BOLTZMANN TRANSPORT EQUATION BASED MODELING OF PHONON HEAT CONDUCTION: PROGRESS AND CHALLENGES
Sandip Mazumder
Abstract
Heat conduction in crystalline materials occurs primarily due to propagating vibrational waves, quantized as phonons. At submicron scales, the phonon mean free paths are often larger than or comparable to the size of the device or system under scrutiny − a regime in which the Fourier law of heat conduction is invalid. The phonon Boltzmann transport equation (BTE) offers an alternative pathway to modeling thermal transport in semiconductor materials at the submicron scale. Unfortunately, the BTE is a seven-dimensional (time, three space variables, two directional variables, and frequency) equation, and is difficult to solve. This paper reviews the progress that has been made to date in solving the phonon BTE along with the challenges facing the present research community. Both deterministic and stochastic (Monte Carlo) methods are reviewed. Beginning with an overview of the various methods for solving the BTE, the paper delves into some of the nuances of each method and their respective pros and cons. Several important applications, including use of the BTE in interpreting state-of-the-art pump probe experimental data, are discussed. Challenges that need to be overcome to make the BTE a viable tool for modeling thermal transport in practical engineering devices are highlighted.