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Using Elasticity to Correct for Boundary Effects in Calculations of Stress-Diffusion Coupling Parameters

Published online by Cambridge University Press:  26 February 2011

Brian Puchala ,
Michael Falk  and
Krishna Garikipati
Brian Puchala
Affiliation:
bpuchala@umich.edu, University of Michigan, Materials Science and Engineering, Materials Science & Engr Dept., 3062 HH Dow Bldg., 2300 Hayward St., Ann Arbor, MI, 48109, United States
Michael Falk
Affiliation:
mfalk@umich.edu, University of Michigan, Department of Materials Science and Engineering, 3062 HH Dow Bldg., 2300 Hayward, Ann Arbor, MI, 48109, United States
Krishna Garikipati
Affiliation:
krishna@umich.edu, University of Michigan, Department of Mechanical Engineering, 2250 G.G. Brown, 2350 Hayward, Ann Arbor, MI, 48109, United States
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Abstract

The effect of stress on diffusion during semiconductor processing becomes important as device dimensions shrink from microns to nanometers. Simulating these effects requires accurate parameterization of the formation and migration volume tensors of the defects that mediate diffusion on the atomistic scale. We investigate the effect of boundary conditions on the accuracy of atomistic calculations of defect formation energies and formation volume tensors. Linear elasticity provides a correction to the effect of the boundaries on the resulting relaxation volume tensor. By a formal proof we show that the correction term is zero for free boundaries and for periodic boundary conditions with zero mean boundary stress. This is demonstrated in the far field for periodic and free boundary conditions for an isotropic (vacancy) and an anisotropic (<110> intersitial) defect in Stillinger-Weber silicon. For periodic boundary conditions, formation volume tensor components converge to within 5% in a 216 atom simulation cell. For free boundary conditions, slow convergence of elastic constants results in slow convergence of formation volumes. Most significantly, this provides a new method to calculate the formation volume from constant volume calculations. This removes the need for relaxing boundaries, allowing for simpler and more efficient algorithms. We apply this method to both the vacancy and the <110> interstitial in Stillinger-Weber silicon.

Keywords

diffusionsimulationdefects
Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 978: Symposium GG – Multiscale Modeling of Materials , 2006 , 0978-GG01-03
Copyright
Copyright © Materials Research Society 2007

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