Band-gap narrowing in heavily defect-doped ZnO

Abstract

Band-gap narrowing has been measured optically for semiconducting zinc-oxide films. All films were $n$ type with carrier densities of 5 \ifmmode\times\else\texttimes\fi{} ${10}^{17}$ - 2 \ifmmode\times\else\texttimes\fi{} ${10}^{20}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. The narrowing appeared suddenly at $n\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{19}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, a carrier density consistent with that expected for the onset of a semiconductor-metal transition. However the gap-shrinkage dependence on carrier concentration was not ${n}^{\frac{1}{3}}$ as expected from predictions based on an electron-gas model, but could be described by the same empirical relation proposed for Si:As and Si:B.