Large band-gap bowing inCu1−xAgxGaS2chalcopyrite semiconductors and its effect on optical parameters

The band-gap bowing in the ${\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Ag}}_{x}\mathrm{Ga}{\mathrm{S}}_{2}$ chalcopyrite alloy is studied using the full-potential linearized muffin-tin orbital method combined with various structural models, including so-called special quasirandom structures. The calculations confirm a large band-gap bowing $(\ensuremath{\sim}0.7\phantom{\rule{0.3em}{0ex}}\mathrm{eV})$ in agreement with recent experimental results. It is found that the large bowing in part arises from a nonlinear behavior of the $c∕a$ ratio with concentration. Layered structures are found to have similar bowing to special quasirandom structures. The nonlinear band-gap behavior also leads to a nonlinear behavior of the index of refraction and the second-order nonlinear optical susceptibility with concentration. The maximum ${\ensuremath{\chi}}^{(2)}$ is found for a 50% alloy and is calculated to be about $27\phantom{\rule{0.3em}{0ex}}\mathrm{pm}∕\mathrm{V}$.