Structure-Property Relationships in Semiconductor Alloys
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STRUCTURE-PROPERTY RELATIONSHIPS IN SEMICONDUCTOR ALLOYS A. SHER,* M.A. BERDING,* S. KRISHNAMURTHY,* M. VAN SCHILFGAARDE,* A.-B. CHEN,** AND W. CHEN** * SRI International, Menlo Park, CA 94025 ** Auburn University, Auburn, AL 36849 ABSTRACT We have demonstrated that the atomic distribution of constituents in semiconductor alloys is never truly random. There are always interactions causing correlations; the degree and nature of the correlations depend on which interactions dominate and on the growth conditions. While we have identified most of the interactions which are expected to cause correlations, not all of them have been treated completely to date. Therefore, some details remain unclear, but the principal effects can now be appreciated in broad terms. TECHNICAL DISCUSSION In the formalism reported here, we start by focusing on small clusters of atoms that are called microclusters. [1-4] Once the microcluster size is selected, then the total energy of the solid is expressed as a sum of cluster energies; and the number of configurations of the solid corresponding to a given total energy is calculated. Microcluster-microcluster interactions are neglected and there are approximations in the microcluster energy calculations, but once the approximations are made, no appreciable additional inaccuracy is introduced in the statistical mechanics arguments leading to microcluster population distributions. The accuracy of the final result for a given physical property, e.g. critical order-disorder transition temperature, differs for different properties, but in general improves as cluster size increases. Two-atom clusters give most trends properly, but details differ from the answers found for the five-atom, sixteen-bond clusters that are the basis for most of the numerical results we present here. We have not attempted to extend the numerical results for larger clusters. We have demonstrated [4] that for an n-atom microcluster in state j, represented schematically as A,_,)B.j(B), corresponding to a given number nj(B) of B atoms if the degeneracy g. = [ &I of a given energy state ej is not split, and if rj depends linearly on nj(B), then the average population distribution xj is always that of a random alloy xj0 . Therefore, only interactions that split the degeneracy or cause a nonlinear variation of ej on nj(B) drive correlations. To be precise, as can be seen from the detailed analysis, the energies ;j- nj(B)t(B), where g(B) is the B atom chemical potential in the grand partition function formalism, are responsible for populations of state j. We have identified three mechanisms that cause appropriate nonlinear variations of ej. The first is strains resulting from bond length mismatches between the constituents. This is illustrated for Hgl_,ZnTe in Fig. 1 where (n - nj(B))
n
nj(B) • o
n
and Ea0and eF,.are the cluster energies in the pure materials. The second, referred to as chemical interactions, is based on potential differences between the constituents responsible for
Mat. Res. Soc. Symp. Proc. Vol. 90.- 1987 Ma
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