Compensation of Shallow Donors by Gallium Vacancies in Monoclinic β - Ga2O3

Abstract

Knowledge of the origin of deep levels and their impact on electrical properties is critical for device applications of \ensuremath{\beta}-${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. By annealing under an oxygen (${\mathrm{O}}_{2}$) atmosphere, the resistivity in shallow-donor (zirconium) doped \ensuremath{\beta}-${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$:$\mathrm{Zr}$ single crystals is found to increase by more than 10 orders of magnitude to (7 \ifmmode\pm\else\textpm\fi{} 4) \ifmmode\times\else\texttimes\fi{} 10 \ensuremath{\Omega} cm, which is comparable to the resistivity achieved by iron ($\mathrm{Fe}$) acceptor doping of (5 \ifmmode\pm\else\textpm\fi{} 3) \ifmmode\times\else\texttimes\fi{} 10 \ensuremath{\Omega} cm. We combine thermoelectric effect spectroscopy and positron annihilation spectroscopy (PAS), which are sensitive to deep levels and concentration of open-volume defects, with modeling of the electrical properties, to study these strongly compensated crystals. We find the compensating level in the ${\mathrm{O}}_{2}$-annealed \ensuremath{\beta}-${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$:$\mathrm{Zr}$ sample to be located at (0.727 \ifmmode\pm\else\textpm\fi{} 0.021) eV (E2*) below the conduction band, which correlates with a vacancy signal from PAS data. The defect is most likely the relaxed split $\mathrm{Ga}$ vacancy ${V}_{\mathrm{Ga}}^{i}$, rather than a simple gallium vacancy, considering theoretical predictions of a small energy barrier to relax. We observe that, due to the unique nature of these vacancies and anisotropy in the monoclinic lattice, the Doppler-broadening parameter is rather small compared with other wide-gap compounds, and in such a case the positron diffusion length is a suitable parameter to estimate the open-volume defect concentration.