Band-gap narrowing has been measured optically for semiconducting zinc-oxide films. All films were $n$ type with carrier densities of 5 × ${10}^{17}$ - 2 × ${10}^{20}$ ${\mathrm{cm}}^{-3\mathrm{}}$. The narrowing appeared suddenly at $n\sim 2\times {10}^{19}$ ${\mathrm{cm}}^{-3\mathrm{}}$, 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.

• Received 2 December 1981

DOI:https://doi.org/10.1103/PhysRevB.25.7836