Probabilistic prediction of the quality factor of micro-resonator using a stochastic thermo-mechanical multi-scale approach

Abstract

As the size of the device is only one or two orders of magnitude higher than the size of the grains, the structural properties, such as the thermo-elastic quality factor (Q), of micro-electro-mechanical systems (MEMS) made of poly- crystalline materials exhibit a scatter, due to the existing randomness in the grain size, grain orientation, surface roughness. In order to predict the probabilistic behavior of micro-resonators, the authors extend herein a previously developed stochastic 3-scale approach to the case of thermoelastic damping. In this method, stochastic volume elements (SVEs) are defined by considering random grain orientations in a tessellation. For each SVE realization, the mesoscopic apparent elasticity tensor, thermal conductivity tensor, and thermal dilatation tensor can be obtained using thermo-mechanical computational homogenization theory. The extracted mesoscopic apparent properties tensors can then be used to define a spatially correlated mesoscale random field, which is in turn used as input for stochastic finite element simulations. As a result, the probabilistic distribution of the quality factor of micro-resonator can be extracted by considering Monte-Carlo simulations of coarse-meshed micro-resonators, accounting implicitly for the random microstructure of the poly-silicon material