Simulation of Unsteady Small Heat Source Effects in Sub-Micron Heat Conduction

TLDR: In this article, the authors present a study of hot spot behavior in the phonon Boltzmann transport equation (BTE) in the retardation fiber approximation using a finite volume method.

Abstract: In compact transistors, large electric fields near the drain side create hot spots whose dimensions are smaller them the phonon mean free path in the medium. In this paper we present a study of unsteady hot spot behavior. The unsteady gray phonon Boltzmann transport equation (BTE) is solved in the retardation fibre approximation using a finite volume method. Electron-phonon interaction is represented as a heat source term in the phonon BTE. The evolution of the temperature profile is governed by the interaction of four competing time scales: the phonon residence time in the hot spot and in the domain, the duration of the energy source, and the phonon relaxation time. The influence of these time scales on the temperature is investigated. Both boundary scattering and heat source localisation effects are observed to have considerable impact on the thermal predictions. Comparison of BTE solutions with conventional Fourier diffusion analysis reveals significant discrepancies.