Establishing Composition Dependent k · p Parameters for (Al,Ga)N Alloys

Deep UV (Al,Ga)N-based light emitters exhibit very low quantum efficiencies when compared to UV emitters at longer wavelengths. To improve the efficiencies of e.g. (Al,Ga)N-based light emitting diodes, theory and simulation can help to guide the device design. The theoretical framework underlying device simulations is often based on drift-diffusion models coupled with a self-consistent Schrodinger-Poisson equation solver. To achieve accurate and predictive models, understanding the composition dependence of material input parameters is of central importance. We target the composition dependence of k · p parameters in Al_xGa_(1-x)N alloys by using density functional theory (DFT) to obtain effective band structures from alloy disordered supercells. Building on these effective band structures, a numerically efficient fitting scheme based on the Sobol-sequence method is employed to extract effective electron masses, m_e(x), Luttinger-like parameters A_i(x), with i=1· 6, and crystal field splitting energy, Δ_CF, as a function of Al content, x, in the system. Our calculations reveal that for m_e(x) a linear interpolation of the GaN and AlN values provides a good description of the DFT data. However, for A_i(x) and Δ_CF(x) this simple approximation breaks down and we find that composition dependent bowing parameters are required to describe effective DFT band structures accurately.