| This dissertation deals with the thermal properties of semiconductors, the interaction between thermal and electrical transport, and the numerical methods for their simulation. The approach is based on the Boltzmann transport equation which is used to describe the behavior of both electrons and phonons and their interaction with each other, as well as their interaction with external potentials by coupling the transport equations with the Poisson equation. Several methods of solving the transport equations and simulating charge and thermal transport are developed and utilized. For one-dimensional systems like carbon nanotubes, the equations for transport and potentials are discretized in space, momentum, and time, and solved by an explicit upwind method. For the simulation of devices like MOSFETs, the full-band Monte Carlo method is extended to include the full phonon dispersion relationship and the transport of phonons, while the interactions between phonon modes are based on perturbation theory. Coupling between electrons and optical phonons, and their subsequent decay toward equilibrium, are found to play a large role in determining the temperature distributions in silicon devices. High electric fields cause strong emission of g-process longitudinal optical phonons. Their low velocity and the time taken to decay into intermediate longitudinal and transverse acoustic phonon pairs cause a peak in the temperature distribution in the drain region of MOSFETs. Anharmonic three-phonon decay and the use of the full dispersion relationship allow a detailed simulation of heat transfer and determination of temperature maps in silicon devices. Methods presented herein are applicable to a wide range of semiconductor materials including compound semiconductors, as well as many geometries such as bulk and nanowires. |
