Determination of the Fermi Level Position in Dilute Magnetic Ga$_{1-x}$Mn$_{x}$N Films

We report on a combined theoretical and experimental determination of the Fermi level position in wurtzite Ga$_{1-x}$Mn$_{x}$N films with $x=4\%$ and $x=10\%$ as grown by molecular beam epitaxy. By means of ellipsometric measurements the real part of the frequency-dependent conductivity is determined. An electronic model in the framework of the effective bond-orbital model is parameterized in order to theoretically reproduce the measured transport properties. Predictions for the long-wavelength behaviour as a function of the Fermi level are made. The corresponding density of states obtained in this model is in qualitative agreement with first-principle calculations. The absence of a significant experimental peak in the AC conductivity for small frequencies indicates that the Fermi level lies in a gap between two Mn-related impurity bands in the host band gap.