Dynamics of electron temperature and the relaxation times of electron–phonon system of a metal film

Abstract

A nonlinear integro-differential dynamic equation for electron temperature Te has been obtained for the case of transient heating of a metal film at low temperatures. The equation describes the process of heat transfer from electrons to phonons and the exchange of phonons between the film and the substrate. The heating of the film by a low-power oscillating thermal source has been thoroughly considered. Within the framework of linear response, we have established a relation between the frequency dispersion of the amplitude of Te and the characteristic time of electron–phonon collisions (τe) as well as the mean phonon escape time from the film (τes). In the next (quadratic) order of the perturbation theory, we have obtained a dc correction to Te and demonstrated that its frequency dependence also contains information about the times τe and τes. The results have been extended to dirty metal films. Various possibilities of the experimental determination of the times τe and τes have been discussed.