Heat conduction for dielectric thin films from the Casimir to diffusion limit
Master of Science
The heat transfer in electrically insulating thin film materials is predominantly governed by phonons and is accurately described when the phonon mean free path is either much smaller than the order of the thickness of the material (the thick limit) or when there is no phonon scattering (the thin limit). The thick limit model, which is referred to as Fourier's equation, and the thin limit model, which is referred to as the Casimir limit, differ primarily in the distribution function used to describe the excitation state of phonons. This difference arises because scattering alters the excitation levels of the phonons. Whereas the Fourier's equation phonon distribution function is derived using the Boltzmann transport equation, the Casimir limit phonon distribution is given by the Bose-Einstein statistics. This paper first relates the elastic properties of a solid to the phonon description of a crystal's energy to obtain the phonon distribution using the Boltzmann Transport Equation. It will then explain why Fourier's equation breaks down at the nano/microscale level and develop a general heat flux equation which also describes the regime between the Casimir limit and Fourier's Equation.
Mechanical engineering; Condensed matter physics