Electron Wave Function in Semiconductor Crystal

Abstract

The research on semiconductor crystal is a combination of solid-state physics and quantum physics. In this area, Bloch's theorem can be used to describe the periodic structure of crystals, and Schrödinger's equation can be used to describe the energy distribution of free electrons. This paper attempts to combine the two to quantitatively calculate the electron wave function in semiconductor crystals. The main research problem of this paper is to confirm the electron wave function in semiconductor crystals. This paper adopts the method of perturbation theory, using Bloch's theorem and Schrödinger equation to handle with the Kronig-Penney model. Finally, the effective mass of electrons in semiconductor crystals was obtained. This paper uses some advanced mathematical knowledge in this process, such as Taylor expansion and second-order non-degenerate perturbation theory. This mathematical knowledge played a large role in the derivation process. This work demonstrates that the Bloch’s theorem serves as a useful approach to handle a series of quantum-mechanical problems in solid-state physics.