Possible bandgap values of graphene-like ZnO in density functional theory corrected by the Hubbard U term and HSE hybrid functional

Predicting the realistic bandgap of a semiconductor is critical to its applications. A relatively new two-dimensional semiconducting structure with few experimental reports is graphene-like ZnO (g-ZnO). Although the bandgaps of various bulk structures of ZnO are well-known experimentally and theoretically, there is not yet any experimental report on the bandgap of g-ZnO. On the other hand, the standard density functional theory (DFT) grossly underestimates the bandgap of metal oxides, especially in the case of the bulk wurtzite ZnO with the predicted bandgap of similar to 0.72 eV as compared to the experimental bandgap of similar to 3.3 eV. There are two widely used approaches to partly resolve the problem of DFT: (1) the computationally expensive use of hybrid functionals and (2) the computationally inexpensive inclusion of the Hubbard on-site Coulombic term (DFT+ U). Here, we studied the dependence of the bandgap on the parameters existing in both approaches. We showed that by increasing the mixing parameter in HSE hybrid functional, one could linearly widen the bandgap of g-ZnO. Next, we showed that by increasing the Hubbard U term applied to Zn 3d orbitals, one could widen the bandgap. However, even high values of the term are not alone able to properly improve the bandgap. On the other hand, we found that by increasing the Hubbard U term applied to O 2p orbitals, one could again widen the bandgap. Lastly, we derived the parametrized dependence of the bandgap calculated in both approaches. In particular, we show that the optimal values of UZn-3d and UO-2p found by others for bulk wurtzite ZnO could be used as a first guess for g-ZnO to correct its bandgap in computational works. However, a better prediction will be achieved based on the future experimental bandgap values of g-ZnO.