Direct- and indirect-energy-gap dependence on Al concentration in ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{Sb}$ $(x<~0.41)$

The absorption spectra of ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{Sb}$ alloys $(x<~0.41),$ measured at low temperatures, have been fitted including the contribution of direct and indirect transitions, taking into account the excitonic effects. This procedure yields accurate values of the energy of the direct Γ-Γ gap, $E_g^{\Gamma }\mathrm{}\left(x\right),$ as a function of the composition and allows the determination of the composition dependence of the energy of the indirect $\Gamma -L$ gap, $E_g^L\mathrm{}\left(x\right).$ The results show that the dependence of the energies of the two gaps on the Al mole fraction for $x<~0.41$ is linear instead of quadratic, as reported so far. The extrapolation of this result to the whole $x$ range $(0\mathrm{}<~x<~1)$ is discussed. A value of the $\Gamma -L$ crossover concentration ${(x}_c=0.22)$ significantly lower than the commonly accepted one ${(x}_c=0.35)$ has been obtained.