Hall Effect Studies of Doped Zinc Oxide Single Crystals

Abstract

Measurements of the Hall coefficient and the electrical conductivity of single-crystal specimens of $n$-type ZnO at temperatures between 55\ifmmode^\circ\else\textdegree\fi{}K and 300\ifmmode^\circ\else\textdegree\fi{}K are reported. An analysis of carrier concentration vs temperature indicates that "as-grown" crystals contain more than one active donor. Crystals with low initial donor concentrations were doped with H or interstitial Zn or Li, allowing a single-donor-level analysis. Doping was accomplished by interstitial diffusion followed by a rapid quench. Each of the added donors gives rise to a hydrogen-atom-model donor center whose ionization energy is ${E}_{D}=0.051$ ev for ${N}_{D}<5\ifmmode\times\else\texttimes\fi{}{10}^{16}$ ${\mathrm{cm}}^{\ensuremath{-}3}$. Lithium was also found to introduce a small concentration of acceptors, presumably due to an exchange between interstitial and substitutional positions. The quantity ${(\frac{{m}^{(N)}}{m})}^{\frac{3}{2}}{D}^{\ensuremath{-}1}$, where ${m}^{(N)}=\mathrm{d}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}\ensuremath{-}\mathrm{o}\mathrm{f}\ensuremath{-}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{s}''$ effective mass and $D=\mathrm{donor}\mathrm{degeneracy}$, was found to be about 0.19 for all three donors, indicating that if $D=2$ then ${m}^{(N)}=0.5$. The low-frequency dielectric constant of ZnO was redetermined as $\ensuremath{\kappa}=8.5$. The effective mass associated with the electron found in a hydrogen-like orbit is then ${m}^{(H)}=0.27m$, and the observed decrease of ${E}_{D}$ with increasing ${N}_{D}$ corresponds to the overlap of these large orbits.The Hall mobility is 180 ${\mathrm{cm}}^{2}$ ${\mathrm{volt}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ at 300\ifmmode^\circ\else\textdegree\fi{}K and increases with decreasing temperature. It has been analyzed for lattice and impurity scattering. The optical-mode scattering mobility has been calculated from both the perturbation and intermediate-coupling theories making use of the effective mass, ${m}^{(H)}$, so that no adjustable parameters were included. The two theories agree for ZnO since it turns out to have a polar-mode electron coupling constant of $\ensuremath{\alpha}=1$. The mobility so obtained is in good agreement with experiment and indicates that optical-mode scattering is important above 200\ifmmode^\circ\else\textdegree\fi{}K. Some acoustical-mode scattering also appears to be present. At low temperatures the mobility appears to be limited by impurity scattering.