Surface and impurity states

Abstract

Abstract We have so far seen that the electron states of a periodic structure are described by Bloch functions which form energy bands as a function of k, and that these bands are such that, in general, forbidden energy gaps exist between them. It is reasonable to expect, on the other hand, that electrons which arise from impurities or from surface states in the crystal will not give rise to periodic states and will not, therefore, be described by Bloch functions. We must expect, accordingly, that the corresponding energies may appear in the forbidden energy gaps, as will be confirmed in this chapter. The first thing which we shall do is to look for the possible existence of states in the gap, and this will lead in§ 1 to the Tamm states. We shall then consider a simple model of surface states (Shockley states) in§ 2. A more detailed method of calculation of surface and impurity states, proposed by Koster and Slater, will be discussed in § 3 and will serve as a simple introduction to the use of Green functions. A practical example of this treatment will be given in § 4.