Scattering of phonons from a high-energy grain boundary in silicon: Dependence on angle of incidence

We use molecular-dynamics simulation to elucidate phonon scattering from the high-energy Sigma 29 twist grain boundary in silicon. In particular, we have computed the dependence of energy transmission through the grain boundary on the wavelength and angle of incidence. Transmission through the grain boundary is found to be predominantly a function of the incident phonon frequency. In agreement with previous results, modes with wave vectors perpendicular to the grain-boundary plane exhibit relatively large energy-transmission coefficients. However, as the wavelength decreases and frequency increases, the energy transmission through the interface tends to sharply decrease. To develop a comprehensive picture of elastic phonon scattering, we have studied longitudinal-acoustic, transverse-acoustic, and some longitudinal-optical modes. By considering a simple theory that relates the energy-transmission coefficients to the Kapitza conductance, we are able to make a quantitative prediction based on detailed transmission probabilities. Predictions obtained using this model are relevant for comparison to both the classical (i.e., high-temperature) and quantum (i.e., low-temperature) regimes. We discuss the temperature dependence of the Kapitza conductance and suggest avenues of inquiry including experimental verification.