DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Fundamental Principles for Calculating Charged Defect Ionization Energies in Ultrathin Two-Dimensional Materials

Abstract

Defects in two-dimensional (2D) materials are becoming prominent candidates for quantum emitters and scalable optoelectronic applications. However, several physical properties that characterize their behavior, such as charged defect ionization energies, are difficult to simulate with conventional first-principles methods, mainly because of the weak and anisotropic dielectric screening caused by the reduced dimensionality. We establish fundamental principles for accurate and efficient calculations of charged defect ionization energies and electronic structure in ultrathin 2D materials. We propose to use the vacuum level as the reference for defect charge transition levels (CTLs) because it gives robust results insensitive to the level of theory, unlike commonly used band-edge positions. Furthermore, we determine the fraction of Fock exchange in hybrid functionals for accurate band gaps and band-edge positions of 2D materials by enforcing the generalized Koopmans’ condition of localized defect states. We found that the obtained fractions of Fock exchange vary significantly from 0.2 for bulk hexagonal boron nitride (h-BN) to 0.4 for monolayer h-BN, whose band gaps are also in good agreement with experimental results and calculated GW results. The combination of these methods allows for the reliable and efficient prediction of defect ionization energies (the difference between CTLs and band-edge positions). We motivatemore » and generalize these findings with several examples including different defects in monolayer to few-layer h-BN, monolayer MoS2, and graphane. Lastly, we show that increasing the number of layers of h-BN systematically lowers defectionization energies, mainly through CTLs shifting towards vacuum, with conduction band minima kept almost unchanged.« less

Authors:
 [1];  [1];  [2];  [1]
  1. Univ. of California Santa Cruz, Santa Cruz, CA (United States)
  2. Argonne National Lab. (ANL), Lemont, IL (United States); Univ. of Chicago, Chicago, IL (United States)
Publication Date:
Research Org.:
Argonne National Laboratory (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1490339
Alternate Identifier(s):
OSTI ID: 1488641
Grant/Contract Number:  
AC02-06CH11357; AC02-05CH11231; SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Materials
Additional Journal Information:
Journal Volume: 2; Journal Issue: 12; Journal ID: ISSN 2475-9953
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; Quantum informatoin science; Quantum materials

Citation Formats

Smart, Tyler J., Wu, Feng, Govoni, Marco, and Ping, Yuan. Fundamental Principles for Calculating Charged Defect Ionization Energies in Ultrathin Two-Dimensional Materials. United States: N. p., 2018. Web. doi:10.1103/PhysRevMaterials.2.124002.
Smart, Tyler J., Wu, Feng, Govoni, Marco, & Ping, Yuan. Fundamental Principles for Calculating Charged Defect Ionization Energies in Ultrathin Two-Dimensional Materials. United States. https://doi.org/10.1103/PhysRevMaterials.2.124002
Smart, Tyler J., Wu, Feng, Govoni, Marco, and Ping, Yuan. Thu . "Fundamental Principles for Calculating Charged Defect Ionization Energies in Ultrathin Two-Dimensional Materials". United States. https://doi.org/10.1103/PhysRevMaterials.2.124002. https://www.osti.gov/servlets/purl/1490339.
@article{osti_1490339,
title = {Fundamental Principles for Calculating Charged Defect Ionization Energies in Ultrathin Two-Dimensional Materials},
author = {Smart, Tyler J. and Wu, Feng and Govoni, Marco and Ping, Yuan},
abstractNote = {Defects in two-dimensional (2D) materials are becoming prominent candidates for quantum emitters and scalable optoelectronic applications. However, several physical properties that characterize their behavior, such as charged defect ionization energies, are difficult to simulate with conventional first-principles methods, mainly because of the weak and anisotropic dielectric screening caused by the reduced dimensionality. We establish fundamental principles for accurate and efficient calculations of charged defect ionization energies and electronic structure in ultrathin 2D materials. We propose to use the vacuum level as the reference for defect charge transition levels (CTLs) because it gives robust results insensitive to the level of theory, unlike commonly used band-edge positions. Furthermore, we determine the fraction of Fock exchange in hybrid functionals for accurate band gaps and band-edge positions of 2D materials by enforcing the generalized Koopmans’ condition of localized defect states. We found that the obtained fractions of Fock exchange vary significantly from 0.2 for bulk hexagonal boron nitride (h-BN) to 0.4 for monolayer h-BN, whose band gaps are also in good agreement with experimental results and calculated GW results. The combination of these methods allows for the reliable and efficient prediction of defect ionization energies (the difference between CTLs and band-edge positions). We motivate and generalize these findings with several examples including different defects in monolayer to few-layer h-BN, monolayer MoS2, and graphane. Lastly, we show that increasing the number of layers of h-BN systematically lowers defectionization energies, mainly through CTLs shifting towards vacuum, with conduction band minima kept almost unchanged.},
doi = {10.1103/PhysRevMaterials.2.124002},
journal = {Physical Review Materials},
number = 12,
volume = 2,
place = {United States},
year = {Thu Dec 20 00:00:00 EST 2018},
month = {Thu Dec 20 00:00:00 EST 2018}
}

Journal Article:

Citation Metrics:
Cited by: 47 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Development of exchange-correlation functionals with minimal many-electron self-interaction error
journal, May 2007

  • Cohen, Aron J.; Mori-Sánchez, Paula; Yang, Weitao
  • The Journal of Chemical Physics, Vol. 126, Issue 19
  • DOI: 10.1063/1.2741248

First-principles calculations of the dielectric properties of silicon nanostructures
journal, January 2008

  • Hamel, S.; Williamson, A. J.; Wilson, H. F.
  • Applied Physics Letters, Vol. 92, Issue 4
  • DOI: 10.1063/1.2839332

Progress, Challenges, and Opportunities in Two-Dimensional Materials Beyond Graphene
journal, March 2013

  • Butler, Sheneve Z.; Hollen, Shawna M.; Cao, Linyou
  • ACS Nano, Vol. 7, Issue 4, p. 2898-2926
  • DOI: 10.1021/nn400280c

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
journal, September 2009

  • Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola
  • Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502
  • DOI: 10.1088/0953-8984/21/39/395502

Fully Ab Initio Finite-Size Corrections for Charged-Defect Supercell Calculations
journal, January 2009


Accuracy of G W for calculating defect energy levels in solids
journal, July 2017


Deep-to-shallow level transition of Re and Nb dopants in monolayer MoS 2 with dielectric environments
journal, September 2015


Proof that E n i = ε in density-functional theory
journal, December 1978


Optimized norm-conserving Vanderbilt pseudopotentials
journal, August 2013


Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy
journal, December 1982


Resolution of the Band Gap Prediction Problem for Materials Design
journal, March 2016

  • Crowley, Jason M.; Tahir-Kheli, Jamil; Goddard, William A.
  • The Journal of Physical Chemistry Letters, Vol. 7, Issue 7
  • DOI: 10.1021/acs.jpclett.5b02870

Quantum emitters in two dimensions
journal, October 2017


First-principles determination of defect energy levels through hybrid density functionals and GW
journal, March 2015


Truncation of periodic image interactions for confined systems
journal, June 2006


Assessing the accuracy of hybrid functionals in the determination of defect levels: Application to the As antisite in GaAs
journal, August 2011


XSEDE: Accelerating Scientific Discovery
journal, September 2014

  • Towns, John; Cockerill, Timothy; Dahan, Maytal
  • Computing in Science & Engineering, Vol. 16, Issue 5
  • DOI: 10.1109/MCSE.2014.80

First-principles electrostatic potentials for reliable alignment at interfaces and defects
journal, March 2017

  • Sundararaman, Ravishankar; Ping, Yuan
  • The Journal of Chemical Physics, Vol. 146, Issue 10
  • DOI: 10.1063/1.4978238

JDFTx: Software for joint density-functional theory
journal, January 2017


Engineering two-dimensional electronics by semiconductor defects
journal, October 2017


Concept of dielectric constant for nanosized systems
journal, September 2003


Nonempirical hybrid functionals for band gaps and polaronic distortions in solids
journal, March 2018


Defect engineering of two-dimensional transition metal dichalcogenides
journal, April 2016


Monolayer to Bulk Properties of Hexagonal Boron Nitride
journal, October 2018

  • Wickramaratne, Darshana; Weston, Leigh; Van de Walle, Chris G.
  • The Journal of Physical Chemistry C, Vol. 122, Issue 44
  • DOI: 10.1021/acs.jpcc.8b09087

Electronic Structure and Luminescence of Quasi-Freestanding MoS 2 Nanopatches on Au(111)
journal, July 2016


Insights into Current Limitations of Density Functional Theory
journal, August 2008


First-Principles Calculations of Point Defects for Quantum Technologies
journal, July 2018


Efficient many-body calculations for two-dimensional materials using exact limits for the screened potential: Band gaps of MoS 2 ,   h -BN, and phosphorene
journal, October 2016


Hexagonal boron nitride is an indirect bandgap semiconductor
journal, January 2016


Using Wannier functions to improve solid band gap predictions in density functional theory
journal, April 2016


Density‐functional thermochemistry. III. The role of exact exchange
journal, April 1993

  • Becke, Axel D.
  • The Journal of Chemical Physics, Vol. 98, Issue 7, p. 5648-5652
  • DOI: 10.1063/1.464913

Screening and many-body effects in two-dimensional crystals: Monolayer MoS 2
journal, June 2016


Convergence of density and hybrid functional defect calculations for compound semiconductors
journal, September 2013


Length dependence of ionization potentials of transacetylenes: Internally consistent DFT/ G W approach
journal, November 2015


Charged Point Defects in the Flatland: Accurate Formation Energy Calculations in Two-Dimensional Materials
journal, September 2014

  • Komsa, Hannu-Pekka; Berseneva, Natalia; Krasheninnikov, Arkady V.
  • Physical Review X, Vol. 4, Issue 3
  • DOI: 10.1103/PhysRevX.4.031044

Self-consistent hybrid functional for condensed systems
journal, May 2014


Hole Localization in Molecular Crystals from Hybrid Density Functional Theory
journal, June 2011


Color Centers in Hexagonal Boron Nitride Monolayers: A Group Theory and Ab Initio Analysis
journal, April 2018


Determination of Formation and Ionization Energies of Charged Defects in Two-Dimensional Materials
journal, May 2015


Accurate formation energies of charged defects in solids: A systematic approach
journal, June 2017

  • Vinichenko, Dmitry; Sensoy, Mehmet Gokhan; Friend, Cynthia M.
  • Physical Review B, Vol. 95, Issue 23
  • DOI: 10.1103/PhysRevB.95.235310

Nonuniform sampling schemes of the Brillouin zone for many-electron perturbation-theory calculations in reduced dimensionality
journal, January 2017


Quantum emission from hexagonal boron nitride monolayers
journal, October 2015

  • Tran, Toan Trong; Bray, Kerem; Ford, Michael J.
  • Nature Nanotechnology, Vol. 11, Issue 1
  • DOI: 10.1038/nnano.2015.242

Bright UV Single Photon Emission at Point Defects in h -BN
journal, June 2016


Coupling of excitons and defect states in boron-nitride nanostructures
journal, April 2011


Calculating excitons, plasmons, and quasiparticles in 2D materials and van der Waals heterostructures
journal, June 2017


Optically Discriminating Carrier-Induced Quasiparticle Band Gap and Exciton Energy Renormalization in Monolayer MoS 2
journal, August 2017


Observation of monolayer valence band spin-orbit effect and induced quantum well states in MoX2
journal, August 2014

  • Alidoust, Nasser; Bian, Guang; Xu, Su-Yang
  • Nature Communications, Vol. 5, Issue 1
  • DOI: 10.1038/ncomms5673

First-principles calculations for point defects in solids
journal, March 2014

  • Freysoldt, Christoph; Grabowski, Blazej; Hickel, Tilmann
  • Reviews of Modern Physics, Vol. 86, Issue 1
  • DOI: 10.1103/RevModPhys.86.253

Role of Si and Ge as impurities in ZnO
journal, November 2009


Defect levels through hybrid density functionals: Insights and applications
journal, March 2011

  • Alkauskas, Audrius; Broqvist, Peter; Pasquarello, Alfredo
  • physica status solidi (b), Vol. 248, Issue 4
  • DOI: 10.1002/pssb.201046195

Electrostatics-based finite-size corrections for first-principles point defect calculations
journal, May 2014


G W Approximation of the Many-Body Problem and Changes in the Particle Number
journal, October 2009


Defect Energy Levels in Density Functional Calculations: Alignment and Band Gap Problem
journal, July 2008


Hybrid Surface-Phonon-Plasmon Polariton Modes in Graphene/Monolayer h-BN Heterostructures
journal, June 2014

  • Brar, Victor W.; Jang, Min Seok; Sherrott, Michelle
  • Nano Letters, Vol. 14, Issue 7
  • DOI: 10.1021/nl501096s

New algebraic formulation of density functional calculation
journal, June 2000


Native point defects and impurities in hexagonal boron nitride
journal, June 2018


Optimization algorithm for the generation of ONCV pseudopotentials
journal, November 2015


G W calculations using the spectral decomposition of the dielectric matrix: Verification, validation, and comparison of methods
journal, April 2013


Generalization of Dielectric-Dependent Hybrid Functionals to Finite Systems
journal, October 2016


Quasiparticle GW calculations for solids, molecules, and two-dimensional materials
journal, June 2013


First-principles DFT + G W study of oxygen vacancies in rutile TiO 2
journal, February 2014


First-principles investigation of quantum emission from hBN defects
journal, January 2017

  • Tawfik, Sherif Abdulkader; Ali, Sajid; Fronzi, Marco
  • Nanoscale, Vol. 9, Issue 36
  • DOI: 10.1039/C7NR04270A

First-principles engineering of charged defects for two-dimensional quantum technologies
journal, December 2017


Organic Electronic Materials: Recent Advances in the DFT Description of the Ground and Excited States Using Tuned Range-Separated Hybrid Functionals
journal, April 2014

  • Körzdörfer, Thomas; Brédas, Jean-Luc
  • Accounts of Chemical Research, Vol. 47, Issue 11
  • DOI: 10.1021/ar500021t

Correspondence of defect energy levels in hybrid density functional theory and many-body perturbation theory
journal, September 2013


Large Scale GW Calculations
journal, May 2015

  • Govoni, Marco; Galli, Giulia
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 6
  • DOI: 10.1021/ct500958p

Advanced capabilities for materials modelling with Quantum ESPRESSO
journal, October 2017

  • Giannozzi, P.; Andreussi, O.; Brumme, T.
  • Journal of Physics: Condensed Matter, Vol. 29, Issue 46
  • DOI: 10.1088/1361-648X/aa8f79

Universal slow plasmons and giant field enhancement in atomically thin quasi-two-dimensional metals
journal, February 2020


Quantum Emission from Hexagonal Boron Nitride Monolayers
conference, January 2016

  • Tran, Toan Trong; Bray, Kerem; Ford, Michael J.
  • CLEO: QELS_Fundamental Science, Conference on Lasers and Electro-Optics
  • DOI: 10.1364/cleo_qels.2016.ftu4d.1

Advanced capabilities for materials modelling with Quantum ESPRESSO
text, January 2017


Defect Energy Levels in Density Functional Calculations: Alignment and Band Gap Problem
text, January 2008


Coupling of excitons and defect states in boron-nitride nanostructures
text, January 2011


Hole Localization in Molecular Crystals From Hybrid Density Functional Theory
text, January 2011


Quasiparticle spectra from a non-empirical optimally-tuned range-separated hybrid density functional
text, January 2012


First-principles DFT+GW study of oxygen vacancies in rutile TiO2
text, January 2014


Self-consistent hybrid functional for condensed systems
text, January 2015


Hexagonal boron nitride is an indirect bandgap semiconductor
text, January 2015


Accurate formation energies of charged defects in solids: a systematic approach
text, January 2017


JDFTx: software for joint density-functional theory
text, January 2017


Advanced capabilities for materials modelling with Quantum ESPRESSO
text, January 2017


First-principles Engineering of Charged Defects for Two-dimensional Quantum Technologies
text, January 2017


Works referencing / citing this record:

Substrate effects on charged defects in two-dimensional materials
journal, August 2019


Optical absorption induced by small polaron formation in transition metal oxides: The case of Co 3 O 4
journal, October 2019


Ab initio theory of the nitrogen-vacancy center in diamond
journal, September 2019


Dielectric dependent hybrid functionals for heterogeneous materials
text, January 2019