skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Substitutional impurity in single-layer graphene: The Koster–Slater and Anderson models

Abstract

The Koster–Slater and Anderson models are used to consider substitutional impurities in free-standing single-layer graphene. The density of states of graphene is described using a model (the M model). For the nitrogen and boron impurities, the occupation numbers and the parameter η which defines the fraction of delocalized electrons of the impurity are determined. In this case, experimental data are used for both determination of the model parameters and comparison with the results of theoretical estimations. The general features of the Koster–Slater and Anderson models and the differences between the two models are discussed. Specifically, it is shown that the band contributions to the occupation numbers of a nitrogen atom in both models are comparable, whereas the local contributions are substantially different: the local contributions are decisive in the Koster–Slater model and negligible in the Anderson model. The asymptotic behavior of the wave functions of a defect is considered in the Koster–Slater model, and the electron states of impurity dimers are considered in the Anderson model.

Authors:
 [1]
  1. Russian Academy of Sciences, Ioffe Physical–Technical Institute (Russian Federation)
Publication Date:
OSTI Identifier:
22645498
Resource Type:
Journal Article
Resource Relation:
Journal Name: Semiconductors; Journal Volume: 50; Journal Issue: 6; Other Information: Copyright (c) 2016 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; BORON; COMPARATIVE EVALUATIONS; DENSITY OF STATES; DIMERS; ELECTRONIC STRUCTURE; ELECTRONS; GRAPHENE; IMPURITIES; LAYERS; NITROGEN; WAVE FUNCTIONS

Citation Formats

Davydov, S. Yu., E-mail: sergei-davydov@mail.ru. Substitutional impurity in single-layer graphene: The Koster–Slater and Anderson models. United States: N. p., 2016. Web. doi:10.1134/S106378261606004X.
Davydov, S. Yu., E-mail: sergei-davydov@mail.ru. Substitutional impurity in single-layer graphene: The Koster–Slater and Anderson models. United States. doi:10.1134/S106378261606004X.
Davydov, S. Yu., E-mail: sergei-davydov@mail.ru. 2016. "Substitutional impurity in single-layer graphene: The Koster–Slater and Anderson models". United States. doi:10.1134/S106378261606004X.
@article{osti_22645498,
title = {Substitutional impurity in single-layer graphene: The Koster–Slater and Anderson models},
author = {Davydov, S. Yu., E-mail: sergei-davydov@mail.ru},
abstractNote = {The Koster–Slater and Anderson models are used to consider substitutional impurities in free-standing single-layer graphene. The density of states of graphene is described using a model (the M model). For the nitrogen and boron impurities, the occupation numbers and the parameter η which defines the fraction of delocalized electrons of the impurity are determined. In this case, experimental data are used for both determination of the model parameters and comparison with the results of theoretical estimations. The general features of the Koster–Slater and Anderson models and the differences between the two models are discussed. Specifically, it is shown that the band contributions to the occupation numbers of a nitrogen atom in both models are comparable, whereas the local contributions are substantially different: the local contributions are decisive in the Koster–Slater model and negligible in the Anderson model. The asymptotic behavior of the wave functions of a defect is considered in the Koster–Slater model, and the electron states of impurity dimers are considered in the Anderson model.},
doi = {10.1134/S106378261606004X},
journal = {Semiconductors},
number = 6,
volume = 50,
place = {United States},
year = 2016,
month = 6
}
  • In this paper we present the results of our Slater-Koster or tight-binding interpolation of the single-particle energy eigenvalues of a complex crystal. The parameters occurring in the model Hamiltonian are determined by fitting the eigenvalues to [ital ab] [ital initio] values. The error in these fits can be reduced to the same value (less than 1 mRy per point), as is usual for simple materials with a highly symmetric structure. We also studied the variation of the parameters in the model Hamiltonian as a function of lattice geometry. Although one expects that these parameters are simple functions of the bondmore » length, our results did not reveal such a simple behavior. Hence, we conclude that Slater-Koster interpolation schemes are very useful tools for calculating electronic properties for a given geometry, but that their use in calculating forces on atoms is suspect.« less
  • A tight-binding procedure is presented for fitting electronic band structures of crystals. It is based on a fully automated method of determining all possible independent matrix elements for arbitrary crystal structures. A fit, using this method, for the band structure of hexagonal close-packed Tc is more than an order of magnitude better than previous fits.
  • The need for tight-binding total-energy representations of interatomic forces has renewed interest in Slater-Koster parametrization of electron band structure. For larger numbers of parameters, as in multicomponent systems, and to truly test issues of transferability, it is advantageous to have means of directly calculating these parameters. Here we derive analytic expressions for the two-center Slater-Koster hopping parameters, effective site energies, and effective crystal-field parameters in terms of the one-electron Hamiltonian {ital matrix} elements in any localized minimal basis, and analogous quantities for the overlap. We apply these expressions to the cubic diamond phases of Si and B, and the zinc-blendemore » phase of SiB at three volumes each, using spd, nonorthogonal full potential linear muffin-tin orbital matrix elements calculated with a linked or contracted minimal basis. {copyright} {ital 1997} {ital The American Physical Society}« less
  • Two-center Slater-Koster integrals may be expressed as linear combinations of simpler polynomials that can either be factored or are of lower power in the direction cosines. This structure facilitates their tabulation and manipulation, as illustrated here by providing the complete set of s-f two-center integrals in this manner, as well as values of their m,m{sup {prime}}-matrix dot products. The latter provide useful constraints for testing analytic or coded forms of these functions. These dot products also define a transformed two-center expansion which provides more convenient treatment of crystal-field terms. {copyright} {ital 1998} {ital The American Physical Society}