Validation of an Enhanced Dispersion Algorithm for Use With the Statistical Phonon Transport Model

Abstract

Abstract Computer simulations of quasi-particle based phonon transport in semiconductor materials rely upon numerical dispersion relations to identify and quantify the discrete energy and momentum states allowable subject to quantum constraints. The accuracy of such computer simulations is ultimately dependent upon the fidelity of the underlying dispersion relations. Dispersion relations have previously been computed using empirical fits of experimental data in high symmetry directions, lattice dynamics, and Density Function Theory (DFT) or Density Functional Perturbation Theory (DFPT) approaches. The current work presents high fidelity dispersion relations describing full anisotropy for all six phonon polarizations with an adjustable computational grid. The current approach builds upon the previously published Statistical Phonon Transport Model (SPTM), which employed a first nearest neighbor lattice dynamics approach for the dispersion calculation. This paper extends the lattice dynamics approach with the use of both first and second nearest neighbors interactions that are quantified using published interatomic force constants calculated from DFT. The First Brillouin Zone (FBZ) is segmented into eight octants of high symmetry, and discretized in wave vector space with a 14 by 14 by 14 grid. This results in 65,586 states of unique wave vector and frequency combinations. Dispersion calculations are performed at each of the six faces of the wave vector space volume elements in addition to the centroid, resulting in 460,992 solutions of the characteristic equations. For the given grid, on the order of 108 computations are required to compute the dispersion relations. The dispersion relations thus obtained are compared to experimental reports available for high symmetry axes. Full anisotropic results are presented for all six phonon polarizations across the range of allowable wave vector magnitude and frequency as a comprehensive model of allowable momentum and energy states. Results indicate excellent agreement to experiment in high symmetry directions for all six polarizations and illustrate an improvement as compared to the previous SPTM implementation. Dispersion relations based on the lattice dynamic model with first and second nearest neighbor atomic interactions relying upon DFT calculated inter-atomic force constants provides an accurate high fidelity energy and momentum model for use in phonon transport simulations.