Josh A. Conway, Member, IEEE, Jon V. Osborn, Member, IEEE, and Jesse David Fowler
Abstract—The insertion of microelectromechanical systems(MEMS) components into aerospace systems requires advancedtesting to characterize performance in a space environment.Here, we report a novel stroboscopic interferometer test systemthat measures nanometer-scale displacements of moving MEMSdevices. By combining video imagery and phase-shift interferom-etry with an environmental chamber, rapid visualization of thedynamic device motion under the actual operational conditionscan be achieved. The utility of this system is further enhanced byintegrating the interferometer onto the chamber window, allowingfor robust interferometric testing in a noisy environment withoutrequiring a floating optical table. To demonstrate these uniquecapabilities, we present the time-resolved images of an electrosta-tically actuated MEMS cantilevered beam showing the first-orderto sixth-order plate modes under vacuum. [2006-0264]
Index Terms—Interferometry, microelectromechanical devices,microelectromechanical systems (MEMS) metrology, stroboscopicinterferometer system, vacuum systems.
I. INTRODUCTION
THE HARSH environments and stringent reliability re-quirements of aerospace systems demand detailed knowl-
edge of the motion of all mechanical and electromechanicaldevices [1]. The functional performance must be well under-stood, and the failure modes must be catalogued. While thismay entail a straightforward analysis for macroscopic devices,microscopic electromechanical structures require new tools tostudy their response under various conditions. In the exist-ing art, static, quasi-static, and vibrometer-based methods [2],[3] are employed, and the motion of microelectromechanicalsystems (MEMS) is then analytically reconstructed. Theseinferential results can be unacceptable for the requirementsof modern aerospace applications. For instance, quasi-staticmeasurements are often lacking in precision when related todynamic operation, particularly near a mechanical resonance.Vibrometer-based measurements, on the other hand, providetremendous precision for dynamic measurement but are notable to yield a complete picture of the device motion. While
Manuscript received November 22, 2006; revised February 21, 2007. Thiswork was supported by The Aerospace Corporation under the Mission OrientedInvestigation and Experimentation program, which was funded by the U.S. AirForce Space and Missile Systems Center under Contract FA8802-04-C-0001.Subject Editor O. Solgaard.
J. A. Conway and J. V. Osborn are with The Aerospace Corporation,Los Angeles, CA 90009 USA (e-mail: [email protected]; [email protected]).
J. D. Fowler is with the Department of Mechanical and Aerospace En-gineering, University of California, Los Angeles, CA 90095 USA (e-mail:[email protected]).
Digital Object Identifier 10.1109/JMEMS.2007.896710
vibrometry is able to map amplitude and phase of vibrationacross a surface, it cannot yield static topographic information.
Direct measurement of moving parts makes new demandson the test system. To study the motion of microscopic me-chanical parts, one cannot simply attach sensors, and noncon-tact measurement techniques are required. The environmentsin which MEMS operate further complicate the measurementprocess. The characterization of MEMS devices for terrestrialapplications typically must be performed at partial pressuresof gas and over a range of temperatures to replicate packagedenvironments and to optimize their performance. Emergingapplications of MEMS in space systems, however, require func-tionality under extreme environmental conditions. Such appli-cations include spatial light modulation on the cryogenic focalplane of imaging systems [4], switching and phase modulationfor massively parallel phased arrays [5], and thermal controldirectly on the skin of surfaces [6]. In these situations, packag-ing may be minimal, temperature ranges may be extreme, andpressure may be as low as the vacuum of space. The testingconditions must therefore match the operational environmentfor MEMS technology to establish itself in this market.
In response to these challenges, various test systems havebeen reported in the literature. There are those specifically de-signed for space applications, which recreate the temperaturesand pressures of the space environment but employ probe orscanning techniques that do not give a complete picture ofthe device dynamics or topology [1], [7]. In contrast, opticalstroboscopic MEMS test systems have been reported [8]–[12],which characterize devices in motion. These yield a completepicture of the dynamic motion and surface structure of thedevice down to the nanometer scale, but those reported in theliterature only operate under ambient conditions. Neither ofthese classes of test systems can make dynamic measurementswhile simulating the pressures that are encountered in space andthe upper atmosphere. This is a critical point because MEMSdynamic response changes markedly when the damping ofatmospheric pressure is removed, particularly near mechanicalresonant frequencies [13]–[17].
Addressing these issues, our solution is based on a fusionof these designs. By integrating an environmental test chamberwith a stroboscopic imaging interferometer, we have created asystem capable of generating a complete picture of the devicedynamics with variable environmental control. This combina-tion of techniques, however, goes further than simply addingnew environmental controls to standard stroboscopic phase-shift interferometry. In fact, the system becomes much morethan the sum of its parts. Our results show that the integrationof the interferometer directly onto the environmental chamber
CONWAY et al.: STROBOSCOPIC IMAGING INTERFEROMETER FOR MEMS PERFORMANCE MEASUREMENT 669
Fig. 1. Optical layout of the MEMS stroboscopic interferometer.
greatly reduces the measurement errors that are incurred fromexternal vibrations, which has limited the utility of manyinterferometric measurement systems. By keeping all of theinterferometer optics rigidly attached to the faceplate of theenvironmental chamber, deep-subwavelength out-of-plane res-olution has been achieved in a very noisy laboratory withoutthe use of a floating optical table. This single advance has thecapability of bringing interferometric MEMS characterizationout of the controlled laboratory environment and onto thefactory floor.
II. OPTICAL DESIGN
Our test system is based on the stroboscopic Michelsoninterferometer. It achieves nanometer-scale out-of-plane res-olution interferometrically and diffraction-limited lateral res-olution (∼1 µm) using microscope objectives. Although itrelies on sampling measurements during cyclical motion ofthe device, only five intensity images are used to reconstructeach “frozen” surface per time step of motion. At standardvideo refresh rates of 15 Hz, this makes for rapid frame ac-quisition, which is robust in the face of environmental noise.Because a video camera is employed as a detector array, nolateral scanning is required. This popular optical design hasbeen reported in the literature [18], and our instrument designevolved out the work of Muller [8]–[10]. In our attempt torecreate Muller’s stroboscopic measurement system, we foundthat those designs proved too susceptible to vibrations to yieldreproducible results in our noisy laboratory environment. Evenwith 1.5-in optical post assemblies, a floating optical table, andheavy laser isolation curtains, noise continued to plague thissystem. Resolution of this problem led to several importantimprovements, which are to be discussed later in the text.Although we have machined hardware and developed softwareto perform the data acquisition and processing operations, thedesign is simple enough to be replicated in other laboratories,unlike white-light and more complicated interferometers [19].
The layout for the test system is illustrated in Fig. 1. Thelight source is a fiber-coupled diode laser operating at 635 nm(Melles Griot 57ICS062/SP/HS). This laser is directly modu-lated such that the beam is pulsed on and off with a program-mable delay in synchrony with the MEMS driving signal. Indoing so, this stroboscopic source is able to “freeze” the device
at any phase of its high-speed motion, even when employingslow cameras and detectors. To keep the image from blurringwith the MEMS motion, the duty cycle (defined here as theoptical pulse duration/period of the MEMS driving signal)was kept below 0.01. This low duty cycle, however, has theeffect of greatly reducing the optical power falling on thecamera (Pulnix TM-1020). Because the out-of-plane resolutiondepends strongly on the number of digitized bits in the detectedsignal [20], it is necessary to cover the 8-bit dynamic range ofthe camera. To correct for this without introducing expensivehigh-power lasers, focusing optics were introduced into theoptical path to concentrate the beam onto the region of intereston the device. It is important to note that microscope objectivesshould not be used for this task. High-numerical-aperture opticsmake calibration very difficult due to their rapidly changingphase front near the focus. This is because the radius of cur-vature of the phase must change from a very small quantitynear the focus, to infinity at the actual focal spot [21]. If thereference mirror and test device are not equidistant from theirobjective lenses, the phase fronts will have different curvatures.After unwrapping, this curvature translates into warped surfacereconstructions even if the sample and reference mirrors areboth perfectly planar. Although the peak output power of ourlaser source is 7 mW, we have found that a low-magnificationlens system can easily correct phase-curvature problems whileconcentrating enough light to saturate the charge-coupled de-vice (CCD) camera.
After the focusing optics, the beam encounters a nonpo-larizing beam splitter. This sends half of the light into theenvironmental chamber and onto the MEMS device under test.The remaining half of the optical beam is sent to a referencemirror on a lead zirconate titanate transducer, forming thesecond arm of a Michelson interferometer. These beams thenrecombine and interfere, allowing one to determine out-of-plane displacement. The nature of the measurement can allowfor measurement sensitivity down to the nanometer scale [19].However, as seen from a different perspective, this sensitivitymakes the measurement prone to error from noise and vibration.Nanoscale displacement or vibration in any part of the opticalpath in either arm is translated into measurement error. Thereader is reminded that the phase-unwrapping process cangreatly amplify these errors by incorrectly adding or subtractingmultiples of λ/2. It is precisely for this reason that externalnoise has plagued optical interferometric measurements andwhy most systems only operate in highly isolated laboratoryenvironments.
To correct for this, we have integrated the interferometeronto the faceplate of the environmental chamber. The beamsplitter is fixed with optical epoxy to the chamber window,and the reference mirror is bolted directly to the commonchamber faceplate. Because the interferometer measures rela-tive displacement between the two arms, the measurement isexceedingly sensitive to noise in this region. To correct forthis, the optical path of each arm was kept shorter than 2 cm.These simple design changes had a profound effect on theperformance of the interferometer. Although the majority of thedata reported in this paper was taken on a floating optical table,it was later found that the performance was not significantly
670 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 16, NO. 3, JUNE 2007
Fig. 2. MEMS cantilever device (a) imaged by a scanning electron micro-scope (SEM) and (b) imaged directly in interferometer system showing a fringepattern. (c) Graphical rendering of the cantilever beam illustrating the profile.
degraded when the table was not floating. In addition to this, thesystem was able to take data with nanometer-scale out-of planeresolution in an exceptionally noisy environment and while thechamber was rigidly attached to an operating roughing pumpand turbo pump. Unlike the holographic techniques or the use ofspecialized interferometers [11], our design achieves this highstability without the use of custom components. The powerof this architecture is that it can be assembled from commonlaboratory equipment.
After the beams recombine at the beam splitter, a longworking distance objective is used to image the device ontoa CCD camera. This system takes an entire image at a time;thus, no lateral scanning is required. The captured image iscovered with fringes, as shown in Fig. 2(b). To obtain theactual phase data from the fringe pattern, we used phase-shiftinterferometry [18]. This entails translating the reference mirrorlongitudinally by a fixed displacement between each frame. Ofthe various recipes for this, we employed Hariharan’s algorithm[22], which uses intensity data at five known positions of thereference mirror to generate phase data. This yields the relativephase modulo 2π. Converting this wrapped phase to absolutephase in two dimensions is still considered an unsolved problemin the field [23]. To unwrap the phase over its full range, weused the method of Volkov and Zhu [24]. The absolute phase(denoted by ψ) is calculated using
ψ = Re
{1
2πiF−1
[F (∂xψ)qx + F (∂yψ)qy
q2x + q2y
]}(1)
where F and F−1 represent the Fourier and inverse Fouriertransforms, respectively, and q represents the wave vector ina given direction. Equation (1) requires the gradient of the
absolute phase, which can be calculated directly from thewrapped phase [25] using
The gradient in the y-direction is determined in a similarmanner by permuting the x and y dimensions in (2). Combiningthe two equations yields an initial value for the absolute phase.From (1), it can be seen that the dc term of the Fourierexpansion must be dropped (qx=0 = qy=0 = 0) because of theresultant null in the denominator. To resolve this ambiguity,the wrapped phase is then subtracted from this unwrappedphase, and the resultant difference is rounded to the nearest 2π.The wrapped phase is added back, and the absolute phase isobtained.
III. RESULTS
To demonstrate the capabilities of this MEMS stroboscopicinterferometer, we have examined the motion of a MEMScantilever beam test structure. The sample device is composedof two electrical bond pads that are connected to two-doped150 × 150 µm overlapping polysilicon layers, with an isolating2-µm air gap, supported by a 134 × 30 µm polysilicon beam,as also shown in Fig. 2. The holes in the paddle, which aredesigned to aid in MEMS oxide release, are also evident. Underelectrical bias, electrostatic deflection downward of the upper2-µm-thick cantilevered polysilicon region of interest occurs.A sinusoidal electric drive signal results in a cyclical devicemotion proportional to drive signal amplitude and in-phase withthe driving waveform. This device was chosen for analysisbecause flexible polysilicon beam structures of this type arevery common in MEMS radio frequency switches, rate sensors,accelerometers, and many other MEMS devices.
For a given frequency, drive voltage, and chamber pressure,the MEMS stroboscopic interferometer can generate a surfacereconstruction of the cantilever at various “frozen” phases ofits motion. This is illustrated in Figs. 3 and 4, which showthe first and second sets of three resonant modes of the deviceat 10 mtorr operating pressure. These resonant modes werestimulated with sinusoidal drive signals at 74 640, 217 150,475 450, 880 100, 1 313 430, and 1 452 230 Hz, respectively.This is the first time that plate modes on this scale have beendirectly imaged [26], as known to the authors. Because thequality factor (Q-factor) varies between modes, the amplitudeof the drive signal was changed to give a clear picture of thedevice motion. The deformation of the cantilever can be clearlyseen in all sets of surface reconstructions. Also evident fromthe surface reconstructions is the ridge across the center of thedevice. This artifact of fabrication is approximately 10 nm highand is very clear from this measurement.
To verify that we have correctly identified each of the firstsix resonant modes of the cantilever test structure, we haveperformed finite-element modeling (FEM) of the complete 3-Ddevice structure. This modeling was performed using FEMLabMultiphysics software from COMSOL, Inc. [27]. This mechan-ical 3-D model is constructed from the original mask files of
CONWAY et al.: STROBOSCOPIC IMAGING INTERFEROMETER FOR MEMS PERFORMANCE MEASUREMENT 671
Fig. 3. Several phases of the MEMS cantilever for the first three resonant modes. All units are in micrometers.
the cantilever device. We have used the COMSOL materialsproperty database library values for polysilicon. When runningthe model, a Young’s modulus of 130 GPa was chosen suchthat the device resonance at the second eigenfrequency mostclosely matched that of the stroboscopic measurement. This isin agreement with empirically derived values of polysilicon,which have been measured between 132 and 174 GPa [28]. Allother material properties were set to their default values. TheCOMSOL eigenfrequency 3-D Solid, Stress–Strain solver wasselected, with boundary conditions set such that all stationarysurfaces were fixed. The first six eigenmodes are shown inFig. 5. These modeled results are in good agreement with bothour measured frequencies and mode shapes. Table I shows thevalues of measured and modeled results, all with errors lessthan ±5%.
The strength of the resonant mechanical modes is also a crit-ical parameter for these devices. To quantify this, we measuredthe mechanical response to a sinusoidal drive voltage aroundthe first resonance frequency. Cantilever devices of this typehave a nonlinear quasi-static response to the driving signal and“pull-in” toward the lower electrode at a given threshold voltage[29]. To minimize this effect, the amplitude of the drive voltagewas changed at each pressure to keep the peak displacementbelow 2 µm at resonance. The motion of a small region near thefree edge of the cantilever is illustrated in Fig. 6(a). Due to de-
vice destruction during temperature cycling, a different MEMSdevice was used for these tests. This device is identical to thatof Fig. 2, except that the single 134 × 30 µm polysilicon beamis replaced by a pair of 64 × 30 µm beams, as shown in theinset of Fig. 6(b). The mechanical response was then recordedabout the first resonance peak, and the Q-factor was computedfrom the central frequency divided by the spectral full-widthat half-maximum of the mechanical displacement amplitude.The Q-factor for the fundamental mode at several pressures isplotted in Fig. 6(b). This plot not only illustrates the transitionto intrinsic damping near 10 mtorr but also underscores the crit-ical importance of the environmental chamber. At atmosphericpressures, this mode is heavily overdamped and would be verydifficult, if not impossible, to study quantitatively. Thus, we seethat without the combination of vacuum pressures, nanoscalesensitivity, and high-speed measurement, the complete motionof the 3-D modes of Figs. 3 and 4 could not be studied.
The authors know of no reported measurement system em-ploying a single measurement that is capable of this metrology.There are reports of vibrometer test systems with vacuumchambers [30], but these systems cannot image surface topol-ogy directly [9] and place a great deal of strain on the scanningmechanism. It is nontrivial to translate the focusing optics or theMEMS device inside a vacuum chamber, although a confocalsolution has been implemented. Digital holographic solutions
672 JOURNAL OF MICROELECTROMECHANICAL SYSTEMS, VOL. 16, NO. 3, JUNE 2007
Fig. 4. Several phases of the MEMS cantilever for the second three resonant modes. All units are in micrometers.
such as the Lyncée Tec DHM R1000 can provide a tool thatis able to measure mechanical transients, which is in contrastto the repeated motion that is required here. Unfortunately,this system is limited to drive frequencies below 100 kHz and,therefore, cannot reproduce the modes in Figs. 3 and 4. White-light interferometry systems such as the Wyko DMEMS, whichcan strobe up to 1 MHz [31], suffer from similar high-frequencylimitations. This is not to preclude the possibility of alteringthe test equipment to achieve higher frequency operation [32],employing a system that uses a combination of white-lightinterferometry and vibrometry such as the Polytec MSA-400or a system of white-light and phase-shift interferometries suchas Micro Photonics Zoomsurf 3D. We stress that although weknow of no reported system that has all of the capabilitiesthat are required to measure these plate modes, one could bebuilt from competing technologies. The novelty and power ofthis system are in its simplicity, ease of operation, accessibilityto the researcher, and noise immunity implicit in the design.Unlike packaged measurement systems, changing out the partsto add new capabilities is simple. For instance, the maximumdevice frequency that can be measured is determined by thelaser modulation bandwidth. Telecom lasers with modulated
bandwidths greater than 1 GHz are now widely available andcan be added to this system.
To quantify the vertical (interferometric) resolution in thepresence of noise in real system operation, we undertook astatistical analysis. For this paper, we acquired 200 phase-unwrapped surfaces of the static cantilever device over thecourse of 10 min. This timescale is longer than the typicalmeasurement but was needed to achieve a large statisticalsample. It was seen that the device, as a whole, drifted onthe order of 10 nm during the experiment. To compensatefor this, the motion of the substrate was calculated and thensubtracted from that of the cantilever. After removing the drift,the standard deviation of out-of-plane position was calculated at4224 individual points on the cantilever from these 200 surfacereconstructions. The median standard deviation was calculatedto be 2 nm, which is a surprisingly small result in a very noisylaboratory. Most of this noise can be attributed to the cameraitself, as we used an uncooled CCD that demonstrated a root-mean-square (rms) dark noise of approximately 11.2 out of thefull-scale 255 (8 bits) when there was no illumination. MonteCarlo simulations using a Gaussian fit to this noise showedthat the camera added approximately 1.5 nm of out-of-plane
CONWAY et al.: STROBOSCOPIC IMAGING INTERFEROMETER FOR MEMS PERFORMANCE MEASUREMENT 673
Fig. 5. COMSOL 3-D FEM results of the MEMS cantilevered test structure.Eigenfrequencies and mode shapes of the first six resonant modes are shown.
TABLE IEIGENFREQUENCIES FOR MEASURED AND MODELED MODES
USING COMSOL MULTIPHYSICS 3-D FEM,SOLID, STRESS–STRAIN SOLVER
Fig. 6. (a) Displacement of a single point on the cantilever at the fundamentalresonance (70 040 Hz). (b) Q-factor of the fundamental mode over pressure.Inset shows an SEM image of the cantilever under test.
uncertainty to our measurement. This large noise source canbe rectified by either upgrading to a scientific grade low-noise camera or by averaging several data sets. The reader isalso reminded, however, that these pixels represent an area ofapproximately 1 µm2. For any real material, there will be aheight variation across the pixel of much larger than 2 nm. Forinstance, 2 nm across the pixel represents a perfectly planarsurface that is tilted by 0.1146◦ from the normal or a perfectlyoriented surface with 2 nm of rms roughness.
IV. CONCLUSION
We have demonstrated the design and functionality of a novelstroboscopic imaging interferometer for MEMS metrology. Thenanoscale precision and high-frequency capabilities make thisan ideal MEMS characterization tool for devices that can beelectrically actuated. By making the environmental chamber anintegral part of the measurement system, we have ruggedizedour optical interferometric instrument. The interferometer canfunction in noisy environments, greatly extending the utility ofthis high-precision technique.
The combined attributes of our system enable the directobservation and measurement of large-area (∼500 × 500 µm)complex 3-D motions and high-order 3-D plate modes ofMEMS devices dynamically operating frequencies in excessof 1.4 MHz. Many MEMS applications such as spatial lightmodulators, inertial rate sensors, and accelerometers demon-strate performance that lack in respect to their macroscopiccounterparts. Measurement capability such as ours can providecritical mechanical MEMS metrology well in excess of first-order, second-order, or third-order modal analysis. These mea-surement data directly provide the MEMS designer observablemeasurements of deformations due to high-order modes andallow proper error attribution to their sources.
Our novel tool was used to image many of the resonantmodes of a cantilevered beam structure. The mechanical 3-Dbending modes that were observed in this MEMS device,while well known in structural mechanics of large objects, arevery difficult to directly measure for micrometer-scale MEMSdevices. Direct observation, measurement, and surface recon-struction of MEMS devices while under full dynamic operationprovides a unique metrology capability for understanding andobserving the complex behavior of micromechanical structures.
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Josh A. Conway (M’04) received the B.S. degree in physics and the M.S.degree in electrical engineering from the University of Illinois at Urbana-Champaign in 1999 and 2001, respectively, and the Ph.D. degree in electricalengineering with an emphasis in photonics from the University of California,Los Angeles, in 2006.
He is currently a member of Technical Staff at The Aerospace Corporation,El Segundo, CA. Before this, he designed photonic subsystems for intersatellitelaser communications for the Boeing Company. This work has led to numerouspatents in the field of optical interferometry.
Dr. Conway is a member of The International Society for Optical Engineers.
Jon V. Osborn (S’85–M’87) received the B.S. andM.S. degrees in electrical engineering from the Uni-versity of Southern California, Los Angeles, in 1985and 1994, respectively.
From 1985 to 1997, he was with the Space Sci-ences Laboratory, The Aerospace Corporation, LosAngeles, as a member of Technical Staff, devel-oping space instrumentation for near-earth spacephysics research, including single-event effects test-ing and evaluation of spaceborne microelectronicdevices. Major programs and projects included
CRRES/MEA, POLAR/CEPPAD, and CLUSTER/IES. In 1997, he joined theElectronics Photonics Laboratory, The Aerospace Corporation, as a ResearchScientist, actively investigating advanced microelectronic technologies for usein space systems, including radiation-tolerant deep-submicrometer CMOS,CMOS/SOS, and MEMS device technologies. Since 2004, he has been theManager of the Microelectronics Reliability and Radiation Effects Section,Microelectronics Technology Department.
Mr. Osborn was an Aerospace Corporation Fellow during 1993–1994. He hasbeen a Registered Professional Engineer in the State of California since 1994.
Jesse David Fowler received the A.A. degree inauto/diesel mechanics from the Universal TechnicalInstitute, Phoenix, AZ, in 1991, the B.S. degreein mechanical engineering from New Mexico StateUniversity, Las Cruces, in 1998, and the M.S. degreein mechanical engineering from the University ofCalifornia, Los Angeles (UCLA), in 2003. He iscurrently working toward the Ph.D. degree in me-chanical engineering at UCLA.
He has worked at Los Alamos National Labora-tory, Sandia National Laboratory, and The Aerospace
Corporation in a research support capacity. He held the Materials CreationTraining Program Fellowship from 2002 to 2003. His current research interestsinclude discrete droplet microfluidics, chemical microsensors, and MEMSmetrology.
Mr. Fowler is a member of Tau Beta Pi and Pi Tau Sigma. He is a certifiedEngineer-in-Training in the State of New Mexico.
