Optical properties of ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As alloys

A method is described for calculation of the real (${\epsilon }_1$) and imaginary (${\epsilon }_2$) parts of the dielectric function of semiconductors at energies below and above the lowest direct band edge, in which the model is based on the Kramers-Kronig transformation and strongly connected with the electronic energy-band structure of the medium. The method reveals distinct structures at energies of the $E_0$, $E_0$+${\Delta }_0$, $E_1$ ($E_1$+${\Delta }_1$), and $E_2$ critical points (CP’s). The indirect-gap transitions also take an important part in the spectral dependence of ${\epsilon }_2$. Analyses are presented for ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As alloys, and results are in satisfactory agreement with the experimental information over the entire range of photon energies (0–6.0 eV). The compositional dependence of the optical-transition strength at energies of each CP and indirect gap is also given and discussed.