Hall Effect Studies of Doped Zinc Oxide Single Crystals

Measurements of the Hall coefficient and the electrical conductivity of single-crystal specimens of n-type ZnO at temperatures between 55^ and 300^ 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 E₃=0. 051 ev for N₃<510^16 cm^-3. Lithium was also found to introduce a small concentration of acceptors, presumably due to an exchange between interstitial and substitutional positions. The quantity ({m^{ (N) }m) }^3{2}D^-1, where m^ (N) =density-of-states'' effective mass and D=donordegeneracy, 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 =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 E₃ with increasing N₃ corresponds to the overlap of these large orbits. The Hall mobility is 180 cm^2 volt^-1 sec^-1 at 300^ 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 =1. The mobility so obtained is in good agreement with experiment and indicates that optical-mode scattering is important above 200^. Some acoustical-mode scattering also appears to be present. At low temperatures the mobility appears to be limited by impurity scattering.