Trap-limited diffusion of Zn in β−Ga2O3

Diffusion of Zn in (001)- and $(\overline{2}01)$-oriented $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ was studied using secondary-ion mass spectrometry and first-principles calculations based on hybrid and semilocal functionals. The $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ samples were sealed in quartz ampules together with a piece of metallic Zn and heated to temperatures of 900--1100 ${}^{\ensuremath{\circ}}\mathrm{C}$ for 1 h. The Zn concentration profiles as a function of depth were simulated by employing the trap-limited diffusion model. From this model the migration barrier for Zn diffusion was found to be ${E}_{m}=2.2\ifmmode\pm\else\textpm\fi{}0.2\phantom{\rule{4.pt}{0ex}}$ and $2.1\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{4.pt}{0ex}}\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ in the (001) and ($\overline{2}01$) orientations of $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$, respectively, with corresponding dissociation energies of ${E}_{d}$ = 3.5 $\ifmmode\pm\else\textpm\fi{}1.1$ and $3.2\ifmmode\pm\else\textpm\fi{}0.6\phantom{\rule{4.pt}{0ex}}\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$. Results from the first-principles calculations predict an interstitialcy mechanism for the Zn diffusion when it is not in its trapped state. Using the nudged elastic band method, we obtain a barrier of 1.6 eV for migration of Zn split interstitials $({\mathrm{Zn}}_{i})$ in both the [001] and $[\overline{2}01]$ directions, in accordance with the results obtained from the trap-limited diffusion model. Interestingly, the Ga vacancy is found to be able to trap two Zn atoms forming a shallow donor complex labeled ${\mathrm{Zn}}_{i}{\mathrm{Zn}}_{\mathrm{Ga}}$. The energy needed for ${\mathrm{Zn}}_{i}$ to dissociate from this donor complex is estimated to be 2.99 eV, in reasonable agreement with the trap dissociation energies extracted from the diffusion model.