Ebook: Energy Band Theory

Solid state physics has grown rapidly in the past two decades. Unprecedented developments in technology have been accompanied by a substantial refinement and extension of the fundamental theory. New phenomena have been discovered and interpreted, and old puzzles clarified. The one-electron theory has come to maturity with the development of powerful methods of calculation and successful applications to real crystals. It is now possible to describe the results of numerous experiments concerning both semiconductors and metals in the language of band theory in a consistent fashion with the use of a small number of parameters. Calculations from first principles are able to reproduce most of the important qualitative features and some quantitative characteristics of the energy levels of actual materials.

This book contains a discussion of the principles and methods of the calculation of the energy levels of electrons in crystals. In Chapter I, the language of band theory is developed with attention to the general features of band structures which may be deduced from considerations of crystal symmetry. Chapter 2 includes a description of the principal methods for the solution of the Schrodinger equation in a periodic potential together with a survey of the problems encountered in the construction of the potential function in the Hartree-Fock approximation. Some of the results of experimental investigations of the band structures of materials, including the alkali metals, the noble metals, and common semiconductors, are surveyed in Chapter 3, and compared with theoretical calculations. The effects of external perturbations, including electric and magnetic fields, on band structures are considered in Chapter 4, together with a discussion of the energy levels of electrons bound to point impurities. A calculation of optical constants is also included.