ABSTRACT
A crystal consists of a periodic configuration of atoms, which is called a crystal lattice. There are different kinds of crystal lattices and they are classified, according to their symmetries, which specify invariant properties for translational and rotational operations. This chapter discusses configuration of the atoms in three important kinds of crystal structures: rock-salt type, zinc-blende type and wurtzeite type. In an isolated state, each atom has electrons that exist in discrete electronic energy levels, and the states of these bound electrons are characterized by atomic wave functions. The chapter describes a method to evaluate these electronic band structures in a quantitative way using quantum mechanics and discusses the motion of electrons under the influence of electric fields generated by atoms that take some definite space configuration specified by the symmetry of the crystal lattice. It introduces the Pseudopotential method and the Linar Combination of Atomic Orbital (LCAO) method, which are frequently applied to outer-shell valence electrons in semiconductors.
