Electron-phonon interaction and lattice thermal conductivity

Abstract

Phonons in a metal have a finite lifetime due to the emission of electron-hole pairs. This process leads to an electron-phonon contribution ${W}_{\mathrm{ep}}^{p}$ to the thermal resistance, which limits the lattice thermal conductivity ${\ensuremath{\kappa}}_{p}$. We present a summary of the available experimental data on ${W}_{\mathrm{ep}}^{p}$, emphasizing uncertainties and contrasting results from different types of experiments. Methods of obtaining better data are suggested. We show that the available data are in fair agreement with a simple theoretical estimate $\mathrm{lim}(T\ensuremath{\rightarrow}O){W}_{\mathrm{ep}}^{p}{(\frac{T}{{\ensuremath{\theta}}_{D}})}^{2}=0.42 {\ensuremath{\Omega}}_{a}^{\frac{1}{3}}N\ensuremath{\lambda}$(K cm/W), where ${\ensuremath{\Omega}}_{a}$ is the atomic volume in ${\mathrm{\AA{}}}^{3}$, $N$ is the Fermi-energy density of states (1 spin) in states/eV, and $\ensuremath{\lambda}$ is the electron-phonon mass enhancement. The fact that most of the experimental points fall below this estimate is probably the result of anisotropy and mode dependence of the electron-phonon coupling.