Monte Carlo Study of Phonon Transport in Solid Thin Films Including Dispersion and Polarization

TLDR

The Boltzmann Transport Equation (BTE) is the most accurate model for phonon heat flow in solid nonmetallic thin films, but its general form is analytically and numerically challenging, and prior solutions have often ignored dispersion and polarization coupling. This study introduces a comprehensive Monte Carlo method to solve the full BTE for phonon transport in thin films. The method models dual phonon polarizations, nonlinear dispersion, and individual scattering processes—including branch transitions and phonon creation/destruction—and is validated across diffusive to ballistic regimes. Validation against silicon thin‑film experiments shows close agreement, and simulations reveal that above 100 K transverse acoustic phonons dominate energy transport.

Abstract

The Boltzmann Transport Equation (BTE) for phonons best describes the heat flow in solid nonmetallic thin films. The BTE, in its most general form, however, is difficult to solve analytically or even numerically using deterministic approaches. Past research has enabled its solution by neglecting important effects such as dispersion and interactions between the longitudinal and transverse polarizations of phonon propagation. In this article, a comprehensive Monte Carlo solution technique of the BTE is presented. The method accounts for dual polarizations of phonon propagation, and non-linear dispersion relationships. Scattering by various mechanisms is treated individually. Transition between the two polarization branches, and creation and destruction of phonons due to scattering is taken into account. The code has been verified and evaluated by close examination of its ability or failure to capture various regimes of phonon transport ranging from diffusive to the ballistic limit. Validation results show close agreement with experimental data for silicon thin films with and without doping. Simulation results show that above 100 K, transverse acoustic phonons are the primary carriers of energy in silicon.