Composition dependent $\mathbf{k}\cdot\mathbf{p}$ band parameters for wurtzite (Al,Ga)N alloys from density functional theory

UV emitters based on the semiconductor alloy aluminium gallium nitride, (Al,Ga)N, have attracted significant interest in recent years due to their potential for optoelectronic devices. To guide the design of such devices with improved efficiencies, theoretical frameworks based on so-called k.p methods have found widespread application in the literature. Given that k.p models are empirical in nature, parameters such as effective masses or crystal field splitting energies of (Al,Ga)N alloys have to be provided as input from first-principles calculations or experiment. Although these parameters are available for GaN and AlN, detailed information on their composition dependence is sparse. Here, we address this question and provide (Al,Ga)N band parameters for widely used k.p Hamiltonians. We start from density functional theory (DFT) to sample the electronic structure of (Al,Ga)N alloys over the full composition range. The k.p parameters are treated as free parameters to reproduce the DFT data. For GaN and AlN the parameters extracted here agree well with literature values. When turning to the composition dependence of the k.p parameters, our calculations show that most parameters deviate significantly from a linear interpolation of the GaN and AlN values, an approximation widely made in the literature. Moreover, to describe changes in the band parameters with Al content, composition dependent bowing parameters have to be considered for an accurate description of the DFT data. Finally, our analysis also provides initial insight into consequences of the nonlinear composition dependence of the k.p parameters for the electronic structure of (Al,Ga)N alloys. We find that in particular the band ordering is affected by the nonlinear evolution of the crystal field splitting energy with composition, an important aspect for the light polarization characteristics of high Al content (Al,Ga)N alloys.