Транспорт тепла фононами в модели Ландауэра–Датты–Лундстрома

Abstract

Based on the 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 thermal conductance 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 the 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.