Native point defects and doping in ZnGeN$_2$

A computational study within the framework of density functional theory is presented for native defects and doping in ZnGeN$_2$. We study the three types of vacancies $V_{\rm Zn}$, $V_{\rm Ge}$, $V_{\rm N}$, cation antisite defects Zn$_{\rm Ge}$, Ge$_{\rm Zn}$, and potential n-type (O$_{\rm N}$, Ga$_{\rm Zn}$) and p-type Ga$_{\rm Ge}$ dopants. The cation antisite defects are found to have significantly lower formation energy than the cation vacancies. The charge neutrality condition pins the Fermi level close to the the crossing of the ${\rm Zn}_{\rm Ge}^{-1}$ acceptor with the ${\rm Ge}_{\rm Zn}^{2+}$ donor, and intrinsic $p$-type doping would result. The $V_{\rm N}$ is found to be a rather deep donor. ${\rm Ge}_{\rm Zn}$ is found to behave as a shallow donor. Oxygen impurities are found to strongly prefer the ${\rm O}_{\rm N}$ subsitutional site and are found to be shallow donors with a very low energy of formation. Energies of formation of ${\rm Ga}_{\rm Zn}$ and ${\rm Ga}_{\rm Ge}$ are lower than those of the cation antisites. Thus good solubility is expected and these impurities can hence pin the Fermi level at the crossing of the donor ${\rm Ga}_{\rm Zn}^{+1}$ with the acceptor ${\rm Ga}_{\rm Ge}^{-1}$, and efficient $p$-type doping should result.