Concentration dependence of the E$_{ +}$ transition in dilute GaAs$_{1-x}$N$_{x}$ alloy.

We investigate dilute isoelectronic doping in molecular-beam epitaxially-grown GaAs using low-temperature micro-photoluminescence to measure the above-bandgap transition energies of $E_{+}$ and the spin-orbit transition, $E_{SO}$. In the case of dilute nitrides, GaAs$_{1-x}$N$_{x}$, we examine the functional shape of the concentration dependence of E$_{+}(x)$ in the low-$x$ limit, with $x$ as low as 0.04 {\%}. Comparison with the concentration dependence of the E$_{0}$ bandgap gives compelling evidence against the picture of bandgap reduction via repulsion of the conduction band minimum from the impurity level acting alone.