Improved refractive index formulas for the AlxGa1−xN and InyGa1−yN alloys

A detailed understanding of the nitride refractive indices is essential for the modeling and design of III–N laser structures. In this article, we report on the assessment of the refractive index data available for the nitride alloys and present formulas for evaluating the refractive indices for variations in both composition and photon energy. For ${\mathrm{Al}}_x{\mathrm{Ga}}_{\text{1−x}}\mathrm{N},$ an expression is given which fits well to experimental data below $\text{x<0.38,}$ sufficient for the molefractions found in the cladding layers of III–N lasers. Due to the almost complete lack of experimental refractive index data for ${\mathrm{In}}_y{\mathrm{Ga}}_{\text{1−y}}\mathrm{N},$ we propose an expression to give a first-order approximation for the refractive index.