Software Design Considerations for Testing Dynamics of MEMS/Microsystems Phillip L. Reu‡*, David S. Epp‡, O. Burak Ozdoganlar† ‡
Sandia National Laboratories MS 0847, P.O. Box 5800 Albuquerque, NM 87185
†
Department of Mechanical Engineering Carnegie Mellon University Pittsburgh, PA 15213
Abstract Micro-electromechanical systems (MEMS) are used in many applications such as sensors, actuators, optical devices, and fluidic channels. Their advantage arises from seamless integration of mechanical functionality at micrometer scale with electrical circuitry. Dynamic behavior of MEMS devices, especially those with moving or overhanging components, must be well understood to ensure their proper functionality and reliability. This paper presents the design of dynamic-testing software for experimental investigation of MEMS dynamics including linear and nonlinear multi-physics phenomena. The software integrates data acquisition, control, adaptive parameter selection, data processing, and data saving functions within the same framework. It is also designed to be flexible enough to allow possible future applications to be integrated easily. Softwaredesign considerations, including resolution of the Fourier transform, spectral leakage, and optimization of excitation and response signals, are given in detail. The effectiveness of the software is shown by dynamic testing of various MEMS beams under varying ambient pressure. Keywords: MEMS, modal testing, nonlinear vibration, experimental MEMS modal testing
Introduction Micro-electromechanical devices have been increasingly important as many fields focus on the miniaturization of devices and systems. Current applications include sensors (motion, pressure, chemical, optical), actuators, fluidic channels, and optical devices. The geometry of MEMS devices has become increasingly complex to meet the demands for increased mechanical functionality. As MEMS devices move from laboratory to market, strict reliability requirements are imposed. For these reasons, understanding the behavior of MEMS devices has become critical to their proper functionality and reliability. Vital to this understanding are dynamic testing methods and equipment for experimental investigations and model validation efforts of MEMS multi-physics phenomena. Dynamic testing for microsystems poses unique challenges [1]. Due to their small size, MEMS components possess natural frequencies considerably higher than that of macro-scale structures. Most standard modal testing equipment cannot be used at such high frequencies. Also, large surface-to-volume ratios of MEMS structures render the surface forces significant. Generally, surface forces are nonlinearly dependent on the motion of structures. Finally, the small size of MEMS devices necessitates non-contact excitation and measurement methods. Thus, dynamic testing of MEMS/microsystems imposes new equipment requirements and methodology. A base-excitation test facility for dynamic testing of microsystems was described in [2]. That work primarily focused on the design and evaluation of testing equipment. It was highlighted [1-2] that one of the biggest obstacles preventing effective nonlinear testing of MEMS dynamics and multi-physics phenomena is the lack of a software framework that would facilitate accurate and automated testing. Due to the aforementioned unique challenges, the testing software must be designed specifically for dynamic testing of microsystems. This paper presents design and implementation of a dynamic testing software framework for dynamic testing of MEMS/microsystems. The software is similar to commercial modal test software packages currently available on the market, but has important enhancements particular to MEMS testing. It is capable of controlling excitation and response characteristics, acquiring input and output data, and post-processing the collected data. A large number of tests can be conducted using this software without need for human intervention. Both nonlinear and linear phenomena can be tested using the software.
*
Corresponding Author,
[email protected]
The test-facility hardware will be briefly covered in the next section. Since it is the primary means for testing nonlinearities, stepped-sine testing method will then be discussed. Special attention will be given to the software and Data Acquisition (DAQ) details required to yield accurate results for nonlinear systems. Spectral leakage, Fast Fourier Transform (FFT) resolution, Frequency Response Function (FRF), DAQ synchronization and FFT averaging techniques will be discussed.
Experimental Setup and Equipment The software developed in this work will be integrated into the experimental facility described in [2]. The experimental facility includes a laser Doppler vibrometer (LDV) coupled with an optical microscope, a vacuum chamber, a miniature shaker with piezoelectric actuation, a vacuum pump with pressure controls, a power amplifier for piezoelectric actuation, and a highfrequency data acquisition system. The effectiveness of the software will be shown through a set of experiments on microbeams at varying ambient pressures. These experiments will utilize cantilever beams 18-µm wide and with lengths from 100 to 1000 µm. The beams were made of polycrystalline silicon, with a nominal gap of 2 or 6.3 µm between the beam and the substrate (see Fig. 1a). The microbeams were mounted onto a miniature shaker. The miniature shaker (schematic shown in Fig. 1b) included a piezoelectric actuator, a seismic mass, and a suspension mechanism (foam) that was placed in a vacuum chamber (shown in Fig. 2a) that would allow the pressure to be varied from atmospheric to 0.4 mTorr. This range of pressures allowed “gas damping” to be studied from the continuum regime through transitional and into the non-continuum regimes. The gas damping forces between the beam and the substrate are nonlinear with the displacement of the beam and are a good example of the type of nonlinear dynamics encountered in MEMS modal testing. The vibration response was measured using a Polytec Laser Doppler Vibrometer (LDV) Model OFV-3001 controller and fiber interferometer. The fiber was routed through an Olympus microscope (see Fig. 2b) to focus the laser onto the beam with a spot size of approximately 2 µm.
(a) Figure 1:
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(a) SEM of cantilever beams used in gas damping study. (b) Schematic of base excitation system.
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Figure 2: (a) Test Facility vacuum chamber with electrode feedthrough and MEMS sample. (b) Fiber interferometer and microscope used for microsystem testing.
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The LDV was controlled by the software via RS-232 serial communications to control instrument sensitivity and to monitor signal strength. A National Instruments PXI chassis was used to house the DAQ hardware and was connected to the computer with an MXI-3 PCI interface card for high-speed communication with the equipment. The driving signal was supplied with a PXI-5411 arbitrary waveform generator (40 MSamples/sec) with a 12-bit resolution. The LDV velocity signal and the driving signal were simultaneously measured using a PXI-6534 DAQ card with a 4 MSample/sec acquisition rate and 12-bit resolution. Figure 3 is a schematic of the software-controlled equipment.
Amplifier In PC Control Computer & LabVIEW Based Software
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Figure 3: Test hardware schematic.
Testing Nonlinear Vibrations of MEMS devices In modal testing, the choice of excitation signal critically influences the response characteristics [3-5]. Random, pseudorandom, chirp, transient, and periodic/harmonic excitation signals are typically employed. Although random, pseudo-random, 1 and chirp signals are very effective and quick in determining the response of an ideally linear structure within a wide range of frequencies, using these signals on nonlinear structures may result in a distorted understanding. Testing of nonlinear dynamics require strict controls of amplitude and frequency of the excitation/response characteristics. Stepped-sine testing offers distinct advantages for testing nonlinear dynamics. In addition to enabling accurate controls of amplitude and frequency of excitation signals, a significant improvement in signal-to-noise ratio is realized by confining the entire driving energy to a single frequency. Stepped-sine testing is conducted by exciting the sample with a single frequency sinusoidal signal. The dynamic response of the sample is then measured. The phase and amplitude at the driving frequency is the traditional “step data”. However, for more detailed nonlinear studies, the entire frequency and amplitude response (FFT data) at each excitation step may also be analyzed. By stepping through all of the frequencies of interest it is possible to characterize the dynamic response of a nonlinear system. The excitation amplitude may be varied at each frequency to keep the response amplitude constant at every frequency, as required by some nonlinear-dynamics investigations. Because stepped-sine testing removes the inherent limitations in FFT sample length, as compared to broadband excitation signals, an increased frequency resolution can be achieved. This increased frequency resolution is vitally important for describing response characteristics of structures with small damping ratios, such as microsystem components under vacuum. The biggest disadvantage of the stepped-sine testing method is the requirement of longer testing times. It is possible to use an adaptive frequency stepping (by detecting the “slope” of the response in the frequency domain) to mitigate this drawback. In addition, the testing software can be automated to function without human intervention, thus reducing the burden of increased testing times. Stepped-sine testing also imposes additional requirements to testing hardware and software. These include the need to control sampling rates and frequency resolution to minimize measurement errors due to spectral leakage and inadequate FFT frequency resolution. An extremely large amount of data may be created during testing and methods to deal with this must be considered. The dynamic test software does on-line “real-time” data analysis to minimize the storage requirements and to simplify post-processing and analysis. Sinusoidal excitation at frequencies at and around resonance causes a potentially large variation in excitation response and requires that the software-controlled DAQ system cope with a wide range of inputs without diminishing the accuracy of the measurement.
Software Overview The software was designed to give the user explicit control of important data collection variables and allow the option to perform either linear or nonlinear dynamic testing. Software functionality is covered in this section, with more detail given as to the importance of these features in the following section on software methodology. A screen-shot of the MEMS dynamic test software “front panel” is shown in Fig. 4.
1
Structures that respond in a linear fashion within the frequency range of interest are considered ideally linear in this text.
The minimum frequency resolution required to obtain accurate stepped-sine results necessitates that there be FFT data at the center of each frequency step. The Nyquist sampling theorem dictates that the highest frequency accurately measured is at less than half of the baseband span (the sampling rate of the DAQ card). The software automatically calculates the optimum FFT resolution based on the frequency settings and baseband span. By increasing the frequency lines beyond the minimum resolution, the span multiplier allows “super” FFT resolution to be obtained. This super resolution allows data to be captured accurately at frequencies other than the excitation frequency, as typically encountered in nonlinear systems. The relationship between these parameters and their effect on resolution are discussed in detail in the next section.
Figure 4: MEMS dynamic test software screen shot. The output amplitude of the function generator card (and the driving signal used with the miniature shaker) can be set either from the front panel for constant amplitude throughout the test, or read in from a data file. The data file option is important when a different excitation level is desired at each frequency step, and can be used to maintain a constant response level by changing the driving amplitude to correct for the large responses near resonances. This is accomplished by doing a pre-scan. The driving amplitudes required to maintain a constant response may then be calculated. Automation of this process may be implemented on future versions of this software. Dynamic MEMS testing requires flexibility in the method of data collection. While this software focuses on stepped-sine testing, its functionality is not limited to those tests only. The function generator card and on-line data analysis allow the user to conduct the typical linear modal tests within the same software. Using software selectable signals, such as white noise, the FRF (or other spectrum analyzer type calculations) of a test system may be readily established, displayed and saved for postprocessing. In addition to the standard function generator signals, arbitrary waveforms of any type can be designed and used for sample excitation. Data acquisition parameters are controlled via the front panel to allow the greatest test flexibility possible. Typical acquisition settings such as AC/DC coupling and triggering parameters such as slope and level are all software selectable. DAQ input limits that control the on-board amplification may also be set on a per channel basis or left for auto-scaling by the software.
For most tests, software controlled auto-scaling of the acquisition card and LDV is recommended to optimize signal quality. The large variation in the response of MEMS devices (especially when in vacuum) often causes the vibration amplitude to change by factors of 100 or more. The software automatically measures the response and scales the LDV to the best measurement range, and then sets the DAQ card to its optimum setting to minimize quantization noise. This combination ensures the highest signal-to-noise ratio without going out-of-range and invalidating the measurement. The dynamic test software allows for automation of a series of tests. Complete control of all the inputs may be recorded in an automation file. The software can then read the settings from the automation file and conduct a large number of individual tests, recording the data for later analysis, without human intervention. This functionality is important to remedy long testing times required during stepped-sine testing, particularly near resonant frequencies at low pressures. Three file types may be used to record the data during testing. These include the signal time-history, frequency response and “step data”. All three file-types created by the software are formatted to allow easy importing of the data into MatLab® or MSExcel® for post-processing and analysis. Time-history data may be useful for some nonlinear post-processing, although it creates very large data files. The most common form to save the data is in the frequency domain. The frequency domain information can be saved at each frequency of the stepped-sine test (with automatically incremented file naming) for postprocessing and detailed inspection of any system nonlinearities. The software allows the user to select from a number of standard analysis options to perform on-line data processing for converting from the time to the frequency domain before saving the data. These on-line functions include the standard FFT, FRF and cross-spectrum calculations. A typical FFT response for a cantilever microbeam with a single frequency excitation is shown in Fig. 5a. The slight rise in the noise floor is due to the dynamics of the LDV, and the roll-off around 350 kHz is due to the bandwidth limitations on the LDV (at the higher sensitivity used for this sample). Recording the frequency domain data at only the driving frequency for each test-frequency step creates the stepped-sine response, or step data. The step data includes the amplitude, phase and coherence. An example of step data is shown in Fig. 5b for two stepped-sine tests on a single microbeam. The first test involved using a course step size of 1 kHz over the frequencies of 1 kHz to 100 kHz to find the approximate location of the resonant peak. The second test used a smaller step size (50 Hz) for a more detailed study of the resonant frequency. Under higher vacuum conditions, the step size can be further decreased to yield even better resolution to allow accurate calculation of the resonant frequency and damping parameters. The step data is the traditional output for stepped-sine testing and requires careful control of the acquisition and frequency resolution as outlined in the software methodology section. 45
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Important test diagnostic information is also included in the step data file to aid the user in ascertaining the signal quality. The diagnostic data includes important software settings, LDV sensitivity and laser return signal strength. The LDV laser signal strength is an important indication of the noise level for a given measurement and a measure of the quality of the acquired response signal.
Software Methodology The following sections briefly describe the most important data acquisition and software details used to ensure accurate nonlinear dynamic measurements. Most of the techniques can be used with almost any DAQ hardware and should be implemented whenever possible.
Anti-Aliasing An important and often overlooked aspect of computer controlled DAQ is the inclusion of antialiasing filters. Even if the signal is well known, there is always the possibility of high frequency noise appearing as a real signal in the frequency range of interest. This is especially true when searching for nonlinearities in the frequency spectrum. Digital filtering is not able to prevent aliasing and many high-end DAQ cards include built-in analog antialiasing filters for this reason. The current system, a National Instruments PXI-6534 card, includes software selectable antialiasing at either 50 kHz or 500 kHz. All antialiasing filters display roll-off well before the actual cut-off frequency specified. Because of this, inaccurate amplitude levels may be measured even well below the cut-off frequency and care should be taken to understand where this could occur in the frequency domain. Action should be taken to avoid measurements in these frequency ranges. FFT Bins and Stepped-Sine The nature of the Fast Fourier Transform (FFT) is such that the frequency information is contained in bands (called “bins” here) defined from n −1
FreqDomain( f ) = F{TimeSignal (t )} = ∑ Amplitude n × e − j 2πik / n for k = 0, 1, 2, …, n-1,
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where n is the number of samples. The time signal obtained from the DAQ card is translated into frequency and amplitude information via Eq. (1). The Fourier transformation into the frequency domain can be visualized as a series of bandpass filters centered at each frequency bin. If a signal falls between two bins, each will share some of the signal energy, but neither will possess the entire signal energy. This can lead to both frequency and amplitude ambiguity in the measurement. This error is avoided in the software by adjusting the bin size and location to ensure that the test frequency is at the center of a frequency bin. This is accomplished by calculating the sample size from the baseband span, span multiplier and the step size as
SampleSize =
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The span multiplier increases the frequency resolution to assist in capturing higher-order harmonics that may be contained in the nonlinear responses being measured. This increased accuracy is not without the cost of increased sample time. This tradeoff is considered worthwhile for the ability to capture the amplitude of the response accurately. For large step sizes this “super” resolution is very practical, but as the step size decreases, sampling times can become unacceptably long.
Spectral Leakage Spectral leakage is another aspect that must be considered when evaluating the accuracy of the amplitude information obtained from the FFT. An inherent assumption of the FFT algorithm is that the time signals are repeating periodic functions and they are periodic in intervals that exactly correspond to the acquired signal length. In practice this is difficult to obtain, and is why windowing is usually required to minimize leakage. While they do minimize the errors in the resulting spectral measurement, windows are not error free. The most commonly used Hanning window, for instance, can have an error of up to 1.42 dB for a simple sinusoidal signal not at the center of a frequency bin [6]. This reiterates the importance of having frequency bins at the drive frequency, as well as for the need to reduce spectral leakage. To reduce these unwanted window effects, the DAQ card was controlled to capture only an integer number of cycles. This was accomplished using Phase Lock Loop (PLL) techniques to synchronize the function generator and data acquisition card. This was done using the built-in PXI functionality allowing synchronization of DAQ devices through the backplane. A comparison of three samples showing the difference between using PLL, using only windowing and neither using PLL nor windowing is shown in Fig. 6a. The PLL method reduces the leakage by the largest amount as seen by its narrowest frequency spike. The windowed technique is very similar, but some frequency spreading can still be seen. The last case where neither technique was used is obviously unacceptable due to the greatly degraded signal quality (especially frequency resolution). Quantization Errors Digital discretization of signals, whether for output or input always results in quantization errors, i.e. the discrete nature of the output signal results in noise in the FFT spectrum. In general, the higher the number of bits, the lower the noise. Both Fig. 6a and 6b show this quantization error for the function generator and DAQ system together, as small harmonic spikes in the frequency domain. The noise error was considered acceptable having a four order-of-magnitude difference between the peak and the neighboring noise spikes.
Settling Time The stepped-sine method assumes that the response is due only to the constant sinusoidal driving signal. For this reason it is important to “delay” the measurement until any transients diminish. The appropriate delay time can be found experimentally by observing the FFT response. To reduce the settling time, and minimize the test time, the software was swept from one frequency to the next. This removed the step load to the system created by instantaneous frequency steps that create a large transient response. After arriving at the next frequency, a user-selectable delay is available to wait until any remaining transients die out. Vector Averaging To further improve the signal to noise ratio, FFT vector averaging was used. Vector averaging (as opposed to RMS averaging) uses the complex FFT results to calculate the average at each frequency across the spectrum. Noise, by its very nature, has random phase content and tends to average to zero over a period of time, decreasing the noise floor of the measurement. In order to not average out the intended measurement, it is important to have a constant phase for each sample of the signal. This phase information is lost if the DAQ card is allowed to “free-run”. The signal acquisition is therefore triggered on the drive signal which is not very noisy and has excellent trigger characteristics. Figure 6b shows a comparison between two types of averaging and not averaging. Vector averaging results in the lowest noise floor, with the RMS technique being fairly similar and both are better than no averaging. The RMS technique, however, cannot be used in the current testing due to the loss of phase information that is critical to modal analyses. 10
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FFT versus FRF The frequency response function (FRF) is customarily used to describe the dynamic response of a linear system. Theoretically, the FRF is calculated by the ratio of simultaneously measured driving signal and associated response. It is critically important that the two signals be measured simultaneously to prevent introducing any artificial phase lag between the drive signal and the response. For most signal types, the FRF is calculated from a ratio of cross and auto power correlation functions, since this method yields increased numerical stability and noise reduction. However, when using stepped-sine input, the former, theoretical means is more suitable for calculation of the FRF. This is due to the fact that the power at any frequency other than the excitation frequency is negligible.
Autoscaling LDV and DAQ To minimize the DAQ noise, the software controls both the LDV and DAQ scaling. The Polytec LDV is controlled via RS-232 communications and the sensitivity is optimized at each frequency step to create the largest output signal (mm/s/V) for the DAQ card to read. The velocity setting is saved as part of the step data file. Due to hardware limitations of the LDV, at each scaling level there is a different dependence of the signal phase as a function of frequency [7]. This critical phase error is corrected for in the software to yield a smooth and accurate phase plot regardless of scaling level or scaling level changes. After maximizing the velocity signal, the best DAQ card amplification is chosen to minimize the quantization noise of the analog to digital conversion.
Summary This paper describes a LabView®-based software developed to facilitate dynamic testing of MEMS/microsystems. The software can be applied to investigate linear and nonlinear dynamics, including experimental investigations and model validation activities related to multi-physics phenomena. Stepped-sine testing using the developed software has been highlighted as an effective way of conducting experimentation on nonlinear systems. The software functionality and methodology has been given in detail. To evaluate the software, nonlinear gas damping data was collected on microcantilevers under varying pressure levels. Those results are presented in a companion paper in the current conference proceedings [8]. The flexibility of the hardware and software allowed dynamic measurements on a number of different MEMS components for ongoing research and design projects. Future additions to the software may include adaptive response control for nonlinear vibrations.
Acknowledgements Authors extend their appreciation to following individuals from Sandia National Laboratories; Bruce Hansche and Eric Stasiunas for reviewing the article. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000.
References [1] Ozdoganlar, O. B., Hansche, B., and Carne, T., Experimental Modal Analysis for Microsystems, Proceedings of the International Modal Analysis Conference, 2002. [2] Epp, D., Ozdoganlar, O. B., Chaplya, P., Hansche, B., Carne, T., A Base Excitation Test Facility for Dynamic Testing of Microsystems, Proceedings of the International Modal Analysis Conference, 2003. [3] Heylen, W., Lammens, S., Sas, P., Modal Analysis Theory and Testing, Katholieke Universiteit Leuven, 1999. [4] Maia, N., Silva, J., He, J., Lieven N., Lin, R., Skingle, G., To, W-M., Urgueira, A., Theoretical and Experimental Modal Analysis, Research Studies Press, England, 1998. [5] Ewins, D. J., Modal Testing: Theory, Practice and Application, Research Studies Press, Baldock, Hertfordshire, England , 2nd edn., 2000. [6] Cerna, M., Harvey, A., The Fundamentals of FFT-Based Signal Analysis and Measurement, Application Note 041, National Instruments, July 2000. [7] Polytec user manual for the Laser Doppler Vibrometer OFV-3001 Controller. [8]
Epp, D.S., Ozdoganlar, O.B., and Sumali, H., Dynamic Measurement of Gas Damping Effects in MEMS, Current Proceedings, SEM International Congress X, 2004.
