GaN and InN conduction-band states studied by ellipsometry

Abstract

The complex dielectric function (DF) of wurtzite InN and GaN as well as zinc blende GaN was measured by spectroscopic ellipsometry between 14 and $32\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ with synchrotron radiation. In this spectral region, the DF of InN and GaN originates from $\mathrm{Ga}\phantom{\rule{0.2em}{0ex}}3d$ and $\mathrm{In}\phantom{\rule{0.2em}{0ex}}4d$ core level transitions to unoccupied conduction-band states. The $\mathrm{Ga}\phantom{\rule{0.2em}{0ex}}3d$ and $\mathrm{In}\phantom{\rule{0.2em}{0ex}}4d$ electronic states are highly localized and show almost no dispersion. We use these core states as a reference in order to probe the conduction bands. For this purpose, the imaginary part is compared to the density of empty $p$-orbital-like electronic states located around the cation atomic site, as calculated by density-functional theory in the local density approximation. The constant splitting of absorption features in the DF is attributed to the spin-orbit splitting of the $d$ states. $\ensuremath{\Delta}{d}_{5∕2\ensuremath{-}3∕2}$ is found to be $0.82\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for the $\mathrm{In}\phantom{\rule{0.2em}{0ex}}4d$ and $0.41\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for the $\mathrm{Ga}\phantom{\rule{0.2em}{0ex}}3d$ level, respectively. On wurtzite samples with the $c$ axis in the surface plane, ellipsometry measurements give access to both independent dielectric tensor components ${\ensuremath{\epsilon}}^{\ensuremath{\parallel}}$ and ${\ensuremath{\epsilon}}^{\ensuremath{\perp}}$, respectively. The observed anisotropy is induced by a directional dependence of empty $p$ states yielding a ${p}^{\ensuremath{\parallel}}$-DOS (density states) different to the ${p}^{\ensuremath{\perp}}$-DOS.