Formation of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>E</mml:mi><mml:mn>4</mml:mn><mml:mo>*</mml:mo></mml:msubsup></mml:math> level in implanted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mr

Deep-level transient spectroscopy measurements were conducted on He-implanted $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ thin films to study the ${E}_{4}^{*}$ level, which is a known irradiation-induced defect that is energetically positioned $1.5\phantom{\rule{0.16em}{0ex}}\mathrm{e}\mathrm{V}$ below the conduction band minimum. We find that the formation of ${E}_{4}^{*}$ after implantation is strongly dependent on a reverse-bias annealing step, where the activation energy for the thermally-activated introduction of ${E}_{4}^{*}$ is estimated to be $\ensuremath{\sim}2.4\phantom{\rule{0.16em}{0ex}}\mathrm{e}\mathrm{V}$. Contrary to previous reports, we find, for some of the measured diodes, that the level is stable upon subsequent measurements. From first-principles calculations of the intrinsic defects, we find that the properties of the ${V}_{\text{O1}}$ and ${V}_{\text{O3}}$ configurations of the oxygen vacancy closely agree with the experimental observations for the ${E}_{4}^{*}$ level. A model is suggested where the reverse bias lowers the Fermi-level position in the depletion region of the diode and changes the relative formation energies of the possible configurations of the oxygen vacancy; the formation of ${E}_{4}^{*}$ then results from an increase in the relative stability of the O1 and O3 configurations of ${V}_{\mathrm{O}}$.