[ieee 2011 ieee students' technology symposium (techsym) - kharagpur (2011.01.14-2011.01.16)]...

Proceeding of the 2011 IEEE Students' Technology Symposium

14-16 January, 2011, lIT Kharagpur

Effect of Voltage Induced Electrostatic Forces on MEMS Capacitive Accelerometer

Banibrata Mukherjee , K B M Swamy , Sougata Kar , Siddhartha Sen Department of Electrical Engineering

Indian Institute of Technology, Kharagpur Kharagpur-721302, India

Abstract-In this paper the effect of electrostatic forces due to applied excitation voltage on MEMS capacitive accelerometer has been presented. A set of parallel plates often termed as combs or fingers along with a proof mass and a set of spring constitute the basic structure of a capacitive accelerometer. Some of the

fingers are fixed while others are movable. The proof mass moves so that the movable fingers attached with it with applied acceleration. This movement changes the gap between the fixed and movable fingers and capacitance between the fixed and movable fingers changes which is measured through proper electronic circuitry for electrical output. A few numbers of fingers are also included in the structure for self test purpose,

called as actuation fingers. This type of structure is often tested electro-statically by applying exterual voltage signal to the actuation fingers. This external voltage on the actuation fingers generates electrostatic force which causes the proof mass along with the movable fingers attached with it to move. In this paper the effect of applied voltage and the electrostatic force caused by it has been analyzed. The nature of the

displacement of the proof mass has also been described. In the electrostatic analysis semi double frequency component is observed when the structure is actuated with an external electrical voltage.

Keywords: MEMS Electrostatic-actuation,

frequency component.

I.

Capacitive Accelerometer, Electrostatic force, Double

INTRODUCTION

MEMS based accelerometers are widely used in recent years. Among different types of MEMS based accelerometers the most commonly used one is of capacitive type. It has been increasing in popularity due to its high sensitivity, repeatability, temperature stability, design flexibility, lower cost and power usage [2]. It finds applications in different fields like Tilt/Roll Sensing, to isolate vibration of the mechanical system from the outside sources (Example: Rough Road detection), to determine the severity of the impact or to log when an impact has occurred, Vehicle Skid Detection (Often used with systems that deploy smart breaking to regain the control of vehicle) [2] etc.

MEMS based capacitive accelerometers are normally connected to CMOS circuits for capacitance sensing and to provide electrical output for further signal processing. In most of the cases the electronic interface circuit requires dc bias along with a time varying excitation signal. As mentioned before some actuation fingers are also included for self test of the structure without any acceleration. Externally applied voltage in the actuation voltage generates electrostatic force that causes the movement of the proof mass. Therefore proper analysis of the effects of all these bias and excitation voltages is necessary for testing and characterization of the structure. It would also help for better understanding of the dynamic behavior of the MEMS accelerometer structure.

In the literature [4] - [5] the effect of bias voltage polarity and the response for different normalized displacement have been analyzed. In [3] mainly the effect of electrostatic force in different configuration along with the pull in analysis has been presented. But detail analysis of the displacement response due to electrical actuation has not been studied before which indeed can be very useful for characterization and self test of the structure.

In this paper the mechanical response of the device (i.e. the nature of movement) due to electrical actuation has been analyzed in detail and simulation results have been presented.

II. THEORY AND MODELLING

In general a MEMS accelerometer device consists of3 parts, (a) the proof mass or seismic mass (b) U shaped springs/tethers (c) inter-digitated comb structures. The whole of seismic mass element is supported by these tethers, suspended at a distance of few microns above the substrate. The construction of the device is shown in Fig.I. A series of rectangular fingers projected from either side of the central mass, each acting as one plate of a parallel plate variable capacitor. The other plates interleave with the moving mass plate and are anchored to the substrate. Each set of one movable finger along with two fixed fingers in its either sides is called one comb cell. Out

TS11MEMS01084 978-1-4244-8943-5/11/$26.00 ©2011 IEEE 253

of those comb cells, a set of few comb cells are designed as test cells, mainly used for self-test of the structure. The fingers in that test cells are called test or actuation fingers and the remaining fingers are called sense fingers. The equivalent simplified model for the accelerometer can be represented as shown in Fig. 2. The proof mass is free to move in a plane perpendicular to the tethers and parallel to the substrate. Whenever acceleration is applied in this direction, the displacement of the proof mass is detected as the change in capacitance between the fixed and movable comb electrodes. This change in capacitance is fed to the signal conditioning electronics circuit [ 7] [ 8]. The specifications of a sample accelerometer structure considered here are given in Table I.

Figure l. Accelerometer structure

Plcho!" Point

!vIovetble COUll>

Figure 2. Schematic structure of the device

T ABLE I . DEVICE DIMENSION Proof mass dimension Length

Width

Movable finger Overlapping Length

Width

No. of to tal fingers (sense +test)

Structural layer thickness

Gap between movable and fixed finger

TS11MEMS01084

462 �m

66 �m

120 �m

3.5 �m

52

3.5 �m

2 �m

Proceeding of the 2011 IEEE Students' Technology Symposium

14-16 January, 2011, lIT Kharagpur

The effective mass (i.e. the mass of the central plate (seismic mass) and attached fingers) and spring constants are calculated from the device dimensions and are given in Table II as follows:

TABLE II. MAss AND SPRING CONSTANTS OF STRUCTURE Mass(M) 4.27 X 10- kg

Spring constant(k) 6.6 N/m

A. Electrostatic Analysis In electrostatic analysis a driving signal is

applied across the fixed actuation fingers with respect to the movable finger. Due to the applied voltage signal in actuation fingers an electrostatic force equivalent to that of the force due to actual acceleration is developed. This makes the whole device to be acted under a virtual acceleration, thus resulting in the displacement of the proof mass, which in turn can be measured by the remaining sensing fingers in a regular manner. For the analysis of the effect of the applied voltage the force balance equation (static analysis or steady state condition) has been considered.

For static analysis it is assumed that the device under analysis will move until a dynamic equilibrium of forces is obtained [1] [7]. Therefore the force balance equation for the structure can be written as

F inertia + F damping + F elastic + F electrostatic = 0 (1 )

As inertia and damping forces are not significant they are neglected in the static analysis, so (1) can be reduced to

F elastic + F electrostatic = 0 (2)

An equivalent model for the electrostatic has been shown in Fig. 3. In this case as mentioned earlier, no external acceleration is applied, rather the voltage across test fingers induces electrostatic force which causes the movement of the structure. In general an electronic interfacing circuit is used to detect the change in capacitance due to the movement of the fingers and to convert the mechanical movement to suitable voltage output. This interfacing circuit requires some reference voltage for its successful operation. Actually the arrangement is such that when applied acceleration is zero, the output of the interfacing chip is equal to its reference voltage.

254

K I fixed

d I movable

d I Test fingers

Figure 3. Equivalent model in electrostatic testing.

It means that at movable finger node always the reference voltage is present and output due to applied acceleration changes with respect to the reference voltage (Vo). So when an excitation voltage is applied in actuation finger, the effective voltage across movable finger and fixed actuation fmger becomes equal to the difference between the applied voltage and reference voltage. The nature of the driving signal across fixed test/actuation fingers and movable fingers are generally considered as time varying excitation and it can be purely an a.c. or a combination of a.c. and d.c. bias.

Now the electrostatic force generates in between the plates and the elastic force of the spring can be written as [6]

Where,

F nEoErA

V2 electrostatic = 2(d-x)2

n= no. of fingers

A= overlapping area

d= gap between movable and fixed fmgers

x= displacement caused by electrostatic force

Eo= permittivity of space= 8.85 X 10 -12 F/m

Er= relative permittivity of the dielectric used between the electrodes

V= applied voltage

F elastic = - k x

Now for static analysis

F elastic = F electrostatic

Therefore equation (2) can be rewritten as

TSIIMEMS01084

Proceeding of the 2011 IEEE Students' Technology Symposium

14-16 January, 2011, lIT Kharagpur

k x= nEA

V2 2 (d-X)2

Where, E = EOEr = Eo (for air dielectric Er =1)

(3)

Now for various types of applied voltage V, the response of the structure will be analyzed.

1) V = V I sin rot

It means in fixed actuation finger VI sin rot is applied along with a d.c. bias equal to the reference voltage.

So effective V = Vo + VI sin rot - Vo = VI sin rot

Then equation (3) can be written as

nEA V12 k x = -- - (1- cos2rot) 2(d-x)Z 2

and it simplifies to

where, normalized displacement XI = xld.

(4)

Putting other parameter values in above equation from device dimension given in Table: 1 and Table: 2 and if no. of Test fingers is (n) = 4, then equation (4) can be written as,

3 2 -6 V1Z X I -2xI +XI= 141Xl O - (l-cos 2rot) (5) 2 2) V= Vo-Vl sin rot

It means in fixed actuation finger only VI sin rot is applied. So the effective voltage V = Vo -VI sin rot

Then,

2 2 2 V1Z V = (V 0 -V I sin rot) = [ (Va + -) - 2 V 0 V I 2 V1Z sin rot - -2- cos 2rot]

Now equation (3) can be written as

nEA 2 V1Z . V1Z k x = 2(d-x)2 [ (Va + -2-) -2V oVlsm rot - -2- cos

2rot]

which is simplified to

xl (1 -x1)2 = nEA

[ (V 2 V1Z) 2 V V .

2kd3 a + -2- - 0 I sm rot

V1Z - cos 2rot] 2 (6)

255

Putting other parameter values in above equation from device dimension given in Table I and Table II and if no. of Test fingers is (n) = 4, then equation (6) can be written as,

V1Z 2V 0 Vlsin wt - - cos 2wt]

2 (7)

From this equation we can easily find the time response for normalized displacement.

III. SIMULATION AND ANALYSIS

Based on the models established in the previous sections, simulations have been carried out to find time response plots for normalized displacement using MA TLAB. Different graphs are plotted and analyzed for different applied voltage for electro actuation testing conditions. Here again, different cases of applied voltage "V" is considered and the time response for displacement of structure is plotted. Now (6) provides the responses which is a cubic equation, so it has three solutions for XI. But XI is normalized displacement and so its range is within 0 to 1. As value of XI comes closer to 1 pull-in occurs. It has been found that among three solutions of XI , two solutions are very much closer to 1, only one solution comes closer to 0 (order 10 -3). Therefore only that one solution has been considered here and accordingly plots are given below:

Case 1: Only a.c. signal is applied (V = VI sin wt).

V = 1 sin (200rrt), frequency is 100 Hz.

The normalized displacement response of the structure according to (5) is plotted in Fig. 4.

_4 :x 10 1.5

o o

/I

II

n .1\ 1\

.... . . • • • •• • •• •

fI

..... • • • I

:1\ . .. ,

• • I

1\

0_01 0.02 0.03 0_04 0.05 Tbne(sec)

Figure 4. Normalized displacement for V= I sin (200m).

Normalized displacement amplitude is 1.4 X 10 -\p­p) with frequency of 200 Hz.

Case 2: Combined ac signal with dc reference is applied (V = V 0 - VI sin wt).

TSIIMEMS01084

Proceeding of the 2011 IEEE Students' Technology Symposium 14-16 January, 2011, lIT Kharagpur

Now different sub-cases have been considered.

a) Vo > VI, (b) Vo = VI, (c) Vo < VI . For all the cases signal frequency is 100Hz.

a) Yo> VI (Vo= 2.25V and VI = IV)

5 14 )12 � 10 '5 8

� E 6 � 4

2 �--��--��--��--��� o 0_01 0_02 0_03 0_04 0_05

Tim"(s,,,,)

Figure 5. Normalized displacement for V= 2.25 -I sin (200m)

Normalized displacement Amplitude is 0.00125 with 100Hz frequency.

b) Vo= VI= 2.25V

For this condition the simulated response has been plotted in Fig. 6. Normalized displacement is 0.0028 with 100Hz frequency.

-3 3 x 10

"5 2_5 5 � 2 i � 1-5 � � 1 E Q 0_5 Z

o ��������������� o 0.01 0.02 0_03 0_04 0_05

Time(sec) Figure 6. Normalized displacement for V= 2.25 - 2.25 sin 200rrt

c) VO < VI, for this condition we have considered five different cases.

1) Vo< VI (Vo= 2.25V, VI = 2.5V)

The normalized displacement response of the structure according to (7) is plotted in Fig. 7(a). Normalized displacement Amplitude is 0.0031 with 100Hz frequency. In lower half of the response ripple is observed.

256

3.5 x 10

i 3 S 2.5 .., i- 2 � "5 1.5 � 1 E � 0.5

.3

O������==�������� o 0.01 0.02 0.03 0.04 Time(sec)

0.05 Figure 7(a). Normalized displacement for V= 2.25 -2.5sin 200m.

Time(sec) Figure 7(b). Normalized displacement for V= 2.25 - 3sin 200m.

Normalized displacement Amplitude is 0.0038 with frequency of 100Hz and the ripple is prominent with 0.16Xl O·3 amplitude.

3) Vo < VI (Vo = 2.25 V, VI = 5V)

o��--��--��--��--��� o 0.01 0.02 0.03 0.04 0.05 Time(sec)

Figure 7(c). Normalized displacement for V= 2.25 - 5sin 200m.

Normalized displacement Amplitude is 0.0075 with frequency of 100 Hz and the normalized ripple amplitude is 0.001.

TSIIMEMS01084

Proceeding of the 2011 IEEE Students' Technology Symposium 14-16 January, 2011, lIT Kharagpur

4) Vo< VI (Vo= 2.25V, VI = 8V)

5 � i- 0.01 ;;a il � E 0.005 Z

TiIne(sec) Figure 7(d). Normalized displacement for V= 2.25 - 8sin 200m.

Normalized displacement Amplitude is 0.015 with 100Hz of frequency and the normalized ripple amplitude is 0.005.

5) Vo< VI (Vo= 2.25V, VI = l OV)

For this condition the simulated response has been plotted in Fig. 7(e).

The normalized displacement amplitude is 0.022 with frequency of 100Hz and the normalized ripple amplitude is 0.008.

0.05 TiIne(sec)

Figure 7(e). Normalized displacement for V= 2.25 - I Osin 200m.

A. Observations

In electro-actuation testing when only ac sine wave signal is applied across the fixed test/actuation electrode and movable electrode, the output wave frequency gets doubled fully (as shown in Fig. 4). But when the sine wave signal along with a d.c. reference as offset is applied, the frequency of output wave depends mainly on the amplitude of sinusoidal signals with respect to the amplitude of d.c offset. The characteristics of displacement caused by the

257

electrostatic force for different signal amplitude have been shown in Fig. 5, 6 and 7.

In case of 2(a) dc offset amplitude (Vo) is greater than ac wave amplitude (V I ) (Fig. 5), whereas, in case of 2(b) dc reference amplitude (Vo) is equal to ac wave amplitude (V I ) and the output (normalized displacement) has yet same frequency component as input (Fig. 6). Actually when Vo ;?: VI. the magnitude of the double frequency component "Vlz

cos 20)t" in (7) does not contribute large value. 2

So only the single frequency component dominates in output whereas the double frequency component gets suppressed.

However for case 2(c) dc reference amplitude (Vo) is lesser than ac signal amplitude (V I) and some interesting responses have been observed with the increasing value of VI. The responses are shown as in Fig. 7(a) - 7(e). As value of VI increase gradually ripples are observed in the lower part of the sine wave. The magnitude of the ripple increases gradually with the increase in V I and it appears as semi double frequency component in the normalized displacement response. Actually when Vo < VI. the

V1Z magnitude of the double frequency component "-

2 cos 20)t" in (7) is not less significant compared to single frequency component and its effect is observed in output in form of dipping in one half of sinusoidal wave output.The magnitudes in all the cases are observed to be very well within the limits of pull in displacement.

IV. CONCLUSION

The detailed analysis on electrical actuation of MEMS based accelerometer has been presented here. The characteristics of the displacement caused by the electrostatic force have been focused. To characterize the device and to understand its

TSllMEMS01084

Proceeding of the 2011 IEEE Students' Technology Symposium

14-16 January, 2011, lIT Kharagpur

operation using self test configuration such analysis is essential. Actually in self test configuration sinusoidal input is a common and standard input signal. That's why we should be aware of the effect of increasing the magnitude of applied sine wave. In this analysis, it has been observed that, the frequency of output waveform gets doubled compared to input frequency when only sinusoidal signal is applied across test fingers. But when ac signal along with a dc bias is applied, the frequency component of output depends on amplitude of a.c magnitude. When its amplitude is greater than dc offset, the interesting phenomena of the presence of the double frequency component appears in the output. This analysis will be very much helpful to characterize similar type of MEMS structure with electrical actuation through test fingers.

REFERENCES

[1] L.A Rocha,"Dynamics and Nonlinearities of the Electro­Mechanical Coupling in Inertial MEMS", PhD Thesis, Delft University ofTechnology,2005

[2] Akila Kannan, "Design and Modeling of a MEMS based Accelerometer with pull in analysis", M.sc thesis, Electrical & Computer Engineering, The University of British Columbia, 2008

[3] M.H.Bao,H.Yang,H.Yin,S.Q.Chen "Effects of electrostatic forces generated by the driving signal on capacitive sensitive devices",Sens. And Actuators A 84,213-219, 2000

[4] Lufeng Che, Bin Xiong, Linxi Dong,Yuelin Wang, " Effects of bias voltage polarity on differential capacitive sensitive devices", Sens. and Actuators A 112, 253-261, 2004

[5] Hu Xuemei, Tian Linhong, "Research & Analysis of Bias Voltage on Variable-Capacitance Micromechanical Accelerometer", International Conference on Intelligent Information Hiding and Multimedia Signal Processing, 2008

[6]Minhang Bao, Analysis and Design Principles of MEMS Devices, Elsevier, 2005

[7] E. Cretu, "Inertial MEMS Devices-Modeling,Design and Application", PhD Thesis, Delft University of Technology, 2003

[8] Nadim Maluf, An Introduction to Microelectromechanical Systems Engineering, Artech House, 2000

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