The atomic limit of finite element modeling in MEMS: Coupling of length scales

We describe concurrent multiscale simulations of the behavior of sub-micron Micro-Electro-Mechanical Systems (MEMS), focusing on the dynamics and ther modynamics of micro-resonators as an archetypical example. The coupling of length scales methodology we have developed employs a conventional finite e lement model of the large-scale peripheral regions, but in the important ce ntral region the mesh would need to be collapsed to the atomic scale. Here an atomistic description is seamlessly coupled into the finite elements in order to give a very precise description of the dynamics of the few million atoms in this region. This novel technique accurately models the behavior of the mechanical components of MEMS down to the atomic scale. This article addresses general issues involved in this kind of multiscale simulation, w ith a particular emphasis on the technical details of how finite element an alysis is extended to ensure a reliable model as the mesh spacing is refine d to the atomic scale. We also discuss how the coupling of length scales te chnique has been used to identify atomistic effects in sub-micron resonator s. These effects include a shift in the resonant frequency away from the va lue predicted by continuum elastic theory, new dissipation mechanisms due t o surface processes and pronounced finite temperature effects.