Precise Determination of the Direct-Indirect Band Gap Energy Crossover In Al$_{\mathrm{x}}$Ga$_{\mathrm{1-x}}$As*

Al$_{\mathrm{x}}$Ga$_{\mathrm{1-x}}$As is a technologically important semiconductor material system for optoelectronic applications due to its type I band alignment with GaAs under nearly lattice-matched conditions. Heterostructure design often relies on exactly controlling the relative positions of the $\Gamma $ and X conduction band edges, yet despite over three decades of research on this alloy, the precise energy and composition of the direct-indirect band gap crossover is still not well resolved. We report the results of our most recent investigation of Al$_{\mathrm{x}}$Ga$_{\mathrm{1-x}}$As (0.28 \textless $x$\textless 0.42) epitaxial films, in which the observation of concurrent photoluminescence (PL) emission peaks from the direct and indirect band gaps combined with time-resolved PL information yields a precise determination of the direct-indirect band gap crossover energy and composition.