Electron wave optics in semiconductors

Abstract

Starting from fundamental principles, quantitative analogies between quantum mechanical electron waves in semiconductor materials and electromagnetic optical waves in dielectrics are presented. This, in turn, suggests many new classes of electron wave optical devices such as narrow-band superlattice interference filters. Phase effects associated with an electron wave are incorporated using an ‘‘electron wave phase refractive index’’ that is proportional to the square root of the product of the electron effective mass and the electron kinetic energy. It is shown that the amplitude of an electron wave is analogous to the electric field of a TE polarized electromagnetic wave (or to the magnetic field of a TM polarized electromagnetic wave) in a dielectric. Amplitude effects associated with an electron wave are incorporated using an ‘‘electron wave 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 total electron transmissivity and reflectivity of a semiconductor superlattice is presented. For illustration, an electron wave interference filter that is the counterpart of a multilayer quarter-wave stack thin-film optical interference filter is designed as a variable band gap and variable thickness semiconductor superlattice. Numerous new electron optical devices are suggested.