Equivalent network approach for electron wave propagation and its applications

Abstract

With a view to exploring the analysis and design method which provides a good engineering perspective for electron wave devices using the quantum effect phenomena, the electron wave propagation is formulated from a circuit theory viewpoint. In this paper, the electron wave obliquely incident on the heterointerface is treated. First, the quantum mechanical quantities are transformed to the electromagnetic quantities. Then the transmission line equation and the equivalent circuit for the electron wave propagation are derived. Next, the problem of propagation of the electron wave obliquely incident on the heterointerface is studied in detail by means of its equivalent circuit. The reflection and transmission coefficients and the reflection and transmission probabilities are then calculated. At the same time, the conditions for existence of the Brewster angle and the critical angle for the total reflection are described. Evaluation of the Goos-Hänchen shift is also carried out. Further, it is shown that the eigenvalue equation for the guided mode in the electron waveguide can easily be derived by the application of the transverse resonance condition well known in circuit theory. The problem of propagation of the electron waves normally incident on the heterointerface such as in the quantum well and the potential barrier are contained in the present formulation as a special case.