Direct determination of band-gap renormalization in degenerately doped ultrawide band gap β-Ga2O3 semiconductor

${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ is emerging as a promising wide band-gap semiconductor for high-power electronics and deep ultraviolet optoelectronics. It is highly desirable to dope it with controllable carrier concentrations for different device applications. This work reports a combined photoemission spectroscopy and theoretical calculation study on the electronic structure of Si doped ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ films with carrier concentration varying from $4.6\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{0.28em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$ to $2.6\ifmmode\times\else\texttimes\fi{}{10}^{20}\phantom{\rule{0.28em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$. Hard x-ray photoelectron spectroscopy was used to directly measure the widening of the band gap as a result of occupation of conduction band and band-gap renormalization associated with many-body interactions. A large band-gap renormalization of 0.3 eV was directly observed in heavily doped ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$. Supplemented with hybrid density functional theory calculations, we demonstrated that the band-gap renormalization results from the decrease in energy of the conduction band edge driven by the mutual electrostatic interaction between added electrons. Moreover, our work reveals that Si is a superior dopant over Ge and Sn, because $\mathrm{Si}\phantom{\rule{0.28em}{0ex}}3s$ forms a resonant donor state above the conduction band minimum, leaving the host conduction band mostly unperturbed and a high mobility is maintained though the doping level is high. Insights of the present work have significant implications in doping optimization of ${\mathrm{Ga}}_{2}{\mathrm{O}}_{3}$ and realization of optoelectronic devices.