ATOMISTIC SIMULATION OF MEMS RESONATORS THROUGH THE COUPLING OF LENGTH SCALES

We present simulations of the dynamic and temperature dependent behavior of Micro-Electro-Mechanical Systems (MEMS). We focus on the vibrational behavior of micron-scale resonators made of silicon and quartz. These inherently atomistic simulations are extended by recently developed parallel algorithms which enable a coupling of length scales. The novel techniques used in this simulation accurately model the behavior of the mechanical components of MEMS down to the atomic scale. The algorithmic and computational avenue applied here represents a significant departure from the usual finite element analysis of MEMS based on continuum elastic theory. An atomistic simulation consisting of millions of atoms is used in regions of significantly anharmonic forces and large surface area to volume ratios or where internal friction due to defects is anticipated. This corrects the expected, but previously unquantified, failure of continuum elastic theory in the smallest MEMS structures. Peripheral regions of MEMS, which are well-described by continuum elastic theory, are simulated using finite elements for efficiency. The two techniques run concurrently and mesh seamlessly, passing information back and forth. We present simulations of the vibrational behavior of micron-scale silicon and quartz oscillators. Our results are contrasted with the predictions of continuum elastic theory as a function of size, and the failure of the continuum techniques is clear in the limit of small sizes. We also extract the Q value for the resonators and study the corresponding dissipative processes.