Superlattice electron wave optics

Abstract

Starting from fundamental principles, quantitative analogies between electron waves in semiconductor materials and electromagnetic waves in dielectrics are presented. This in turn suggests a new class of electron wave optical devices such as narrowband superlattice interference filters. Phase effects associated with an electron wave are incorporated using the electron wave vector, which is proportional to the square root of the product of the effective mass and the electron kinetic energy. It is shown that the amplitude of a free electron wave is analogous to the electric field of a TE polarized electromagnetic wave in a dielectric. Amplitude effects associated with an electron wave are incorporated, using an effective amplitude refractive index that is proportional to the square root of the ratio of the kinetic energy to the effective mass. A simple expression for the critical angle for total internal reflection of an electron wave is developed. By analogy to the electromagnetic optical case, the overall electron transmissivity and reflectivity of a semiconductor superlattice are determined.