The effects of vacancy defects upon thermal conductivity in bulk crystalline silicon (c-Si) were examined using non-equilibrium molecular dynamics simulations. While most vacancies were thought to remain in the form of clusters in bulk c-Si, recent theoretical studies had predicted that small vacancy clusters energetically prefer to be fourfold coordinated by nullifying dangling bonds. Hence, three different-sized fourfold vacancy clusters, tetra- (V4), hexa- (V6), and dodeca-vacancy (V12) were considered here, with particular emphasis on studying how phonon transport was affected by vacancy concentration and cluster size in association with fourfold coordination-induced lattice distortions. The simulations showed that thermal conductivity (κ) rapidly drops with vacancy concentration (nv) with an inverse power-law relation (κ∝nv-α, with α ≈ 0.7–1.1 depending on cluster size); the presence of 1.5% vacancies led to a 95% reduction in κ as compared to the defect free c-Si. When nv was low (<1%), the reduction of κ with nv appeared to be a function of cluster size, and the size effect became unimportant as nv increased above 1%. The correlation between phonon scattering and cluster size, based upon the relative rates of phonon-vacancy scattering associated with defect-induced strain fields, was considered. The dependence of phonon mean free path upon vacancy concentration and cluster size was also estimated.

Effects of Vacancy Defects on Thermal Conductivity in Crystalline Silicon - a Nonequilibrium Molecular Dynamics Study. Y.Lee, S.Lee, G.S.Hwang: Physical Review B, 2011, 83[12], 125202