Abstract
Impurities and defects frequently govern materials properties, with the most prominent example being the doping of bulk semiconductors where a minute amount of foreign atoms can be responsible for the operation of the electronic devices. Several computational schemes based on a supercell approach have been developed to get insights into types and equilibrium concentrations of point defects, which successfully work in bulk materials. Here, we show that many of these schemes cannot directly be applied to two-dimensional (2D) systems, as formation energies of charged point defects are dominated by large spurious electrostatic interactions between defects in inhomogeneous environments. We suggest two approaches that solve this problem and give accurate formation energies of charged defects in 2D systems in the dilute limit. Our methods, which are applicable to all kinds of charged defects in any 2D system, are benchmarked for impurities in technologically important -BN and 2D materials, and they are found to perform equally well for substitutional and adatom impurities.
- Received 10 March 2014
DOI:https://doi.org/10.1103/PhysRevX.4.031044
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Published by the American Physical Society
Erratum
Erratum: Charged Point Defects in the Flatland: Accurate Formation Energy Calculations in Two-Dimensional Materials [Phys. Rev. X 4, 031044 (2014)]
Hannu-Pekka Komsa, Natalia Berseneva, Arkady V. Krasheninnikov, and Risto M. Nieminen
Phys. Rev. X 8, 039902 (2018)
Popular Summary
Impurities and defects frequently dictate the properties of materials. For example, foreign atoms in semiconductors provide extra charge carriers and govern electronic properties. The physics of charged dopant atoms in bulk materials is now well understood, in part because of the efficient computational schemes developed for calculating charged defect characteristics within the framework of density-functional theory. However, these schemes do not work for two-dimensional semiconductors (e.g., transition-metal dichalcogenides), which are among the most intensively studied materials, because of large, spurious electrostatic interactions between defects. We suggest two approaches that solve this problem and provide accurate formation energies of charged defects in two-dimensional systems in the dilute limit.
Charged defects have been only rarely studied, and simple extrapolations of formation energies in two-dimensional semiconductors often lead to incorrect and divergent results. We calculate the properties of charged defects in technologically important materials such as -BN and , taking into account intralayer and interlayer interactions. We construct the dielectric constant profile by assuming that the profile follows the charge-density distribution of the system. The second technique is based on choosing a special level of vacuum between periodic images in the two-dimensional sheets. The proposed computational schemes solve the problem of accurate calculations of defect formation energies in two-dimensional systems, and our methods perform equally well for substitutional and adatom impurities.
The schemes that we propose may be an important step toward a better understanding of the role that charged impurities play in realistic, two-dimensional semiconductors and insulators that have widespread technological uses.