Electron relaxation times due to the deformation-potential interaction of electrons with confined acoustic phonons in a free-standing quantum well

The confined acoustic phonons in free-standing quantum wells are considered in detail. The Hamiltonian describing interactions of the confined acoustic phonons with electrons in the approximation of the deformation potential and the corresponding electron transition probability density are derived. They are used to analyze the electron scattering times (inverse scattering rate, momentum relaxation time, and the energy relaxation time) in the test-particle approximation as well as in the kinetic approximation. It is shown that the first dilatational mode makes the main contribution to electron scattering in the lowest electron subband. The contribution of the zeroth mode and the second mode are also essential while the modes of higher order are insignificant. Our analysis is performed for both nondegenerate and degenerate electron gases. It is shown that electron scattering by confined acoustic phonons interacting through the deformation potential is substantially suppressed up to the electron energies corresponding to the energy of the first dilatational mode.