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

A nonlinear integro-differential dynamic equation for electron temperature T-e 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 T-e and the characteristic time of electron-phonon collisions (tau(e)) as well as the mean phonon escape time from the film (tau(es)). In the next (quadratic) order of the perturbation theory, we have obtained a dc correction to T-e and demonstrated that its frequency dependence also contains information about the times tau(e) and tau(es). The results have been extended to dirty metal films. Various possibilities of the experimental determination of the times tau(e) and tau(es) have been discussed. (C) 2013 AIP Publishing LLC