Electron Propagation in Periodic Potentials

University essay from KTH/Teoretisk fysik; KTH/Teoretisk fysik; KTH/Teoretisk fysik

Author: Klas Karis; Deborah Merzan; Jacob Wärnhjelm; [2011]

Keywords: ;

Abstract:

In this bachelor thesis we study the propagation of electrons in crystals. The crystalline

structure is modeled as a one dimensional periodic potential primarily composed of delta

function potential barriers.

We use two different models to describe how a particle behaves in such a periodic

structure. The first model is the Kronig Penney model described by S. Gasiorowicz in

[

1]. The second model is described by Olsen and Vignale in the article "The Quantum

mechanics of electric conduction in crystals" [

3]. We show that there exists certain ranges

of energy for which electron propagation can occur, namely the allowed energy bands separeted

by regions of forbidden energies. In addition, we solve the Schrödinger equation

numerically for some simple cases and reproduce some of the results seen from the two

mentioned models.

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