Direct-energy-gap dependence on Al concentration inAlxGa1−xAs

The direct exciton energy at 2 K in ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As epitaxial layers (0.10<x<0.75) has been determined by optical transmission measurements. Microprobe analysis has been employed for the evaluation of the aluminum concentration. From these data, the direct-energy-gap dependence on x has been obtained; its comparison with the literature clearly shows that the relation $E_{\mathrm{gap}{}^{\Gamma }(\mathrm{x}}$) commonly used in the optical determination of the alloy concentration must be revised. Contrary to older evaluations, our determination of the nonlinear contribution to $E_{\mathrm{gap}{}^{\Gamma }(\mathrm{x}}$) agrees with the theoretically predicted values.