Perturbation analysis on large band gap bowing of dilute nitride semiconductors

Contrary to the conventional empirical law, band gap of dilute nitride semiconductors decreases with nitrogen concentration. In spite of a number of investigations, origin of this “large band gap bowing”, is still under debate. In order to elucidate this phenomenon, we investigate change of band edge energies of GaN${}_x$As${}_{1-x}$ due to nitrogen by using the perturbation theory. It is found that energy shift of conduction band edge is arising from mixing between $\mathrm{\Gamma }$- and L-states and/or $\mathrm{\Gamma }$- and X-states induced by displacement of Ga atoms around N. We also found that the valence band edge state shows upward shift in spite of negative potential of nitrogen. These results are well understood from character of the wavefunctions and symmetry of the perturbation potential.