Relaxation rates of electrons in a quantum well embedded in a finite-size semiconductor slab

We calculated the momentum and energy relaxation rates of 2D electrons interacting with acoustic phonons in a quantum well situated close to the surface of a semiconductor slab in which the quantum well is embedded. These rates depend on the mechanical conditions at the surface of the slab and deviate substantially from the values corresponding to a quantum well situated in the bulk of an infinite crystal. At low enough temperatures the quantization of the acoustic modes becomes important and has an effect on the relaxation rates.