Electron-phonon heat exchange in layered nano-systems

We analyze the heat power P from electrons to phonons in thin metallic films deposited on free-standing dielectric membranes in a temperature range in which the phonon gas has a quasi two-dimensional distribution. The quantization of the electrons wavenumbers in the direction perpendicular to the film surfaces lead to the formation of quasi two-dimensional electronic sub-bands. The electron-phonon coupling is treated in the deformation potential model. If we denote by T-e the electrons temperature and by Tph the phonons temperature, we find that P-(0)(T-e)-P-(1)(T-e,T-ph).