Length mismatch in random semiconductor alloys. IV. General multinary compounds

We generalize previous theory on the length-mismatch problem in random semiconductor alloys to deal with an arbitrary number of components on each sublattice. We also calculate the lengthdistribution functions for any two sites in the crystalline alloy. It is found that the properly scaled length-distribution functions are independent of the types of atomic species, and the first and second moments of the distributions are calculated. We illustrate these results with computer simulations performed on ${\mathrm{Si}}_x{\mathrm{Ge}}_{1-x}$, and apply these results to the pseudoternary alloy ${\mathrm{Cd}}_{1-x-y}{\mathrm{Mn}}_x{\mathrm{Zn}}_y\mathrm{Te}$.