TIME-RESOLVED MEASUREMENT of OPTICAL MEMS USING ...

TIME-RESOLVED MEASUREMENT of OPTICAL MEMS USING STROBOSCOPICINTERFEROMETRY

Matthew R. Hart, Robert A. Conant, Kam Y. Lau and Richard S. MullerBerkeley Sensor & Actuator Center, University of California, Berkeley CA 94720-1774, USA

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ABSTRACTWe report a system for MEMS characterization thatallows us to measure dynamic out-of-planedisplacement and deformation of micromachinedstructures with nanometer accuracy and sub-microsecond time resolution. The system, based ona stroboscopic phase-shifting interferometer,collects data over an imaged two-dimensional area,permitting rapid measurement without the need forpoint-by-point scanning. An integrated computer-control and data-acquisition unit automates thedata-collection process, and allows a detailedpicture of microstructure dynamics to be built up inminutes. The high out-of-plane sensitivity of themethod makes it particularly suitable forcharacterizing actuated micro-optical elements forwhich even nanometer-scale deformations canproduce unacceptable performance reductions. Asan illustrative example, we present a study of thedynamic behavior of a polysilicon surface-micromachined scanning mirror that was fabricatedin the MCNC MUMPS process.

INTRODUCTIONSurface micromachining has been used to createminiaturized optical systems on a chip [1, 2].Optical MEMS devices have many applicationsincluding fiber-optic switching, bar-code scanning,direct-projection display, and spectroscopy. Theoptical components, such as mirrors, beamsplittersand lenses, which form the building blocks of thesesystems, must be manufactured to very stricttolerances in order to perform their intendedfunctions well. Modern grinding, polishing andtesting methods have made macro-scale opticalcomponents having surfaces finished to accuraciesof a few tens of nanometers commonplace. Similarcontrol over the form of thin-film micromachinedstructures has yet to be achieved. In addition tostatic buckling caused by film stresses and stressgradients, actuated microsystems suffer fromdynamic mechanical effects, such as air drag andexcitation of higher-order resonant modes. Theseeffects cause time-dependent deformations thatcannot readily be predicted using analytical orfinite-element models. The deformations are oftensmall from the perspective of device mechanicalbehavior, but can cause significant degradation to

optical performance. The ability to characterizedynamic-deformation effects experimentally istherefore crucial to the development of actuatedmicro-optical systems.

Time-resolved measurements of nanometer-scaledisplacements across the entire surface of a micro-structure are difficult or impossible to performusing conventional MEMS metrology techniquessuch as SEM, AFM, and optical microscopy. Forthis reason, there has been growing interest inalternative characterization methods. Laser Dopplervibrometry [3] provides high-speed, nanometer-resolution displacement measurements, but isessentially a single-point technique, requiring alaser spot to be scanned over the structure undertest. Davis and Freeman [4] have described analternative that uses stroboscopic video microscopycombined with machine-vision algorithms to trackboth in- and out-of-plane motions. They haveachieved nanometer-scale displacement resolutionfor in-plane motion. However, the system describedin reference [4] has not demonstrated the highlydetailed measurements of out-of-plane deformationthat are needed to characterize optical surfaces.

The technique that we have used, stroboscopicinterferometry [5], although it does not measure in-plane motion, gives extremely precise, time-resolved out-of-plane measurements over animaged two-dimensional area. When combinedwith phase-shifting techniques [6], out-of-planedisplacement resolutions as small as 1nm can beachieved.

In this paper we report the first application of thismethod to dynamic characterization of fold-upsurface-micromachined structures [1]. Afterdescribing our experimental setup, we presentmeasurements taken from a fold-up scanningmicromirror that was fabricated in the MCNCMUMPS process. These measurements allow us topredict the dynamic optical properties of the mirror.The technique presented is not limited to theanalysis of micro-optical components, but can beused to provide insight into the mechanicalbehavior of a wide range of actuated MEMSdevices.

STROBOSCOPIC INTERFEROMETERA schematic of our MEMS characterization setup isshown in Figure 1. The heart of the system is a

Twyman-Green interferometer formed by apolarizing beamsplitter, a flat reference mirror andthe MEMS device under test. Half- and quarter-wave plates are used to provide a continuouslyvariable split ratio between the beams in the twointerferometer arms, allowing high-contrastinterference patterns to be produced for test-surfacereflectivities between roughly 5 and 100%. Thelight source is a 658 nm laser diode (HitachiHL6501MG), rated for a CW output power of 35mW and driven by a circuit producing 500 ns-widecurrent pulses. A function-generator card inside thecontrolling PC triggers the pulse-generating circuitand also drives the MEMS device via either atransformer or a high-voltage amplifier. Typicaldrive voltages for our devices are on the order of20-100 V peak-to-peak.

The interferogram is imaged onto a CCD array, thatrelays the data to a frame-grabber card in the PC.Our imaging system can resolve in-plane featuresdown to approximately 2 µm. A piezoelectrictranslation stage (Polytec PI P-753.11C) steps thereference mirror axially to provide the phase shiftsrequired for measurement.

Data acquisition is co-ordinated by an integratedsoftware package that: (1) controls the timing andfrequency of the MEMS-drive signal and laser-trigger pulses, (2) steps the position of the referencemirror, and (3) reads data from the CCD camera.After initial interferometer alignment, themeasurement process is completely automated. In atypical run, we read data at 64 different laser-pulse-to-drive-signal time delays τ distributed over one

period of mechanical motion. This data-acquisitionprocess can be completed in less than five minutes.The data are processed using a five-point phase-measuring algorithm [6] combined with a phase-unwrapping algorithm to give a detailed picture ofthe structure motion and deformation. The out-of-plane measurement repeatability of our system isbetter than 2 nm, allowing us to quantify extremelysmall-amplitude motions with high accuracy.

Our present setup provides two different MEMS-drive modes: sinusoidal excitation for single-frequency analysis between 200 Hz and 15 kHz,and square-wave excitation for measurements ofmechanical ringing. Using the square-wave drivemode, we can measure motion at frequencies ashigh as 500 kHz, through Fourier-analysistechniques. The upper-frequency bound for bothmodes is imposed by our function-generator cardand is not a fundamental limit of the method.

DYNAMIC CHARACTERIZATION of aSCANNING MICROMIRROR

We have used the stroboscopic interferometer setupto measure the motion and deformation of ascanning surface-micromachined micromirror. Themirror (see Figure 2) is a combdrive-actuated fold-up polysilicon device (fabricated in the MCNCMUMPS process), designed to operate as the line-scanner in a MEMS raster-scanning display [7].The combdrive tilts the mirror about an axisdefined by the torsion hinges. This tilting motionscans a reflected light beam through angles as largeas 20 degrees. One figure-of-merit for these devicesis the ratio of the total beam-scan angle to the far-field beam divergence. In a display application, thisratio defines the number of resolvable pixels themirror can generate in one scan line [8]. Ideally (for

Figure 2: SEM showing the type of fold-up micromirrorused in our experiments. The mirror itself is a 1.5 µm-thick polysilicon plate supported on a frame by 2 µm-wide torsion hinges. The mirror and frame are orientedat approximately 90° to the substrate.

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Figure 1: Schematic of the phase-shifting stroboscopicinterferometer system. HWP is a half-wave plate, QWPare quarter-wave plates, PS is a piezoelectric stage, andPOL is a linear polarizer.

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a perfectly planar mirror), the far-field beamdivergence is governed by diffraction due to thefinite mirror size. In practice, however, stress-induced mirror curvature causes beam divergencethat exceeds that of diffraction-limitedperformance. Measurement of the mirrordeformation allows the additional divergence to bequantified, and the true mirror performance to bepredicted. For the mirror used in these experiments,inspection under the interferometer (with the mirrorat rest) revealed a roughly parabolic, convexdeformation with a center-to-edge surface-heightdifference of approximately 1.2 µm. This figure isfairly typical for surface-micromachinedmicromirrors of this size, fabricated in the POLY2layer of the MUMPS process. Althoughundesirable, this static deformation can be largelycompensated using simple external optics [8].

Of greater concern are the dynamic deformationsthat occur when the mirror is actuated. To quantifythese, we scanned the mirror in air at roomtemperature and pressure at its resonant frequency(6.2 kHz). We took a series of time-resolvedsurface-height measurements for a range of timedelays τ covering one complete period of motion.To make the small mirror deformations moreapparent, we subtracted a number of terms from themeasured data. First, the gross mirror tilt wasremoved by subtracting a least-squares-fit planefrom each individual data set. Then, using ameasurement close to the midpoint of the scan, theoverall defocus term due to the static component ofthe deformation was estimated by fitting a parabolato the measured mirror shape. This single best-fitparabola was then subtracted from each of the time-resolved surface-height maps. Four resultingresidual surface-height maps, showing themeasured mirror deformation over one-half periodof the motion, are plotted in the left-hand column ofFigure 3 (note the difference in vertical andhorizontal axes scales). Alongside each of theseplots, the corresponding far-field spot size(estimated from the measured data after defocuscorrection) is shown. Referring to the top-left plotof Figure 3, our measurements show the residualmirror shape (after defocus correction) near thestart of the scan to be planar to within 250 nm.Consequently the estimated far-field spot is close tothe diffraction-limited size. However, as the scanprogresses, an increasing saddle-shapeddeformation can be seen with a maximumamplitude of almost 1.5 µm. Although thisdeformation is mechanically small, it is sufficient tocause a significant enlargement of the far-field spotas shown in the middle column of Figure 3. Thehigh sensitivity of the technique is apparent when

viewing dynamic deformations of the mirror frame.The plots in the right-hand column of Figure 3reveal periodic bending of the vertical framemembers. Although the maximum amplitude of thismotion is only on the order of 100 nm, it is easilyresolved by the interferometer. Our measurementsillustrate the wealth of information on these subtle,but important mechanical effects, that thecharacterization technique makes available. Themethod provides valuable feedback in the MEMSdesign process that can shorten development cyclesand permit systematic improvements in deviceperformance.

CONCLUSIONSWe have demonstrated a stroboscopic phase-shifting interferometer system for dynamicmeasurement of MEMS devices. An integratedcomputer-controller facilitates rapid devicecharacterization. The instrument providesnanometer-scale out-of-plane measurementresolution, and is particularly useful forcharacterizing optical MEMS, in which the controlof surface deformations is critical.

REFERENCES[1] K. Y. Lau, “MEM's the word for optical beammanipulation,” in IEEE Circuits and Devices Magazine,vol. 13, 1997, pp. 11-18.

[2] M. C. Wu, “Micromachining for optical andoptoelectronic systems,” Proceedings of the IEEE, vol.85, pp. 1833-1856, 1997.

[3] L. E. Drain, The laser Doppler technique. Chichester:John Wiley & Sons, 1980.

[4] C. Q. Davis and D. M. Freeman, “Using a lightmicroscope to measure motions with nanometeraccuracy,” Optical Engineering, vol. 37, pp. 1299-1304,1998.

[5] R. C. Gutierrez, K. V. Shcheglov, and T. K. Tang,“Pulsed-source interferometry for characterization ofresonant micromachined structures,” presented at Solid-State Sensor and Actuator Workshop, Hilton Head Island,SC, USA, 1998.

[6] J. E. Greivenkamp and J. H. Bruning, “Phase shiftinginterferometry,” in Optical Shop Testing, D. Malacara,Ed., Second ed. New York: John Wiley & Sons, Inc,1992, pp. 501-597.

[7] R. A. Conant, P. M. Hagelin, U. Krishnamoorthy, O.Solgaard, K. Y. Lau, and R. S. Muller, “A raster-scanning full-motion video display using polysiliconmicromachined mirrors,” presented at Transducers '99,Sendai, Japan, 1999.

[8] P. M. Hagelin and O. Solgaard, “Optical raster-scanning displays based on surface-micromachinedpolysilicon mirrors,” IEEE Journal of Selected Topics inQuantum Electronics, vol. 5, pp. 67-74, 1999.

Figure 3: Left-hand column – four time-resolved measurements of micromirror deformation, taken with the mirrorscanning at 6.2 kHz. Mirror tilt and defocus terms have been subtracted from the measured data to show the changes inshape more clearly. Contours, showing lines of equal residual surface height have been projected onto the base of eachplot. Middle column – prediction of mirror performance based on the measured data. The far-field spot is close todiffraction-limited near the beginning of the scan (top image), but spreads out significantly as the scan progresses. Right-hand column – measured deformation of the mirror-support frame, showing a bending motion with approximately 100nm amplitude.

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