Concepedia

XVII. The effect of free electrons on lattice conduction

Philosophical magazine · 1956 · 182 citations · 5 references

TL;DR

Phonon scattering by electrons in a parabolic band, relevant to p‑type germanium, irradiated sapphire, and conducting diamond, is modeled assuming the usual electron–phonon interaction with degeneracy temperature comparable to lattice temperature. An exact formula for the thermal resistance, based on electron–phonon coupling and phonon–phonon interactions, shows that only the high‑energy tail of the electron distribution contributes to scattering due to energy and momentum conservation. The phonon mean free path first decreases as 1/T (or exp(a/T) when electrons are scarce), reaches a minimum, and then rises proportionally to T² as temperature increases.

Abstract

Abstract Abstract The scattering of phonons by electrons is calculated, assuming the usual electron–phonon interaction, for a parabolic band whose degeneracy temperature is comparable with the temperature of the lattice. The contribution to the thermal resistance is given by an exact formula, subject only to justifiable assumptions concerning phonon–phonon interactions. With rising temperature the apparent mean free path of the phonons at first decreases as 1/T (or, if there are very few electrons, as exp (a/T)), but reaches a minimum and then increases as T 2. Energy and momentum conservation then allow only the tail of the electron distribution to contribute to the scattering. The model is thought to apply to certain observations on p-type germanium, irradiated sapphire and conducting diamond.