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NEW WAYS OF MEASURING PULL-IN VOLTAGE AND TRANSIENT BEHAVIOR OF PARALLEL-PLATE CAPACITIVE MEMS TRANSDUCERS C. Glacer1,2 , A. Dehé2 , M. Nawaz2 and R. Laur1 1 Institute for Electromagnetic Theory and Microelectronics (ITEM), University of Bremen, Bremen, Germany 2 Infineon Technologies AG, Neubiberg/Munich, Germany Abstract — In this paper we introduce two new ways of measuring the pull-in voltage and the transient behavior of parallel-plate capacitive MEMS transducers. The advantages in measurement speed and resolution of the socalled fast MEMS test will be discussed as well as an enhanced method, the time-resolved dynamic measurement. With the second method we can visualize the integral displacement of a membrane while measuring the voltage drop of a high frequency signal over a shunt resistor/capacitor. This offers us a new robust and cheap option for tracing moving structures without the need of an optical line of sight. Keywords: MEMS testing, Silicon Microphone, laser Doppler vibrometer, pull-in voltage I – Introduction Acoustical parallel-plate microelectromechanical systems (MEMS) especially for mobile applications are strongly upcoming the last years. With ongoing miniaturization of mobile phone components and the desire for automatic reflow solder processes the requirements for microphones are increasing. Conventional electret condenser microphones suffer from humidity and temperature influences. The Infineon Silicon MEMS Microphone chip set delivers a small size, good reproducibility and stability, low sensitivity to vibration and the ability of low-cost batch fabrication along with a sufficient sound recording quality [1]. Figure 1: Schematic of the Infineon Silicon MEMS Microphone [1]. The membrane (red) and the fixed counterelectrode (blue) can bee seen. The Infineon microphone uses a pressure sensitive diaphragm made out of in poly-Silicon. Along with a preamplifier, the microphone chip converts an impinging sound wave into an electrical output signal with a capacitive transducing concept. Although there is a big market and millions of devices are produced every year, the membrane behavior in such a microphone system is not fully transparent and understood. Especially in case of large deflections, mechanical shocks or extreme sound pressure levels it needs a (scanning) laser Doppler vibrometer (LDV) and a complex sample preparation to monitor the membranes motion. Belong those special measurement setups for further investigations of some systems; every chip has to pass a final inspection. The pull-in voltage (Vp ) can become a key parameter for this purpose. It marks the equilibrium point of the electrostatic attraction force and the mechanical resilience in a voltage controlled capacitive system. This delivers insights about the membrane compliance (k) with a given air gap (d0 ) and area (A) [2]. s 8kd03 (1) Vp = 27εA Despite a simple pass-fail test the system sensitivity (S) can be derived [1] by determining Vp . r 8d0 V0 S= · (2) Vp 27εAk Several methods to detect the pull-in event are existing. The probably simplest way is to look at the membrane while increasing the stimulus voltage step by step. When the pull-in voltage is reached, the closing of the air-gap between the two electrodes will lead to interference fringes which are visible with a microscope. More advanced equipment like a Doppler vibrometer will do the same purpose. Another common method to detect Vp is the usage of a LCR meter. The displacement of the membrane towards the electrode leads to a higher capacitance which can be monitored. As a consequence, the membranes motion over the excitation voltage can be plotted. The voltage where the pull-in acceleration phase begins can be made visible as Vp . This event can be even heard, so that a acoustical detection is another method. In this work new approaches for testing parallelplate sensors and actuators - the fast MEMS test and the time-resolved dynamic measurement - will be presented. This measurement techniques deliver new insights in the transient motion of a micro-mechanically fabricated membrane as well as a fast and exact test method for the pull-in voltage and system resonances. It will be elucidated how the fast MEMS test works and which equipment is necessary for acquisition and data processing. Moreover possible application 25 II – Measurement Setup 20 Measured voltage drop over Cmeas 15 10 Voltage drop over CMeas [mV] fields will be shown and initial results will be presented. Input signal Vstim [V] The concept of the fast MEMS test is relatively simple and bases upon the well-known current mea15 5 surement with a shunt resistor. For the simplest case, the Vp determination, the voltage drop across a resistor 10 0 in series to the capacitive transducer will be metered with an oscilloscope (L E C ROY MSO 44MX S -B). The 5 −10 excitation is realized with a biased signal generator (AGILENT 33220A) which delivers for example a tri0 −10 angular waveform with 0 to 20V back to 0V in 1ms. 0 0.2 0.4 0.6 0.8 1 1.2 Time [ms] If the pull-in voltage is inside this voltage ramp, the capacitance of the parallel-plate actuator will quickly Figure 3: Measured voltage drop across the shunt capacitor. It increase and influence the current through the circuit shows the pull-in event (time index: ≈ 0.5ms) and the release and so the resistors voltage drop. Fig. 2 shows the basic (≈ 0.9ms). setup. In our case, the usage of a shunt capacitor instead of resistor delivered a higher output voltage with a better signal to noise ratio (SNR). 1kHz triangular waveform. This delivered a resolution of 8mV/step for the given signal. Scope GPIB-Control The big disadvantage of this method is that the response signal directly follows the input stimulus fstim . PC with Measurement Therefor we can only extract the pull-in and release MatLab C voltage but not the membranes free motion. Also it is DUT (e.g. SiMic) not possible to resolve the membrane movement when 1 2 the excitation is a mechanical stimulus instead of an C R /C electrical. To get rid of this problem, the time-resolved Simplified equivalent circuit 1 2 dynamic measurement is introduced. For this method we use a series AC voltage source Biased AC stimulus + - + with a sinusoidal signal fHF of small amplitude and high frequency. This signal superimposes the electromechanical stimulus or acts alone with a mechanical Figure 2: Simplified model of the pull-in detection measureexcitation. For a given frequency of typically 1MHz or ment setup. Containing the electrical circuit and an simplified more, the membrane is not capable to follow the signal equivalent circuit of the MEMS capacitances. which lies clearly above the membranes resonance frequency (≤120kHz). The number of scan points s within After the equilibrium point of the acting forces, the one period of the stimulus which can be achieved with membrane encounters a large acceleration due to the this methods can be calculated by s = fHF / fstim . To extract Vout,HF from Vout = Vout,stim +Vout,HF it is increasing electrostatic force. This normally happens at necessary to apply an electrical filter. In this case we around 1/3 of the systems air gap [2]; the el. potential use a software Butterworth band pass filter generated where this large acceleration event starts can be taken in M AT L AB to get rid of Vout,stim and noise. The signal as the pull-in voltage. Due to our capacitive shunt setup processing contains the following steps: it was necessary to form the second derivative to figure out the largest acceleration of the membrane which is 1. Measurement and data transfer; e.g. 100k Samples proportional to the largest change in output voltage. for fHF = 5MHz To do the necessary data processing a software solution with M ATH W ORKS M AT L AB was used. The 2. Spline interpolation in M AT L AB to regain the siAC source as well as the digital storage oscilloscope nusoidal signal shape are controlled by the General Purpose Interface Bus 3. Butterworth band pass filtering; e.g. with 4th order (GPIB) interface. After a measurement the results will and fc = 5MHz ± 0.2MHz be transferred to the PC, derivated twice and the point of the biggest acceleration of Vout gets linked to the 4. Creating the envelope to figure out the amplitude stimulus voltage Vstim . The number of read-out samples of each period are directly influencing the data transfer time and the 5. Result: Signal proportional to the integral of the resolution of the measurement. We worked with a membrane displacement and its capacitance sum compromise of 5000 samples while stimulating with a Measurement Results Static Pull-In Meas meas Change of pull-in voltage over frequency 2.5 III – Results and Discussion A. Fast dynamic pull-in detection To gain statistical values with the introduced pull-in detection method we investigated several wafers containing silicon microphones. For this we used a GPIB controlled lab wafer prober from S UESS M ICROT ECH. Figure 4 shows a distribution of the pull-in voltages across an experimental test wafer containing >10k silicon microphones in total. It can be demonstrated how fine the gradients in the pull-in voltage determination are, so that even technology effects on this wafer can be made visible. When we measure the same wafer again without changing the setup, the median of the deviations particular chips show in their pull-in voltages is Vp,di f f = 8.7mV , which is nearly within the measurement resolution of 8mV /step. 16V 80 60 15V 40 Wafer y 20 Change in pull-in voltage [V] 2 1.5 1 0.5 Change of Vp, electrical fast MEMS test Standard deviation, electrical Change of Vp, optical LDV 0 −0.5 0 0.5 1 1.5 2 2.5 3 Frequency [kHz] 3.5 4 4.5 5 Figure 5: Change of pull-in voltage over frequency. Determined by fast MEMS test and proven by optical measurement. as shown in fig. 5. Here the fast MEMS test is a promising method as the decrease in pull-in voltage over frequency is repeatable for every chip. According to this a correction factor can be extracted and also no steep (rectangular) steps appear in the excitation voltage. B. Time-resolved dynamic measurement (TRDM) 0 14V −20 −40 13V Since a LCR meter delivers exact capacitance values but has in our test setting a minimum settling time of around 2.8ms per point, this tool is not appropriate to perform transient measurements of MEMS microphones. −60 −80 −80 −60 −40 −20 0 Wafer x 20 40 60 80 (a) (b) (c) (d) 12V Figure 4: Pull-in voltage distribution across an experimental test wafer. After 2/3 of the wafer stepping the prober tips lost contact. This resulted in noise which will be filtered out in further measurements. Another advantage of the fast MEMS test is its high measuring speed. With the given resolution the contact time of a chip amounts 2.5ms which includes a safe prober tip contact, the time to trigger and acquire the waveform by the oscilloscope and the command to start stepping to the next chip for the prober. A point which has to be minded is the dynamic effect of different excitation frequencies to the pull-in voltage. In vacuum a steeper excitation slope leads to a higher membrane acceleration and contributes more energy to the system. With a higher measurement frequency and the same maximum amplitude value the slope steepness increases [3]. Compared to a quasi-static pull-in event, the bigger kinetic energy at e.g. 1kHz test frequency leads to a lower effective pull-in voltage. Under normal air pressure this effect gets obliterated by the air damping. With higher frequencies the pull-in voltage drops Figure 6: With a scanning laser Doppler Vibrometer measured displacement of the membrane at certain time points during a pull-in and release event. The motion of a parallel-plate capacitive transducer encountered from a triangular stimulus is shown in figure 6. This measurement was done with a SLDV from P OLYTECH through the perforation holes of the overhead (fixed) counter electrode. It shows the slow deflection of the membrane (a), the first contact between the electrodes (b), the widening of the contact area due to higher voltage (c) and the overshoot after the release (d). The ability of scanning through different measure- ferent transducer types, that the fast MEMS test method is working and delivers good results. It produces a high measurement resolution with a measurement time which only needs one period of a stimulus signal (e.g. 1ms at fstim = 1kHz) while the chip is contacted. Aside from that, the needed equipment is, with a function generator and a digital oscilloscope, common and cheap so that in most labs the setup can be easily implemented. The problem of an overshoot due to high voltage steps around the pull-in point is avoided here. Extracted prop. membrane displacement The enhanced measurement setup, the time-resolved 1 dynamic measurement, can partly compare to optical transient measurements with an SLDV. A disadvantage is that only integral values of the displacement will be delivered, comparable to the capacitance of the MEMS device in the circuit. It is also necessary to compensate 0.5 10 parasitic elements to get correct capacitance readings out of both measurement methods. This will happen in a future step. On the other hand the measurement technique shows several benefits compared to the measurement with an SLDV. Starting by the equipment cost 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 which are only on a fraction of those of a SLDV and Time [ms] going over to the application areas. Because of the fact Coupled oscil. after pull in Membrane oscil. after release that no line of sight is needed, the measurement will 0.12 0.1 also work with build-in and moving chips and offers 0.85 0.08 new ways of monitoring the membrane deflection, so 0.06 the method can be also applied to pressure or bulge tests 0.8 0.04 or any overload test. 0.75 All in all the new fast MEMS test and the time0.72 0.74 0.76 0.78 0.36 0.38 0.4 Time [ms] Time [ms] resolved dynamic measurement are interesting, easy to use and robust methods to determine pull-in voltage Figure 7: Proportional integral membrane motion measured with the time-resolved dynamic measurement with averaging and membrane motion which offers us new fields of (above). Coupled oscillation and mebrane oscillation after application. Prop. displacement [normed] Prop. displacement [normed] Stimulus low pass filtered [V] Prop. displacement [normed] ment points on the membrane is not given with the TRDM since only the voltage drop over a resistor/capacitor in series is measured. Instead the integral movement of the membrane will be recorded. This is of course a disadvantage but sufficient in most applications. A bigger problem is that higher oscillation modes can cancel out their results because of an antiphase vibration. This has to be taken into account and is unavoidable with the current setup. pull in/release. Acknowledgements Figure 7 shows nicely how the membrane gets attracted and suddenly accelerates when the pull-in voltage is reached. In contact membrane and electrode performing a coupled oscillation and the contact area gets bigger with increasing excitation voltage. When Vstim is lowered again, the membrane detaches from the electrode in a different behavior because the mechanical restoring force is now acting. When a certain voltage is reached, the last contact point releases from the electrode which vanishes the adhesion force and causes the membrane to accelerate again. The membrane performs an overshoot over its resting position and oscillates a few times around it. In this case a Fourier transform of the free membrane oscillation after the release delivers a membrane resonance frequency of 65.4kHz under normal pressure and a coupled resonance of 97.5kHz after the pull in event. This fits to measurements done with other equipment under the influence of a bias voltage. IV – Conclusion It has been shown on several thousand chips and dif- The authors would like to thank Dr. Andreas Kenda from the Carinthian Tech Research AG, Austria for making the SLDV results available. References [1] Marc Fueldner. Modellierung und Herstellung kapazitiver Mikrofone in BiCMOS-Technologie. PhD thesis, Technical Faculty University ErlangenNuremberg, Munich, Germany, 2004. [2] Rafael Nadal Guardia. Current Mode Drive of Electrostatic Microactuators. PhD thesis, Universitat Politecnica de Catalunia, 2001. [3] G. Nielson and G. Barbastathis. Dynamic pull-in of parallel-plate and torsional electrostatic mems actuators. Journal of Microelectromechanical Systems, 15(4):811–821, 2006.