Carrier-induced refractive index change and optical absorption in wurtzite InN and GaN: Full-band approach

Abstract

Based on the full band electronic structure calculations, first we consider the effect of $n$-type doping on the optical absorption and the refractive index in wurtzite InN and GaN. We identify quite different dielectric response in either case; while InN shows a significant shift in the absorption edge due to $n$-type doping, this is masked for GaN due to efficient cancellation of the Burstein-Moss effect by the band gap renormalization. Moreover, for high doping levels the intraband absorption becomes significant in InN. For energies below 1 eV, the corresponding shifts in the real parts of the dielectric function for InN and GaN are in opposite directions. Furthermore, we observe that the free-carrier plasma contribution to refractive index change becomes more important than both band filling and the band gap renormalization for electron densities above ${10}^{19}\text{ }{\text{cm}}^{\ensuremath{-}3}$ in GaN, and ${10}^{20}\text{ }{\text{cm}}^{\ensuremath{-}3}$ in InN. As a result of the two different characteristics mentioned above, the overall change in the refractive index due to $n$-type doping is much higher in InN compared to GaN, which in the former exceeds 4% for a doping of ${10}^{19}\text{ }{\text{cm}}^{\ensuremath{-}3}$ at $1.55\text{ }\ensuremath{\mu}\text{m}$ wavelength. Finally, we consider intrinsic InN under strong photoexcitation which introduces equal density of electron and holes thermalized to their respective band edges. The change in the refractive index at $1.55\text{ }\ensuremath{\mu}\text{m}$ is observed to be similar to the $n$-doped case up to a carrier density of ${10}^{20}\text{ }{\text{cm}}^{\ensuremath{-}3}$. However, in the photoexcited case this is now accompanied by a strong absorption in this wavelength region due to ${\ensuremath{\Gamma}}_{5}^{v}\ensuremath{\rightarrow}{\ensuremath{\Gamma}}_{6}^{v}$ intravalence band transition. Our findings suggest that the alloy composition of ${\text{In}}_{x}{\text{Ga}}_{1\ensuremath{-}x}\text{N}$ can be optimized in the indium-rich region so as to benefit from high carrier-induced refractive index change while operating in the transparency region to minimize the losses. These can have direct implications for InN-containing optical phase modulators and lasers.