Structural and electronic properties of ZnGeN$_2$*

ZnGeN$_2$ is a direct-band-gap earth-abundant semiconductor that is a candidate material for photovoltaic and light-emitting devices. Elucidating the potential use of ZnGeN$_2$ in such applications requires an accurate knowledge of its structural and electronic properties, as well as an understanding of the role of native point defects in the material at the microscopic level. Using density functional theory with a hybrid functional, we study the structural and electronic properties of ZnGeN$_2$. We investigate the role of native point defects, specifically antisites, vacancies and interstitials, and discuss their impact on electronic and optical properties.