Relaxation of a two-dimensional electron gas in semiconductor thin films at low temperatures: Role of acoustic phonon confinement

We study the effect of acoustic-phonon confinement on the energy and momentum relaxation of a two-dimensional electron gas in thin films. The interaction via the deformation and piezoelectric potentials with a complete set of phonon modes in films with stress-free and rigid surfaces is taken into account. We demonstrate that in thin films the modification of the phonon properties and screening brings about substantial changes of the electron relaxation rates in comparison to the case of interaction with bulk phonons at low temperatures, where the effective reduction of the phonon spectrum dimensionality takes place. For suspended films, relaxation rates are substantially enhanced: the temperature dependence of the momentum and energy relaxation rates, in films with nonmetallized (metallized) surfaces, is found to be T-7/2 (T-5/2) for both deformation potential and piezoelectric mechanisms. The reason for such an enhancement is the strong scattering of electrons by flexural phonons having quadratic dispersion and a high density of states at low frequencies. Conversely, for films with rigid surfaces the low-temperature relaxation of electrons is exponentially suppressed due to the formation of a gap in the phonon spectrum.