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.

中文翻译：

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单斜β-Ga2O3中镓空位对浅层供体的补偿

深层次的根源及其对电性能影响的知识，对于器件应用的关键β -${嘎}_{\mathrm{2个}}{\mathrm{Ø}}_3$。通过在氧气下退火（${\mathrm{Ø}}_{\mathrm{2个}}$）气氛下，在浅施主（锆的电阻率）掺杂β -${嘎}_{\mathrm{2个}}{\mathrm{Ø}}_3$：$锆$ 发现单晶增加了10个数量级以上，达到（7±4）×10Ωcm，这与铁获得的电阻率相当（$铁$）（5±3）×10Ωcm的受体掺杂。我们将热电效应光谱法和正电子an没光谱法（PAS）结合在一起，对深水平和开孔缺陷浓度敏感，并结合电学性质建模，以研究这些强补偿晶体。我们在${\mathrm{Ø}}_{\mathrm{2个}}$-annealed β -${嘎}_{\mathrm{2个}}{\mathrm{Ø}}_3$：$锆$样品位于导带下方（0.727±0.021）eV（E 2 *），与PAS数据中的空位信号相关。缺陷很可能是松弛的裂缝$嘎$ 空缺 ${\mathrm{伏特}}_{嘎}^{\mathrm{一世}}$，而不是简单的镓空位，而是要考虑到放松的较小能量壁垒的理论预测。我们观察到，由于这些空位的独特性质和单斜晶格中的各向异性，与其他宽隙化合物相比，多普勒展宽参数相当小，在这种情况下，正电子扩散长度是估算的合适参数开孔缺陷浓度。