Effects of vacancy defects on thermal conductivity in crystalline silicon: A nonequilibrium molecular dynamics study

Abstract

We examine the effects of vacancy defects on thermal conductivity in bulk crystalline silicon ($c$-Si) using nonequilibrium molecular dynamics simulations. While most vacancies are thought to remain in the form of clusters in bulk $c$-Si, recent theoretical studies have predicted that small vacancy clusters energetically prefer to be fourfold coordinated by nullifying dangling bonds. Hence, in this work, we consider three different-sized fourfold vacancy clusters, tetra- (${V}_{4}$), hexa- (${V}_{6}$), and dodeca-vacancy (${V}_{12}$), with particular interest in studying how phonon transport is affected by vacancy concentration and cluster size in association with fourfold coordination-induced lattice distortions. Our simulations show that thermal conductivity (\ensuremath{\kappa}) rapidly drops with vacancy concentration (${n}_{v}$) with an inverse power-law relation ($\ensuremath{\kappa}\ensuremath{\propto}{n}_{v}^{\ensuremath{-}\ensuremath{\alpha}}$, with $\ensuremath{\alpha}$ \ensuremath{\approx} 0.7--1.1 depending on cluster size); the presence of 1.5% vacancies leads to a 95% reduction in \ensuremath{\kappa} as compared to the defect free $c$-Si. When ${n}_{v}$ is low (1%), the reduction of \ensuremath{\kappa} with ${n}_{v}$ appears to be a function of cluster size, and the size effect becomes unimportant as ${n}_{v}$ increases above 1%. We discuss the correlation between phone scattering and cluster size, based on the relative rates of phonon-vacancy scattering associated with defect-induced strain fields. We also estimate the dependence of phonon mean free path on vacancy concentration and cluster size.