Abstract

Layered materials are presently under intense study, and most applications require knowledge about their defects. It has been shown earlier that the screened hybrid functional of Heyd, Scuseria, and Ernzerhof (HSE), with parameters tuned to reproduce the relative position of the band edges and to satisfy the generalized Koopmans' theorem in the given material, is capable of providing defect properties very accurately in traditional bulk semiconductors. This success is thought to be connected to the proper description of electronic screening. In this paper we investigate whether such a functional can be optimized for layered compounds, such as GaSe and hexagonal BN (hBN). While we find this to be possible in the bulk materials, as expected, the optimal parameters change significantly in the monolayers (ML), due to the effect of the surface on the electronic screening. For ML GaSe (thickness $\ensuremath{\sim}5\phantom{\rule{0.16em}{0ex}}\AA{}$), where the dielectric constant does not change much within the layer, a reoptimization is possible, while for the atomically thin ML hBN the optimization criteria can only be met approximately. In other words, the accuracy which can be achieved for the electronic structure of defects by a HSE functional will always be less in atomically thin monolayers than in the bulk built from such layers. We also show that the accuracy of HSE functionals, with parameters optimized for the bulk in traditional (nonlayered) bulk semiconductors, also diminishes in surface calculations, even for thick slabs, if the dielectric constant $({\ensuremath{\varepsilon}}^{\ensuremath{\infty}})$ is low. Generally, the accuracy of bulk and surface calculation by any functional can be very different.