Zn Vacancy Formation Energy and Diffusion Coefficient of CVT ZnO Crystals in the Sub-Surface Micron Region

By using positron annihilation spectroscopy methods, we have experimentally demonstrated the creation of isolated zinc vacancy concentrations >10²⁰ cm^-3 in chemical vapor transport (CVT)-grown ZnO bulk single crystals. X-ray diffraction ω-rocking curve (XRC) shows the good quality of ZnO single crystal with (110) orientation. The depth analysis of Auger electron spectroscopy indicates the atomic concentrations of Zn and O are almost stoichiometric and constant throughout the measurement. Boltzmann statistics are applied to calculate the zinc vacancy formation energies (E^f) of ~1.3-1.52 eV in the sub-surface micron region. We have also applied Fick's 2^nd law to calculate the zinc diffusion coefficient to be ~1.07 × 10^-14 cm²/s at 1100 °C. The zinc vacancies began annealing out at 300 °C and, by heating in the air, were completely annealed out at 700 °C.