TY - JOUR
T1 - Macromodel-based simulation and measurement of the dynamic pull-in of viscously damped RF-MEMS switches
AU - Niessner, Martin
AU - Schrag, Gabriele
AU - Iannacci, Jacopo
AU - Wachutka, Gerhard
N1 - Funding Information:
The authors would like to thank H. Mulatz and M. Becherer from the Institute for Technical Electronics of the Munich University of Technology for their efforts to bond samples of the devices and for taking SEM and FIB images with the equipment available at their institute. The authors furthermore acknowledge the Dr. Johannes Heidenhain Stiftung for their financial funding of this work. Appendix A This appendix contains correction factors that take into account the effect of gas rarefaction, and reduce the fluidic resistances given in Section 3.3 , accordingly with decreasing ambient pressure and/or air gap dimensions. The factors Υ BT , Υ C and Υ O are taken from Sattler [12] , who did a thorough review of publications by Beskok [32,33] , Sharipov [34–36] and Veijola [37–40] . The factors Υ Reynolds , Υ BT and Υ O are directly taken from (or based on) publications by Veijola [38–40] and the factor Υ C is taken from Beskok [33] . The expressions read: (25) Υ R e y n o l d s = 1 + 9.638 K n 1.159 (26) Υ B T ≈ Υ R e y n o l d s ⋅ 1 + 0.5 D − 0.5 ⋅ 3 0 − 0.238 1 + 2.471 D − 0.659 (27) Υ C = 1 + 1.085 K n ⋅ a r c t a n ( 8 K n ) 1 + 6 K n 1 + K n (28) Υ O = 1 + 6.703 K n ( 1.577 + K n ) 2.326 + K n ⋅ 1 + 0.688 D − 0.858 Λ 0 − 0.125 1 + 1.7 D − 0.858 Here, = ). Furthermore, Kn λ f / d f denotes the Knudsen number, where λ f is the mean free path, which changes with the ambient pressure P 0 , and d f denotes the characteristic length of the flow. The characteristic length is different for each correction factor (cp. Table 3 D = π / ( 2 K n ) represents the parameter of rarefaction and Λ 0 = L r / ( s r / π ) the ratio of the channel length L r and the side length of the hole s r . The presented correction factors are valid for square holes only. Martin Niessner received the B.Sc. (with honors) and diploma degrees (with honors) in electrical engineering from the Munich University of Technology, Germany, in 2004 and 2005, respectively. He was a visiting graduate student at the University of Illinois, Urbana-Champaign, from 2004 to 2005. In 2006 he joined the MEMS modeling group at the Institute for Physics of Electrotechnology at the Munich University of Technology and is currently working towards the doctorate degree in electrical engineering. His main research interests are the modeling and simulation of coupled effects in microsystems and model verification. Gabriele Schrag received her diploma in physics from the University of Stuttgart in 1993, where she continued her work until 1994. In 1995 she joined the Institute for Physics of Electrotechnology at the Munich University of Technology, working on modeling methods for microdevices and microsystems, with a special focus on fluid–structure interaction and viscous damping effects. In 2002 she received her doctorate degree (with honors) from the Munich University of Technology, her thesis covering the “Modeling of Coupled Effects in Microsystems on Device and System Level”. Since 2003 she has been heading the MEMS modeling group at the Institute for Physics of Electrotechnology. Her research activities are focused on methodologies for the predictive simulation and optimization of microdevices and microsystems, parameter extraction and model verification. Jacopo Iannacci received the M.Sc. degree in electronic engineering from the University of Bologna (Italy) in 2003 and the Ph.D. in information technology in 2007 from the ARCES Research Center (University of Bologna). In 2005 and 2006 he worked at the HiTeC DIMES Technology Center (Technical University of Delft, the Netherlands) in developing packaging solutions for RF MEMS and from October 2007 he joined Fondazione Bruno Kessler (FBK) in Trento (Italy) as Researcher on MEMS technology. His scientific interest is focused on compact modeling, design, optimization, integration, packaging and reliability, of MEMS/RF-MEMS devices and networks for sensors and telecommunication systems. He authored and co-authored about 80 scientific contributions in international conferences proceedings and journal papers. Moreover, he also authored a few book chapters and a couple of books in the field of RF-MEMS technology. Gerhard Wachutka received the doctorate degree from the Ludwig-Maximilians-Universität, Munich, Germany, in 1985. From 1985 to 1988, he was with Siemens Corporate Research and Development, Munich, where he headed a modeling group active in the development of modern high-power semiconductor devices. In 1989, he joined the Fritz-Haber-Institute of the Max- Planck-Society, Berlin, Germany, where he worked in the field of theoretical solid-state physics. From 1990 to 1994, he was head of the microtransducers modeling and characterization group of the Physical Electronics Laboratory at the Swiss Federal Institute of Technology (ETH), Zurich. There, he also directed the micro-transducers modeling module of the Swiss Federal Priority Program M2S2 (Micromechanics on Silicon in Switzerland). Since Spring 1994, he has been heading the Institute for Physics of Electrotechnology at the Munich University of Technology, where his research activities are focused on the design, modeling, characterization, and diagnosis of the fabrication and operation of semiconductor microdevices and microsystems. Professor Wachutka is member of the IEEE, the American Electro-chemical Society, the American Materials Research Society, the ESD Association, the VDE Association for Electrical, Electronic and Information Technologies, the VDI Association of German Engineers, the German Physical Society, the American Physical Society, and the AMA Society for Sensorics.
PY - 2011/12
Y1 - 2011/12
N2 - Abstract: We present a physics-based multi-energy domain coupled macromodel that allows for the efficient simulation of the dynamic response of electrostatically controlled and viscously damped ohmic contact RF-MEMS switches on the system-level. The predictive power of the macromodel is evaluated w.r.t. white light interferometer and laser vibrometer measurements. Furthermore, the macromodel is, concerning accuracy and performance, benchmarked versus two alternative state-of-the-art system-level models. The results obtained with the presented macromodel are in very good agreement with the measured quasi-static pull-in characteristics as well as the pull-in and pull-out transients. Due to its capability to account for multiple structural modes, the presented macromodel produces, among the evaluated models, the result that is closest to the measured phase of initial contact during dynamic pull-in. Moreover, a detailed experimental evaluation of the damping model shows a very good agreement (maximum relative error does not exceed 10%) for ambient pressures ranging from 960 hPa down to approximately 200 hPa. Compared to other damping models, this constitutes a very good result, especially because the models contain only geometric parameters and no problem-specific fit factors are needed to obtain this accuracy. The resulting macromodel is physics-based and, hence, scalable and predictive. Due to its generic nature it can be - in general - adapted for any electrostatically actuated device working in contact mode.
AB - Abstract: We present a physics-based multi-energy domain coupled macromodel that allows for the efficient simulation of the dynamic response of electrostatically controlled and viscously damped ohmic contact RF-MEMS switches on the system-level. The predictive power of the macromodel is evaluated w.r.t. white light interferometer and laser vibrometer measurements. Furthermore, the macromodel is, concerning accuracy and performance, benchmarked versus two alternative state-of-the-art system-level models. The results obtained with the presented macromodel are in very good agreement with the measured quasi-static pull-in characteristics as well as the pull-in and pull-out transients. Due to its capability to account for multiple structural modes, the presented macromodel produces, among the evaluated models, the result that is closest to the measured phase of initial contact during dynamic pull-in. Moreover, a detailed experimental evaluation of the damping model shows a very good agreement (maximum relative error does not exceed 10%) for ambient pressures ranging from 960 hPa down to approximately 200 hPa. Compared to other damping models, this constitutes a very good result, especially because the models contain only geometric parameters and no problem-specific fit factors are needed to obtain this accuracy. The resulting macromodel is physics-based and, hence, scalable and predictive. Due to its generic nature it can be - in general - adapted for any electrostatically actuated device working in contact mode.
KW - Dynamic pull-in
KW - Macromodel
KW - RF-MEMS switch
KW - Rarefaction
KW - Squeeze-film damping
UR - http://www.scopus.com/inward/record.url?scp=82755161051&partnerID=8YFLogxK
U2 - 10.1016/j.sna.2011.04.046
DO - 10.1016/j.sna.2011.04.046
M3 - Article
AN - SCOPUS:82755161051
SN - 0924-4247
VL - 172
SP - 269
EP - 279
JO - Sensors and Actuators, A: Physical
JF - Sensors and Actuators, A: Physical
IS - 1
ER -