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

TL;DR

This study uses full band electronic structure calculations to analyze how n-type doping and photoexcitation affect the refractive index and optical absorption in wurtzite InN and GaN, with implications for optical devices.

Contribution

It provides a detailed comparison of doping effects on InN and GaN's optical properties using a full band approach, highlighting the dominant role of free-carrier plasma in refractive index changes.

Findings

Refractive index change exceeds 4% in InN at 10^19 cm^-3 doping.

InN shows a significant absorption edge shift due to doping, unlike GaN.

Photoexcitation induces similar refractive index changes as doping but with increased absorption.

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. For high doping levels the intraband absorption becomes significant in InN. 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$^{19}$~cm$^{-3}$ in GaN, and 10$^{20}$~cm$^{-3}$ 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$^{19}$~cm$^{-3}$ at 1.55~$\mu$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~$\mu$m is observed to be similar to the n-doped case up to a carrier density of 10$^{20}$~cm$^{-3}$. However, in the photoexcited case this is now accompanied by a strong absorption in this wavelength region due to $\Gamma^v_5 \to \Gamma^v_6$ intravalence band transition. Our findings suggest that the alloy composition of In$_x$Ga$_{1-x}$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.