Influence of indium clustering on the band structure of semiconducting ternary and quaternary nitride alloys

The electronic band structures of In(x)Ga(1-x)N, In(x)Al(1-x)N, and In(x)Ga(y)Al(1-x-y)N alloys are calculated by ab initio methods using a supercell geometry, and the effects of varying the composition and atomic arrangements are examined. Particular attention is paid to the magnitude of and trends in bowing of the band gaps. Indium composition fluctuation (clustering) is simulated by different distributions of In atoms and it is shown that it strongly influences the band gaps. The gaps are considerably smaller when the In atoms are clustered than when they are uniformly distributed. An explanation of this phenomenon is proposed on the basis of an analysis of the density of states and the bond lengths, performed in detail for ternary alloys. Results for the band gaps of In(x)Ga(y)Al(1-x-y)N quaternary alloys show a similar trend. It is suggested that the large variation in the band gaps determined on samples grown in different laboratories is caused by different degrees of In clustering.