Hierarchical finite element simulation of perforated plates with arbitrary hole geometries

Peter Råback, Antti Pursula, and Timo Veijola
CSC - Scientific Computing, FI

Keywords: Squeezed-film-damping, perforated, finite element method

Abstract:
The squeezed-film-damping of micro-electro-mechanical devices may be reduced by creating a number of small holes into the structure. Unfortunately, in the simulation of the devices it is possible to consider only a few holes in detail. A more feasible approach is to homogenize the contribution of the holes over the whole domain. In this paper we follow a hierarchical two-level simulation strategy. We take a unit cell including one hole and compute the flow resistance and the electrical capacitance correction as a function of the aperture. By this homogenization, a full coupled analysis including fluidic, elastic and electrostatic forces is performed. The solution is obtained from a loosely coupled iteration scheme involving a nonlinear Reynolds equation, a nonlinear plate equation, and a reduced order equation for the electric field. We apply the described methodology to a simple micro-mechanical microphone with a perforated backplate. We perform harmonic and transient analysis using ELMER finite element solver. In particular, dynamical pull-in phenomena is modeled with different hole configurations. The selected approach is not restricted to any given geometry and it may therefore be applied to holes of any shape. This is important since the manufacturing technology does not always allow idealized shapes. Additionally, the model does not assume small displacements and it may therefore be applied to study various nonlinearities of the device.

NSTI Nanotech 2003 Conference Technical Program Abstract