Circuit Simulation Model Of Gas Damping In Microstructures With Nontrivial Geometries

Abstract

We present a model for the forces created by gas flow in a narrow gap between moving surfaces in a micromechanical structure. The partial differential equation describing the thin gas film behaviour is realized with a finite difference mesh, satisfying the boundary conditions for the gas flow. Thus different surface geometries and freedoms of motion can be modelled with different mesh topologies. The elements in the mesh are elementary electrical components, controlled sources and capacitances. The model presented is applied to capacitive silicon accelerometers having rectangular holes in the mass.

Comparative numerical study of FEM methods solving gas damping in perforated MEMS devices

“…Papers belonging to the first category are the following: Starr (1990) used heat conduction equation with zero boundary conditions at the holes in modeling damping in an accelerometer. A similar approach was presented in Veijola et al (1995), but an equivalent circuit was constructed to solve the problem with a circuit simulation tool. In Schrag et al (2001), Sattler et al (2002), Sattler and Wachutka (2004), and Schrag and Wachutka (2004), a tilting perforated mirror was analyzed using a finite network method.…”

“…Several analytic models (Skvor 1967;Veijola and Mattila 2001;Veijola et al 2002;Bao et al 2002Bao et al , 2003Homentcovschi and Miles 2004;Mohite et al 2005;Veijola 2006a, b), and dimension-reduction numerical models (Starr 1990;Veijola et al 1995;Schrag et al 2001;Sattler et al 2002;Yang and Yu 2002;Mehner et al 2003;Sattler and Wachutka 2004;Schrag and Wachutka 2004;Veijola 2007) have been published. In most of the publications, the verifications and the validity regime of applicable operation range are missing.…”

Techniques in Residual Stress Measurement for MEMS and Their Applications

“…Gupta [166] has already demonstrated that the models presented in [162] can be readily modified to account for beams with a trapezoidal cross section (instead of ideal prismatic) and for such process artifacts as beam undercut during release etch, provided one is willing to make the geometric measurements needed to support the modeling. In addition, the presence of air in the gap may provide squeeze film damping as well as some additional stiffness and this could introduce errors [167]. Nevertheless, the method is now being successfully applied to structures with high residual stress and compliant supports [168], at least for the purposes of monitoring process uniformity and repeatability.…”

Optimization Strategy for Resonant Mass Sensor Design in the Presence of Squeeze Film Damping

“…Previously, extensive studies on the squeeze film damping have been performed [4][5][6][7] and have focused on the viscous damping and compressible spring effect of the fluid layer confined between parallel closed plates. Finite difference [8] and finite element models [9,10] have been developed. Perforated planar microstructures have also been studied to evaluate the influence of squeeze film damping [11].…”