Many-electron effects on the dielectric function of cubicIn2O3: Effective electron mass, band nonparabolicity, band gap renormalization, and Burstein-Moss shift

We systematically investigate the influence of free-electron concentrations from $1.5\ifmmode\times\else\texttimes\fi{}{10}^{17}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ up to $1.6\ifmmode\times\else\texttimes\fi{}{10}^{21}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$ on the optical properties of single-crystalline ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ in the cubic bixbyite structure. Dielectric functions of bulk crystals and epitaxial films on various substrates are determined by spectroscopic ellipsometry from the mid-infrared $(37\phantom{\rule{4pt}{0ex}}\mathrm{meV}\ensuremath{\approx}300\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1})$ into the ultraviolet $(6.5\phantom{\rule{4pt}{0ex}}\mathrm{eV})$ spectral region. Eight transverse optical phonon modes are resolvable for low carrier-density material. The analysis of the plasma frequencies yields effective electron masses which increase from a zero-density mass of ${m}^{*}=0.18{m}_{0}$ to $0.4{m}_{0}$ at $n={10}^{21}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. This mirrors the nonparabolicity of the conduction band being described by an analytical expression. The onset of absorption due to dipole-allowed interband transitions is found at $3.8\phantom{\rule{4pt}{0ex}}\mathrm{eV}$ for $n\ensuremath{\le}{10}^{19}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. It undergoes a blue-shift (effective Burstein-Moss shift) for higher electron densities as a result of the dominating phase-space filling compared to band gap renormalization. A comprehensive model describing the absorption onset is developed, taking nonparabolicity into account, yielding an accurate description and explanation of the observations. The agreement of modeled and measured absorption onset independently supports the effective electron masses derived from infrared data. The high-frequency dielectric constant of undoped ${\mathrm{In}}_{2}{\mathrm{O}}_{3}$ is found to be ${\ensuremath{\varepsilon}}_{\ensuremath{\infty}}=(4.08\ifmmode\pm\else\textpm\fi{}0.02)$.