Films of pure and Sn-doped semiconducting ${\mathrm{In}}_2$${\mathrm{O}}_3$ were prepared by reactive $e$-beam evaporation. The spectral absorption coefficient was evaluated by spectrophotometry in the (2-6)-eV range. The extracted band gap increases with electron density ($n_e$) approximately as $n_e^{\frac{2}{3}}$ for $n_e\lesssim {10}^{21}$ ${\mathrm{cm}}^{-3\mathrm{}}$. This result is interpreted within an effective-mass model for $n$-doped semiconductors well above the Mott critical density. Because of the high degree of doping, the impurities are ionized and the associated electrons occupy the bottom of the conduction band in the form of an electron gas. The model accounts for a Burstein-Moss shift as well as electron-electron and electron-impurity scattering treated in the random-phase approximation. Experiments and theory were reconciled by assuming a parabolic valence band with an effective mass $\sim 0.6m$. Earlier work on doped oxide semiconductors are assessed in the light of the present results.

• Received 17 April 1984

DOI:https://doi.org/10.1103/PhysRevB.30.3240