Energy Band Theory
In this chapter the one-electron energy band theories for the crystalline solids are presented. The importance of energy band theories for a crystalline solid is due to the fact that many important physical and optical properties of a solid can be readily explained by using its energy band structure. In general, the energy band structure of a solid can be constructed by solving the one-electron Schrödinger equation for electrons in a crystalline solid which contains a large number of interacting electrons and atoms. To simplify the difficult task of solving the Schrödinger equation for the many-body problem in a crystal, the effects that arise from the motion of atomic nuclei must be neglected (i.e., it is assumed that the nuclei are at rest in equilibrium positions at each lattice site). Under this condition, the nuclear coordinates enter the problem only as a constant parameter. However, even though the problem has been confined as a purely electronic one, there are still the many-electron problems in the system which cannot be solved explicitly. Therefore, it is necessary to apply additional approximations to solving the Schrödinger equation for electrons in a crystalline solid.
KeywordsEnergy Band Electron Wave Function Valence Band Maximum Conduction Band Minimum Energy Band Structure
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