The electron-phonon interaction in quasi-two-dimensional semiconductor quantum-well structures

Abstract

Approximate analytic expressions are obtained for the scattering rates and momentum-relaxation rates of an electron in a quasi-two-dimensional quantum well interacting with acoustic, optical and intervalley modes via the deformation potential and with longitudinal optical modes via the polar interaction. These analytic expressions are obtained using a momentum-conservation approximation. The threshold for optical phonon emission, unlike the case in the bulk, is abrupt. All scattering rates are energy-independent and are inversely proportional to L, the thickness of the well. The momentum-relaxation rate associated with the absorption of polar optical phonons, on the other hand, proves to be proportional to L. These properties are shown to lead to a negative differential resistance for pure polar mode scattering, and to the existence of a runaway field for deformation-potential scattering. The self-energy associated with the emission of polar optical phonons at absolute zero is shown to be divergent unless the polar interaction is screened, and some consequences of this for laser and other optical processes are pointed out. The description of scattering by perturbation theory breaks down in very narrow wells.