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Sensors and Actuators A 132 (2006) 8–13

A mechanical-stress sensitive differential amplifier

Vitor Garcia ∗, Fabiano FruettSchool of Electrical and Computer Engineering, University of Campinas, Caixa Postal 6101, CEP 13083-970 Campinas, Brazil

Received 6 September 2005; received in revised form 29 May 2006; accepted 18 June 2006Available online 25 July 2006

bstract

A novel low power totally CMOS compatible mechanical-stress sensitive differential amplifier, which can be used as a pressure sensor, isresented. This amplifier is based on a special designed layout where the stress sensitivity of the input differential pair is maximized and the stressffects on the second stage are minimized. Finite element simulation was used to design the membrane and to locate the element sensor on it.he sensor was fabricated in a CMOS 0.35 �m process. In order to make a pressure sensor without a backside bulk micro-machining process, the

hickness of the die was reduced by a mechanical polishing process. This paper also shows an automated structure used in the pressure sensorsharacterization. To reach a very well controlled pressure, the structure is totally controlled by LabView® Virtual Instruments. The sensor poweronsumption amounts to 3 �W and the sensitivity is adjustable by a convenient external feedback arrangement.

2006 Elsevier B.V. All rights reserved.

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eywords: Piezo-MOS effect; Low-power consumption; Mechanical sensor

. Introduction

Silicon sensors for mechanical signals, e.g. pressure sensorsnd accelerometers are, in general, extremely successful prod-cts. Today, many kinds of silicon sensors for mechanical signalsave been proposed based on the various piezo effects observedn silicon devices [1–3]. Most of these silicon sensors are basedn the piezoresistive effect, which relates the mechanical-stressnfluence on the bulk resistivity of silicon [4]. They consist of a

embrane or cantilever beam in which a piezoresistive Wheat-tone bridge is diffused.

In the sensors based on the piezoresistive effect a signal con-itioning circuit is normally used to amplify the small signalrom the piezoresistive Wheatstone bridge. Thus, these sensorsave two sources of power dissipation: the piezoresistive bridgend the conditioning circuit. These two power budgets make theensor prohibitive to low power applications.

The use of capacitive pressure sensors can be a solution to

his problem. However, capacitive pressure sensors have a highonlinearity, which complicate the circuit interface.

∗ Corresponding author. Tel.: +55 19 3287 7578; fax: +55 19 3289 1395.E-mail addresses: vgarcia@led.unicamp.br (V. Garcia),

abiano@dsif.fee.unicamp.br (F. Fruett).

scpoatt

924-4247/$ – see front matter © 2006 Elsevier B.V. All rights reserved.oi:10.1016/j.sna.2006.06.060

Beside the piezoresistive effect, there are others “piezo”ransduction effects, which can be implemented with bipolar or

OS transistors [5]. Although these piezotransistors are totallyompatible with standard CMOS process, they have been, littlexplored until then.

To overcome the problems displayed by piezoresistive andapacitor/pressure sensors, we present a differential pressureensor based on the piezo-MOS effect. The sensing elementsre MOS transistors, which are optimized to maximize theechanical-stress induced unbalance on a differential pair.The presented sensor joins the Piezo-MOS transistors and the

ignal conditioning circuit together in a single stress-sensing dif-erential amplifier. This sensor exhibits suitable characteristicsuch as low-power consumption, low nonlinearity and adjustableensitivity.

. Piezoresistive effect

The drain current in the MOS transistor, when operating introng inversion, is determined by the channel resistivity. Weonsider that the piezo-MOS effect has a similar behavior as theiezoresistive effect and the influence of the crystallographic

rientation on the magnitude of the piezoresistive effect [6] islso valid for the piezo-MOS effect [7]. First, we will presenthe piezoresistive theory and then generalize it to the piezo-MOSheory.

V. Garcia, F. Fruett / Sensors and Actuators A 132 (2006) 8–13 9

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Table 1Piezoresistive coefficient values for lightly doped silicon

Piezoresistive coefficient PMOS (×10−10 Pa−1) NMOS (×10−10 Pa−1)

π11 0.7 −10.2π

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ig. 1. Uniaxial stress orientation (λ) and resistor alignment (ϕ) related to the1 0 0] crystal axis.

The resistance in an integrated silicon resistor can be calcu-ated by the following equation:

� L

WH

1

qpμ(1)

here L, W and H are the resistor length, width and height,espectively, and q the electron charge. Resistance variationue to stress can be attributed to geometrical deformations andobility change. Based on stress level and the Young’s modulus,

t is easy to show that the geometrical deformations influencen resistivity change is small compared to the stress inducedobility change. Thus, it is a good approximation to write [8]

�R

R� −�μ

μ(2)

here �μ is the stress-induced change in the stress-free mobility.

The relative change in the resistance R can be calculated basedn the resistor alignment and stress orientation. The uniaxialtress orientation (λ) and the resistor alignment (ϕ) have therystal axis [1 0 0] as the reference, as shown in Fig. 1.

The [1 1 0] axis is parallel to the primary wafer flat. Since theafer dice is laid out in rows and columns relative to the waferat, the X- and Y-axes of the layout correspond to the 〈1 1 0〉irections.

In the following equation for the relative change in the resis-ance, we consider a resistor fabricated in the {0 0 1}-waferlane, which is subject to an in-plane uniaxial stress [5]

�R

R� σ

[π11

(1

2+ 1

2cos 2ϕ cos 2λ

)

+ π12

(1

2− 1

2cos 2ϕ cos 2λ

)

+ π44

(1

2sin 2ϕ sin 2λ

)](3)

here �R is the stress-induced change in the stress-free resis-ance R, σ the in-plane uniaxial stress and π11, π12 and π44 arehe piezoresistive coefficients. Typical values of the piezoresis-ive coefficients for lightly doped silicon are shown in Table 14].

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12 −0.1 5.3

44 13.8 −1.4

. Piezo-MOS effect

The effect of the mechanical stress on the characteristics ofOS transistor was measured for the first time in the late 60s

7,9]. The piezo-MOS effect concerns the mechanical-stressnduced change in the inversion layer carrier mobility of the

OS transistor. At present, only a fewer studies were done aboutts applications on mechanical sensors [2,10–12] and stress-nduced mismatches on CMOS devices [13–16].

The drain current expression in a MOS transistor when it isn the strong inversion region is given by

D = μCoxW

L(vGS − VT)2 (4)

here μ is the free-carrier mobility, Cox the gate oxide capaci-ance per unit of area, W and L represents, respectively the widthnd length of the transistor channel, vGS is the gate-source volt-ge and VT the threshold voltage.

If geometrical deformations in the MOSFETs channel andarrier-number variations due to the stress-induced change ofhe energy bandgap can be neglected [17], only the mechanicaltress induced change in the mobility will affect the drain current.he relative drain current variation due to stress can be expressedy

�ID

ID= �μ

μ(5)

ombining Eqs. (2), (3) and (5) we can evaluate the relativehange in drain current. For PMOS transistor, the piezoresistiveoefficients π11 and π12 are much smaller than π44. Thus, thehange in the relative drain current can be maximized when= m45◦ and λ = n45◦, where m and n are any integer numbers.e observe that any direction given by m45◦ or n45◦ correspond

o the 〈1 1 0〉 axes.The relative change in the drain current due to a uniaxial

tress σ parallel to the silicon crystallographic direction [1 1 0]mounts to

�ID

ID� �μ

μ� −±π44

2σ (6)

he sign of the coefficient π44 depends on the direction ofhe drain majority-current flow. This sign is positive for the

OS channel length aligned parallel with the uniaxial stressirection and negative for the MOS channel length alignedransversal with the uniaxial stress direction. The first case is

alled longitudinal MOS (ML) and the second, transversal MOSMT).

Both piezoresistive and piezo-MOS effect have the samehysical origin [7,18]. The applied stress causes a mechanical

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0 V. Garcia, F. Fruett / Sensors

train in the material. The mechanical strain modifies the sili-on crystallographic symmetry, changing the band energy levelsnd modifying the silicon electrical properties, as the resistivity19].

Compression decreases the minimum required energy thelectron needs to remain in the conduction band, increasinghe conductivity. It is the case of transversal MOS transistors

T. Traction has the opposite effect, increasing the minimumequired energy the electron needs to remain in the conductionand, decreasing the conductivity. It is the effect observed inongitudinal MOS transistors ML.

. Finite element analysis

A combination of both transversal and longitudinal MOSransistors is used in the core of the stress-sensing differentialair. A micromechanical model based on finite element analysisFEA) is very suitable in order to optimize the sensor design,aximizing the stress sensitivity and reducing second-order

ffects mainly due to mismatching. The FEA micromechanicalodel can also be used to estimate the magnitude and direction

f the in-plane stress on the surface for a certain differentialressure applied on the sensor. In our case, we are interestedn localizing the stress-sensing differential pair on the regions,hich have maximization of the uniaxial stress in the 〈110〉irections.

A 3D finite element modelling of the sensor with a circularembrane was performed using a mechanical simulation pro-

ram, Ansys®. The model was based on the final shape of theensor after the die attachment in an alumina substrate with aent-hole in the center. The circular membrane edge is deter-ined by the die contact over the edges of the vent-hole.Due to the membrane symmetry only a quarter of the struc-

ure has been simulated. A mesh using 20 nodes structural-solid

lements with anisotropic capabilities was created. Based on theicro-mechanical simulation we defined the membrane thick-

ess equals to 60 �m and the membrane diameter equals tomm.

s

v

Fig. 2. Finite-element simulation for in-plane normal str

ctuators A 132 (2006) 8–13

Fig. 2(a) and (b), shows the finite element simulation for then-plane normal stress in [1 1 0] direction and in-plane normaltress in [1 1 0] direction, respectively. Negative stress meansompression and positive stress means traction. Based on Fig. 2,e observe the positions of maximal traction stress, in the 〈1 1 0〉irections, which amounts to 20 MPa.

. Pressure-sensor differential amplifier

The circuit schematic of the proposed pressure sensor ishown in Fig. 3a. This two stage CMOS differential amplifieras the stress-sensing differential pair, PMOS transistors ML1,

L2, MT1 and MT2, as its core. The current mirror formed by1 and M3 supplies the stress-sensing differential pair with bias

urrent. The differential pair is actively loaded with the currentirror formed by M4 and M5. The second stage consists of6, which is a common-source amplifier actively loaded with

he current-source transistor M2. In order to reduce the stress-nduced mismatch and better to locate the stress-sensing differ-ntial pair around the region of maximal stress, we designed thisifferential pair using/common-centric geometry.

The centric center is positioned at the point of maximal stress,hich is defined by the geometry and position of the sensor on

he die. It is obtained by the mechanical simulations. The channelidth and length of the transistors (MT1, MT2, ML1 and ML2)

re W = 50 �m and L = 10 �m, respectively. Fig. 3b shows theayout of the differential pair.

When pressure is applied to the membrane, the drain cur-ent in the longitudinal differential transistor pair increases andhe drain current in the transversal differential transistor pairecreases. Due to this imbalance in the differential pair current,n offset voltage, proportional to the applied stress, appears onhe output.

For grounded inputs, the equivalent stress-induced input off-

et voltage is given by [20]

offset � Ibias

gm

(±π44

2

)σ (7)

ess in (a) [1 1 0] direction and (b) [1 1 0] direction.

V. Garcia, F. Fruett / Sensors and Actuators A 132 (2006) 8–13 11

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ig. 3. (a) Pressure sensor differential amplifier circuit and (b) common-centricayout of the stress-sensitive differential pair.

here Ibias is the differential-pair bias current and gm is the MOSranscondutance. According to [13], we can simplify Eq. (4) to

offset � π44

2(vGS − VT) σ (8)

here vGS is the gate-source voltage of the differential-pair tran-istors and VT the PMOS threshold voltage.

The close-loop output voltage for a negative feedback con-guration and positive input connected to ground is given by

offset � π44

2(vGS − VT)

(1 + R1

R2

)σ (9)

here R1 and R2 are the feedback network resistors, which definehe close-loop gain.

. Test structure

The test structure was designed to generate a well-controlledressure inside a pressure chamber to characterize the sensor.he test structure is composed by a pressure structure genera-

ion, acquisition-data instrumentation and a pressure reference.ll test structure components are connected to computer byPIB interface. A virtual instrument (VI), implemented withabView®, automatically controls the pressure generation, data

(oi

Fig. 4. Mechanical structure picture.

cquisition and data storage. A mechanical structure picture ishown in Fig. 4.

The pressure generator structure is basically composed by aable of linear displacement, a pressure chamber and a pneumaticylinder. The pressure chamber is connected to the pneumaticylinder. The pneumatic cylinder has its stem full-fixity at theable of linear displacement, which is moved by a step motor.he movement of the table changes the cylinder internal volumeenerating a pressure inside the chamber, where the sensor underest is conditioned. The precise control of the stem course makesossible to obtain a well-controlled pressure inside the chamber.

The step motor is controlled by a driver, composed by aower-driver circuit, a switch unit and a power supply. All ofhem are connected to computer by a GPIB interface. Throughhe VI, the operator defines a numerical vector containing the tar-et pressures. After that, the computer controls the step motor, sohat the pressure inside the chamber reaches the target pressure.uring this action, the pressure reference constantly monitors

he pressure inside the chamber.The pressure sensor output signal is acquired by a data acqui-

ition unit connected to computer by GPIB interface. The acqui-ition unit is controlled by VI. Beside the pressure inside thehamber and sensor output signal, a Pt100 connected to the pres-ure chamber measures the sensor temperature. Fig. 5 shows theardware of the test structure.

All measurement variables: reference pressure, temperaturend output signal of the pressure sensor in test are stored in aata file.

. Realization and results

The differential amplifier was made in the 0.35 �m AMSMOS process with a 4 mm × 4 mm die area. Fig. 6 shows theicrophotograph of the fabricated sensor.As only front side micro-machine is available in the AMS

rocess, the membrane was obtained after the die fabrication.super-polishing mechanical process using Al2O3 reduced the

riginal thickness of the die to 60 �m.

The thin die was attached by room temperature vulcanization

RTV) on an alumina substrate. The attach alignment was basedn the center of a vent hole, with 2 mm of diameter, containedn the center of the alumina substrate. A plastic cup was used

12 V. Garcia, F. Fruett / Sensors and Actuators A 132 (2006) 8–13

are of the structure.

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Fig. 5. Hardw

o protect both the chip and the wire-bond. Fig. 7 shows theross-section of the sensor-packaging scheme.

The sensor was mounted and connected to a vacuum gener-tor, through a pressure chamber. The structure provides well-ontrolled pressure ranging for the sensor tests.

The output voltage vo of the pressure sensor was measured forpplied differential pressure ranging from 0 to 10 psi. The volt-

ge supply was VDD = 1.65 V and VSS = −1.65 V. Fig. 8 showshe measured results for the stress-induced change in the outputoltage.

Fig. 6. Microphotograph of the fabricated sensor.

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Fig. 7. Cross-section of the sensor-packaging scheme.

The result shows an offset of 601 mV and a sensitivity of.90 mV/psi, which were obtained by the close-loop gain equalso 100. The high offset is a result of the mechanical stress effectver the differential pair due to the packaging process. As theifferential pair design is optimized to sense the stress, the dieonding over the alumina generates an offset voltage on theperational amplifier output multiplied by the feedback gain.

Fig. 8 also shows the nonlinearity of the experimental results

n detail. The nonlinearity appears to be less than ±1% for pres-ure up to 10 psi.

The measured power consumption amounts to 3 �W.

Fig. 8. Output voltage and nonlinearity vs. applied pressure.

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V. Garcia, F. Fruett / Sensors

. Conclusions

It has been shown a low-power pressure sensor, which isased on the piezo-MOS effect. This pressure sensor is totallyompatible with standard CMOS process. A mechanical polishechnique was used to obtain a thin membrane instead of a con-entional anisotropic bulk-micro machine etching. The core ofhis sensor is a PMOS stress-sensing differential pair, which hasts layout optimised to maximize the mechanical stress effects.n the other hand, the second stage of the operational amplifier isesigned to minimize the stress effects. The tested sensor showssensitivity of 8.90 mV/psi and a total power consumption of�W that is at least one order of magnitude lower compared to

he power consumption of the well-known piezoresistive pres-ure sensors.

cknowledgments

The authors would like to thank Marcio Biasoli and Marinalvarom Renato Archer Research Center (CenPRA) for their techni-al support with the delicate packaging job. Wellington Romeiroe Melo and Dr. Saulo Finco, also from CenPRA, for the sup-ort with the Mentor Graphics and AMS design kit. They alsohank Amauri Vendemiatti and Pedro Vendemiatti from Industria

ecanica Harmon Ltda for the fruitful discussion about mechan-cal polishing. Fapesp, for providing the Mult-Users Project run.he Brazilian National Council of Scientific and Technologicalevelopment CNPq partially support this research.

eferences

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[4] C.S. Smith, Piezoresistance effect in germanium and silicon, Phys. Rev. 94(1954) 42–49.

[5] F. Fruett, G.C.M. Meijer, The piezojunction effect in silicon, its conse-quences and applications for integrated circuits and sensors, Kluwer, Delft,The Netherlands, 2002, p. 1.

[6] Y. Kanda, Graphical representation of the piezoresistance coefficients insilicon, IEEE Trans. Electr. Dev., ED-29 (1982) 64–70.

[7] D. Colman, R.T. Bate, J.P. Mize, Mobility anisotropy and piezoresis-tance in silicon p-type inversion layers, J. Appl. Phys. 39 (1968) 1923–1931.

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iographies

itor Garcia was born in Sao Paulo, Brazil, in 1977. He received the BEEEegree from University of Campinas (UNICAMP), Campinas, SP, Brazil in002. At the moment he is pursuing his MS degree in Electrical Engineeringrom the same university. His current research interests are in the field of pressureensors and microelectronic circuits.

abiano Fruett received the BEEE degree from the State University of Saoaulo (UNESP-Ilha Solteira), Brazil, in 1994 and the MS degree in Electricalngineering from the University of Campinas (UNICAMP), Campinas, Brazil,

n the beginning1997. In 1997, he joined the group of the Prof. Gerard Meijer athe Delft University of Technology in The Netherlands, where he worked towards

is PhD in the field of electronic sensors. He obtained his PhD in September001. In February 2002, he joined the Department of Semiconductors, Instru-ents and Photonics of the University of Campinas (UNICAMP), Campinas,razil, where he is now Assistant Professor. His research interests are in theeld of pressure and temperature sensors and microelectromechanical systems.