Using Elasticity to Correct for Boundary Effects in Calculations of Stress-Diffusion Coupling Parameters
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0978-GG01-03
Using Elasticity to Correct for Boundary Effects in Calculations of Stress-Diffusion Coupling Parameters Brian Puchala1, Michael Falk2, and Krishna Garikipati3 1 Department of Materials Science and Engineering, University of Michigan, 3062 HH Dow Bldg., 2300 Hayward St., Ann Arbor, MI, 48109 2 Department of Materials Science and Engineering, University of Michigan, 3062 HH Dow Bldg., 2300 Hayward, Ann Arbor, MI, 48109 3 Department of Mechanical Engineering, University of Michigan, 2250 G.G. Brown, 2350 Hayward, Ann Arbor, MI, 48109
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 ( 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 interstitial in Stillinger-Weber silicon. INTRODUCTION Because of its technological significance, understanding diffusion mechanisms in silicon and other semiconductor materials has been the focus of a large body of scientific work. As device dimensions decrease from microns to nanometers, high doping concentrations and very abrupt doping profiles are required to keep resistances low [1]. Dopants introduced by ion implantation create damage in the form of vacancies and interstitials and high temperature anneals are required to repair the damage and allow the dopants to diffuse to substitutional positions where they become electrically activated. Precise control of diffusion during fabrication is necessary and stress effects become increasingly important. Significant complex stress states can arise from strain-engineered epitaxial layers, lattice and thermal expansion coefficient mismatch, growth stresses, interfacial stresses, dislocations, and defect concentrations [2,3]. The effects of these stresses, and the associated and increasingly large stress gradients,
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