Temperature dependence of the dielectric function and the interband critical-point parameters of ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As

The complex dielectric function ε(ω) of ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ As was studied in the 1.4–5.6-eV photon energy region and between 12 and 800 K. By performing a line-shape analysis of the observed structures, the temperature dependence of the interband critical-point energies, broadenings, strength, and excitonic phase angle have been determined. The compositional dependence of these parameters was also obtained, e.g., the temperature dependence shift of the ${\mathrm{E}}_0$ exciton and ${\mathrm{E}}_1$ transitions was found to be 5.5+3.35x (${10}^{\mathrm{-}4}$eV/K). The decrease (increase) in energy (broadening) with increasing temperature was analyzed in terms of average phonon frequencies, giving rise to renormalization of the energies and a broadening of the band gaps. The statistical fluctuation of the alloy composition, which appears as an additional broadening, was found to affect the ${\mathrm{E}}_0$, ${\mathrm{E}}_0$+${\mathrm{\Delta }}_0$, ${\mathrm{E}}_1$, and ${\mathrm{E}}_1$+${\mathrm{\Delta }}_1$ structures. The excitonic character of the ${\mathrm{E}}_1$ and ${\mathrm{E}}_1$+${\mathrm{\Delta }}_1$ transitions shows a systematic change from a localized Lorentzian to two-dimensional character with increasing both Al content and temperature. The ${\mathrm{E}}_2$ structure [${\mathrm{E}}_0^{\prime }$, ${\mathrm{E}}_2$(X), ${\mathrm{E}}_2$(∑), and ${\mathrm{E}}_2$(P) transitions] was found to change its strength and to increase in complexity by going from the Ga- to the Al- rich regime.