A probabilistic multi-scale model for polycrystalline MEMS resonators

The size of micro-electro-mechanical systems (MEMS) is only one or two orders of magni-tude higher than the size of their micro-structure, i.e. their grain size. As a result, the structural properties exhibit a scatter. As an example we study the beam resonator illustrated in Fig. 1(a), made of poly-silicon material, in which each grain has a random orientation. Solving the problem with a full direct numerical simulation combined to a Monte-Carlo method allows the probability density function to be computed as illustrated in Fig. 1(b). However this method-ology is computationally expensive due to the number of degrees of freedom required to study one sample, motivating the development of a non-deterministic 3-scale approach [3]. (a) FE