Comparison of theoretical and simulation-based predictions of grain-boundary Kapitza conductance in silicon

Abstract

We present a comparison between molecular-dynamics (MD) simulation and theoretical calculations using input from wave-packet simulations of the Kapitza conductance of two different grain boundaries in silicon. We find that for a $\ensuremath{\Sigma}3(111)$ twin boundary with minimal disruption of the lattice, the Kapitza conductance is extremely high in contrast to previous results obtained for the $\ensuremath{\Sigma}29(001)$ grain boundary. Theoretical predictions based on input from wave-packet simulations appear to show reasonable agreement with MD results for the $\ensuremath{\Sigma}29(001)$ grain boundary but disagreement by a factor of about ten for the $\ensuremath{\Sigma}3(111)$ boundary. The origin of the apparent discrepancies is analogous to previously noted difficulties in comparing theoretical predictions to experimental measurements of the Kapitza conductance. We show why the apparent discrepancies are large when the interface phonon transmission is high and relatively small when the phonon transmission is low. We demonstrate how the theoretical predictions and MD simulation results can be compared in a consistent and meaningful way, thereby removing the apparent contradictions. These questions also are discussed in the important context of relating MD results to experimental observations.