$E_2$ interband transitions in ${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As alloys

We discuss the interband transitions of ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As alloys with emphasis on the energy region from 4 to 5.5 eV. Analysis of the dielectric-function spectra obtained by spectroscopic ellipsometry at low temperatures and their numerically calculated derivatives yields critical-point energies, broadenings, amplitude, and phase for the valence–to–conduction-band transitions $E_0^{\mathcal{’}}$ $E_0^{\mathcal{’}}$+${\Delta }_0^{\mathcal{’}}$, $E_2$(X), $E_2$(Σ), and $E_2$(P), where X and Γ are the usual symmetry points in the Brillouin zone (BZ), and P designates a region in the ΓXUL plane of the BZ. We discuss the experimental results and the identification of the interband transitions using the band structure and the dielectric function of GaAs and AlAs as obtained from the linear muffin-tin orbitals method and a virtual-crystal approximation for the electronic structure of the ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As alloys. The observed inversion of the relative strengths of the $E_2$(P) and $E_2$(Σ) transitions with increasing Al content (x) is attributed to changes in the parallelism of the energy bands. We reassign the structure previously attributed to $E_2$(P) to $E_2$(Σ), and vice versa. A decrease in the strength of the $E_0^{\mathcal{’}}$ transitions is also observed for large x, whereas the main contribution to the dielectric response is shown to arise from transitions along the Δ direction. The dependence on x of the energy position and the strength of the interband transitions is also given and discussed.