Statistical Mechanics of Dilute Solid Solutions

Abstract

An apparently quite general model for an essentially-ordered semiconductor compound containing impurity traces consists: (1) of atomic point defects randomly distributed over appropriate, equivalent sites and contributing to the internal energy of the crystal by terms linear in the concentration of each type of atomic point defect, and (2) an electronic energy band structure in which the concentration and type of ``impurity'' levels is determined by the concentration and type of atomic point defects. The assignment of donor or acceptor character to the native interstitials and vacancies is predicted in a specific case by analogy with the alkali halides. Otherwise the nature of the binding is irrelevant, provided the un-ionized impurity level associated with each substitutional atomic point defect bears the same charge as that on the substituted atom. From the appropriate quasi-grand partition function, one obtains the usual Fermi-Dirac distribution for electrons as well as distribution functions for the atomic point defects. In addition, one obtains expressions for the chemical potentials of the thermodynamic components. The latter are utilized in a discussion of those aspects of the M–N phase diagram pertinent to the semiconductor compound MN and in a discussion of amphoteric impurities.