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Atomistic Simulation of MEMS Devices via the Coupling of Length Scales

Jeremy Q. Broughton, Farid Abraham, Robert E. Rudd, Noam Bernstein, Efthimios Kaxiras

Research Objectives

Many phenomena in materials involve atomic motion on a wide range of length scales from the atomic to the mesoscopic to the macroscopic. Turbulence and crack propagation are well-known examples. The operation of Micro-Electro-Mechanical Systems (MEMS), is also governed by multi-scale atomistic processes. This Grand Challenge project is concerned with simulation of sub-micron devices and multi-length scale materials phenomena. Limitations in computer performance make molecular dynamics simulations involving more than 100 million atoms prohibitive. As the length scale increases only a decreasing fraction of the information contained in the motion of each atom is relevant to many phenomena, e.g. crack propagation, so it is unnecessary to describe the motion of all atoms on the atomic scale. This observation enables `smart' simulation techniques that hold the promise of aiding in the design of MEMS devices.

Methodology

In FY97, parallel codes that couple different physical descriptions of atomic motion on different length scales were implemented for the first time. Central to the code is a state-of-the-art molecular dynamics (MD) code that can simulate 10's of millions of atoms at finite temperature. The coupling-of-length-scales method (CLS) integrates the MD simulation with concurrent finite element (FE) and tight-binding (TB) simulations operative in adjoining spatial regions. Tight-binding Hamiltonians are used where the smallest length scales are relevant and a quantum mechanical description of the forces on atoms is required, e.g. at a crack tip. On intermediate scales, MD describes the motion of each atom which interacts with other atoms through materials-specific atomic potentials. On the longest length scales a FE simulation includes the coupling to long-wavelength elastic modes. The dynamical connection, or `handshaking,' between these different descriptions is accomplished seamlessly.








Results

A sub-micron scale quartz resonator and cracks propagating in silicon were simulated. Simulations of micro-resonators 80 Angstroms by 150 Angstroms by 2000 Angstroms at room temperature show marked effects of anharmonicity. The addition of 1% vacancies causes substantial plastic deformation. These simulations show effects that cannot be predicted from continuum elastic theory, and demonstrate that the CLS methodology can make definite predictions of device performance.

The figure shows a simulation of strain induced failure of silicon. Stress is indicated by color: the red areas are regions of lowest stress, while regions of highest stress occur at the tips of the void in the center. This demonstrates the continuity of the stress field in the bulk and absence of reflections of stress waves in passing from the region described by MD to the region described by FE, and thus, the seamless coupling of length scales.



Significance

Simulations of sub-micron scale devices and materials failure can provide support crucial to the Navy/Marine/DoD mission. Simulations may be able to predict: operating characteristics of ultra-small MEMS devices used in communications, guidance systems, smart materials, and sensors; and failure and fatigue in materials comprising turbine blades, substrates for semiconductor devices, propeller blades, and ship hulls.


Figures:

Upper: .2 micron silicon micro-resonator (Image courtesy of Prof. M. Roukes, Cal Tech).

Middle: Multi-scale simulation of .2 micron silicon micro-resonator in which 2 million silicon atoms simulated with molecular dynamics are coupled to .1 cubic microns of substrate simulated with finite elements.

Lower: Simulation of crack propagation in Silicon using the Coupling of Length Scales method. With a single simulation different methodologies are used to model different regions fo the system according to the length scale of the phenomena with each region: a quantum electronic structure algorithm (TB) models the Angstrom scale physics, an atomistic algorithm (MD) models the nanoscale physics and a finite element algorithm (FE) models nanoscale to micron-scale physics. Note that the stress waves emanating from the crack tips pass through the MD/FE interface smoothly.



Selected Papers:

  1. "Coarse-grained molecular dynamics and the atomic limit of finite elements," Robert E. Rudd and Jeremy Q. Broughton, Phys. Rev. B 58, R5893 (1998).
  2. "Coupling of Length Scales and Atomistic Simulation of a MEMS device," R.E. Rudd and J.Q. Broughton, Proc. MSM '98 (Computational Publications, Boston, 1998), pp. 287-90.
  3. "Coupling of Length Scales and Atomistic Simulation of MEMS Resonators," Robert E. Rudd and Jeremy Q. Broughton, Proc. SPIE, Vol. 3680 (DTM '99), B. Courtois, et al., eds. (SPIE, Bellingham, Washington, 1999) pp. 104-111.
  4. "Atomistic Simulation of MEMS Resonators through the Coupling of Length Scales," Robert E. Rudd and Jeremy Q. Broughton, J. Modeling and Simulation of Microsystems 1, 26 (1999).
  5. "Spanning the continuum to quantum length scales in dynamic simulation of brittle fracture," F.F. Abraham, Jeremy Q. Broughton, Noam Bernstein and Efthimios Kaxiras, Europhys. Lett. 44, 783 (1998).
  6. "Spanning of the length scales in dynamic simulation," Farid F. Abraham, Jeremy Q. Broughton, Noam Bernstein and Efthimios Kaxiras, Computers in Physics 12, (Nov/Dec 1998), pp. 538-546.
  7. "Concurrent coupling of length scales: Methodology and application," Jeremy Q. Broughton, Noam Bernstein, Efthimios Kaxiras and Farid F. Abraham, Phys. Rev. B 60, 2391 (1999).

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Maintained by Robert E. Rudd -- Last updated on 11 March 2003.
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