A stochastic 3-Scale approach to study the thermomechanical damping of MEMS

A stochastic 3-scale approach is developed to study the thermo-elastic quality factor (Q) of micro-electromechanical systems (MEMS) resonators.
Thermo-elastic damping is one of the major dissipation mechanisms in high-Q micro-resonators, which may have detrimental effects on the quality factor, and has to be predicted accurately. Since material uncertainties are inherent to and unavoidable in MEMS, the effects of those variations have to be considered in the numerical models. To this end, a coupled thermo-mechanical stochastic 3-scale approach is considered. Thermo-mechanical micro-models of poly-silicon materials are used to represent micro-structure realizations. A computational stochastic homogenization procedure is then applied on these statistical volume elements to obtain the probabilistic distribution of the elasticity tensor, thermal expansion and conductivity tensors at the meso-scale. Spatially correlated meso-scale random fields are then generated in order to represent the probabilistic behavior of the homogenized material properties, feeding macro-scale stochastic finite element simulations.