TABLE OF CONTENTS The property which distinguishes semiconductors from other materials concerns the behavior of their electrons, in particular the existence of gaps in their electronic excitation spectra. The microscopic behavior of electrons in a solid is most conveniently specified in terms of the electronic band structure. The purpose of this chapter is to study the band structure of the most common semiconductors, namely, Si, Ge, and related III V compounds. We will begin with a quick introduction to the quantum mechanics of electrons in a crystalline solid.
The properties of electrons in a solid containing 10 23 atoms/cm 3 are very complicated. To simplify the formidable task of solving the wave equations for the electrons, it is necessary to utilize the translational and rotational symmetries of the solid. Group theory is the tool that facilitates this task. However, not everyone working with semiconductors has a training in group theory, so in this chapter we will discuss some basic concepts and notations of group theory. Our approach is to introduce the ideas and results of group theory when applied to semiconductors without presenting the rigorous proofs. We will put particular emphasis on notations that are often found in books and research articles on semiconductors. In a sense, band structure diagrams are like maps and the group theory notations are like symbols on the map. Once the meaning of these symbols is understood, the band structure diagrams can be used to find the way in exploring the electronic properties of semiconductors.
