BALLISTIC ELECTRON-TRANSPORT IN SEMICONDUCTOR HETEROSTRUCTURES AND ITS ANALOGIES IN ELECTROMAGNETIC PROPAGATION IN GENERAL DIELECTRICS

Developments in growth and fabrication technology have produced semiconductor structures with ballistic (collisionless) transport lengths of over a micron. In this paper, a comprehensive set of analogies is established between ballistic electron wave propagation in semiconductors (arbitrary kinetic energy and effective mass) and electromagnetic propagation in general dielectrics (arbitrary permittivity and permeability.) First, electromagnetic results for propagation in nonmagnetic dielectrics are generalized to describe propagation, reflection, and refraction in general dielectrics through the definition of separate phase and amplitude refractive indexes. The expressions for electron wave propagation, reflection, and refraction are then developed and are 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 Ga1-xAlxAs 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. This is the first prediction of an electron wave Brewster angle in semiconductors.