Extensions to the Kronig-Penney model

Author

Nussbaum, Allen

Author_Institution

Dept. of Electr. Eng., Minnesota Univ., Minnapolis, MN, USA

Volume

33

Issue

4

fYear

1990

fDate

11/1/1990 12:00:00 AM

Firstpage

359

Abstract

The Kronig-Penney model uses a periodic array of rectangular wells to deduce the existence of semiconductor energy bands from the solution of the corresponding Schroedinger equation. As part of this procedure, it is necessary to then solve a messy transcendental equation; this difficulty was surmounted by replacing the rectangular array with delta function potentials. The author describes two methods for presenting this topic at the undergraduate level. The first involves solving the one-dimensional Schroedinger equation with a rather complicated potential proposed by W. Prokovjev (1929). The second method uses a quadratic potential in the radial Schroedinger equation

Keywords

Kronig-Penney model; education; semiconductors; teaching; Kronig-Penney model; Schroedinger equation; delta function potentials; education; one-dimensional; periodic array; quadratic potential; rectangular wells; semiconductor energy bands; teaching; transcendental equation; undergraduate; Energy states; Equations; Function approximation; Lattices; Notice of Violation; Physics; Semiconductor devices; Silicon; Solid modeling; Solid state circuits;

fLanguage

English

Journal_Title

Education, IEEE Transactions on

Publisher

ieee

ISSN

0018-9359

Type

jour

DOI

10.1109/13.61090

Filename

61090