Heat transfer by phonons in the generalized transport model

Authors: Kruglyak Yu. A., Shtefan N. Z.

Year: 2017

Issue: 22

Pages: 107-119

Abstract

On the basis of Landauer – Datta – Lundstrom transport model the generalized model of heat transfer by phonons is formulated. Similarly to the Fermi window for electron conductivity the concept of the Fermi window for phonon conductivity is introduced and used to obtain the general expression for the lattice thermal conductivity with the quantum of thermoconductance appearing at the very beginning. There are emphasized the similarity and differences in the construction of the theory of electron conductivity and the theory of heat conduction. There are discussed the thermal conductivity of the conductors, the physical sense of proportionality between the thermal conductivity and specific heat capacity at constant volume, the relationship between the transmission coefficient and the mean-free-path, the calculation of the number of phonon modes and density of phonon states, the Debye model of heat conductivity and scattering of phonons, the temperature dependence of the lattice thermal conductivity, the difference between the lattice thermal conductivity and electron conduction, and quantization of thermal conductivity.

In the present review it is emphasized that the concepts used to describe the electron transport can be successfully transferred to the phonon transport. And in both cases the Landauer approach, generalized subsequently by Datta and Lundstrom, allows a quantitative description of transport processes in conductors of any dimension and in all modes of transport from diffusive to ballistic. Lattice thermal conductivity and electronic conductivity are described very similar as far as the shape of corresponding equations. There are, however, two significant differences related to the physics of electron and phonon processes which are also emphasized in the review.

Tags: Debye model; nanoelectronics; nanophysics; phonon modes; phonon scattering; phonon transport; quantum thermal conductivity; transmission coefficient; дифузійно-дрейфова модель; молекулярна електроніка; нанофизика; наноэлектроника; роль контактів; струм насичення

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