Impurity induced band-gap narrowing in p-type CuIn1 − xGax(S,Se)2

Green's functions modelling of the impurity induced effects in p-type CuIn1 − xGaxS2 and CuIn1 − xGaxSe2 (x = 0.0, 0.5, and 1.0) reveals that: (i) the critical active acceptor concentration for the metal non-metal transition occurs at Nc ≈ 1017–1018 cm− 3 for impurities with ionization energy of EA ≈ 30–60 meV. (ii) For acceptor concentrations NA > Nc, the hole gas of the metallic phase affects the band-edge energies and narrows the energy gap Eg = Eg0 − ΔEg. The energy shift of the valence-band maximum ΔEv1 is roughly twice as large as the shift of the conduction-band minimum ΔEc1. (iii) ΔEv1 depends strongly on the non-parabolicity of the valence bands. (iv) Sulfur based compounds and Ga-rich alloys have the largest shifts of their band edges. (v) A high active acceptor concentrations of NA = 1020 cm− 3 implies a band-gap narrowing in the order of ΔEg ≈ 0.2 eV, thus Eg = Eg0 − 0.2 eV, and an optical band gap of Egopt ≈ Eg0 − 0.1 eV.