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Valence Bands of Germanium and Silicon in an External Magnetic Field

Evtuhov, Viktor (1962) Valence Bands of Germanium and Silicon in an External Magnetic Field. Physical Review, 125 (6). pp. 1869-1879. ISSN 0031-899X. http://resolver.caltech.edu/CaltechAUTHORS:EVTpr62

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Abstract

The problem of the valence band structure of germanium and silicon 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 an extension of methods of Shockley and Kane to include the effects of the magnetic field. The usual approximation of the decoupling of the V1 and V2 bands from the V3 band is not made, thus making the analysis applicable to Si as well as Ge. Spherical energy bands are not assumed in this calculation and the case of kH≠0 is considered. Detailed analysis is carried out for the magnetic field H in the [001] direction. The analytical results obtained are more general than those of 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. The results predict an increase of the hole effective mass with the magnetic field. They also indicate mixing of the Landau levels even at kH=0, which leads to a prediction of new transitions some of which are of "negative mass" type. The mixing is more pronounced in Si than in Ge. Calculations for kH≠0 show that the ε1- levels possess negative curvatures near kH=0. Gradual "crossing" or reordering of the heavy hole levels is found at relatively high kH.


Item Type:Article
Additional Information:©1962 The American Physical Society Received 17 July 1961; revised 23 October 1961 The author would like to thank Professor R. W. Gould for his encouragement and help in the course of this work. He is indebted to Dr. George Birnbaum, Dr. E. O. Kane, Dr. B.Lax, Dr. H. Krömer, and Dr. H. J. Zeiger for stimulating discussions. Thanks are extended to Hughes Aircraft Company for performing the machine computations. This work was performed while the author was a recipient of the Howard Hughes Fellowship in Science and Engineering, and was supported in part by the Office of Naval Research.
Record Number:CaltechAUTHORS:EVTpr62
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:EVTpr62
Alternative URL:http://dx.doi.org/10.1103/PhysRev.125.1869
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5809
Collection:CaltechAUTHORS
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Deposited On:02 Nov 2006
Last Modified:26 Dec 2012 09:15

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