Variational approach to solving the phonon Boltzmann transport equation for analyzing nanoscale thermal transport experiments

Abstract

Over time, technology has shrunk to smaller length scales, and as a result the heat transport in these systems has entered the nanoscale regime. With increasing computational speed and power consumption, there is a need to efficiently dissipate the heat generated for proper thermal management of computer chips. The ability to understand the physics of thermal transport in this regime is critical in order to model, engineer, and improve the performance of materials and devices. In the nanoscale regime, thermal transport is no longer diffusive, and the Fourier heat conduction equation, which we commonly utilize at the macroscale, fails to accurately predict heat flow at the nanoscale. We model the heat flow due to phonons (crystal lattice vibrations), the dominant heat carriers in semiconductors and dielectrics, by solving the Boltzmann transport equation (BTE) to develop an understanding of nondiffusive thermal transport and its dependence on the system geometry and material properties, such as the phonon mean free path. A variety of experimental heat transfer configurations have been established in order to achieve short time scales and small length scales in order to access the nondiffusive heat conduction regime. In this thesis, we develop a variational approach to solving the BTE, appropriate for different experimental configurations, such as transient thermal grating (TTG) and time-domain thermoreflectance (TDTR). We provide an efficient and general methodology to solving the BTE and gaining insight into the reduction of the effective thermal conductivity in the nondiffusive regime, known as classical size effects. We also extend the reconstruction procedure, which aims to utilize both modeling efforts as well as experimental measurements to back out the material properties such as phonon mean free path distributions, to provide further insight into the material properties relevant to transport. Furthermore, with the developed methodology, we aim to provide an analysis of experimental geometries with the inclusion of a thermal interface, to provide insight into the role the interface transmissivity plays in thermal transport in the nondiffusive regime. Lastly, we explore a variety of phonon source distributions that are achieved by heating a system, and show the important link between the system geometry and the distribution of phonons initiated by the heating. We show the exciting possibility that under certain nonthermal phonon distributions, it is possible to achieve enhanced thermal transport at the nanoscale, contrary to the current understanding of size effects only leading to reduced thermal conductivities at the nanoscale for thermal phonon distributions.