Quasiparticle band structure and optical properties of rutile GeO$_2$, an ultra-wide-band-gap semiconductor

Abstract: Rutile GeO$2$ is a visible and near-ultraviolet-transparent oxide that has not been explored for semiconducting applications in electronic and optoelectronic devices. We investigate the electronic and optical properties of rutile GeO$_2$ with first-principles calculations based on density functional theory and many-body perturbation theory. Our band-structure calculations indicate a dipole-forbidden direct band gap at $\Gamma$ with an energy of 4.44 eV and effective masses equal to $m^*{e\perp}$ =0.43$m_0$ , $m^*_{e||}$ =0.23$m_0$ , $m^*_{h\perp}$ =1.28$m_0$ , and $m^*_{h||}$=1.74$m_0$. In contrast to the self-trapped hole polarons by lattice distortions in other wide-band-gap oxides that reduce the hole mobility, holes in rutile GeO$_2$ are delocalized due to their small effective mass. The first allowed optical transitions at $\Gamma$ occur at 5.04 eV ($\vec{E} \perp \vec{c}$) and 6.65 eV ($\vec{E} ||\vec{c} $). We also evaluate the optical absorption coefficient and refractive index along both crystallographic directions. Our estimates for the exciton binding energies using the Bohr model are close to the reported experimental value. The ultra-wide-band-gap and light carrier effective masses of rutile GeO$_2$, coupled with its optical transparency in the visible and near UV are promising for applications in UV-transparent conductors and solar-blind photodetectors.