Compensation of Shallow Donors by Gallium Vacancies in Monoclinic <i>β</i>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><mml:msub><mml:mi>Ga</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow></mml:mrow><mml:mn>3</mml:mn></mml:msub></mml:math>
Santosh K. Swain, Marc H. Weber, Jani Jesenovec, Muad Saleh, Kelvin G. Lynn, John S. McCloy
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.