Phonon transport in micro- nanoscale crystalline materials can be well modeled by the Boltzmann transport equation (BTE). The complexities associated with solving the BTE have led to the development of various numerical models to simulate phonon transport. These models have been applied to predict thermal transport from the di¤use to ballistic regime. While some success using techniques such as the Monte Carlo method has been achieved, there are still a significant number of approximations related to the intricacies of phonon transport that must be more accurately modeled for better predictions of thermal transport at reduced length scales. The objective of the present work is to introduce a Statistical Phonon Transport (SPT) model for simulating thermal transport in crystalline materials from the diffuse to ballistic regime. The SPT model provides a theoretically more realistic treatment of phonon transport physics by eliminating some of the common approximations utilized by other numerical modeling techniques. The SPT model employs full anisotropic dispersion. Phonon populations are modeled without the use of scaling factors or pseudo-random number generation. Three-phonon scattering is rigorously enforced following the selection rules of energy and pseudo-momentum. The SPT model provides a flexible framework for incorporating various phonon scattering mechanisms and models. Results related to the determination of allowable three-phonon interactions are presented along with several three-phonon scattering models. Steady-state and transient thermal transport results for silicon from the diffuse to ballistic regimes are presented and compared to analytical and experimental results. Recommendations for future work related to increasing the robustness of the SPT model as well as utilizing the SPT model to predict thermal transport in practical applications are given.

Library of Congress Subject Headings

Phonons--Mathematical models; Transport theory--Mathematical models; Fluid dynamics--Mathematical models

Publication Date


Document Type


Student Type


Degree Name

Microsystems Engineering (Ph.D.)

Department, Program, or Center

Microsystems Engineering (KGCOE)


Hensel, Edward


Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works. Physical copy available through RIT's The Wallace Library at: QC176.8.P5 B76 2012


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