Ballistic electron transport in semiconductor heterostructures and its analogies in electromagnetic propagation in general dielectrics

A comprehensive set of analogies between ballistic electron wave propagation in semiconductors (arbitrary kinetic energy and effective mass) and electromagnetic propagation in general dielectrics (arbitrary permittivity and permeability) is established. The expressions for electron wave propagation, reflection, and refraction are developed and shown to have the same functional form as in electromagnetics, if analogous definitions of electron wave phase and amplitude refractive indexes are used. The reflectivity characteristics such as total internal reflection (critical angle) and zero reflectivity (Brewster angle) are analyzed as a function of material parameters for both general dielectrics and semiconductor materials. The critical angle and Brewster angle results are then applied to electron wave propagation in Ga_1-xAl_xAs, where it is shown that all interfaces in this material will have both a critical angle and a Brewster angle due to differing effective masses across the interface