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

Abstract

AbstractThe 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.