Coupling of Length Scales and Atomistic Simulation of MEMS Resonators

TL;DR

This paper introduces a multiscale simulation method coupling atomistic and continuum models to accurately analyze the vibrational behavior of MEMS resonators, revealing limitations of traditional continuum theories at small scales.

Contribution

The paper presents a novel multiscale simulation approach combining atomistic and finite element methods for MEMS, enabling detailed analysis of nanoscale effects.

Findings

Atomistic simulations reveal deviations from continuum predictions at small sizes.

The coupled approach efficiently models large MEMS devices with atomic detail in critical regions.

Q values and dissipation mechanisms are characterized for silicon and quartz resonators.

Abstract

We present simulations of the dynamic and temperature dependent behavior of Micro-Electro-Mechanical Systems (MEMS) by utilizing recently developed parallel codes 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. We study the vibrational behavior of one class of MEMS devices: micron-scale resonators made of silicon and quartz. The algorithmic and computational avenue applied here represents a significant departure from the usual finite element approach based on continuum elastic theory. The approach is to use an atomistic simulation in regions of significantly anharmonic forces and large surface area to volume ratios or where internal friction due to defects is anticipated. Peripheral regions of MEMS which are well-described by continuum elastic theory are simulated using finite elements for efficiency. Thus, in central regions of the device, the motion of millions of individual atoms is simulated, while the relatively large peripheral regions are modeled with finite elements. The two techniques run concurrently and mesh seamlessly, passing information back and forth. This coupling of length scales gives a natural domain decomposition, so that the code runs on multiprocessor workstations and supercomputers. We present novel 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.