Band Structure Theory

Abstract

Semiconductor electronics provides an excellent demonstration of the close connection between modern engineering and quantum physics. It was an understanding of the electronic structure of semiconductors in the 1940s that led to the invention of the first transistor (Bardeen and Brattain, 1948; Brattain and Bardeen, 1948; Shockley and Pearson, 1948)—the backbone of modern computers. Since then, quantum mechanics has been an integral part of the progress of modern electronics technology. As devices become smaller, reaching submicron dimensions where electrons and holes traverse the active region of devices without experiencing a collision (the ballistic transport regime), quantum effects become even more important. Band structure studies deal with the energy levels and wave functions of electrons in materials and their relations to material properties. This chapter will begin by introducing the basic concepts of energy bands (Section 5.1). We will then describe two of the simplest band structure methods used for crystalline semiconductors—the tight-binding method (Section 5.2) and the plane-wave method (Section 5.3). The important band structure results for pure semiconductors are summarized in Section 5.4. The difficulties associated with the aperiodic potentials in an alloy and their effects on band gaps are discussed in Section 5.5. The remaining sections are devoted to the treatment of disordered alloys using the Green function methods, including the coherent potential approximation (CPA) (Soven, 1967; Velicky et al., 1968; Kirpatrick et al., 1970) and the perturbation method (PT). Both CPA and PT will be formulated for semiconductor alloys in this chapter and will be used to treat effects on band-edge states. These formalisms will be applied to detailed calculations of band structures of semiconductor alloys in Chapter 7.