NEW WAYS OF MEASURING PULL-IN VOLTAGE AND TRANSIENT BEHAVIOR OFPARALLEL-PLATE CAPACITIVE MEMS TRANSDUCERS

C. Glacer1,2, A. Dehe2, M. Nawaz2 and R. Laur1

1Institute for Electromagnetic Theory and Microelectronics (ITEM), University of Bremen, Bremen, Germany2Infineon Technologies AG, Neubiberg/Munich, Germany

Abstract — In this paper we introduce twonew ways of measuring the pull-in voltageand the transient behavior of parallel-platecapacitive MEMS transducers. The advantagesin measurement speed and resolution of the so-called fast MEMS test will be discussed as well asan enhanced method, the time-resolved dynamicmeasurement. With the second method we canvisualize the integral displacement of a membranewhile measuring the voltage drop of a highfrequency signal over a shunt resistor/capacitor.This offers us a new robust and cheap option fortracing moving structures without the need of anoptical line of sight.

Keywords: MEMS testing, Silicon Microphone,laser Doppler vibrometer, pull-in voltage

I – Introduction

Acoustical parallel-plate microelectromechanicalsystems (MEMS) especially for mobile applicationsare strongly upcoming the last years. With ongoingminiaturization of mobile phone components andthe desire for automatic reflow solder processesthe requirements for microphones are increasing.Conventional electret condenser microphones sufferfrom humidity and temperature influences. TheInfineon Silicon MEMS Microphone chip set deliversa small size, good reproducibility and stability, lowsensitivity to vibration and the ability of low-cost batchfabrication along with a sufficient sound recordingquality [1].

Figure 1: Schematic of the Infineon Silicon MEMS Mi-crophone [1]. The membrane (red) and the fixed counter-electrode (blue) can bee seen.

The Infineon microphone uses a pressure sensitivediaphragm made out of in poly-Silicon. Along with apreamplifier, the microphone chip converts an imping-ing sound wave into an electrical output signal witha capacitive transducing concept. Although there is a

big market and millions of devices are produced everyyear, the membrane behavior in such a microphonesystem is not fully transparent and understood. Espe-cially in case of large deflections, mechanical shocksor extreme sound pressure levels it needs a (scanning)laser Doppler vibrometer (LDV) and a complex samplepreparation to monitor the membranes motion.

Belong those special measurement setups for furtherinvestigations of some systems; every chip has to passa final inspection. The pull-in voltage (Vp) can becomea key parameter for this purpose. It marks the equilib-rium point of the electrostatic attraction force and themechanical resilience in a voltage controlled capacitivesystem. This delivers insights about the membrane com-pliance (k) with a given air gap (d0) and area (A) [2].

Vp =

√8kd3

027εA

(1)

Despite a simple pass-fail test the system sensitivity(S) can be derived [1] by determining Vp.

S =V0

Vp·√

8d0

27εAk(2)

Several methods to detect the pull-in event are ex-isting. The probably simplest way is to look at themembrane while increasing the stimulus voltage step bystep. When the pull-in voltage is reached, the closing ofthe air-gap between the two electrodes will lead to in-terference fringes which are visible with a microscope.More advanced equipment like a Doppler vibrometerwill do the same purpose. Another common method todetect Vp is the usage of a LCR meter. The displacementof the membrane towards the electrode leads to a highercapacitance which can be monitored. As a consequence,the membranes motion over the excitation voltage canbe plotted. The voltage where the pull-in accelerationphase begins can be made visible as Vp. This event canbe even heard, so that a acoustical detection is anothermethod.

In this work new approaches for testing parallel-plate sensors and actuators - the fast MEMS test andthe time-resolved dynamic measurement - will bepresented. This measurement techniques deliver newinsights in the transient motion of a micro-mechanicallyfabricated membrane as well as a fast and exact testmethod for the pull-in voltage and system resonances.It will be elucidated how the fast MEMS test worksand which equipment is necessary for acquisitionand data processing. Moreover possible application

fields will be shown and initial results will be presented.

II – Measurement Setup

The concept of the fast MEMS test is relativelysimple and bases upon the well-known current mea-surement with a shunt resistor. For the simplest case,the Vp determination, the voltage drop across a resistorin series to the capacitive transducer will be meteredwith an oscilloscope (LECROY MSO 44MXS-B). Theexcitation is realized with a biased signal generator(AGILENT 33220A) which delivers for example a tri-angular waveform with 0 to 20V back to 0V in 1ms.If the pull-in voltage is inside this voltage ramp, thecapacitance of the parallel-plate actuator will quicklyincrease and influence the current through the circuitand so the resistors voltage drop. Fig. 2 shows the basicsetup. In our case, the usage of a shunt capacitor insteadof resistor delivered a higher output voltage with a bettersignal to noise ratio (SNR).

DUT (e.g. SiMic)

Biased AC stimulus

PC with

MatLab

Scope

+ - + -

Simplified equivalent circuit 1 2

CStatic

CPull-In

1 2

Measurement

Measurement Results

GPIB-Control

RMeas/Cmeas

Figure 2: Simplified model of the pull-in detection measure-ment setup. Containing the electrical circuit and an simplifiedequivalent circuit of the MEMS capacitances.

After the equilibrium point of the acting forces, themembrane encounters a large acceleration due to theincreasing electrostatic force. This normally happens ataround 1/3 of the systems air gap [2]; the el. potentialwhere this large acceleration event starts can be takenas the pull-in voltage. Due to our capacitive shunt setupit was necessary to form the second derivative to figureout the largest acceleration of the membrane which isproportional to the largest change in output voltage.

To do the necessary data processing a softwaresolution with MATHWORKS MATLAB was used. TheAC source as well as the digital storage oscilloscopeare controlled by the General Purpose Interface Bus(GPIB) interface. After a measurement the results willbe transferred to the PC, derivated twice and the pointof the biggest acceleration of Vout gets linked to thestimulus voltage Vstim. The number of read-out samplesare directly influencing the data transfer time and theresolution of the measurement. We worked with acompromise of 5000 samples while stimulating with a

0.4 0.6 0.8 1 1.20

5

10

15

20

25

Inpu

t sig

nal V

stim

[V]

Measured voltage drop over Cmeas

0 0.2−10

0

5

10

15

Vol

tage

dro

p ov

er C

Mea

s [m

V]

Time [ms]

−10

Figure 3: Measured voltage drop across the shunt capacitor. Itshows the pull-in event (time index: ≈ 0.5ms) and the release(≈ 0.9ms).

1kHz triangular waveform. This delivered a resolutionof 8mV/step for the given signal.

The big disadvantage of this method is that the re-sponse signal directly follows the input stimulus fstim.Therefor we can only extract the pull-in and releasevoltage but not the membranes free motion. Also it isnot possible to resolve the membrane movement whenthe excitation is a mechanical stimulus instead of anelectrical. To get rid of this problem, the time-resolveddynamic measurement is introduced.

For this method we use a series AC voltage sourcewith a sinusoidal signal fHF of small amplitude andhigh frequency. This signal superimposes the electro-mechanical stimulus or acts alone with a mechanicalexcitation. For a given frequency of typically 1MHz ormore, the membrane is not capable to follow the signalwhich lies clearly above the membranes resonance fre-quency (≤120kHz). The number of scan points s withinone period of the stimulus which can be achieved withthis methods can be calculated by s = fHF/ fstim.

To extract Vout,HF from Vout = Vout,stim +Vout,HF it isnecessary to apply an electrical filter. In this case weuse a software Butterworth band pass filter generatedin MATLAB to get rid of Vout,stim and noise. The signalprocessing contains the following steps:

1. Measurement and data transfer; e.g. 100k Samplesfor fHF = 5MHz

2. Spline interpolation in MATLAB to regain the si-nusoidal signal shape

3. Butterworth band pass filtering; e.g. with 4th orderand fc = 5MHz±0.2MHz

4. Creating the envelope to figure out the amplitudeof each period

5. Result: Signal proportional to the integral of themembrane displacement and its capacitance sum

III – Results and Discussion

A. Fast dynamic pull-in detection

To gain statistical values with the introduced pull-indetection method we investigated several wafers con-taining silicon microphones. For this we used a GPIBcontrolled lab wafer prober from SUESS MICROTECH.

Figure 4 shows a distribution of the pull-in voltagesacross an experimental test wafer containing >10k sil-icon microphones in total. It can be demonstrated howfine the gradients in the pull-in voltage determinationare, so that even technology effects on this wafer canbe made visible. When we measure the same waferagain without changing the setup, the median of thedeviations particular chips show in their pull-in voltagesis Vp,di f f = 8.7mV , which is nearly within the measure-ment resolution of 8mV/step.

−80 −60 −40 −20 0 20 40 60 80

−80

−60

−40

−20

0

20

40

60

80

Wafer x

Waf

er y

16V

15V

14V

13V

12V

Figure 4: Pull-in voltage distribution across an experimentaltest wafer. After 2/3 of the wafer stepping the prober tips lostcontact. This resulted in noise which will be filtered out infurther measurements.

Another advantage of the fast MEMS test is its highmeasuring speed. With the given resolution the contacttime of a chip amounts 2.5ms which includes a safeprober tip contact, the time to trigger and acquire thewaveform by the oscilloscope and the command to startstepping to the next chip for the prober.

A point which has to be minded is the dynamic effectof different excitation frequencies to the pull-in voltage.In vacuum a steeper excitation slope leads to a highermembrane acceleration and contributes more energy tothe system. With a higher measurement frequency andthe same maximum amplitude value the slope steepnessincreases [3]. Compared to a quasi-static pull-in event,the bigger kinetic energy at e.g. 1kHz test frequencyleads to a lower effective pull-in voltage. Under normalair pressure this effect gets obliterated by the air damp-ing. With higher frequencies the pull-in voltage drops

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−0.5

0.5

1

1.5

2

2.5

Frequency [kHz]

Cha

nge

in p

ull-i

n vo

ltage

[V]

Change of pull-in voltage over frequency

Change of Vp, electrical fast MEMS testStandard deviation, electricalChange of Vp, optical LDV

0

Figure 5: Change of pull-in voltage over frequency. Deter-mined by fast MEMS test and proven by optical measurement.

as shown in fig. 5.Here the fast MEMS test is a promising method

as the decrease in pull-in voltage over frequency isrepeatable for every chip. According to this a correctionfactor can be extracted and also no steep (rectangular)steps appear in the excitation voltage.

B. Time-resolved dynamic measurement (TRDM)

Since a LCR meter delivers exact capacitance valuesbut has in our test setting a minimum settling timeof around 2.8ms per point, this tool is not appropriateto perform transient measurements of MEMS micro-phones.

(a) (b)

(c) (d)

Figure 6: With a scanning laser Doppler Vibrometer measureddisplacement of the membrane at certain time points during apull-in and release event.

The motion of a parallel-plate capacitive transducerencountered from a triangular stimulus is shown infigure 6. This measurement was done with a SLDVfrom POLYTECH through the perforation holes of theoverhead (fixed) counter electrode. It shows the slowdeflection of the membrane (a), the first contact betweenthe electrodes (b), the widening of the contact area dueto higher voltage (c) and the overshoot after the release(d).

The ability of scanning through different measure-

ment points on the membrane is not given with theTRDM since only the voltage drop over a resis-tor/capacitor in series is measured. Instead the integralmovement of the membrane will be recorded. This isof course a disadvantage but sufficient in most appli-cations. A bigger problem is that higher oscillationmodes can cancel out their results because of an anti-phase vibration. This has to be taken into account and isunavoidable with the current setup.

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

10

Extracted prop. membrane displacement

Time [ms]

Stim

ulus

low

pas

s fil

tere

d [V

]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.5

1

Pro

p. d

ispl

acem

ent [

norm

ed]

0.36 0.38 0.40.75

0.8

0.85

Coupled after pull in

Time [ms]

Pro

p. d

ispl

acem

ent [

norm

ed]

0.72 0.74 0.76 0.78

0.04

0.06

0.08

0.1

0.12

Membrane oscil. release

Time [ms]

Pro

p. d

ispl

acem

ent [

norm

ed]

oscil. after

Figure 7: Proportional integral membrane motion measuredwith the time-resolved dynamic measurement with averaging(above). Coupled oscillation and mebrane oscillation afterpull in/release.

Figure 7 shows nicely how the membrane getsattracted and suddenly accelerates when the pull-involtage is reached. In contact membrane and electrodeperforming a coupled oscillation and the contact areagets bigger with increasing excitation voltage. WhenVstim is lowered again, the membrane detaches from theelectrode in a different behavior because the mechanicalrestoring force is now acting. When a certain voltageis reached, the last contact point releases from theelectrode which vanishes the adhesion force and causesthe membrane to accelerate again. The membraneperforms an overshoot over its resting position andoscillates a few times around it. In this case a Fouriertransform of the free membrane oscillation after therelease delivers a membrane resonance frequencyof 65.4kHz under normal pressure and a coupledresonance of 97.5kHz after the pull in event. This fitsto measurements done with other equipment under theinfluence of a bias voltage.

IV – Conclusion

It has been shown on several thousand chips and dif-

ferent transducer types, that the fast MEMS test methodis working and delivers good results. It produces ahigh measurement resolution with a measurement timewhich only needs one period of a stimulus signal (e.g.1ms at fstim = 1kHz) while the chip is contacted. Asidefrom that, the needed equipment is, with a functiongenerator and a digital oscilloscope, common and cheapso that in most labs the setup can be easily implemented.The problem of an overshoot due to high voltage stepsaround the pull-in point is avoided here.

The enhanced measurement setup, the time-resolveddynamic measurement, can partly compare to opticaltransient measurements with an SLDV. A disadvantageis that only integral values of the displacement will bedelivered, comparable to the capacitance of the MEMSdevice in the circuit. It is also necessary to compensateparasitic elements to get correct capacitance readingsout of both measurement methods. This will happenin a future step. On the other hand the measurementtechnique shows several benefits compared to the mea-surement with an SLDV. Starting by the equipment costwhich are only on a fraction of those of a SLDV andgoing over to the application areas. Because of the factthat no line of sight is needed, the measurement willalso work with build-in and moving chips and offersnew ways of monitoring the membrane deflection, sothe method can be also applied to pressure or bulge testsor any overload test.

All in all the new fast MEMS test and the time-resolved dynamic measurement are interesting, easy touse and robust methods to determine pull-in voltageand membrane motion which offers us new fields ofapplication.

Acknowledgements

The authors would like to thank Dr. Andreas Kendafrom the Carinthian Tech Research AG, Austria formaking the SLDV results available.

References

[1] Marc Fueldner. Modellierung und Herstellungkapazitiver Mikrofone in BiCMOS-Technologie.PhD thesis, Technical Faculty University Erlangen-Nuremberg, Munich, Germany, 2004.

[2] Rafael Nadal Guardia. Current Mode Drive of Elec-trostatic Microactuators. PhD thesis, UniversitatPolitecnica de Catalunia, 2001.

[3] G. Nielson and G. Barbastathis. Dynamic pull-in ofparallel-plate and torsional electrostatic mems actu-ators. Journal of Microelectromechanical Systems,15(4):811–821, 2006.