a novel capacitive pressure sensor

1272 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 14, NO. 6, DECEMBER 2005

A Novel Capacitive Pressure SensorBased on Sandwich Structures

Min-Xin Zhou, Qing-An Huang, Senior Member, IEEE, Ming Qin, and Wei Zhou

Abstract—This paper presents a sandwich structure for a ca-pacitive pressure sensor. The sensor was fabricated by a simplethree-mask process and sealed in vacuum by anodic bonding. Thesensor, which utilizes a combined SiO2/Si3N4 layers as the elasticdielectric layers, exhibits high sensitivity. Mechanical characteris-tics of the sensor are theoretically analyzed based on a compositemembrane theory and evaluated by use of finite element analysis(FEA). Square membrane sensors with side lengths of 800 m,1000 m, 1200 m, and 1500 m were fabricated, providing ameasured sensitivity of 0.08 pF/kPa, 0.12 pF/kPa, 0.15 pF/kPa, and0.2 pF/kPa, respectively. The nonlinearity of the sensor is less than1.2% over a dynamic range 80–106 kPa and the maximum hys-teresis is about 3.3% to the full scale capacitance change. The TCOat 101 kPa is 1923 ppm/ C. All the electrodes of the sensor areleaded from the top side of the chip. Residual pressure in the sealedcavity at room temperature is evaluated by a pressure scanningtest, indicating about 8 kPa. Comparison of experimental resultswith theoretical analysis shows that change of capacitance for thesandwich structure under pressure is mainly due to variation ofthe dielectric constant while geometric variations such as the areachange of electrodes and the thickness change of dielectric layers isabout two orders less than the variation of the dielectric constant.Sensitivity enhancements for the sensor are qualitatively discussedbased on the physical effects of strained dielectrics, including elec-trostriction and flexoelectricity. [1551]

Index Terms—Capacitive pressure sensor, composite mem-brane, electrostriction, flexoelectricity.

I. INTRODUCTION

M ICROMACHINED pressure sensors have found wideapplications in areas such as automotive systems, indus-

trial control, environmental monitoring and biomedical diag-nostics. Capacitive pressure sensors translate a pressure changeinto a capacitance variation, which tend to provide higher sensi-tivity, lower temperature coefficients, more robust structure andlower power consumption compared to piezoresistive devices[1]–[3]. Conventional capacitive pressure sensors generally op-erate by sensing the downward displacement of a thin, flexibleconductive membrane as one of the electrodes, while the otherelectrode is fixed beneath the membrane. Deformation of themovable part due to applied pressure is sensed and translatedinto an electrical capacitance change. As the capacitance valueis inversely proportional to the distance between the two elec-trodes, capacitive devices with traditional structures show non-linear characteristics in response to the applied pressure, causing

Manuscript received March 18, 2005; revised July 1, 2005. This work is sup-ported by National High-Tech Research Program of China (2004AA404030),National Natural Science Foundation of China (60476019), and Natural ScienceFoundation of Jiangsu Province (BK2003052). Subject Editor G. B. Hocker.

The authors are with the Key Laboratory of MEMS of Ministry of Education,Southeast University, Nanjing 210096, China (e-mail: [email protected]).

Digital Object Identifier 10.1109/JMEMS.2005.859100

the sensor compensation to be difficult. Many efforts have beenmade to ameliorate the nonlinearity of capacitive pressure sen-sors [4], [5].

The cavity between the two electrodes of the capacitivepressure sensor and the electrical feedthrough out of the cavitycomplicate the fabrication process, resulting in increased pro-cessing difficulties and cost of the devices. Many methods havebeen developed to realize the cavity structure of the pressuresensor. One approach includes the sacrificial layer depositionand etching by using surface micromachining technology[6]–[8]. The cavity was formed by removing a buried siliconoxide, phosphosilicate glass (PSG) or borophosphosilicateglass (BPSG) layer and sealing by chemical pressure deposi-tion (CVD). The bottom electrode was leaded out through avia opening and subsequent metal deposition. Such seals areknown to be hermetic [7], [9]. In this structure, stiction betweenthe two capacitor plates could be adverse to the reliability ofthe sensors. Other methods to form a sealed cavity involveselectively etching a bulk silicon wafer to define a cavity andthen anodically bonding to glass [1], [3], [10]. The bottomlead (the electrode on the glass substrate) is transferred outsidethrough buried polysilicon encased in dielectric layers or bymetal sputtering to fill the hole through the glass substrate. Par-ticular process steps are required such as glass drilling, epoxyor special metal sealing and chemical-mechanical polishing forprecise height control [3], [10]. Ten masks or more have beenused to implement such structures and most of the masks areused for lead feedthroughs. Special processing involved in thedevices implementation, which is not compatible with silicontechnology, eliminates the advantages of batch fabrication. Inaddition, the complicated fabrication process affects yieldsand may cause potential reliability problems such as hermeticsealing of feedthough and corresponding larger electrical par-asitic and temperature effects.

In order to enhance the sensitivity and linearity of the pres-sure sensor, proposed novel structures combine the area anddistance change of the electrodes [11]. Diagrams with highaspect ratio of area to thickness have been used to achieveultrasensitive absolute capacitive pressure sensors [12]. Besidesthe principles based on electrode deformations of the sensor, asolid-state capacitor incorporating an elastic dielectric betweenthe conductors has been introduced for pressure, stress, strainand tactile sensing [13]. Two to three times larger sensitivityenhancement was achieved with this structure, which may bephysically explained based on the electrostriction effect of theelastic dielectrics.

In this work, a novel pressure sensor employing a sand-wich structure with dielectric layers between two electrodesis realized in order to overcome the processing difficulties

1057-7157/$20.00 © 2005 IEEE

ZHOU et al.: A NOVEL CAPACITIVE PRESSURE SENSOR BASED ON SANDWICH STRUCTURES 1273

Fig. 1. Simplified structure of the composite-membrane capacitive pressuresensor. (a) Side view of the sensor structure and (b) cross section of the structure.

mentioned above [14]. Composite-membrane structures, i.e.,combined SiO /Si N layers, are advantageously utilized forstress compensation [15], [16]. In addition to the simplicityof fabrication, the solid-state capacitor has a more robuststructure and an intrinsically larger initial capacitance valuebeneficial for parasitic restraining and signal processing withinterface circuits. Improved sensitivity and linearity, higherreliability and lower cost can be achieved with such a structure.In Section II, the sensor structure and behavior are introduced.The mechanical and thermal characteristics of the device areanalyzed based on elastic theory. The temperature characteristicdue to silicon-glass bonding and the residual pressure in thecavity are estimated. Sensitivity enhancements of the sensorbased on electrostriction and flexoelectricity effects are quali-tatively discussed. Processing details and experiment results ofthe sensor are presented in Section III. Conclusions are madein Section IV.

II. STRUCTURE AND BEHAVIOR

A. Basic Principles

A schematic of the proposed capacitive pressure sensor witha composite membrane is shown in Fig. 1. The sensor consistsof a sealed pressure-reference cavity formed by silicon-glass an-odic bonding with a composite membrane serving as the sensingelement, which is a variable capacitor with a conductor/dielec-tric/conductor structure on a Si membrane. The top andbottom electrodes are Au and Si layers, respectively, while

the dielectric layers are SiO and Si N . The composite mem-brane provides a flexible structure, deflecting with applied pres-sure that causes area changes of the electrodes and strain in thedielectric layers. The feedthrough problem is avoided since theelectrodes are leaded from the top side of the wafer. No addi-tional steps are needed for the fabrication of the electrode onthe glass and the feedthroughs out of a sealed cavity.

The relative capacitance change of the flexible parallel-platesolid-state capacitor involves the area change of the electrodesand the thickness and relative dielectric constant changes of thedielectrics, which is shown by

(1)

where and are the thickness, area and dielectric constantof the dielectric layer, respectively.

The term is introduced here because the electrodescan be deformable. Area changes of the electrodes are de-termined by the bending shape of the sandwich structure underuniform pressure load. and exhibit the geometryvariation of the structure, while the third term shows thecomposite physical effect of the elastic dielectric layers. Elec-trostriction and flexoelectricity were considered to contributethis change [13], [17], [18]. As a result, the capacitive pressuresensor based on the sandwich structure extends the conventionalprinciples by including the dielectric effects.

B. Mechanical and Thermal Analysis

A mechanical and thermal analysis of a multilayer membraneis essential to understand the principles of sensor operation andoptimization of the sensor design. The capacitance change ofthe sensor due to membrane bending depends on the mechan-ical properties of the materials involved, structural dimensions,and the applied pressure. The structure is treated here as largedeflection since the deflections of the membrane are larger thana half of the membrane thickness. Applied pressure, mechan-ical stress due to temperature changes and residual stress in themembrane are all important factors for the analysis of the sensi-tivity and temperature coefficient of the sensor. For simplicity,a square composite membrane is used in the analysis, and it isassumed that the membrane remains flat when no pressure isapplied. Based on elastic theory, a load-deflection model for themultilayer membrane can be derived by extending a method fora single-layer membrane. A composite membrane model with

layers is shown in Fig. 2. The side length of the mem-brane is . Parameters , andcorrespond to thickness, Young’s modulus, Poisson’s ratio, co-efficient of thermal expansion (CTE) and residual stress of theth layer of the multilayer membrane, respectively. Based on the

flat membrane assumption, the average composite membranestrain is represented by . According to the relationship be-tween strain and stress and the equilibrium conditions of allstresses [16]

(2)

(3)


Fig. 2. Analytical model for the composite membrane under uniform pressure. (a) Coordinate axis presentation of the model for a square membrane where a ishalf of the side length of the diaphragm. (b) Material parameters presentation of the multilayered membrane.

From (3), the normal strain of the multilayer membrane is givenby

(4)

The average composite residual stress in the plane is given by

(5)

Using a similar analysis method, the average composite coeffi-cient of thermal expansion (CTE) of the multilayered membrane

is derived as

(6)

The mismatch resulting from the coefficients of thermal expan-sion (CTE) between the multilayered membrane and the siliconsubstrate induce strain and stress in the membrane with temper-ature changes, which may be derived as [15]

(7)

where is the strain due to thermal expansion, is the CTEof the silicon substrate, is the temperature change.

If the thickness of the multilayer membrane is assumed to bemuch smaller than the length, each layer has the same displace-ments under applied pressure. The strain can be expressed interms of the displacements when large deflections and clampedboundary conditions are assumed [19]

(8)

where and are the normal strain, is the shearing strain,and , and are the displacements in the , and direc-tions, respectively.

Taking the residual stress and thermal stress changes into con-sideration, strains due to pressure are found by the subtractionof the total strain from the residual strain and the thermal mis-match strain, given by [16]

(9)

According to the boundary conditions of the clamped multilayermembrane, the displacement shape functions may be taken asfollowing [20]:

(10)

where and are the maximum displacements in the planeand out of the plane, respectively.

Based on elastic theory and virtual energy analysis tech-niques, the work input by the applied uniform pressure istransformed into the elastic stretching and bending energy ofthe membrane. Since stretching energy of one layer membraneis a linear function of the layer thickness, the total stretchingenergy of the multilayer membrane can be simplified bysumming of the stretching energy of each layer, which is givenby

(11)


The bending energy of a single-layer membrane is propor-tional to the cubic of the thickness, given as follows [20]:

(12)

where are the Young’s modulus, Poisson’s ratio,thickness, and half length of the membrane, respectively. In-serting (10) into (12), the bending energy of the single-layermembrane may be obtained as a function of the maximum outof the plane displacement of the membrane as

(13)

According to (13), the total bending energy of the mul-tilayer membrane may be written as

(14)

The work input by the uniform pressure applied perpen-dicular to the membrane is given by

(15)

The total potential energy of the multilayered membrane,, then, may be written in the form of the max-

imum displacements and to get a displacement solution tothis problem. The total potential energy of the multilayer mem-brane is minimized with respect to and in the displace-ment equations, resulting in a relationship between the uniformapplied pressure and the maximum displacement in the center ofthe membrane utilizing the principle of virtual work [20], whichis shown by

(16)

Fig. 3. FEA results of the maximum displacement of the multilayeredcomposite membrane under the uniform pressure of 100 kPa. The thicknessesof the SiO , Si N , and Au are 0.2 �m, 0.2 �m, and 1500 Å, respectively.The thickness of the p layer ranges from 1 to 5 �m and the side length ofthe membrane ranges from 800 to 1600 �m.

where

and are the parameters representing the effects of theresidual stress and thermal stress on the maximum displace-ment . is the linear parameter between the pressure andunder large deformation, while , and are the nonlinearparameters in the cubic term of . The parameter dependson geometry and material types of the membrane.

C. Load-Deflection Finite Element Analysis

A load-deflection finite element analysis was performed toverify the analytical model derived above. Eight-node Solid45elements in ANSYS ™ were utilized to perform the analysis[21]. There is a tradeoff between the area, thickness and hard-ness of the membrane materials. Larger materials area andthinner layers result in a larger deflection and a higher sensi-tivity. However, the stress in the membrane will be increased sothat the reliability of the membrane is reduced. High sensitivitywith small area and enough hardness is the desired result forthe design. The thicknesses of SiO , Si N and Au are keptunchanged with 0.2 m, 0.2 m, and 1500 Å, respectively,while the thickness of the silicon varies from 1 m to


Fig. 4. FEA results of the maximum von-Mises stress of the multilayered composite membrane under a uniform pressure of 100 kPa. The thicknesses of theSiO , Si N , and Au are 0.2 �m, 0.2 �m and 1500 Å, respectively. The thickness of the p layer ranges from 1 �m to 5 �m and the side length of the membraneranges from 800 �m to 1600 �m.

Fig. 5. Comparison between the model and the FEA results. The pressurerange is from 10 kPa to 110 kpa and the thickness of the p layer is 3 �m and4 �m, respectively. The error of the membrane with dimensions H = 4:55 �mand L = 1000 �m is about 8% and the error of the membrane with dimensionsH = 4:55 �m and L = 1000 �m is about 7.8%.

5 m with a step of 1 m, and the side length changes from800 m to 1600 m with a 200 m step. The ANSYS™ simu-lation results for the maximum deflection of the membrane withvarying side length and thickness are illustrated in Fig. 3. Themaximum von-Mises stresses of the membrane are shown inFig. 4. Comparison of the model and finite element analysis isgiven in Fig. 5, showing that the error of the model is within 8%compared to the finite element analysis results.

D. Thermal Warpage Analysis and Temperature Coefficient ofOffset (TCO)

In the foregoing analysis, the composite-membrane is as-sumed to remain flat when no pressure is applied. However,mismatches between the thermal expansion coefficients of

Fig. 6. Finite element solid model of the sensor structure for thermal warpagesimulation.

the multiple layers induce stress variations, which may causethermal warpage of the sensing composite membrane [22].It is difficult to develop a model to analyze this situation be-cause several materials and complex boundary conditions areinvolved. Finite element analysis is an alternative to solve thisproblem. ANSYS™ is used to simulate the maximum rippledisplacement due to thermal warpage [21]. A 3-D quarter solidmodel was constructed with eight-node Solid95 elements, asshown in Fig. 6. The die size is 3000 m 3000 m and themembrane size is 1000 m 1000 m.

The simulated bonding temperature is 400 C and the deviceis then cooled down to 25 C to evaluate the ripple displace-ment of the membrane at room temperature. Simulation resultsshow that the ripple displacement at the center of the membraneis about 30 Å, which indicates the contribution of thermal mis-match of the multilayer materials to the TCO of the pressuresensor is very small and is not a concern. Initial in-plane stressesin each layer are assumed to be uniform along the thickness.However, stress gradients occur when combing each layer intoa composite membrane. Compensation may occur and the effect


of the stress gradient can be reduced if the multilayers have re-versed initial residual stresses. As a result, the membrane has anearly symmetrical CTE. This is the reason why the simulationresults show that there was a nearly negligible ripple displace-ment in the membrane. The temperature coefficient of offset(TCO) of the sensor is defined as

(17)

where is the zero-pressure capacitance at room temperature,and is the capacitance change per temperature incre-ment. Two factors affect TCO: one is the ripple displacementand the other is the thermal expansion of the membrane. Basedon (16), TCO due to ripple displacement is aboutppm. The contribution of membrane expansion to the TCO canbe simply derived as follows:

(18)

where is the CTE of the silicon substrate, is the equiv-alent CTE of the composite membrane. Based on (6) and (16),the TCO due to expansion is about 0.032 ppm, which is the mainpart of TCO.

E. Sensitivity Analysis and Dielectric Effect

The sandwich structure under load results approximatelyin a bending shape described in (10). The relative capaci-tance change in (1) due to electrode bending can be derivedas . Limited bythe assumption of an elastic deformation and the hardnessof the membrane, the relative maximum area variation of theelectrodes is about the order of 1/1000. As analyzed in SectionII-A, the relative normalized change due to geometry variationsis about 0.002.

The sensor response may be enhanced due to the contribu-tion of the dielectric properties of the elastic dielectric materialsunder deformation. Electrostriction exhibits the effect of uni-form deformation on the dielectric constant, which is describedby [13]

(19)

In the case of a clamped sandwich structure in this paper,the relative thickness change of the dielectric layers

, can be approximately estimated as the relativearea change based on an assumption of an un-changed dielectrics volume, which is reasonable since themembrane can deflect freely along the thickness directionalthough it is constrained in the directions. As a re-sult, and , where

and [13]. indi-cates that the dielectric material amplifies the sensor sensitivitydue to the electrostriction enhancement effect. Several timesenlarged sensitivity can be achieved over geometry variationcontributions.

In addition to the electrostriction enhancement of the dielec-tric layers, the electric polarization caused by the inhomoge-neous strain in elastic dielectric materials also makes contribu-tions to the sensor response, which may be explained by theflexoelectric effect of dielectric materials. Flexoelectric effectis one of the piezoelectric effects that exhibit the relationshipbetween the electric polarization and the applied electric stress[17], which is defined by the following relation:

(20)

where is the th component of the flexoelectric polarization,is the flexoelectric coefficient, is the elastic strain and

is the coordinate position, respectively. Flexoelectricity isconsidered to be a property of all solid elastic dielectrics sinceit is controlled by a fourth-rank tensor. Not only the uniformstress or strain but also an inhomogeneous deformation such asstrain gradients can be associated with flexoelectric effect. As aresult, the transverse strain gradient along the thickness of themembrane induces an additional polarization.

Capacitance is defined as the ratio between the electric chargeand the electric potential. Additional polarization or charge den-sity between the electrics under uniform potential canbe regard as a capacitance change per unit area, , which isgiven by

(21)

Therefore, a capacitance enhancement due to flexoelectricity isinduced. For the flat membrane under uniform perpendicularload only transverse strain effects exist so that the flexoelectriceffect can be derived based on similar analysis [18]

(22)

This additional polarization can also be regarded as the dielec-tric constant change due to the flexoelectric effect , whichis defined as

(23)

where is the dielectric parameter responsible for the effect ofbending deformation on the permittivity change of the material.

F. Residual Pressure in Cavity

Some gases are still trapped in the cavity although the anodicbonding was performed under nominally vacuum conditions.Therefore, the pressure in the cavity is not at absolute vacuum,which affects the initial state of the deflection of the membrane,and an additional contribution to the temperature coefficient of


offset (TCO) is introduced. The effect of the residual pressureis discussed as follows.

is defined as the residual pressure where the mem-brane is flat at temperature . Then, at any temperature T andany uniform pressure , the pressure in the cavity is givenby

(24)

where is the volume of the cavity when the net pressure onthe membrane is zero and is the volume change due to pres-sure applied at temperature . Thus, the net pressure applied tothe membrane at temperature with an external load is re-duced to be . As a result, the uniform load would varywith the temperature, thereby causing additional TCO contribu-tions from the residual pressure. Based on the bending shapefunction assumption described in (10), the load-deflection rela-tionship can be rewritten as

(25)

where and are the half side length of the top plane andbottom plane of the anisotropically etched cavity, is themaximum displacement under uniform pressure , and

is the right side of (16).The residual pressure in the cavity can be estimated using ascanning pressure measurement to be discussed in the nextsection.

III. RESULTS

A. Fabrication

The process flow for the composite membrane capacitivesensor is shown in Fig. 7. A three-mask silicon-on-glass (SOG)process was utilized for the device fabrication. Double-sidepolished (100) p-type silicon wafers with a thickness of 400 mwere chosen as the substrate material. The processing startedwith a full-wafer unmasked solid-source boron diffusion at1175 C to obtain a nominal etch-stop thickness of 4 m. Theheavily doped layer defines the lower electrode of the device.To minimize the stress gradient along the thickness direction ofthe wafer, an annealing process after diffusion was performedat 1200 C in nitrogen atmosphere for about 30 min. The waferwas followed by a 0.2 m dry thermal oxide grown in anoxygen ambient as the first dielectric layer. Next, low-pressurechemical-vapor deposition (LPCVD) Si N with a thicknessof 0.2 m was double-sided deposited as the second dielectriclayer and to serve as a mask for silicon backside etching. Thethermal oxide and LPCVD Si N on the front side of thewafer were patterned for contact openings and subsequently a200/300/1000 Å of a composite Ti-Pt-Au layer was depositedon the wafer to contact the doped silicon as the leadtransfer. The Ti-Pt-Au layer was then etched back leavingthe area for bottom electrode contact and the top electrode.

Fig. 7. Process flow of the capacitive pressure sensor with a sandwichstructure.

Si N on the backside of the wafer was then patterned usingplasma dry etching to expose the back-etching window. Next,the wafer was put into an ethylenediamine-pyrocatechol-water(EPW) etchant solution to etch the exposed silicon. The etchstops on the layer. The backside SiO and Si N was thenstripped away for the anodic bonding process. Corning Pyrex#7740 glass with a thickness of 500 m was partially dicedto a depth of about 450 m before anodic bonding in order toeasily separate the devices, and wafer-level silicon-glass anodicbonding was performed. The wafer was first heated to 400 C ata low pressure of Bar for good heat transfer and thenthe bonding chamber was pumped down at a vacuum pressureof about Bar. The voltage applied between the siliconwafer and the glass was sequenced through 200, 400, 600,and 800 V, respectively. The whole bonding process lasted forabout 15 min. The composite membrane was deflected down-ward under normal atmospheric pressure after anodic bonding,showing that the bonding process was successfully completed.

Capacitive devices with different side lengths were designedand fabricated. A capacitive pressure sensor with side length of1200 m is shown in Fig. 8. Since the SEM photos were takenfrom the specimens that were put into an approximately vacuumenvironment with a pressure of about Bar, the mem-brane bends upward due to the residual pressure in the cavity.The close view of the cross section of the multilayered mem-brane is illustrated in Fig. 8(b). The layer is nearly uniformwith a thickness deviation less than 0.1 m. The membrane re-mains flat, showing good stress compensation of the multilay-ered composite membrane.


Fig. 8. SEMs of the fabricated devices. (a) Top view of a capacitive device.The side length of the membrane is 1200 �m; (b) A close view of themultilayered membrane, the thicknesses of the p , SiO , Si N , and Aulayers are 4 �m, 0.2 �m, 0.2 �m and 1500 Å, respectively.

B. Measurement Setup

Sensor measurements were performed in a test chamber con-nected to pressure control equipment. The test setup is shownin Fig. 9. The sensor was put into the chamber and the elec-trodes were connected outside of the chamber through an elec-trical interface. The pressure in the chamber was produced andcontrolled stably by the pressure controller. The dynamic rangeand pressure steps were set with a software package in the PCoperating system of the equipment. Therefore, a quasiautomaticmeasurement can be performed using such a system. The ca-pacitance change of the sensor was measured with a YD 2810BPrecision LCR meter at 10 kHz with a resolution of 0.01 pF.Sensors with side lengths of 800 m, 1000 m, 1200 m, and1500 m were measured inside the chamber, respectively. Testresults of sensitivity, temperature response, linearity, stabilityand hysteresis are presented as follows.

C. Pressure Response

The pressure response of the sensor includes sensitivity, lin-earity, hysteresis and stability. These parameters are important

to the overall sensor performance. The sensitivity is definedas the capacitance change versus pressure change. A typicalmeasurement result of a sensor with a side length of 1500 mis given in Fig. 10. The dynamic range of the applied pres-sure is 80 kPa–106 kPa and the test temperature is 21.7 C.The measured capacitance of the sensor varies from 257.67 pFto 263.64 pF with increasing pressure, and from 263.79 pF to257.65 pF with decreasing pressure, showing a sensitivity ofabout 0.2 pF/kPa. The nonlinearity over the full range is lessthan 2.3% to the overall capacitance change, while the nonlin-earity of 80–91 kPa, 91–100 kPa, and 100–106 kPa is less than0.8%, 1.2%, and 0.9% to each corresponding capacitance vari-ation during the ranges, respectively. The maximum hysteresiserror occurs in the range of 91–100 kPa and the error of thecapacitance change over the full range is about 3.3%. A pre-liminary stability measurement of the sensor was performed at22 C and 50% relative humidity under 101 kPa for two weeks.No measurable drift was found using the YD 2810B PrecisionLCR meter with a resolution of 0.01 pF, which shows that thestability of the sensor under normal atmosphere is better than0.01% FS/24 hours. Sensor drifts due to humidity changes from10% to 80% relative humidity under 101 kPa were also ob-served, indicating a tolerable variation of about 0.002% FS per1% relative humidity change.

D. Residual Stress in Membrane

The residual stress in the layer affects the initial state ofthe membrane. Although an annealing step was performed afterthe boron diffusion, a small displacement of the membrane stillexists due to the stress gradient along the thickness. The residualstress can be measured using a full-field optical method [23]. Aspecimen with a 400- m-thick silicon wafer doped with a 4 m

layer was used for the measurement. The stress in thelayer is derived based on the traditional Stoney formula

(26)

where is the curvature radius of the membrane, arethe Young’s modulus, Poisson’s ratio and thickness of the sil-icon substrate, respectively, and and are the residualstress and thickness of the p++ layer, respectively.

Curvature of the composite structure was measured with aBI Instruments BGS6341 curvature radii meter. The profile ofthe bending structure is illustrated by the instrument. The ra-dius of curvature was obtained from the profile data. The de-rived residual stress of the layer is about 24 MPa after theannealing step.

E. Residual Pressure at Room Temperature

A scanning pressure test was used to evaluate the residualpressure in the cavity after silicon glass anodic bonding. A ca-pacitive device with length of 1500 m was selected for test,and the measurement was performed at 20.3 C with pressureranging from 3 to 12 kPa. The sensing membrane of the sensoris deflected downward when the applied pressure is larger thanthat inside the cavity. The output of the sensor increases or de-creases monotonically with the applied pressure under this con-dition. However, when the pressure in the chamber is less than


Fig. 9. Experiment setup for the capacitive pressure sensors measurements.

Fig. 10. Typical measured pressure response for a capacitive pressure withside length of 1500 �m at 21.7 C.

Fig. 11. Residual pressure in the cavity. The pressure ranges from 3–12 kPaand the test temperature is 20.3 C.

Fig. 12. Temperature coefficient of offset (TCO) of the capacitive pressuresensors at a pressure of 101 kPa.

that in the cavity, the membrane bends upward and the capaci-tance starts to increase again as the external pressure decreasesdue to the deformation of the membrane. Therefore, a min-imum capacitance value occurs for zero differential pressure atwhich the residual pressure in the cavity at the test temperatureequals to the applied pressure. The measurement result is givenin Fig. 11. The residual pressure at 20.3 C is about 8 kPa. Sincethe output of the sensor is not monotonic when the applied pres-sure varies from a value less than the residual pressure to onelarger than residual pressure, it will not determine whether themeasured pressure is less or larger than the residual pressuredue to the same outputs. Ideally, the lower limit of the pres-sure sensor in applications is approximately equal to the residualpressure.


F. Temperature Response

Fig. 12 shows the TCO of the capacitive pressure sensorsat 101 kPa. All the sensors have a total thickness of 4.55 mwhile the side length varies from 800 to 1500 m. The TCOof all the sensors are positive over the temperatures from

C to 60 C. A typical TCO of the sensor with a 1500 mside length is about 1923 ppm/ C and the capacitance changeis about 4 pF over the whole temperature range. The CTEmismatch between the silicon substrate and the glass, and theresidual pressure in the cavity are the two main sources of theTCO. The TCO of the sensors is relatively large. However,it is repeatable and predictable, thus, it can be eliminated bymeans of on-chip ASIC’s, digital calibration/compensation andsoftware arithmetic [8], [24], [25].

IV. DISCUSSION AND CONCLUSIONS

A vacuum-sealed capacitive absolute pressure sensor basedon sandwich structures has been proposed and fabricated. Theexperimental sensitivity of the sensor is two orders of magni-tude larger than that estimated solely from the geometry de-formations. The flexoelectric effect of the dielectric materialscontributes to this sensitivity enhancement. Electrostriction en-hancement amplifies also the sensitivity output. However, suchan improvement is limited to about one order of magnitude ac-cording to the model proposed by Shkel and Ferrier [13]. Hence,the sensitivity enhancement is qualitatively due to the dielectriceffects under deformation. Flexoelectric parameters of SiO andSi N , such as , and , are required for a detailed investi-gation, especially in the design of such sensors. Capacitive sen-sors with sandwich structures extend the conventional principlesby taking into account the dielectric effects due to deformationsuch as uniform strain and strain gradient related to the structuretwisting or bending. This principle may be also used as a basicelement for other MEMS devices.

The environmental conditions such as temperature and hu-midity may affect the dielectric properties of the dielectriclayers. Sensor packaging would reduce these environmentaleffects. In our experiment, a typical TCO of the sensor is about1923 ppm/ C, which can be effectively compensated by inter-face electronics, digital or software calibration. Sensor drifts dueto humidity changes from 10% to 80% relative humidity wereabout 0.002% FS per 1% relative humidity change. A prelim-inary stability measurement shows the stability of the sensorunder normal atmosphere is better than 0.01% FS/24 hours.

Future work should pay attention to the detailed physical ex-planation and available model for the design of capacitive sen-sors with sandwich structures. Test structures for the measure-ment of the dielectric parameters due to deformations are alsorequired. Single layer or multilayer dielectric materials may alsobe a consideration for the optimized sensor design.

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Min-Xin Zhou was born in 1978. She received theB.S. and M.S. degrees in 2000 and 2003, respec-tively, all in electronic engineering from SoutheastUniversity, Nanjing, China. He is currently pursuingthe Ph.D. degree in the Department of electronicengineering, Southeast University.

His research work focuses on microsensors designby CMOS compatible technology.


Qing-An Huang (S’89–M’91–SM’95) was born in1963, China. He received the B.S. degree from HefeiUniversity of Technology in 1983, the M.S. degreefrom Xidian University in 1987, and the Ph.D.degree from Southeast University in 1991, all inelectrical engineering. His Ph.D. research concernedmicromachined GaAs piezoelectric sensors.

After graduation, he joined the faculty as anAssistant Professor at the Department of ElectronicEngineering of Southeast University. He becamean Associate Professor in 1993, a Full Professor in

1996, and was awarded specially appointed Prof. for Chang Jiang Scholarin 2004. He was a Visiting Scholar with Hong Kong University of Scienceand Technology in 1997. He has served as vice-chairman of the Departmentsince 1997, and is also founding director of Key Lab of MEMS of Ministryof Education in China. He authored a book entitled Silicon MicromachiningTechnology (Science, 1996, China), published over 70 reviewed internationaljournal/conference papers, and holds seven Chinese patents.

Dr. Huang was a winner of Grade-I Natural Science Award of Ministryof Education of China in 2002, and received National Outstanding YouthScience Foundation. He has served as a Reviewer for Journal of AppliedPhysics, Applied Physics Letters, Journal of Micromechanics & Micro-engineering, Journal of Micro-Electro-Mechanical Systems, IEEE SensorsJournal, and Editor-in-Chief of Chinese Journal of Electron Devices, DeputyEditor-in-Chief of Chinese Journal of Sensors and Actuators. He served asConference Co-Chair for SPIE-Microfabrication and Micromachining ProcessTechnology and Devices (vol. 4601, Nov. 2001), and Program Member of firstto fourth IEEE Sensors Conference. He is currently serving as Council forNational plan of MEMS for Ministry of Science and Technology of China.

Ming Qin was born in 1967, China. He receivedthe B.S. degree from Wuxi Institute of Technologyin 1988 and the M.S. and the Ph.D. degrees fromSoutheast University, China, in 1994 and 1997,respectively, all in electrical engineering.

After graduation, he joined the faculty as an As-sistant Professor at the Department of Electronic En-gineering of Southeast University, China. He becamean Associate Professor in 1999 and a Full Professorin 2003. He was a Postdoctoral Researcher with theHong Kong University of Science and Technology in

1999. He has served as Director of CMOS MEMS Branch at Key Lab of MEMSof Ministry of Education in China. He has published over 20 reviewed interna-tional journal/conference papers, and holds four Chinese patents.

Wei Zhou was born in 1980. He received the B.S.degree in electronic engineering from Southeast Uni-versity, China in 2003. He is currently working to-ward the M.S. degree in the area of CMOS pressuresensors at Southeast University, China.

a novel capacitive pressure sensor

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