.5 Impedance to be measured . . . . . . . . . . . . . . . . . . . . . . 105

5.3.6 Nonlinearity to be measured . . . . . . . . . . . . . . . . . . . . . 107

5.4 Constraints Imposed by CMOS . . . . . . . . . . . . . . . . . . . . . . . 108

5.4.1 CMOS process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.4.2 Die area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.4.3 Power consumption . . . . . . . . . . . . . . . . . . . . . . . . . 108

5.4.4 CMOS-sensor interfacing . . . . . . . . . . . . . . . . . . . . . . 109

5.5 Precision Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . .. 109

5.5.1 Precision of published results . . . . . . . . . . . . . . . . . . .. 110

5.5.2 Precision is important, accuracy is not . . . . . . . . . . . .. . . 111

5.5.3 Precision vs. SNR . . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.5.4 Specifications of commercial instruments . . . . . . . . . .. . . . 112

5.5.4.1 Solartron EIS instruments . . . . . . . . . . . . . . . . . 112

5.5.4.2 CHI 660 . . . . . . . . . . . . . . . . . . . . . . . . . . 113

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5.5.4.3 Axopatch 200B patch clamp . . . . . . . . . . . . . . . 113

5.5.4.4 Impedance-to-Digital ICs . . . . . . . . . . . . . . . . . 113

5.5.5 Our target precision . . . . . . . . . . . . . . . . . . . . . . . . . . 114

5.6 Uncertainty propagation . . . . . . . . . . . . . . . . . . . . . . . . . .. 114

5.6.1 Uncertainty propagation for simple impedance calculation . . . . . 115

5.6.2 Uncertainty propagation for our impedance calculation . . . . . . . 116

5.6.3 Precision requirements correspond to noise requirements . . . . . . 117

5.7 Transfer function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.7.1 Approximate transfer function . . . . . . . . . . . . . . . . . . .. 118

5.7.2 More realistic transfer function . . . . . . . . . . . . . . . . .. . 119

5.7.3 Choice ofCf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

5.7.4 Choice ofRf . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

5.7.5 T-network equations . . . . . . . . . . . . . . . . . . . . . . . . . 123

5.8 Noise Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5.8.1 OTA voltage noise . . . . . . . . . . . . . . . . . . . . . . . . . . 124

5.8.2 OTA current noise . . . . . . . . . . . . . . . . . . . . . . . . . . 125

5.8.3 T-network thermal noise . . . . . . . . . . . . . . . . . . . . . . . 126

5.8.4 T-network amplification of OTA noise . . . . . . . . . . . . . . .. 127

5.8.5 T-network flicker noise . . . . . . . . . . . . . . . . . . . . . . . . 129

5.8.6 Electrical noise fromZDUT . . . . . . . . . . . . . . . . . . . . . . 130

5.8.6.1 Johnson noise ofRsol . . . . . . . . . . . . . . . . . . . 130

5.8.6.2 Johnson noise ofRleak . . . . . . . . . . . . . . . . . . . 131

5.8.6.3 Noise of CPECsur f . . . . . . . . . . . . . . . . . . . . 131

5.8.6.4 Affinity binding noise . . . . . . . . . . . . . . . . . . . 132

5.8.7 Acquisition noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

5.9 Relative Importance of Noise Sources . . . . . . . . . . . . . . . .. . . . 133

5.10 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . 137

5.10.1 Sensitivity toZDUT . . . . . . . . . . . . . . . . . . . . . . . . . . 137

5.10.2 Sensitivity to other parameters . . . . . . . . . . . . . . . . .. . . 138

5.11 Model Parameter Estimation from Tone Data . . . . . . . . . . .. . . . . 140

5.12 Putting it Together: Required Circuit SNR . . . . . . . . . . .. . . . . . . 141

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6 CMOS Design 145

6.1 OTA Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

6.2 Folded Cascode Architecture . . . . . . . . . . . . . . . . . . . . . . .. . 146

6.3 Transistor Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

6.3.1 Thermal noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

6.3.2 Flicker noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

6.3.3 Noise simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

6.4 Minimizing OTA Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

6.4.1 Input devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

6.4.2 Cascode devices . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

6.4.3 Load devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

6.4.4 Total noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

6.5 Effectivegm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

6.6 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .153

6.7 Slewing Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153

6.8 Cascode Biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

6.9 Constant-gm Biasing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

6.9.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

6.9.2 Traditional constant-gm bias . . . . . . . . . . . . . . . . . . . . . 157

6.9.3 Shortcomings in traditional constant-gm bias . . . . . . . . . . . . 158

6.9.4 Proposed constant-gm bias . . . . . . . . . . . . . . . . . . . . . . 159

6.9.5 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

6.10 OTA Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

6.11 Overview of Two-tone Measurement . . . . . . . . . . . . . . . . . .. . 162

6.11.1 IM tones generated fromZDUT . . . . . . . . . . . . . . . . . . . . 164

6.12 Why Is Tone Cancellation Needed? . . . . . . . . . . . . . . . . . . .. . 165

6.13 Tone Cancellation Requirements . . . . . . . . . . . . . . . . . . .. . . . 165

6.13.1 Nonlinearity ofCf . . . . . . . . . . . . . . . . . . . . . . . . . . 167

6.13.2 Nonlinearity ofRf . . . . . . . . . . . . . . . . . . . . . . . . . . 167

6.13.3 Nonlinearity ofZf . . . . . . . . . . . . . . . . . . . . . . . . . . 168

6.13.4 Mixing ofωB andωA tone arising fromZf . . . . . . . . . . . . . 168

xv

6.13.5 Swing considerations . . . . . . . . . . . . . . . . . . . . . . . . . 169

6.13.6 Other possible sources of IM tones . . . . . . . . . . . . . . . .. . 169

6.13.7 Mixing of 2ωB tone withωA tone . . . . . . . . . . . . . . . . . . 170

6.14 Cancellation Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . .171

6.15 Digital Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

6.16 Validation of Cancellation Scheme . . . . . . . . . . . . . . . . .. . . . . 175

6.17 CMOS Implementation of Tone Cancellation . . . . . . . . . . .. . . . . 177

6.17.1 Comparator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177

6.17.2 Multiplier and integrator . . . . . . . . . . . . . . . . . . . . . .. 182

6.17.3 Requirements in terms of transconductance control .. . . . . . . . 182

6.17.4 Variable transconductor . . . . . . . . . . . . . . . . . . . . . . .184

6.18 Noise of Tone Cancellation Circuitry . . . . . . . . . . . . . . .. . . . . . 187

6.18.1 Decision to increaseRcancel . . . . . . . . . . . . . . . . . . . . . 187

6.18.2 Resistor and switch thermal noise . . . . . . . . . . . . . . . .. . 187

6.18.3 Resistor flicker noise . . . . . . . . . . . . . . . . . . . . . . . . . 188

6.18.4 Switch flicker noise . . . . . . . . . . . . . . . . . . . . . . . . . . 189

6.18.5 Noise from off-chip drivers . . . . . . . . . . . . . . . . . . . . .. 189

6.18.6 Summary of noise from cancellation circuit . . . . . . . .. . . . . 190

6.19 CMOS Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

7 Measured CMOS Performance 192

7.1 CMOS Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192

7.2 Chip Interfacing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

7.3 Tone Cancellation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194

7.4 Impedance Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195

7.5 Biological Measurements . . . . . . . . . . . . . . . . . . . . . . . . . .. 199

7.6 Significance of Measurement Results . . . . . . . . . . . . . . . . .. . . . 199

8 Conclusion 202

8.1 Summary and Contributions . . . . . . . . . . . . . . . . . . . . . . . . .202

8.2 Areas for Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204

xvi

A Useful Trigonometry Identities 206

Bibliography 207

xvii

List of Tables

2.1 Debye length and corresponding capacitance density forcommon elec-

trolytes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

2.2 Summary of selected label-free affinity impedance biosensors . . . . . . . . 47

3.1 Discrete components chosen for PCB implementation and selection criteria. 65

5.1 Minimum, typical, and maximum impedances to be measured. . . . . . . . 105

5.2 Reported impedance changes corresponding to the limit of detection of

nonfaradaic impedance biosensors. . . . . . . . . . . . . . . . . . . . .. . 111

5.3 Error propagation formulas for uncorrelated variablesA andB. . . . . . . . 115

5.4 Computed noise of various components of the T network at the amplifier

output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

5.5 Worst-case flicker noise estimates for on-die resistors. . . . . . . . . . . . . 130

6.1 Transistor dimensions for folded cascode design. . . . . .. . . . . . . . . 147

xviii

List of Figures

2.1 Generalized affinity biosensor, showing (a) the information flow, (b) the

physical arrangement, and (c) the steps involved. . . . . . . . .. . . . . . 10

2.2 Sandwich assay vs. label-free detection. . . . . . . . . . . . .. . . . . . . 12

2.3 Circuit models for non-faradaic and faradaic interfaces. . . . . . . . . . . . 24

2.4 Example non-faradaic and faradaic impedance data. . . . .. . . . . . . . . 25

(a) Nyquist representation. . . . . . . . . . . . . . . . . . . . . . . . . . 25

(b) Bode representation . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.5 Double layer capacitance vs. electrode potential. . . . .. . . . . . . . . . . 33

2.6 Origin of ionic double layer capacitance. . . . . . . . . . . . .. . . . . . . 35

(a) Molecular-level depiction. . . . . . . . . . . . . . . . . . . . . . . .35

(b) Potential distribution. . . . . . . . . . . . . . . . . . . . . . . . . . .35

3.1 Physical components of the measurement system. . . . . . . .. . . . . . . 60

(a) Layout of 6x6 electrode chip. . . . . . . . . . . . . . . . . . . . . . 60

(b) Chip in socket. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.2 Fabrication steps for electrode array chip. . . . . . . . . . .. . . . . . . . 61

3.3 Basic impedance measurement architecture. . . . . . . . . . .. . . . . . . 63

3.4 Measurement circuit implemented on PCB. . . . . . . . . . . . . .. . . . 64

3.5 Final PCB implementation. . . . . . . . . . . . . . . . . . . . . . . . . .. 66

(a) LabView interface for impedance measurement. . . . . . . . .. . . 68

(b) LabView sub-VI for tone extraction. . . . . . . . . . . . . . . . . .. 68

3.6 Example fit impedance data, from DNA experiments. . . . . . .. . . . . . 79

3.7 Best-fit parameters for many electrodes on same chip measured vs. time. . . 80

3.8 Early impedance data showing clear change upon DNA hybridization. . . . 81

xix

3.9 Csur f magnitude and phase vs. DC bias for BSA-functionalized electrodes. . 83

4.1 Csur f vs. DC bias for three differently-functionalized electrodes. . . . . . . 86

4.2 Capacitance vs. DC bias for the non-biological DUT. . . . .. . . . . . . . 93

4.3 Fluorescent micrograph of chip showing target binding as expected. . . . . 94

4.4 CPE magnitude, phase, and impedance at 1 kHz vs. bias. . . .. . . . . . . 96

(a) Before target addition . . . . . . . . . . . . . . . . . . . . . . . . . 96

(b) After target addition . . . . . . . . . . . . . . . . . . . . . . . . . . 96

4.5 Changes inα1 can indicate target binding. . . . . . . . . . . . . . . . . . . 97

5.1 System diagram, indicating on-chip vs. off-chip functionality. . . . . . . . . 103

5.2 Possible values ofZDUT based on measurements of our 300µm square

biofunctionalized electrodes. . . . . . . . . . . . . . . . . . . . . . . .. . 106

5.3 MeasuringZDUT using an OTA with feedback impedanceZf and input

excitationVtest. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.4 A more realistic version of Figure 5.3. . . . . . . . . . . . . . . .. . . . . 119

5.5 System transfer functionT for various corners ofZDUT . . . . . . . . . . . . 121

5.6 A T-network is used to form an equivalent resistor to rolloff the DC gain

of the TIA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

5.7 Conversion between T andΠ networks. . . . . . . . . . . . . . . . . . . . 124

5.8 Referring OTA noise to the system input. . . . . . . . . . . . . . .. . . . . 125

5.9 Network for deriving the T-network noise contributions. . . . . . . . . . . . 127

5.10 Noise gain from amplifier input to system input with different T-network

gains. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

5.11 Noise sources referred to system input for minimumZDUT . . . . . . . . . . 134

5.12 Noise sources referred to system input for typicalZDUT . . . . . . . . . . . 135

5.13 Noise sources referred to system input for maximumZDUT . . . . . . . . . . 136

5.14 Simulated sensitivity ofT to ZDUT , expressed in fractional sensitivity. . . . 138

5.15 Simulated sensitivity ofT to ZDUT , expressed in fractional sensitivity. . . . 139

5.16 Simulated maximum excitationVtestfor theZDUT corners. . . . . . . . . . . 142

5.17 Simulated total noise density referred to the system input for theZDUT

corners. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

xx

5.18 Simulated SNR ofZDUT determination for theZDUT corners. . . . . . . . . 144

6.1 Final folded cascode design . . . . . . . . . . . . . . . . . . . . . . . .. . 147

6.2 Circuit to generate bias voltages for the folded cascodeamplifier shown in

Figure 6.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

6.3 Simulated OTA gain vs. output voltage for typical transistor corner. . . . . . 156

6.4 A simple constant-gm bias circuit and associated differential pair. . . . . . 158

6.5 A modified constant-gm bias circuit and associated amplifier. . . . . . . . . 160

6.6 Implemented constant-gm circuit, including relevant parts of the main

amplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

6.7 Simulated temperature dependence ofgm of relevant transistors in our

constant-gm circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

(a) The transconductance of M1 and M2 vs. temperature. . . . . .. . . 163

(b) The transconductance of the input transistor vs. temperature. . . . . . 163

6.8 SNR plots for IM tones show that they can be quantified within 1% (40 dB)

as desired. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

(a) SNR forωA±ωB. . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

(b) SNR forωA±2ωB. . . . . . . . . . . . . . . . . . . . . . . . . . . . 166

6.9 Tone cancellation scheme. . . . . . . . . . . . . . . . . . . . . . . . . .. 172

6.10 Feedback concept for the cancellation scheme. . . . . . . .. . . . . . . . . 173

6.11 Simplified schematic of the digital phase sensitive detector. . . . . . . . . . 174

6.12 Master comparison circuit for each channel of tone cancellation. . . . . . . 176

6.13 Simulink simulations demonstrating effectiveness ofour tone cancellation

algorithm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

(a) SimulatedVout vs. time for capacitive DUT. . . . . . . . . . . . . . . 178

(b) Simulated I/Q DAC attenuation factors vs. time for same system. . . 178

6.14 Transient plots of the simulated running count and DAC attenuation factors. 179

6.15 Simulated rate of running counter movement vs. tone ratio of ωB andωA

tones. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180

6.16 Core of the latched comparator design. . . . . . . . . . . . . . .. . . . . . 181

6.17 More detailed version of Figure 6.11. . . . . . . . . . . . . . . .. . . . . 183

xxi

6.18 Schematic of a 2-bit resistor-string DAC with switch resistance. . . . . . . 185

6.19 Effective transconductanceGm vs. attenuation factorn= DAC codemax DAC code. . . . 186

7.1 Optical chip micrograph, with detail of one measurementpixel. . . . . . . . 193

7.2 Spectrum ofVout before and after the tone cancellation circuitry is enabled. 196

7.3 Measurements of test capacitance before and after a small increment,

demonstrating reproducibility of about 0.2%. . . . . . . . . . . . . . . . . 197

7.4 Experimental measurement ofZDUT SNR/precision compared with the

simulated SNR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 198

7.5 Impedance spectrum measured with the integrated measurement system

before and after the introduction of streptavidin. . . . . . . .. . . . . . . . 200

xxii

Chapter 1

Introduction and Outline

1.1 Motivation

Affinity biosensors are increasingly important tools for detecting DNA, proteins, cells,

and other biomedical analytes. Although optical sensor readout is prevalent today, purely

electronic readout would reduce system cost, size, and power. Analytes can be detected via

impedance changes in the electrode-solution interface by using an electrode coated with a

probe that selectively captures the analyte of interest. Importantly, impedance biosensors

allow analyte binding to be monitored in real-time and without the use of the labeling

compounds required by most affinity biosensors.

Impedance biosensors traditionally use a single functionalized electrode interrogated

using a bulky and expensive impedance analyzer. Reducing the size and cost of the

measurement system enables new applications, and leveraging semiconductor technology

enables compact and inexpensive biosensors. There is a trend towards using biosensor

arrays, which allow multiple analytes to be detected simultaneously and which mitigate

limitations inherent in individual sensors. CMOS biosensor arrays have recently been used

to detect labeled biomolecules electronically [1, 2], optically [3], and magnetically [4, 5].

Label-free impedance biosensors avoid the added cost and complexity of using labels, but

to date a completely integrated impedance biosensor analyzer has not been demonstrated.

1

2 CHAPTER 1. INTRODUCTION AND OUTLINE

The principal goal of this work is to demonstrate an integrated array of impedance

analyzers for biosensor applications. After building a discrete measurement system, we in-

vestigate the bias-dependence (nonlinearity) of the electrode-solution interface impedance

and demonstrate that changes in nonlinearity can be used to discriminate analyte capture

at a functionalized surface. We design and implement an array of CMOS impedance

analyzers that can simultaneously measure both the impedance and nonlinearity of an array

of impedance biosensors.

1.2 Organization

Chapter 2 introduces the field of impedance biosensors, and is important for understanding

the context, terminology, and significance of the remainderof the dissertation.

Chapter 3 describes a complete impedance biosensor system that we designed and im-

plemented, including sensor array fabrication, surface chemistry, measurement electronics,

and data processing. The measurement circuitry presented in this chapter uses discrete

components on a printed circuit board; analogous integrated circuits were later designed

but the remainder of the measurement system was used for all experiments.

Chapter 4 begins with an explanation of nonlinearity in impedance biosensors from

a theoretical point of view. A method to measure the nonlinearity and impedance

simultaneously is discussed, as are corresponding changesto the measurement system.

The chapter concludes with measurement results suggestingthat changes in nonlinearity

(analogous to changes in the small-signal impedance) can beused to detect biomolecule

binding.

In fields where circuits and biology meet, determining the required circuit specifications

based on the biological situation is a particular challenge. We devote Chapter 5 to a

discussion of the constraints and specifications for an integrated impedance analyzer. Of

particular interest is noise, which fundamentally limits the resolution of the impedance

measurement. The various noise sources are cataloged and their magnitudes estimated.

This knowledge is used iteratively during the circuit design to ensure that the (modeled)

noise does not prevent detection of 0.1% impedance changes.

1.2. ORGANIZATION 3

Chapter 6 describes the design of a 36-pixel impedance measurement IC in a 0.18 µm

CMOS process. First we discuss the operational transconductance amplifier, which is the

heart of the impedance-measuring circuit and the dominant noise source. The second half

of the chapter explains the concept and implementation of tone cancellation circuitry, which

enables the IC to determine nonlinearity concurrently withimpedance.

Chapter 7 summarizes the measured performance of the fabricated IC, and Chapter 8

concludes by summarizing both the contributions of this work and areas for future research.

Chapter 2

Label-free Impedance Biosensors

Many workers in the field of electrical biosensors are unfamiliar with certain concepts

and experimental results that have direct bearing on their work. This lack of background

knowledge is understandable, because the fields of biology,chemistry, electrical engineer-

ing, and physics all converge in biosensors. Furthermore, the primary literature relating to

impedance biosensors is scattered throughout technical journals and conferences in these

separate fields, making it difficult to acquire the necessaryfundamental knowledge, to say

nothing of following advances in the field.

This chapter is essentially a tutorial for both the electrical engineer and the biochemist

to become familiar with concepts related to impedance biosensors. The reader is

encouraged to skim this chapter now, making certain to understand the italicized terms and

concepts, and return for explanation of unfamiliar concepts encountered in the remainder

of this thesis. We conclude with a survey of the impedance biosensor literature and a listing

of the most critical areas for future research, only a subsetof which could be addressed in

this thesis. This chapter is a revised and selectively expanded version of our 2007 review

paper [6].

We begin by introducing label-free impedance biosensors and the reasons they hold re-

search interest. Important affinity biosensor concepts arediscussed in Section 2.2, focusing

on limits to biosensor performance, and concepts relating to the impedance measurement

are explained in Section 2.3. Subsequently we discuss the possible mechanisms by which

binding may modulate the interface impedance and briefly summarize other practical

4

2.1. IMPEDANCE BIOSENSORS: WHAT AND WHY 5

details. In Section 2.5 we critically review prior researchon affinity impedance biosensors,

focusing on label-free DNA and protein sensors. To conclude, we summarize the status

of affinity-based impedance biosensors and identify the obstacles preventing increased

application and commercialization. We attempt to paint a balanced picture between the

progress being made and oft-minimized obstacles in this still-nascent research area.

2.1 Impedance Biosensors: What and Why

2.1.1 Definition of impedance biosensors

A biosensoris a device designed to detect or quantify a biochemical molecule such as

a particular DNA sequence or particular protein. Most biosensors areaffinity-based,

meaning they use an immobilized captureprobethat binds the molecule being sensed —

the targetor analyte— selectively. Thus the challenge of detecting a target in solution is

transformed into the challenge of detecting a change at a localized surface. This change in

surface properties can be measured in a variety of ways.Electrical biosensorsrely solely

on the measurement of currents and/or voltages to detect binding [7, 8, 9]. Thus, this

category excludes sensors which require light (e.g. surface plasmon resonance (SPR) or

fluorescence), use mechanical motion (e.g. quartz crystal microbalance (QCM) or resonant

cantilever), use magnetic particles, etc. Due to their low cost, low power, and ease of

miniaturization, electrical biosensors hold great promise for applications where minimizing

size and cost is crucial, such as point-of-care diagnosticsand biowarfare agent detection.

Electrical biosensors can be further subdivided accordingto how the electrical mea-

surement is made, including voltammetric, amperometric/coulometric, and impedance

sensors. Voltammetry and amperometry involve measuring the current at an electrode as

a function of applied electrode-solution voltage. These approaches are DC or pseudo-

DC and intentionally change the electrode conditions. In contrast,impedance biosensors

measure the electrical impedance of an interface in AC steady state with constant DC bias

conditions. Most often this is accomplished by imposing a small sinusoidal voltage at

a particular frequency and measuring the resulting current; the process can be repeated

at different frequencies. Taking the current-voltage ratio at each frequency yields an

6 CHAPTER 2. LABEL-FREE IMPEDANCE BIOSENSORS

impedance spectrum. This approach, known asElectrochemical Impedance Spectroscopy

(EIS), has been used to study a variety of electrochemical phenomena over a wide frequency

range [10]. If the impedance of the electrode-solution interface changes when the target

analyte is captured by the probe, EIS can be used to detect that impedance change.For our

purposes, we define impedance biosensors as techniques for the detection of biological

molecules by measuring impedance changes of the capture probe layer. Impedance

measurement does not require special reagents and is amenable to label-free operation as

will be explained in Section 2.1.3.

2.1.2 Related fields

Impedance biosensors can detect a variety of target analytes by simply varying the probe

used. Here we focus on detection of DNA and proteins, though impedance sensors have

also been used for other biology-related purposes such as:

1. detection of small molecules of biological relevance (e.g. [11, 12, 13, 14])

2. monitoring changes in cellular state which occur in response to environmental

conditions (e.g. [15, 16, 17, 18])

3. detection of cell presence or cell concentration (e.g. [19, 20, 21, 22])

4. monitoring lipid bilayers, especially with membrane proteins (e.g. [23, 24])

5. mapping impedance structure using a scanning probe (e.g.[25, 26, 27])

Besides biosensor applications, electrochemical impedance spectroscopy (EIS) has been

used to characterize coatings, track corrosion processes,study charge transfer in fuel cells,

and a wide variety of other purposes.

Field-effect biosensors are a separate but closely relatedclass of electrical biosensors

which are often confused with impedance biosensors. Their readout mechanism is

fundamentally potentiometric, but AC readout techniques are often used. They operate by

field-effect modulation of carriers in a semiconductor by nearby charged particles [28, 29].

Ion-sensitive field-effect transistors (ISFETs) and theirrelatives (“EnFETs,” “BioFETs,”

etc.) are the canonical examples [30], but devices based on similar mechanisms include

2.1. IMPEDANCE BIOSENSORS: WHAT AND WHY 7

semiconducting nanowires [31, 32], semiconducting carbonnanotubes [33], electrolyte-

insulator-semiconductor structures [34, 35, 36, 37], suspended gate thin film transistors

[38], and light-addressable potentiometric sensors [39, 40].

These field-effect sensors rely on the interaction of external charges with carriers

in a nearby semiconductor and thus exhibit enhanced sensitivity at low ionic strength

where counter-ion shielding is reduced, as explained in a recent review [41, 42] and

evidenced by the low salt concentrations often used (e.g. [31, 35]). Even though the

response of field-effect sensors can be characterized by channel conductance or capacitance

of the electrolyte-insulator-semiconductor interface, we restrict our review to cases in

which the impedance of the biological layer itself is measured. Note that some sensors

labeled “capacitive biosensors” (e.g. [43, 44, 45, 46]) perform measurements of probe-

insulator-semiconductor interfaces where capacitive changes could occur both within the

semiconductor (due to the field effect) and also within the probe layer (the focus of this

review). Deconvolving the contributions is difficult, and these sensors will be largely

ignored.

A few researchers have studied impedance biosensors that are not affinity-based,

but based on measurement of the species in the bulk. However,the affinity step is

the mechanism to distinguish between the target and other molecules in the sample.

Accordingly, non-affinity measurements lack specificity, requiring either a labeling step

that is specific or else a pure target sample to quantify. Examples include measurements

of protein structure and polymerization [47], monitoring of yeast cell concentrations [48],

and measurements of DNA concentrations [49]. Dielectric spectroscopy has likewise been

applied to biosensing, but is subject to the same limitations [50, 51].

It is also possible to use an affinity step that occurs in bulk solution instead of at

a surface. This approach is commonly used with optical readout strategies such as

Fluorescence Resonance Energy Transfer (FRET), but electrical detection of the binding

requires a label in every case of which we are aware. Such a label could conceivably be

detectable via bulk measurements as just cited. Here we focus on label-free sensors.


2.1.3 Why study impedance biosensors?

The most promising applications of electrical biosensors are those that value low cost, small

instrument size, and high speed of analysis, but not cutting-edge accuracy nor detection

limits. Point-of-care diagnostics— a measurement and diagnosis at a bedside, in an

ambulance, or during a clinic visit — are a promising application area [52, 53, 54]. If the

cost and time per data point were reduced, screening for various cancer and disease markers

using an electrical biosensor could become part of routine medical checkups. Other

applications include biowarfare agent detection, consumer test kits, bioprocess monitoring,

and water quality testing. One key question is whether impedance biosensors can have

sufficient selectivity for use in real-world applications,as biological samples typically

contain an uncontrolled but significant amount of non-target molecules. Another potential

application is the determination of biomolecular affinity coefficients, in which pure target

samples are used (typically done with SPR at present). In short, impedance biosensors have

the potential for simple, rapid, label-free, low-cost detection of biomolecules.

2.1.4 Further reading

Our purpose is to familiarize the reader with the terminology of affinity impedance

biosensors, along with their associated benefits and challenges so that the reader will

be able to understand and critically read the primary literature. Many of the concepts

discussed are also applicable to other types of affinity biosensors. Here we focus on general

principles of label-free affinity impedance biosensors andcompare the methods and results

of different investigators.

For further reading, we suggest the following resources. Anexcellent 2003 review of

impedance biosensors by Katz and Willner focuses on faradaic techniques and impedance

amplification using labels [55]. Lisdat and Shäfer offer a more recent review of impedance

biosensors [56], similar in approach to our 2007 review [6] but broader in scope and

less detailed. An earlier review of capacitive biosensors includes capacitive biosensors

on semiconductor substrates with field-effect contributions [57] (though the distinction

between field-effects and interface effects is not made). Classic texts by Macdonald on

EIS [10] and Bard and Faulkner on electrochemistry [58] are good resources. Various

2.2. AFFINITY BIOSENSOR CONCEPTS 9

approaches to electrical protein sensors were reviewed in 1991 and 2000, but only

touch cursorily on impedance methods [59, 60]. Various electrochemical DNA detection

approaches reviewed by Gooding [61] and more recently by Moeller [62], similarly

treat impedance techniques only briefly. Finally, recommended definitions and relevant

performance criteria for the entire field of electrical biosensors have been articulated by

Thévenot [7].

2.2 Affinity Biosensor Concepts

2.2.1 Affinity biosensor = affinity + sensor

As depicted in Figure 2.1 and represented in the term itself,affinity-based biosensors divide

the problem of detecting a particular biomolecule into two parts:

1. Theaffinity step, or binding of the desired target by an immobilized probe (ideally

excluding binding of non-target species)

2. Thereadout step, or detecting a change in the surface properties caused by the target

binding

The affinity step is controlled by the surface chemistry and biochemical binding interaction,

while the readout step is based on the physics of detection plus all associated signal

processing.Though affinity binding and transducer readout can be studied and optimized

independently, they are intertwined in the final system; either one can limit overall system

performance.

2.2.2 Probe-target binding

The affinity step can be treated in terms of receptor-ligand binding theory [63, 64, 65]:

Probe+Targetkonko f f

Probe·Target (2.1)


Kd =koff

kon, probe coverage

Readout/transducer type

Post-processing

Amplifier

Data Acquisition

Transducer

Selective Probe

Acquired

Electrical

Chemical

(a) (b) (c)

Measured change

Target concentration

Instrumentation

Target surface coverage

Surface property change

Figure 2.1: Generalized affinity biosensor, showing (a) theinformation flow, (b) thephysical arrangement, and (c) the steps involved.

The equilibrium dissociation constantKd of the probe-target pair is defined as:

Kd =ko f f

kon=

[Probe][Target][Probe·Target]

, (2.2)

where we have used the square brackets to denote the concentration of the respective

chemical species.Kd is used as a measure of the binding strength because the fraction

of probe bound at equilibrium (Θ) is determined by the relative values ofKd and[Target]:

Θ =[Probe·Target]

[Probe]+ [Probe·Target]=

[Target][Target]+Kd

(2.3)

This is one form of the famous Langmuir adsorption isotherm,which describes surface

binding for identical non-interacting binding sites. Increasing the surface probe densityσleavesΘ unchanged but allows the measured surface property change —typically related

to the actual density of target molecules bound, orσΘ — to increase. However, too high

a probe density may actually inhibit target binding due to steric hindrance or other effects

[66, 67].


Despite the ability to monitor binding in real-time, the majority of published label-

free impedance biosensors make only an endpoint measurement after equilibrium has been

reached. However, kinetic considerations are particularly important at low concentrations,

where detection limits are usually determined [68, 69] and when diffusion of the target to

the recognition surface takes longer than the binding interaction [70].

2.2.3 To label or not to label?

Arguably the major motivation for studying impedance biosensors is their ability to perform

label-free detection. Most biosensors require alabelattached to the target. During readout

the amount of label is detected and assumed to correspond to the number of bound targets.

Labels can be fluorophores, magnetic beads, active enzymes with an easily detectable

product, or something else featuring easy target conjugation and convenient detection. To

facilitate detection the label generally is very distinct from anything else in the system. This

strategy might be considered a form of amplification. Redox-active labels are commonly

used in other types of electrical biosensors.

Despite those advantages, labeling might be undesirable for several reasons. Labeling

increases the amount of sample preparation required, adding time and expense. Attaching

a label can also drastically change the binding properties of the biomolecule. Finally, the

yield of the target-label coupling reaction is highly variable [71]. These problems are

relatively minor concerns for DNA sensors, due to DNA’s chemical homogeneity and ease

of labeling during PCR amplification, but are especially serious for protein targets.

Thus, an indirect labeling scheme often referred to as asandwich assayis usually

used for protein detection (see Figure 2.2) [63, 72]. This assay requires two probes

that bind to different regions of the target, yielding enhanced selectivity but increasing

development costs and limiting use in research settings. The first probe is immobilized on

the solid support, the analyte is introduced, and then asecondary probeis introduced after

washing. This second probe is labeled or can be detected by introducing yet another labeled

“probe” that binds to all the secondary probes. The widespread ELISA (Enzyme-Linked

ImmunoSorbent Assay) [73] technique is the canonical example of a sandwich assay.


+ 2ry probe + labeled(d) (e)

3ry probe2ry probe+ labeled

(c)

immobilized probe + target

(a) (b)

“label-free”

Figure 2.2: Generalized sandwich assay versus label-free detection. The secondaryantibody can provide increased selectivity and allows a well-known entity to be labeledinstead of the (variable) target. However, a label-free scheme allows real-time detectionand eliminates the time and cost of labeling.


2.2.4 Label-free operation

When a target biomolecule interacts with a probe-functionalized surface, changes in the

electrical properties of the surface (e.g. dielectric constant, resistance) can result solely

from the presence of the target molecule. Thus, no label is required for impedance sensing;

this is particularly advantageous for protein detection asexplained above. However,

because labeling can augment selectivity (e.g. using the sandwich approach with second

probe) and enhance sensitivity (e.g. using a label that greatly changes the impedance),

some impedance biosensors in the literature use a label. However, labeling requires extra

time and sample handling, either before affinity capture or afterwards.

Besides the time and expense benefits of omitting the labeling step, label-free operation

enables detection of target-probe binding in real time [74], an ability that label-based

systems generally do not possess. Real-time sensing confers at least two major advantages

over endpoint detection. First, time averaging of binding/unbinding events can improve

measurement accuracy. Second, it allows determination of affinity constants by curve-

fitting the sensor output in a manner very similar to SPR [75].1 The termdirect biosensor

has also been used to mean that the properties of the unmodified biomolecule generate a

measurable signal [34, 59, 77], which we define aslabel-free.

QCM [78], related mechanical techniques [79], and SPR [76, 80, 81] are notable

examples of non-electrical, label-free, real-time biosensors (overview in [82]).

One challenge with any type of label-free biosensors is thata relatively small change

in surface properties occurs upon binding, requiring sensitive readout methods. Selectivity

in real-world samples poses the second major challenge, as discussed next.

2.2.5 Selectivity

Affinity-based biosensors exploit the selectivity of the probe biomolecule to confer

selectivity to the overall sensor system.Selectivity— sometimes termedspecificitydespite

contrary recommendations [83] — means that the sensor responds only to the target analyte

and not to other similar molecules.Generally speaking, label-free biosensors cannot

1For accurate results certain effects including diffusion rate and steric hindrance must be accounted for,just as in SPR [76].


distinguish between specific and non-specific interactionsexcept through probe selectivity,

regardless of the readout method.This limitation has tremendous impact, especially in

complexsamples, in which many different biomolecule species are present. Using an

engineering analogy, one may say that a complex sample is onein which the common-

mode chemical signal is large. The probe acts as a filter that allows selective detection of

the small desired signal.

Selectivity is especially important in real-world samples, where the target concentration

can be orders of magnitude below the concentration of related non-target biomolecules. For

instance, blood serum typically contains∼70 mg/mL total protein content, yet prostate

specific antigen (PSA), a biomarker for prostate cancer, needs to be detected at 2 ng/mL to

be clinically useful [84, 85]. Thus, a biosensor that can detect 1 ng/mL PSA in saline

but manifests even a 1 ppm response to blood proteins would beuseless in a clinical

setting unless the serum is depleted of interfering proteins or some other compensation

is made. Thus, a trade-off exists between selectivity requirements and sample preparation

complexity for most real-world applications.It is our opinion that obtaining adequate

selectivity in complex real-world samples is the most daunting challenge for the field of

biosensors in general, including impedance biosensors.

A closely related concept isnon-specific binding, in which non-target biomolecules

stick to the probe layer, preventing target binding or causing a false positive signal. To

alleviate this problem, the sensor chamber is often pre-exposed to a solution containing

a blocking agentsuch as bovine serum albumin (BSA) or salmon sperm DNA which non-

specifically adsorbs (hopefully not occupying the probe binding sites), reducing subsequent

non-specific binding from the actual sample.Anti-fouling agentssuch as polyethylene

glycol can also be deposited on areas surrounding the sensorto prevent target depletion via

non-specific binding [86, 87, 88]. Use of blocking agents is not yet a systematic science,

but several approaches have been found to work in specific situations (e.g. [89, 90, 91]).

A differential sensor scheme can be used to (imperfectly) subtract out the non-specific

component of the sensor response (see Section 2.4.3). Washing the sensor surface before

readout can sometimes improve selectivity by washing away non-specifically adsorbed

molecules while leaving the target intact. In ahomogeneous assaythis washing step is

not necessary [92].


2.2.6 Limit of detection and reproducibility

The most cited figure of merit for any chemical sensor is thelimit of detection, or the

smallest amount of target that can be reliably detected. Occasionally the termsensitivity

is used, which also refers to the slope of the response curve [93, 94]. Unfortunately,there

is no universal method for determining the limit of detection, which greatly complicates

comparison of published results.This parameter can be determined by measuring the

sensor response to a dilution series of the target and determining the smallest concentration

at which the sensor response is clearly distinguishable from the response to a blank

solution. However, some investigators do not measure the sensor response to a blank

solution (not necessarily zero) and thus may state an overly-optimistic detection limit.

Other investigators calculate a limit of detection based onthe slope of the dose-response

curve and the standard deviation of the blank response according to [95], without actually

demonstrating reproducible detection at the reported concentration. Worse yet is the

practice of computing the detection limit based on the dose-response slope and the

measured noise of the readout method.

Requirements for the limit of detection vary widely by application. As examples,

consider that the aforementioned cancer biomarker PSA needs to be detected at∼ 2 ng/mL

[84, 85]. Human chorionic gonadotropin, used in home pregnancy tests and also as a cancer

marker, indicates pregnancy when above 5 ng/mL in urine but exceeds 1µg/mL several

weeks into pregnancy [96, 97] Other biomarkers of clinical interest, such as cytokines, exist

in the blood in pg/mL concentrations. Conventional techniques like colorimetric ELISAs

routinely obtain pg/mL detection limits if the probe-target affinity is high.

Detection limits are almost always determined in the absence of confounding non-target

biomolecules. Because such clean samples rarely occur in real-world applications, reported

limits of detection are not necessarily a good predictor of real-world performance, as

discussed in Section 2.2.5. To demonstrate clinical utility, biosensors should be challenged

with mixed target/non-target samples to test selectivity and sensitivity simultaneously.

Fundamentally, the achievable limit of detection is bounded by the strength of the

probe-target interaction (see Equation 2.3 or [98]) together with the minimum detectable

σΘ, or amount of bound target. For this reason commercial ELISAkits with identical


readout technology have varying limits of detection for different targets. Real-time readout

may improve the achievable detection limit by monitoring the transient sensor response,

allowing the binding signal to be separated from the slower non-specific adsorption signal

and drift in the readout electronics.

Variation between sensors affects the detection limit because a separate calibration

step rarely can be performed for each sensor. Although the readout step may introduce

some uncertainty, the affinity step is the main source of variability, especially via the

probe density and affinity. Most investigators do not account for such variation when

reporting detection limits because of the large number of experiments required. However,

reproducibility will affect the practical limit of detection.

Because of the two-step detection scheme,the limit of detection in many practical situa-

tions is dictated by non-specific binding and/or lack of sensor reproducibility.However, for

impedance biosensors, the reported detection limit is often the target concentration required

to induce the minimally-detectable change in impedance based on the intrinsic electronic

noise of the impedance readout.

2.2.7 Dynamic range

If the sensor is to be used to quantify the analyte concentration and not just detect its

presence, the range of measurable concentrations is important. Thedynamic rangeis

the range between or ratio of the largest measurable target concentration and the limit

of detection. The upper limit is almost invariably set by thesaturation of the probe with

target molecules (Θ = 1), and so is determined by the affinity step. If the detectionlimit is

sufficiently small, the dynamic range can be extended by simply performing measurements

with a dilution series of the sample. Real-time measurements also can enhance dynamic

range.

The smallest detectable change in target concentration is the resolution (defined as

output uncertainly — due to both systematic and irreduciblenoise — divided by the slope

of the response curve). While uncommon in the affinity biosensor literature, we propose

that resolution be given more prominence in characterizingaffinity biosensors when the

application requires quantification of the target concentration.


2.2.8 Stability

Stability refers to the ability to fabricate, store, and transport thebiosensor to the end

user without significant changes in performance. In essenceit is a measure of sensor

reproducibility over time. The “bio” part of the biosensor (i.e. probe layer) is far more

vulnerable to degradation than the “sensor” part, as light,oxygen, and heat can degrade

biomolecules [99]. Stability is less problematic in a research setting where the sensor can

be used immediately after preparation. It can be at least partially counteracted by using

internal controls or calibration steps. Storage media and conditions are very important in

achieving a reasonable shelf life.Stability is primarily determined by the surface chemistry

and storage conditions, not by the readout scheme.

2.2.9 Amplification

The biosensor signal is eventually acquired and amplified electronically. Amplification

can take place in the chemical domain as well, but all chemical amplification schemes for

electrical biosensors to our knowledge rely on either target labeling (including the sandwich

approach) or cycling of a redox species. Thus amplification techniques lie outside the

domain of label-free impedance biosensors. One amplification approach is the (enzyme)

label-catalyzed precipitation of an insoluble material onto the electrode [100, 101, 102,

103]. Electroless deposition of silver onto metallic nanoparticle labels has also been used

[104, 105, 106, 62]. Various methods have been reported for post-affinity attachment of

charged and/or bulky particles that alter the interface impedance [107, 108, 109, 110].

2.2.10 Multiplexing

Detecting several targets in the same biological sample is possible if different surface

regions are functionalized with different probes. Multiplexing is desirable because it

reduces time, cost and sample volume per data point. Becauseelectrical signals are readily

steered, it is possible to detect various analytes using a single readout circuit shared between

separate probe-functionalized regions. Regardless of readout mechanism, multiplexed

protein detection is complicated by cross-reactivity — a probe binds to multiple targets


or vice versa — which severely limits the possible degree of multiplexing and is especially

troublesome in real-world situations [111, 112, 113, 114].However, a panel of several

biomarker measurements has far more diagnostic power than asingle biomarker can

provide [115]. Thus, efforts to develop multiplexed protein biosensors will surely continue,

though the challenge of cross-reactivity will have to be overcome.The principal limitation

of multiplexing arises from the affinity step and not the readout step for impedance

biosensors.

2.2.11 What really limits biosensor performance?

It is apparent that the limits of label-free affinity biosensor performance are more often set

by the affinity step than by the readout step. This suggests the need for further research

efforts in probe immobilization chemistries and minimization of non-specific binding,

while recognizing the fundamental limits of finite probe affinity, selectivity, and density.

Where the affinity step limits performance, it is important to realize that readout

techniques with lower sensitivity to the binding signal canbe used to obtain overall equal

results.Some investigators claim that impedance techniques have extremely low limits of

detection compared with optical or other readout methods (e.g. [57]) while others disagree

(e.g. [116]). We are of the opinion that the readout sensitivity afforded by impedance

sensing is inferior to other label-free techniques but is sufficient for many applications,

precisely because the affinity step often bounds the overallbiosensor performance.

Impedance biosensors may also be useful when moderate sensitivity is required at a very

low cost and/or using a very small instrument. However, we doubt that label-free affinity

impedance biosensors will ever achieve the same sensitivity of label-based techniques such

as conventional ELISAs due to the limitations of both label-free detection (eliminating the

possibility of chemical amplification) and sensitivity of impedance readout.

2.3. ELECTROCHEMICAL IMPEDANCE CONCEPTS 19

2.3 Electrochemical Impedance Concepts

In this section, we explain concepts related to measuring the electrical impedance of the

electrode-electrolyte interface. Some of these concepts will be familiar to an electrical

engineer, but others will only be familiar to students of electrochemistry.

2.3.1 Apply a voltage, measure a current

Small-signal electrical impedance is defined as the ratio ofan incremental change in voltage

to the resulting incremental change in current. Graphically, impedance is the reciprocal

slope of the current-voltage (I-V) curve. To measure impedance experimentally, either

an AC test voltage or AC test current is imposed while the other variable is measured.

Mathematically, if the applied voltage is

Vtest=VDC+VACsin(ωt) (2.4)

and the resulting current is

Itest= IDC+ IACsin(ωt −φ) , (2.5)

then the impedanceZ(ω) has magnitudeVAC/IAC and phaseφ. Alternatively, impedance

can be represented by a real component and an imaginary (out of phase) component, or a

vector on the complex plane. In general, impedance depends on both the bias condition

(VDC) and the measurement frequency (ω).

A lock-in amplifier or similar device can be used to apply an input tone and accurately

measure the output signal at the same frequency. Impedance spectroscopy consists of

repeating the measurement process at different frequencies, yielding Z(ω). Voltage

excitation is usually employed in EIS because the most troublesome parasitic impedances

(through the solution) are in parallel with the measured impedance. The electrode-

electrolyte interface impedance is usually strongly dependent onω and weakly dependent

on VDC.


In impedance biosensors, the applied voltageVtest should be quite small — usually

10 mV in amplitude or less — for several reasons. First, the current-voltage relationship

is often linear only for small perturbations [117], and onlyin this regime is impedance

strictly defined. An equivalent statement is that the impedance depends upon DC bias. If

the application of the measurement signalVtest changes the impedance then the impedance

is not uniquely determined. We will revisit this assumptionin Chapter 4 and find that

changes in nonlinearity can actually be used to sense binding. If faradaic processes occur

(defined in Section 2.3.4), nonlinearity is especially prominent because the propensity for

electron transfer generally depends exponentially on the difference between the oxidation

potential and the applied potential [58].

A second reason for using a small excitation signal is to avoid disturbing the probe

layer. Covalent bond energies are on the order of 1–3 eV but probe-target and electrode-

probe binding energies can be much less and applied voltageswill apply a force on

charged molecules. This second consideration also appliesto the bias voltageVDC

across the electrode-solution interface. Correctly performed, electrochemical impedance

spectroscopy does not damage or even disturb the biomolecular probe layer, which is an

important advantage over voltammetry or amperometry wheremore extreme voltages are

usually applied.

Variations of standard impedance spectroscopy include using multiple excitation

frequencies simultaneously [118, 119], exciting with white noise [10], and exciting with

a voltage step [120]. Such approaches could decrease the time required per measurement

and avoid problems due to the fact that impedance is ill-defined if the system is changing

during the measurement. However, the integrity of these approaches will be compromised

by any nonlinearity in the I-V relationship.

2.3.2 Electrodes

At minimum two electrodes are needed to measure electrolyte-solution impedance, and

usually three are used. The current is measured at theworking electrodewhich is usually

biofunctionalized with the probe. In order to establish a desired voltage between the


working electrode and solution, electrical contact must bemade with the solution using

a reference electrode and/or counter electrode.

The solution potential cannot be controlled simply by dipping in a piece of wire held

at a particular voltage, because the solution-metal interface has a built-in potential that

depends on the surface composition, electrode microstructure, and ionic composition of the

solution. Areference electrodemaintains a fixed, reproducible electrical potential between

its metal contact and the solution, allowing a known voltageto be applied between the

electrolyte solution and working electrode. Silver-silver chloride electrodes are the most

common type of reference electrodes used in impedance biosensors. The built-in potential

of the Ag/AgCl interface is constant; the potential of the solid/liquid AgCl/Cl – interface

is also constant as long as the chloride concentration in solution is fixed (in general any

Cl– released or plated onto the AgCl should be negligible). A so-called pseudoreference

or quasireference electrode can suffice as a substitute under certain conditions but should

be avoided if possible; it consists of a piece of wire which exhibits facile charge transfer

with the solution such as Pt [121]. One common faux pas in electrical biosensors is the

failure to use a reference electrode, thus leaving the bias conditionVDC across the measured

electrode-electrolyte interface poorly controlled.

Thecounter electrodesupplies current to the solution to maintain the desired electrode-

solution voltage, usually in an electronic feedback loop with the reference electrode

monitoring the solution voltage. The counter electrode is often much larger than the

working electrode so that it can easily supply the required current and so its interface

impedance will be negligible compared to that of the workingelectrode.

Merging the functionality of the counter and reference electrodes is possible if the

reference electrode can supply the required current and if the ohmic voltage drop in

solution is small or unimportant. Small electrodes facilitate such an arrangement [58].

Note that the remaining electrode should have the functionality of the reference electrode

in that a reproducible voltage can be applied to the solution. It should also have the

functionality of the counter electrode in that a sufficient current can be passed to or from

the solution. If the electrodes are combined, the 3-electrode measurement becomes a 2-

electrode measurement. In this case, the combined impedance of both electrodes and


solution is measured, whereas in a 3-electrode impedance measurement only the impedance

between the reference electrode and working electrode is measured.

2.3.3 Instrumentation

A potentiostatis a circuit that imposes a desired command voltage between the solution

and working electrode while simultaneously measuring the current flowing between them.

Electrically speaking, it contains a feedback loop that controls the counter electrode’s

current such that the solution voltage (measured by the reference electrode) matches the

command voltage. Meanwhile, the working electrode is held at ground while the current

through it is measured using a transimpedance amplifier. Thus, the potentiostat imposes

a voltage across the electrode-electrolyte interface and measures the resulting current,

as required for impedance measurement. (If the counter and reference electrodes are

merged, no feedback loop is necessary but the impedance can be calculated similarly.)EIS

analyzersare potentiostats designed especially for measuring AC impedance, and typically

operate over frequency range of 10−2–105 Hz. Computer control is ubiquitous for both

potentiostats and EIS analyzers, and digital post-processing is commonly employed.

2.3.4 Faradaic vs. non-faradaic

It is important to distinguish between non-faradaic and faradaic biosensors. In electrochem-

ical terminology, afaradaicprocess is one where charge is physically transferred across an

interface, usually in the form of an electron transfer from the electrode to an ion in solution

or vice versa. However, transient currents can flow without actual charge transfer innon-

faradaic processes (e.g. as in charging a capacitor). In the electrical domain, a perfect

non-faradaic interface is represented by a capacitor, and afaradaic interface is represented

by a resistor. Actual electrode-solution interfaces can have both faradaic and non-faradaic

components.

In faradaic impedance spectroscopya redox species is alternately oxidized and reduced

at an electrode by the transfer of an electron to or from the metal. The voltage above which

a redox species tends to be oxidized and below which it tends to be reduced is called the

oxidation potential, and is a characteristic of both the molecule and its environment. It


encodes only the thermodynamic tendencies but not kinetic effects. Faradaic EIS requires

the addition of a redox-active species and DC bias conditions — usually near the oxidation

potential — such that neither redox state becomes depleted.In contrast, no additional

reagent is required for non-faradaic impedance spectroscopy, making non-faradaic schemes

somewhat more amenable to point-of-care applications. Theexperimental work of this

dissertation is non-faradaic. The termcapacitive biosensorusually designates a sensor

based on such a non-faradaic scheme, and usually refers to one that makes measurements

at a single frequency.

2.3.5 Data fitting

The measured impedance spectrum can be used to extract equivalent values of resistances

and capacitances if a circuit model is assumed a priori, though there is not a unique model

[122]. Figure 2.3 shows typical circuit models, and Figure 2.4 shows example impedance

data. It is not always necessary to fit the data to a model, and even the best models of

the electrode-solution interface either do not fit measurements at extremes of frequency or

else require so many fitting parameters as to be useless. Usually the raw impedance data

is fit to a model and changes in model elements are reported as the sensor output. Other

times, the impedance at a particular frequency is used. Depending on the values of the

respective model circuit parameters, data at a particular frequency can contain information

about various circuit elements or be dictated primarily by one element, as indicated in

Figure 2.4b.

Complex nonlinear least squares (CNLS)fitting [123] is needed to incorporate both

magnitude and phase in the fitting process and is available inseveral free (e.g. LEVM)

and commercial (e.g. ZView, ZSimpWin) software packages. The CNLS fitting procedure

outputs error bounds on different circuit elements (based on goodness-of-fit), which

sometimes are erroneously shown in plots as error bars. Interpreting impedance spectra

is sometimes more art than science, as discussed in [124]. The Kramers-Kronig transform

can act as an independent check against invalid experimental data [10, 122]. Impedance

data can be presented as either magnitude/phase plots vs. frequency (e.g. Figure 2.4b) or


(a)

(b)

Rsol

Zw Rct

Rleak

Rsol

Csurf

Csurf

Figure 2.3: Typical circuit models for (a) non-faradaic and(b) faradaic interfaces. SeeSection 2.3.6 for an explanation of the circuit elements.

Nyquist plotswhere the impedance is plotted a complex plane with each point representing

the impedance at a different frequency (e.g. Figure 2.4a).

2.3.6 Circuit models

Figure 2.3 shows the two most common models used to fit impedance biosensor data,

depending on whether a faradaic or non-faradaic measurement is made. Here we discuss

the relationship between circuit elements and the underlying physical processes, with the

caveat that in practice the choice of a fitting model is often empirical and different physical

effects may be wrapped into a single model element [122].

The solution resistance,Rsol, arises from the drift of the ions in bulk solution in response

to the applied voltage, and thus is generally not affected bytarget binding. Knowing the

sensor geometry and solution conductivity (calculable from diffusion coefficients of the

constituent ions) allowsRsol to be predicted, although it is usually simply treated as a

fitting parameter because its exact value is rarely significant.

The capacitance between the metal electrode and ions in solution,Csur f, can be modeled

as a series combination of the surface modification capacitance and the ionic double layer


100 200 300 400 500

100

200

Re(Z)/kΩ

−Im

(Z)/

kΩ 0.02 Hz

10 Hz

300 Hz

10 kHz

10 Hz300 Hz

50 Hz

non−faradaicfaradaic

(a) Nyquist representation with selected frequencies labeled.

10−2

10−1

100

101

102

103

104

105

106

103

104

105

106

Frequency/Hz

|Z|/Ω

Zw

Rleak

Rct C

surf

Rsol

non−faradaicfaradaic

10−2

10−1

100

101

102

103

104

105

106

153045607590

−∠

Z/°

Zw

Rleak

Rct

Csurf

Rsol

(b) Magnitude/phase vs. frequency representation. The dominant impedance contribu-tion in various frequency ranges is labeled.

Figure 2.4: Example non-faradaic and faradaic impedance data; data generated usingRsol = 1 kΩ, Csur f = 10 nF with m= 0.9, Rleak = 500 kΩ, Rct = 100 kΩ, andZw

coefficient 10−5.


capacitance. The component due to surface modification depends on the thickness and

dielectric constant of the probe layer. It can be thought of as a parallel plate capacitor,

whose capacitance is given byC = εrε0A/t, whereεr is the relative dielectric constant,A

is the electrode area, andt is the insulator thickness. The ionic double layer capacitance

arises from the electrostatic attraction of ions in solution to a charged electrode, and will

be treated in detail in Section 2.3.8. The capacitanceCsur f is often modeled by aconstant

phase elementinstead of a pure capacitance, as explained in Section 2.3.7.

In parallel with the surface capacitance there is a resistive path modeled byRleak for

non-faradaic sensors or the series combination ofZw andRct for faradaic sensors. Although

Rleak is theoretically infinite if no redox species are present, inpractice it is finite, for

reasons discussed below. TheWarburg impedance, Zw, is only of physical significance in

faradaic EIS. It is a manifestation of the delay arising fromdiffusion of the electroactive

species to the electrode [58, 122].Zw is only appreciable at low frequencies, is affected

by convection (and thus may be invalid for experimental timescales), and has a phase

shift of −45. Thecharge transfer resistance, Rct, encodes the resistance corresponding

to the electron transfer between electrode and the relevantredox species. Its value is a

manifestation of two effects: the energy potential associated with the oxidation or reduction

event at the electrode (i.e. the overpotential) along with the energy barrier of the redox

species reaching the electrode due to electrostatic repulsion or steric hindrance.

The two circuit elements most commonly used as indication ofaffinity binding in

impedance biosensors areCsur f for non-faradaic biosensors andRct for faradaic ones. The

rationale is that target binding changes the surface dielectric constant and/or thickness in

the former case and modulates the redox species’ access to the electrode in the latter.

2.3.7 Constant phase element

It has long been recognized that the impedance of solid electrodes usually deviates from

purely capacitive behavior. The actual behavior is empirically modeled as aconstant phase

element (CPE). The complex impedance of a CPE is given by

ZCPE =1

(ıω)mA(2.6)


whereA is analogous to a capacitance,ω is the frequency expressed in rad/sec, andm

is the so-called CPE phase parameter. It can easily be seen that m=1 corresponds to a

capacitor andm=0.5 corresponds to a Warburg element;m for Csur f modeling is typically

between 0.85 and 0.98. The phase shift of a CPE is−mπ2 . For impedance biosensors

at frequencies whereCsur f dominates there is a phase shift of approximately−80 and a

sub-1/ f impedance vs. frequency rolloff. A constant phase element can be thought of as

a frequency-dependent resistor in addition to a pure capacitor, and can be modeled as a

network of resistors and capacitors over a range of frequencies.2

CPE behavior has come to be expected on solid electrodes by experimentalists and

can be explained mathematically as dispersion in local capacitance values. Microscopic

roughness can cause this effect [126, 127], but a convincingreview by Pajkossy [128]

suggests that microscopic chemical inhomogeneities and ion adsorption play an even

larger role (supported by data in [129, 130, 131]). Jorcin summarizes these effects and

demonstrates that the composite electrode impedance can have a CPE character even if the

localized impedance is strictly capacitive [132]. Solid electrodes can be expected to have

a certain amount of CPE behavior, and thus modeling the electrode-solution interface as

purely capacitive is simplistic and can reduce the quality of data fitting.

2.3.8 Double-layer capacitance

When a charged surface is in contact with an electrolyte, it attracts ions of opposite

charge. This attractive tendency is opposed by the randomizing thermal motion of the

ions, resulting in a buildup of ions with opposite charge near the surface. This local charge

imbalance prevents the electric field emanating from the charged surface from penetrating

very far into solution.3 The characteristic length of this spatial decay of the electric field

is called theDebye length. We will see that the locally-enhanced population of ions acts

like the second plate of a capacitor, and the charge-voltageratio is termed thedouble layer

capacitanceor diffuse layer capacitance.

2Tools exist to automatically generate such networks and Cadence’s Spectre recently added support underthe circuit primitivefracpole [125].

3This shielding effect is a huge bane to field-effect sensors because the electric field originating fromcharged molecules in solution is largely screened and neverreaches the field-sensitive semiconductor.


Because of the importance that the double layer will play in the remainder of this

dissertation, we wish to develop here both idealized mathematics and a qualitative

understanding regarding the double layer capacitance.

2.3.8.1 Mathematical treatment

Here we assume a 1D model where the electrode-electrolyte interface is atx=0 and the

bulk solution is at+∞. The treatment that follows is based on that in the texts of Bard [58],

Stokes [133], Israelachvili [134], and Butt [135].

The charged surface gives rise to an electrostatic potential relative to the neutral bulk

of the ionic solution. This potential affects the distribution of ions, which in turn affects

the local potential. Solving for the equilibrium distribution of ions requires combining the

Poisson and Boltzmann equations.

The Poisson equation relates the electrostatic potential to the charge density and for our

purposes can be expressed asd2φdx2 =−ρ(x)

εrε0(2.7)

whereφ is the electric potential,ρ is the charge density, andεrε0 is the total dielectric

constant.

In an ionic solution, the charge density can be written as

ρ(x) = ∑i

ci(x)ziq (2.8)

where the summation is over all ionic species,ci is the local ion concentration,zi is the ion

valence (e.g.−1 for Cl–), andq is the unit charge.

The electrostatic potential will alter the local ion concentration because the ions are free

to move in response to the field. The chemical potentialµ is the sum of the electrostatic

potential and concentration-dependent chemical potential and may be written as

µ= zqφ+kT lnρ (2.9)


In equilibrium, the chemical potential of all ions will be equal. Consequently, each ion

species will be distributed according to the Boltzmann relationship

ρi(x) = exp

(−ziqφ(x)kT

)

c∗i ziq, (2.10)

where we introduce the symbolc∗i to represent the bulk concentration of ionic speciesi

(recall that in the bulk, the potentialφ is zero). The ionic species are assumed to interact

with each other only electrostatically (via the mean potential φ).

Combining Equations 2.7 and 2.10 yields the Poisson-Boltzmann equation, which is the

mathematical basis for treatment of electrostatic interactions in ionic media. In our case,

the Poisson-Boltzmann equation is

εrε0d2φdx2 =−q∑

iexp

(−ziqφ(x)kT

)

c∗i zi . (2.11)

This expression is usually simplified as

εrε0d2φdx2 =−q∑

i

(

1− ziqφ(x)kT

)

c∗i zi (2.12)

by invoking a linear approximation of the exponential, assuming that the potentialziφ is

small compared with the thermal voltage. Even though this assumption does not always

hold (especially near the charged surface), we proceed for now using this assumption

because it permits an analytic solution forφ(x).Because electroneutrality holds in the bulk (∑c∗i zi = 0), Equation 2.12 can be simplified

tod2φdx2 =

qφ(x)εrε0kT ∑

iz2i c∗i (2.13)

which can be further simplified to

d2φdx2 =

(

1λD

)2

φ(x) (2.14)


if we defineλD, the Debye length, as

λD ≡√

εrε0kT

q2∑i z2i c∗i

=

√

εrε0kT

1000q2NAv∑z2i c0

i

. (2.15)

Here the second equivalent expression is in terms of the molar concentrationc0i instead of

a number density for computational convenience (NAv is Avogadro’s number).

The differential equation 2.14 can be solved by inspection to obtain the spatial potential

in terms of the potentialφ0 at x=0, the solution interface:4

φ(x) = φ0exp

(

− xλD

)

(2.16)

Thus, the Debye lengthλD is the characteristic length of the electric field’s exponential

decay as it penetrates the ionic solution.

We now turn our attention to calculating the relationship between the surface charge

σ0 and surface potentialφ0. They are related via Gauss’ Law according to the following

expression:5

σ0 =−εrε0

(

dφdx

)

z=0(2.17)

If we continue to assume that the electrostatic potential issmall compared with the thermal

voltage, we obtain the following linear relationship between the surface charge and surface

potentialφ0

σ0 =εrε0φ0

λD(2.18)

by which it can be seen that the small-signal capacitance is simply given by

Cdl =dσ0

dφ0=

εrε0

λD(2.19)

4For the mathematically rigorous, the requisite boundary conditions are set by electroneutrality and zerofield in the bulk.

5Consider an enclosed volume from the interface extending into the bulk solution which contains theentire diffuse layer such that the only field flux is through the interface. Also note that electroneutrality in thebulk requires that the total double layer charge be the same as the surface charge.


A more general form of Equation 2.18 is called the Grahame equation. Starting with

the full Poisson-Boltzmann equation (2.11) and noting the identity

d2φdx2 =

12

ddφ

(

dφdx

)2

(2.20)

it can be seen thatddφ

(

dφdx

)2

=−2qεrε0

∑i

exp

(−ziqφ(x)kT

)

c∗i zi . (2.21)

Integrating and using the fact that bothφ and its derivative are zero in the bulk, we obtain6

(

dφdx

)

x=0=

√

2kTεrε0

∑i

c∗i

(

exp

(−ziqφ0

kT

)

−1

)

(2.22)

and plugging into Equation 2.17 yields the surface charge7

σ0 =

√

2kTεrε0∑i

c∗i

(

exp

(−ziqφ0

kT

)

−1

)

. (2.23)

If we assume the electrolyte is a 1:1 salt (e.g. NaCl) with concentrationc0 then

Equation 2.23 leads to the following oft-quoted expressionfor surface charge:

σ0 =√

8εrε0kTc0sinh

(

qφ0

2kT

)

(2.24)

The small-signal capacitance density of the ionic double layer in a 1:1 salt can then be

calculated:

Cdl =dσ0

dφ0=

ε0εr

λDcosh

(

qφ0

2kT

)

(2.25)

2.3.8.2 Important observations

The Debye length (defined in Equation 2.15) depends on the square-root of the ionic

strength. To double the Debye length the electrolyte must therefore be diluted by a factor

6here we ignore the sign of the square root because it is easilydeduced by the sign of the potential at theelectrode

7ibid.


Electrolyte λD Capacitance Comments10 mM NaCl 3.1 nm 0.23 µF/mm2 same for any other 1:1 electrolyte

100 mM NaCl 0.97 nm 0.73µF/mm2 same for any other 1:1 electrolyte1000 mM NaCl 0.31 nm 2.3 µF/mm2 same for any other 1:1 electrolyte

10 mM PO4 buffer @ pH 6.6 2.3 nm 0.31 µF/mm2 60% NaH2PO4, 40% Na2HPO410 mM PO4 buffer @ pH 7.0 2.1 nm 0.34 µF/mm2 40% NaH2PO4, 60% Na2HPO410 mM PO4 buffer @ pH 7.4 1.9 nm 0.37 µF/mm2 20% NaH2PO4, 80% Na2HPO4

10 mM PBS @ pH 6.6 0.77 nm 0.92 µF/mm2 PO4 buffer+ 138 mM NaCl, 2.7 mM KCl10 mM PBS @ pH 7.0 0.76 nm 0.93 µF/mm2 PO4 buffer+ 138 mM NaCl, 2.7 mM KCl10 mM PBS @ pH 7.4 0.75 nm 0.95 µF/mm2 PO4 buffer+ 138 mM NaCl, 2.7 mM KCl

Table 2.1: Debye length and corresponding capacitance density for common elec-trolytes.

of four. Polyvalent ions (e.g. Mg2+) are particularly important because in the Debye length

calculation the ion concentration is weighted byz2i (Equation 2.15). In buffers, pH can

affect the relative concentrations of different valence making computations more involved

[136], but our measurements are performed inphosphate buffered saline (PBS)which is

predominantly composed of a 1:1 salt.

Table 2.1 shows calculated Debye lengths and correspondingcapacitance densities for

some representative solutions. The Debye length at physiologic ionic strengths (where

DNA and proteins retain their native functionality and structure) is about 0.9 nm.

The arrangement of a charged electrode (or sheet of surface charge) and nearby layer

of oppositely charged ions is conceptually similar to a double-plate capacitor. Even though

the “plate” composed of ions is spatially distributed, Equations 2.19 and 2.25 demonstrate

that the effective capacitor spacing is the Debye length. The double layer capacitance is

consequently roughly 0.8 µF/mm2 at physiologic ionic strengths.

If an insulator covers the electrode (e.g. an insulating probe layer), forming a

capacitance, the double layer capacitance appears in series with it [137]. In impedance

biosensors, the ionic double layer usually plays a minor role in the overall measured

impedance by design, either because it is so large relative to series capacitance of the

probe layer (for non-faradaic sensors), or else because theparallel path throughZw and

Rct dominates at relevant frequencies (for faradaic sensors).We have treated it at length

here because it will be important for the nonlinearity measurements explained in Chapter 4.


−100 −75 −50 −25 0 25 50 75 1000

1

2

3

4

5

φ0 [mV]

Cd [

µF/m

m2 ]

Double layer capacitance vs. bias for NaCl solutions

1 M NaCl100 mM NaCl10 mM NaCl

Figure 2.5: Calculated ionic double layer capacitance for several NaCl concentrationsversus electrode potential. Note the minimum capacitance occurs when the potential iszero, corresponding to zero surface charge.


Note from Equation 2.25 that the double layer capacitance isa function ofφ0. The

capacitance is minimized whenφ0=0, which is the condition called thepoint of zero charge

(PZC). For a metal electrode, the PZC corresponds to a particular electrode-solution bias

voltage. For dielectric surfaces, including that of biological molecules, the zero charge

condition is set by the pH of solution. The pH where the surface has no net charge is called

theisoelectric pointor pI. Thus we see thatCsur f in biosensors is a function of the DC bias.

Furthermore, this bias-dependence is a source of nonlinearity in the I-V relationship as will

be explored in Chapter 4.

2.3.8.3 Stern’s modification for adsorbed charge

The treatment above is commonly referred to as the Gouy-Chapman or Debye-Hückel

model, and implicitly treats ions as point charges. However, the ions have finite size and

ions may adsorb to a bare electrode; these effects are accounted for in the Gouy-Chapman-

Stern model [58, 135].

If some of the oppositely charged ions adsorb onto the electrode, the electric field in

solution is reduced. The same effect can occur with dipoles such as water, as depicted in

Figure 2.6a. This layer of adsorbed ions and water moleculesdefines theinner Helmholtz

plane, and solvated ions can approach only as close as theouter Helmholtz plane. Taken

together, these layers of ions immediately adjacent to the surface comprise theStern layer.

In essence, the electrode’s surface charge plus the charge of the Stern layer creates an

effective surface charge and corresponding effective interface potential which can then

be used in conjunction with the equations above to describe the diffuse ionic layer. The

effective potential outside the Stern layer is commonly referred to as thezeta potential, and

can be measured by several experimental techniques.

The Stern layer is commonly represented by a capacitance in series with the diffuse

ionic layer capacitance, and the series combination of bothis the double layer capacitance

as shown in Figure 2.6b.

If the surface adsorption is ion-specific, then the treatment becomes more involved; the

interested reader is referred to Bard’s treatment [58]. If ions in the solution can specifically

adsorb to an interface functionalized with a probe molecule, the capacitance of the interface

can change even if the target molecule does not bind, as observed by Moulton [140].


-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

-

+

+

+

+

+

+

+

+

++

+

+

ChargedMetal

Electrolyte

IHP OHPHydrationsheath

+

Solvated(+) ion

Water dipole(arrow points to +charge on dipole)

Unsolvated(-) ion

Diffuse space charge

(a) Molecular-level depiction of the ionic double layer.Solvated ions of opposite charge are attracted to theinterface. Ions can adsorb directly onto the metal,although this is not shown. From [138], who adaptedit from [139].

OHP

10 20 30 40 500.0

0.2

0.4

0.6

0.8

1.0

LD

V0

CICH CG=

x ()

V/Vo

0

Hydration sheath

Fixed sheet of ions at interface

Diffuse layer - ionic cloudB

ulk

elec

trol

yte

Linear Profile

Exponentialdecay(approximate)

(b) Potential distribution resulting from theionic double layer, with reduced poten-tial at further distances from the electrode.From [138], who adapted it from [58].

Figure 2.6: Origin of ionic double layer capacitance.


2.3.8.4 Response time

If the electrode potential is varied at extremely high frequencies, the movement of the

ions in the diffuse double layer cannot move fast enough to cancel the electric field, as

treated in Bazant [141]. Superficially, the time scale of response is approximately given

by the square of the Debye length divided by the diffusion constant of the ions. For ions

with D = 2×10−5 cm2/sec and Debye length of 1 nm, the time scale is about 0.5 ns,

corresponding to RF frequencies. Bazant shows that these time scales can be significantly

longer and depend on the thickness of the Stern layer, electrode geometry, and electrode

spacing. However, for frequencies of interest in impedancebiosensors ( 1 MHz) it is safe

to assume that the ionic double layer responds instantaneously to the applied voltage.

2.3.9 Scaling electrode size

What is the optimal electrode size for affinity impedance biosensors? Electrode size

greatly impacts the magnitude of measured impedance, and can be chosen so that the

instrument’s frequency range yields as much useful information as possible. Likewise,

the range of measurement frequencies can be chosen according to what circuit element

one is trying to measure. It is unclear whether measurement at higher frequencies is

desirable from the instrumentation standpoint. Higher frequencies will be less affected

by drift and noise in the measurement electronics, but also complicate laboratory data

acquisition and increase any errors from parasitic capacitances and inductances. It is

unclear from the primary literature the extent to which the biomolecules have a frequency-

dependent dielectric constant (treated in Section 2.4.1).Several investigators have reported

unexplained impedance drift at frequencies of roughly 100 Hz and below, while others

routinely make measurements in precisely this frequency regime.

DecreasingCsur f (e.g. by reducing the electrode area or increasing insulator thickness)

increases the capacitive impedance, allowing measurementof capacitive behavior at higher

frequencies. DecreasingRsol (e.g. by increasing salt concentration) mainly affects thehigh-

frequency impedance plateau, and shifts the transition region slightly to higher frequencies.

For non-faradaic sensors, decreasingRleak tightens the circle in the Nyquist representation,

2.4. PRACTICAL ISSUES IN IMPEDANCE BIOSENSORS 37

shortening the transition region in the Bode magnitude plot, and making it difficult to

measureCsur f at low frequencies.

If a typical impedance biosensor is scaled in all dimensionsby a factorλ < 1, Csur f

andZw will decrease byλ2 (increasing the impedance),Rleak andRct will increase byλ2,

andRsol will decrease byλ. Thus, isomorphically decreasing the biosensor dimensions

is expected to shift the impedance curve to higher frequencies and higher impedances.

It also increases the range of frequencies over whichCsur f dominates, but the transition

frequency betweenRleak andCsur f remains unchanged. This simple analysis neglects many

second-order effects such as electrode shape and non-uniformity of current flow across the

electrode surface.

Madou provided a general treatment of biosensor miniaturization and discusses scaling

other varieties of electrical biosensors [142]. Decreasing the sensor area reduces the

absolute number of immobilized probes. While the fractional impedance change upon

target binding is expected to remain constant, the absolutechange may be more difficult

to measure, depending on the noise or drift inherent in the measurement process. Also,

decreasing the number of probes will increase the stochastic noise of probe-target binding

[143]. However, small geometries may be beneficial for reducing diffusion times and

increasing the density of multiplexed biosensors. It has been shown that miniaturizing

any type of affinity biosensor leads to trade-offs between settling time and limit of detection

[144, 69, 145]. We are not aware of a general theoretical treatment of scaling considerations

for impedance biosensors beyond the cursory analysis above. This lack currently inhibits

the identification of optimum parameters for sensor design.

2.4 Practical Issues in Impedance Biosensors

2.4.1 What causes an impedance change?

What actually causes the measured impedance change in a label-free impedance biosensor?

Displacement of water? Change in intrinsic dielectric properties? Increased resistance

to faradaic current stemming from electrostatic repulsion? Other phenomena? Various

theoretical models have been proposed to explain the observed change in impedance upon


target binding. An improved understanding of the connection between target binding and

impedance change would enable improved biosensor design and sensitivity. Different

investigators utilize different types of changes, even to detect the same target.

In general, for label-free measurements it is expected thatimpedance changes will be

most pronounced if the target is substantially larger than the probe or has significantly

different properties (dielectric constant, charge state,etc.) [57]. However, various

investigators have obtained results not explained by this simple hypothesis, using various

targets on the same sensor [146, 147]. Effects due to the affinity step (e.g. probe

immobilization density,Kd, loss of probe activity, etc.) may or may not explain the

discrepancy.

A charged surface presents either an attractive or repulsive force to ions near the

electrode. This observation is especially relevant for faradaic sensors because the

interaction of the charged redox species with the charged probe layer can significantly

affectRct (the same phenomenon could also be observed by a shift in the redox potential,

e.g. [148]). This effect has been used to rationalize changes inRct upon binding of a charged

target for SAMs [149], for DNA sensors [150, 151], and for protein sensors [152, 153, 154].

Note that surface charge is also dependent on pH, temperature, and other factors.

Impedance might be affected in certain situations by the ability of the surface groups to

ionize. In acid-terminated self-assembled monolayers (SAMs), changing the pH changes

the charge state of the terminal acid and can affect the measured capacitance by up to 50%

[155, 156]. The impact of this effect diminishes with increasing chain length and increasing

ionic strength (as expected by a series capacitance model),and involves a complex interplay

among electrode potential, the repulsion or attraction of charged ions to the surface [157,

158] and possibly solvent structure [156]. Conceptually this sensitivity may be understood

as the result of adding the Stern layer of bound charge to the Gouy-Chapman double layer

model (see Section 2.3.8), and is treated theoretically in [159, 160]. Miura et al. noted

a 40% increase in capacitance upon capture of K+ at a SAM-electrolyte interface [161].

Note that the probe and target molecules usually have pH-dependent charge states (usually

referred to in terms of thepI, or pH at which the net charge is zero), as can the probe

attachment surface. This sensitivity implies that pH needsto be carefully controlled, with


its effect ideally being treated as a common-mode disturbance using a differential method

(see Section 2.4.3).

For acid-terminated SAMs at pH values where the terminal acid is partially ionized, the

applied voltage in EIS actually induces protonation/deprotonation, which contributes sig-

nificantly to the measured impedance at certain frequenciesnear 10 Hz. This phenomenon

depends on the specific details of (de)protonation kinetics, and was recently treated

experimentally and theoretically [162]. This is one physical explanation for the finite value

of Rleak in non-faradaic sensors, and suggests that surface ionization may introduce an

additional impedance component that is pH-dependent and not usually modeled (a model

is derived in [162]). Janek et al. also noted an anomalous impedance at low frequencies,

perhaps due to this effect or due to dipole effects [163].

Applying a voltage between the electrode and solution can cause the thickness of a

DNA coating to either increase or decrease, presumably due to the electrostatic interaction

of the charged electrode with the charged DNA [164]. Changesin film height have also

been observed in certain short peptides having an intrinsicdipole moment [165], and in

loosely-packed gold-thiol SAMs [166]. Likewise, an applied voltage might induce change

in conformation for any probe/target pair with charge, and is a plausible mechanism for

impedance change.

It has been noted that ssDNA is floppy and thus prone to lying near the surface, implying

that ions might have greater access to the surface after hybridization [41, 167]. However,

any steric decrease inRct upon hybridization competes with an electrostatic increase due

to additional fixed charge.Csur f might also increase upon hybridization, as ions would be

able to come closer to the electrode surface, but there are confounding effects.

Changes in molecular conformation could also introduce a change in impedance, in

Csur f, Rct, or Rleak. The former has been exploited for a sensor using a protein whose

conformation changes upon binding of heavy metal ions [12] (though other possible

explanations exist, cf. [161]), and the latter effect used to study the double layer structure

[168]. It has been shown that dsDNA conformation changes canbe induced by varying

ionic and/or pH conditions, resulting in significant changes in measuredRleak and Rct

[150, 27]. Likewise, protein conformation can be significantly affected by ionic and/or


pH conditions [169], which implies that if protein conformation affects the measured

impedance then these factors need to be tightly controlled.

In non-faradaic sensors, it is common to rationalize changes in Csur f as arising

from displacement of water and solvated ions from the surface upon target capture.

Binding should increase thicknesst and decreaseεr of the overall probe layer (εr ∼ 2–

5 for biomolecules versus 80 for water at low frequencies), decreasing capacitance. A

typical conceptual explanation includes three capacitorsin series: a dielectric layer of the

insulation (SAM or otherwise), a dielectric layer of the probe layer, and the double-layer

capacitance. To allow measurement of the probe layer capacitance, the insulating layer

should be as thin as possible [57, 170]. Imperfect insulation, modeled byRleak in parallel

with the capacitance, can reduce the sensitivity of the measured impedance to the change

in Csur f. Changes inRleak are occasionally employed as a sensor output, as in [150, 171],

and can be independently assessed using cyclic voltammetrywith a redox couple.

Dipoles in the SAM headgroup can contribute to measured capacitance because dipoles

affect the dielectric constantεr [172, 173]. This observation could partially explain

variation in response between otherwise similar targets. Note thatεr is not strictly constant

over frequency, as dipoles may be able to react to slow-moving excitation fields but not

to higher-frequency ones. This research area, termeddielectric spectroscopy[174], has

received limited attention in the biosensing community [50, 175, 51]. It is usually used

to measure bulk solutions at high frequencies ( 1 MHz, Csur f negligible) and is thus

quite distinct experimentally from conventional surface-sensitive impedance biosensors

( 1 MHz, Csur f important). (SPR could be considered localized dielectricspectroscopy

at optical frequencies.) Some biomolecule dielectric relaxation effects may be detectable

at frequencies in the kHz range [50, 176]. However, these effects usually are neither

surface-sensitive nor specific, so dielectric spectroscopy seems better suited to studying the

behavior of biomolecules (e.g. [177]) or measuring the concentration of a pure biomolecule

sample (e.g. [49]), than to distinguishing between similarbiomolecules. Gebbert et

al. rationalizes the use of kHz measurement frequencies by estimating that the dipole

response of a bound antibody/antigen pair occurs at 6 kHz or below [170], although

without experimental confirmation. Measuring at frequencies corresponding to dielectric


relaxation times between those of free and bound molecules might give some binding-

specific information. Changes inεr over the range of measurement frequencies is not

typically modeled during the curve fitting process. While irrelevant for most impedance

biosensors, exploiting this variation may prove useful.

Particularly in the case of polymer-immobilized impedancebiosensors, the target

binding event might modulate the properties of the surrounding material in such as way that

the impedance changes [178, 179], as in field effect sensors (see Section 2.1.2). Polymer-

coated electrodes (see Section 2.5.5) often have an impedance that varies significantly with

applied DC bias [180]. The double-layer capacitance (see Section 2.3.8) depends weakly

on DC bias [58, 172] and thus provides another mechanism by which the DC bias can affect

the measured impedance.

Finally, a measurable impedance change might arise from an increase in DNA

conductivity upon hybridization. Though not fully understood, dsDNA has significant

electronic conductivity due to the base pair stacking [181,182, 27]. While this property

has been used to detect DNA hybridization using redox labelsor redox-active intercalators8

(e.g. [183]), measuring changes in DNA conductance via impedance spectroscopy would be

difficult to distinguish from common-mode changes. The factthat DNA is a polyelectrolyte

implies that surrounding positive counterions can also affect surface impedance. It has been

observed that tethered DNA probes trap counterions, creating a local high-salt environment,

implying that the ionic strength at the surface, which determines double layer capacitance,

can differ from that of the bulk solution [148].

2.4.2 Response curve

The response curve is the relationship between the sensor output variable (e.g.Rct, change

in imaginary part of the impedance at a particular frequency, etc.) and the sample target

concentration. For all affinity biosensors, this response curve arises from two separate

relations. The first corresponds to the affinity step (σΘ([Target]), relating surface coverage

to bulk target concentration), while the second corresponds to the readout step (∆Z(Θ),

relating impedance change to surface coverage). When[Target] Kd, Θ ≈ 1 and the

8molecules that insert themselves between base pairs in a double-strand DNA


impedance response saturates. For[Target] Kd, Θ ∝ [Target]. Most of the reported

explanations for the impedance change (see Section 2.4.1) predict ∆Z ∝ Θ, and thus one

would expect the sensor output to be proportional to the target concentration in the low-

concentration regime.

In contrast to this prediction, it is commonly observed thatthe response curve is

logarithmic in[Target] until saturation (e.g. [170, 184, 185]) as pointed out by Bart et al.

[186]. If the probe-target binding energy is heterogeneous(e.g. polyclonal antibody probes

or distribution in binding site availability), then the assumptions of the Langmuir isotherm

are violated and the Temkin isotherm is a better model [187].Because the Temkin isotherm

predictsΘ ∝ log([Target]), it might explain the observed response. It is also possiblethat

the relationship between target coverage and impedance response∆Z(Θ) is logarithmic,

as is the case with most field-effect biosensors [188]. Some authors (e.g. [189, 190])

have obtained good fits of experimental data with the Langmuir isotherm, and there has

been at least one report of sensor response being exponential in target concentration [191].

One complicating factor is whether the binding is controlled kinetically or reaches true

equilibrium during the experiment.

Understanding the exact nature of theΘ([Target]) and∆Z(Θ) transfer functions could

lead to improvements in affinity biosensors and would enablegreater understanding of

impedance change mechanisms. Some investigators attempt to measure target surface

coverage independently using techniques such as QCM, SPR, or label-based techniques

(e.g. [192, 193]).

There is no standardized method for determining biosensor dose-response curves [186],

and the challenge of reproducibility further confounds this issue. Investigators with flow-

through apparatus often use successive injections of target, with binding assumed to be

cumulative and irreversible. Other methods may introduce variation by regenerating the

probe layer between experiments or using completely different sensors for different points

on the response curve. This latter method is expected to capture the most non-reproducible

behavior and may most closely represent biosensor performance in the real world.


2.4.3 Differential measurement

Utilizing a differential measurement scheme can eliminatevariations in the sensor output

caused by disturbances unrelated to the sensed quantity. For example,Rsol andCsur f

are affected by salt concentration, pH, and temperature. Impedance changes due to

uncontrolled changes of these factors may swamp out the tinyimpedance change caused

by target-probe binding. In complex samples, non-specific binding is also expected to give

a response unrelated to target concentration.

To compensate, a “reference” sensor can be used (this sensoris not the same as

the reference electrode discussed in Section 2.3.2). Ideally, no target binding occurs

on the reference sensor but it otherwise has an identical response to the sample. The

signal then consists of the difference between the working and reference sensor responses,

hopefully eliminating any “common-mode” response due to extraneous environmental

factors. However, the differential response may contain contributions from common-mode

changes due to imperfect matching. The less controlled the sample composition, the more

difficult it is to select a reference “probe” coating and ensure cancellation of other effects.

Making an impedance measurement before and after target binding, while attempting to

hold everything else constant, could also be considered a differential measurement in some

sense, though we hesitate to apply this term. Particularly if working and reference sensors

react similarly to non-specific binding, differential schemes can enhance both selectivity

and sensitivity of the overall system [194, 116, 195].

2.4.4 Probe attachment chemistry

As we have seen, the affinity aspect of affinity biosensors is often the limiting factor for

biosensor performance. Thus, it is critical that the probe molecule be attached to the sensor

surface in a way that maintains probe specificity and activity while inhibiting non-specific

binding. We cannot fully review biosensor surface chemistry here, but give a few results

relevant to impedance biosensors.

Many impedance biosensors utilize self-assembled monolayers (SAMs) to attach

probes at the electrode-solution interface. The most common types of attachment

chemistries are based on thiols bound to gold surfaces [196]and siloxanes to oxide


surfaces [197]. Other chemistries are based on polymer attachment layers, other covalent

attachment schemes, or non-covalent physisorption. ThiolSAMs are the most studied

and are prevalent in impedance biosensors. The SAM can be formed and the probes

subsequently immobilized on top or else the probes themselves can be formed as a SAM.

For non-faradaic sensors a tightly-packed (highRleak) SAM is desirable, in contrast

with faradaic sensors where the electrode surface needs to be accessible to the redox species

but not to adsorption of other molecules [99]. SAMs composedof longer straight carbon

chains form more dense monolayers due to hydrophobic interactions of the chains. The

general rule of thumb is that C11 or greater gives packed films [198, 199], but Mirksy et

al. reportedCsur f drift due to thiol desorption using a C11 SAM but not for a C16 SAM

[189, 200]. SAM desorption is one example of why a sensor might have a response

to a blank solution. Boubour reported that over 40 hours of incubation was needed to

form a tightly-packed SAM, as determined by observing purely capacitive behavior at low

frequencies [201], whereas it has been elsewhere reported as 15–20 hours depending on

SAM composition [202] and as little as 2 hours [99].

It is important to remember that SAMs are only good electrical insulators over a window

of DC bias voltages, depending on the terminal group and chain length. For gold-thiol

SAMs with hydrophilic headgroups, DC conduction (i.e. finite Rleak) is noted even at 0 V

bias vs. Ag/AgCl with a C16 SAM in the absence of a redox species [203]. This conduction

is likely due to voltage-induced structural rearrangementof the SAM that results in pinholes

[204] or permeation of SAM with ions or water molecules [205]. Extreme DC bias voltages

can actually oxidize or reduce the bonds between a metal electrode and biological probe

layer (reported reported values for gold-thiol are summarized in [205]). This effect has

been utilized to selectively functionalize electrodes [206, 207, 208, 209]. Air exposure can

also oxidize the thiol-gold bonds [167]. Lai et al. recentlypublished an important report

of thio-SAM stability during dry storage, concluding that longer SAMs are more stable

and that preservatives can ensure stability over one month with reproducible results [99].

The hexacyanoferrate(II/III) redox couple used almost universally in faradaic impedance

sensors can degrade the electrode-SAM interface over time,particularly when exposed to

light [210, 211], as well as reduce the activity of peptide layers [212].


One additional approach to probe attachment is to form a polymer layer onto the

electrode. This layer can be electrolytically deposited (review in [213]) or else via a

charged polymer that attaches to the surface via many weak interactions (e.g. [214, 215]).

Probes can either be embedded in the polymer layer or be attached to the polymer surface

afterwards. If a polymer attachment is used, the polymer’s electrical properties must be

understood and be compatible with the readout approach. Specific examples will be given

in Section 2.5.5.

2.4.5 DNA vs. protein biosensors

Using oligonucleotides,9 most often DNA, as probes and targets may be somewhat more

convenient for research purposes than using antibodies or proteins. Oligonucleotides are

readily available in purified form, immobilization chemistry is relatively mature, and hy-

bridization exhibits relatively robust selectivity. However, it is unclear whether impedance

DNA biosensors have any commercial viability because various detection technologies

already exist for DNA (e.g. DNA microarrays, pyrosequencing, real-time polymerase

chain reaction), and other technologies are being researched (e.g. voltammetry using

redox-labeled DNA). However, DNA-based sensors can demonstrate proof-of-principle for

protein impedance biosensors and elucidate properties of the electrode/solution interface.

Additionally, a market may exist for inexpensive and portable impedance-based DNA

diagnostics where moderate sensitivity is sufficient.

Aptamersare oligonucleotide or peptide sequences which bind selectively to a desired

target, including proteins [216, 217]. They are chosen by anin vitro selection process

that identifies a monomer sequence that tightly binds the target, starting from a large

library of random sequences [218, 219]. Aptamers are considered promising alternatives

to antibodies for capture probes because of facile production, well-understood tethering

chemistry, and perhaps reduced cross-reactivity [220].

As already mentioned briefly in Section 2.2.3, protein detection appears to be the

more likely real-world application of affinity impedance biosensors because labeling

proteins is difficult and impedance sensing can be label-free. Additionally, difficulties

9a short nucleic acid polymer


in cross-reactivity and non-specific binding severely affect protein sensors, allowing less

sensitive readout techniques to be used with equal overall results (i.e. the detection limit

is constrained by the affinity step, rather than by the readout step). Only moderate levels

of multiplexing are practical for protein assays, and this requirement represents a good fit

with the moderate levels of multiplexing easily achievablewith impedance biosensors.

Most published reports use target proteins of real-world interest but in highly purified

conditions. Much effort is still required to bring about robust analysis of clinical samples

using impedance biosensors to enable point-of-care applications. Key challenges include

poor reproducibility, non-specific binding, and the complex and highly variable nature

of clinical samples. Some protein sensors are termed “immunosensors” in the primary

literature because they detect antibodies or antigens. Because antibodies and most antigens

are proteins, we make no distinction here.

If an antigen is used as the probe, target antibodies can be detected. Judged on a per

molecule basis, these “reverse” arrays [221] could be more sensitive than those using a

large capture antibody to detect a small protein, if the measured impedance depends on

target size. These sorts of antibody sensors could be usefulfor allergen screening and for

detecting autoimmune disorders.

2.5 Summary of Published Label-free Affinity Impedance

Biosensors

Here we summarize many researchers’ efforts as published inthe technical literature. Table

2.2 contains a summary of selected label-free affinity impedance biosensors for quick

comparison, but the text summarizes many additional reports. It is interesting to note that

reported detection limits have not systematically improved with time. We speculate that

reasons might include limitations in the affinity step, different definitions of the limit of

detection, limitations related to common-mode disturbances, and an increased awareness

of challenges related to sensor reproducibility.

2.5.P

UB

LISH

ED

PR

IOR

AR

T4

7

Probe TargetLimit of

DetectionMeasurement Type Var-

iable Excitation Surface Chemistry ReferenceYearRef. Comments

antibody hIgG 50 ng/mL ID-electrodenon-faradaic

Z @freq

100Hz? polymer/probe mix electrode w/ or w/oAb

1991[222]

one of first affinity impedancebiosensors

antibody IgG, anti-IgG est.< 1 ng/mL 2-electrodenon-faradaic

Csur f 100mV @ 1kHz silane, linker after-before, timecourse

1992[170]

antibody α-fetoprotein est. 50 ng/mL 2-electrodenon-faradaic

Z @freq

1.5 kHz silane, linker IgG-coated electrode 1997[194]

antibody HSA 1000 ng/mL 2-electrodenon-faradaic

Csur f 10mV @ 20Hz various compared time course 1997[189]

results with HDA + linker

antibody IL-2 est. 0.05 ng/mL 3-electrodenon-faradaic

Csur f 50 mV step SAM, linker, C12 diluent after-before 1998[184]

antibody interferon-γ 0.00000002 ng/mL 3-electrodenon-faradaic

Z @freq

10mV @ 113Hz SAM, linker time course 2001[223]

flow system, large non-specific signal

antibody Schistosomajaponicum

0.1 ng/mL 3-electrodenon-faradaic

Csur f 50 mV step PrA linker, thiol diluent after-before, timecourse

2002[224]

antibody IgG 100 ng/mL 3-electrodenon-faradaic

Z @freq

10mV @ 10kHz conducting polymerentrapment

blank-coatedelectrode

2002[116]

antibody vitellogenin 420 ng/mL 3-electrodenon-faradaic

Rct 10mV @ 10-105 Hz conducting polymer, linker after-before 2004[225]

redox species in polymer

antibody HSA 1.6 ng/mL 3-electrodenon-faradaic

Z @freq

10mV @ 34Hz polymer, linker after-before 2005[185]

optimized several parameters

antibody transferrin 0.08 ng/mL 3-electrode faradaic Csur f 50 mV step Au nanoparticles,conducting polymer

after-before, timecourse

2005[226]

antibody α-fetoprotein 10000 ng/mL 3-electrodenon-faradaic

Csur f 50 mV step various compared after-before 2006[227]

similar results for all surfacechemistries

antigen anti-HRP 0.024 ng/mL 3-electrode faradaic Csur f 10 mV @0.05-104 Hz

SAM, linker after-before 2005[228]

antigen anti-Der f2 est. 2000 ng/mL 3-electrode faradaic Rct 5 mV @10-1-105 Hz

MPTS, Au nanoparticles after-before 2006[229]

Au deposited on GCE

antigen antibody 0.005 ng/mL 3-electrodenon-faradaic

Csur f 50 mV step thiol-probe, C16 diluent after-before 2006[230]

reverse array to test probecomposition

aptamer lysozyme est. 1000 ng/mL 3-electrode faradaic Rct 5 mV @10-2-105 Hz

avidin after-before 2005[152]

aptamer IgE 19 ng/mL 3-electrode faradaic Rct 5 mV @ 103-105 Hz SAM, linker 2005[231]

small electrode array

aptamer thrombin 3.6 ng/mL 3-electrode faradaic Rct 5 mV @ 1-105 Hz thiol-probe, C6 diluent after-before 2006[153]

ssDNA ssDNA 0.0000000002nM 3-electrodenon-faradaic

Csur f 50 mV step thiol-DNA, C2 diluent after-before, timecourse

1999[232]

with very long target, largenon-specific signal

ssDNA ssDNA 4 nM 3-electrode faradaic Rct 10 mV @10-2-105 Hz

silane, Ag nanoparticle after-before 2005[233]

ssDNA ssDNA 100 nM 3-electrodenon-faradaic

Rct 10 mV @0.5-105 Hz

polymer after-before 2005[234]

PNA ssDNA est. 0.2 nMfaradaic

Rct thiol-PNA, C6 diluent time course 2005[27]

measured kinetics

Table 2.2: Summary of salient characteristics of selected label-free affinity impedance biosensors. Detection limitsareestimated if not explicitly stated in reference.


2.5.1 Early affinity impedance biosensors

Credit for the first capacitive affinity biosensor is widely given to Newman [235], who

in 1986 used interdigitated electrodes covered by insulation and an antibody probe. In

1988, Taylor et al. reported an impedimetric sensor for the small molecule neurotransmitter

acetylcholine and a related neurotoxin using protein receptors isolated from animal tissue

[11]. Interdigitated gold electrodes were coated with a polymer, either with or without

the receptor, and a bridge configuration was used to detect the differential impedance

change. Several years later with very similar apparatus, they reported detection of as little

as 50 ng/mL of antibody hIgG [222].

Many early impedance biosensors were based on a metal or semiconductor coated with

a thin layer of native oxide to which the probes were attached. Some of these sensors

worked at least partially on field-effect principles, whichare not considered here. Using

a thin native oxide on doped silicon and biasing the silicon to the strong accumulation

region (insuring that field effects were negligible), Maupas et al. were unable to detect

impedance changes using a silane-antibody coupling, but observed significant changes in

the impedance of a polymer-antibody film when exposed to alpha-fetoprotein target, with

a detection limit of 10–20 ng/mL [236]. Subsequently, using antibody-functionalized

platinum electrodes, they reported a poorer detection limit (∼ 100 ng/mL) for alpha-

fetoprotein by measuring differential impedance changes at 1.5 kHz [194]. Though non-

specific binding of serum proteins greatly reduced sensitivity (limitation of the affinity

step), they claimed reproducible impedance changes on the order of 1%. Gebbert et al.

used an electrochemically grown tantalum oxide with controlled thickness as an insulator,

and were able to detect anti-mouse-IgG to around 1 ng/mL levels with mouse-IgG as a

probe by measuring capacitance at 1 kHz in real time, though non-specific binding was

significant [170].

2.5.2 Potentiostatic step

Lund University researchers pioneered the use of the potentiostatic step technique for

impedance biosensors. In this technique a voltage step is applied and the resulting current

is fit to a simple RC model. The instrumentation is described in [172, 120]. Relatively

2.5. PUBLISHED PRIOR ART 49

low electrolyte concentrations and a fast potentiostat arerequired to capture the initial

part of the curve. Any CPE-like behavior (see Section 2.3.7)of the interface is neglected.

However, a complete measurement may be made quite quickly.

In 1997 Berggren reported an impressive detection limit of 0.5 pg/mL for the protein

hCG, noting that sensors with probes for two other antigens (HSA and IL-2) gave much

smaller responses [147]. In 1998 similar results were reported for IL-2, and even more

impressive results for IL-6, though the detection limits were not specified [184]. In

this same report they compared two different methods of antibody coupling. The same

investigators later constructed a DNA biosensor based on the same principle, and reported a

detection limit of 0.2 aM for a 179mer ssDNA target using 26mer and 8mer oligonucleotide

probes [232]. They used a target much larger than the probe, but a still-impressive 1–

5 aM limit of detection is expected for identical-length targets. However, there was a large

non-specific binding signal for unrelated DNA, and reproducibility was poor. A hiatus

ensued, but recently results have been published with much higher detection limits. In

2005 they described a continuous monitoring of human serum albumin for bioprocess

monitoring, where greatly reduced sensitivity is adequate(measurement range was well

above 10µg/mL) [237]. Collaborating researchers Limbut et al. experimented with three

different surface chemistries for antibody immobilization, and obtained roughly 10µg/mL

detection limits for the alpha-fetoprotein target in each case [227].

Other investigators have recently used the same measurement approach. Jiang et al.

used faradaic EIS measurements to validate the simple RC model used for potentiostatic

step readout and then used the latter to detect a protein using an antibody capture agent,

claiming a detection limit of 10 ng/mL [238]. In an excellent paper, Zhang et al. detected

trace impurities of an enantiomeric drug by cleverly tethering the small molecule to be

detected as the probe layer, taking advantage of the comparatively large size of the antibody

recognition agent [230]. One disadvantage is that such a sensor cannot be prepared

beforehand. Nevertheless they demonstrate good reproducibility and low non-specific

response, and report an absolute detection limit of 5 pg/mL, as well as detecting a 10 ppm

enantiomeric impurity. Other reports using the potentiostatic step method include Jiang

[146] and Hu [226] (both detailed in Section 2.5.6), and Wanget al. who claim a 2.5 pg/mL

limit of detection for low-weight protein r-HV2 using a faradaic measurement [239].


2.5.3 Non-faradaic studies

In 1997 Mirsky et al. used anti-HSA antibodies attached to a tightly packed SAM via a

linker, collecting data at 20 Hz where the impedance was purely capacitive [189]. Notably,

they monitored the capacitance change during probe immobilization in order to estimate

probe density, and were thus able to normalize the subsequent change upon target binding

and improve response reproducibility (10–30% over severaltrials). Though the reported

detection limit is very modest (1µg/mL), the paper demonstrates an understanding of the

issues that need to be addressed. Slightly earlier, Rickertet al. reported detecting antigen

capture of an antibody using both faradaic and non-faradaicmeasurements ofCsur f and

concluded that non-faradaic was preferable. They observedsignificant non-specific binding

and drift with time, but the initial change inCsur f did allow detection down to at least

1 µg/mL levels [212].

British investigators Davis et al. used low-frequency non-faradaic measurement to

detect plasmid DNA [240, 215]. They used identical DNA as theprobe, with both probe

and target dissociated into single strands before use. Interestingly, the probes were simply

adsorbed to a polymer attachment layer composed of the positively-charged polymer

polyethyleneimine (PEI). The reported detection limit of 1fg/mL, corresponding to 23 aM,

which is quite respectable, although significant sensor drift was reported.

Ma et al. reported significant (10–20%) impedance changes upon target DNA hybridiza-

tion, compared with negligible changes on the non-specific control electrode, using non-

faradaic EIS [103] (subsequently they attempted amplification with disappointing results).

Target concentrations were very high so no detection limit was determined.

Lasseter et al. measured impedance of biotin-functionalized surfaces upon avidin

binding over a very wide frequency range in a non-faradaic scheme [192]. They observed

that the main impedance change occurred at frequencies so low (< 1 Hz) that theRleak was

the main affected equivalent circuit element. This behavior suggests that the binding might

be more readily detected using faradaic EIS.

In 2001 Dijksma et al. published work reporting the unprecedented detection limit of

0.02 fg/mL for protein interferon-γ using a non-faradaic measurement of an antibody-

modified SAM [223]. Like a few other investigators, they madeuse of a flow cell and


introduced controlled amounts of antigen followed by buffer washes. Although they

reported significant non-specific binding, they found that it could be largely corrected by

subsequent washing steps. A follow-up study replicated these results and independently

verified from signal-to-noise considerations that the optimal measurement frequency had

previously been used [186]. Their idea of determining the binding signal-to-noise ratio

at different frequencies is a powerful concept. However, repeatability and non-specific

response were somewhat problematic. Interestingly, a positive DC bias of 200 mV

increased the sensor response.

2.5.4 Faradaic studies

Faradaic impedance biosensors almost always monitor changes inRct when affinity binding

occurs. Liu et al. reported a DNA sensor based on faradaic impedance spectroscopy and

were easily able to detect 1 nM of 15mer target [190]. The observed change inRct is

presumably due to electrostatic repulsion between the negatively-charged redox species

and negative charge on the DNA backbone. To increase fractional Rct change probes were

made of PNA, a DNA mimic with a neutral backbone.

The Lee and Kraatz group have published a series of papers demonstrating that

mismatched DNA can be distinguished from perfectly matcheddsDNA by differences in

Rct between the B and M conformations of DNA (which can be selected based on ion

concentrations and pH) [151, 241, 242]. They also detected mismatches by changes inRct

when the mismatch-binding-protein MutS was introduced [243]. Akagi et al. demonstrated

discrimination of single nucleotide polymorphisms (mismatch of a single base pair) by

extending the probe strand via ligation and measuring resulting change inRct arising from

that extension rather than from the hybridization itself. Although these operations add

extra steps (contrary to the spirit of label-free detection), they claim detection limits in the

pg/mL range, or much less than 1 nM [244].

Xu et al. published a report using aptamer probes on a small array of electrodes which

were interrogated using faradaic EIS [231]. Upon binding ofthe IgE target,Rct increased

significantly. Sensitivity using aptamer probes was higherthan using antibody probes. The

sensor showed good reproducibility and the multiplexed setup makes it possible to include


reference electrodes for differential measurement. They estimated a 0.1 nM (∼ 20 ng/mL)

limit of detection.

Cai et al. reported a thrombin sensor using an aptamer probe on a microfabricated gold

electrode [153]. They noted increases inRct and hypothesize that thrombin acts as a

hydrophobic insulator (despite the fact that it is positively charged and the redox species

is negatively charged). Using three replicates, they reported no non-specific binding of

hemoglobin or BSA and a detection limit of 3.6 ng/mL. Ding et al. noticed an increase in

Rct accompanied by a tiny decrease inCsur f using µg/mL concentrations of biotin exposed

to an avidin-functionalized gold electrode, and reported adetection limit of 20 ng/mL

[154]. In contrast with these two reports, Rodriguez et al. noted a decrease inRct upon

target binding to an aptamer probe [152]. This decrease was explained by the fact that

the target had a significant positive charge but the probe wasnegatively charged, and thus

target binding decreased the electrostatic barrier for thenegative redox species. This result

demonstrates that competing effects determine∆Rct, implying that this detection strategy

may not be generalizable.

Ameur et al. used a SAM-functionalized gold electrode in a flow cell with various routes

to antibody immobilization in an early faradaic study [245]. They reported detection limits

of 5–10 pg/mL depending on the functionalization route. Pyun et al. reported the use of a

flow cell with faradaic measurement [228]. Few details of theactual data or analysis are

provided, but they assert that changes inCsur f allowed quantification of an antibody against

immobilized horseradish peroxidase — commonly used as an enzyme label but here used

as a probe — over an enormous dynamic range of 6 orders of magnitude from the detection

limit of 24 pg/mL. BecauseCsur f is being measured, a non-faradaic measurement also

should be possible. Likewise, Hays et al. used a faradaic measurement to detect hemoglobin

binding at functionalized electrodes [193]. The impedancechange was primarily in the

imaginary component of low frequency impedance, suggesting thatCsur f was the principal

model element affected and could be measured by non-faradaic means.


2.5.5 Polymer films

One approach to electrode functionalization is to use polymer films, typically electropoly-

merized, to which biomolecular probes can be attached or entrapped [213]. Either faradaic

or non-faradaic measurement can subsequently be employed.Often the deposited polymer

contains redox centers or is semiconducting, in which case it may act as an extension of the

metal electrode. In this section we only highlight biosensors where the polymer’s electrical

properties are utilized, whereas biosensors which use a polymer as a probe attachment

mechanism only are mentioned in the appropriate section.

The earliest impedance biosensors by Newman [235] and Taylor [11] used non-

conducting polymer films. In 2001 Lillie et al. observed changes in impedance phase angle

at low frequencies when a conducting polymer film with embedded antibodies was exposed

to luteinizing hormone, allowing detection in a clinically-relevant concentration range

[246]. Sadik compared various polymer functionalization chemistries with a differential

system and reported a detection limit of 100 ng/mL for target IgG, though significantly

lower detection limits were observed for cyanazine-BSA target if a very large AC excitation

was used [116]. More recently, Wu et al. used a thin insulating polymer to create a

non-faradaic capacitive sensor [185]. They achieved the impressive detection limit of

1.6 ng/mL for the HSA target after optimizing antibody density, pH,and measurement

frequency, and also showed evidence for excellent reproducibility and selectivity against

non-specific binding.

Darain et al. used a conducting polymer film to detect a fish sexbiomarker. No

external redox species was added, but theRct of the polymer film itself was observed to

depend on target binding and allowed detection down to 0.42 µg/mL in pure samples and

discrimination of fish sex using serum samples [225]. Ouerghi et al. demonstrated response

of a conducting polymer coated with antibodies to IgG concentrations in the range 10–

80 ng/mL in non-faradaic conditions at very low frequencies, though no blank solution

or non-specific target was tested [191]. Tlili et al. utilized a very similar approach with a

ssDNA probe detect complementary DNA down to 100 nM [234]. Changes in the electrical

properties of a conducting polymer were the proposed explanation in similar work on a

DNA hybridization sensor [179] and an antibody sensor [178].


2.5.6 Special electrode surfaces

Recently, several researchers have attempted to increase electrode surface area by deposit-

ing nanoparticles in order to increase the number of attached probes (σ) and therefore

increase the sensitivity. Li et al. deposited gold electrochemically onto an electrode for

a faradaic impedance sensor that detected a DNA intercalating drug by noting changes in

Rleak in parallel to the SAM in the fit model [171]. Huang et al. used faradaic EIS with

an allergen probe immobilized on an electrode coated with gold nanoparticles to detect

antibodies in the range of 10s of µg/mL via increasedRct [229]. A similar approach with

silver nanoparticles was used by Fu et al. to detect DNA down to 4 nM [233]. Hu et al. used

gold nanoparticles loaded on top of a polymer-coated electrode to immobilize antibodies

[226]. With a potentiostatic step readout they were able to detect transferrin concentrations

ranging from 80 pg/mL to 100 ng/mL, though the sensor showed over 10% non-specific

response.

In 2002 Zhou et al. reported an impressive detection limit of0.1 ng/mL for an antibody-

based sensor for a protein disease marker, but unfortunately there were no follow-up

publications [224]. Jiang et al. used alumina sol-gel surface with antibodies detected hIgG

and two liver fibrosis markers [146] using a potentiostatic step method (see Section 2.5.2).

The reported limit of detection was about 1 ng/mL for individual analytes. Notably, cross-

reactivities were explicitly tested and were below 10% except at concentrations below

10 ng/mL, in which case they were significantly worse.

DeSilva et al. published an early report using a film of platinum islands coated with an

antibody probe as the sensor surface [247] with impedance readout at 100 Hz. Although

the reported 0.4 ng/mL limit of detection is impressive, only three sensor surfaces were

measured, and thus little characterization of the non-specific response could be performed.

A similar approach was undertaken by Pak in 2001 [248] with similar limitations, and to

the our knowledge this approach has not been pursued recently.

2.5.7 Interdigitated electrodes

As already mentioned, the earliest capacitive biosensors were based on interdigitated

electrodes [235, 11, 222]. Interdigitated electrodes (IDEs) can be easily fabricated by


conventional microfabrication techniques and are used forvarious types sensors [249].

The impedance measured is between the two (usually identical) electrodes, and very often

no explicit electrical connection is made with the solution, in stark contrast with the other

types of impedance biosensors mentioned in this review. Depending on geometry, the inter-

electrode capacitance can degrade sensitivity to changes at the electrode-solution interface.

While not a label-free approach, conductometric amplification using silver deposition (see

Section 2.2.9) typically uses exposed interdigitated electrodes.

Interdigitated electrodes for label-free affinity biosensing are still being explored.

Laureyn et al. characterized IDEs with nanoscale fingers andreported an impedance change

during probe immobilization but did not report on target binding [250]. Hang et al.

described changes in impedance between Pt IDEs upon DNA hybridization [251]. Very

large DNA concentrations were used. Interestingly, they noted that theRsol component

varied the most upon hybridization, notCsur f.

2.5.8 Miniaturization efforts

In the push to miniaturize impedance/capacitance biosensors, several researchers have at-

tempted to create integrated circuits to perform the measurement. One of these approaches

is to determine the charge required to bring the interface toa particular voltage, implicitly

measuring the capacitance. This technique neglects many intricacies of the actual interface

impedance (e.g. voltage dependence ofCsur f, Rleak) but is simple to implement and has

been shown to give significant changes in both discrete [252]and integrated [253, 254]

implementations. The same investigators have more recently reported essentially an

integrated potentiostatic step approach with the disadvantages noted in Section 2.5.2. Even

though in all these publications, high concentrations of target DNA were used and the

reproducibility data is poor or nonexistent, we think this is a worthwhile line of research.

Recently an integrated multipurpose electrochemical sensor for biomolecular detection was

presented. While impressive electrical performance was achieved, very few measurements

with a biofunctionalized surface were reported [255, 195].Finally, there has been a recent

proposal of implementing a full impedance spectroscopy measurement on a silicon die,


although it is our opinion that the proposed methodology will be difficult or impossible to

implement [256]. Note that, at least conceptually, this proposal is very similar to the work

undertaken in this thesis.

2.6 Conclusions and Research Directions

It has been repeatedly demonstrated that protein and DNA binding to immobilized probes is

detectable by measuring impedance changes of electrode-solution interfaces, but there are

many aspects requiring further refinement. Some of these issues are applicable to all affinity

biosensors regardless of readout technology, while othersare unique to impedance readout.

The detection limit is affected by both the affinity and the readout steps. Some investigators

report sub-ng/mL limits of detection while other investigators report figures orders of

magnitude higher. There has been no systematic improvementin reported detection limits

during the past 15 years of label-free affinity biosensor research.

Arguably the most daunting issue facing affinity biosensorsin general is the problem of

selectivity in the presence of large concentrations of non-target material. This obstacle can

be overcome by using labels and/or labeled secondary probes. However, both of these

solutions are contrary to the goal of creating a point-of-care detection device because

they require extra time, add extra sample preparation steps, and increase overall system

complexity. This challenge is common to all label-free affinity sensors, no matter what

readout method is used.

Therefore, we suggest that investigators devote increasedattention to the non-specific

response of their sensors, and demonstrate selectivity to the chosen analyte in the presence

of large background concentration of non-specific interferents. A first step towards this goal

is reporting the sensor response to a large excess concentration of non-target molecules in

order to test specificity. A second step is to include a small concentration of target in a

background of non-target. We suggest that investigators begin to routinely report such

data, anticipating applications where this will be more important than the “clean” limit of

detection. We applaud those authors who include non-specific binding data in publications,

even if it appears unfavorable.

2.6. CONCLUSIONS AND RESEARCH DIRECTIONS 57

Researchers should validate their reported detection limit by showing that the sensor

response to blank and target solutions is significantly different over multiple trials.

Furthermore, we suggest that reproducibility data be explicitly presented, such as by

reporting the coefficient of variance of multiple experiments (ideally on different days using

different sensors). The methodology for determining the response curve should be stated

and reproducibility data presented clearly along with the response curve.

Mechanisms by which the affinity interaction changes the measured interface

impedance need to be studied in greater detail. There is needfor both experimental

and theoretical work in this regard, and the challenge is compounded by the more

general problem of assigning measured impedance to a particular physical or chemical

phenomenon. To date, most publications present a brief theoretical model which is

supported by their observations. Comprehensive studies ofa particular impedance change

model with different probe/target combinations and verifying predicted trends have not

been undertaken to our knowledge. With an understanding of the molecular mechanisms

underlying impedance change, the optimal conditions and anoptimal measurement

approach can be chosen rationally (e.g. faradaic measurement of ∆Rct or non-faradaic

measurement of∆Csur f).

A need exists for a thorough theoretical treatment of scaling effects in impedance

biosensors, as explained in Section 2.3.9. Electrode size impacts the required measurement

frequency range, and measurement accuracy depends on measurement frequency and

instrumentation design. Optimizing these parameters may allow smaller impedance

changes to be detected, which may lower the detection limit.

Instrumentation is lacking for sensor arrays and for hand-held point-of-care applica-

tions. Only limited progress has been made in implementing arrays of affinity impedance

sensors. However, sensor arrays are valuable for several reasons. First, redundancy can be

built-in by simply having multiple sensors dedicated to a single target, with the individual

sensor responses combined to improve reproducibility and accuracy. Second, if different

sensors are used to detect different targets then a panel of biomarkers can be assayed

simultaneously. This parallelism is advantageous for disease diagnosis and reduces cost

and sample volume per data point. Furthermore, electrical biosensors are appealing in part

because of the ability to make multiplexed measurements. Todate, virtually all published


affinity impedance sensors are based on bulky single-channel EIS instrumentation. Only

limited efforts have been expended in miniaturization of the electronics for point-of-care

applications, though extensive development may be premature.

As in all scientific research, high-quality publications should clearly establish the

context of prior related work and compare results with others’, even if performance is

inferior [257]. In 2005 Kissinger proposed several criteria for high-quality biosensor

publications, including demonstration of utility in the proposed application under practical

conditions (including non-target background and relevantconcentration levels) [258]. He

also makes insightful comments on the state of biosensor research.

After two decades of research effort and hundreds of publications, no product based

on label-free affinity impedance-based biosensors has enjoyed widespread commercial

success. To achieve that goal, progress needs to be made on several fronts. Some progress

can come in simply optimizing existing affinity impedance biosensors, but larger problems

remain. As has been clearly demonstrated, some of these challenges are in the biological

realm (affinity step), and some are in the physical realm (readout step), but all need to be

solved in the context of the entire system. Future research in the area of label-free affinity

biosensors should be targeted towards applications that leverage the techniques’ advantages

(low cost, small size, low power, simplified sample preparation, and moderate multiplexing

capability) without requiring exquisite sensitivity.

Chapter 3

PCB Impedance Biosensor

Measurement System

3.1 Measurement System Overview

This chapter describes our discrete prototype system for obtaining impedance spectra of

biofunctionalized electrode-electrolyte interfaces. Wedesigned and fabricated an array of

electrodes for reasons stated in Section 2.6. After describing the electrode fabrication, we

discuss the socket used to make electrical contact with the electrodes in Section 3.3. The

discrete measurement circuits (on a PCB) are explained next. In Section 3.6 we describe

the coordinating LabView program which applies the excitation signal, captures the output

signals, and extracts amplitude and phase information. A postprocessing calibration

step is performed for various reasons detailed in Section 3.7, followed by fitting of the

impedance spectra to a circuit model. In Section 3.9 we describe how the electrodes are

biofunctionalized, and we conclude the chapter by presenting some measured impedance

data.

3.2 Fabrication of Electrode Array Chip

We utilize standard microfabrication techniques to make our electrode arrays, which consist

of a 6-by-6 grid of 300µm square electrodes with 600µm pitch. The chip is made on

59

60 CHAPTER 3. PCB MEASUREMENT SYSTEM

(a) Layout of electrode array chip, with 36electrodes in the center. Each electrode has adedicated contact pad on the chip perimeter.

(b) Electrode chip sitting inside of the customsocket (clamshell lid is not shown). The O-ring, which provides a seal, is visible under theelectrode chip, which is upside down.

Figure 3.1: Physical components of the measurement system.

a quartz substrate, and each chip is 14 mm square. Each electrode is connected to a

corresponding 900µm square pad on the perimeter of the chip, as shown in Figure 3.1a.

During impedance measurements, an O-ring in the socket contains the solution above the

electrodes while leaving the contact pads dry. We designed the layout and high-level

process flow, and the fabrication was performed in the Stanford Nanofabrication Facility

by a paid consultant.

The electrodes, traces, and contact pads are made of sputter-deposited gold above a

thin adhesion layer1 which are patterned in a single liftoff step. The traces connecting

electrodes with the corresponding contact pads are passivated with silicon dioxide. No

leakage current is detectable when exposed to electrolyte,verifying the passivation quality.

Initially the passivation was etched to expose the electrodes and pads, but XPS analysis

showed that the electrodes were still partially covered with oxide. Thus we subsequently

adopted a liftoff process to define passivation openings, atthe expense of an extra mask

1in various runs Ti, Ta, and Cr were used

3.3. SOCKET FOR CHIP INTERFACING 61

2

3 4

5 6

87

1

Gold Photoresist Silicon Dioxide Adhesion Silicon Dioxide

Electrode Trace

Figure 3.2: Fabrication steps for electrode array chip.

and extra process step. Before dicing, a thick protective layer of photoresist is applied. The

process flow is shown schematically in Figure 3.2.

3.3 Socket for Chip Interfacing

We2 designed a custom socket to for making electrical contact between the chip and mea-

surement electronics without requiring wirebonding or a probe station. This arrangement

was invaluable to speed up experiments. Figure 3.1b shows the chip sitting inside the

socket, which was made by Synergetix (Kansas City, KS).

The thermoplastic socket incorporates doubly compressible pins at locations corre-

sponding to the contact pads on the chip. It attaches to the underside of a printed circuit

board, thus electrically connecting the electrodes to the PCB. An O-ring rests between the

2Erik Anderson did the lion’s share of this work in conjunction with Synergetix


socket and the chip to contain the liquid. A clip-on clamshell “lid” with a spring-loaded

plunger secures the chip in the socket from below, compressing the pogo pins and holding

the O-ring in place. A hole in the PCB allows liquid access from above.

3.4 Impedance Measurement Architecture

As explained in Section 2.3.1, impedance is the complex-valued ratio of the incremental

voltage to the incremental current through a device under test (DUT). The electrode-

electrolyte impedance depends on measurement frequency and on the DC bias point.

Impedance can be measured by either of two methods:

1. Applying a test voltage across the DUT and measuring the resulting current

2. Applying a test current through the DUT and measuring the resulting voltage

The latter method is difficult to apply in impedance biosensors because of poorly-controlled

alternate current paths that may exist in the solution. For impedance biosensors the applied

test voltage must be relatively small — usually 10 mV amplitude or less — to ensure that

the I-V curve is measured over a small enough region to be linear (see Section 2.3.1 for

more detail).

Multiple circuit topologies exist for applying a known voltage excitation and measuring

the resulting current. Chapter 2 of Agilent’s Impedance Measurement Handbook contains

brief explanations of the major architectures and a comparison table [259]. We require an

approach that works well in the kHz range and can be easily automated, and the “auto-

balancing bridge method” is the only such architecture.

Shown in Figure 3.3, this configuration is a textbook inverting amplifier where the DUT

acts as the one of the gain-setting elements.3 Because the transfer function depends on the

impedance of the DUT,ZDUT can be determined by measuringVout with knownVtest and

Zf . This measurement architecture is the core of the various measurement circuits designed

in the entirety of this dissertation.

3The designation “auto-balancing bridge” refers to the factthat the amplifier automatically the DUTcurrent with the current throughZf .

3.5. PCB DESIGN 63

−

+

Vout

Vtest

Vout = -Vtest (Zf /ZDUT)

ZDUT

Zf

ADC

Electrodechip

PCB PC with dataacquisitioncard

Figure 3.3: The basic measurement architecture selected for impedance measurement,including the PCB measurement system.

Relevant for our application is that any parasitic capacitance associated with the DUT-

amplifier connection is unimportant in this architecture because the node is a virtual ground.

The same architecture can be made to work at very high frequencies by constructing the

amplifier with a null detector, phase detector, integrator,and modulator; this modification

is used in precision impedance analyzers. However, a conventional op-amp has sufficient

gain to serve as the active element for the modest frequencies (≤ 100 kHz) we are interested

in.

3.5 PCB Design

According to the chosen measurement architecture, we implemented the circuit shown in

Figure 3.4 using discrete components on a printed circuit board (PCB). The functionalized

electrode — the DUT — is placed between the voltage source applying Vtest and a

transimpedance amplifier, which convertsItest into a proportional voltage as already

explained. Different DUTs are measured serially, using a selection multiplexor (or mux)

between the input array and the measurement circuit.

Following the initial transimpedance stage, we use a instrumentation amplifier for

additional gain, followed by a low-gain inverting amplifieras an anti-aliasing filter and

to drive the cable connecting the data acquisition system. In later designs we replace


−

+

−

+

10R

R

ZDUT,1 32

:1

ZDUT,32

ADCFFTSelect DUT

Tone Ratio (output)

0.1-100 kHz

PC with LabViewand ADC/DAC card

chip

V1electrode

AV

Zf1

−

+

V2

AV

RtCtVtest

Stepped freq

Zf2

Itest

Figure 3.4: The impedance measurement circuit implemented. Note that two channelsare excited by the same test voltage and measured ratiometrically, but only the firstchannel contains the varying DUT. Operation of the circuit is described in Section 3.5.The LabView control program is discussed in 3.6, and mismatch and nonidealities areaccounted for via a calibration step as explained in 3.7.

3.5. PCB DESIGN 65

Function Part Important Criteriaop-amp OPA627 low noise, JFET input (low bias/noise current)instrumentation amp INA111 low noise, gain resistor-set for flexibilityZf 10 MΩ ‖ 33 pF large transimpedance gain for noise, corner∼ 3 kHzanalog mux ADG708 low on-resistance, low leakage

Table 3.1: Discrete components chosen for PCB implementation and selection criteria.

the instrumentation amplifier with an active filter with modest gain and add capacity for

additional filtering. These later revisions also include a high-pass filter to remove unwanted

low frequency tones used for nonlinearity characterization (discussed in Chapter 4).

Vtest must be known in order to measure the amplitude and phase ofItest relative to

Vtest. One elegant method of measuringVtest and simultaneously eliminating systematic

errors is to use a nominally identical measurement channel excited with the sameVtest, but

with a fixed impedance replacingZDUT . Then both channels are measured and the relative

amplitude and phase of the tone at the two outputs is determined as described in Section 3.6.

This ratiometric signal is subsequently converted into theequivalent impedance based on

calibration data, as described in Section 3.7, which also corrects for various nonidealities.

In early prototypes, the electrodes were connected to the measurement circuitry using

jumpers to select the electrode to be measured. We added analog multiplexers to facilitate

automated measurement of many electrodes. Even though for most experiments only 16

electrodes are measured (4 on each corner of the chip), muxesallow automated access to

32 of the 36 electrodes, and the others can be connected manually if needed. Four separate

8:1 low-resistance analog muxes were used to create a 32:1 mux, and the corresponding

control logic was implemented as a LabView VI which controlled 7 digital lines (4 to

enable correct mux plus 3 address lines). Interfacing with this±2.5 V part required the use

of separate voltage regulators and resistive dividers to attenuate the 5 V control lines from

the data acquisition card.

The precision of the impedance measurement depends on the precision of tone

amplitude/phase extraction, which in turn depends on the noise of the electronics. Because

of the circuit architecture, the current noise of the op-ampis quite important. The best op-

amp available for our application was determined to be the OPA627, which has extremely


Figure 3.5: The completed PCB, with labeled sections. This is the final implemen-tation, which contains both low-pass antialiasing filters as well as high-pass filters toremove the low-frequency excitation signal discussed in Chapter 4

.

small bias current, correspondingly small current noise, and reasonably small voltage noise

(including a low 1/ f noise corner).

3.6 Data Acquisition and Signal Extraction

A home-built LabView program4 controls the data acquisition and extracts the meaningful

information from the acquired waveforms.

4also called a “virtual instrument” or VI in the National Instrument parlance

3.6. DATA ACQUISITION AND SIGNAL EXTRACTION 67

The PCB connects to a National Instruments 6259 16-bit data acquisition card via a

SHC68-68-EPM shielded cable. The card can acquire multiplechannels using a shared

ADC with a rate of 1 MHz/N whereN is the number of channels (in this caseN = 2).

This allows a maximum 500 kHz rate, which corresponds to 2.5 times oversampling for

the maximum excitation frequency of 100 kHz.

The NI6259 also supplies the excitation signal via an analogoutput (2.86 MHz, 16-bit

DAC) controlled by LabView. Because the required excitation can be as small as 1 mV but

the LSB of the analog output is 0.15 mV, we configure the DAC to output an amplified

version and then attenuate by 20 dB on the PCB, as shown in Figure 3.4.

The LabView VI acquires theV1 andV2 signals and extracts the tone information from

the signal so that the raw data does not need to be stored. The following algorithm is used:

1. Compute the frequency spectrum ofV2 using a FFT

2. Determine which frequency binf0 contains the maximum signal amplitude5

3. Make sure thatf0 is very close to the expected value

4. Extract the FFT magnitude and phase of bothV1 andV2 at f0

5. Compute the complex ratio of the fourier componentsξ ≡ V1| f0V2| f0

6. Writeξ to the output file

Tone estimation is done using an FFT instead of least squaresfitting to a pure sine wave

for various reasons. As Bertocco and Narduzzi point out, a 4-parameter sine fit yields a

slightly more accurate estimation with a number of practical disadvantages [260]. The sine

fit would require postprocessing of the raw data, increasingboth the required measurement

time (to write the raw data to the hard drive) and also the postprocessing time. Secondly,

the acquired signal is not a pure tone but has spurs (e.g. at 60Hz) that might bias the sine

fit in the case that the excitation frequency is an integral multiple.

Different excitation frequencies are applied serially. A waiting period of several

hundred milliseconds plus a randomized delay is inserted between the initial application

5Signal bleeding into adjacent bins is conveniently reducedbecause the excitation signal and dataacquisition share the same board-level clock.


(a) The LabView interface allows the user to select which electrodes are to bemeasured in what order, the excitation frequency span and step, the excitationamplitude, and the repetition of the identical measurementto detect changes inZDUT . For programming reasons, only one sampling rate andVtest amplitudeare applied in a given frequency range, but multiple defined run in immediatesuccession.

(b) As described in the text, LabView finds the excitation tone in the referencechannel, extracts the appropriate fourier components fromboth channels, andsaves only the complex ratio of the tones for analysis.

3.7. CALIBRATION METHOD 69

of the excitation signal and the start of data acquisition toallow the system to reach steady

state and to randomize any phase bias (this time could probably be reduced if necessary).

Each frequency sweep generates a set of frequency-ξ pairs that represent an impedance

spectrum.

After one full frequency sweep, a different electrode can beselected and measured.

This selection is performed via the NI6259 digital output lines controlling analog muxes as

previously explained. An outer loop allows the same sequence of electrodes to be measured

multiple times to track impedance changes.

3.7 Calibration Method

3.7.1 Why is calibration needed?

In theory, one channel of time-domain data could be used to compute the impedance if

Zf and Av andVtest were perfectly known. Because we do not or cannot know these

parameters as precisely as needed, we use a ratiometric approach as already described.

Then a computation based on calibration data transforms thetone ratio into an impedance.

The measurement circuit outputs two voltages, ideally bothpure tones at the excitation

frequency:

1. V1 contains information aboutZDUT assumingVtest is known

2. V2 contains information aboutVtest

As already explained, the Fourier component of this tone is extracted for bothV1 and

V2 using spectral analysis routines, and the complex ratio (ξ ≡ V1V2

) of these quantities is

computed and stored. Note that a ratiometric measurement byitself is unaffected by gain

errors in the (single) ADC and thereby significantly relaxesthe need for an accurate and

stableVtest.

However, potential nonidealities inξ remain due to signal leakage between measure-

ment channels, systematic phase error from non-simultaneous sampling,Zf mismatches

between the channels,6 amplifier gain mismatches, and unequal filter characteristics. To

6in fact, the exact value ofZf is not known!


eliminate these effects, a calibration transformation is computed based on data measured

with known “impedance standards” in place ofZDUT . This calibration transform is

subsequently applied to experimental data, simultaneously correcting for nonidealities and

transforming the measured ratioξ into an impedance value. This method is conceptually

similar to those used by Schröder et al. [261], Bordi [176], and in test equipment calibrated

using open/short/50Ω loads.

3.7.2 Derivation of calibration equations

Here we derive the equations used to compute the calibrationcoefficients and subsequently

correct the experimental data. Assuming that the measurement channels are linear,V1 and

V2 can be expressed in terms of the DUT impedance and unknownsai andbi :

V1 = Vtest

(

a1

ZDUT+b1

)

(3.1a)

V2 = Vtest

(

a2

ZDUT+b2

)

(3.1b)

By combining 3.1a and 3.1b and adopting a shorthand whereVi represents the Fourier

coefficient at the excitation frequency, it can be shown that

ξ ≡ V1

V2=

ZDUT +k0

k1ZDUT +k2(3.2)

wherek0, k1, andk2 are constants, oneki triplet for each measurement frequency. Three

known impedances must be measured to calculate the threeki values. Then for three known

impedancesZn

ξn =Zn+k0

k1Zn+k2;n= 1,2,3 (3.3)

3.7. CALIBRATION METHOD 71

we can solve forki and obtain7

k0 =ξ2ξ3Z1(Z3−Z2)+ξ1(ξ3Z2(Z1−Z3)+ξ2(Z2−Z1)Z3)

ξ2ξ3(Z2−Z3)+ξ1(ξ2(Z1−Z2)+ξ3(Z3−Z1))(3.4a)

k1 =ξ3(Z2−Z1)+ξ2(Z1−Z3)+ξ1(Z3−Z2)

ξ2ξ3(Z2−Z3)+ξ1(ξ2(Z1−Z2)+ξ3(Z3−Z1))(3.4b)

k2 =ξ1Z1(Z2−Z3)+ξ3(Z1−Z2)Z3+ξ2Z2(Z3−Z1)

ξ2ξ3(Z2−Z3)+ξ1(ξ2(Z1−Z2)+ξ3(Z3−Z1))(3.4c)

A triplet of calibration coefficients —k0, k1, and k2 — is thus obtained at every

measurement frequency. Furthermore, we use the sameVtest amplitude for both calibration

measurements and DUT measurements to ensure any amplitude dependence is captured.

The calculatedki values are then used to transform the measuredξ values into

impedances during post-processing. The equation for doingso can be trivially derived

from Equation 3.2 and is

ZDUT =k0−k2ξk1ξ−1Ω

(3.5)

where each of theki values has units of ohms.

3.7.3 Implementation

“Known” values for the discrete resistors and capacitors used as calibration impedances

were obtained from a handheld multimeter and LCR meter. Bothare accurate with within

1%.8 These parts are soldered into the PCB and inserted in place ofZDUT via jumpers

during calibration measurements.

For each data set collected, various calibration impedances (usually 8 R-C combinations

plus open circuit) are measured. We use three of the calibration datasets to generate the

calibration coefficients and the others to verify the correctness of the calibration. Initially,

we generated the calibration coefficients from a purely resistive element,9 a series R-C

chosen to be about the same impedance as the DUT, and an open circuit. Later we changed

7I recommend Mathematica for such a tedious process!8Some inaccuracy is acceptable because it simply introducesa fixed scale error in all corrected data

without affecting the precision.9a higher resistance at lower frequencies and lower resistance at high frequencies, to match more closely

the DUT impedance


to using three disjoint R-C combinations that encompassed the range of possible DUT

impedances.

We automate the computation of calibration coefficients using a Matlab script. Using

yet another Matlab script, we convert measured data into corrected impedance spectra

according to Equation 3.5. New calibration data must be collected whenever there is a

change in measurement frequencies used, change inVtest amplitude, or revision of the

PCB. Empirically we verified that calibration data remains valid over a period of months,

provided that the sameVtest amplitudes and frequencies are used on the same PCB.

3.8 Data Analysis

With the corrected impedance spectrum, we are prepared to fitthe data to a circuit model

as described in Section 2.3.5. Because there is no faradaic current, the model shown in

Figure 2.3(a) is used and values ofCsur f, Rleak, andRsol are extracted. This fitting process is

automated using a Matlab script which loops over each impedance spectrum and performs

the following:

1. Formats the impedance data and adds a header containing fitting instructions and

initial parameter guesses10

2. Calls an external program11 to perform the complex non-linear least squares

regression

3. Saves the program output to a file

4. Compiles the best-fit parameters and theχ2 value (indication of the goodness-of-fit)

from the output files into a single tab-delimited file for subsequent analysis

The values of the model parameters are analyzed as functionsof measurement time, surface

functionalization, array position, or other parameters ofinterest. Before analysis, any

outlier data is removed from consideration on the basis ofχ2 values being higher than

10earlier done via a separate Perl script11we use an old version of ZView, which actually calls the freely-available LEVM program to perform the

fitting

3.9. SURFACE FUNCTIONALIZATION 73

usual. These most often arise from poor chip-socket connections or problems with the

surface functionalization.

3.9 Surface Functionalization

Probe immobilization on the electrode surfaces was initially performed by Heng Yu, a post-

doctoral surface chemist in our research group, and consisted of various methods of forming

thiol-based self-assembled monolayers on the surface. Because initial measurement results

were inconsistent, we changed to a functionalization process in which polyelectrolyte films

were deposited over the entire chip surface followed by probe spotting. This method

provided more consistent results. Another benefit was that the relatively simple surface

chemistry procedures could be performed by us, without relying on a surface chemist.

Probes were spotted by hand after depositing the polyelectrolyte attachment layer over

the entire array region. Although a robotic spotter was available, we never used it because

neither throughput nor uniformity was crucial. It is difficult to functionalize adjacent

electrodes differently without a robotic spotter, so we manually spot entire corner regions

of the array using a pipette tip. For each corner, the 4 outermost electrodes are measured,

for a total of 16 electrodes measured with up to 4 probes.

For virtually all surface chemistry, the buffer is phosphate buffered saline (PBS) pH 7.4

(Sigma, St. Louis, MO), which consists of 10 mM pH-adjusted phosphate buffer, 138 mM

NaCl, and 2.7 mM KCl. This same buffer is used as the electrolyte during impedance

measurements.

3.9.1 Polyelectrolyte film deposition

The first step in biofunctionalizing the chips is to coat themwith polyelectrolyte, which

is a polymer possessing charged groups along the chain. The chip surface (mostly silicon

oxide) is negatively charged, so a positively charged polymer will adsorb electrostatically

and result in a strongly attached film. The thickness of the polyelectrolyte layer self-limits

by electrostatic repulsion, and independent experiments performed by SGTC staff chemist

Henrik Persson suggest that the final film thickness is 1–3 nm.


We use the following procedure:

1. Remove the protective photoresist by generously rinsingthe electrode chip in acetone

followed by isopropyl alcohol, then blowing it dry with inert gas

2. 5–10 minute UV-O3 treatment in UVO cleaner (Model No 42, Jelight Co, Irvine,

CA)

3. Pipette a 1% poly(ethyleneimine) (pH 7.5, MW 60 kDa) solution onto the electrode

array area while avoiding the perimeter contact pads (a similar polymer, poly(L-

lysine), is used in some experiments)

4. Incubate for 5–30 minutes at room temperature in a humidity chamber

5. Rinse well in water, blow dry with inert gas

6. (optional but recommended) Bake at 120C for 60–120 minutes, cool

7. (optional but recommended) Pipette a dilute mixture of poly(L-lysine) and

poly(acrylic acid) onto the electrode array area, then incubate, rinse, and dry (as

with the base polymer)

The surface chemistry routes diverge after polymer deposition, depending on what probe is

used.

3.9.2 Attaching DNA

To adsorb DNA non-covalently, adapted from [215]:

1. Obtain solution of desired DNA product from PCR

2. (optional) Concentrate DNA using SpeedVac

3. Denature the DNA12 by boiling for 5 minutes in open Eppendorf tube using heat

block filled with water12i.e. convert double-stranded DNA into single-stranded DNA

3.9. SURFACE FUNCTIONALIZATION 75

4. Immediately place tube on ice for 5 minutes (can store at 4C after this step)

5. Spot probes where desired

6. Incubate for 45 minutes at room temperature in humidity chamber

7. Wash in hybridization buffer, blow dry with inert gas

8. Add 1 mg/mL salmon sperm DNA as blocking agent over entire electrode array


10. Wash with hybridization buffer, blow dry with inert gas

3.9.3 Attaching proteins

To covalently attach proteins, we use NHS/EDC coupling chemistry to form amine-reactive

sites from the acid sites on the polyelectrolyte. These amine-reactive sites are subsequently

exposed to protein probes,13 resulting in protein covalently bound to the surface.

1. Dissolve EDC14 and NHS15 in water separately and then mix to obtain a final

concentration of 50 mg/mL of each

2. Mix NHS and EDC solutions and immediately pipette over entire electrode array


4. Rinse well with water (e.g. 30 seconds under running DI), blow dry with inert gas

5. Spot concentrated protein solution

6. Incubate and rinse (details vary, see below)

For experiments using antibodies as capture probes, it is important to insure that the

antibodies are immobilized in a functional form. For this reason, protein A/G is covalently

bound to the surface, which subsequently captures the Fc region of IgG antibodies,16

13virtually all proteins have tertiary amines available for binding141-Ethyl-3-[3-dimethylaminopropyl]carbodiimide15N-Hydroxysuccinimide16Immunoglobulin G, the most abundant type of antibody, is famously “Y”-shaped, with the constant Fc

region at the bottom and two variable Fab portions with binding sites on the end


leaving the Fab recognition sites available for target capture. The process used for antibody

immobilization is as follows:

1. Apply 0.1 mg/mL protein A/G in buffer to the NHS/EDC-activated surface

2. Incubate overnight at 4C in humidity chamber

3. Rinse with buffer, blow dry with inert gas

4. Spot IgG antibodies where desired (0.1 mg/mL in buffer)


6. Rinse in buffer, blow dry with inert gas

7. Apply blocking IgG over entire array area to fill remainingvacant sites



In other experiments, proteins such as bovine serum albumin(BSA)17 and BSA-biotin are

directly immobilized on the NHS/EDC-activated surface using the following procedure.

1. Spot 0.1 mg/mL protein probe in buffer (e.g. BSA or BSA-biotin) to the NHS/EDC-

activated surface



4. Apply 0.1 mg/mL blocking BSA over entire array area to fill remaining vacant

binding sites



7. (optional) Store in buffer

17a very common protein most often used to block non-specific binding

3.10. OTHER MEASUREMENT DETAILS 77

3.10 Other Measurement Details

Our choice to measureZDUT between 100 Hz and 100 kHz is based on preliminary

measurements and the information content contained in the impedance (explained in

Section 2.3.5 and shown graphically in Figure 2.4b). Below 100 Hz, the impedance

becomes increasingly difficult to measure and provides little additional information for our

non-faradaic sensors. Additionally, many investigators report significant low-frequency

drift. Rsol dominates the total impedance above roughly 50 kHz for our electrode size, and

we do not expectRsol to contain any information about probe-target binding.

As a general practice, we space excitation frequencies logarithmically. The LabView

primitives ensure that the excitation tone fits into the DAC buffer, so the requested

excitation frequencies are not precisely the same as the frequencies actually generated (e.g.

101.725 Hz instead of 100 Hz). The tone extraction algorithm accommodates this fact.

We useVtest amplitudes in the range of 1 mV to 10 mV. The upper bound is set by

linearity considerations, as already explained, and within this range the input amplitude

is simply adjusted to achieve a reasonable output amplitudefor data acquisition. Because

the transfer function is a function of frequency, differentamplitudes are used for different

frequency ranges.

We also alter the sampling rate over the frequency range, taking care always to remain

above the Nyquist rate. Instead of measuring each frequencyfor a fixed period, we collect

a fixed number of samples (216) to minimize the time required for FFT execution. The

sampling rate is adjusted for each decade of frequency to ensure that many periods of the

excitation signal are acquired. Sampling rates between 30 kHz and 500 kHz are routinely

used, corresponding to measurement times between 2.1 and 0.13 seconds per frequency,

respectively.

Measurements of fixed impedances (capacitors and resistors) establish that the repeata-

bility of individual measurement is in the vicinity of 0.1%. The LabView program has the

ability to repeat the tone measurement and appropriately average theξ estimates, but this

additional processing is unnecessary in general.

The excitation signal is applied via a Ag/AgCl electrode inserted into the PBS buffer

from above, through the hole in the PCB visible in Figure 3.4.Because PBS contains a


fixed concentration of Cl– , the contact has a reproducible built-in potential which wetake

as our zero reference (+81 mV vs. Ag/AgCl/sat. KCl). A two-electrode measurement is

possible because the reference electrode can supply the required current and the solution

resistance is small, as explained in Section 2.3.2. The AgClpellet is stored in PBS between

experiments for equilibration. Besides the external AgCl counter/reference electrode, we

usually connect the 20 unmeasured electrodes in the array tothe excitation signal as

additional counter electrodes.

3.11 Representative Impedance Data

Figure 3.6 shows measured impedance spectra along with the best-fit curves before

and after hybridization, from experiments with a polyelectrolyte-functionalized chip and

adsorbed genomic DNA probes. The data here comes from a “positive” array location,

meaning that the target DNA is complementary to the probe andhybridization is expected.

The fitting curves match the data very well, as is typical. Note that the change in impedance

values is less than 10%. However the change inCsur f is actually significant because of the

corresponding CPE phase parameter change from 0.90 to 0.93 (fit values in the caption).

Figure 3.7 shows data from the same set of experiments as Figure 3.6, this time

plotting the best-fit values obtained for all 16 electrodes at 4 separate measurements.

The functionalized electrodes’ impedance is measured twice before exposure to the target

DNA (measurements 0 and 1 in the figure) and twice after the target incubation and

hybridization (measurements 3 and 4). The blue lines indicate electrodes with no expected

hybridization (“negative”) and the red lines are the locations with putative hybridization.

TheCsur f component changes considerably between the two pre-incubation measurements,

and then more dramatically as a result of target exposure forboth the positive and negative

electrodes.Rsol decreases slightly with time as expected due to partial evaporation of the

electrolyte. It also has a small systematic variation arising from the electrode position on

the array.Rleak is so large as to be meaningless to the fit.

Figure 3.8 contains early data demonstrating that DNA hybridization can be discerned

on the basis of impedance changes. The impedance change upontarget hybridization at

11 kHz is plotted in Nyquist form. For electrodes functionalized with a complementary

3.11. REPRESENTATIVE IMPEDANCE DATA 79

102

103

104

105

103

104

105

|Z| [

Ω]

26−Jul−07 genomic DNA, Electrode 1

measured data pre−hybbest fit pre−hybmeasurement data post−hybbest fit post−hyb

102

103

104

105

−90

−75

−60

−45

−30

−15

0

−∠

Z/°

102

103

104

105

−0.1

−0.05

0

0.05

0.1

Nor

mal

ized

∆|Z

|

Frequency [Hz]

Rsol

Rleak

Csurf

Figure 3.6: Example fit impedance data, from DNA experiments. Pre-hybridizationdata fit withRsol = 1190Ω, Csur f,A = 14.3“ nF”, Csur f,m = 0.903,Rleak = 56.8 MΩ.Post-hybridization data fit withRsol = 1220Ω, Csur f,A = 10.6“ nF”, Csur f,m = 0.935,Rleak> 1000 MΩ.


Figure 3.7: Best-fit parametersRsol andCsur f vs. time for 16 electrodes measured 4separate times, twice before exposure to the target and twice afterwards. See text formore details.


Figure 3.8: Early impedance data showing clear change upon DNA hybridization. Notethat the change in the imaginary component of the impedance serves as a clear indicatorof the electrodes where hybridization occurred.

DNA strand — the “positive” probes — there is an increase in the imaginary part of

impedance of at least 350Ω, whereas those electrodes where no binding is expected

show less than an 80Ω increase. This data shows a very clear discrimination between

hybridization and none, but the result was not very reproducible. This measurement

used silane surface chemistry during the period of experimentation with various surface

chemistry approaches. Data from two separate chips are shown combined.

The value ofCsur f depends significantly on DC bias, as seen in Figure 3.9. BSA is

attached covalently to the electrode surface, and 8 electrodes are measured (2 from each

corner of the chip) repeatedly. For clarity, here we only plot the first set of measurements.

At roughly 50 mV vs. Ag/AgCl/PBS there is a minimum in CPE magnitude. This and


other experiments indicate that minima in CPE magnitude correspond to maxima in CPE

phase, suggesting thatCsur f behaves more like an ideal capacitor at the isoelectric point

(see Section 2.3.8). The dependence of the impedance on DC bias is explored in Chapter 4,

where an improved method of generating similar data is explained.


Figure 3.9: Best-fit parametersCsur f magnitude and phase measured for 8 electrodesas the DC bias was swept. See text for more details.

Chapter 4

Using Nonlinearity as a Sensed Variable

The core ideas contained in this chapter were presented at the 2008 IEEE Engineering in

Medicine and Biology Conference and published in the corresponding proceedings [262].

As explained in Section 2.3.1, the electrode-solution interface has an inherently

nonlinear current-to-voltage (I-V) characteristic. The standard impedance biosensor

measurement approach, as explained in Section 2.3.5, is

1. Fix the DC bias point of the electrode-solution interface

2. Apply a small sinusoidal voltage excitation at various frequencies

3. Fit the resulting data to a circuit model to extract model parameters (e.g. surface

capacitanceCsur f)

As stated previously, the excitation voltage must be small compared with the thermal

voltage (VT ' 26 mV) to ensure a linear response [117]. Because of the inherent

nonlinearity, the resulting model parameters are only valid at the chosen DC bias point.

To measure the impedance as a function of both frequency and bias, it is possible to repeat

the frequency sweep at different bias voltages at the expense of extra measurement time

[263].

Although nonlinearity constrains the allowable excitation amplitude (and thus requires

more sensitive detection circuitry than LCR meters or similar instruments), we show here

that the nonlinearity of the biofunctionalized interface can be exploited as a sensed variable

84

4.1. EARLY NONLINEARITY MEASUREMENTS 85

along with the small-signal impedance. Changes in I-V nonlinearity can indicate target

binding to the probe-functionalized electrode. We proposeand demonstrate a method for

quantifying the impedance’s dependence on bias voltage by superimposing a second large

excitation tone which varies the “DC” bias. The amount of nonlinearity is encoded in

the magnitude of the resulting intermodulation tones, without requiring extra measurement

time.

4.1 Early Nonlinearity Measurements

We performed several experiments to characterize the bias dependence of functionalized

electrode-solution interface impedance, motivated by reports that others had optimized the

DC bias point for greater biological sensitivity (e.g. [186]). In these early experiments we

took the straightforward approach of measuring the impedance spectra at different fixed

DC bias points, one bias at a time.

Figure 4.1 shows the best-fitCsur f values vs. DC bias, before and after incubation

with target DNA, for three electrodes functionalized with different probes. Note that

the capacitance changes by about 5% over a DC bias range of a few hundred millivolts.

The electrodes have different absolute capacitance values, but in each case the capacitance

increases after incubation with the target. The change is largest for the positive probe (to

which the target molecules are expected to bind), modest forthe negative probe, and very

small for the non-probe electrode. This suggests that the impedance changes are related to

target binding, as the same effect noted in the previous chapter.

The measured data support the conceptual model thatCsur f is composed of two

capacitances in series: one composed of the biofunctionalized surface layer and the second

from the (nonlinear) ionic double layer capacitance. This model is explained further in

Section 2.3.6. Recall from Section 2.3.8 that the double layer capacitance versus DC bias

curve is concave up, with a minimum value at the bias point corresponding to the potential

of zero charge. This capacitance doubles at approximately a75 mV deviation from this

bias point. However, the double layer capacitance is much larger than the probe layer

capacitance, making the former a minor contribution to the series capacitance. For the

electrode dimensions and buffer used, the expected double layer capacitance is roughly

86 CHAPTER 4. USING NONLINEARITY AS A SENSED VARIABLE

−200 −150 −100 −50 0 50 100 150 200

6

7

8

9

10

11

12

DC bias vs. AgCl/PBS [mV]

CP

E m

agni

tude

with

m=

0.92

["nF

"]

negative probe beforenegative probe afterpositive probe beforepositive probe afterno probe beforeno probe after

Figure 4.1: Best-fit values ofCsur f measured at different DC biases for threedifferently-functionalized electrodes.

84 nF, meaning it contributes about 10% of the totalCsur f in the data plotted in Figure 4.1.

Thus, the observed nonlinearity is expected to be an attenuated version of the double layer

nonlinearity, and our measurements are consistent with this model.

4.2 Nonlinearity of Double Layer Capacitance

Recall from Section 2.3.8 that an ionic double layer capacitance forms at the interface

between ionic liquids and charged surfaces. In a nutshell, charge on the surface attracts

4.3. MATHEMATICS OF NONLINEARITY 87

ions of opposite charge, and the (mobile) ion layer forms thesecond terminal of a capacitor-

like structure. The observed capacitance value depends on the amount of surface charge;

increased surface charge results in a more concentrated ionic cloud and increases the

capacitance. Thus, the measured double layer capacitance changes quite significantly with

DC bias point, as illustrated in Figure 2.5, underscoring that the double layer capacitance

is nonlinear.

To illustrate this point we analyze the capacitance of the ionic double layer according to

the Gouy-Chapman theory. From Section 2.25, and assuming a monovalent 1:1 electrolyte

(e.g. NaCl) on a bare electrode, we have

Cdl(φ) =(

228µF/cm2)√

c0

mol/L

(

1+18

(

φVT

)2)

(4.1)

wherec0 is the electrolyte concentration,φ is the surface potential relative to the potential

of zero charge (PZC),VT is the thermal voltage, and the series expansion for hyperbolic

cosine has been truncated after the quadratic term. To measure Cdl we must impose a

nonzero excitation voltageφ, which changes the value ofCdl we are trying to measure! If

a 50 mV amplitude tone atf0 is used,Cdl changes by about 50% during the measurement,

generating a tone at 3f0 with an amplitude about 10% of that of thef0 tone.

However, the voltage dependence in actual impedance biosensors is much less because

the electrode surface is coated with a layer of attached probe molecules and is not exposed

directly to the ions. The double layer capacitance appears in series with the capacitance of

this probe layer, as explained in Section 4.1.

This simple example demonstrates the non-linear nature of the “impedance” being

measured. Furthermore, our analysis suggests that changesin the PZC — for example,

due to binding of a charged target molecule — can be detected via a change in surface

capacitance and/or change in nonlinearity of that capacitance.

4.3 Mathematics of Nonlinearity

Weakly nonlinear systems are mathematically modeled withVolterra series. Just as a

Taylor series can be used to approximate an analytic function with a power series and


appropriate coefficients, a Volterra series expresses small nonlinear excursions about a

linear operating point using a power series with coefficients to approximate the nonlinear

effects [264]. Computation with Volterra series is more complicated in systems which have

“memory” elements, including capacitors and inductors; this is certainly the case for our

system. For a thorough treatment of Volterra series, the reader is referred to [264, 265].

Here we derive some salient results that can be more rigorously explained using the

framework of Volterra series, trying to avoid delving deeper than needed.

4.3.1 Nonlinear capacitors

For an ideal capacitor,Q=CV whereQ is the stored charge,C is the capacitance, andV is

the applied voltage. It follows thatI = dQdt =CdV

dt . Now assume that the capacitance is not

fixed, but depends on the voltage according to

C(V) =C0+C1V +C2V2. (4.2)

To measure the capacitance we apply a small sinusoidal voltage across it and measure the

resulting current. At first glance it appears thatQ =C(V)V and soI = dQdt = d

dt [C(V)V].

This expression is incorrect; it fails to conserve charge in general [266, 267]. This failure

arises from using an expression based on charge conservation in a linear capacitor, instead

of using a more general charge conservation expression.

The correct relation between current and voltage for a nonlinear capacitor is

I =C(V) dVdt (4.3)

and it follows that

I = C0dVdt

+C1VdVdt

+C2V2dV

dt

= C0dVdt

+C1

2dV2

dt+

C2

3dV3

dt. (4.4)

4.4. TWO-TONE APPROACH TO NONLINEARITY MEASUREMENT 89

Thus, if the capacitor is nonlinear, the “apparent” 2nd-order nonlinear coefficient (based

on the resulting current) isC12 , not C1. Similarly, the “apparent” 3rd-order nonlinear

coefficient isC23 .

4.3.2 Double layer“varactance”

We can express the double layer capacitance as a nonlinear capacitance in the form

Cdl =C0+C1V +C2V2 (4.5)

whereV is the applied voltage relative to the PZC. From Equation 4.1derived for a 100 mM

1:1 monovalent salt at room temperature, the coefficients are:

C0 = 72.1 µF/cm2

C1 = 0

C2 = 13500µF/(

cm2 V2) . (4.6)

Note that the normalized second nonlinearity coefficientC2C0

is 188 V−2 (or equivalently,

HD3 = +36 dB for a 1 V tone!). For comparison, the nonlinearity of typical discrete

capacitors is usually measured in units of ppm V−2. The double layer capacitance is

more accurately termed the double layer “varactance.”It has primarily a quadratic voltage

dependence according to the Gouy-Chapman theory; ion-specific effects and the Stern layer

can add a linear voltage dependence [58].

4.4 Two-tone Approach to Nonlinearity Measurement

Here we propose and explain a technique to measure both the impedance and nonlinearity

at the same time, without requiring separate sweeps at different bias points. This method

enables more rapid measurements of nonlinearity at the expense of more complex circuitry.

Nakata et al. noted in 1996 that the voltage dependence of impedance biosensors can be

measured by quantifying harmonic multiples of a large excitation tone [268]. However, one


practical difficulty is that the harmonic tones are widely spaced and may be out of range of

the acquisition instrument. Hence this method has not been widely adopted.

4.4.1 Motivation for a two-tone approach

Our early nonlinearity measurements, such as those shown inFigure 4.1, were obtained

after making only a minor change to the original PCB. However, the required measurement

time was substantial. Besides being an experimental inconvenience, long measurement

times can introduce errors because the interfacial impedance may have a slow drift. As

noted in Chapter 3, each spectrum takes about 30 seconds to acquire, leading to a single

value ofCsur f. Thus, the data shown in Figure 4.1 required nearly half an hour to obtain.

4.4.2 Mathematical explanation

We use a superposition of two excitation tones to measure theimpedance and nonlinearity

of the device under test (DUT) simultaneously. In our case, the DUT is the biofunc-

tionalized electrode-solution interface. The DUT’s nonlinear I-V characteristic generates

intermodulation (IM) products from the input tones which are related to the nonlinearity,

just as a mixer does [269].

Instead of the usual single-tone excitation (see Section 2.3.1), we use a two-tone input

excitation

Vtest= Acos(ωAt)+Bcos(ωBt) (4.7)

where the two components are a swept-frequency tone at frequencyωA, amplitudeAVT

(used to measure the small-signal impedance); and a fixed low-frequency tone at frequency

ωB, amplitudeBA andωBωA (used to vary the effective DC bias).

Nonlinearity generates IM tones at all linear combinationsof integer multiples ofωA

andωB, but the ones of principal interest reside atωA ± nωB for n=−2. . .2.

We approximate the nonlinear DUT impedance as

ZDUT(ω) = Z0(ω)(

1+α1Vtest+α2V2test

)

(4.8)

4.4. TWO-TONE APPROACH TO NONLINEARITY MEASUREMENT 91

whereZ0(ω) is the small-signal impedance, andα1 andα2 encode the bias dependence (for

notational simplicity, we ignore the fact thatα1 andα2 depend on frequency). For our trans-

impedance measurement circuit (Figure 3.4), the transfer function is−Zf (ω)/ZDUT(ω).Then

Vout =−VtestZf (ω)Z0(ω)

1


. (4.9)

If the nonlinearity is relatively weak — i.e.|α1Vtest|1 and∣

∣α2V2test

∣

∣1 — we can rewrite

the denominator using the approximation(1+δ)−1'1− δ for δ 1. This assumption

is justified by measured data including those presented in Section 4.1, and was also

confirmed a posteriori. By applying this approximation to Equation 4.9 and invoking some

trigonometric identities (see Appendix A), it can be shown that the output tones nearωA

are given by

Vout =−Z f (ωA)Z0(ωA)

Acos(ωAt) (4.10)

+ 12α1AB

Z f (ωA−ωB)Z0(ωA−ωB)

cos((ωA−ωB)t)

+ 12α1AB

Z f (ωA+ωB)Z0(ωA+ωB)

cos((ωA+ωB)t)

+ 14α2AB2Z f (ωA−2ωB)

Z0(ωA−2ωB)cos((ωA−2ωB)t)

+ 14α2AB2Z f (ωA+2ωB)

Z0(ωA+2ωB)cos((ωA+2ωB)t)

+ other terms far removed fromωA

whereA, B, andZf (ω) are known or measurable.1 Note that the conventional impedance

(Z0) as well as the linear (α1) and quadratic (α2) terms of its voltage dependence can be

quantified by measuring the tone amplitudes atωA±nωB for n = −2. . .2. Conveniently,

these IM tones are all nearby in frequency becauseωB ωA. Just like conventional EIS,

the measurement is repeated at various values ofωA until the relevant frequency range has

been spanned.

1Here we have assumed the nonlinearity is capacitive and included factors12 and 13 in the first and second

IM tones, respectively, according to Section 4.3.1.


4.5 Modifications to PCB Measurement System

We superimpose a small-signal tone (ωA) with amplitude 2 mV (swept from 100 Hz to

100 kHz in 13 steps) and a larger, slower tone (ωB) at 17 Hz with 50 mV amplitude. We use

a modified PCB measurement system, as described in Chapter 3,to enable the measurement

of IM tones. The revised PCB includes a 2-pole active high-pass filter with passband

gain after the initial transimpedance amplifier (see Figure3.4) in order to attenuate the

ωB tone before data acquisition. Correspondingly, the gain ofthe initial transimpedance

stage is reduced to ensure thatVout does not approach the op-amp supply voltages, to avoid

introducing another source of nonlinearity.

The LabView VIs controlling data acquisition and tone extraction are modified to

extract the IM tones from theVout signal on the DUT measurement channel. To estimate

the transfer functionZf /Z0 for the IM frequencies instead of just theωA frequencies

(see Section 3.7), a finer-grained set of calibration data iscollected and the calibration

coefficients are interpolated at each IM frequency.

4.6 Measurement Data

4.6.1 System characterization

To characterize the performance of our modified measurementsystem, we use three AM

varactor diodes in parallel with a fixed capacitance to create a non-biological DUT with

bias-dependent impedance. Values are chosen to be similar to the biological DUT. The

same measurement and post-processing procedure describedabove is followed to obtain

the capacitance of the non-biological DUT as a function of DCbias point. The capacitance

is measured over a±100 mV range of DC biases using both a commercial LCR meter and

our measurement system. The nonlinearity coefficients measured at 0 mV bias at 1 kHz are

used to extrapolate the capacitance vs. bias over the same range.

Figure 4.2 shows the resulting curve of capacitance vs. bias. As expected, the extracted

series resistance and CPE phase parameter are 1.00 kΩ and 1.00, respectively. The

4.6. MEASUREMENT DATA 93

−100 −75 −50 −25 0 25 50 75 100

12.2

12.25

12.3

12.35

12.4

12.45

12.5

Bias [mV]

Cap

acita

nce

[nF

]

10 nF

1 kΩ

Figure 4.2: Measured capacitance vs. DC bias for the DUT shown. The solid curve ispredicted from the measurement ofZ0, α1, andα2 at 0 mV bias. The circles are theZ0

values measured by our apparatus with applied DC bias, and the squares are measuredwith a commercial LCR meter.

nonlinearity coefficients obtained are of sufficient accuracy to enable prediction of the bias-

dependent capacitance within 0.1% over the±100 mV range. Furthermore, our system’s

measurements agree closely with those of the commercial LCRmeter.

4.6.2 Biological measurements

Biological measurements follow the same general procedures outlined in Chapter 3. For

these proof-of-principle experiments, biotin is the probeand avidin (or close relative strept-

avidin) is the target. The target was purchased in a form pre-conjugated with a fluorophore

(FITC) so that probe-target binding could be verified using amicroarray scanner (see Figure

4.3). The surface functionalization process is described in Section 3.9.3.


Figure 4.3: Fluorescent micrograph of chip showing FITC-labeled target binding in thetwo corners with biotin probe as expected. Because of backside illumination, the goldelectrodes and traces areas appear dark. Some of the contactpads are visible and thelocation of the O-ring is indicated.

We measure the impedance and nonlinearity of the biotin-functionalized interface

before and after avidin binding. At frequencies 15 kHz the impedance is dominated

by the CPE representing the electrode-solution capacitance. As mentioned above, the

measured CPE can be thought of as a series combination of the ionic double layer

capacitance and the capacitance of the probe layer. The best-fit Csur f (as a CPE) along with

the total impedance at 1 kHz before and after binding are shown in Figure 4.4. Note that

the minimum CPE value (or maximum impedance) shifts to more negative potentials upon

target addition. Interestingly, the CPE phase also dependson DC bias, with a maximum

value at maximum impedance. The total impedance magnitude depends on both CPE

magnitude and phase parameters (see Section 2.3.7); the balance of these factors results in


a monotonic relationship between impedance and bias in the rightmost plots, whereas the

concave curves extrapolated from nonlinearity measurements assume that the CPE phase

parameter is constant.

The double layer capacitance exhibits voltage dependence,as explained in Section

4.2. The Gouy-Chapman theory predicts a double layer capacitance of about 84 nF for

our electrodes in PBS. Thus at 1 kHz, roughly 8% of the appliedvoltage drops across

the ionic double layer and the remainder appears across the biofunctionalized interface.

As α2 ' 188 V−2 for the similar double layer capacitance model in Section 4.3.2, we

expect to measureα2'14 V−2 but observe only about half that value. We attribute the

discrepancy to the crude double layer model used in the foregoing calculation. In reality

one contribution of the ionic capacitance is independent ofbias voltage (predicted by the

Stern modification to the Gouy-Chapman theory as explained in Section 2.3.8.3) which will

reduce the nonlinearity.

The double layer capacitance is minimized at the PZC, or the applied potential at which

there is no net surface charge (see Equation 4.1). Figure 4.4shows that the DC bias

corresponding to minimum capacitance changes upon target binding, suggesting that the

surface charge is changed. In fact, the probe surface (BSA, pI'5) is negatively charged

and the target (avidin, pI'10) is positively charged at the measurement pH of 7.4. We

conclude that the observed changes in nonlinearity depend at least partly on changing

surface charge, which modulates the voltage-dependent double layer capacitance. Thus,

detecting target binding via nonlinearity may be somewhat akin to the action of field-effect

biosensors, which detect surface charge by other means [188].

A multitude of investigators have used impedance changes todetect probe-target

binding, as reviewed in Section 2.5 and [6]. Besides the results just discussed, data shown

in Figure 4.5 demonstrate that changes in nonlinearity can also be used to indicate target

binding. In this experiment,α1 increases where binding occurs (n= 4, representing 4

electrodes on the same chip) and decreases or remains constant if there is no binding (n=8).

These measurements are from various electrodes from a single chip measured at 0 mV bias

after exposure to 250 ng/mL avidin for 1 minute. This behavior agrees with the trend

observed in Fig. 4.4 in which the putative PZC shifts. In thisparticular set of measurement


0 50 100 150

10

11

12

13

14

15

Electrode Bias [mV]

CPE Magnitude ["nF"]

0 50 100 150

0.9

0.905

0.91

0.915

0.92

0.925

Electrode Bias [mV]

CPE phase parameter

0 50 100 150

24

25

26

27

28

29

30

Electrode Bias [mV]

|ZDUT

| @ 1 kHz [kΩ]

(a) Before target addition

0 50 100 150

10

11

12

13

14

15

Electrode Bias [mV]

CPE Magnitude ["nF"]

0 50 100 150

0.9

0.905

0.91

0.915

0.92

0.925

Electrode Bias [mV]

CPE phase parameter

0 50 100 150

24

25

26

27

28

29

30

Electrode Bias [mV]

|ZDUT

| @ 1 kHz [kΩ]

(b) After target addition

Figure 4.4: Measured CPE magnitude, CPE phase, and impedance at 1 kHz frommultiple electrodes on a single chip before and after introduction of 1µg/mL avidin.Measurements are taken at 0 mV, 75 mV, and 150 mV bias vs. AgCl/PBS. The solidlines show the impedance values extrapolated from the nonlinear terms at 75 mV andthe open circles show the measured values; the inaccuracy stems from changes in theCPE phase between these bias points.


BSA−biotin BSA−0.2

−0.1

0

0.1

∆ α 1 [V

−1 ]

Change in α1 upon binding

Figure 4.5: Changes inα1 for positive and negative probes upon introduction of250 ng/mL avidin, demonstrating that changes in nonlinearity can indicate targetbinding.

data, the change in impedance does not relate systematically with target binding, but the

change in nonlinearity does.

Over all biological measurements we observe|α1| values in the range of 0.1–1 V−1

and|α2| values in the range of 2–10 V−2. For our 50 mV excitation this range satisfies the

assumptions used in deriving Equation 4.10.


4.7 Implications of our observations

Our experiments suggest that changes in the surface charge of the biofunctionalized

electrode can be detected by nonlinearity measurements of the PZC-dependent double

layer capacitance. This sensitivity suggests an alternatesensing route to field-effect

schemes (see Section 2.1.2). One important advantage relates to the screening effect which

forms the double layer capacitance. In field effect sensors,charge screening decreases

the signal in the semiconducting channel, so investigatorsare forced to work at low salt

concentrations [41]. However, these unnatural conditionsalter the binding behavior of

biomolecules. In contrast, our approach of measuring surface charge via the double layer

capacitance actually benefits from using physiological ionconcentrations (e.g. PBS or

100 mM NaCl) because the double layer capacitance gives riseto the wanted signal.

However, the relationship between measured nonlinearity and the surface charge might be

more complicated if factors besides the double layer “varactance” contribute to the interface

nonlinearity. We feel that further investigation of this idea is merited.

The interface capacitance is the origin of the nonlinearitywe observe, as no redox

species are present in our experiments (the measured parallel resistance is>50 MΩ). In

contrast, faradaic impedance measurements depend strongly on DC bias [270], implying

that a nonlinear measurement approach might be even more useful for faradaic biosensors.

In fact, it has been shown that using large excitation signals in single-frequency faradaic

AC voltammetry can speed up the determination of electrochemical variables [271].

4.8 Conclusions

A two-tone excitation allows the concurrent measurement ofimpedance nonlinearity and

small-signal impedance. Applied to impedance biosensors,this method can either reduce

the total measurement time in cases where bias dependence isexplicitly measured (e.g.

[263]), or else provide information about bias dependence that can be useful in discerning

probe-target binding (e.g. detecting surface charge). Initial experiments demonstrate that

protein binding can be discriminated on the basis of nonlinearity changes alone.

4.8. CONCLUSIONS 99

This two-tone measurement approach can be used in any impedance-measurement

application in which nonlinearity or bias-dependence is ofinterest. Though at present

it requires semi-custom apparatus, such functionality could be incorporated readily into

future commercial instruments. Elucidating the physical causes of impedance nonlinearity

in biological interfaces requires further research. Measuring nonlinearity may prove a

fruitful tool in the ongoing efforts to improve the performance of electrical biosensors.

Chapter 5

Requirements for CMOS Impedance

Measurement System

Our objective is to demonstrate a functioning integrated array of impedance biosensor

analyzer circuits. Before embarking on the detailed design, an essential prerequisite is to

understand the requirements placed on the circuit. Methodologies to determine the required

specifications for such measurement systems has not been treated in the literature, and

most investigators use commercial instruments and do not focus attention on whether the

instrument performance is the limiting factor in the overall experiment.1 For most electrical

biosensor circuits, determining the appropriate electrical specifications is more challenging

than designing to meet those specifications.

5.1 Detection Steps

As detailed in Chapter 2, affinity biosensors capture a desired biomolecule and subse-

quently measure the resulting change in the surface properties. For impedance biosensors,

the impedance of the electrode-solution interface is the measured surface property. We have

extended this approach to also detecting changes in the “nonlinearity” (the bias dependence

of the interface impedance), as discussed in Chapter 4.

Detecting biomolecules using impedance can be broken down into three tasks:

1In most cases it probably is not.

100

5.1. DETECTION STEPS 101

1. Capture target molecules on the probe-functionalized surface (affinity capture)

2. Ensure that changes in impedance correspond to target capture (selectivity)

3. Measure small changes in impedance (readout)

We briefly describe each of these steps below.

5.1.1 Affinity capture

Target capture, discussed in Section 2.2.2, is a biochemical operation that lies outside the

scope of this dissertation. Briefly, the strength of the probe-target interaction (represented

by Kd) determines how much of the target will bind for a specified solution concentration

at chemical equilibrium. Reaching chemical equilibrium may take hours, with dynamics

determined by kinetic parameterskon andko f f . Attaching probes to the electrode without

degrading their target-binding capability is an importantchallenge.

5.1.2 Selectivity

Impedance changes can be caused by many factors other than target binding, including non-

specific binding (adsorption) of non-target biomolecules to the probe layer (Section 2.2.5);

change in pH, salt concentration, temperature, or other such condition; and degradation of

the probe layer.

The ability to control these impedance-determining factors limits the biochemical

“resolution” in the sense that target-induced impedance changes must be discriminated

from changes arising from other effects. As noted in Section2.4.3, differential mea-

surement schemes can partially compensate for these unwanted impedance changes.

This aspect of impedance biosensors, although important, is outside the scope of this

dissertation.

5.1.3 Readout

We now focus our attention on the measurement system’s ability to measure small

impedance changes. We will consider commercial EIS analyzers to be the “gold standard”

102 CHAPTER 5. REQUIREMENTS FOR CMOS MEASUREMENT SYSTEM

by which to judge our integrated impedance analyzer. As single-channel benchtop

instruments, their design is much more flexible and can incorporate parts made from

many different fabrication processes. It would be a huge victory if a multichannel CMOS

impedance analyzer could merely approach the performance of an expensive commercial

instrument. Furthermore, identifying the limitations to circuit performance is a valuable

exercise.

5.2 Measurement System Architecture

Figure 5.1 shows the necessary system components of the impedance measurement system

using the autobalancing bridge architecture.2 These components are the same for both

conventional and two-tone measurements:

1. Biofunctionalized electrodes of gold or similar material (forms the Device Under

Test, or DUT)

2. Stepped-frequency sinusoidal excitation voltageVtest supplied via a reference/auxil-

iary electrode

3. Transimpedance amplifier (TIA) to convert the resulting current to a voltageVout

4. Analog-to-digital converter (ADC) to provide a digital representation ofVout

5. FFT analyzer to extract impedanceZDUT based onVtest andVout

5.2.1 The TIA is our focus

All of these functions could be performed using a monolithicbut multifunctional integrated

circuit, with the electrodes added directly on top of the CMOS die using post-processing.

However, the effort required to integrate all these components is beyond the scope of

this thesis. We therefore focus on implementing the third and most critical component,

a transimpedance amplifier (TIA), using a standard CMOS process. A fully integrated

2Section 3.4 explains why we chose this architecture.

5.3. REQUIREMENTS RELATED TOZDUT 103

−

+

ZD

UT

Vout

Vtest

ADC

Rsol

Rleak

CsurfAu electrode

solution

on-chip

AgCl

probe

analyte

ZDUT = -ZfVtest/Vout

Zf

FFT

ADC FFT

computeZDUT

socket

Figure 5.1: System diagram, indicating on-chip vs. off-chip functionality.

TIA implementation for impedance biosensors not been previously demonstrated directly,

but the other required components have been demonstrated informs readily adaptable to

impedance biosensors. We implement the other four components off-chip to complete the

measurement system.

5.3 Requirements Related toZDUT

Experiments using our custom PCB-based measurement apparatus and our electrode array

are described in Chapters 3 and 4. Results from these experiments yield specifications for

measurements of the interface impedanceZDUT .

5.3.1 Electrodes

The CMOS-based system uses the same 6 by 6 array of 300µm square gold electrodes

described in Chapter 3.

In principle, the sensor electrodes could be added on top of standard CMOS dice

using lithographic post-processing similar to the work described by Levine [2] or Heer

[130]. An alternative route is to electroplate metals (or electrolessly deposit using a similar

reaction) on openings to the top metal layer. Although this integration is a logical step in


the continued development of integrated impedance biosensors, use of on-chip electrodes

necessitates some sort of post-processing because the metals available in conventional

CMOS technology, aluminum and copper, are unsuitable. Theyform surface oxides, can

slowly dissolve, and are not easily biofunctionalized. As the focus of this research is

the measurement of impedances, solving the problem of integrated sensor electrodes is

deferred to others, and only external electrodes are used.

5.3.2 Multiplexing

To take full advantage of the sensor array, it is desirable tointerrogate all the electrodes

simultaneously. Although we do not have the other system components (e.g. on-chip

ADCs) to implement a complete, parallel 36-channel measurement system, our aim

is to demonstrate the feasibility of implementing the TIA circuitry for such parallel

measurements. Thus, we provide one instance (“pixel”) of the measurement circuit for

each of the 36 electrodes on the same CMOS die.

5.3.3 Frequency range

The range of excitation frequencies which contain relevantinformation about target

binding depends on the type of measurement being performed,the electrode size, surface

functionalization, and other parameters. For instance, impedance biosensors based on

faradaic measurement ofRct usually require sub-Hz frequencies, but 100 Hz is often

a practical lower bound for non-faradaic sensors because the uninteresting parameter

Rleak dominates at lower frequencies. At high frequencies,Rsol dominates the total

impedance in both faradaic and non-faradaic sensors (see Figure 2.4b), but is usually not

a parameter of interest. Scaling the electrode size shifts the range of relevant frequencies

(see Section 2.3.9). The measurement frequency range is an important design specification

because it determines amplifier bandwidth requirements, bounds the sampling frequency,

and influences the required measurement time.

Based on experiments with our PCB data acquisition system and the 36-electrode test

chip presented in Chapter 3, changes in the impedance over the range of roughly 100 Hz to

20 kHz are the best indicator of target binding. As anticipated from the discussion in the


Parameter minimumZDUT typicalZDUT maximumZDUT

Csur f A 30 “nF” 15 “nF” 7.5 “nF”Csur f m 0.95 0.92 0.87Rsol 700Ω 1 kΩ 1.5 ΩRleak 25 MΩ 50 MΩ 1000 MΩ

Table 5.1: Minimum, typical, and maximum impedances to be measured.

preceding paragraph, the total impedance is dominated byRleak at lower frequencies and by

Rsol at higher frequencies. In order to accommodate the expectedfrequency range with an

adequate margin, we target our custom impedance-measuringIC for excitation frequencies

between 100 Hz and 100 kHz.

5.3.4 Excitation amplitude

To guarantee linearity during the impedance measurement, as explained at the start of

Chapter 4, the applied voltage across the electrode-solution interface for impedance mea-

surement cannot exceed 5–10 mV. Even though we also are intentionally superimposing

a large excitation to provoke nonlinearity, we use a small-signal tone of only 2 mV for

our nonlinearity experiments (see Section 4.5), and generally less than 5 mV for other

measurements.

In short, the amplitude ofVtest must be no more than 10 mV, and preferably less than

5 mV.

5.3.5 Impedance to be measured

The magnitude of the impedance to be measured, combined withthe maximum allowable

voltage excitation, dictates the currentItest that must be sensed. The impedance and

SNR requirements collectively constrain the maximum allowable noise levels from the

measurement circuit. The complex-valued fitting procedurerequires that both impedance

magnitude and phase be measured to extract the best-fit modelparameters. In our case, the

phase ofZDUT phase lies between 0 and−90 over the measured frequency range.


102

103

104

105

103

104

105

106

|Z| [

Ω]

102

103

104

105

−100

−80

−60

−40

−20

0

Frequency [Hz]

Pha

se [d

eg]

Rsol

Rleak

Csurf

Figure 5.2: Possible values ofZDUT based on measurements of our 300µm squarebiofunctionalized electrodes. The dotted line corresponds to a 7.5 nF capacitor in serieswith a 1 kΩ resistor.


Based on experiments with our PCB measurement system and the36-electrode test

chip, the interface impedance of the solution-electrode interface can be very roughly

modeled as 1 kΩ resistor in series with a 7.5 nF capacitor. Accounting for the slightly

non-capacitive nature ofCsur f using a constant phase element (CPE) (Section 2.3.7), we

identify the relevant range of circuit parameters from our measurement data, as plotted in

Figure 5.2 and listed in Table 5.1. The impedance spectra corresponding to the maximum

and minimum sets of parameters contain all possible impedances and are used as the corner

cases for subsequent modeling.

Over the entire frequency range,ZDUT is between 500 kΩ and 700Ω, a range of

57 dB. Assuming 5 mVVtest amplitude, the resulting current amplitude is between 10 nA

and 7µA. BecauseZDUT is roughly capacitive, the TIA transfer function can be made

more uniform over frequency by using a capacitive feedback network. For our nonfaradaic

sensing scheme, the interface capacitanceCsur f is expected to be the main circuit element

that will vary upon target binding.

Table 5.1 shows the parameters representing the threeZDUT corners that we will use

in modeling. These parameters include the maximum and minimum impedances specified

above over the entire frequency range.

5.3.6 Nonlinearity to be measured

We want to measure the voltage dependence (nonlinearity) ofthe interfacial impedance

using the two-tone scheme described in Chapter 4. The nonlinearity is described by coef-

ficientsα1andα2, where the DUT impedance isZDUT(ω) = Z0(ω)(


)

.

In our biological measurements using the PCB measurement system we observe|α1| values

in the range of 0.1–1 V−1 and |α2| values in the range of 2–10 V−2. Our goal, which is

somewhat arbitrary, is to measure these with a precision of 1% of the full-scale value, using

a 50 mV large-signal excitation at a low frequencyωB.

Much of the design complexity of our CMOS implementation results from the

requirement to quantify impedance and nonlinearity simultaneously using the two-tone

approach. Because of the restricted swing of the CMOS amplifiers (compared with the

substantially larger values allowed by the±8 V supplies in the PCB implementation), a


tone-cancellation scheme is implemented to assure that theωB tone does not saturate the

OTA output. The resulting circuit-level requirements of the tone-cancellation circuitry are

discussed in Section 6.13.

5.4 Constraints Imposed by CMOS

5.4.1 CMOS process

The chip is implemented in a 0.18 µm standard CMOS process generously provided by

National Semiconductor (Santa Clara, CA). It is a two-poly,five-metal process with 1.8 V

core devices, 3.3 V I/O devices, poly-poly capacitors and non-silicided resistors.

5.4.2 Die area

As previously mentioned, our goal is to create an array of measurement circuits, one for

each electrode in the 6 by 6 array. National Semiconductor’sloose requirement is that the

die be no larger than 3 mm square. Choosing each measurement pixel to be no more than

400 µm on a side allows a comfortable 300µm perimeter for bondpads and test circuits

within a 3 mm-square die.

Extreme scaling of the measurement circuitry carries no benefit. When using external

electrodes, as in our case, the bondpads effectively determine the required area. On the

other hand, if the electrodes are added directly on top of theCMOS circuitry via post-

processing, then the electrode pitch must be sufficiently large to separately attach the

capture probes to each electrode. This requirement corresponds to about 100µm minimum

pixel size.

5.4.3 Power consumption

Power consumption itself is only of secondary importance inforeseeable applications of

an integrated impedance biosensor array, but thermal considerations set an effective upper

bound on the power consumption. If the electrodes are directly on top of the CMOS die,

then the allowable power dissipation is determined by what fraction of the dissipated power

5.5. PRECISION REQUIREMENTS 109

reaches the probe layer, the temperature stability of the probe layer, and any temperature

effects on probe-target interaction.

These considerations are difficult to quantify without case-specific experimental data,

but we expect biological effects to be minimal if the heatingis less than 1C. The only

publication we found with data on surface temperature rise for biosensor application reports

that 25 mW/mm2 resulted in a 2.3 C rise in surface temperature when packaged [195].

Even though our electrodes are on a separate chip, we choose to dissipate no more than

10 mW/mm2 of active pixel area to demonstrate proof-of-principle fora fully integrated

system with a 1C temperature rise. Given our target pixel area of 400µm square, that

limit corresponds to 1.6 mW per pixel, or 0.5 mA from a 3.3 V supply. This current is

generous and is not an important constraint for our design.

5.4.4 CMOS-sensor interfacing

In our implementation each measurement pixel requires two bondpads, one to connect

with the electrode DUT and another for the output signalVout. Our 36-electrode array

consequently requires 72 bondpads for interfacing. Note that the input connections are

not required if the electrodes are fabricated on top of the CMOS die with post-processing.

Furthermore the number of required output connections would reduce greatly if the ADC

step were performed on the same CMOS die. Such reductions arenot necessary in

the present work, but may be desirable in future implementations. Finally, additional

bondpads are used for supply voltages as well as for the cancellation circuitry which enables

nonlinearity measurement.

5.5 Precision Requirements

The biological limit of detection (LoD), discussed in Section 2.2.6, is the smallest

concentration of target biomolecules in solution that can be reproducibly detected. It can

be limited by multiple factors, both practical and fundamental. The most important factors,

listed in rough order from least to most fundamental in nature, are:


1. Irreproducibility in surface chemistry, biology, or other aspect of the sensing

interface;

2. Non-specific binding (important in practical settings but not in a clean system);

3. Temporal fluctuations inherent in sensing interface;

4. Electronic noise of measurement circuit; and

5. Strength of probe-target binding interaction (Kd).

We aim to design a measurement circuit with sufficiently low noise that the circuitry

does not impose the bound on the limit of detection. It is important to understand what

performance is “good enough” because improving the noise performance of an integrated

measurement circuit (for a fixed fabrication process) requires extra power, die area, and/or

design complexity.

To understand what noise performance is “good enough,” we first searched the literature

on impedance biosensors to see what impedance changes previous work has been able to

resolve at the biological limit of detection. The publishedwork used expensive benchtop

instruments. We assume either that the apparatus does not limit the sensitivity, or that we

cannot hope to do better using a circuit designed in standardCMOS. Our goal consequently

is to design an integrated impedance analyzer that providesmeasurements as precise as

previously reported.

5.5.1 Precision of published results

A thorough literature review of impedance biosensors is presented in Chapter 2. Out of

many the reviewed publications using nonfaradaic sensing,five provide information about

the measurement precision by specifying both the impedancechange at the biological limit

of detection and also the nominal impedance. The resulting data is shown in Table 5.2.

It appears from this meta-analysis that a typical limit of detection corresponds to

roughly a 0.1% change in the measured impedance. Measurement circuitrycapable of

distinguishing even smaller impedance changes therefore exceeds the system-level need.


∆ZDUT @ LoD ZDUT,nominal Precision Measured Quantity Ref.

31 pF 66 nF 0.05% Z @ 34 Hz [185]100 pF 100 nF 0.1% Z @ 113 Hz [223]20 pF 30 nF 0.07% Csur f [170]600 pF 60 nF 1% Csur f [189]N/S N/S ∼ 0.1% Z @ 1.5 kHz [194]

Table 5.2: Reported impedance changes corresponding to thelimit of detection ofnonfaradaic impedance biosensors.

5.5.2 Precision is important, accuracy is not

We pause here to underscore the difference betweenaccuracy and precision. Even

though these terms are colloquially used interchangeably,precision and accuracy have

distinct meanings. Accuracy reflects nearness to the truth,whereas precision reflects

reproducibility of repeated measurements.

Because the impedance-measuring circuit is used to track impedance changes over time,

precision (i.e. reproducibility) is critically important, but accuracy is not. Stated another

way, we desire to observe thedifference∆Z between two measurements ofZDUT . If the

measurements are very precise then∆Z can be known with a great degree of certainty even

if ZDUT is not. The accuracy of the computed∆Z is determined by the precision of each

separateZDUT measurement.

Applying this idea to our CMOS implementation of an impedance-measurement circuit,

fixed deviations inZf will not affect the accuracy of∆Z to first order. Likewise, “offsets”

in the biological parameters (e.g. different probe density) and initial impedance ofZDUT

are of secondary concern. However, inherent electronic noise sets a fundamental limit on

the attainable precision. Noise can be reduced by choice of circuit topology and transistor

sizing, but cannot be completely eliminated. Furthermore,any drift in offset voltages and/or

ZDUT due to temperature changes, changes in salt concentration due to evaporation, etc.

will affect the accuracy of∆Z over the corresponding time period.


5.5.3 Precision vs. SNR

When we speak of measurement precision, we speak of limitations imposed by the

uncertainty due to random noise. For instance, if repeated measurements of a 1 kΩ resistor

fluctuate with an RMS value of 1Ω, that fluctuation corresponds to 0.1% precision. Others

might say that the resolution of the impedance measurement is 0.1%. Yet others would

say that the measurement has a signal-to-noise ratio (SNR) of 60 dB. For our purposes,

precisionandresolutionare interchangeable, and are the reciprocal of the SNR (where the

SNR refers to the impedance measurement itself).

Because impedance is computed from measurements of currentand/or voltage, the SNR

of those contributing measurements determines (but is not synonymous with) the SNR of

the impedance measurement. This point will be addressed further in Section 5.6.

5.5.4 Specifications of commercial instruments

Here we summarize the advertised specifications of some commercial instruments used

for impedance biosensor measurements. We expect our CMOS circuit to have inferior

performance, but it is useful to have a baseline for our expectations. Note that each of these

instruments can only measure one electrode at a time.

5.5.4.1 Solartron EIS instruments

The Solartron Analytical 1287 Electrochemical Interface and 1260 Impedance Analyzer

are commonly used in tandem for electrochemical impedance spectroscopy (EIS) mea-

surements of all types, including impedance biosensors. Judging from publications, this

instrument is the most widely used by impedance biosensor experimentalists. The cost

for instruments and software is about $35,000. The smallest current resolvable by the

1260 is 200 pA. Assuming the same limit holds for extracting the amplitude of a

sinusoidal excitation, that current corresponds to 0.1% precision using our worst-case

corner (maximumZDUT at 100 Hz with a 10 mV excitation). On a separate plot, the

datasheet advertises 0.1% magnitude and 0.1 phase resolution for impedances less than

100 kΩ but achieving this performance would require an unsuitablylarge 1 V excitation.


5.5.4.2 CHI 660

The CH Instruments model 660 workstation is also in common use for interrogating

impedance biosensors. It is a general-purpose electrochemistry instrument with an EIS

mode. The datasheet claims a current resolution of 10 fA (although minimum detectable

current is much greater; the bias current is in the pA range).No information is given

regarding noise power spectral density nor the time required to obtain such a resolution.

The claimed current resolution may only be achievable with pseudo-DC electrochemistry

measurements. A 10 pA precision corresponds to a 0.05% precision using a 10 mV

excitation to measure our maximumZDUT at 100 Hz.

5.5.4.3 Axopatch 200B patch clamp

Patch clamp instruments are designed to measure the small ionic currents in neuronal cells.

We are not aware of patch clamps being used to perform impedance biosensor experiments.

A patch clamp uses a transimpedance amplifier where the command voltage applied to the

non-inverting node of a feedback amplifier is externally controlled. Generally, they are

optimized for low current noise in the sub-kHz frequency range. The $12,000 Axopatch

200B is the best such instrument, and is specified to provide an input-referred current noise

of less than 1 fA/√

Hz from 30 Hz up to 4 kHz. Assuming a 1 second integration time,

this noise performance corresponds to a remarkable 1 fA precision. These TIAs typically

are limited to operation below about 10 kHz. An additional practical limitation is that the

best patch clamps use an integrator-differentiator input stage, and the integrator needs to be

reset periodically. Thus, there are small dead windows in the output signal at uncontrolled

intervals, complicating FFT analysis.

5.5.4.4 Impedance-to-Digital ICs

Analog Device’s AD5933 is a $10 commercial IC specifically designed for impedance-to-

digital conversion. The architecture of the AD5933 is identical to our pixel architecture,

with the ADC and FFT analyses performed on-chip. However, the AD5933 uses an

excitation signal amplitude (Vtest) that is much too large for impedance biosensors. Its

advertised impedance SNR is 60 dB, but it is unclear if that value is achieved with the


minimum excitation (100 mV amplitude) or only with the maximum excitation. Assuming

optimistically that the specification holds for the minimumVtest and that this signal can be

attenuated so the DUT is exposed to only a 10 mV excitation, the resulting SNR would be

40 dB.

Capacitance-to-digital converters such as the $5 AD7745 donot allow an impedance

spectrum to be measured, but quantify the capacitance attached to its input usingΣ-∆techniques. The maximum capacitance measurable by the AD7745 is a paltry 17 pF, and

the voltage across the capacitor is neither user-controlled nor constant as is required for

impedance biosensors.

5.5.5 Our target precision

Based primarily on the aforementioned experimental results and secondarily on the

specifications of commercial instruments in use for impedance biosensors, we adopt as

our goal to achieve an impedance precision of 0.1% with 1 second of measurement time

for each frequency. We expect that achieving such a specification will assure that the

system-wide limit of detection is not set by the measurementapparatus but rather by other

(biological) factors.

5.6 Uncertainty propagation

Here we discuss how the precision of electrical measurements (e.g. voltage amplitudes at

the excitation frequencies) are related to the precision ofquantities computed from those

measurements (e.g.ZDUT). For a more comprehensive treatment see Taylor’s text [272].

There is an uncertainty associated with every real-world measurement, for instance,

from random electronic noise. When calculating a result based on measured quantities, the

uncertainty of this result can also be calculated. Iff (x1,x2, . . . ,xn) where eachxi has an

associated uncertainty∆xi , and if thexi variables are uncorrelated,3 then the uncertainty of

3if any of thexi ’s are correlated, a more complicated expression must be used

5.6. UNCERTAINTY PROPAGATION 115

Function Uncertainty

X = A±B ∆X =√

∆A2+∆B2

X = AB ∆X =

√

(B∆A)2+(A∆B)2 = |AB|√

(∆AA

)2+(∆B

B

)2

X = AB ∆X =

√

(∆AB

)2+(

A∆BB2

)2=∣

∣

AB

∣

∣

√

(∆AA

)2+(∆B

B

)2

Table 5.3: Error propagation formulas for uncorrelated variablesA andB.

the computed functionf is

∆ f =

√

n

∑i=1

(

∂ f∂xi

∆xi

)2

. (5.1)

From this equation the uncertainty propagation formulas for algebraic combinations of

two variables can be derived, as shown in Table 5.3 for reference. Note that uncorrelated

uncertainties, like electronic noise arising from independent processes, add in quadrature.

5.6.1 Uncertainty propagation for simple impedance calculation

Consider calculatingZDUT as the ratio of a voltageVtest and a currentItest, with

corresponding uncertainties∆Vtest and∆Itest. The uncertainty∆ZDUT can be derived from

Equation 5.1 as:

ZDUT =Vtest

Itest±∆ZDUT , (5.2)

∆ZDUT =

√

(

∂Z∂V

∆Vtest

)2

+

(

∂Z∂I

∆Itest

)2

= ZDUT

√

(

∆Vtest

Vtest

)2

+

(

∆Itest

Itest

)2

(5.3)

Expressing Equation 5.3 as a fractional uncertainty we see that

∆ZDUT

ZDUT=

√

(

∆Vtest

Vtest

)2

+

(

∆Itest

Itest

)2

, (5.4)


which states the intuitively satisfying result that both current and voltage should be

quantified precisely in order to make a precise impedance measurement. For such a

measurement, we cannot assume thatVtest is the exact voltage advertised by the function

generator, nor can we assume thatVtest has exactly the same magnitude over time. In the

foregoing analysis of commercial instruments, we optimistically assumed that the precision

was dictated only by the current measurement. Partly for this reason, both our PCB-based

and integrated measurement implementations measureVtest independently using a second

measurement channel, as shown in Figures 3.4 and 5.1.

5.6.2 Uncertainty propagation for our impedance calculation

Our PCB has two output voltages:V1, which encodes the DUT currentItest, andV2, which

encodes the applied voltageVtest. LabView extracts the tone amplitude of both signals

using an FFT, and the ratio of these amplitudes is recorded asthe variableξ ≡ V1V2

. By

virtue of this ratiometric technique, slight changes inVtest amplitude do not affect the

result. Systematic nonidealities in the amplifier chain areeliminated by convertingξ into

an impedance using pre-calculated calibration coefficients (see Section 3.7). Errors in the

fixed calibration coefficients affect the accuracy ofZDUT but not the precision. Recall that

the precision ofZDUT corresponds to the accuracy of∆ZDUT , which is the true quantity

of interest. However, uncertainties or noise in the measured amplitudes ofV1 andV2 will

affect the accuracy of∆ZDUT .

The uncertainty inZDUT depends on the uncertainty inξ, which in turn depends on the

uncertainty inV1 andV2. We begin by restating the relationship betweenZDUT , tone ratio

ξ, and the computed calibration coefficientski . From Equation 3.5

ZDUT =k0−k2ξk1ξ−1Ω

(5.5)

5.6. UNCERTAINTY PROPAGATION 117

By applying Equation 5.1, it can be shown that

∆ZDUT =∂ZDUT

∂ξ∆ξ

= −ZDUT

(

k1− k2/ZDUT

k1ξ−1Ω

)

∆ξ

' −ZDUT

(

∆ξξ

)

, (5.6)

where the final approximation assumes that the calibration step only corrects for minor

effects beyond the proportional relationship betweenV1 andV2 (i.e. k1 is relatively large

andk2 is relatively small). We then can see that

∆ZDUT

ZDUT'−∆ξ

ξ, (5.7)

and that leaves us only to compute the relative uncertainty in ξ ≡ V1V2

. It can be trivially

shown from Equation 5.1, or from the third entry in Table 5.3,that the uncertainty is

∆ξξ

=

√

(

∆V1

V1

)2

+

(

∆V2

V2

)2

(5.8)

from which we conclude that

∆ZDUT

ZDUT'−

√

(

∆V1

V1

)2

+

(

∆V2

V2

)2

. (5.9)

Thus we see that the fractional uncertainties ofV1 andV2 add in an RMS fashion to yield

the fractional uncertainty in the computedZDUT .

5.6.3 Precision requirements correspond to noise requirements

Random noise primarily determines the impedance measurement precision of our circuit.

If we assume that bothV1 andV2 have the same fractional noise, Equation 5.9 informs us

that we require a 0.07% precision of both voltages (circuit-level SNR of 63 dB),to attain

an overall 0.1% precision in∆ZDUT (impedance SNR of 60 dB).


−

+

Vout

Vtest

Vout = T Vtest

ZDUT

Zf

ADC

Figure 5.3: MeasuringZDUT using an OTA with feedback impedanceZf and inputexcitationVtest.

By knowing the maximum input signalVtest and the circuit noise referred to the system

input, the SNR can be trivially computed. The remainder of this chapter analyzes all

the noise sources and how they transfer to the input, and concludes with an overall SNR

calculation.

5.7 Transfer function

An operational transconductance amplifier (OTA) forms the core of the TIA circuit, along

with the feedback network with impedanceZf . We use a feedback network composed of

a parallel capacitor and resistor, orZf = Cf ‖ Rf . In this section we compute the transfer

function of theZDUT /TIA combination and discuss the choice ofCf andRf . These results

will be subsequently applied to noise.

5.7.1 Approximate transfer function

In the basic transimpedance topology we have selected (Figure 5.3), the current flowing

through the device under test (DUT) is converted to a voltageby the feedback impedance

Zf and the OTA. For an ideal amplifier, we can write by inspection

Vout =− Zf

ZDUTVtest. (5.10)

5.7. TRANSFER FUNCTION 119

VoutVtest

Zf

ZDUT Vx

gmVx Rout CL

Figure 5.4: A more realistic version of Figure 5.3, including the effective transconduc-tancegm and output resistanceRout of the OTA. A load capacitanceCL has also beenincluded.

For notational purposes, we define the system transfer function T as the complex-valued

ratio of the output voltage to input voltage, or

T ≡ Vout

Vtest. (5.11)

The DUT impedance can be determined by measuring the transfer function and knowing

the feedback impedance according to

ZDUT =−Zf

T. (5.12)

5.7.2 More realistic transfer function

We assumed the OTA was ideal in the previous introduction. Although MOS input

transistors assure negligible input current at all frequencies of interest, our IC amplifier

will not have infinite gain. Here we derive the transfer function of the circuit shown in

Figure 5.4, which is a more realistic version of Figure 5.3. This circuit includes the effects

of amplifier output resistance and load capacitance. We expect the dominant pole to be

formed byRout and the combination of capacitance inZf andCL, and so this model does

not include the amplifier’s high-frequency poles. Such an omission is unimportant here,

as the neglected poles will exist at frequencies much higherthan the 100 kHz maximum

excitation frequency.


The DC gain of the amplifier is given byADC = gm,inRout. For typical amplifier

architecturesgm,in is the effectivegm of the entire amplifier and so we simplify notation

by simply writinggm. Invoking current conservation to eliminate the variableVx, it can be

shown that the closed-loop transfer function is given by

Vout

Vtest≡ T =− ADCZf −Rout

ADCZDUT +sCLRout(

ZDUT +Zf)

+Rout+Zf +ZDUT, (5.13)

where only the last terms of both numerator and denominator are negligible over the

specified measurement conditions for the expected values ofZDUT andZf . Writing this

equation as a function of component values ofZf andZDUT leads to no further insight.

In the mid-band (approximately 300 Hz to 10 kHz)T decreases slightly with frequency

because of the sub-unity factorm in the CPE representingCsur f. Note thatT is reduced

at high frequencies compared with the derivation assuming an ideal amplifier. Figure 5.5

shows the transfer functionT for minimum, typical, and maximum DUT impedances as

defined in Table 5.1.

5.7.3 Choice ofCf

CapacitorCf is the dominant feedback element over the frequency range ofinterest

(100 Hz–100 kHz). We use capacitive feedback for several reasons. Most important is

the fact thatZDUT is roughly capacitive over that frequency range and we are interested

in detecting changes in that capacitance. Furthermore a feedback capacitor does not add

noise, unlike a feedback resistor.

There are several considerations for choosing the size of the capacitor. A larger

capacitor reducesT and correspondingly allows a largerVtest, which then increases the SNR

for a fixed amount of noise. However, the allowable amplitudes ofVtest are constrained by

linearity considerations. In addition a larger capacitor consumes more die area.

The exact value ofCf is unimportant because we are looking for changes inT that

correspond to changes inZDUT . For our initial design analysis we use a 25 pF capacitor,

which corresponds to 20% of the pixel area. In the final designCf is increased to 30 pF by


102

103

104

105

101

102

103

Frequency [Hz]

|Vou

t/Vte

st|

System Transfer Function T

Minimum ZDUT

Typical ZDUT

Maximum ZDUT

Figure 5.5: System transfer functionT for various corners ofZDUT , computed usingEquation 5.13 and assuming realistic values forADC, Rout, andCL based on designsimulations and the chosenZf . The dotted curve is for the typicalZDUT but using thesimple expression forT in Equation 5.12.


co-locating a comb capacitor on top of a poly-poly capacitor, allowing an increase in the

SNR.

5.7.4 Choice ofRf

An on-die resistorRf is added in parallel withCf to roll off the DC gain of the TIA and

provide input bias current to the OTA. By reducing the TIA gain for theωB tone used for

nonlinearity measurements, the requirements for the tone cancellation scheme described in

Section 6.13 can be relaxed. To obtain roll-off at 100 Hz, a 50MΩ resistor is required.

However, a somewhat smaller resistor is favored to further attenuate theωB signal and

also to facilitate on-chip implementation. 25 MΩ is a good target based on preliminary

calculations.

BecauseRf needs to be highly linear (as any nonlinearity there would confound the

measurement of the nonlinearity ofZDUT ), we preclude the use of diode-connected MOS

pseudoresistors [273] or floating MOSFET resistors. Also, area constraints prevent us

from implementing a monolithic 25 MΩ resistor; a poly resistor with width of twice the

minimum gate length requires approximately 1% of the pixel area per MΩ.

As shown in Figure 5.6, we use a resistive T-network to synthesize the equivalent of a

largeRf with only a fraction of the die area that would be required fora monolithic resistor.

A T-network is a combination of three resistors that leads toa larger effective resistance

between two terminals. T-networks are usually not used in precision circuitry because they

add noise and degrade offset voltage, but a careful analysisreveals that these shortcomings

are tolerable in our particular situation. Importantly, the linearity of a T-network is the same

as its component resistors.


−

+

Cf

ZDUT Vout

Vtest

+− Vn

R1

R2

R3

Requiv

Figure 5.6: A T-network is used to form an equivalent resistor to roll off the DC gainof the TIA.

5.7.5 T-network equations

A T-network (or star or wye network) famously is equivalent to aΠ-network (or∆ network),

as shown in Figure 5.7, with the following transformations:

RA = R1+R3+R1R3

R2(5.14)

RB = R1+R2+R1R2

R3

RC = R2+R3+R2R3

R1

If we define the “gain”G of the T-network to beG ≡ 1+ R3R2

, then the equivalent

resistanceRequiv of the T-network between nodes X and Z is

Requiv= RA = GR1+R3. (5.15)

It appears that resistorR1 is multiplied by a factorG, which can be made very large by

choosingR2 R3. For example, ifR1 = R3 = 2 MΩ andR2 = 200 kΩ, thenG= 11 and


R1

R2

R3 RA

RB RC

Z

Y

XZ

Y

X

=Figure 5.7: Conversion between T andΠ networks.

the equivalent resistance is 24 MΩ. These are the values we select in our CMOS design,

where node X is tied to the amplifier input, node Z is the amplifier output, and node Y is

the reference voltage (signal ground).

In this example,RB =RC = 2.4 MΩ. In our circuit,RB sits between the amplifier virtual

ground and the signal ground and has only the OTA offset voltage across it.RC is connected

between the amplifier output and the signal ground and loads the amplifier. If needed, a

buffer could be added to drive the T-network feedback, but the loading actually is beneficial

in our case as we will see. The noise and offset amplification properties of the T-network

will be addressed in Section 5.8.3.

5.8 Noise Analysis

In this section we enumerate all the different noise sourcesand refer them all to the terminal

of ZDUT whereVtest is applied. The SNR is then easily computed by dividing the input

signalVtest by the composite circuit noise referred to the same node.

5.8.1 OTA voltage noise

The amplifier that forms the core of the measurement circuit has voltage noise and current

noise, generally referred to its own input. What is important to us, however, is the noise

referred to the input of the entire circuit, whereVtest is applied, as shown in Figure 5.8.

First we compute the relationship between OTA voltage noiseVn and the equivalent

noise at the circuit input. Using the realistic model for theOTA as shown in Figure 5.4, it

5.8. NOISE ANALYSIS 125

−

+

Vout

(Vtest) ZDUT

Zf

+ −

refer noiseto here

Vn

In

Figure 5.8: Referring OTA noise to the system input.

can be shown that

Vout

Vn=− ADC

(

Zf +ZDUT)

ADCZDUT +sCLRout(

ZDUT +Zf)

+Rout+Zf +ZDUT. (5.16)

This expression is almost identical to the transfer function from the system input to the

output becauseZf ZDUT (i.e. T 1). To refer this noise to the input of the system, we

simply divide byT (Equation 5.13) and obtain the result that

Vtest

Vn=

ADC(

Zf +ZDUT)

ADCZf −Rout' 1. (5.17)

Thus we see that the amplifier input-referred noise can be considered as if it were directly

at the system input.

5.8.2 OTA current noise

We expect the OTA’s input-referred current noise to be extremely small because it will be

implemented in CMOS technology. However, other sources of noise currents exist, notably

from the cancellation circuitry that enables two-tone measurements. Here we derive the

relationship to refer current noise at the amplifier input tothe system input.

Any noise current at the amplifier input flows throughZf and acts the same as current

through the DUT. Using the more realistic circuit model in 5.4, it can be shown that the


corresponding output voltage is

Vout

In=−ZDUT

ADCZf −Rout

ADCZDUT +sCLRout(

ZDUT +Zf)

+Rout+Zf +ZDUT, (5.18)

which when referred to the system input is exactly

Vtest

In= ZDUT . (5.19)

Thus we see that any current noise at the amplifier input can bereferred to the system input

by simply multiplying by the DUT impedance. BecauseZDUT is capacitive, the effect of

this noise is more pronounced at lower frequencies. IfIn has a 1/ f character then the

input-referred current noise will have a 1/ f 2 dependence.

5.8.3 T-network thermal noise

The T-network has several potentially troubling noise properties that merit investigation

in some detail here. We begin by showing that the thermal noise of the T-network itself

is larger than that of a monolithic resistor with the same resistance, by the same factorG

which multiples the resistanceR1 in the equivalent resistance calculation.

Element Noise Gain (V/V) Noise Power at Output

R1 1+ R3R2

(4kTR1)G2

R2R3R2

(4kTR2)(G−1)2

R3 1 (4kTR3)

Vn 1+ R3R2

V2n G2

Table 5.4: Computed noise of various components of the T network at the amplifieroutput.G≡ 1+ R3

R2is the gain boost factor.

It is straightforward to derive the noise transfer functions for the network appearing in

Figure 5.9 (the resistor noise sources are not shown), and the output-referred results are

summarized in Table 5.4. The noise contributions fromR1 andR2 are amplified byG and


−

+

Cf

ZDUT Vout

Vtest

+− Vn

R1

R2

R3

Requiv

Figure 5.9: Network for deriving the T-network noise contributions.

(G−1) respectively. The total output noise from the resistors themselves is given by

V2out,noise=(4kTR1)G2+(4kTR2)(G−1)2+(4kTR3) (5.20)

With some gentle algebra, it follows that

V2out,noise=

(

4kTRequivG)

, (5.21)

indicating that the thermal noise of the equivalent resistor is increased by a factor ofG. In

our previous example, the synthesized 24 MΩ resistor withG= 11 exhibits the noise of a

264 MΩ resistor. Fortunately, this noise remains insignificant compared with other noise

sources in our circuit.

5.8.4 T-network amplification of OTA noise

The last entry in Table 5.4 indicates another potentially troublesome aspect of the T-

network: the OTA input-referred noise power is amplified by afactor of G2 at the TIA

output. The same expression applies to the DC amplifier offset.


101

102

103

104

105

0

0.5

1

1.5

2Noise Gain (op−amp input to system input)

Noi

se G

ain

(dB

)

Frequency (Hz)

G=1G=4G=16

Figure 5.10: Noise gain from amplifier input to system input with different T-networkgains. The low-frequency noise gain is governed by the low-frequency behavior ofZDUT , which here is assumed to have 50 MΩ Rleak.

Fortunately, it can be shown that the effect of this added noise is negligible for two

reasons:

1. Cf dominates the total feedback impedance over the frequency range of interest, so

the added noise is filtered by the capacitor within that band.

2. More important,ZDUT Rf over the frequency range of interest. Thus, the OTA

noise gets shunted through the DUT instead of going through the feedback network

where the T-network topology would amplify it.

Figure 5.10 shows the computed transfer function for the noise between OTA input and the

system input for several different values ofG based on an idealized but still representative

system model. Recall from Section 5.8.1 that referring the amplifier noise to the system

input multiplies it by a factor near unity as long asZf ZDUT . This unity transformation

holds even for the T-network as long as the impedance inequality is well satisfied, as it is

in our case.


5.8.5 T-network flicker noise

A final note of concern regarding use of a T-network to formRf is the flicker noise of the

on-chip resistors. Whatever flicker noise power is present in the resistors will be multiplied

by a factorG, compared with an equivalent monolithic resistor. By implementing a 24 MΩresistor using a T-network withG = 11 we expect flicker noise power to increase by that

same factor.

It has been well documented that polysilicon resistors exhibit flicker noise arising from

the action of charge traps at or near the grain boundaries [274]. The charge-trapping model

explains the increase in resistor flicker noise with DC current. The flicker noise can be

empirically modeled by

V2n =

KR2

fV2

WL=

KR3V2

fW2Rtotal(5.22)

whereK is a process-dependent scale factor,R is the sheet resistance (175Ω/ for

our process technology),f is the frequency,W and L are the resistor width and length

respectively, andV is the voltage across the resistor [269]. The process modelsprovided

to us do not include resistor flicker noise, but from analyzing and interpolating data from

Brederlow et al. [274] we arrive at a pessimisticK = 1×10−26 S2 m2 for the p-doped poly

resistors in our process. This value is significantly worse than the estimate in Lee’s text

[269]. To reduce the flicker noise, we can increase the resistor area and/or decrease the

DC voltage across it. Choosing a resistor with smaller sheetresistance will decrease flicker

noise but may consume a prohibitive amount of die area.

Because we have a time-varying current instead of a DC current, it is unclear how to

choose the factorV in Equation 5.22 properly. We use the peak value ofVdd/2 = 1.65 V

to yield a conservative estimate. The flicker noise cornerfc is the frequency at which the

thermal noise and flicker noise have equal power; flicker noise dominates wheref < fc.

Equating the resistor’s Johnson noise and flicker noise yields

fc =KRV2

4kTL2 =KR3

V2

4kTR2totalW

2(5.23)

where we have used the fact thatRtotal = RLW . For a given resistor implemented in a

polysilicon layer with sheet resistanceR, only the resistor widthW is under control of


Resistance Width Length Pixel % 1/f fc @ 1.65 V 1/f fc @ 50 mV

40 kΩ 180 nm 41 µm 0.02% 170 kHz 156 Hz40 kΩ 400 nm 91 µm 0.05% 34 kHz 32 Hz1 MΩ 180 nm 1029µm 0.44% 272 Hz < 1 Hz1 MΩ 400 nm 2286µm 1.3% 55 Hz < 1 Hz25 MΩ 180 nm 25714µm 11% < 1 Hz < 1 Hz25 MΩ 400 nm 57143µm 32% < 1 Hz < 1 Hz

Table 5.5: Worst-case flicker noise estimates for on-die resistors.

the designer. For a doubling in width, the corner frequencyfc decreases by four times but

the area increases by four times as well. Resistors with lesstotal resistance have larger

corner frequencies. Table 5.5 shows the estimated flicker noise corners based on Equation

5.23 with worst-case values ofK andV. We conclude that the resistor flicker noise is not a

concern except potentially for resistances less than 1 MΩ.

5.8.6 Electrical noise fromZDUT

The electrode-electrolyte impedance being measured asZDUT has some inherent electrical

noise besides its biological irreproducibility. We expectnoise from the following sources:

1. Johnson noise ofRsol

2. Johnson noise ofRleak

3. Johnson noise of the real part ofCsur f

4. Noise due to the stochastic nature of target binding and unbinding

5.8.6.1 Johnson noise ofRsol

Because the electrode-solution interface is in thermal equilibrium for our non-faradaic

impedance measurement, only dissipative elements such as the solution resistanceRsol

contribute noise [275]. The Johnson noise due to the solution resistance has a white power

spectral density given by

V2n = 4kTRsol (5.24)


This noise appears directly at the system input, and its magnitude is small compared with

other noise sources becauseRsol ∼ 1 kΩ.

5.8.6.2 Johnson noise ofRleak

The shunt resistanceRleak contributes noise, but it is filtered by the parallel surface

capacitance (more correctly, a capacitor-like CPE). For a parallel RC network with

resistanceR and capacitanceC, it can be shown that the equivalent noise of the resistor

as seen by the rest of the system is

V2n (ω) = 4kTR

∣

∣

∣

∣

11+ ıωRC

∣

∣

∣

∣

2

. (5.25)

At frequencies high enough that the capacitor dominates theparallel combination —ω (RC)−1 — the equivalent noise can be well approximated by

V2n (ω)'

4kTω2C2R

. (5.26)

Thus, a larger resistor both reduces the amount of noise power at a given frequency above

the corner frequency, and also reduces the corner frequency. In our case withR= Rleak>

25 MΩ andC = Csur f > 5 nF, the cutoff frequency is at most 1.3 Hz and the noise will

be strongly filtered in our frequency range of interest (above 100 Hz). Thus we can safely

ignore the noise contribution ofRleak.

5.8.6.3 Noise of CPECsur f

The fluctuation-dissipation theorem implies that only dissipative circuit elements have

thermal noise [275], which is the reason that capacitors have no intrinsic thermal noise. The

constant phase element (CPE) representingCsur f is mostly capacitive but has a frequency-

dependent real part that depends on the phase parameterm. Whether or not the real part

of the CPE impedance adds noise is an unresolved question in the literature, but we expect

that the answer depends on the physical explanation for the CPE behavior in each specific

case (see Section 2.3.7).


For electrode-electrolyte interfaces, one author suggests that the real part of the CPE

contributes noise [276], whereas another author looked fornoise in a simple electrode-

electrolyte system and only detected noise that could be explained byRleak [277]. To be

pessimistic, we include thermal noise of the real part ofCsur f in our simulations. This noise

also appears directly at the system input, and is given by

V2n (ω) = 4kTRe

(

1(ıω)mA

)

=4kTAωm cos

(π2

m)

.

5.8.6.4 Affinity binding noise

The affinity binding process is stochastic, implying that the number of bound target

molecules at any instant in time has some uncertainty. This will contribute to system-level

noise even if the readout process is completely noiseless. Hassibi et al. showed theoretically

that the SNR is proportional to the number of target particles in the system and depends on

the capture probability (influenced byKd) [144]. The power spectral density of this affinity

capture noise rolls off at frequencies above 1/(2πτ), whereτ is the composite on-off time

of binding.

It is impossible to quantify this noise without specific information about the target-

probe pair, probe functionalization, and other biologicalfactors. Furthermore, measure-

ment of the required parameters includingKd is fraught with difficulties, especially at a

surface. Thus, we consider this binding noise source part ofthe “biological noise” referred

to in Sections 5.5 and 5.5.1 and do not directly consider it inthe design of the measurement

circuit.

5.8.7 Acquisition noise

Sampling theVout signals with an analog-to-digital converter (ADC) adds noise to the

measurement. In comparing ADCs, the important figure of merit in this regard is the

ENOB, or effective number of bits, which represents the ADC resolution after quantization

noise and the internal noise is taken into account. In essence, the ENOB is the SNR of the

data converter system.

5.9. RELATIVE IMPORTANCE OF NOISE SOURCES 133

The RMS noiseσ of each ADC sample is then given by

σ =Vf ullscale

2ENOB . (5.27)

It can be shown that taking the FFT of the time-domain signal divides white noise evenly

across all frequency bins, and thus the acquisition noise power in each FFT bin for N

samples is given by

V2n =

σ2

N. (5.28)

If the excitation signal falls into a single FFT bin (if an integral number of ADC samples

are taken during one cycle of the sinusoidalVtest), then Equation 5.28 directly gives the

output-referred noise power associated with the data acquisition process. This noise is

input-referred by simply dividing by the square of the signal transfer functionT.

The 16-bit ADC in the NI data acquisition board we use has an ENOB of 14 bits.

For purposes of noise simulations, we assume sampling for 1 second at each excitation

frequency.

5.9 Relative Importance of Noise Sources

We developed Matlab code to visualize the relative importance of the various noise sources

mentioned above, and here we show some representative plots. The OTA noise in these

plots comes from the simulated performance of the designed amplifier, which is discussed

in the next chapter. This noise is dominated by the 1/ f noise of the input transistors,

discussed in Section 6.4, despite efforts to minimize it in the design.

We have not yet discussed the tone-cancellation circuitry,but we include its noise

contribution on these summary plots. Its noise appears as a noise current at the inverting

input of the OTA, and is referred to the system input by multiplying by ZDUT , as shown in

Section 5.8.2. See Section 6.18 for more details.

Figures 5.11, 5.12, and 5.13 show the resulting noise contributions referred to the

system input for three different values ofZDUT , minimum, typical, and maximum

respectively. The amplifier voltage noise is the dominant noise source until about 40 kHz,


102

103

104

105

10−18

10−17

10−16

10−15

10−14

10−13

10−12

Frequency [Hz]

Vn2 a

t sys

tem

inpu

t [V2 /H

z]

Noise PSD Contributions Referred to System Input

TotalMain OTALF CancellationADCR

f (T−network)

Rsol

Csurf

Figure 5.11: Noise sources referred to system input for minimumZDUT .

5.9. RELATIVE IMPORTANCE OF NOISE SOURCES 135

102

103

104

105

10−18

10−17

10−16

10−15

10−14

10−13

10−12

Frequency [Hz]

Vn2 a

t sys

tem

inpu

t [V2 /H

z]



f (T−network)

Rsol

Csurf

Figure 5.12: Noise sources referred to system input for typicalZDUT .


102

103

104

105

10−18

10−17

10−16

10−15

10−14

10−13

10−12

Frequency [Hz]

Vn2 a

t sys

tem

inpu

t [V2 /H

z]



f (T−network)

Rsol

Csurf

Figure 5.13: Noise sources referred to system input for maximumZDUT .

5.10. SENSITIVITY ANALYSIS 137

when the ADC noise becomes more important due to decreasingT. The noise resulting

from the tone cancellation circuitry is comparable to the OTA noise at 100 Hz for the

largestZDUT value, but rolls off as 1/ f 2. It is negligible for typical and minimumZDUT

impedances. Noise arising fromRsol, Csur f, andRf are all negligible for our situation.

5.10 Sensitivity Analysis

In Section 5.7.2 we derived the transfer function of the DUT-TIA combination using

a simplified (but not ideal) OTA model. In this section we derive expressions for the

sensitivity of the transfer functionT to changes inZDUT and other circuit parameters.

5.10.1 Sensitivity toZDUT

The sensitivity of the transfer function to changes inZDUT relates the circuit-based SNR

to the SNR or precision of the impedance calculation. For instance, if a 0.2% impedance

change induces a 0.1% change in the transfer function and the transfer functioncan be

determined within 0.1%, then the impedance can only be determined within 0.2%.

The relationship between changes inZDUT and changes inT is obtained by taking the

partial derivative of Equation 5.13 with respect toZDUT :

∂T∂ZDUT

=−T2ADC+1+sCLRout

ADCZf −Rout. (5.29)

The fractional change inT caused by a fractional change inZDUT is then

∆TT

=∂T

∂ZDUT

∆ZDUT

T(5.30)

= ∆ZDUTADC+1+sCLRout

ADCZf −RoutT

= −∆ZDUT

ZDUT

(

1+Zf

ZDUT

sCLRout+RoutZ f

+1

sCLRout+ADC+1

)−1

. (5.31)

Note that this sensitivity is a complex number. We expect thesensitivity to be close to

unity when the amplifier is ideal (infiniteRout), and the derivation suggests that minimum


102

103

104

105

0

0.2

0.4

0.6

0.8

1

Frequency [Hz]

Fra

ctio

nal S

ensi

tivity

Sensitivity of T to ZDUT

Maximum ZDUT

Typical ZDUT

Minimum ZDUT

Figure 5.14: Simulated sensitivity ofT to ZDUT , expressed in fractional sensitivity.

T results in maximum sensitivity (the case of maximumZDUT ). The load capacitance acts

to diminish sensitivity as the frequency increases.

Figure 5.14 shows the sensitivity computed using Equation 5.31 and values forADC,

Rout, and CL based on design simulations. This sensitivity acts as a scale factor in

computing the voltage SNR required to obtain the desired 0.1% impedance resolution.

Depending on frequency, the resolution inT needs to be between 1 and 2.5 times the

resolution required forZDUT becauseT does not change as much asZDUT does.

5.10.2 Sensitivity to other parameters

Just as we derived the sensitivity of the transfer function to changes inZDUT , we can derive

or numerically calculate the sensitivity to changes in other (circuit-related) parameters in

5.10. SENSITIVITY ANALYSIS 139

102

103

104

105

0

0.2

0.4

0.6

0.8

1

Frequency [Hz]

Fra

ctio

nal S

ensi

tivity

Sensitivity of T to Various Factors

ZDUT

Zf

gm

Rout

CL

Figure 5.15: Simulated sensitivity ofT to ZDUT , expressed in fractional sensitivity.

Equation 5.13. Figure 5.15 shows the result, again using values from design simulations.

At high frequencies the transfer functionT is somewhat sensitive to every parameter, while

at low frequencies it is mainly sensitive to changes inZDUT andZf .

Ideally, only ZDUT will change during an experiment, but it is important for us to

consider that other factors might change if the ambient temperature changes. If temperature

change induces a change inT by changing circuit properties, it could be confused with

a change inT caused resulting from changes inZDUT .4 We can safely assume that the

temperature will change no more than 1C during an experiment in a laboratory setting.

The transfer function is relatively sensitive to changes inthe on-chip feedback

impedanceZf . Fortunately, the poly resistors and poly-poly capacitor used have small

4ZDUT may also change with temperature, as pointed out earlier.


temperature coefficients. Models give the resistor temperature coefficient (TC) as

−60 ppm/ C, so a 1C change will changeT by less than 0.006% via the resistive T-

network. The poly-poly capacitor is specified to have an evensmaller TC of 25 ppm/ C.

Thus Zf will not change enough to affect the specified precision evenif the ambient

temperature changes by 1C during the experiment.

In a mostly-completed amplifier design with traditional biasing, the simulated

temperature sensitivity of the input transconductancegm,in is about−2000 ppm/ C.

For high frequencies the fractional sensitivity approaches 0.5, suggesting that a 1C

change would induce a 0.1% change in the measured transfer function. Consequently we

include constant-gm biasing for the amplifier (see Section 6.9) to reduce the temperature

dependence ofgm,in and the resulting temperature dependence of the system transfer

function.

Simulations suggest that the TC of amplifierRout is about 3000 ppm/C over all process

corners. The 0.5 fractional sensitivity at high frequencies suggests a 1C change will cause

T to change by up to 0.15%, more than our specified precision. Fortunately, the T-network

loads the amplifier output. The load resistance seen at the amplifier output is 2.4 MΩ(see Section 5.7.5) which is comparable to the intrinsicRout of the OTA. Because of this

loading, the effective TC ofRout is halved, and is just within the specified 0.1% precision

for the desired temperature budget. This result is fortuitous, as there are generally no simple

methods for stabilizing the output resistance of the amplifier against temperature changes.

The sensitivity to changes inCL is included in Figure 5.15 for completeness. The

simulated 50 pF load capacitance is primarily external to the CMOS die and is expected to

have very small temperature dependence.

5.11 Model Parameter Estimation from Tone Data

Recall from Section 2.3.5 that best-fit parameter values forCsur f, Rsol, and Rleak are

extracted from impedance values measured at different frequencies using a complex

nonlinear least squares (CNLS) regression. Each of the impedance measurements has an

associated uncertainty arising from circuit noise. Because of the complicated mathematics

of the fitting process, however, the uncertainty of the best-fit parameters cannot be

5.12. PUTTING IT TOGETHER: REQUIRED CIRCUIT SNR 141

computed by a straightforward application of the error propagation formulas discussed in

Section 5.6. Furthermore, the sensitivity of the parametervalues to errors in impedance

values depends on what circuit component dominates the total ZDUT at that frequency.

Along with the best-fit parameters, the CNLS algorithm produces a confidence estimate for

each parameter based on how much that value could change without significantly altering

the goodness-of-fit. This confidence estimate is empirical and not rooted in the actual

uncertainty of each impedance measurement.

It is reasonable to expect that measuring the impedance at 13different frequencies

each with 0.1% precision may enableCsur f determination to better than 0.1%. But we

cannot say how much better, if at all. Furthermore, a common measurement approach for

impedance biosensors is to forego spectral measurements and instead monitor changes at a

fixed frequency whereZDUT is known to be sensitive to target binding. Thus, we are careful

to specify the required impedance precision as 0.1% for a single frequency measurement.

5.12 Putting it Together: Required Circuit SNR

We conclude at the end of Section 5.6 that if each of the two channels (one forZDUT , the

other to acquireVtest indirectly) has 63 dB of SNR then the impedance could be calculated

with a precision of 0.1%. We add a 12 dB margin to our design goals, in case the transistor

noise models are not accurate. Thus we aim to have 72 dB SNR forZDUT determination

(or 75 dB for each channel).

Having some information about the final (simulated) OTA design, we assume that the

output swing will be about±800 mV with adequate gain. We can compute the maximum

input excitationVtest such thatVout is within that swing andVtest is less than 5 mV, shown

in Figure 5.16. The total noise referred to the system input is summarized in Figure 5.17

from the plots in Section 5.9. The ratio of the maximum signalto the total noise yields the

SNR of the transfer function. This SNR is then multiplied by the sensitivity ofT to ZDUT

to yield the SNR of theZDUT determination, shown in Figure 5.18.5

Obtaining of the SNR ofZDUT determination (Figure 5.18) has been the primary object

of this chapter. The SNR increases with frequency until about 20 kHz primarily because

5this includes a SNR loss of 3 dB because bothV1 andV2 have noise as discussed in Section 5.6.3.


102

103

104

105

0

1

2

3

4

5

Frequency [Hz]

Max

imum

Exc

itatio

n A

mpl

itude

[mV

]

Maximum Excitation Amplitude

Maximum ZDUT

Typical ZDUT

Minimum ZDUT

Figure 5.16: Simulated maximum excitationVtestfor theZDUT corners.

the 1/ f noise of the OTA decreases. Simulations suggest that our circuit design meets the

desired SNR specifications over the entire frequency range.This result is no coincidence,

for we used these Matlab scripts to understand the requirements for the OTA and designed

the circuitry accordingly. The design is described in the next chapter.

5.12. PUTTING IT TOGETHER: REQUIRED CIRCUIT SNR 143

102

103

104

105

10−16

10−15

10−14

10−13

Frequency [Hz]

Vn2 a

t sys

tem

inpu

t [V2 /H

z]

Total Noise PSD Referred to System Input

Maximum Z

DUT

Typical ZDUT

Minimum ZDUT

Figure 5.17: Simulated total noise density referred to the system input for theZDUT

corners.


102

103

104

105

70

75

80

85

90

95

100

105

Frequency [Hz]

SN

R [d

B]

ZDUT

SNR (T SNR + ZDUT

sensitivity + Excitation)

Maximum ZDUT

Typical ZDUT

Minimum ZDUT

SNR Spec

Figure 5.18: Simulated SNR ofZDUT determination for theZDUT corners.

Chapter 6

CMOS Design

Having established the requirements for the integrated measurement circuitry in the

preceding chapter, we now discuss its implementation. Design of the operational transcon-

ductance amplifier (OTA),1 which forms the core of the transimpedance amplifier (TIA),

is considered in Sections 6.1 through 6.10. The tone cancellation circuitry, which enables

the simultaneous measurement of the nonlinearity by eliminating the large-amplitude, low-

frequency excitation from the output, is explained in Sections 6.11 to 6.18. The final section

describes the circuit layout.

6.1 OTA Specifications

We saw in Sections 5.8 and 5.9 that the amplifier noise is the dominant noise source,

and that the total noise determines the precision of the impedance measurement. Thus,

minimizing the noise of the OTA is of paramount importance.

For a fixed gain, maximizing the output swing increases the allowable input signal,

and therefore increases the precision of the impedance measurement, as described in

Section 5.12. To increase the available swing, we implementthe OTA using 3.3 V I/O

transistors (Lmin = 0.4 µm), instead of the 1.8 V core transistors.

Minimizing temperature sensitivity of the overall transfer function T (see Sec-

tion 5.10.2) necessitates the use of a constant transconductance bias network. For the same

1recall that an OTA is essentially an op-amp without an outputbuffer

145

146 CHAPTER 6. CMOS DESIGN

reason,Rout must be made as large as possible so thatT (and its corresponding temperature

sensitivity) is determined more byZf than byRout.

The OTA must be stable with the chosen capacitive feedback and with any additional

off-chip loading. It should have sufficient output current to drive its load at the maximum

excitation frequency and the maximumT. The choice of feedback network affects these

requirements, and discussed in Sections 5.7.3 and 5.7.4.

As detailed in Section 5.4.3, our power allowance is about 500 µA per pixel from a

3.3 V supply, of which we allot 400µA to the OTA.

Finally, the die area of the OTA core must stay within the limits described in

Section 5.4.2, or 200µm on a side (corresponing to about 25% of the pixel area) as a

rough bound.

6.2 Folded Cascode Architecture

We decided to use the folded cascode OTA architecture after studying the trade-offs

associated with different architectures [278]. Benefits ofthe folded cascode include

low noise (if the input stage carries most of current), largeoutput swing, graceful

accommodation of load capacitance owing to a dominant pole at output, and reasonable

input common-mode range.

The final transistor-level OTA design is shown in Figure 6.1,with associated transistor

dimensions in Table 6.1. The ratiogm/Id listed in the final column is a measure of

“transconductance efficiency” and provides a useful way of speaking about the inversion

level of transistors:gm/Id values approaching 20 are subthreshold and values below 4 are

in strong inversion or saturation. We will see that thegm/Id ratio is useful in analyzing

amplifier noise. For a fixed transistor length, thegm/Id bias point is controlled by the

current density.

The next sections will address various aspects that lead to this final design.

6.2. FOLDED CASCODE ARCHITECTURE 147

VddVdd

Vin, p Vin, n Vout

Vcasc, p

Vbias, n

Vcasc, n

M1a M1b

M2a M2b M2a M2b

M3bM3a

M4a

M5a M5b

M4b

M7

15I I

M6a M6b

I15I

30I

Vbias, p

Figure 6.1: Final folded cascode design

Device W/L gm/Idµm /µm V−1

M1a,b 720/4 13.2M2a,b 256/8 3.1M3a,b 128/1 18M4a,b 64/4 15.1M5a,b 64/4 14.8M6a,b 60/1 8.5M7 120/6 4.0I 12.7µA

Table 6.1: Transistor dimensions for folded cascode design.


6.3 Transistor Noise

Chapter 5 explains how electronic noise limits the achievable SNR and thus the measurable

change inZDUT . This section provides background information on transistor noise relevant

to the OTA design described in the following section.

6.3.1 Thermal noise

The noise power spectral density due to the channel resistance’s thermal noise is [269]

i2n,ds= 4kTγgd0 (6.1)

where ideallyγ is 2/3 in saturation and unity in the triode regime (suggesting that thermal

noise in weak inversion may be slightly higher than in saturation for identicalgm). For long-

channel devices,gd0 is the same asgm in saturation, hence the more common statement

[278] that

i2n,ds= 4kTγgm. (6.2)

If we refer the drain current noise density to the input gate,we obtain

V2n,gs= 4kTγg−1

m (6.3)

which suggests that increased transconductance reduces input-referred noise. When a

transistor is used as a switch it operates in the triode regime and the resulting noise is

V2n,gs= 4kTRon. (6.4)

6.3.2 Flicker noise

Flicker noise is often called 1/ f noise because its power spectral density (PSD) is inversely

proportional to frequency. It is widely held that flicker noise in MOSFETs arises from

carrier traps in the oxide whose occupancy fluctuates on relatively long time scales, causing

small random changes in the threshold voltage [279, 280, 281]. Hung’s physics-based

6.3. TRANSISTOR NOISE 149

model agrees well with measurements [282] and a simplified version is given in Equation

6.6. It has also been shown that large signal excitation can reduce 1/ f noise, presumably

by (re)setting the traps to a known state [283, 284, 281]. Because the fabrication details of

NMOS and PMOS devices differ, the mechanism for noise in these devices may also differ

[285].

The conventional models for drain current and corresponding gate-referred flicker noise

PSD in MOSFETs is [269, 278]:

i2n,ds,1l f =K f

Cκox

g2m

WL1

f β (6.5)

V2n,gs,1/ f =

K f

Cκox

1WL

1

f β (6.6)

whereK f is a process-dependent constant,κ is either 1 or 2 depending on the model

formulation (κ = 2 in Hung’s model),β ' 1, and the other parameters have their usual

meaning. It is readily observed that flicker noise is reducedby using transistors with large

area and thinner gate oxide, all else held equal.

It is widely held that PMOS devices intrinsically have less 1/ f noise, because of the

common observation that they are less noisy (e.g. [280]). However, this difference is

thought to be due to the buried channel used in traditional PMOS devices and the noise

advantage of PMOS transistors is process-dependent [269].

It is generally agreed that subthreshold biasing yields thebest input-referred 1/ f noise

performance. This is attributable to the relatively highgm/Id, giving more transconductance

(and hence gain) for a fixed current [286, 287, 273], and also because a capacitive divider

with the depletion capacitance reduces the fraction of noise that appears between the gate

and source [280]. However, thermal noise in the subthreshold region increases, so care is

required in carrying out any specific design [286].

6.3.3 Noise simulations

To make informed decisions about the OTA architecture it is important to understand the

noise properties of the transistors available to us. Using the provided device models,

simulations of both NMOS and PMOS transistors in a simple configuration allows


extractions of the input-referred noise at low frequencies, at differing operating points.

Flicker noise, modeled by Equation 6.6, is the dominant noise source in our frequency band

of interest (0.1–100 kHz), and so we extract the process-dependent flicker noise scaling

parameterK f as a proxy for transistor noise. Although we expect the 1.8 V devices to have

less flicker noise, we need to use the 3.3 V devices to obtain sufficient output swing. For

comparison purposes, we vary the overdrive voltageVov = Vgs−Vth and transistor length

while maintaining a width of 1µm andVds= 1 V.2

Our simulations suggest that NMOS devices have slightly less input-referred flicker

noise than PMOS devices in our process. Furthermore, longerchannels lead to lower

noise even more than Equation 6.6 predicts (i.e.K f decreases with length). The rule of

thumb that subthreshold transistors provide superior flicker noise performance applies. The

frequency scaling factorβ is not unity for either polarity of transistor based on our models;

for NMOS it is slightly smaller and for PMOS slightly higher.We conclude that we should

use relatively long NMOS input transistors biased with low overdrive voltage (subthreshold

or near threshold) for lowest flicker noise.

6.4 Minimizing OTA Noise

In analyzing the OTA noise in this section, we consider only the dominant flicker noise.

We refer the contributions of each transistor to the OTA input as voltage noise. We refer to

the design shown in Figure 6.1.

6.4.1 Input devices

We expect the dominant noise source to be the input transistor because it is subject to

the entire amplifier gain, whereas noise injected in later stages is amplified less [269]. It is

apparent from Equation 6.6 that increasing the dimensionsW andL will decrease the flicker

noise of these devices. Increasing the area proportionately increases the amplifier input

2To simulate the noise voltage, the transistor drain must be loaded by a high impedance, not tied to avoltage source. We determine the current flowing through a transistor with a voltage source biasingVds andthen apply that same current to an identical transistor via an ideal current source. The noise of the this seconddevice is extracted from the simulator. In an actual circuit, we expect the load transistors to have a high outputresistance compared tog−1

ds , justifying our simulation with a current source load.

6.4. MINIMIZING OTA NOISE 151

capacitance, which is problematic in many cases. In our case, however, input capacitance

is of negligible importance because the amplifier input is a virtual ground and the source

impedance of the current is relatively low. Thus, we are freeto use very large input

transistors to reduce the noise, limited only by the available die area and available current.

Based on simulations described in the previous section, we use NMOS input transistors

because they have slightly less 1/ f noise and higher transconductance (for higher OTA

gain) for a given current. We bias the input devices in moderate inversion to reduce

noise, withgm/Id ' 13. UsingL = 4 µm gives a reasonable width (W = 720 µm) for

this transconductance efficiency and our budgeted current (200µA each branch).

6.4.2 Cascode devices

Cascode devices are common-gate stages which act as unity current buffers, potentially

turning a non-ideal current source into one with a larger output impedance. Until the

frequency is high enough that the gate capacitance becomes important (much larger than

100 kHz), gate voltage fluctuations caused by noise in the cascoding devices add no noise

to the system. Thus, transistors M3, M4, and M6 contribute nonoise.

Unless intrinsic capacitance is an issue, it is desirable for cascode devices to be biased

at largegm/Id, both to maximize the output resistance and to minimize the requiredVds to

remain in saturation.

6.4.3 Load devices

The flicker noise voltage of the load devices (M2 and M5) is referred to the OTA input

by multiplying by thegm of the device in question, reflecting the resulting current to the

input transistors, and then dividing by thegm of the input transistors. Thus load devices

should have small transconductance compared with the inputdevices for reduced noise,

suggesting that the load transistors should have a smallgm/Id ratio.


6.4.4 Total noise

Referring to Figure 6.1 and assuming for simplicity that alldevices have the same value of

K f , we can write the total input-referred noise as

V2n,in = 2

K f

f

(

1W1L1

+1

W2L2

(

gm,2

gm,1

)2

+1

W5L5

(

gm,5

gm,1

)2)

. (6.7)

Plugging in values from Table 6.1 we can write

V2n,in = 2

K f

W1L1 f

(

1+W1L1

W2L2

(

16I(gm/Id)2

15I(gm/Id)1

)2

+W1L1

W5L5

(

I(gm/Id)5

15I(gm/Id)1

)2)

(6.8)

' 2K f

W1L1 f

(

1+1.41

(

16(3.1)15(13.2)

)2

+11.3

(

1(14.8)15(13.2)

)2)

' 2K f

W1L1 f(1+0.09+0.06)

We estimate that the total input-referred noise is only 15% more than the noise inherent in

the input devices themselves. The noise contribution from the PMOS load devices (M2a,b)

is minimal because they have a smallgm/Id value compared with the input devices (i.e. they

have higher current density). For the NMOS output-stage NMOS loads (M5a,b), we use a

largegm/Id to increase the output swing, reducing the noise contribution by using only 7%

of the input stage current in the output stage.

6.5 Effectivegm

In a slight variation of the traditional folded cascode design, we add cascode devices M6a,b

to the input branch to ensure that the effective transconductance of the OTA approaches

the transconductance of the input devices (M1a,b). The input devices are wide because

they carry almost all of the total current. Unfortunately they then possess a small output

resistance that shunts some of the differential output current.

6.6. STABILITY ANALYSIS 153

To mitigate this effect, we boost the output impedance of theinput branch by adding

cascode devices M6a,b. As a result, the OTA’s effective transconductance is nearly identical

to that of the input devices. In contrast, without M6a,b about half the transconductance

is lost. Additionally, the cascode devices improve stability by reducing the parasitic

capacitance at the folding node.

6.6 Stability Analysis

One motivation to choose the folded cascode OTA architecture is its ease of compensation

to avoid spontaneous oscillation. The dominant pole is formed by feedback capacitorCf

in combination with the amplifier’s output resistance,Rout. Any capacitance added to

the amplifier output (e.g. bond pads, an ADC input off-chip) will make the OTAmore

stable, whereas loading generally decreases stability in other architectures that depend on

an internal dominant pole. The unity gain frequency is givenby gm,in/Ctotal.

The lowest-frequency non-dominant pole is formed by the capacitance at the M2/M3

junction and thegm of M3 [288, 278]. The cascode devices M6a,b help reduce the

capacitance at this node because they are smaller than the large input devices.

Simulations usingCf = 25 pF as the only amplifier load give a 40 phase margin over

all process corners. The final design uses a somewhat larger feedback capacitance (30 pF),

making the system correspondingly more stable. Any added load capacitance from the

bondpad and external connections will further stabilize the frequency response.

6.7 Slewing Analysis

Our amplifier design uses only a small fraction of its total current in the output stage, so

we must ensure that sufficient slew current is available to drive the anticipated load. The

current available for slewing is the total output stage current, 2I ' 25 µA. The current

required to drive the loadCtotal =Cf +CL is

Islew=CtotaldVout

dt =(

CL+Cf)

(2π f0)Vin T (6.9)


where we have assumed a pure sinusoidal output with frequency f0. Note that the required

current is proportional to frequency. Fortunately, the transfer functionT is inversely

proportional to frequency above about 20 kHz (see Figure 5.5). Under the worst-case

scenario ofCL = 100 pF and minimumZDUT , the maximum slewing current is less than

9 µA for a 5 mV input excitation at 100 kHz, or only 40% of the available current. Thus, we

are not in danger of being slew-limited even though only a small fraction of the quiescent

current is allocated to the output branch.

6.8 Cascode Biasing

The output swing of the amplifier is a key factor in limiting the system SNR. If the swing

is larger, the input signal can be larger, which leads to a higher SNR and more precise

impedance measurement. The key to maximizing the swing is generating appropriate

cascode bias voltagesVcasc,n andVcasc,p in Figure 6.1. IfVcasc,n is too high, swing will

be reduced because a lowVout will cause the cascode device M4b to fall out of saturation

and no longer provide a large output resistance. If, on the other hand,Vcasc,n is too low, then

devices M5a,b will not have enoughVds to remain in saturation and the output resistance

similarly plummets. We need to generate bias voltages whichgive sufficientVds to M5a,b

and M2a,b without wasting headroom.

We use a modified “magic battery” circuit which utilizes a small device to generate

a voltage of approximately 2Vov, the minimumVds for proper operation [289]. Shown

in Figure 6.2, it utilizes devices with the same current density as the main amplifier for

maximum accuracy.Vre f is the voltage applied to the noninverting input of the OTA, and

ensures that the bottom NMOS devices have the sameVds as current source device M7 in

the OTA.

One instance of this bias generating circuit is placed in each pixel. A master bias current

is distributed to each pixel from the constant-gm circuit discussed in the next section.

The simulated gain of our single-ended OTA, shown in Figure 6.3, exceeds 72 dB over

a span of about±800 mV centered at 1.35 V. Because the OTA input voltage is the same as

the quiescent output voltage in the TIA configuration, we bias the OTA usingVre f = 1.35.

6.8. CASCODE BIASING 155

Vdd

Vcasc, p

Vbias, n

Vref Vcasc, n

Vbias, p

WL

(1/4)

WL

(1/4)

I/2

II

2I

current fromconstant-gmcircuit

I/2

Figure 6.2: Circuit to generate bias voltages for the foldedcascode amplifier shown inFigure 6.1.


0 0.5 1 1.5 2 2.5 30

1000

2000

3000

4000

5000

6000

7000

8000

Vout

[V]

Gai

n [V

/V]

Gain of Main Amplifier (Simulated)

Figure 6.3: Simulated OTA gain vs. output voltage for typical transistor corner.

6.9. CONSTANT-GM BIASING 157

6.9 Constant-gm Biasing

6.9.1 Motivation

In Section 5.10.2 we note the requirement that the amplifier input transconductance be

insensitive to changes in temperature, so that a 1C change in ambient temperature will

lead to a change in the TIA transfer functionT of much less than 0.1%. However, using

conventional biasing, the TC ofgm,in is 2000 ppm/ C, corresponding to a 0.1% change

in T for a 1 C temperature change. Constant-gm biasing is a strategy to stabilize the

transconductance of a transistor against variations in process, supply voltage, and also

temperature. We are primarily interested in the latter.

6.9.2 Traditional constant-gm bias

Constant-gm biasing is treated briefly in many circuit design textbooks such as Lee [269]

(section 10.6) and Baker [290] (section 20.1). A basic circuit is shown in Figure 6.4.

It involves a pair of transistors with equal drain currents and gate voltages, but different

gm/Id. One of the transistors (M2) is wider by a factorm and degenerated with resistor

R.3 The simultaneous decrease inVov andVgs results ingm being determined bym andR,

instead of characteristics such as process, supply, and temperature. Furthermore, because

both m andR are under designer control, transconductance can be tightly specified. The

gate voltage of M1/M2 can then act as a master bias for slave devices, conferring on them

the gm properties of M1/M2. A final motivation to use constant-gm biasing is to have an

external “knob” inR to adjust the current consumed by on-die circuits with greater control

than a bias voltage affords.

With the simplifying assumption that M1 and M2 are long-channel devices biased in

strong inversion and neglecting back-gate bias effects,gm andId are given by

gm =2IdVov

(6.10a)

Id =12

µCoxWL

V2ov (6.10b)

3R can be on-chip, off-chip, or even a switched capacitor resistive equivalent [291].


Vdd

R

M1 M2

WL

WLm

I

VbiasN

M7

kIkI

constant gm generator biased amplifier

Vin

LW2k

M1a M1b

I gm,ingm,in

Figure 6.4: A simple constant-gm bias circuit and associated differential pair.

whereVov ≡ Vgs−Vth. From these idealized long-channel equations, it can be shown that

the transconductances of M1 (dimensionsWL ) and M2 (dimensionsmW

L ) are

gm,1 =2R

(

1− 1√m

)

(6.11a)

gm,2 =2R

(√m−1

)

= gm,1√

m (6.11b)

These are the classic expression for constant-gm biasing. Lee provides some advice on

approaching the implied performance in practice, making sure the transistors satisfy the

prior assumptions of being long-channel devices in strong inversion [269].

6.9.3 Shortcomings in traditional constant-gm bias

Expressions 6.11a and 6.11b do not explicitly include a temperature term, but it can be

seen that at least one ofgm,1,gm,2 must vary with temperature. The current density in

M1 and M2 is different by a factorm, meaning they operate at differentgm/Id. As the

temperature increases,I must increase to maintain the samegm despite reduced carrier


mobility. BecauseI changes and the devices have differentgm/Id ratios, thegm of the

devices will change differently (the current mirror enforces Id,1 = Id,2). In practice, the

current-temperature relationship of M1 and M2 will strike acompromise such that the

gm values have opposite temperature coefficients (each of which is relatively small in

magnitude).

Equations 6.11a and 6.11b do not hold outside of strong inversion because the

relationships used to derive them, Equations 6.10a and 6.10b, only apply in strong

inversion. Nicholson and Phang showed that constant-gm biasing is also possible in the

weak inversion (i.e. subthreshold) regime [292]. In moderate inversion, unfortunately,

there are no closed-form equations relatingVov, gm, and Id, and the technical literature

conspicuously lacks methods for constant-gm biasing in this region. However there

are general methods for using a reference conductance to settransconductance through

conventional feedback arrangements.

6.9.4 Proposed constant-gm bias

Our application demands that the main amplifier’s input devices have stable transconduc-

tance (gm,in) over temperature. As discussed in Section 6.4, our OTA input devices operate

in moderate inversion (gm/Id ∼ 13, orVov ∼ 4VT) for noise reasons. Note that biasing the

current source transistor (M7 in Figure 6.4) for constant-gm does not produce the intended

effect. If M1/M2/M7 are all in strong inversion,gm,7 will be relatively independent of

temperature as desired, butgm,in will vary with temperature because the input transistors

operate at differentgm/Id. On the other hand, operating the current source M7 in moderate

inversion is undesirable because its output resistance will decrease.

Our idea, shown in Figure 6.5, is to bias transistors M1 and M2with gm/Id ratios on

either side of the input transistors’gm/Id ratio, meaning(gm/Id)M1 <(gm/Id)in <(gm/Id)M2.

This is easily arranged by choosing 1< nk < m. As the temperature changes,gm,1 andgm,2

will change in opposite directions, but the resulting current will have approximately the

correct dependence on temperature to maintain constantgm,in. A current mirror transfers

this current to M7, which is operated in strong inversion even though input transistors

M1a,b operate in moderate inversion for constant transconductance. Transistors M1 and


Vdd

R

M1 M2

WL

WLm

I

VbiasN

M7

kI

constant gm generator biased amplifier

Vin

L2

W22k

M1a M1b

gm,in

M7a

W2L2

I WLn

kI

Figure 6.5: A modified constant-gm bias circuit and associated amplifier.

M2 are chosen to have the same length as the input devices M1a,b to keep length-dependent

effects from introducing errors.

6.9.5 Implementation

Following the proposal of the last section, we use ratiom= 3 for the devices in the constant-

gm network, where the amplifier input devices have a current density corresponding to

m= 2. The correspondinggm/Id values are 10.7 (M1), 13.3 (M1a,b), and 14.9 (M2).

Temperature changes will affectgm of M1 and M2 in such a way that the resulting

current I will hold gm approximately constant for devices that have intermediategm/Id

such as M1a,b. Simulations of the temperature performance show that the TC ofgm,in

remains within±100 ppm/ C over all process corners. Figure 6.7b shows the temperature

dependence of the circuit at the typical process corner.

Using our technique, simulated changes inT due to changes ingm,in with the

allowed 1C temperature change is 0.005%, well within the specification of 0.1%, or


Vdd

R

M1 M2

WL

WL3

2I

VbiasN

M7

constant gm biased amplifier

Vin

15

M1a M1b

gm,in

M7a

W’L’

2I

WL15

15I

startup network

W’L’

WL

1u32u

4u3u

L=4uW=48u

W’=8uL’=6u

Ma

Mz

McMb acrosschip

36 replicas

15I

Figure 6.6: Implemented constant-gm circuit, including relevant parts of the mainamplifier.


an improvement of 26 dB compared with the case without constant-gm biasing. Note that

gm,in will vary over process, but this variation is acceptable forour application.

We cascode M1/M2 and the PMOS mirror devices in the constant-gm cell for improved

Id matching. Other techniques, such as those involving feedback [293, 291], can be used

for low-headroom designs.

Placing as much of the resistanceR on-chip as possible avoids stability problems with

parasitic bondpad capacitance [292]. Analysis shows that including a 2 kΩ resistor on-chip

is possible. An external potentiometer with nominal value 800Ω is used to tune the current

to account for process variations and inaccuracy in the on-chip resistor.

The constant-gm network of Figure 6.5 is regrettably stable at zero current,so a startup

circuit is required. As shown on the left of Figure 6.6, we usea startup network similar

to [294] in which a very weak PMOS pull-up device Mz initiallyleaks current into Ma.

This leakage current turns on Mb and Mc, forcing current to flow in the main constant-

gm network. Once the main circuit is in its desired state, transistors Mb and Mc have

negativeVgs and turn off, so the startup network consumes negligible current during regular

operation.

6.10 OTA Offset

The I/O devices used for the OTA design have Pelgrom coefficients of 9.6 mV µm. For

our input devices this value corresponds to an estimated random offset of 0.2 mV in each

device, or a standard deviation of less than 0.3 mV for the overall amplifier offset. Even

though the resistive T-network amplifies the offset by factor of G= 11, OTA offset voltages

are not critical, partly because a dynamic cancellation mechanism removes the DC offset.

6.11 Overview of Two-tone Measurement

We now discuss the tone cancellation scheme which enables two-tone excitation for

simultaneous measurement of impedance and nonlinearity.

Recall from Section 4.4 that the nonlinearity of the electrode-electrolyte impedance

ZDUT can be approximated as

6.11. OVERVIEW OF TWO-TONE MEASUREMENT 163

0 10 20 30 40 50268

270

272

274

276

278

M1

Tra

nsco

nduc

tanc

e [u

S]

Temperature [degC]

gm

of Constant−gm

Transistors vs. Temperature

0 10 20 30 40 50368

370

372

374

376

378

M2

Tra

nsco

nduc

tanc

e [u

S]

(a) The transconductance of M1 and M2 in the constant-gm network haveopposite temperature dependencies.

0 10 20 30 40 50

2515.8

2516

2516.2

2516.4

2516.6

2516.8

2517

2517.2

Inpu

t Tra

nsco

nduc

tanc

e [u

S]

Temperature [degC]

gm

of Input Transistors vs. Temperature

(b) The transconductance of the input transistor changes byless than0.06% over 50C by use of the novel constant-gm network.

Figure 6.7: Simulated temperature dependence ofgm of relevant transistors in ourconstant-gm circuit.


ZDUT(ω) = Z0(ω)[

1+α1(ω)Vin+α2(ω)V2in

]

, (6.12)

where parametersα1 andα2 represent the linear and quadratic voltage-dependence of the

impedance being measured. As explained in Section 5.3.6, our objective is to quantify

the nonlinearity coefficientsα1 andα2 within 1% of their full-scale values of 1 V−1 and

10 V−2, respectively.

We use the two-tone excitation method described in Section 4.4 with a 50 mV input tone

at ωB = 17 Hz to vary the bias point. That excitation combines with the small-signal tone

at ωA (swept from 100 Hz to 100 kHz) in the nonlinear DUT to generateintermodulation

(IM) tones atωA±ωB andωA±2ωB that are proportional to the nonlinearity coefficients

α1 andα2. Changes in nonlinearity can be inferred from changes in IM tone amplitudes.

We will see that the mixing tone amplitudes are small relative to the main tone atωA but

above the noise floor.

6.11.1 IM tones generated fromZDUT

Here we compute the amplitude of the IM tones generated by theDUT nonlinearity. These

will be compared with the IM tones generated from the measurement circuit to ensure that

the latter are negligible.

We adopt the convention of writing the amplitude of a tone at frequencyω as‖ω‖. The

input tone amplitudes are‖ωA‖in ≤ 5 mV and‖ωB‖in = 50 mV, and output tones have

amplitudes‖ωA‖out = ‖ωA‖in |T(ωA)| and ‖ωB‖out, whereT(ω) represents the transfer

function at frequencyω (which depends onZ0). The intermodulation (IM) tones from

nonlinearity ofZDUT nearωA derived in Equation 4.10 can be restated in this terminology

as

‖ωA±ωB‖out = 12α1‖ωA‖in‖ωB‖in |T(ωA±ωB)| (6.13a)

‖ωA±2ωB‖out = 14α2‖ωA‖in‖ωB‖2

in |T(ωA±2ωB)| (6.13b)

6.12. WHY IS TONE CANCELLATION NEEDED? 165

To determine whether changes in these IM tones can be distinguished from noise, the

IM tones at the OTA output can be converted into equivalent input tones4 and compared

with the total input-referred noise (computed in Section 5.8 and plotted in Figure 5.17).

Using the full-scale values forα1 andα2, we obtain the plots of SNR vs. frequency shown

in Figure 6.8. The SNR is above 40 dB in both cases, suggestingthat changes of 1% in

their full-scale values can be detected in the presence of the expected electronic noise.

6.12 Why Is Tone Cancellation Needed?

At ωB = 17 Hz, the magnitude of the TIA transfer function|T| is between 10 and 60,5

which means that the corresponding output tone’s magnitude(without any cancellation,

and in the absence of swing limitations) would lie between 0.5 V and 3 V. The swing of the

OTA is ±800 mV, so such a large tone would saturate the OTA output and make accurate

quantification any of the tonesωA±nωB impossible. Furthermore, the compression at the

edges of the swing would mix theωA andωB tones, confounding detection of the IM tones

generated by the DUT. Neither concern is relevant with the PCB implementation of the

measurement circuit because the commercial op-amps used operate from±8 V supplies.

Our integrated implementation uses a 3.3 V supply voltage, however, so modification is

needed to permit simultaneous measurement of the nonlinearity and impedance. Hence,

we need to include tone cancellation circuitry to reduce theamplitude of theωB tone at the

OTA output.

6.13 Tone Cancellation Requirements

The ωB tone at the OTA output will mix with theωA tone due to the (slightly) nonlinear

transfer function of the TIA. Here we calculate how large aωB tone can be present at the

OTA output (‖ωB‖out) without generating significant intermodulation from thissource.6

4the expressions in Equation 6.13 are input-referred by simply dividing by T5depending on the exact value ofZDUT within the limits we determined; see Section 5.3.56“significant” being defined as affecting the measurement ofα1 andα2 more than the desired precision


102

103

104

105

50

55

60

65

70

75

80

Frequency [Hz]

SN

R [d

B]

SNR for ωA

± ωB

Minimum Z

DUT

Typical ZDUT

Maximum ZDUT

(a) SNR forωA±ωB.

102

103

104

105

40

45

50

55

60

65

70

75

Frequency [Hz]

SN

R [d

B]

SNR for ωA

± 2ωB

Minimum Z

DUT

Typical ZDUT

Maximum ZDUT

(b) SNR forωA±2ωB.

Figure 6.8: SNR plots for IM tones show that they can be quantified within 1% (40 dB)as desired.

6.13. TONE CANCELLATION REQUIREMENTS 167

The allowable residualωB tone determines how effective the tone cancellation needs to be.

The aim of this section is to determine the maximum allowable‖ωB‖out.

Because the amplifier gain is much larger than the TIA transfer function,7 the circuit-

derived intermodulation ofωA and ωB will arise primarily from the nonlinearity of the

feedback impedanceZf . Determining the allowable‖ωB‖out requires an estimate of the

the nonlinearity coefficientsβ1 andβ2 of the integratedRf andCf that form the feedback

network.

6.13.1 Nonlinearity ofCf

Our process specifications state that the typical nonlinearity of a poly-poly capacitor is

10 ppm V−1 with a maximum of 30 ppm V−1, but no specific information regarding

second-order nonlinearity is provided. Baker suggests that poly-poly caps have voltage

nonlinearity in the neighborhood of 10 ppm V−1 [290], whereas Razavi offers more

pessimistic estimates of 500 ppm V−1 and 50 ppm V−2 [278]. Older texts from Tsividis

and Laker estimate 100 ppm V−1 and 50 ppm V−1 respectively [295, 296]. The spread in

values reflects the effects of evolving and variable processtechnology options.

6.13.2 Nonlinearity ofRf

The voltage linearity of unsilicided p-poly resistors (thetype we use) is the best of all

available CMOS resistors [269]. Unfortunately, our designmodels contain no information

about nonlinearity and we must extrapolate from other sources. Baker’s text gives

nonlinearity coefficients in a typical submicron CMOS process as 600 ppm V−1 and

150 ppm V−2 [290]. Laker, on the other hand, estimates the nonlinearityas 200 ppm V−1

[296], while Allen and Holberg state that 100 ppm V−1 [297] is typical.

Importantly, the nonlinearity of the synthesized equivalent resistor using a T-network is

never greater than the nonlinearity of its component resistors. This was verified by SPICE

simulation, using all possible combinations of nonlinearity polarity.

7compare Figure 6.3 with Figure 5.5 if in doubt


6.13.3 Nonlinearity ofZf

Based on the above information, we useZf nonlinearity coefficients ofβ1 = 500 ppm V−1

andβ1 = 500 ppm V−2 for our calculations. Our estimates are probably very pessimistic,

especially becauseCf dominates the totalZf over most of the relevant frequency range and

its first-order nonlinearity is known to be 16 times less thanthe assumed value.

6.13.4 Mixing ofωB and ωA tone arising from Zf

Here we derive the maximum residual signal atωB (‖ωB‖out) that can be tolerated at the

amplifier output without affecting the determination of theDUT nonlinearity coefficients

by unwanted mixing of components atωA andωB arising from the slightly nonlinearZf .

The IM tones arising fromZf are given by

‖ωA±ωB‖out,Z f = β1‖ωB‖out‖ωA‖out (6.14a)

‖ωA±2ωB‖out,Z f = β2‖ωB‖2out‖ωA‖out. (6.14b)

First we compute the first-order nonlinearity. To ensure that ‖ωA±ωB‖out,Z f will not

affect the measurement ofα1, we require that it be less than the change in theωA±ωB tone

arising from the minimum detectable change inα1, ∆α1. Mathematically, we require that

β1‖ωB‖out‖ωA‖in |T(ωA)| < 12∆α1‖ωA‖in‖ωB‖in |T(ωA±ωB)|

‖ωB‖out

‖ωB‖in/

∆α1

2β1(6.15)

where we have made the assumption that|T(ωA)| ' |T(ωA±ωB)| because the transfer

function is relatively smooth andωB ωA. This result tells us that the effective transfer

function magnitude atωB (with tone cancellation) must be less than the worst-case value

of ∆α12β1

= 10.

Now we compute the second-order nonlinearity. To ensure that ‖ωA±2ωB‖out,Z f will

not affect the measurement ofα2, we require that it be less than the change in theωA±2ωB

tone arising from the minimum detectable change inα2, ∆α2. Mathematically, we require

6.13. TONE CANCELLATION REQUIREMENTS 169

that

β2‖ωB‖2out‖ωA‖in |T(ωA)| < 1

4∆α2‖ωA‖in‖ωB‖2in |T(ωA±ωB)|

‖ωB‖out

‖ωB‖in/

√

∆α2

4β2(6.16)

which means that the effective transfer function magnitudeat ωB (with tone cancellation)

must be less than the worst-case value of√

∆α24β2

= 7.

The native transfer function’s magnitude atωB = 17 Hz is between 10 and 60,

depending on the exact value ofZDUT , or almost 20 dB more than allowed in the worst

case. From considerations ofZf linearity it is apparent that the tone cancellation must

attenuate the transfer function atωB by at least 20 dB. Based on linearity considerations,

the allowable amplitude of theωB tone at the output can be 300 mV at most.

6.13.5 Swing considerations

As noted in Section 6.12, another reason to cancel the low-frequency tone is to maximize

the output swing available for the primary tone atωA as well as for the intermodulation

tones. Even if theωB component is reduced by 20 dB, the maximum output amplitude

of 300 mV atωB still consumes nearly 40% of the OTA swing. As theωB tone contains

no useful information, we wish to maximize the swing available for the primaryωA tone.

Consequently our goal is to ensure that theωB tone consumes no more than 50 mV of the

swing. This criterion is satisfied if the tone cancellation circuitry ensures that the effective

transfer function atωB is unity or less.

6.13.6 Other possible sources of IM tones

Other confounding tones can arise from various combinations of the DUT-generated IM

tones mixing again by the nonlinearZf , including


‖ωA±2ωB‖out = β1‖ωA‖out‖2ωB‖out (6.17a)

‖ωA±2ωB‖out = β1‖ωA±ωB‖out‖ωB‖out (6.17b)

‖ωA±2ωB‖out = β1‖ωA±ωB‖out‖3ωB‖out (6.17c)

‖ωA±ωB‖out = β1‖ωA±2ωB‖out‖ωB‖out (6.17d)

‖ωA±ωB‖out = β1‖ωA±ωB‖out‖3ωB‖out (6.17e)

These tones add to those generated by the DUT and can corrupt the measurement (because

we assume that all IM tones arise exclusively from the DUT’s nonlinearity). Analysis

reveals that these mixing tones fortunately will not be significant, with the exception of the

component given by Equation 6.17a, which we therefore evaluate in more detail here.

6.13.7 Mixing of2ωB tone with ωA tone

The DUT nonlinearity will generate a tone at 2ωB with amplitude given by

‖2ωB‖out =12α1‖ωB‖2

in |T(2ωB)| , (6.18)

or 143 mV for the maximum DUT nonlinearity (α1,max= 1 V−1) and maximum value of

|T|= 115 at 2ωB = 34 Hz. We do not explicitly measure this tone, but it will mix with the

ωA tone at the output and generate a tone atωA±2ωB, which could confound the tone at

the same frequency generated by the quadratic nonlinearity(α2) of the DUT. The resulting

tone at the output is

‖ωA±2ωB‖out,mix = β1‖2ωB‖out‖ωA‖out (6.19)

whereas the tone from the DUT nonlinearity is given by

‖ωA±2ωB‖out,DUT = 14α2‖ωA‖in‖ωB‖2

in |T(ωA±2ωB)| . (6.20)

To detect∆α2 within 0.1 V−1 as desired, we require that

6.14. CANCELLATION SCHEME 171

β1‖2ωB‖out‖ωA‖out < 14∆α2‖ωA‖in‖ωB‖2

in |T(ωA±2ωB)|β1(1

2α1‖ωB‖2in |T(2ωB)|

)

(‖ωA‖in |T(ωA)|) < 14∆α2‖ωA‖in‖ωB‖2

in |T(ωA±2ωB)|⇒ 2β1α1T(2ωB) / ∆α2. (6.21)

For the worst-case values ofα1 = 1 V−1, |T(2ωB)| = 115, andβ1 = 500 ppm V−1, the

requirement becomes∆α2 > 0.06 V−2, whereas we had previously specified detection of

∆α2 within 0.1 V−2. We conclude that the IM tone atωA±2ωB generated by nonlinearity

in Zf may perturb the measured value ofα2 almost as much as the specified precision.

If our pessimistic estimates forZf nonlinearity are indeed accurate, we must reduce

the amplitude of the 2ωB tone at the output to ensure accurate nonlinearity measurement.

Besides this consideration, the 2ωB tone may consume up to 18% of the OTA swing, which

would reduce the allowable amplitude of theVtest tone atωA and correspondingly degrade

the SNR of the impedance measurement by 2 dB. Acting on the result of this analysis, our

circuit design includes the ability to cancel the output tone at 2ωB if α1 is sufficiently large.

6.14 Cancellation Scheme

The fundamental idea of our cancellation scheme is to injectinto the summing node of the

TIA a sinusoidal current at frequencyωB and equal in amplitude but in antiphase with the

ωB current through the DUT. This strategy removes the largeωB signal from the output

while maintaining it across the DUT, as required for IM tone generation. As depicted

in Figure 6.9, the cancellation current (Icancel) is automatically adjusted by feedback to

minimize theωB content ofVout. Quadrature voltage signals at frequencyωB are connected

to variable transconductors to createIcancel. Each variable transconductor consists of a

resistor-string digital-to-analog-converter (DAC) connected to the current summing node

through a fixed resistorRcancel. An independent feedback network sets the value of each

DAC. A linear combination of scaled quadrature currents cancreate any current with phase

between 0° and -90°, which is more than sufficient for our system, where the phase ofZDUT

at ωB is known to be between−73 and−86.


n1RDAC

(1-n1)RDAC

Rcancel

−

+

ZDUT

0 ≤ni ≤1

Vout

VI

Vin

Icancel

on-chipIDUT

n2RDAC

(1-n2)RDAC

Rcancel

VQ

feedback setsni values so

Rf

Cf

36 independent pixels

for tone @ ωB

-B cos(ωBt)

-B sin(ωBt)

A sin(ωAt)+ B sin(ωBt)

shared

variabletransconductor

transconductorvariable

Icancel≈ -IDUT

Figure 6.9: Tone cancellation scheme to assess nonlinearity of ZDUT using a two-toneinput. The tone atωB is canceled at the output via automatic adjustment of the resistor-string DACs, leaving the tones atωA and the intermodulation tones unaffected.

6.15. DIGITAL FEEDBACK 173

−

+

Vout

VB = B sin(ωBt)

on-chip

−

+

Gm

Icancel

amount of ωBin Vout

Figure 6.10: Feedback concept for the cancellation scheme.

Each pixel has its own 4-channel cancellation network, witheach channel consisting of

a variable transconductor and feedback control. The input voltages are shared among all

pixels. Figure 6.9 shows only two channels for cancelling the I and Q components ofωB;

two additional channels are implemented for cancellation of DC offsets the tone at 2ωB.

The transconductor settings (represented byni) are set by autonomous feedback networks

on a per-pixel basis.

Figure 6.10 shows how the feedback control adjustsIcancel to cancel the output tone.

TheωB component ofVout (the OTA output signal) is computed by multiplyingVout by a

reference signal atωB. The demodulated DC component of the result is proportionalto

theωB content ofVout, and controls a variable transconductor which converts thereference

signal into currentIcancel at the same frequency. This demodulation scheme detects only

the ωB component in phase with the reference signal, necessitating parallel quadrature

detection with summed output currents.

6.15 Digital Feedback

Note from Figure 6.10 that our tone cancellation method requires multiplying the OTA

Vout by a reference signal atωB and averaging the result. This process can be understood

as implementing a phase-sensitive detector. We realize both the multiplier and integrator

in digital form. Control of variable transconductorGm is achieved using a resistor-string


−

+Vout

Vref

Vi

−

+ Φ

=01

=FF

Φ

Φ

U/D

SR

Count8

U/D

SR

Count8

ni

Reset

running count of (Vi ⊗ Vout)

DAC control

Reset

NB: both countersreset to mid-scale

shared

Figure 6.11: Simplified schematic of the digital phase sensitive detector that imple-ments the tone-cancelling feedback system.

DAC, as shown in Figure 6.9 and detailed in Section 6.17.4. Figure 6.11 shows a simplified

schematic of the digital implementation of the phase-sensitive detector.

The OTA outputVout and a replica of the I (or Q) signal are both compared to mid-

scale at a rate determined by an external clock. The resulting digital outputs are multiplied

(XORed) and integrated using an up-down counter. Overall, the running count decreases

if Vout and the reference signal are in phase, increases if they are antiphase, and remains

approximately unchanged if they are in quadrature or uncorrelated. When this counter

reaches its upper/lower limit, the corresponding DAC valueis incremented/decremented.

If too much cancellation current is provided, for example, the running counter decreases

6.16. VALIDATION OF CANCELLATION SCHEME 175

until the DAC is decremented, reducing the amount of cancellation current. The net result

is a bang-bang controller that acts to minimize theωB component ofVout. The multiplier of

Figure 6.10 corresponds to the comparators and XOR gate and the integrator corresponds

to the two counters.

We use two separate 8-bit counters instead of a single 16-bitcounter to provide

hysteresis so that DAC transitions occur at least 127 comparisons apart. Loop stability

is guaranteed by clocking the comparators/counters slowlyenough that the DAC cannot be

updated more than one perωB period. Thus, the switching rate of the comparator clock

signalφ will not exceed 2159 Hz whenωB = 17 Hz.

The aggregate running count is unaffected byωA content ofVout as long asωA is not an

exact multiple ofωB. Care must be taken to ensure that eachωA frequency is harmonically

independent ofωB.

The DUT current atωB is slightly phase shifted by the TIA, so we similarly shift the

replica I/Q signals used for the reference signal to the comparator as shown in Figure 6.12

(the comparator shown in Figure 6.11 is the same as in the upper left corner of Figure

6.11). The voltageVLO alternates between binary 0 and binary 1 with frequencyωB, and is

distributed to all pixels to act as one input of the XOR multiplier. In the final design this

circuit is repeated three times, once for each tone cancellation channel (it is not required

for DC cancellation).

A version of this digital feedback scheme was proposed in 1992 by Shoval et al. to

cancel DC offsets [298]. We have extended this approach for cancellation of AC signals.

6.16 Validation of Cancellation Scheme

A simplified Simulink model validates the tone cancellationconcept. Incorporating a

constant phase element (CPE) inZDUT is cumbersome, so we use a capacitive DUT for

these simulations. Figures 6.13a and 6.13b show the resulting transient signals of the

output voltage and the discrete attenuation factors (n) set for the I and Q resistor-string

DACs. The output saturation seen until 3 seconds has no effect on the algorithm. The I

DAC attenuation decreases consistently near its maximum rate, and the Q DAC attenuation

decreases more slowly until both reach an approximate “steady state” of alternating


−

+

Zf

nRDAC

(1-n)RDAC

Rcancel−

+

Zf

ZDUT

0 ≤ n ≤ 1

VB = B sin(ωBt)

Vin = A sin(ωAt) + B sin(ωBt) on-chip

−

+

VLO

Vout

to all pixels

Vref Φ

Figure 6.12: The master comparison circuit for each channelof tone cancellation. Thiscircuit generates theVLO signal (a digital square wave at frequencyωB) shown in Figure6.11.

6.17. CMOS IMPLEMENTATION OF TONE CANCELLATION 177

between adjacent codes. At this point the output voltage is almost completely cancelled

(staying within±12 mV of the nominal output voltage). Figure 6.14 shows a detailed view

of the running counters plotted relative to their maximum value. When the running count

underflows/overflows, the DAC-controlling counter decrements/increments.

To ensure that our cancellation approach functions even when large ωA tones are

present, a Matlab script simulates the algorithm using different tone ratios. Figure 6.15

shows the results, where the x-axis is the ratio ofωA andωB amplitudes, and the y-axis

represents the net movement of the running count (1 for moving in the correct direction

each comparison, 0 for staying the same on average, and−1 for moving in the wrong

direction each comparison). To maintain‖ωB‖out < 50 mV when‖ωA‖out is at its swing-

limited maximum of 800 mV amplitude, we require the algorithm to function at−24 dB.

The efficacy of the algorithm depends somewhat on the harmonic relationship betweenωA

andωB, but our simulations show that the algorithm works “well” down to at least−30 dB,

meaning that the DAC adjusts to cancel the signal at a rate of at least 40% the maximum

rate if perfectly in phase. Simulink simulations (not shown) further validate this conclusion.

6.17 CMOS Implementation of Tone Cancellation

6.17.1 Comparator

We use a regenerative comparator latch patterned after Songet al. [299] shown in Figure

6.16. It is similar to the Yukawa latch [300] but has zero static power dissipation. When

clock signalφ is low the outputs are pre-charged high, eliminating possible memory effects.

When φ goes high the input voltages are compared. Positive feedback from the cross-

coupled transistors speeds the process. Symmetric buffer inverters are attached to the

regenerative nodes both to increase the speed of switching the load capacitance and also to

reduce systematic offset (only one side drives the load capacitance). The result is latched

until φ goes low again. Note from Figure 6.11 that the counter is updated on the same

falling transition that resets the comparator, but propagation delay ensures that the counter

input is valid.


0 2 4 6 8 10 12

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

time [s]

Vou

t [V]

Output voltage vs. time

(a) SimulatedVout vs. time for capacitive DUT.

0 2 4 6 8 10 120

0.1

0.2

0.3

0.4

0.5

time [s]

n =

atte

nuat

ion

fact

or

DAC attenuation factor vs. time

I DACQ DAC

(b) Simulated I/Q DAC attenuation factors vs. time for same system.

Figure 6.13: Simulink simulations demonstrating effectiveness of our tone cancellationalgorithm.


9 9.2 9.4 9.6 9.80

0.5

1

Cou

nt/M

ax C

ount

Running count and attenuation factor vs. time

I running countQ running count

9 9.2 9.4 9.6 9.80

0.2

0.4

time [s]

atte

nuat

ion

fact

or

I DACQ DAC

Figure 6.14: Transient plots of the simulated running countand DAC attenuationfactors. Note that when the running count overflows or underflows, the DAC counteris incremented or decremented.


−60 −50 −40 −30 −20 −10 0−0.2

0

0.2

0.4

0.6

0.8

1

tone ratio ||ωB||/||ω

A|| [dB]

net c

ount

rat

e

Simulated net count rate vs. tone ratio

ωA

= 170 Hz

ωA

= 173 Hz

ωA

= 176 Hz

ωA

= 178.5 Hz

Figure 6.15: Simulated rate of running counter movement vs.tone ratio ofωB andωA

tones.


φ

V+

Q

φ φ

V−

φ

Figure 6.16: Core of the latched comparator design (input preamplifiers not shown).

A chain of two differential preamplifiers, each a one-stage diode-connected OTA,

separates the actual comparator inputs from the nodesV+ andV− as shown in Figure 6.16.

The preamplifiers prevent “kickback” transients from coupling back to the OTA output

voltageVout. The drain node of the comparator core input devices switches suddenly and

injects a current spike at the gate, but with no adverse effect because the gate is driven by

a preamplifier, not the OTA. The preamplifiers also reduce thecomparator offset by using

transistors somewhat larger than the input devices of the regenerative comparator core.

In the context of the feedback system, the offset voltage of the comparator determines

the smallestωB signal that can be detected. It does not, however, cause the feedback loop

to settle on an incorrectGm value because the output of the comparator is multiplied by

a square wave with 50% duty cycle and then integrated. As longas the offset voltage is

much less than 50 mV we expect no adverse effects. To reduce the input-referred mismatch

it is important thatφ transition quickly. Any mismatch between switch thresholdvoltages

gives rise to large comparator mismatches if the switches donot turn on simultaneously.

Clock buffers ensureφ has fast edges even if the clock signal provided to the IC doesnot.

Monte Carlo simulations using mismatch models suggest thatthe standard deviation of the

input-referred comparator offset voltage is 7 mV, well within the requirements.


6.17.2 Multiplier and integrator

As already stated, the multiplier is implemented as a simpleXOR gate.

The integrator is implemented by two 8-bit counters. Because one counter drives

the resistor-string DAC (as part of the variable transconductor), synchronous counters are

required. We use a standard synchronous counter design based on a series of JK flip-flops

[301]. One benefit of this implementation is that no additional circuitry is needed to derive

the underflow/overflow signals required.

For testing purposes, external controls are provided for control of the resistor DAC via

the signalsTest, φext, andUDext. A more detailed version of the digital feedback scheme

is shown in Figure 6.17.

6.17.3 Requirements in terms of transconductance control

Recall from Section 6.14 that a variable transconductor converts the input voltage (VI and

counterparts) into a current injected at the TIA input alongwith the DUT current. Because

the frequencyωB is well below the corner frequency implied byRf ‖ Cf , the transfer

function from the transconductor input to the OTA output is given by

Vout

VI'−GmRf (6.22)

whereGm represents the effective transconductance of the DAC-resistor combination.

In Section 6.13 we determined that the component ofVout at ωB should be 50 mV or

less. For noise reasons (discussed below), we use transconductor input signals (VI and

counterparts) with amplitude of 150 mV, or about three timesas large as theωB signal

across the DUT. We can compute the required increment ofGm consistent with canceling

the current within the specified amount as

∆Gm =1

3Rf= 14 nS (6.23)

In essence, the LSB of the discrete transconductance must beless than 14 nS.

To determine the maximum value ofGm, consider the case where the entire cancellation

current Icancel is provided by a single variable transconductor and the DUT current


−

+Vout

Vref

Φ

VLO

−

+Φ1

running count of(VLO ⊗ Vout)Φ1

Φ2

U/D

SR

Count8

max

min

U/D

SR

Count8

max

min

Φ1

Φ2

resetcompare

Reset

Vref

Reset

Φ2

MSB

OF

MSB

OF

DAC control

Count<7>

prevents wrapping DAC count

Test

UDext

both counters "reset" to mid-scale

D Q 0

1

D Q

Φext

Φ2

Φ2

update count, possibly update DAC

Φ1 compare

reset instead of wrapping

Figure 6.17: More detailed version of Figure 6.11, including circuitry for testing tonecancellation manually and to prevent wrapping of the count that controls the variabletransconductor.


is maximized (minimumZDUT ). This case is pessimistic because the phase ofZDUT

never reaches 0 or −90, as can be seen in Figure 5.2. In this situation, the required

transconductance is

Gm,max=1

3ZDUT,min= 0.9 µS (6.24)

where the factor of 3 arises from the scaled transconductor input signal, as noted earlier.

Combined with the earlier result, we conclude thatGm,max' 64∆Gm, corresponding to

a requirement for 5 bits of transconductance control.8 To allow for process variations

and nonlinearity in the transconductor, we implement an 8-bit variable transconductor

with nominal∆Gm of 4.7 nS. Cancellation of the DC and 2ωB terms have less stringent

requirements, but for simplicity we use identical circuitsfor all four tone cancellation

channels.

6.17.4 Variable transconductor

As derived in Section 6.17.3, we require a variable transconductor with step size of less

than 14 nS and with total transconductance of more than 900 nS. We use a resistor-string

DAC as a controllable voltage divider. This voltage is converted into a current by a fixed

resistorRcancel connected between the resistor-string DAC and the virtual ground of the

OTA, as shown in Figures 6.9 and 6.12.

We define the attenuation factorn ≡ DAC code28−1 as the fraction of the maximum

transconductor output, so the resistor-string DAC has an output voltagenVI . The 8-bit DAC

consists of 256 series resistors with nominal resistance of315Ω each (RDAC∼ 80 kΩ ). One

tap point is connected to the DAC output through a binary network of switch transistors,

implemented with 3.3 V NMOS devices with the gate switched between 0 V and 3.3 V,

whileVd 'Vs ' 1.35 V.

The effective transconductanceGm of the composite structure is approximatelynR−1cancel,

which ranges between 0 and 1.2 µS with Rcancel = 800 kΩ. The nominalGm,max is

33% larger than required, to provide more than enough marginfor the 20% maximum

process-related inaccuracy in resistor values. Accounting for the resistance of the switch

network and loading from the resistor DAC, a more accurate expression for the effective

8In the original design, the factor of 3 was omitted and we thought we needed another 1.6 bits of control


A0

A0

A0

A1

A0

A1

=R

R

R

R

4RRswitch

Figure 6.18: Schematic of a 2-bit resistor-string DAC, showing the resistanceRswitch

of the binary switch network (implicit in the other figures).The actual circuit uses an8-bit resistor-string DAC.Rswitchappears in series withRcancel in connecting the DACto the current summing node of the OTA.


0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1

1.2

1.4

Effective Gm

vs. attenuation factor

attenuation factor

tran

scon

duct

ance

[uS

]

actual G

m

ideal Gm

Figure 6.19: Effective transconductanceGm vs. attenuation factorn= DAC codemax DAC code.

transconductance is

Gm =n

Rcancel+Rswitch+RDAC(n−n2). (6.25)

The loading ofRDAC makesGm somewhat nonlinear, but as long as the DNL is not

significant then each step will still have∆Gm < 14 nS as required. The nominal DNL for

our design is less than 0.1LSB, resulting in a maximum∆Gm step of 5 nS. The simulated

Gm value versus attenuation factorn is plotted in Figure 6.19.

The residual tone of both I and Q signals at the OTA output is atmost12∆GmRf times the

input tone, so we expect the quadrature error to be√

22 (5 nS)(24 MΩ)(150 mV) = 12 mV,

which is within the desired range of 50 mV. As shown in Section6.13, the DUT

nonlinearity generates IM tones much larger the TIA nonlinearity does after the tone

cancellation.

6.18. NOISE OF TONE CANCELLATION CIRCUITRY 187

6.18 Noise of Tone Cancellation Circuitry

The tone cancellation circuitry adds noise which affects the precision of bothZDUT and

nonlinearity measurement. Following the pattern of Section 5.8, this noise can be referred

to the system input and added to the other noise contributions. The plots in Section 5.9

include the noise contributions derived in this section.

Sources of noise in the tone cancellation circuitry includethermal noise of resistors

RDAC, Rcancel, andRswitch (the NMOS switch network); flicker noise of resistorsRDAC and

Rcancel; flicker noise of NMOS switches; and exogenous noise (e.g. from off-chip amplifiers

drivingVI , VQ).

6.18.1 Decision to increaseRcancel

As will be shown below, the dominant noise sources in the tonecancellation circuitry

are resistive thermal noise and resistive flicker noise. To reduce both contributions, we

implementRcancel as a resistor three times as large as would be required if the inputVI

were of the same amplitude as theωB component ofVtest. So we useRcancel= 800 kΩinstead 267 kΩ and increase the tone cancellation input voltages by a factor of 3 (150 mV

instead of 50 mV). This modification requires added die area to implementRcancel and

external amplification circuitry, but reduces the noise from the tone cancellation circuitry

to tolerable levels.

6.18.2 Resistor and switch thermal noise

If the resistance of the switch network in the DAC asRswitch (see Figure 6.18), the net

resistanceRequiv between the virtual ground and the input forVI is

Requiv = Rcancel+Rswitch+((1−n)RDAC||nRDAC) (6.26)

= Rcancel+Rswitch+(

n−n2)RDAC.


The thermal noise of a MOSFET switch is simply given by its on-resistance, and so the

thermal noise of a single channel of the tone cancellation circuit is exactly the same as

would be generated by a resistor with valueRequiv, or

I2n =

4kTRequiv

. (6.27)

This noise current is equivalent to a noise voltage at the system input, found by multiplying

the current by the factorZDUT , as described in Section 5.8.2. Thus, the resistive thermal

noise from the variable transconductor at the system input is given by

V2n,in = 4kT

|ZDUT |2Requiv

' 4kT|ZDUT |2Rcancel

(6.28)

where the final step is justified by noting thatRcancel = 800 kΩ, Rswitch' 23 kΩ, and

RDAC= 80 kΩ. IncreasingRcancelby a factor of three reduces the thermal noise contribution

by nearly a factor of three, as stated earlier.

6.18.3 Resistor flicker noise

The on-chip resistors have flicker noise as described in Section 5.8.5. This voltage noise

induces a current inversely proportional toRequivwhich, when multiplied byZDUT , allows

us to refer it to the system input. The resistive flicker noisereferred to the system input is

given by

V2n,in =

KR3V2

fW2(Rcancel+(n−n2)RDAC)

|ZDUT |2

R2equiv

' KR3V2 |ZDUT |2

fW2R3cancel

(6.29)

where we have again assumed that the switch resistance is small compared with the

resistance of the poly resistors composingRcancel and RDAC.9 IncreasingRcancel by a

factor of 3 decreases the noise power from the resistors by a factor of 3.10 Furthermore,

implementingRcancelas a 800 kΩ resistor instead of a 267 kΩ resistor decreases the flicker

noise corner frequency and correspondingly diminishes theeffect of resistive flicker noise.

9The other parameters relating to the flicker noise are described in Section 5.8.5.10TheV term in the numerator is also proportional to the resistance.

6.18. NOISE OF TONE CANCELLATION CIRCUITRY 189

6.18.4 Switch flicker noise

The flicker noise model provided to us by the foundry computesthe flicker noise current in

a triode (switch) transistor as

I2n,ds=

K0

f

I1.4ds

L2 (6.30)

whereK0 is a process-dependent parameter andIds is the required cancellation current.

Some theoretical models give the exponent ofIds as 1 whereas others give 2; our model

uses an intermediate exponent. Note also theL2 term in the denominator instead of the

gate areaWL. The correct choice is a function of the exact mechanism of flicker noise

[280, 302]. The “knob” available to reduce the switch flickernoise is the transistor length.

The resulting noise current is referred to the system input by multiplying by ZDUT , so

for N = 8 switches we have

V2n,in = N

K0

f

I1.4cancel

L2 |ZDUT |2 (6.31)

at the system input. Note that this noise contribution changes with Gm becauseIcancel

changes.

The LSB switches are implemented as 0.68/0.4 (in µm/µm) for area reasons, but the

other switches are a generous 2/1, rendering the expected flicker noise from the switches

negligible. Typical reasons to minimize switch size, such as charge injection and switching

speed, are unimportant for our application.

6.18.5 Noise from off-chip drivers

Off-chip amplifiers supply voltageVI and the corresponding inputs of the other tone

cancellation channels. Each amplifier drives theRDAC of all the pixels in parallel (about

2.2 kΩ), with a 17 Hz tone of 150 mV amplitude. The output voltage noise of the amplifier

appears as noise at the variable transconductor input, and the noise transfer function to

the system input isGmZDUT . With an input-referred amplifier noise ofV2n,amp and off-chip

amplificationAV = 3, the noise at the system input is

V2n,in = A2

VV2n,ampG

2mZ2

DUT (6.32)


which is also dependent on the DAC setting (which, in turn, setsGm according to Equation

6.25).

We use Texas Instrument’s INA627 for the off-chip amplifier.It has a typical input-

referred noise of 8 nV/√

Hz at 100 Hz and a white noise of 4.5 nV/√

Hz. The noise

contributed by this amplifier is negligible compared with that from the tone cancellation

circuitry.

6.18.6 Summary of noise from cancellation circuit

The noise plotted in Section 5.9 includes the contributionsfrom all of these sources

(Equations 6.28, 6.29, 6.31, and 6.32) combined into the curve labeled “LF Cancellation.”

The computed noise is quadrupled to account for all four tonecancellation channels.

Because the noise power spectral density from the tone cancellation circuit is propor-

tional to the square ofZDUT , the worst-case scenario is whenZDUT is at its maximum

expected value. In this case our models predict that noise from the tone cancellation

circuitry will be comparable to that from the OTA (see Figure5.13).

6.19 CMOS Layout

Here we highlight some important points regarding the layout. The floorplan is overlaid

on the chip micrograph shown in Figure 7.1. Test and support circuitry is placed along the

outside of a 6x6 array of measurement pixels.

All analog transistors (in both the OTA and comparator) are implemented in a common

centroid arrangement using multiple fingers to enhance device matching. Dummy devices

are included on the ends of each row for etch uniformity.

As already noted, we implementCf ' 30 pF as a parallel combination of a poly-poly

capacitor (nominally 19.7 pF) and comb capacitors located just above the poly-poly cap

(nominally 10.3 pF).

We use p-doped unsilicided resistors with a generous width of 0.72 µm (four times the

minimum poly width), to improve matching and accuracy. An added benefit of increased

width is reduced flicker noise, per Equation 5.22.

6.19. CMOS LAYOUT 191

The (small amount of) excess area within each pixel is filled with bypass capacitors to

stabilize both the 3.3 V analogVDD andVre f (the latter acts as a small-signal ground for the

OTAs and tone cancellation circuitry). Bypass capacitors are also added within the digital

section between the 1.8 V digitalVDD andVSS.

To reduce coupling of switching noise to the analog portionsof the circuit, we use guard

rings around both the digital block and the comparator. Furthermore, the 1.8 V digital block

and comparators are placed as far as possible from the sensitive analog inputs of the OTA.

It is well-known that distributing bias over long distancesis better performed in the

current domain. The constant-gm network is on the side of the die. The resulting current

is mirrored and then distributed to each pixel, where it is used to generate bias voltages for

each OTA locally.

Including I/O traces between the pixels, the final pixel sizeis 380µm by 370µm, within

our target of 400µm per side. In retrospect, more room should have been reserved between

the pixels for wiring to the bondpads, as the trace resistance of the connections is as high

as 110Ω. This additional resistance will be measured as part ofRsol.

Chapter 7

Measured CMOS Performance

7.1 CMOS Specifications

We implemented a 6x6 array of impedance biosensor measurement pixels in a standard

0.18 µm CMOS process, allowing simultaneous monitoring of 36 probe-functionalized

electrodes. The periphery of the chip contains support and test circuits, as shown in Figure

7.1, with the bulk of the die dedicated to the 6x6 array of impedance analyzer pixels.

Each pixel contains a transimpedance amplifier (TIA) and tone-cancellation circuitry as

described in Section 6. The tone cancellation circuit occupies about half of the pixel area,

and the remainder is split betweenRf , Cf , and the operational transconductance amplifier

(OTA).

Each pixel occupies 380µm by 370µm, or 12% less total area than our upper limit of

400µm square. Each pixel of the fabricated chip consumes 1.9 mW of power, compared

with our goal of 1.6 mW. While the measured value is nearly 20% higher than intended,

power consumption is not a practical concern because the measurement circuit and sensor

electrodes are on separate microchips (see Section 5.4.3).

We noted pixel-to-pixel variation in the output range of theOTA of a few hundred

millivolts, which we attribute to variations in the cascodebiasing network shown in Figure

6.2. This variation suggests that implementing the bias circuit with (1/4)-size devices may

have been too aggressive;(1/5) or (1/6)-size devices would have been a better choice to

ensure that the load devices remain in saturation. The transfer function of the integrated

192

7.1. CMOS SPECIFICATIONS 193

Figure 7.1: Optical chip micrograph, with detail of one measurement pixel.

194 CHAPTER 7. MEASURED CMOS PERFORMANCE

transimpedance amplifiers exhibits> 20% intra-die variation, which we also attribute to

problems with the OTA biasing that lead to greatly reduced OTA gain. Measurements with

the best pixels indicate that the feedback impedance is approximately 36 pF‖ 24 MΩ,

compared with the design value of 30 pF‖ 24 MΩ. Although this discrepancy causes

a slightly different transfer function than originally planned (and reduces the maximum

allowable excitation in some cases), it is not important at the system level because we are

striving to detect temporalchangesin impedance as measured by the same TIA.

7.2 Chip Interfacing

Electrical connections between the electrode array and thetest PCB are made using the

same custom socket developed for the PCB measurement system(see Section 3.3). The

CMOS die is bondwired to a ceramic LCC package (LCC08421, Spectrum Semiconductor,

San Jose CA) that fits into a PCB socket (P2084S-A-AU, Plastronics, Irving TX), and the

two sockets are connected via the test PCB. For convenience we use a standard 84 pin

package, implying that only a subset of the pixel outputs canbe simultaneously monitored.1

Fluidic interfacing is identical to that previously described (Sections 3.3 and 3.10). There

is no need to encapsulate the bondwires to prevent liquid exposure because the electrode

array and CMOS readout circuitry consist of separate chips.

7.3 Tone Cancellation

We test tone cancellation using a capacitiveZDUT with 17 Hz quadrature signals generated

by an Analog Devices 9854 quadrature direct digital synthesizer. The tone amplitude at

the cancellation inputsVI/VQ is 150 mV, with 50 mV applied acrossZDUT along with the

2 mV ωA tone (1 kHz for data below). The 2 kHz clock signalφ is slow enough to ensure

stability of the feedback network.

1Monitoring all 36 outputs simultaneously would be impossible without adding more external ADCs inany case. Recall that our principal goal is to demonstrate a functional TIA measurement core, which can bedone with designed interface.

7.4. IMPEDANCE PRECISION 195

We include an enable signal for each tone cancellation channel. When disabled there

should not be a connection between the resistor-string DAC and the resistorRcancel (see

Figure 6.9) because no switch in the DAC switch network is turned on. However, we

observe that theVI /VQ signal appears at the OTA output even when the DACs are nominally

disconnected, suggesting that the switch network does not turn completely off. Thus, the

digital feedback network can never completely turn off the variable transconductor, which

leads to incompleteωB cancellation for a capacitiveZDUT .

The output spectrum before enabling cancellation is shown in the dotted blue line of

Figure 7.2 (φ not supplied, DACs disabled). Note the intermodulation (IM) tones nearωA,

generated from mixing ofωA and ωB components at the nearly-saturating OTA output.

These spurious tones would prevent accurate measurement ofthe IM tones generated

by the ZDUT nonlinearity. The solid red line represents the output spectrum after the

sampling clock is applied and the DACs are enabled. The residual ωB output tone has

a 100 mV amplitude, compared with the desired maximum amplitude of 50 mV, due to the

aforementioned switch leakage.

Recall that one cancellation channel is reserved for DC offset cancellation. It injects

a DC current at the OTA input to ensure thatVout is centered aboutVre f .2 The observed

raw output offset of the OTA is roughly 100 mV (remember that the T-network causes

an offset gain of more than 20 dB). This level of offset would be problematic because

any offset reduces the usable output swing by the same amount. However, enabling the DC

cancellation successfully reduces the output offset to negligible levels (< 10 mV), centering

Vout onVre f .

7.4 Impedance Precision

A capacitiveZDUT is used to quantify the precision of the impedance measurement. A 2 mV

excitation signal at various frequencies is used for simplicity. The fact that the maximum

permitted input signal may be somewhat larger3 implies that the measured impedance

precision is not necessarily optimal, but it does representa typical use case. The impedance

2more precisely, that its median value isVre f3see Figure 5.16


101

102

103

10−8

10−6

10−4

10−2

Frequency [Hz]

Pow

er S

pect

ral D

ensi

ty [V2 /H

z]

Effect of Cancellation on Vout

Spectrum

ωB @ 17 Hz ω

A @ 1 kHz

Cancellation disabledCancellation enabled

Figure 7.2: Spectrum ofVout before and after the tone cancellation circuitry is enabled,with ωA = 1 kHz andωB = 17 Hz. Note the IM tones are significantly reduced (herethe DUT is linear, so ideally there would be no IM tones).

7.4. IMPEDANCE PRECISION 197

0 5 10 15 206.7

6.72

6.74

6.76

6.78

6.8

trial

Cap

acita

nce

[nF

]

Sensitivity to Capacitance Change

Figure 7.3: Measurements of test capacitance before and after a small increment,demonstrating reproducibility of about 0.2%.

spectrum is measured ten times in succession, theZDUT capacitance is slightly increased,

and another ten impedance spectrum measurements are carried out. The capacitance values

extracted from curve-fitting the resulting impedance data are shown in Figure 7.3. The

standard deviation of the best-fit capacitance over repeated measurements is 0.2% of the

nominal capacitance.

The precision of the impedance measurement versus frequency is computed from

the same data by calculating the variance of the impedance magnitude as repeatedly

measured under nominally identical conditions. The result, plotted in Figure 7.4, is that

the impedance measurement has a signal-to-noise ratio between 50 and 60 dB (depending

on the frequency). This finding is consistent with a 0.2% precision in the extracted

capacitance, and indicates that having an impedance spectrum does not necessarily increase

the precision of the best-fit model parameters (see Section 5.11).

The experimentally-determined impedance precision is 20 dB inferior to the simula-

tions presented in Section 5.12. Separate measurements show that the flicker noise of the


102

103

104

105

50

60

70

80

90

100

Frequency [Hz]

SN

R [d

B]

SNR of ZDUT

Measurement

Predicted − ZDUT,max

Predicted − ZDUT,typ

Predicted − ZDUT,min

Measured

Figure 7.4: Experimental measurement ofZDUT SNR/precision compared with thesimulated SNR.

7.5. BIOLOGICAL MEASUREMENTS 199

fabricated IC is much greater than the provided circuit models indicate. Because flicker

noise from the OTA is the dominant noise source, our simulations were overly optimistic.

Nevertheless, the resulting 0.2% precision is sufficient to perform many impedance

biosensor readout tasks, although not quite good enough to ensure that the limit of detection

is always set by biological factors instead of the instrumentation according to our meta-

analysis in Section 5.5.1.

7.5 Biological Measurements

To validate the correct operation of the integrated circuitwe functionalize a chip with

BSA-biotin, similar to prior measurements of nonlinearity(see Section 4.6.2). After

measurement of the impedance spectrum, a saturating concentration of streptavidin is

introduced and the impedance is measured again. The data, shown in Figure 7.5, indicate

that target binding causesCsur f to increase from 16.1 “nF” to 17.4 “nF”, representing an

impedance decrease of about 10%. This result is consistent with prior measurements using

the PCB-based measurement system.

7.6 Significance of Measurement Results

Despite several minor shortcomings, the CMOS impedance analyzer array can make

meaningful biological measurements, demonstrating that impedance biosensor arrays can

be monitored by inexpensive and compact circuitry. Such a demonstration is a necessary

step towards the oft-quoted goal of producing a handheld biosensor.4 This work represents

the first completely integrated array of impedance analyzers for biosensors. Furthermore,

we demonstrate the use of tone cancellation in the context ofimpedance (and impedance

nonlinearity) measurement, as well as for DC offset cancellation.5

Straightforward remedies exist for each shortcoming of ourintegrated impedance

analyzer array. In order to improve the impedance resolution to the desired 0.1%, a

4However, many of the system-level challenges are biological and chemical.5In early 2010 we became aware of concurrent work with similarobjectives in the Hassibi group at

University of Texas, reported in February 2010 [303].


102

103

104

105

103

104

105

|Z| [

Ω]

Biotin Electrode, Before vs. After Streptavidin

measured beforebest fit beforemeasured w/streptavidinbest fit w/streptavidin

102

103

104

105

−90

−75

−60

−45

−30

−15

0

−∠

Z/°

102

103

104

105−0.2

−0.1

0

Nor

mal

ized

∆|Z

|

Frequency [Hz]

Figure 7.5: Impedance spectrum before and after introduction of streptavidin (biotinis the probe), as measured with the integrated measurement system. The bottom panelshows the normalized change in impedance.

7.6. SIGNIFICANCE OF MEASUREMENT RESULTS 201

different fabrication process could be used (e.g. BiCMOS orlow noise analog) or else a

redesign of the OTA could be undertaken at the expense of added pixel area. Our tone

cancellation scheme is effective, but can be improved further by minor modifications to

reduce switch leakage in the resistor-string DACs. As discussed in Section 5.2, other

electronic components could be integrated on the same CMOS die, including the sensor

electrodes, analog-to-digital conversion, and DSP for data analysis.

Chapter 8

Conclusion

8.1 Summary and Contributions

This dissertation has described improvements in readout circuitry for impedance biosen-

sors. We achieved the principal goal of this work, namely, todemonstrate miniaturized

detection circuitry for impedance detection of biologicalagents in an array format. Here

we briefly revisit the results and significant contributionsof this work.

Chapter 2 contains a comprehensive review of the field of impedance biosensors. Most

of this content has been published in our 2007 review paper [6], which has been cited 50

times within 2.5 years of its publication. Besides summarizing the status of the field and

identifying faux pas prevalent in the literature, we identify important areas for impedance

biosensor research. The remainder of this dissertation addresses two of these areas, namely

the implementation of multiplexed impedance biosensor arrays and design of measurement

circuitry in an integrated circuit.

Next we designed and implemented a impedance measurement system for an array

of functionalized electrodes. As described in Chapter 3, wefabricated an array of 36

gold microelectrodes and designed an interface mechanism to provide electrical contact

to all electrodes. We implemented impedance-measuring circuitry on a custom PCB,

and assembled a data acquisition and analysis system which extracts the impedance

spectra from the raw data. In collaboration with biologistsand chemists at the Stanford

Genome Technology Center, we developed protocols to attachbiological probes to the

202

8.1. SUMMARY AND CONTRIBUTIONS 203

electrode surface. Measurements using both DNA and proteinprobe/target pairs with

our electrode array and measurement system confirmed published reports that changes in

surface impedance correspond to target binding.

A fundamentally important observation is that the electrode-solution impedance de-

pends on the DC bias across the interface; i.e. the I-V characteristic of the interface is

nonlinear. This fact is mentioned in the literature but not appreciated by many researchers.

As explained in Chapter 4, measurements using our PCB measurement system revealed

target binding changed the bias dependence of the surface capacitance, suggesting the

possibility of using changes in the nonlinearity to detect binding. We developed a two-

tone measurement scheme to allow simultaneous measurementof both nonlinearity and

small-signal impedance, and implemented the scheme in a modified PCB. Measurements

using the modified system confirmed our prior observations that changes in nonlinearity

could be used to detect target binding, thus rediscovering the little-investigated concept

of “impedance nonlinearity biosensors.” Our nonlinearitymeasurements were consistent

with the hypothesis that changes in nonlinearity are causedby changes in the surface

charge via the (nonlinear) ionic double layer capacitance.This hypothesis implies that

such nonlinearity sensors could substitute for field-effect biosensors, with the advantage

that physiological salt concentrations can be used.

Next we implemented an array of integrated measurement circuits to demonstrate that

impedance readout could be miniaturized and multiplexed. We began by analyzing the

requirements for each measurement pixel, as detailed in Chapter 5. Our meta-analysis of

the literature suggested that a 0.1% impedance measurement precision would be sufficient

to ensure that the system’s limit of detection is set by biological factors rather than the

measurement instrument. We determined the required circuit-level specifications based on

the goal of achieving 0.1% precision and the previously-measured characteristicsof our

electrodes. The most important circuit specification is thetotal circuit noise referred to the

system input, which determines the precision of the impedance estimation. Our analysis

suggested that flicker noise of the operational transconductance amplifier would dominate

the circuit noise.

In light of our previous results with nonlinearity, we designed an integrated measure-

ment circuit to allow simultaneous impedance and nonlinearity measurements based on

204 CHAPTER 8. CONCLUSION

the two-tone measurement scheme. Because of the low supply voltages this requires

a more complicated circuit approach than employed in the PCBsystem, in order to

prevent the low-frequency tone from saturating the amplifier output. We used a scheme

analogous to the well-known technique used in “noise-cancelling headphones,” injecting

an antiphase current at the amplifier input to cancel the low-frequency input signal required

for nonlinearity measurement. Quadrature phase-sensitive detectors autonomously set

the cancellation signal to the correct amplitude and phase.We implemented this tone

cancellation circuitry in each measurement pixel, along with a low-noise operational

transimpedance amplifier and passive feedback network. Thechip was fabricated in a

0.18µm CMOS process.

Results in Chapter 7 indicate that the integrated measurement system is functional but

does not quite meet all of the target specifications. The primary goal for the integrated

impedance analyzer was to measure impedance with 0.1% precision. However, flicker

noise in the fabricated chip is about 20 dB worse than the foundry’s models, resulting

in an actual precision of about 0.2% over the specified range of frequencies (100 Hz to

100 kHz). The tone cancellation circuitry is also operational, but 6 dB worse than desired

due to switch leakage in the tone cancellation DACs.

Taken as a whole, the work presented in this dissertation suggests that changes in both

impedance and nonlinearity can be used to detect biologicalbinding. We demonstrated

that the instrumentation used to measure the impedance changes can be miniaturized and

multiplexed, enabling portable detection of multiple analytes in parallel.

8.2 Areas for Future Work

The work described in this thesis could be expanded in many ways, and here we note only

a few of significant value to the nascent field of impedance biosensors.

Our observation that changes in the nonlinearity can indicate target binding only

scratches the surface of vast possibilities. For example, it would be interesting to

study whether nonlinearity changes actually derive from surface charge via the minimum

potential of the double layer capacitance as we have hypothesized. If so, impedance

may be used to detect surface charge in a way that is preferable to field-effect sensors,

8.2. AREAS FOR FUTURE WORK 205

because the ionic strength can remain high during the measurement (this avoids perturbing

native biomolecular behavior). Because changes in nonlinearity may also arise from other

mechanisms, it is important to understand these other sources so that systems can be

engineered to enhance the measured change and hence improvethe detection limit.

An important void in the impedance biosensor field is a systematic study of the

mechanisms by which target binding changes the interface impedance. Existing theories,

though useful conceptually, are ad hoc and have limited predictive power. Use of advanced

surface imaging techniques and careful electrical measurement might elucidate the causes

of impedance change so that it can be rationally enhanced, which in turn would improve

limits of detection.

As the size of the electrode changes, so does the respective impedance (although the

fractional change in impedance upon binding is expected to remain constant). At very

small sensor sizes, the stochastics of target binding may beevident. It would be interesting

to consider electrode scaling in more detail, trying to determine the optimum sensor size, or

given a fixed area, determining whether multiple small sensors are preferable to one large

sensor.

Finally, nonspecific binding of unintended targets is a tremendous practical challenge,

and further work towards optimizing probe surfaces and processing sensor data to eliminate

false signals is a challenging area that merits further research effort.

Appendix A

Useful Trigonometry Identities

e±ıθ = cosθ± ısinθ (A.1)

sin(θ±φ) = sinθcosφ±cosθsinφ (A.2)

cos(θ±φ) = cosθcosφ∓sinθsinφ (A.3)

sinθcosφ =12[sin(θ+φ)+sin(θ−φ)] =

12[sin(θ+φ)−sin(φ−θ)] (A.4)

sinθsinφ =12[cos(θ−φ)−cos(θ+φ)] (A.5)

cosθcosφ =12[cos(θ−φ)+cos(θ+φ)] (A.6)

cos2 θ =12+

12

cos(2θ) (A.7)

cos3 θ =

(

34

cosθ+14

cos3θ)

(A.8)

206

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