Submicrometer phonon systems are becoming increasingly relevant in modern day technology. Phonon mechanisms are notably relevant in a number of solid-state devices including lasers, LEDs, transistors, and thermoelectrics. Proliferation of these devices has been driven by advancements in silicon-on-insulator technology. These advancements have allowed for the manufacture of devices with complex nanostructures and dimensions deep in the sub-microscale regime. However, accompanying improvements in the manufacture and design of novel crystalline systems is the requirement for accurate computational approaches for phonon modeling in nanostructured, anisotropic, and complex materials. The phonon Boltzmann transport equation is uniquely well suited to modeling energy transfer at the nano- and micro- meter length scales and is therefore an excellent candidate for this simulation task. However, current Boltzmann modeling approaches utilize a range of assumptions and simplifications that restrict their validity to isotropic, nominally one or two dimensional, or compositionally simple systems.

In this dissertation we present an original finite volume-based methodology for the solution of the three dimensional full Brillouin zone phonon Boltzmann transport equation. This methodology allows for separate real and reciprocal space discretization. By taking a sampling of vibrational modes throughout the first Brillouin zone our methodology captures three unique sources of phonon anisotropy. We investigate the effect of phonon anisotropy in a fin field effect transistor, calculating the effect that incorporating various sources of anisotropy has on the resultant temperature fields.

In a second study, we consider phonon flow through silicon nanowires with a modified boundary geometry. The three-dimensional flow fields are calculated and thermal transport below the Casimir limit is observed. Reduction in thermal conductivity is a result of maximizing the phonon backscatter that occurs in our phononic system. The backscatter serves to create regions of highly misaligned phonon flux. In addition, our silicon nanowire geometry has properties analogous with a high-pass phonon filter.

In the final study we apply our Boltzmann transport methodology to the simulation of phonon transport in the energetic material, RDX. We study phonon transport in the vicinity of a material hotspot, the location at which chemistry initiates in the material. By applying Boltzmann modeling, applied for the first time to this material, we gain valuable insights into the interplay between thermal transport and phonon modes linked with initiation.