Vibration Nullification of MEMS Devices using Input Shaping

Vibration Nullification of MEMS Devices using Input Shaping Scott Jordan and Eric Lawrence, Polytec PI ABSTRACT The active silicon microstructures known as Micro-Electromechanical Systems (MEMS) are improving many existing technologies through simplification and cost reduction. Many industries have already capitalized on MEMS technology such as those in fields as diverse as telecommunications, computing, projection displays, automotive safety, defense and biotechnology. As they grow in sophistication and complexity, the familiar pressures to further reduce costs and increase performance grow for those who design and manufacture MEMS devices and the engineers who specify them for their end applications. One example is MEMS optical switches that have evolved from simple, bistable on/off elements to microscopic, freelypositionable beam steering optics. These can be actuated to discrete angular positions or to continuously-variable angular states through applied command signals. Unfortunately, elaborate closed-loop actuation schemes are often necessitated in order to stabilize the actuation. Furthermore, preventing one actuated micro-element from vibrationally cross-coupling with its neighbors is another reason costly closed-loop approaches are thought to be necessary. The Laser Doppler Vibrometer (LDV) is a valuable tool for MEMS characterization that provides non-contact, real-time measurements of velocity and/or displacement response. The LDV is a proven technology for production metrology to determine dynamical behaviors of MEMS elements, which can be a sensitive indicator of manufacturing variables such as film thickness, etch depth, feature tolerances, handling damage and particulate contamination. They are also important for characterizing the actuation dynamics of MEMS elements for implementation of a patented controls technique called Input Shaping, which we show here can virtually eliminate the vibratory resonant response of MEMS elements even when subjected to the most severe actuation profiles. Figure 1. Vibrometer displacement measurement of MEMS device when exposed to narrow pulse of 150 Volt amplitude. Figure 2. Open loop actuation of device using square wave excitation with the embeddable Input Shaping algorithm applied to the MEMS control, resulting in virtually vibration-free actuation with instant settling. ScottJ@polytecpi.com, http:/www.polytecpi.com; 6537 Fall River Dr., San Jose, CA 95120 USA EricL@polytecpi.com, http:/www.polytecpi.com; 1342 Bell Ave, Suite 3A, Tustin, CA 92780 USA

In this paper, we will demonstrate the use of the LDV to determine how the application of this compact, efficient algorithm can improve the performance of both open- and closed-loop MEMS devices, eliminating the need for costly closed-loop approaches. This can greatly reduce the complexity, cost and yield of MEMS design and manufacture. Keywords: MEMS, Input Shaping, vibration cancellation, active damping, speed optimization 1. BACKGROUND Silicon micro-electromechanical systems (MEMS) have been an important semiconductor category for approximately eight years. MEMS is now an established commercial technology and has been commercialized in both passive and active implementations. MEMS technology is the basis for most automotive airbag sensors and many video and PC projection units. The latter were the first optical MEMS application, coming on the market approximately eight years ago. In particular, the use of active silicon micromirror arrays for optical switching is an area of great economic and technical promise for the telecommunications industry, which must flexibly provision and route optical data communications over long fiber trunks and then around and through dense regional and metropolitan areas. As data rates increase, it becomes less and less practical to perform this switching electronically. Optical MEMS switches and cross-connects allow optical data channels to be switched directly without an optical-to-electronic-to-optical conversion. MEMS manufacturing and control present unique challenges. The perforated wafers are difficult to handle, and the micromechanisms are delicate and very sensitive to particulate contamination. Yield issues have meant that only a handful of semiconductor companies manufacture large quantities of MEMS silicon notably Texas Instruments and JDS Uniphase s Chronos subsidiary. Optical MEMS are available both in bistable and multiply- or continuously-positionable formats. Bistable MEMS designs usually employ at least one hard-stop to define a repeatable position for the moving element. This presents its own dynamical issues. MEMS technology is rapidly expanding beyond its core sensor and micro-optical markets to include active mechanisms which perform a wider variety of motions, including long-travel motions and multiple-degree of freedom motions. Miniature tripod and other parallel kinematic multi-axis designs have been demonstrated, for example by researchers at Sandia National Laboratory. While commercial applications of these designs are still some years off, the physical challenges posed in their manufacture and control are evident today. 2. VIBRATION IN MEMS MEMS devices exhibit classical Hookes resonant behavior when disturbed and when actuated. Figure 1 shows representative behavior, as imaged by a laser Doppler vibrometer, when a MEMS micromirror is actuated to a (nonhardstopped) set point with a step command. The motion of the unit towards its eventual set point is characterized by resonant behavior, manifested as overshoot and ringing at a characteristic frequency. As is typical, the damping is light (, as would be expected from the monolithic silicon from which MEMS devices are manufactured, and the overshoot is typically on the order of the commanded step or even greater. Interestingly, this vibrational behavior is also a reasonably sensitive measure of the MEMS device s health and quality of manufacture: for example, an over-etched MEMS device may exhibit an anomalously low resonant frequency. MEMS dynamics are readily imaged using non-contact laser Doppler vibrometry. A variety of instruments based on this principle are available, including Polytec s single-point and differential units and scanning systems capable of imaging a large area for sophisticated modal analysis. These have found broad application in the MEMS industry for both developmental diagnostics and production metrology.

3. ADDRESSING VIBRATION Conventionally, the usual approach to eliminating overshoot and ringing in any active device would be to integrate position feedback elements and implement a closed-loop control system. However, this is effective only against in-loop (observable) vibrations. It also extracts penalties in cost, complexity, reliability, yield and bandwidth. And in the case of an array of densely-packed MEMS elements, it does nothing to avert the possibility that rapid actuation of one element might disturb its neighboring elements through recoil transmitted through their common substrate. Any disturbance thus transmitted could be addressed only within the responsiveness of the adjacent units servos. Since servos are error-driven, this guarantees that disturbances propagating from MEMS to MEMS would result in unwanted modulation of the devices positions resulting, for example, in modulation of the optical signals they are reflecting. Fortunately, recent technical advances have produced a novel control technology suitable for any type of open- or closed-loop actuations which improves throughput by typically three orders of magnitude by eliminating settling dwells and allowing the most aggressive motion profiles. This same technology has proven its value in improving optical MEMS actuation speed an increasingly critical consideration for differentiating between various MEMS providers. A review of vibrational physics is worthwhile here. After a motion, the amplitude of the resonant ringing of each element in a structure scales as e -t/τ, where τ is the time constant for each element s resonant characteristics i. For structures with damping characteristics typical of precision mechanisms (see Table 1), τ ~ (ω n ζ) 1 where ω n is the resonant angular frequency and ζ is the damping ratio for the resonance. ζ is commonly defined as the ratio of the damping for the resonance versus critical damping (ζ= C/C c ) and varies from 0 (no damping) to 1 (critical damping) (see Figure 3). Fres (Hz) ωn (rad/sec) 75 471.24 0.0005 4.244 0.001 2.122 0.005 0.424 0.01 0.212 0.05 0.042 0.1 0.021 150 942.48 0.0005 2.122 0.001 1.061 0.005 0.212 0.01 0.106 0.05 0.021 0.1 0.011 Table 1. Time constant W for various damping coefficients, ], and resonant frequencies, Z n ζ τ

Mechanical Damping 2.5 Position 2 1.5 1 0.5 Zeta = 0.001 Zeta = 0.01 Zeta = 0.1 Zeta = 0.3 0 tim e Figure 3. Generic mechanical damping behavior after a rapid motion, shown for various damping ratios, ]. The amplitude of the ringing diminishes with time as e -t/, where W ~ (Z n ]) -1. Clearly, physics dictates worsening process throughputs as actuation tolerances tighten. Today, damping is not the only tool for eliminating out-of-loop resonances. A patented ii, real-time feedforward technology called Input Shaping was developed based on research at the Massachusetts Institute of Technology and commercialized by Convolve, Inc., (New York, NY; http://www.convolve.com). Commercially, it is an integrated option for Polytec PI s latest digital piezo positioning controllers (Figure 4), in which it is marketed as the Mach Throughput Coprocessor. Here it takes the form of a compact algorithm which scales and sequences any positioning command in real-time to result in optimally fast positioning with zero residual vibration in the motion device, load and adjacent componentry. For motor control, the technology is available as an option from Galil, Delta Tau and Motion Engineering (MEI). Figure 4. Piezo controller (shown with PCI fiber interface) includes patented vibration-cancellation technology This robust and easily-implemented technology acts transparently in real time to prevent the motion-driven excitation of resonances throughout the system, including all fixturing and ancillary componentry. The Throughput Coprocessor is also available implemented in a stand-alone unit intended for upgrading existing open- and closed-loop nanopositioning systems with analog inputs. In this implementation, it is inserted in series between the commanding computer or waveform generator and the analog input of the piezo nanopositioning system. This is a useful format for investigating the application of Input Shaping on MEMS actuation.

Figure 5. In Polytec PI s NanoAutomation implementation, Input Shaping is applied in series between the commanding PC or position-waveform generator and the input to the piezo nanopositioning controller. For investigating MEMS dynamics, a stand-alone implementation has proven effective used in the same way. 4. A MACRO WORLD EXAMPLE OF INPUT SHAPING APPLICATION Fabrication of Fiber Bragg Gratings (FBGs) is a good example of an application that benefits from this technology. FBGs are important elements of optical networks that select an individual wavelength from the multitude of waves running down a multiplexed fiber. The FBG is a diffraction grating fashioned deep within a fiber or waveguide through interferometric optical exposure. To improve the spectral characteristics of the finite-length grating, grating transitions are apodized via nanometer-precision scanning motions of optics in the exposure apparatus iii using a high-quality piezo nanopositioning stage. The process is exquisitely demanding, but the results are tremendous: a simple, compact, rugged, entirely passive device capable of precisely isolating a single wavelength. As more and more channels are crammed down a fiber, the selectivity of FBGs must keep pace. Inaccuracies from vibrations of structures throughout the tool begin to count. Not only must the positioners in the tooling perform to nanometer-scale levels, but all unwanted relative motions in all components of the tooling must be suppressed. Airisolation tables address ambient disturbances, but resonances driven by the scanning can still take hundreds of milliseconds to damp out an unacceptable throughput penalty. Input Shaping addresses this directly by literally eliminating the resonances before they start (compare Figure 6 and Figure 7). Figure 6. Quasi-sinusoidal phase-mask dither waveform is corrupted by fixturing resonances. Figure 7. Same input waveform as in Figure 6, with structural resonances nullified. The benefit is even more impressive for harsher motions such as sawtoothwaves. Elimination of structural resonances results in higher-fidelity Bragg gratings: narrower channelwidths, higher efficiency.

Figure 8. Coarse/fine air-bearing/piezo stage. The closed-loop piezo stage is used for high-throughput nm-scale mask position modulation in FBG manufacture; vibration-nullification technology shown in Figure 7 allows higher production throughput while optimizing grating fidelity for narrower channel-width and improved efficiency. (Photo courtesy Dover Instruments.) 5. VIBRATION CANCELLATION IN MEMS Input Shaping obviously poses a tantalizing possibility for avoiding the cost and complexity of closing the loop around a MEMS element to address its overshoot and resonant ringing (and that of its neighbors) as seen in Figure 1. The compactness of the Input Shaping algorithm and its robustness to unit-to-unit variations makes it highly practical for embedding into MEMS controllers for four purposes: Optimization of MEMS elemental positioning times Elimination of settling intervals in open- and closed-loop actuation Prevention of parasitic excitation of adjacent elements in MEMS arrays Bandwidth increase (gain-boosting) in closed-loop actuation, eliminating overshoot-and-ringing issues in underdamped actuation. The benefits of applying Input Shaping to MEMS controls are readily quantifiable by using a Polytec laser Doppler vibrometer. Although Input Shaping works with any type of motion point-to-point, continuous waveform, random we chose square-wave actuation for our tests since these present the most severe dynamical forces to the devices under test. Figure 9 through Figure 12 show LDV displacement and spectral measurements before and after implementing Input Shaping in series with the position-command signal for an open-loop MEMS switching/scanning element. The implementation process is a simple one, requiring a straightforward measurement of the resonant characteristics of the MEMS device using the vibrometer. This defines the real-time operating parameters for configuring the Input Shaping. The resonances of each micro-optical element are instantly eliminated, regardless of actuation profile. The resonant reaction of neighboring MEMS elements is eliminated as well.

Figure 9. Displacement response of MEMS micromirror to open-loop square-wave input, as measured with a Polytec laser Doppler vibrometer. Ringing response of the mirror is observed. Figure 10. Same device as in Figure 9, with the embeddable Input Shaping algorithm applied to the MEMS controls. Figure 11. Spectral plot of vibrometry data for device in Figure 9, without Input Shaping. Note the substantial resonance peak. Figure 12. Spectral plot of Vibrometry data in Figure 10, showing the nullification of resonances by Input Shaping in the MEMS controls. The resonance peak seen in Figure 11 is eliminated. Even in closed-loop actuations, Input Shaping poses advantages. Proportional and integral gains can often be significantly boosted as well, with Input Shaping addressing the overshoot and oscillation about the terminal position that are otherwise characteristic of overboosted/underdamped applications. This can further improve the switching throughput of many devices compared to critical damping. However, the elimination of resonant behavior as demonstrated in Figure 10 may eliminate the need for closed-loop actuation in the first place a significant cost-andcomplexity advantage. In any case, a closed-loop implementation may still be necessary for calibrated actuation of multiply- or continuously-positionable MEMS elements, but it would no longer be required for dynamical reasons. The spectral plots shown in Figure 11 and Figure 12 illustrate a fundamental difference between Input Shaping and active damping, alignment stabilization or other after-the-fact compensation of unwanted resonant behavior. In those situations, compensation occurs after the device is observed to have begun ringing, with the aim of counteracting the unwanted motion or extracting energy from the resonance and converting it into heat or storing it elsewhere in the system. These all take time, since basically the horse is out of the barn and the damage must be undone. Furthermore, these classical compensation approaches act only on observable (in-the-loop) errors. Input Shaping, by comparison, prevents energy from entering the resonant mode in the first place and is effective on unobservable errors, such as those imposed upon adjacent structures. Optimized implementations of Input Shaping further address the uniquely nonlinear actuation physics of specific MEMS designs, including hard-stopped units. To further illuminate the impact of Input Shaping on MEMS dynamics, the Polytec s Micro Scanning Vibrometer (MSV) was used for mapping a device s deflection shape response. This system is shown below in Figure 13. By scanning the vibrometer s laser beam in x and y direction, the LDV technique can be extended to full-area measurement and display. This technique scans an area on a point-by-point basis to measure the velocity field of the structure. From these data the operating deflection shape at any given frequency or time sample can be determined. The data compiled

from this measurement is shown in Figure 14 as 3D time domain animation to quantify the devices actuation. The authors of this paper can supply the actual animated AVI file showing of this response upon request via email. Figure 13. The Micro-Scanning Vibrometer. Figure 14. The Polytec Micro Scanning Vibrometer shown in Figure 13 was used to compile time domain animations of actuated MEMS dynamic response. (Animations available by email from authors.) Top: squarewave actuation of the MEMS micromirror with Input Shaping. Both a frame of the animation and the time plot of the mirror s position are shown. Bottom: square-wave actuation position-vs.-time plot without Input Shaping. The desired square-wave motion profile is almost indiscernible against the resonant response of the element.

6. CONCLUSION MEMS are a new type of device that present some challenges familiar from classical mechanics. Just as settling behavior has come to dominate the process-throughput times in applications ranging from semiconductor lithography to disk-drive track-profiling head tests, settling time is now the primary application pacer for many MEMS attenuation, switching and cross-connect applications. And the same easily-implemented, patented controls technology which has proven so effective in boosting throughput and enhancing precision in production nanopositioning applications can now be applied to improving the actuation speed and competitiveness of MEMS devices and systems. The compact Input Shaping algorithm is a practical and highly embeddable addition to MEMS controller circuits for both open- and closed-loop actuation. In fact, the dramatic benefits of Input Shaping on open-loop actuation may eliminate the need for closed-loop approaches in the first place, resulting in significant cost savings and a potentially simpler, more reliable MEMS device. 7. ACKNOWLEDGMENTS The authors would like to thank Mark Tanquary of Convolve, Inc., and David Oliver of Polytec PI for their assistance in this research. The assistance of Applied MEMS in providing devices to test is appreciated. i A fine references for the physics of resonant vibrations is Modern Control Engineering by Katsuhiko Ogata (Prentice- Hall, 1970, ref. Pp271-272). A remarkable on-line reference can be found at http://bits.me.berkeley.edu/~beam/spr95/theory/detsys/detsys_1.html. ii This technology is protected by one or more of the following US and foreign Patents licensed from Convolve, Inc.: US 4,916,635; US 5,638,267; 0433375 Europe; 067152 Korea, and other Patents pending. Mach, Throughput Coprocessor and NanoAutomation are trademarks of Polytec PI, Inc. Input Shaping is a trademark of Convolve, Inc. iii Ibid.