Calculation of Kapitza Resistance with Kinetic Equation

Abstract

A new method for the calculation of interfacial thermal resistance in the case of heat transport through the interface by phonons is introduced herein. The novelty of the suggested approach consists of the consideration of all the consequences of a nonequilibrium character of phonon‐distribution functions during heat transfer. The well‐described diffuse mismatch model is used to introduce a model set of transmission and reflection amplitudes of phonons at the interface. An exact analytical solution for the proposed model is derived. Finally, the problem is solved for a set of transmission and reflection amplitudes characterized by a free parameter.

Electronic Kapitza resistance and related kinetic coefficients at an interface between n-type semiconductors

“…To do so, we use the system of equations introduced in [39], adapted for electrons. The core feature of this method is the introduction of matching equations for the distribution functions at the interface.…”

“…Alike paper [39] we introduce the Chapman-Enskog conditions [47]. Since the total number of electrons is conserved, there are two such conditions, instead of one, which was the case for phonons.…”

“…To find conditions for transmission and reflection amplitudes we assume the uniform scattering at the interface. We also assume like in the paper [39], that the fraction of the energy flux dissipated in a certain direction does not depend on the angle of incidence. It yields…”

“…Now we solve the system of equations (24 -28) with the dispersion relations (29) and the set of amplitudes (30,32). The method is analogous to the one presented in [39].…”

“…Here we propose a formalism based on Boltzmann kinetic equation, which was developed for phonon heat transfer through interface [38,39]. For electrons not only the energy density and energy flux but also the electric charge and electric current are conserved.…”