Low-temperature anomalous specific heat without tunneling modes: A simulation fora−Siwith voids

Abstract

Using empirical potential molecular dynamics we compute dynamical matrix eigenvalues and eigenvectors for a 4096 atom model of amorphous silicon and a set of models with voids of different sizes based on it. This information is then employed to study the localization properties of the low-energy vibrational states, calculate the specific heat $C(T),$ and examine the low-temperature properties of our models usually attributed to the presence of tunneling states in amorphous silicon. The results of our calculations for $C(T)$ and ``excess specific-heat bulge'' in the ${C(T)/T}^{3}$ vs T graph for voidless $a\ensuremath{-}\mathrm{Si}$ appear to be in good agreement with experiment; moreover, our investigation shows that the presence of localized low-energy excitations in the vibrational spectrum of our models with voids strongly manifests itself as a sharp peak in ${C(T)/T}^{3}$ dependence at $T<3 \mathrm{K}.$ To our knowledge this is the first numerical simulation that provides adequate agreement with experiment for the very-low-temperature properties of specific heat in disordered systems within the limits of harmonic approximation.