title: Determination of formation and ionization energies of charged defects in two-dimensional materials.
abstract: We present a simple and efficient approach to evaluate the formation energy and, in particular, the ionization energy (IE) of charged defects in two-dimensional (2D) systems using the supercell approximation. So far, first-principles results for such systems can scatter widely due to the divergence of the Coulomb energy with vacuum dimension, denoted here as L_{z}. Numerous attempts have been made in the past to fix the problem under various approximations. Here, we show that the problem can be resolved without any such assumption, and a converged IE can be obtained by an extrapolation of the asymptotic IE expression at large L_{z} (with a fixed lateral area S) back to the value at L_{z}=0. Application to defects in monolayer boron nitride reveal that defects in 2D systems can be unexpectedly deep, much deeper than the bulk.
authors.affiliation: State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China.
authors.forename: Dan
authors.initials: D
authors.lastname: Wang
authors.affiliation: State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China.|Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
authors.forename: Dong
authors.initials: D
authors.lastname: Han
authors.affiliation: State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China.
authors.forename: Xian-Bin
authors.initials: XB
authors.lastname: Li
authors.affiliation: State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China.
authors.forename: Sheng-Yi
authors.initials: SY
authors.lastname: Xie
authors.affiliation: State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China.
authors.forename: Nian-Ke
authors.initials: NK
authors.lastname: Chen
authors.affiliation: State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China.|Institute of Theoretical Chemistry, Jilin University, Changchun 130012, China.
authors.forename: Wei Quan
authors.initials: WQ
authors.lastname: Tian
authors.affiliation: Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
authors.forename: Damien
authors.initials: D
authors.lastname: West
authors.affiliation: State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China.
authors.forename: Hong-Bo
authors.initials: HB
authors.lastname: Sun
authors.affiliation: State Key Laboratory on Integrated Optoelectronics, College of Electronic Science and Engineering, Jilin University, Changchun 130012, China.|Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
authors.forename: S B
authors.initials: SB
authors.lastname: Zhang