Band-gap narrowing and band structure in degenerate tin oxide (SnO2) films

Abstract

Films of tin oxide (${\mathrm{SnO}}_{2}$) were deposited on a quartz substrate by the chemical-vapor-deposition technique. Carrier densities in the range 6.1\ifmmode\times\else\texttimes\fi{}${10}^{19}$--1.3\ifmmode\times\else\texttimes\fi{}${10}^{21}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ were obtained by varying the thickness from 0.20 to 1.55 \ensuremath{\mu}m. The transmittance and reflectance were measured in the wavelength range 0.2--0.9 \ensuremath{\mu}m. The band gap as well as the transition width were found to increase with increasing carrier density. The present data, along with the results reported for ${\mathrm{SnO}}_{2}$ films by some other workers, have been analyzed by taking into account the narrowing, which is due to electron-electron and electron-impurity scattering, and the Burstein-Moss widening, which is due to the filled lower states in the conduction band. Experiment and theory are reconciled by assuming a valence-band effective mass \ensuremath{\sim}1.0${\mathit{m}}_{0}$. Adding the narrowing for different carrier densities to the observed widening at respective concentrations gives the actual Burstein-Moss widening. Other reported data for ${\mathrm{SnO}}_{2}$ films can be fit very well to the present effective-mass values. However, the intrinsic band gap ${\mathit{E}}_{\mathit{g}0}$ works out to be different for different workers and seems to be a function of deposition conditions. It is also shown that the narrowing at the center of the band is much higher than that corresponding to the Fermi wave number and the difference increases with ${\mathit{n}}_{\mathit{e}}$. A distortion in the shape of the bands is thereby expected at high carrier densities.