Conducting mechanism in the epitaxialp-type transparent conducting oxideCr2O3:Mg

Epitaxial $p$-type transparent conducting oxide (TCO) $\mathrm{C}{\mathrm{r}}_{2}{\mathrm{O}}_{3}:\mathrm{Mg}$ was grown by electron-beam evaporation in a molecular beam epitaxy system on $c$-plane sapphire. The influence of Mg dopants and the oxygen partial pressure were investigated by thermoelectric and electrical measurements. The conduction mechanism is analyzed using the small-polaron hopping model, and hopping activation energies have been determined, which vary with doping concentration in the range of 210--300 \ifmmode\pm\else\textpm\fi{} 5 meV. Films with better conductivity were obtained by postannealing. The effect of postannealing is discussed in terms of a crystallographic reordering of the Mg dopant. The highest Seebeck mobilities obtained from thermoelectric measurements are of the order of ${10}^{\ensuremath{-}4}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{2}{\mathrm{V}}^{\ensuremath{-}1}{\mathrm{s}}^{\ensuremath{-}1}$. We investigate the fundamental properties of a Mg dopant in a high crystalline quality epitaxial film of a binary oxide, helping us understand the role of short range crystallographic order in a $p$-type TCO in detail.