@inproceedings { 06c_Lukas-Cretu, title = {Experimental verification of rarefied gas squeezed-film damping models used in MEMS}, journal = {Proceedings of IMECE 2006, 2006 ASME International Mechanical Engineering Congress and Exposition, Nov. 5-10, Chicago, USA}, year = {2006}, month = {November 5-10}, publisher = {ASME}, organization = {ASME}, type = {inproceedings}, address = {Chicago, Illinois, USA}, abstract = {IMECE2006-14451 Technical Publication Experimental Verification of Rarefied Gas Squeezed-Film Damping Models used in MEMS Authors Lukas Mol, Delft University of Technology Luis A. Rocha, University of Minho Edmond Cretu, University of British Columbia Reinoud F. Wolffenbuttel, Delft University of Technology Abstract For MEMS structures in which the size of a small gap between two plates changes in time, the resulting pressure changes relative to the plate velocity are described by the Reynolds equation. An analytical solution for the forces acting on the plates can be found if certain boundary conditions are assumed [1]. Two concerns about this squeezed-film theory are: a) The validity of the continuum hypothesis - at a certain limit the typical intermolecular distances are comparable to the device dimensions and the continuum fluid equations can no longer appropriately describe the flow behavior (rarefied gas) [2]. b) The assumption of ambient gas pressure at the plate borders [3]. This condition is true if the plate dimensions are large compared to the film thickness. However, in practical surface-micromachined MEMS the fringe effects considerably increase the damping force (35%), for ratios between plate width and gap size as high as 20 [4]. Several compact models for micromechanical squeezed-film dampers including these rarefaction and border effects have been proposed in literature [3-5], yet experimental validation is almost completely lacking [6]. The experimental verification measurement is based on an on-off closed-loop electrostatic actuation of a capacitive structure that achieves dynamic yet stable electrode positioning over the entire gap [7]. For each arbitrary position of the electrode within the gap, the AC part of the displacement is basically a small signal excitation applied to a linear system. During the _off_ period of excitation (voltage is zero) there is no electrostatic force applied to the structure, and the system can be modeled as a pure 2nd order mechanical system. Since initial conditions are known, the damping coefficient can be computed from the time series of position measurements. Devices fabricated in the Bosch epi-poly process [8] were used to measure the damping coefficient. For gaps from 2.2 um down to 0.4 um (Knudsen numbers ranging from 0.03 to 0.18) the existing compact model was used to compute the predicted damping coefficient [3]. Next, using the described method the damping coefficient was measured and the results compared. Analysis of measurements reveals amongst others that border effects are dominant at gaps larger than 1200 nm, while rarefaction effects are dominant for more narrow gaps. It is also clear from the experimental results that both effects are present during device motion. This measuring technique is expected to give a new insight into the damping problem at high Knudsen numbers and may further improve the accuracy of the squeeze-film models. References [1] J.J. Blech, _On Isothermal Squeeze Films_, J. Lubrication Technology, 105, pp. 615-620, 1983 [2] F. Sharipov and V. Seleznev, _Data on internal rarefied gas flows_, in J. Phys. Chem. Ref. Data, Vol 27, 3, pp. 657-706, 1998 [3] T. Veijola, A. Pursula and P. Raback, _Surface Extension Model for MEMS Squeezed-Film Dampers_ in Proc. DTIP_05, 2005, pp. 235-241. [4] S. Vemuri, G.K. Fedder and T. Mukherjee, _Low-order squeeze film model for simulation of MEMS devices_, in Proc. MSM_00, 2000, pp. 205-208 [5] R. Sattler and G. Wachutka, _Compact Models for Squeeze-Film Damping in the Slip Flow Regime_, in Proc. Nanotech_04, 2004, pp. 243-246. [6] P.G. Steeneken, Th. G. S. M. Rijks, J.T.M. van Beek, M.J.E. Ulenaers, J. De Coster and R. Puers, _Dynamics and squeeze film damping of a capacitive RF MEMS switch_, in J. Micromech. Microeng., 15, pp. 176-184, 2004. [7] L.A. Rocha, E. Cretu and R.F. Wolffenbuttel, _Using Dynamic Voltage Drive in a Parallel-Plate Electrostatic Actuator for Full-Gap Travel_, in J. Microelectro-mechanical Sys., Vol 15, 1, pp. 69-83, 2006 [8] http://www.europractice.bosch.com/en/start/index.htm Session: MEMS-5 Test and Device Characterization}, URL = {http://www.asmeconferences.org/Congress06/TechnicalProgramOverview.cfm#27}, author = { Mol, Lukas and Rocha, Luis A. and Cretu, Edmond and Wolffenbuttel, Reinoud F.} }