Frank Herman

Lattice vibrational spectrum of germanium

Abstract The Born-von Karman theory of crystal dynamics has been applied to the diamond structure, and the most general force system involving interactions between each atom and its first through sixth order neighbors has been derived. The macroscopic elastic constants and the frequencies of selected lattice vibrational modes have been expressed in terms of the 21 independent parameters entering into this force system. It will be shown that the experimental elastic constants and lattice frequencies along the [100] and [111] axes cannot be fitted to force models based only on general 1° and 2° neighbor interactions. The addition of general 3° and 4° neighbor interactions does not improve the situation, but the further addition of 5° (and higher order) neighbor interactions does. It is possible to obtain physically plausible force models which fit all the data considered within experimental error by the use of onlv general 1° throueh 5° interactions. The nature and the limitations of the derived force models Gili be discussed.

The Electronic Energy Band Structure of Silicon and Germanium

This article, which is of a tutorial character, is concerned with three broad subjects: (a) the theory of electronic energy bands in a perfect crystal; (b) the electronic energy band structure of silicon and germanium crystals; and (c) the relationship between some of the electrical and optical properties of these crystals and their energy band schemes. The article is essentially an introduction to the quantum theory of crystals, with silicon and germanium serving as illustrative examples. As such, the article should appeal particularly to electronic engineers and physicists working in the field of solid state electronics. A knowledge of quantum mechanics is probably not essential to the understanding of major portions of this paper. The following topics are treated: crystal symmetry and crystal geometry; electronic quantum states in a perfect crystal; the energy band scheme; occupancy of the electronic quantum states; the hole concept; the effective mass tensor; velocity and acceleration of electrons and holes; the spin-orbit interaction and its consequences; the energy band structures of silicon and germanium; the band structure of germanium-silicon alloys; theory of lattice vibrations; the phonon concept; collisions between electrons or holes and phonons; the electrical conductivity; optical absorption and emission processes.

X. Speculations on the Energy Band Structure of Zinc-Blende-Type Crystals∗

ABSTRACT We have developed a semi-empirical perturbation scheme for the purpose of relating the energy band structures of diamond-type and zinc-blende-type crystals. Our sole objective is to predict the approximate location of the valence and conduction band edges in the reduced zone for some of the better known zinc-blende-type crystals. In this paper we explain how the perturbation scheme operates. Since a more complete account will appear in The Physical Review (Herman 1955), we will restrict ourselves here only to the essentials. A brief discussion of the effect of the spin-orbit interaction upon the band structure of zinc-blende-type crystals is also included in the present paper. † Communicated by the Author.