Modeling gas damping and spring phenomena in MEMS with frequency dependent macro-models

In this paper, we present an efficient macromodel extraction technique for gas damping and spring effects for arbitrarily shaped MEMS devices. The technique applies an Arnoldi-based model-order-reduction algorithm to generate low-order models from an FEM approximation of the linearized Reynolds equation. We demonstrate that this approach for generating the frequency-dependent gas-damping model is more than 100 times faster than previous approaches, which solve the linearized Reynolds equation using a transient FEM solver. The low-order gas-damping model can be easily inserted into a system-level modeling package for transient and frequency analysis. The simulated results are in good agreement with experimental results for four different devices.

[1]  M. Esashi,et al.  Simple modeling and simulation of the squeeze film effect and transient response of the MEMS device , 1999, Technical Digest. IEEE International MEMS 99 Conference. Twelfth IEEE International Conference on Micro Electro Mechanical Systems (Cat. No.99CH36291).

[2]  W. E. Langlois.  Isothermal squeeze films , 1961 .

[3]  J. J. Blech.  On Isothermal Squeeze Films , 1983 .

[4]  M. Gretillat,et al.  Effect of air damping on the dynamics of nonuniform deformations of microstructures , 1997, Proceedings of International Solid State Sensors and Actuators Conference (Transducers '97).

[5]  Lawrence T. Pileggi,et al.  PRIMA: passive reduced-order interconnect macromodeling algorithm , 1997, ICCAD 1997.

[6]  T. Veijola,et al.  Model for gas film damping in a silicon accelerometer , 1997, Proceedings of International Solid State Sensors and Actuators Conference (Transducers '97).

[7]  Dennis S. Greywall,et al.  Phenomenological model for gas-damping of micromechanical structures , 1999 .