A GENERAL DERIVATION OF THE DENSITY OF STATES FUNCTION FOR QUANTUM-WELLS AND SUPERLATTICES

The intent of this paper is to provide the reader with a detailed summary of the development of the density of states (DOS) functions for two-dimensional systems. Specifically, the DOS is derived for an infinite quantum well, a finite well, and a periodic array of coupled wells (a superlattice). Many authors state that the DOS is "simply ..." without references, yet many who are new to the subject of two-dimensional systems may not see the "simplicity," for instance, of the derivation of the DOS for a superlattice. We also show the relationships between the expressions for each case when the appropriate limits are taken. This comparison shows the consistency that such a general derivation furnishes to each expression. © 1990.