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Theory of the Valence Band Energy Level Structures of Germanium and Silicon in an External Magnetic Field

Citation

Evtuhov, Viktor (1961) Theory of the Valence Band Energy Level Structures of Germanium and Silicon in an External Magnetic Field. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-08092007-144751

Abstract

The problem of the valence band structure of Ge and Si in the presence of an external magnetic field is considered from a quantum mechanical point of view. The analysis is carried out using first and second order perturbation theory. The approach is, in principle, similar to that of W. Shockley and E. O. Kane, but is modified in some important essentials to include the effects of the magnetic field. The analytical results obtained are somewhat more general than those of J. M. Luttinger but reduce to the latter if certain approximations are introduced. Numerical calculations of the Landau energy levels are carried out for certain special cases, of which the most important are the following:

1. Magnetic field ϰ in the [001] direction, kH = 0; nonspherical symmetry character of energy bands and the coupling of V1 and V2 bands to the V3 band included.

2. Magnetic field ϰ in the [001] direction, kH ≠ 0; nonspherical symmetry character of energy bands included, decoupling of V1 and V2 bands from the V3 band assumed.

In addition, a set of algebraic equations is derived whose solution should yield the valence band Landau levels for the cases of the magnetic field in the [101] and the [111] directions. However, no numerical calculations are performed for these cases.

The results of the calculations indicate the presence of some interesting transitions between the Landau levels of Ge and Si, as well as the possible presence of other interesting effects which may be observable. Certain of these seem to offer potential millimeter-wave applications possibilities, some of which are discussed.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Electrical Engineering; Physics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Minor Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Gould, Roy Walter
Thesis Committee:
  • Gould, Roy Walter
Defense Date:1 October 1960
Additional Information:Thesis title listed in 1961 Commencement Program varies from actual thesis: Theory of the Valence Band Energy Level Structures of Ge and Si in an External Magnetic Field.
Funders:
Funding AgencyGrant Number
Office of Naval Research (ONR)220(13)
Radio Corporation of AmericaUNSPECIFIED
Howard Hughes Fellowship in Science and EngineeringUNSPECIFIED
Record Number:CaltechETD:etd-08092007-144751
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-08092007-144751
Related URLs:
URLURL TypeDescription
http://resolver.caltech.edu/CaltechAUTHORS:20190304-180652654Related ItemElectron Tube and Microwave Laboratory Technical Report 16
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3078
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:14 Aug 2007
Last Modified:07 Mar 2019 01:31

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