A Pull-in Operation Mode Accelerometer

IEEE SENSORS 2006, EXCO, Daegu, Korea / October

22-25,

2006

A

Pull-in

Operation

Mode

Accelerometer

LukaszPakula, PatrickFrench Delft University of Technology Micro-electronics andComputer Engineering

Delft, The Netherlands l.pakula@ewi.tudelft.nl

Abstract In this paper anaccelerometer, which measuresthe pull-in time to obtain the acceleration ispresented. As the pull-intime is a semidigital signal, the outputof the devicecanbe measured with a full digital circuit. No analogue readout circuit is required. The sensitivity and nonlinearity are

comparable with the differential capacitive sensing devices. The accelerometer has been fabricated by surface micromachining using Al as the mechanical layer and phosphosilicate glass as the sacrificial layer. The initial measurementshave beenperformed.

I. INTRODUCTION

The surface micromachined accelerometers usuallyhave low pull-in voltages and therefore the capacitive sensing is difficultto achieve [1].W. C.Tangproposed anovel

digital

accelerometer in 1994

[2],

in which the pull-in

voltage

is measuredtoobtain the acceleration since the pull-involtage is the function of the acceleration.

Ithas been foundby the authors that thepull-in time is also a function of the acceleration [3]. An

accelerometer,

whichmeasuresthepull-intime,has beenproposed.

The principle of the device is shown in Fig. 1. By applyingthepulsevoltages X1 and

02

tothe electrodes 1 and

2 alternately, the mass is pull-in at the stoppers 1 and 2

alternately. T1 is thepull-intime from the stopper 1 to2, and T2ispull-in tome from the stopper2 to 1. When there is no

acceleration in the x direction,

TI=T2=To.

If there is an

acceleration in thex direction, the differential pull-in

time,

AT=T2-T1,

is proportionaltothe acceleration. AT is a pulse-width-modulated signal and can be measured with a

digital

circuit. The sensitivity and the

non-linearity

are similar to

-* a

that of the differentialcapacitive sensing.

The device has been fabricated by the surface micromachining technology. The pull-in time can be obtained either bymeasuringthe contact between the mass

and the stopperorbythecapacitivesensing.

II. PRINCIPLE

The movement of the massbetween the stoppers canbe describedbytheequation:

gg0A

V2

mx+cx+kx _ 2 +ma

2(d0 x) (1)

whereais theacceleration, Vthedrivingvoltage,Athearea

of the electrode,

do

the initial electrode gap and x the displacement. To keep the device working in the pull-in mode,thedrivingvoltagemustbehigherthan the minimum pull-involtage and theprevious pulsevoltage should be held long enoughtomake surethat the initial condition isx=0.

To discuss the characteristics ingeneral, adimensionless equation is preferred. The corresponding dimensionless equationof(1)is

(2)

F ~~~~~(_

c ~

w2

where x=x/do, x =

d/d,

x =

d2x/dr2,

=cot,

Electrode 1

Stopper

1I I WN.H 0

II

Electrode 2

0g2

IN

Stopper

2 ol~~~

021

X VI

\4

IoL 2~~~~~~~~~

Figure1.Theprincipleof thepull-inoperationmode

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}2006

IEEE

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IEEESENSORS 2006, EXCO, Daegu, Korea / October 22-25, 2006

o) the circular resonant frequency, ; the damping ratio,

F

eOAV2

/(2kd ) the dimensionless driving force and a

ma/kdo

the dimensionless acceleration. The driving force mustfulfilF >

4/27,

which iscorresponding tothe minimum pull-in voltage.

a7

is always smaller than 1 accordingtothedefinition.

When the dampingis zero, the analytical pull-in time can

be obtained [3]. The differentialpull-intime Ar=z2-z1 is

A1r=2sa±+1na+3+(a3) (3)

The nonlinearity of the pull-in accelerometer isO I)

which is the same order of the ratio (17 / 4)na3/(2saZ). The nonlinearity of the pull-in mode is similar to the differential

capacitive

sensing.

When the damping is non zero but also not high, (2) cannotbe solvedanalytically.Matlab was used toanalysethe equationnumerically. Fig. 3 shows the gain with respect to

the electrostatic force andFig. 4thenonlinearityinthe range of a E[-0.1,0.1]. Xused in the calculations is 0.5.

It canbe observed that both the gain and thenonlinearity increase with the damping and saturate when the damping ratio is largerthan 1.

where

-)

2F (I-X

)(1

+

A)

3 2 dax

(4)

5 3

1

2-)

( 2F (I -XI+A 7 2 2

(5)

where±2 is thepositionsof the stoppers.

It canbe obtained from(3)that Ar isproportionalto the acceleration. The gain of the device can be defined as

G=2s/r0.Fig. 2 shows thegainwith respectto F and X.

Bycomparison,thegainof the differential capacitive sensing is 2. Therefore, the gain of the pull-in accelerometer is comparable to that of the normal accelerometer with the differentialcapacitive sensing.

5 4 3 2 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 F 1

Figure3. Thegainasthe function ofF andQ.Xissupposedtobe

0.5. 8 0.1 0.2 0.3 0.4 0.5 0.6 F 0.7 0.8 4 3 2 4 1 0 0 0.2 0.4 0.6 0.8 A

Figure2. Thegainasthe function ofF andX

Figure4. Nonlinearityasthe function ofF andQXissupposedtobe

0.5.

As the damping in an accelerometer is usually changed with thedisplacement, the influence of the variabledamping is also analysed. The dominant damping in the system is supposedto be the squeeze film damping,whichmeans that thedampingratio isinversely proportionaltothe cube of the electrode gap. Itis observed that thegain increases with the dampingfaster than inFig. 3.

1-4244-0376-6/06/$20.00 }2006

IEEE F, 6 F 1128 I S =

(A

+

X)--2 (A

n=

(A,

X-)--2,

(A

IEEE SENSORS 2006, EXCO, Daegu, Korea / October 22-25, 2006

lal

= A/D -I

f fo

(%)

Figure5. Theamplitude-frequency relation

The pull-in operation process is a pulse-width modulation process [4]. The bandwidth of the device is determined by thesamplingrate.

In principle, the larger the sampling rate, the larger the bandwidth. The theoretical maximum sampling rate of the pull-inaccelerometer is ahigherthan theresonantfrequency. However,the sampling rate is limited by several factors.

Firstly, the sampling pulse width must be larger than the maximum pull-in time, which is determinedby the full-scale required.

Secondly, the sampling pulsewidthmustbe long enough

to make sure that the speedof the mass is 0 before thenext

pulse because the measurement is sensitive to the initial conditions and the vibration of the mass at the pull-in position causes errors. Inthis paper, the pulse width of the driving voltage is set to be

1/ft,

where

f0

is the resonant

frequency. Afullmeasuring circle is

2/tf.

Inotherwords,the sampling frequency

isf0/2.

Fig. 5 shows the amplitude-frequency relation of a device with

;=0,

X=0.5 andF=0.3. The relation is obtained by

Fouriertransformof the theoretical output. The bandwidth of the device is 13.4% of theresonantfrequency.

When the acceleration is very large, the structure does notpull-in. The maximum acceleration that can be measured is a function of the operating voltage. To simplify the analysis, the maximum acceleration is estimated with the initial conditions x=0andx =0.

When the damping is very high, the maximum acceleration is:

(7)

III. DESIGN

Based on the above analysis the surface micromachined accelerometer has beendesign. The device structure is made by 3ptm thick aluminium. The mass is supported by four folded beams. The mass is

400[tmx800itm.

Each fold of the beam is2.5jtmxl50 tm. Interdigitatedelectrodes are used to drive the mass. There are 62fingersoneach side of the mass. Each finger is

3[tmxlOO[tm.

The finger-electrode gap is 2ptm. The mass-stopper gap is 1ltm. The mass-substrate gap is Itm.

The electrical and mechanical properties have been calculated. Theresonantfrequencyis calculatedtobe 4 kHz. When the displacementis 0,the dampingratio is calculated

to be 0.057. The pull-in voltage is calculated to be 4.86V. The pull-in voltage offingers is higher than IOV when the massis at thepull-in position.

The static anddynamic properties of the accelerometer in pull-inmodeareanalysed numericallywith Matlab software. When thedriving voltage is8V,thepull-intime is calculated

to be 77jts. Fig. 6 shows the differential pull-in time with respect to the acceleration, which was obtained by simulation. Thenon-linearityis 0.87%FS.

Thepull-intime can be obtained eitherby measuringthe

contact between the mass and the stopper or by the capacitive sensing.

AT(ps)

15F

10F

5 -6 -5 -4 -3 -2 1 -5 -10 #,~ ~~~~~~. a

(g)

I .' 1 2 3 4 5 6 27F

la

<3 -1 (6) 4

For the device with light damping, the maximum acceleration islarger than(6) dueto over-shooting [1]. The maximum acceleration of the device without damping is given by:

Figure6. Theoutputunder the8Vdriving voltage

IV. FABRICATIONANDMEASUREMENTS

The device has been fabricated by the surface micromachining technologywithAl asthe mechanical layer and PECVD PSG (phosphosilicate glass) as the sacrificial layer, respectively.

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}2006 IEEE

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IEEE SENSORS 2006, EXCO, Daegu, Korea / October 22-25, 2006

Thefabrication process is as follows:

1. First the 1urm PECVD 4% PSG (4% of phosphorus in PSG) was deposited on oxidised silicon wafer in Novellus system andpatternedtoform sacrificiallayer. 2. Next the 3ptm low temperature Al was sputtered in

Trikon Sigma sputter coater. Afterlithography the layer was patterned in Trikon Omega 201 plasma etcher, formingthe device.

3. The structure was released byremoving PSG sacrificial layer in 73%HF (fluoric acid) with addition of iso-propanol. To prevent problem of stiction the freeze dryingprocess wasemployed after sacrificial step. Fig. 7shows the SEMphoto of the device.

Prior to the packaging the capacitance-voltage measurement wasperformed. The results are shown inFig. 8. Thepull-in voltages weremeasuredto be 8. 1V and 8.7V inthepositive and the negativedirections, respectively. The pull-in voltages are higher than the theoretical values and slightly asymmetric. That could be the explained by the slightdeformation of thestructure(SEMphotoinFig. 7).

The asymmetry of the pull-in voltages can be compensated bythe drivingcircuit. It canbe observed that the resonant frequency changes with the bias voltage. The resonant frequency and the damping ratio at 2V DC + IV AC aremeasured to be 4.97 kHz and 0.024, while the data

at 3V DC+2.18V AC are 4.87 kHz and 0.022. Initial experiments have shown the change in pull-in time of

5[ts

from 0 to 1G. 0.30 ,- 0.28 s 0.26 a) Q i 0.24 X 0.22 U 0.20 0.18 -0 90 80 70 60 - 50 ' 40 > 30 20 10 0 2 4 6 8 10 Voltage (V) Figure 8. CV measurement 12 14 3V DC+2.2V AC ",IN 2VDC+IVAC 3 3.5 4 4.5 f(KHz)

Figure7. TheSEMphotoofthedeviceand theclose-upsof the

stopperand thefingers.

Figure9. Frequencyresponse

V. SUMMARY

Apull-in accelerometer, which features a digital output,

has beendesignedand fabricatedbysurfacemicromachining technology. The pull-in voltages have been measured. The

pull-intime measured from 0to IG is5ts

ACKNOWLEDGEMENTS

The authors wish to thank the IC process group of DIMES for technical assistance. This research is supported by the Dutch Technology Foundation, STW (project DMF

.5103), Applied Science Foundation of NWO and the

technologyprogrammeofMinistryof Economic Affairs.

REFERENCES

[1] M.Baoetal, Effects of electrostatic forces generatedbythedriving

signal on capacitive sensing devices, Sensors and Actuators, A84, Issue3,pp.213-219.

[2] W.C. Tang,Digital Capacitive Accelero-meter,US Patent5353641,

Oct.11,1994.

[3] H.Yangetal.Anoveloperation mode foraccelerometers, Pacificrim

workshop ontransducers andmicro/nano technologies, July22-x24,

2002,Xiamen, China, pp.303-306.

[4] R. E.Ziemer,W.H. Tranter,Principlesof communicationssystems,

modulation and noise.HoughtonMifflinCompany,1985.

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