design of an soi-mems high resolution capacitive type single axis acceleromete

8/7/2019 Design of an SOI-MEMS high resolution capacitive type single axis acceleromete

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Microsystem TechnologiesMicro- and Nanosystems

Information Storage and

Processing Systems

ISSN 0946-7076

Volume 16

Number 12

Microsyst Technol (2010)

16:2057-2066

DOI 10.1007/

s00542-010-1146-1

Design of an SOI-MEMS high resolution

capacitive type single axis accelerometer


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T E C H N I C A L P A P E R

Design of an SOI-MEMS high resolution capacitive type singleaxis accelerometer

Kalyan Kumar Mistry K. B. M. Swamy

Siddhartha Sen

Received: 12 April 2010 / Accepted: 7 September 2010 / Published online: 25 September 2010

Springer-Verlag 2010

Abstract In recent years, high resolution micro acceler-

ometers are increasingly finding various applications indifferent segments of life. The current work deals with the

design of a high resolution single axis accelerometer based

on SOI-MEMS technology. Accordingly two different

approaches for designing comb type, capacitive, SOI-

MEMS accelerometer is presented. Initially a system level

approach using a simulation platform from SABER is

carried out to obtain the basic design. Later, a device level

design is carried out by building three dimensional (3D)

geometric models using finite element (FE) simulations

through CoventorWare software. Different design param-

eters like mechanical and electrical sensitivity, capacitance

values, resonant frequency, etc. are obtained in either of the

cases and compared. The design is optimized based on the

overall sensitivity and the system noise level both electrical

and mechanical, respectively. The complete design is

worked out in accordance with the silicon on insulator

based multiuser MEMS fabrication processes (MUMPs)

technology from MEMSCAP foundry.

1 Introduction

Recently, development of high resolution MEMS accelero-

meters have led to increased application, such as in auto-

motives, e.g. for enhancing vehicular stability, roll-over

detection, providing better dynamics of wheels on the road,

etc. in various industries, e.g. for tilt and shock detection,

precision vibration measurements, etc. in biomedical

sciences, e.g. for application in diagnostic and health mon-

itoring devices, etc. (Khine et al. 2008; Ratcliffe et al. 2008;

Ko-Ho and Young-Ho 2003).

Silicon on insulator (SOI) based MEMS sensors are

among the few proven devices where successful design and

fabrication could be accomplished for applications requir-

ing high sensitivity, high resolution, and low noise (Amini

and Ayazi 2004; Amini et al. 2005, 2006; Kiihamki et al.

2004; Milanovic 2002). SOI substrates have excellent

mechanical properties because of the availability of single

crystal silicon as structural material. The other advantages

of using SOI-MEMS technology are (1) feasibility of fab-

rication of very high aspect ratio structures by using deep

reactive ion etching (DRIE), (2) effective electrical isola-

tion between two silicon layers by an oxide layer resulting

in superior electrical performances, (3) compatibility with

integrated circuits, fabrication process for monolithic inte-

gration of MEMS, and ICs and (4) capability for making

cavities conductivity wafer bonding. Thus, SOI technology

and processes happen to be a compelling choice for making

devices like high performance micro-gyroscopes and

accelerometers (Manut et al. 2004; Bais and Majlis 2008;

Albarbar et al. 2009). The technology can be used to fab-

ricate high aspect ratio comb type accelerometer structures

that can give superior performance as compared with sim-

ilar devices realized using polycrystalline silicon (Poly-Si)

thin film technology.

K. K. Mistry (&)

Central Mechanical Engineering Research Institute (CSIR),

M G Avenue, Durgapur 713209, India

e-mail: [email protected]; [email protected]

K. B. M. Swamy

Advanced Technology Development Center,

Indian Institute of Technology Kharagpur,

Kharagpur, West Bengal, India

e-mail: [email protected]

S. Sen

Electrical Engineering Department,

Indian Institute of Technology Kharagpur,

Kharagpur, West Bengal, India

e-mail: [email protected]

123

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DOI 10.1007/s00542-010-1146-1


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MEMSCAP foundry (http://www.memscap.com) offers

an established process to realize SOI based MEMS devices

named as SOIMUMPs. SOI wafers (Fig. 1) with different

structural layer thickness (10 and 25 lm structural silicon

with sandwich oxide and 400 lm base or handle layer),

coupled with DRIE techniques for high aspect ratio mi-cromachining used in this process forms the hallmark of

the SOIMUMPs technology.

The accelerometer design discussed in this paper is

based on the SOIMUMPs. The structures are proposed to

be fabricated by deep dry etching of SOI wafer. It can be

designed so as to add an extra mass underside the proof

mass (using handle layer), in order to reduce Brownian

noise floor (Amini et al. 2006). On the other hand, the

increased comb overlap area due to the thick structural

layer coupled with a small gap between fingers (achieved

through DRIE), results in large capacitance values compare

to their polysilicon thin film counterparts. Using SOIM-UMPs, it is also possible to design and realize longer

beams for increased sensitivity, yet with much lower cross

axis sensitivity, and practically no adhesion or stiction

related issues. The design and simulation of high resolu-

tion, capacitive type, single axis in-plane SOI-MEMS

accelerometer, intending for fabrication in SOIMUMPs is

discussed in the subsequent sections.

2 Electromechanical design

Accelerometer can be dynamically modeled as a simplespring-mass damper system (Fig. 2). When the acceler-

ometer is excited along the sense direction with an accel-

eration a, the proof mass suspended by a beam or spring

is displaced under the effect of inertial force in a direction

opposite to the applied acceleration. The mechanical sen-

sitivity of the accelerometer is defined as the displacement

of proof mass per unit of gravitational acceleration (g)

(g = 9.8 m s-2). The basic equation (1) of the system is

given by (Ko-Ho and Young-Ho 2003),

Md2x

dt2 Ddx

dt Kx F Ma 1

where M = mass of the proof mass, D = damping coeffi-

cient of the system, K= beam or spring stiffness,a = acceleration along the sense direction, x = displace-

ment of the proof mass

Therefore,

a d2x

dt2 D

M

dx

dt K

Mx

2

Using Laplace transform,

x s a s

1

s2 DM

KM

3At steady state, the displacement x is dependent on the

stiffness K of the beam or spring and the mass M of the

proof mass.

The relation is given by (Eq. 4),

x MK

a 4

In a comb type capacitive accelerometer, the central

proof mass, suspended through four sets of U shaped

beams and anchored at two points, moves longitudinally in

a direction opposite to that of applied acceleration. A series

Fig. 1 Cross section of SOI

substrate of SOIMUMPS wafer

Fig. 2 Dynamic model of basic accelerometer

2058 Microsyst Technol (2010) 16:20572066

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of comb fingers (electrodes) attached on either side of the

proof mass (movable combs) is interleaved with another

series of comb fingers anchored to the substrate (fixed

combs). Each pair of fixed and movable comb fingers form

a parallel plate capacitor with air as the dielectric medium.

For an acceleration a, a displacement x of the proof

mass causes a change in the gap between the fixed fingers

and the movable fingers of the comb, leading to a change in

the overall capacitance value. The combs are designed in

such a way that for any deflection along the sense axis, the

gap between one set of finger increases while the other set

of finger decreases, forming a differential capacitance

sensor (Fig. 3).

The proof mass is suspended between two pairs of

folded beams which are fixed firmly to the substrate at two

points. The shape, material, and geometry of these beams

very much define the stiffness of the spring. Lowering of the

spring stiffness reduces the natural frequency of the accel-

erometer, resulting in reduced bandwidth of operation. Low

stiffness value also cause suspension problems, with a

possibility of the moving structure to stick to its substrate. It

may also increase cross sensitivity and reduce the selectivity

of the sensor. Hence, to achieve a desired performance, there

is a need to carefully optimize the design of the moving

system, so as to achieve stiction free movement of the proof

mass and also reduce the cross axis sensitivity.

The capacitance sensitivity of the accelerometer is

defined as the change in capacitance per unit of gravita-

tional acceleration. At zero acceleration, the static capaci-

tance is obtained from the equation (Minhang 2005),

C1 C2 C0 e0NLetd

5

where C1 = static capacitance of comb-1, C2 = static capac-

itance of comb-2, N = number of fingers, Le = electrode

length, t = electrode thickness, d = gap between movable

and fixed finger, e0 = permittivity of free spaceFor, displacement x of the proof mass in the sense

direction, the gap between fixed and movable fingers of

combs increase on one side (comb-1) and decrease on the

other side (comb-2) (shown in Fig. 3).

Therefore, the new comb capacitance of comb-1 is given

by,

C01 e0NLet

d x 6

)C01 e0NLet

d 1 xd

7

Similarly, the new comb capacitance of comb-2 is given

by,

C02 e0NLet

d x 8

)C02 e0NLet

d 1 xd

9So, differential capacitance between two combs is given

by,

DC

C02

C01

e0NLet

d

1 xd 1 x

d

1 xd 2 ! 10DC e0NLet

d

2x

d

2xC0

d;

forx ( d; xd

2is neglible

11

Hence, from Eq. 11 we can infer that the differential

capacitance between combs is inversely proportional to the

gap between fixed and movable fingers of comb for

infinitesimally small displacement.

Fig. 3 Designed model of

lateral movement differential

capacitance accelerometer

Microsyst Technol (2010) 16:20572066 2059

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Another important design parameter for a high resolu-

tion accelerometer is the mechanical noise known as

Brownian noise equivalent of acceleration (BNEA). The-

oretically, BNEA can be estimated as (Gabrielson 1993;

Abdolvand et al. 2007; Hyoungho et al. 2006).

BNEA

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4KbTD

p

M ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4KbTxo

MQr

12

where Kb = Boltzman constant, T = absolute temperature,

xo natural frequency of the structure ffiffiffiffiffiK

M

r; 13

M = proof mass,

Q quality factor of the accelerometer MxoD 14

In order to achieve high sensitivity and low mechanical

noise, overall mass of the accelerometer need to be increase.

For this, the most viable option is to increase the thickness

of the proof mass, keeping the mass area constant. It isneedless to mention that SOI-MEMS is one of the best way

for simultaneously obtaining such a large proof mass as

well as increased capacitance value. The increase in

capacitance is due to the increased overlap area of comb

capacitance, formed by increased structural thickness.

The other noise contributing factor in capacitive MEMS

accelerometer is by electronic noise called circuit noise

equivalent of acceleration (CNEA) (Hyoungho et al. 2006).

This is produced in signal conditioning circuit or interface

circuit used for transducing capacitance to measurable

electrical voltage output. CNEA depends on both the

capacitive resolution of the comb structure and capacitancesensitivity of the accelerometer (Eq. 15).

It is given by,

CNEA DCminS

15

where DCmin = minimum change of capacitance,

S = capacitance sensitivity, i.e. change of capacitance per

unit g.

It is to be noted that capacitance sensitivity of a dif-

ferential capacitive type accelerometer depends on four

parameters, namely, proof mass, spring stiffness, gap

between fingers of comb and static capacitance (Eq. 16).

S DCa

2Cod

M

K

16

In order to optimize different design parameters for the

MEMS accelerometer structure, the effect of gap between

fingers of comb on the device sensitivity, BNEA and

CNEA are studied using Eqs. 116. The characteristic

relation between BNEA and gap (d) between the comb

fingers is seen to be inversely proportional to each other i.e.

increasing d reduces BNEA (Fig. 4). On the other hand

CNEA is directly proportional to the gap between comb

fingers i.e. increasing d increases CNEA (Fig. 5). But,capacitance sensitivity (S) and static capacitance (Co) value

of the accelerometer increases with reducing gap between

the comb fingers (Fig. 6). However, foundry specific

design rules for SOIMUMPs fabrication processes have

put a limitation on minimum gap size to 2 lm using DRIE.

Hence during design, the minimum gap between the fingers

of combs is chosen to be (1) 2.5 lm and (2) 3 lm to ensure

its manufacturability.

3 Design and simulation

Design approach for MEMS devices using finite element

(FE) based modeling and analysis tools are mostly time and

Fig. 4 BNEA versus capacitance gap size

Fig. 5 CNEA versus capacitance gap size


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resource intensive. So, the initial design was carried out

using a system level software tool called SABER

(http://www.synopsys.com). A preliminary estimation was

done using the governing equations (given in Sect. 2) for

different mechanical and electrical parameters. Next, in the

SABER simulation, different parts like beams, rigid plate

and comb fingers available in its parametric library were

imported and assembled together, maintaining proper

geometrical coordinates (Fig. 7). It is to be noted that the

accelerometer model was built in a schematic representa-

tion. Necessary input data, like material properties,

boundary conditions, etc. were applied to the accelerometer

model and simulations were run. The typical simulation

time for both mechanical and electrical or coupled analysis

does not exceed 10% of the CPU time for similar type ofsimulations using FE tools. Two models (I and II) were

constructed in compliance with SOIMUMPs foundry pro-

cess and simulated using SABER.

3.1 Simulation results for Model-I

Simulation results show that for Model-I, the natural fre-

quency of the structure obtained along the sense (X-axis) is

2.00 kHz (Fig. 8). The natural frequencies along other axes

(Z- and Y-axis) are 7.36 and 11.95 kHz, respectively.

These values are much higher as compared to the value

along the sense axis. For sensitivity analysis, the inputacceleration was varied from 0 to 1 g linear range with a

step increment of 1 mg, along the sense direction. The

maximum displacement of the proof mass is found to be

64.3 nm/g for a 10 lm thick structure (Fig. 9). The

Fig. 6 Sensitivity versus capacitance gap size

Fig. 7 Architect model of SOI-

MEMS accelerometer


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maximum capacitance sensitivity of 31.9 fF/g is observed

for a device with structural layer thickness of 25 lm.

However, the different performance parameters obtained

for Model-I (shown in Table 1) is found to be less than the

desired. The main reason being that, the resolution of the

capacitance signal conditioning circuit required to be

integrated with the accelerometer structure was assumed to

be not less than 0.2 fF. Hence, the Model-I, required

Fig. 8 Frequency response for Model-I

Fig. 9 Sensitivity plot for Model-I

Table 1 SABER simulated

results of Model-I for different

structural thickness

Silicon

thickness

(lm)

Static

capacitance

(pF)

Natural

frequency

(kHz)

Sensitivity

per 1 g

acceleration

Sensitivity

per 10 mg

acceleration

10 C1 = 1.119 X = 1.58 DC1 = 13.9 fF DC1 = 0.139.fF

C2 = 1.119 Y = 4.85 DC2 = 13.9 fF DC2 = 0.139 fF

Z = 1.88 Dx = 64.23 nm Dx = 0.65 nm

25 C1 = 2.224 X = 2.18 DC1 = 31.9 fF DC1 = 0.319 fF

C2 = 2.224 Y = 6.37 DC2 = 31.88 fF DC2 = 0.318 fF

Z = 8.98 Dx = 27.3 nm Dx = 0.27 nm


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suitable modifications to achieve a resolution better than,

0.2 fF equivalent to a mg resolution in terms of

acceleration.

3.2 Design of Model-II using SABER platform

To improve the sensitivity of Model-I, the mechanical

parameters of the structure were modified. To reduce the

stiffness to the required level, the spring length was

increased to 600 lm and spring width was reduced to

6 lm. As a result, stiffness of the Model-II got reduced

from 51.2 N/m (as was the case of Model-I) to 6.4 N/m.Different design dimensions of both the Models (I and II)

are as shown in Table 2. Model-II was also simulated alike

Model-I, using SABER tool. The results show that, the

natural frequencies of the structure of Model-II are reduced

(in comparison to Model-I) to 1.09, 4.27 and 9.10 kHz

along the X-, Y- and Z-axis, respectively (Fig. 10). The

simulation shows a clear improvement in the displacement

sensitivity of Model-II, which is found to be 217 nm/g.

Table 2 Design dimensions of Model-I and II

Parameter Model-I Model-II

Length of proof mass (Lp) 2,000 lm 2,000 lm

Width of proof mass (Wp) 400 lm 400 lm

Length of spring (Ls) 400 lm 600 lm

Width of spring (Ws) 8 lm 6 lm

Finger length (Lf) 300 lm 300 lm

Finger width (Wf) 5 lm 5 lm

Length of electrode (Le) 280 lm 280 lm

Capacitance gap size (d) 3 lm 2.5 lm

Number of electrode per side (N) 70 70

Fig. 10 Frequency response for Model-II

Fig. 11 Sensitivity plot for Model-II


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Because of this, the capacitance sensitivity is also found to

have improved for each comb pair up to 113.9 fF/g

(Fig. 11). Now, this capacitance can be easily resolved by

aforementioned signal conditioning circuit for capacitance

transduction.

3.3 Finite element (FE) simulation of Model-II

The schematic model of the system built in SABER for

system level simulation has been used to extract a 3D

geometry of the structure (Model-II). A mesh model with

regular solid brick elements was generated using Coven-

torWare software tool and an FE simulation was run for

different mesh sizes until convergence was achieved

(http://www.coventor.com). FEM based simulation results

show different modes of domain frequencies which are in

close match with the simulation results of system level.

Visualization of modal analysis shows that the system level

simulated natural frequencies obtained in X, Y and Z

direction corresponds to mode frequencies 1, 2 and 3,respectively, in FE simulation. Table 3 shows displacement

of the structure for an excitation of 1 g acceleration along

the sense direction. Node displacement of 197 nm/g

achieved in the sense axis closely matches with the system

level displacement value (217 nm/g) and thus validates the

simulated results. Sensitivity and frequency response for

silicon thickness 10 and 25 lm, respectively, of Model-II,

are as shown in Table 4. It is clear from the results that

thickness of 25 lm gives better performance due to larger

mass and larger overlap area of comb capacitance.

Figures 12 and 13 show the 3D model used for FE analysis

and the displacement results with contour images, respec-

tively, of Model-II.

4 Pull-in and self test analysis of Model-II

When voltage is applied between the parallel plate elec-

trodes separated by air gap, the plates experience a force

called electrostatic force. This force attracts the comb

electrodes towards each other. Even for zero acceleration,

if the displacement of the movable plates exceeds one-third

Fig. 12 Frequency response for Model-II by FE simulation

Fig. 13 Layout view of SOI-MEMS accelerometer Model-II

Table 3 Comparison of FE simulated displacement sensitivity for

Model-I and II (for 25 lm structural thickness)

Model-I Model-II

Node-X displacement (nm) 29.81 197

Node-Y displacement (nm) 1.23 9 10-1

8.18 9 10-1

Node-Z displacement (nm) 4.26 9 10-2

2.82 9 10-1

Table 4 Simulation results of Model-II (FE analysis)

Silicon

thickness

(lm)

Static

capacitance

(pF)

Natural

frequency

(kHz)

Sensitivity

per 1 g

acceleration

Sensitivity

per 10 mg

acceleration

10 C1 = 1.119 X = 1.88 DC1 = 78.77 fF DC1 = 0.888 fF

C2 = 1.119 Y = 3.78 DC2 = 78.7 fF DC2 = 0.888 fF

Z = 1.37 Dx = 433 nm Dx = 4.25 nm

25 C1 = 2.224 X = 1.09 DC1 = 113 fF DC1 = 1.06 fF

C2 = 2.224 Y = 9.10 DC2 = 113 fF DC2 = 1.05 fF

Z = 4.27 Dx = 217 nm Dx = 2.17 nm

Fig. 14 3D model of SOI-MEMS accelerometer Model-II


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of the original gap (due to applied voltage), it becomes

unstable and accelerates to snap in with the fixed combs.

This minimum voltage at which the plates collapse is

called pull-in voltage (Ko-Ho and Young-Ho 2003;Minhang 2005). It is to be noted that to avoid undesirable

effects in comb structures capacitive type accelerometer,

the pull-in voltage must be at a higher value, as compared

to the voltage applied to the comb fingers for sensing. This

needs careful attention during design. To analyze the pull-

in voltage for Model-II, voltage was applied to the sense

fingers in increasing mode. From the simulation results it is

observed that the pull-in voltage for the structure is about

44.5 V.

Also, for self test mechanism, a total of eight number of

test fingers were attached on both sides at either ends of the

proof mass, with dimensions equal to that of sense fingers.

A self check voltage was applied to the test fingers in

increasing mode to create electrostatic force. The results

show that for an applied actuation voltage of 15 V to the

test fingers, the proof mass displacement of 215 nm is

achieved (Fig. 14) which is equivalent to 1 g accelerationapproximately.

5 Cross axis sensitivity analysis of Model-II

Cross axis sensitivity is the measure of displacement along

sense direction (X-axis) for an acceleration applied in other

axes (Y- and Z-axis) (Fig. 15). In practical applications of

an accelerometer, the cross axis sensitivity must be as low

as possible to attain good selectivity (Manut et al. 2004).

Cross axis displacement sensitivity was investigated for

Model-II by applying accelerations in both Z- and Y-axisseparately. It is observed that, the structure has a maximum

cross axis sensitivity of 1.2% along Z-axis (Fig. 16).

6 Conclusions

Design of high a resolution, single axis, capacitive

SOI-MEMS accelerometer is presented in the paper. Two

different designs of comb type accelerometer models

Fig. 15 Displacement visualization in color contours for Model-II

Fig. 16 Displacement versus actuation voltage of Model-II


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(Model-I and II) were pursued to arrive at a structure,

satisfying the target performance. Accordingly, simulations

using SABER platform and FE based CoventorWare tools

were carried out and compared. It is found that, the Model-

II matches the performance requirements in terms of

mechanical sensitivity, capacitance values, off-axis sensi-

tivity, etc. All the structures were designed in compliance

with the SOIMUMPS processes and rules, such that, themanufacturability of the design is ascertained.

Acknowledgments The work reported here is a part of the Master

Thesis work of the first author. He is particularly thankful to the

Director, CMERI, Durgapur for rendering all sorts of cooperation for

conducting the research work. First author is also thankful to Mr

Abhijit Mahapatra, Scientist CMERI for his technical help.

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