TABLE OF CONTENTS We now apply the group theoretical notations to the electron energy band structure of the diamond- and zinc-blende-type semiconductors. Since the electrons move in the presence of a crystal potential, their wave functions can be symmetrized to reflect the crystal symmetry, i. e., written in a form such that they belong to irreducible representations of the space group of the crystal. However, in order to highlight the symmetry properties of the electron wave function, we will assume that the crystal potential is vanishingly small. In this empty lattice or nearly free electron model, the energy and wave functions of the electron are those of a free particle as given by (2.18) and (2.17), respectively. The electron energy band is simply a parabola when plotted in the extended zone scheme. This parabola looks much more complicated when replotted in the reduced zone scheme. It looks especially intimidating when the wave functions are labeled according to the irreducible representations of the point group of the crystal. Such complications have resulted from using the crystal symmetry which was supposed to simplify the problem! The simplification, however, occurs when we consider the band structure of electrons in a non-empty lattice in the remaining sections of this chapter. In this section we will use group theory to analyze the symmetry properties of nearly free electron band structures in both zinc-blende- and diamond-type crystals.
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