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^∘{}K and 300^∘{}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 ED=0.051 ev for ND<5×10¹⁶ 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)3/2D^-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 κ=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 ED with increasing ND corresponds to the overlap of these large orbits.The Hall mobility is 180 cm² volt^-1 sec^-1 at 300^∘{}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 α=1. The mobility so obtained is in good agreement with experiment and indicates that optical-mode scattering is important above 200^∘{}K. Some acoustical-mode scattering also appears to be present. At low temperatures the mobility appears to be limited by impurity scattering.