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A nanoscale bridge-type resonator is simulated using concurrent multiscale modeling techniques. The resonator consists of a bar of semiconductor that has been etched free from the substrate so that it can oscillate. For the simulation, the resonator has been divided into regions in which atomistic physics is important and regions that are well described by continuum mechanics. The atomistic regions are simulated with MD and the continuum regions are simulated with finite element modeling. Each provides the boundary conditions for the other as the run simultaneously in the simulation.

Concurrent Multiscale Modeling of Nanoscale MEMS


Robert E. Rudd and Byeongchan Lee

Methods: Molecular Dynamics, Multiscale Simulation

The miniaturization of mechanical devices is the primary theme in the development of Micro-Electro-Mechanical Systems (MEMS). The qualitatively new possibilities afforded by these systems arise because of the precision of microscopic components, the economy of scale in semiconductor fabrication, and the emergence of new phenomena in the scaling to small sizes. The vast majority of MEMS mechanical devices operate at engineering scales of microns and larger, but a new class of MEMS devices are being developed at the nanoscale. Fundamental challenges to MEMS design arise for these ultrasmall devices, because the conventional rules for device engineering based on continuum mechanics are violated by the atomic nature of materials: the atomic-level discreteness of matter affects the behavior of ultrasmall MEMS.
This work is a theoretical study of atomistic phenomena in the context of silicon MEMS micro-resonators. The challenge of modeling these devices is compounded by the fact that the atomic-scale effects cannot be separated cleanly from larger-scale phenomena, and the system exhibits strongly-coupled multiscale behavior, governed by the interplay between physics at the Angstrom, nanometer and micron scales. A direct, atomistic simulation of the billions of atoms involved is prohibitive, and it would be inefficient. Instead, we have developed a new concurrent multiscale methodology, which uses finite elements to model processes in the substrate and atomistics to model processes in the smallest features of the device. The two are run concurrently to attain a self-consistent model of the entire system.
In this work we have conducted simulations of the vibrational behavior of micron-scale oscillators. We find anomalous surface effects that are due to atomistic processes. They show up in temperature-dependent shifts of the resonant frequency, degradation of the quality factor (increased dissipation) and extreme compliance. These 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 nanoscale MEMS.

SELECTED PUBLICATIONS


  1. R.E. Rudd, "Coarse-grained molecular dynamics for computer modeling of nanomechanical systems," Intl. J. on Multiscale Comput. Engin. 2, 203-220 (2004).
  2. R.E. Rudd and J.Q. Broughton, "Concurrent Coupling of Length Scales in Solid State Systems," Phys. Stat. Sol. (b) 217, 251 (2000).
  3. R.E. Rudd and J.Q. Broughton, "Coarse-grained molecular dynamics and the atomic limit of finite elements," Phys. Rev. B 58, R5893 (1998).
  4. R.E. Rudd and J.Q. Broughton, "Atomistic Simulation of MEMS Resonators through the Coupling of Length Scales," J. Modeling and Simulation of Microsystems 1, 29 (1999).

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Maintained by Robert E. Rudd -- Last updated on 27 March 2006.
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