Length mismatch in random semiconductor alloys. I. General theory for quaternaries

We have studied the length-mismatch problem in random semiconductor alloys. In this paper, the first of three, we obtain an analytic solution for the quaternary zinc-blende alloys A1-xBxC1-yDy. The solution incorporates the effects of the lattice via topological rigidity parameters and is exact under the assumptions that the force parameters do not vary from site to site, and that the unstrained atomic radii are additive. We obtain the mean bond lengths for the nearest and next-nearest neighbors. We also show that the length-distribution functions for the nearest-neighbor bonds AC, AD, BC, and BD are identical apart from shifts in the centers and weights. Results have been checked against computer simulations. Special cases of this theory are the pseudobinary alloys such as Ga1-xInxAs, which are discussed in paper II, and the binary alloys Si1-xGex, either crystalline or amorphous, which are discussed in paper III.