A Band-Gap Energy Model of the Quaternary Alloy In_xGa_yAl_1?x?yN using Modified Simplified Coherent Potential Approximation

Based on modification of the simplified coherent potential approximation, a model for the band-gap energy of In_xGa_yAl_1?x?yN is developed. The parameters of the model are obtained by fitting the experimental band-gap energy of their ternary alloys. It is found that the results agree with the experimental values better than those reported by others, and that the band-gap reduction of In_xGa_yAl_1?x?yN with increasing In or Ga content is mainly due to enhanced intraband coupling within the conduction band, and separately within the valence band.