TRANSDUCERS ’01 EUROSENSORS XVThe 11th International Conference on Solid-State Sensors and Actuators, Munich, Germany, June 10 – 14, 2001

USING THE PULL-IN VOLTAGE AS VOLTAGE REFERENCE

E. Cretu, L.A. Rocha and R.F. WolffenbuttelDelft University of Technology, ITS/Et, DIMES, Mekelweg 4, 2628 CD Delft, The Netherlands

Phone: +31 15 278 6287, Fax. +31 15 278 5755, email: R.F. Wolffenbuttel@its.tudelft.nl

SUMMARY

The reproducibility of the pull-in voltage of a singleside clamped free-standing beam has been investigatedfor application as a DC voltage reference. A 2 mm longbeam has been fabricated in an epipoly process with, atthe tip, poly-poly electrodes extending into the axialdirection for electrostatic lateral deflection and a comb-drive operating in the normal lateral beam direction.The DC voltage is applied to the electrodes to causepull-in and the comb drive actuator is used to restorelateral beam position. The device can be operated infeedback or as a seesaw, by using these two sets ofelectrodes. The reproducibility of the pull-in voltageappears to be mainly limited by charge injection.

INTRODUCTION

MEMS technology is gradually also penetrating intomainstream Instrumentation and Measurementapplications [1]. Although most microsystems are inprinciple instruments designed for measuring a non-electrical quantity, and thus serving a measurementapplication, the I&M application area can be defined asthe field, where the instrument is the purpose and notthe means. MEMS technology has a huge potential forcontributing to critical components in a professionalinstrument, such as AC-to-DC converter or internal DCreference.

The earliest contribution was in thermal RMS-to-DCconverters. Thermal AC measurement uses theequivalent Joule heat generated in a resistor by an ACor DC voltage or current. Devices operating on thisprinciple are composed of a heater, to which the ACinput is connected, and a thermal sensor that provides aDC output. The heater design aims on reproducibilityby using a heating resistor material with low TCR andwide bandwidth by using a low-resistance with aminimum parasitic series inductance and parallelcapacitance. The heating of the resistor with respect toambient temperature is measured and for that reasonthe resistor is to be placed on a thermally isolatingmembrane. Moreover, the measurement of atemperature difference is preferred, rather than themembrane temperature.

Silicon microtechnology has a huge potential for fabri-cation of such devices, because:• Silicon oxide and silicon nitride membranes can be

fabricated using micromachining technologies,• Compatible post-microelectronic sensor technolo-

gies can be used for the fabrication of NiCr resis-tors,

• Bulk micromaching can be used to increase thethermal capacitance of the heated membrane, thusenabling the implementation of the time integra-tion that is required for the RMS value and

• Thermopiles can be integrated in silicon usingdoped and/or deposited layers.

Two different implementations are available. The firstis composed of a ring-shaped heating resistor and alarge number of thermocouples on a thermally isolatingmembrane (e.g. Cu-CuNi thermocouples on a 200 nmSi3N4- 400 nm SiO2- 200 nm Si3N4 membrane) [1, 2].Bulk micromachining enables the formation of a largesuspended thermal mass (obelisk) that improves thelow-frequency response.

The alternative thermal RMS-to-DC converter in sili-con is based on the use of a bipolar differential transis-tor pair for measuring the temperature difference [1].The AC input drives a resistor and the temperature ofthe thermally isolated island (the input part) containingthis resistor and a temperature sensing bipolar transis-tor increases as a result. A feedback configuration isused that drives an identical resistor/transistor combi-nation on another thermally isolated membrane (thecompensating part), until both islands are at the sametemperature. At steady state, the DC voltage required todrive the compensating part is the DC equivalent of theRMS voltage hat drives the input part. It is important tonote that for proper operation, the two sets of heatingresistor/temperature sensing resistor combinations arethermally isolated with respect to both ambient andeach other.

Recently, MEMS technologies are used to realise anelectrostatic RMS-TO-DC converter [3-5]. This deviceis composed of two wafers, one silicon wafer with abulk-micromachined suspended membrane and oneglass wafer with a fixed electrode. Bonding results in

TRANSDUCERS ’01 EUROSENSORS XVThe 11th International Conference on Solid-State Sensors and Actuators, Munich, Germany, June 10 – 14, 2001

the membranes facing each other with typically 4 µmspacing. The electrostatic force between the membranesis proportional to the square of the voltage. Squaring anAC voltage with frequency ωac results in a DC compo-nent and a component at 2ωac. Operation is based oncapacitive measurement of the slowly varying (DC)displacement and requires suppression of non-DC dis-placements. This static displacement is set by the mem-brane area and suspension beam dimensions. The dy-namics of the displacement is set by the squeeze-filmdamping and the suspension beams arrangement.

In this paper another I&M application of MEMS tech-nology is investigated; the use of the pull-in voltage ofa microstructure as DC voltage reference.

The pull-in voltage of beams of different designs hasbeen investigated with the purpose of using themicromechanical structure as an on-chip voltagereference. Such a device may find application inintegrated circuits, next to the conventionally usedbandgap reference, and in metrology, where Zenerreferences are widely used as so-called “transferstandard” [6]. The operation of a Zener diode is basedon avalanche breakdown and is associated with a highnoise level. The major design issues in themicromechanical design are: (1) the reproducibility ofthe pull-in voltage, (2) the thermo-mechanical noiselevel and (3) the circuits required for practicaloperation.

THE PULL-IN VOLTAGE

As the electrostatic force in a vertical field is inverselyproportional to the square of the deflection and therestoring force of the beam is, in a first approximation,linear with deflection, an unstable system results incase of a deflection, v, beyond a critical value, vcrit. Thepull-in voltage, Vpi, is defined as the voltage that isrequired to obtain this critical deflection. For a stableequilibrium deflection the second derivative of thepotential energy of the system to deflection should bepositive: ∂2Up/∂v2>0, thus Vpi results from ∂2Up/∂v2= 0.The potential energy is composed of the bending en-ergy, Ub, the strain energy, Us and the potential energyof the excitation (the potential energy of the electro-static force, Uel). The theory on the pull-in voltage hasbeen developed around a beam with both ends clampedand yields [7]:

( ) ( )

( )( )( )

( )

2 22

20 0

2

30

2 2 31/40

4

4432

3125

L L

x y x

pi L

o

x y x

o

d v x dv xE I dx S dx

dx dxV

v xW dx

d v x

E I S L d

WL

ε

ππ

ε

+

=

−

+ =

∫ ∫

∫

where Ex denotes the Young’s modulus, Sx the stress inthe beam in the length direction, Ly the moment ofinertia, do the nominal spacing between the beam andthe counter electrode, W the width and L the length ofthe beam.

Several limitations of the clamped-clamped beam makethis device structure not suitable for voltage reference.

Firstly, the reproducibility would be limited by long-term drift due to residual stress relaxation. Therefore, asingle-ended clamped beam or a plate with foldedsuspension should be used.

The pull-in voltage of a single-ended clamped beamcan be obtained by modifying the expression shown.The modelling indicates a pull-in voltage at the beamdimensions of about 13 V. The actual pull-in voltage isstrongly depending on device dimensions. However, asthis application area is primarily concerned aboutstability, any deviation of the actual pull-in voltagefrom the design target is not critical.

The second design consideration results from anothersource of uncertainty, which is the thermo-mechanicalenergy. This can be included in the analysis as anadditional excitation noise term in the potential energyof the system. For low-noise operation squeeze filmdamping should be minimised.

Thirdly, reliability concerns do not allow thecontinuous bouncing of the beam. Moreover, the pull-involtage should preferable be made availablecontinuously, which results in a circuits solution withthe structure operating as a seesaw [1] or in feedback.

Prototypes have been realised in the Bosch epipolyprocess [8]. Basically an 11 µm thick structuralpolysilicon layer is patterned and released in a surface-micromachining alike process. DRIE is used to achievehigh aspect ratio polysilicon structures, which arereleased using sacrificial etching of a buried layer.

TRANSDUCERS ’01 EUROSENSORS XVThe 11th International Conference on Solid-State Sensors and Actuators, Munich, Germany, June 10 – 14, 2001

Figure 1, Photograph of a detailed view of the tip of thefabricated microstructure.

The devices are single-ended clamped beams movingin-plane of the wafer with localised parallel plateactuation at the free-standing tip. Figure 1 shows one ofdevices used for the pull-in measurements. A 2 mmlong beam has been fabricated with both poly-polyelectrodes for electrostatic lateral deflection and acomb-drive positioned at the tip. The DC voltage isapplied to the electrodes to cause pull-in and the combdrive actuator is used to restore lateral beam position.

RESULTS AND DISCUSSION

Figure 2 presents the first experimental results withVpi= 12.5 V. Short-term reproducibility is in the mV-range, despite the crude detection technique used so far.Experiments from another group on a metal-siliconelectrode combination show a polarity dependent driftof about 0.5%/50hrs. [1, 6]. This is not acceptable inI&M applications. The source of drift has beenidentified as charging of the (native) oxide of the

polysilicon beam. After coating the silicon with a metalmuch better results are expected. Measurements arescheduled to verify the long-term reproducibility.

REFERENCES

[1] R.F. Wolffenbuttel, D.D.L. Wijngaards andC.J. van Mullem, Proc. Symposium on Micro-technology in Metrology and Metrology in Mi-crosystems, Delft, The Netherlands, August31-September 1, 2000, 151 pp.

[2] M. Klonz and T. Weimann, Accurate thin-filmmulti-junction thermal converter on a siliconchip, IEEE Tr. ED, Vol. 38, No. 2, April1989, pp.335-337.

[3] B.P. van Drieënhuizen and R.F. Wolffenbuttel,Integrated electrostatic RMS-to-DC converterusing IC-compatible surface micromachining,Proc. Transducer 95, Stockholm, Sweden,June 25-29 1995, pp. 130-133.

[4] M. Bartek, Z. Xiao, C.J. van Mullem and R.F.Wolffenbuttel, Bulk micromachined electro-static RMS-to-DC converter: design and fabri-cation, Proc. MME00, Uppsala, Sweden, Oc-tober 1-3 2000.

[5] J. Kyynäräinen, A.S. Oja and H. Seppä, Amicromechanical RMS-to-DC converter, Con-ference digest of CPEM2000, pp . 699.

[6] A.S. Oja, J. Kyynäräinen, H. Seppä and T.Lampola, A micromechanical DC-voltage ref-erence, Conference digest of CPEM2000, pp.701.

[7] H.A.C. Tilmans, and R. Legtenberg, Electro-statically driven vacuum-encapsulatedpolysilicon resonators, Part 2, Theory and per-formance, Sensors and Actuators A 45(1994)67-84.

[8] Bosch Micromachining proc, http://www.vdivde-it.de/mst/imsto/Europractice/Bosch/

Figure 2, Measurements results for one of the devices.The parameter used for monitoring the pull-in is thevoltage of a stopper contact. The release voltage atabout 10.9 V indicates sticking.