Managing thermal energy generation and transfer within the nanoscale devices (transistors) of modern microelectronics is important as it limits speed, carrier mobility, and affects reliability. Application of Fourier’s Law of Heat Conduction to the small length and times scales associated with transistor geometries and switching frequencies doesn’t give accurate results due to the breakdown of the continuum assumption and the assumption of local thermodynamic equilibrium. Heat conduction at these length and time scales occurs via phonon transport, including both classical and quantum effects. Traditional methods for phonon transport modeling are lacking in the combination of computational efficiency, physical accuracy, and flexibility. The Statistical Phonon Transport Model (SPTM) is an engineering design tool for predicting non-equilibrium phonon transport. The goal of this work has been to enhance the models and computational algorithms of the SPTM to elevate it to have a high combination of accuracy and flexibility. Four physical models of the SPTM were enhanced. The lattice dynamics calculation of phonon dispersion relations was extended to use first and second nearest neighbor interactions, based on published interatomic force constants computed with first principles Density Functional Theory (DFT). The computation of three phonon scattering partners (that explicitly conserve energy and momentum) with the inclusion of the three optical phonon branches was applied using scattering rates computed from Fermi’s Golden Rule. The prediction of phonon drift was extended to three dimensions within the framework of the previously established methods of the SPTM. Joule heating as a result of electron-phonon scattering in nanoscale electronic devices was represented using a modal specific phonon source that can be varied in space and time. Results indicate the use of first and second nearest neighbor lattice dynamics better predicted dispersion when compared to experimental results and resulted in a higher fidelity representation of phonon group velocities and three phonon scattering partners in an anisotropic manner. Three phonon scattering improvements resulted in enhanced fidelity in the prediction of phonon modal decay rates across the wavevector space and thus better representation of non-equilibrium behavior. Comparisons to the range of phonon transport modeling approaches from literature verify that the SPTM has higher phonon fidelity than Boltzmann Transport Equation and Monte Carlo and higher length scale and time scale fidelity than Direct Atomic Simulation. Additional application of the SPTM to both a 1-d silicon nanowire transistor and a 3-d FinFET array transistor in a transient manner illustrate the design capabilities. Thus, the SPTM has been elevated to fill the gap between lower phonon fidelity Monte Carol (MC) models and high fidelity, inflexible direct quantum simulations (or Direct Atomic Simulations (DAS)) within the field of phonon transport modeling for nanoscale electronic devices. The SPTM has produced high fidelity device level non-equilibrium phonon information in a 3-d, transient manner where Joule heating occurs. This information is required due to the fact that effective lattice temperatures are not adequate to describe the local thermal conditions. Knowledge of local phonon distributions, which can’t be determined from application of Fourier’s law, is important because of effects on electron mobility, device speed, leakage, and reliability.

Library of Congress Subject Headings

Phonons--Mathematical models; Transport theory--Mathematical models; Heat--Transmission

Publication Date


Document Type


Student Type


Degree Name

Engineering (Ph.D.)

Department, Program, or Center

Engineering (KGCOE)


Edward C. Hensel

Advisor/Committee Member

Risa J. Robinson

Advisor/Committee Member

Michael Schertzer


RIT – Main Campus

Plan Codes