Energy and momentum relaxation of two-dimensional electron gas due to near-surface deformation scattering

We model the influence of a cap layer with a fixed thickness placed on top of a semi-infinite heterostructure on the energy and momentum relaxation rates for two-dimensional electrons localized in the lowest subband of a quantum well, and interacting with the acoustic phonon via the deformation potential. The relaxation rates are derived from the corresponding balance equations for a small deviation from the thermodynamic equilibrium. Our results indicate that at low temperatures the efficiency of the scattering is changed substantially depending on the mechanical conditions at the surface; the cases of free and rigid surfaces are considered. The dependencies of the electron energy and momentum rates on the distance from the electron layer to the surface, on the temperature and electron concentration are analyzed. It is shown that the efficiencies of relaxation are changed substantially (up to two times for standard parameters of GaAs or InAs based quantum wells) depending nonmonotonically on the distance of the 2D layer to the surface and on the electron temperature.