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Experimental verification of rarefied gas squeezed-film damping models used in MEMS

Publication Type:

Conference Paper


Proceedings of IMECE 2006, 2006 ASME International Mechanical Engineering Congress and Exposition, Nov. 5-10, Chicago, USA, ASME, Chicago, Illinois, USA (2006)




Technical Publication

Experimental Verification of Rarefied Gas Squeezed-Film Damping Models
used in MEMS


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


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

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]

Session: MEMS-5 Test and Device Characterization