MEMSMTODARPADARPA

Piezoelectric MEMS Resonator Measurement and Characterization

April 6, 2004

Joung-Mo Kang, David Carter, Doug White, and Amy DuwelThe Charles Stark Draper Laboratory

MEMSMTODARPADARPA

Presentation Overview

1. Background and device models

2. Filter design

3. L-Bar measurements

4. Parasitic investigations

5. Conclusion

MEMSMTODARPADARPA

Device Overview and Goals

Desired: a high performance RF channel-select filter bank on a chip — 0.3-3 GHz frequencies — high selectivity high Q— compatible with silicon IC technologies— small size high density— low loss— device characteristics defined by lateral geometry

18 x 5.5 m bar with 3.5 m tethers10 x 5 m bar with 1 m tethers

MEMSMTODARPADARPA

Device Structure

resonator

Ctethers

Circuit Model

MEMSMTODARPADARPA

Longitudinal Resonance

Longitudinal Mode Shape• tethers placed at displacement node

• longitudinal displacement amplitude on the order of nm

• other types of mechanical resonances cancel out in charge at lower frequencies

MEMSMTODARPADARPA

Butterworth Van-Dyke Model

MEMSMTODARPADARPA

R C L

C0

wlC z

t0

28we

ltL

2

28

tc

lweC

28we

c

Q

tR

MEMSMTODARPADARPA

BVD Impedance Function

860 865 870 875 880 885 890 895 900 905 91010

2

104

106

108

Impe

danc

e M

agni

tude

(

)

860 865 870 875 880 885 890 895 900 905 910-90

-45

0

45

90

Impe

danc

e P

hase

(de

gree

s)

l = 5.5 m

w = 3.0 m

t = 0.5 m

Q = 10,000

L = 342 H

C = 0.096 fF

R = 189

C0 = 2.98 fF

MEMSMTODARPADARPA

Filter Design

• Review existing crystal filter topologies and assess performance metrics.

• Down-select a filter topology based on specifications set by RF group.

• Define fabrication requirements and tolerances to achieve desired performance with each topology

Primary Objectives:

MEMSMTODARPADARPA

Dual Resonator Ladder

VinVoutRL

RS

Zp

Zs

-35

-30

-25

-20

-15

-10

-5

Mag

nitu

de (

dB)

-35

-30

-25

-20

-15

-10

-5

Mag

nitu

de (

dB)

Dual Resonator Ladder Filter Response

740 760 780 800 820 840 860Frequency (MHz)

740 760 780 800 820 840 860Frequency (MHz)

-90

0

90

Pha

se (

degr

ees)

-90

0

90

Pha

se (

degr

ees)

MEMSMTODARPADARPA

Lattice Filter

Vin VoutR

R

Zb

Za

Zb

Za

Impedance of Za and Zb

ZaZb

Full filter response

wa wb

MEMSMTODARPADARPA

Lattice Filter

Lattice Filter Response

-30

-25

-20

-15

-10

-5

Mag

nitu

de (

dB)

-30

-25

-20

-15

-10

-5

Mag

nitu

de (

dB)

-270

-180

-90

0

90

Pha

se (

degr

ees)

-270

-180

-90

0

90

Pha

se (

degr

ees)

775 780 785 790 795 800 805 810 815 820 825 830Frequency (MHz)

775 780 785 790 795 800 805 810 815 820 825 830Frequency (MHz)

MEMSMTODARPADARPA

Simple Ladder Filter

Vin C12RL

RS

Z=sL+1/sC Z=sL+1/sC

Vout

102 103 104 105 106

-140

-120

-100

-80

-60

-40

-20

Frequency (MHz)

Magnitude (dB)

Simple Ladder Filter Response

-35

-30

-25

-20

-15

-10

-5

Mag

nitu

de (

dB)

-270

-180

-90

0

90

Pha

se (

degr

ees)

-35

-30

-25

-20

-15

-10

-5

Mag

nitu

de (

dB)

-270

-180

-90

0

90

Pha

se (

degr

ees)

798 799 800 801 802Frequency (MHz)

798 799 800 801 802Frequency (MHz)

Wideband Response

MEMSMTODARPADARPA

Simple Ladder Filter

797.5 798 798.5 799 799.5 800 800.5 801 801.5 802 802.5

-30

-20

-10

0

Filt

er T

rans

mis

sion

(dB

)

data1

data2

data3

797.5 798 798.5 799 799.5 800 800.5 801 801.5 802 802.5-270

-180

-90

0

90

Pha

se (

degr

ees)

no mismatch

0.1 %

0.3 %

Effect of bar length mismatch on filter characteristic

Nominal values:

l = 6.04 mw = 3.22 mt = 0.5 m

RS, RL = 1758 C12 = 113.2 fF

MEMSMTODARPADARPA

Vin

Vout

RS

RL

C12

Vin

RS

Vout

RL

C12

Mechanically Coupled Devices

MEMSMTODARPADARPA

Device Measurement

• Confirm successful operation of resonators and accuracy of the analytic model (f vs. l, spurious modes)

• Fit measurements to a discrete circuit model, adjust model if necessary, and extract resonator parameters (ie, determine resonator Q)

• Use resonator performance results and analysis of parasitics to guide process and design improvements

Primary Objectives:

MEMSMTODARPADARPA

Device Measurement

Device (GSG configuration)

5 m

3 m

~800 MHz resonator structure

C

Co

L R

RL

RS

MEMSMTODARPADARPA

First Round DevicesLongitudinal axis

AlN

contactcontact

C

Co

L R

RL

Rs

Cthru

S21

(dB

)

100

50

675 800 MHz 925

0

Cthru=0

Cthru=2pF

5 m Bar, Q=104

30

20

10

140 160 MHz 180

Cthru=2pF

25 m Bar, Q=103

S21

(dB

)

MEMSMTODARPADARPA

First Round L-Bar Resonance

-16

-15.9

-15.8

-15.7

-15.6

-15.5

69

70

71

72

73

146 150147 149148

Frequency (MHz)

Pha

se (

degr

ees)

S21

(dB

)

Cthru ~ 2 pF

MEMSMTODARPADARPA

Measurement Results

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

200

400

600

800

1 / m

Freq

uenc

y (M

Hz)

~ 3.8 GHz - m

12

E

=

-21

-20

-19

-18

-17

-16

-15

120 130 140 150 160

Frequency (MHz)

S21

(dB

)

30 m bar

25 m bar

Fundamental Length Resonances

Fundamental Width Resonances

-9

-8

-7

-6

600 700 800 900

Frequency (MHz)

MEMSMTODARPADARPA

Second Round L-Bar

-80

-70

-60

-50

-40S

21 M

agni

tude

(dB

)

100 200 300 400 500 600 700 800 900 100060

70

80

90

100

110

Pha

se (

degr

ees)

Frequency (MHz)

10 m x 5 m device showing length and width modes

MEMSMTODARPADARPA

Fit to ModelS21 data from 10m x 5m device

Parasitics modeled as port capacitance and resistance

BVD circuit parameters

•R= 35 k•L= 1 mH•C=0.047 fF•C0=12.7 fF •Q of ~125

MEMSMTODARPADARPA

Metal-Oxide-Silicon Structures

0 100 200 300 400 500 600 700 800 900 1000-100

-80

-60

-40

-20

0

S2

1 M

ag

nitu

de

(d

B)

0 100 200 300 400 500 600 700 800 900 1000-200

-100

0

100

200

Ph

ase

(d

eg

ree

s)

Frequency (MHz)

MEMSMTODARPADARPA

Glass Substrate

0 500 1000 1500 2000 2500 3000

-100

-80

-60

OP6 on Glass

S21

Mag

nitu

de (

dB)

0 500 1000 1500 2000 2500 30000

50

100

150

Pha

se (

degr

ees)

Frequency (MHz)

datasimulation

OP6 fit parameters:

- pure open to ground

- 1.43fF thru capacitance

MEMSMTODARPADARPA

Glass Substrate

OP1 fit parameters:

- pure open to ground

- 2.6fF thru capacitance0 500 1000 1500 2000 2500 3000

-100

-80

-60

OP1 on Glass

S21

Mag

nitu

de (

dB)

0 500 1000 1500 2000 2500 30000

50

100

150

Pha

se (

degr

ees)

Frequency (MHz)

datasimulation

MEMSMTODARPADARPA

Conclusions

• Filter designs will be implemented on upcoming mask layout. Mechanically coupled device will be used.

• An accurate model of parasitics is vital for obtaining useful device measurements.

• Ongoing work to define explanation for the 100 MHz resonance on silicon substrate, and the wideband phase noise

MEMSMTODARPADARPA

AcknowledgementsDraper Engineering

Amy Duwel, David Carter, Doug White

Draper FellowsPaul Calhoun, Luke Hohreiter

Draper Program ManagerJames Sitomer

Acknowledgements:Draper: Connie Cardoso, Mert Prince, Mark April,

Mark Mescher and Mathew VargheseMIT: Prof. Charles Sodini

DARPA: Contract # DAAH01-01-C-R204

MEMSMTODARPADARPA

S-parameters

2-port

network

Po

rt 1

Po

rt 2

V1+ V1

- V2- V2

+

jkVV

V

kj

i

i j

,0

S

MEMSMTODARPADARPA

Z-parameters

2-port

network

Po

rt 1

Po

rt 2

I1 I2 +

V1

-

+

V2

-

V1 = Z11I1 + Z12I2

V2 = Z21I1 + Z22I2

MEMSMTODARPADARPA

Two-port model

Zb

Zc Za

cba

cba11 ZZZ

ZZZZ

cba

ca12 ZZZ

ZZZ

cba

bac22 ZZZ

ZZZZ

1222a

Z-Z

ZZ

12b

Z

ZZ

1211c

Z-Z

ZZ Z = Z11Z22-Z12

2

MEMSMTODARPADARPA

Transformed Zb Impedance Data

1.5 2 2.5 310

0

101

102

103

Zb Magnitude and Phase

Impe

danc

e M

agni

tude

(

)

1.5 2 2.5 3-2

-1

0

1

2

Impe

danc

e P

hase

(ra

dian

s)

Frequency (GHz)

fs fp

|Zs|

|Zp|

LC

1π2

ss fw

0C

C1π2

spp wfw

RRCj1

RZ

0

s

sw

20

220

2

0

pRC

1

RC

RCj-1Z

pp

p

ww

w

MEMSMTODARPADARPA

BVD Model Fitting

0

10

20

30

40

50

60Zb Magnitude and Phase

Impedance Magnitude (dB)

1.5 2 2.5 3-2

-1

0

1

2

Impedance Phase (radians)

Frequency (GHz)

datadatamodel

R = 2.76 , L = 91.6 nH, C = 0.061 pF, C0 = 1.54 pF

MEMSMTODARPADARPA

Filter Design Constraints

• Q assumed to be a function of the process and static• Two degrees of freedom, l and w/t• Resonant frequency fixes l uniquely• For a given frequency, the other degree of freedom

controls the “impedance level”• C/C0 fixed by piezoelectric materials parameters

Constraints placed on equivalent circuit parameters bybar geometry: