Knowledge of the origin of deep levels and their impact on electrical properties is critical for device applications of β-${\mathrm{Ga}}_2{\mathrm{O}}_3$. By annealing under an oxygen (${\mathrm{O}}_2$) atmosphere, the resistivity in shallow-donor (zirconium) doped β-${\mathrm{Ga}}_2{\mathrm{O}}_3$:$\mathrm{Zr}$ single crystals is found to increase by more than 10 orders of magnitude to (7 ± 4) × 10 Ω cm, which is comparable to the resistivity achieved by iron ($\mathrm{Fe}$) acceptor doping of (5 ± 3) × 10 Ω 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 β-${\mathrm{Ga}}_2{\mathrm{O}}_3$:$\mathrm{Zr}$ sample to be located at (0.727 ± 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.

• Received 24 July 2020
• Revised 10 February 2021
• Accepted 21 April 2021

DOI:https://doi.org/10.1103/PhysRevApplied.15.054010