In this paper we review the basic theoretical aspects as well as some important experimental results of the band anticrossing effects in highly electronegativity-mismatched semiconductor alloys, such as GaAs_1-xN_x and In_yGa_1-yAs_1-xN_x. The many-impurity Anderson model treated in the Coherent potential approximation is applied to these semiconductor alloys, In which metallic anion atoms are partially substituted by a highly Electronegative element at low concentrations. Analytical solutions of the Green's function provide dispersion relations and state broadenings for the Restructure conduction bands.
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