Localized Phonon Densities of States at Grain Boundaries in Silicon

Since it is now possible to record vibrational spectra at nanometer scales in the electron microscope it is of interest to explore whether defects such as dislocations or grain boundaries will result in measurable changes of the spectra. Phonon densities of states were calculated for a set of high angle grain boundaries in silicon. Since these boundaries are modeled by supercells with up to 160 atoms, the density of states was calculated by taking the Fourier transform of the velocity-velocity autocorrelation function from molecular dynamics simulations based on new supercells doubled in each direction. In select cases the results were checked on the original supercells with fewer atoms by comparison with the densities of states obtained by diagonalizing the dynamical matrix calculated using density functional theory. Near the core of the grain boundary the height of the optic phonon peak in the density of states at 60 meV was suppressed relative to features due to acoustic phonons that are largely unchanged relative to their bulk values. This can be attributed to the variation in the strength of bonds in grain boundary core regions where there is a range of bond lengths. It also means that changes in the density of states intrinsic to grain boundaries are unlikely to affect thermal conductivity at ambient temperatures, which are most likely dominated by the scattering of acoustic phonons.