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

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018. ; Cataloged from PDF version of thesis. ; Includes bibliographical references (pages 133-140). ; 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 ...