  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.
