Erratum: Charged point defects in the flatland: accurate formation energy calculations in two-dimensional materials (Physical Review X (2014) 4 (031044) DOI: 10.1103/PhysRevX.4.031044));Charged point defects in the flatland: Accurate formation energy calculations in two-dimensional materials

Physical Review X

Volumn 4, Issue 3, 2014, Pages

  Komsa, Hannu Pekka ^a   Berseneva, Natalia ^a   Krasheninnikov, Arkady V ^a   Nieminen, Risto M ^a  

^a AALTO UNIVERSITY   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

BORON NITRIDE; LAYERED SEMICONDUCTORS; MATERIALS PROPERTIES; MOLYBDENUM COMPOUNDS; POINT DEFECTS; SEMICONDUCTOR DOPING;

BULK SEMICONDUCTORS; COMPUTATIONAL SCHEMES; ELECTRONIC DEVICE; EQUILIBRIUM CONCENTRATION; FORMATION ENERGIES; SUPERCELL APPROACH; TWO-DIMENSIONAL (2D) SYSTEMS; TWO-DIMENSIONAL MATERIALS;

IMPURITIES;

EID: 84907029433     PISSN: None     EISSN: 21603308     Source Type: Journal    
DOI: 10.1103/PhysRevX.8.039902     Document Type: Erratum

References (52)

1. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, Two-Dimensional Atomic Crystals, Proc. Natl. Acad. Sci. U.S.A. 102, 10451 (2005).
2. A. K. Geim and K. S. Novoselov, The Rise of Graphene, Nat. Mater. 6, 183 (2007).
3. Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, Electronics and Optoelectronics of Two-Dimensional Transition Metal Dichalcogenides, Nat. Nanotechnol. 7, 699 (2012).
4. M. Chhowalla, H. S. Shin, G. Eda, L.-J. Li, K. P. Loh, and H. Zhang, The Chemistry of Two-Dimensional Layered Transition Metal Dichalcogenide Nanosheets, Nat. Chem. 5, 263 (2013).
5. Defects in Solids, edited by R. J. D. Tilley (Wiley-Interscience, Hoboken, NJ, 2008).
6. H. Terrones, R. Lv,M. Terrones, and M. S. Dresselhaus, The Role of Defects and Doping in 2D Graphene Sheets and 1D Nanoribbons, Rep. Prog. Phys. 75, 062501 (2012).
7. Q. Peng, J. Crean, A. K. Dearden, C. Huang, X. Wen, S. P. A. Bordas, and S. De, Defect Engineering of 2D Monatomic-Layer Materials, Mod. Phys. Lett. B 27, 1330017 (2013).
8. 2, Appl. Phys. Lett. 99, 102109 (2011).
9. P. O. Lehtinen, A. S. Foster, A. Ayuela, A. Krasheninnikov, K. Nordlund, and R. M. Nieminen, Magnetic Properties and Diffusion of Adatoms on a Graphene Sheet, Phys. Rev. Lett. 91, 017202 (2003).
10. D. Jena and A. Konar, Enhancement of Carrier Mobility in Semiconductor Nanostructures by Dielectric Engineering, Phys. Rev. Lett. 98, 136805 (2007).
11. 2 Single Crystal, Phys. Rev. Lett. 110, 247201 (2013).
12. H. Qiu, T. Xu, Z. Wang, W. Ren, H. Nan, Z. Ni, Q. Chen, S. Yuan, F. Miao, F. Song, G. Long, Y. Shi, L. Sun, J. Wang, and X. Wang, Hopping Transport through Defect-Induced Localized States in Molybdenum Disulphide, Nat. Commun. 4, 2642 (2013).
13. 2 Monolayers, Phys. Rev. B 88, 245440 (2013).
14. S. Tongay, J. Suh, C. Ataca, W. Fan, A. Luce, J. S. Kang, J. Liu, C. Ko, R. Raghunathanan, J. Zhou, F. Ogletree, Jingbo Li, Jeffrey C. Grossman, and J. Wu, Defects Activated Photoluminescence in Two-Dimensional Semiconductors: Interplay between Bound, Charged, and Free Excitons, Sci. Rep. 3, 2657 (2013).
15. Se´rgio Azevedo, J. R. Kaschny, Caio M. C. de Castilho, and F. de Brito Mota, A Theoretical Investigation of Defects in a Boron Nitride Monolayer, Nanotechnology 18, 495707 (2007).
16. H.-P. Komsa, J. Kotakoski, S. Kurasch, O. Lehtinen, U. Kaiser, and A. V. Krasheninnikov, Two-Dimensional Transition Metal Dichalcogenides under Electron Irradiation: Defect Production and Doping, Phys. Rev. Lett. 109, 035503 (2012).
17. 2 Systems, Phys. Rev. B 87, 100401 (2013).
18. 2: An Atomically Thin Dilute Magnetic Semiconductor, Phys. Rev. B 87, 195201 (2013).
19. N. Berseneva, A. V. Krasheninnikov, and R. M. Nieminen, Mechanisms of Postsynthesis Doping of Boron Nitride Nanostructures with Carbon from First-Principles Simulations, Phys. Rev. Lett. 107, 035501 (2011).
20. B. Huang and H. Lee, Defect and Impurity Properties of Hexagonal Boron Nitride: A First-Principles Calculation, Phys. Rev. B 86, 245406 (2012).
21. 2, Phys. Rev. B 89, 205417 (2014).
22. Advanced Calculations for Defects in Materials: Electronic Structure Methods, edited by A. Alkauskas, P. Dea´k, J. Neugebauer, A. Pasquarello, and C. G. Van de Walle (Wiley VCH, Weinheim, Germany, 2011).
23. C. G. Van de Walle and J. Neugebauer, First-Principles Calculations for Defects and Impurities: Applications to III-Nitrides, J. Appl. Phys. 95, 3851 (2004).
24. I. Dabo, B. Kozinsky, N. E. Singh-Miller, and N. Marzari, Electrostatics in Periodic Boundary Conditions and Real-Space Corrections, Phys. Rev. B 77, 115139 (2008).
25. R. Rurali, M. Palummo, and X. Cartoixa`, Convergence Study of Neutral and Charged Defect Formation Energies in Si Nanowires, Phys. Rev. B 81, 235304 (2010).
26. N. A. Richter, S. Sicolo, S. V. Levchenko, J. Sauer, and M. Scheffler, Concentration of Vacancies at Metal-Oxide Surfaces: Case Study of MgO(100), Phys. Rev. Lett. 111, 045502 (2013).
27. A. Y. Lozovoi, A. Alavi, J. Kohanoff, and R. M. Lynden-Bell, Ab Initio Simulation of Charged Slabs at Constant Chemical Potential, J. Chem. Phys. 115, 1661 (2001).
28. M. Otani and O. Sugino, First-Principles Calculations of Charged Systems and Interfaces: A Plane-Wave Nonrepeated Slab Approach, Phys. Rev. B 73, 115407 (2006).
29. K. T. Chan, H. Lee, and M. L. Cohen, Possibility of Transforming the Electronic Structure of One Species of Graphene Adatoms into that of Another by Application of Gate Voltage: First-Principles Calculations, Phys. Rev. B 84, 165419 (2011).
30. S. B. Zhang and J. E. Northrup, Chemical Potential Dependence of Defect Formation Energies in GaAs: Application to Ga Self-Diffusion, Phys. Rev. Lett. 67, 2339 (1991).
31. Mo, and the impurities from their bulk phases.
32. G. Kresse and J. Hafner, Ab Initio Molecular Dynamics for Liquid Metals, Phys. Rev. B 47, 558 (1993).
33. G. Kresse and J. Furthmu¨ller, Efficiency of Ab Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set, Comput. Mater. Sci. 6, 15 (1996).
34. J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett. 77, 3865 (1996).
35. H.-P. Komsa, T. T. Rantala, and A. Pasquarello, Finite-Size Supercell Correction Schemes for Charged Defect Calculations, Phys. Rev. B 86, 045112 (2012).
36. P. Piquini, R. J. Baierle, T. M. Schmidt, and A. Fazzio, Formation Energy of Native Defects in BN Nanotubes: An Ab Initio Study, Nanotechnology 16, 827 (2005).
37. G. Makov and M. C. Payne, Periodic Boundary Conditions in Ab Initio Calculations, Phys. Rev. B 51, 4014 (1995).
38. R. Rurali and X. Cartoixa`, Theory of Defects in One-Dimensional Systems: Application to Al-catalyzed Si nanowires, Nano Lett. 9, 975 (2009).
39. H.-P. Komsa and A. Pasquarello, Finite-Size Supercell Correction for Charged Defects at Surfaces and Interfaces, Phys. Rev. Lett. 110, 095505 (2013)
40. See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevX.4.031044 for implementation details on the correction method, sensitivity of the correction on the model parameters, and results for triangular carbon defects in h-BN.
41. F. Giustino and A. Pasquarello, Theory of Atomic-Scale Dielectric Permittivity at Insulator Interfaces, Phys. Rev. B 71, 144104 (2005).
42. C. Freysoldt, P. Eggert, P. Rinke, A. Schindlmayr, and M. Scheffler, Screening in Two Dimensions: GW Calculations for Surfaces and Thin Films Using the Repeated-Slab Approach, Phys. Rev. B 77, 235428 (2008).
43. P. Cudazzo, I. V. Tokatly, and A. Rubio, Dielectric Screening in Two-Dimensional Insulators: Implications for Excitonic and Impurity States in Graphane, Phys. Rev. B 84, 085406 (2011).
44. T. C. Berkelbach, M. S. Hybertsen, and D. R. Reichman, Theory of Neutral and Charged Excitons in Monolayer TransitionMetalDichalcogenides, Phys. Rev. B 88, 045318 (2013).
45. R.W. Nunes and X. Gonze, Berry-Phase Treatment of the Homogeneous Electric Field Perturbation in Insulators, Phys. Rev. B 63, 155107 (2001).
46. L. Wirtz, A. Marini, and A. Rubio, Excitons in Boron Nitride Nanotubes: Dimensionality Effects, Phys. Rev. Lett. 96, 126104 (2006).
47. 2 from First Principles, Phys. Rev. B 86, 241201 (2012).
48. A. Alkauskas, P. Broqvist, and A. Pasquarello, Defect Energy Levels in Density Functional Calculations: Alignment and Band Gap Problem, Phys. Rev. Lett. 101, 046405 (2008).
49. H.-P. Komsa, P. Broqvist, and A. Pasquarello, Alignment of Defect Levels and Band Edges through Hybrid Functionals: Effect of Screening in the Exchange Term, Phys. Rev. B 81, 205118 (2010).
50. W. Chen and A. Pasquarello, Correspondence of Defect Energy Levels in Hybrid Density Functional Theory and Many-Body Perturbation Theory, Phys. Rev. B 88, 115104 (2013).
51. P. Rinke, A. Schleife, E. Kioupakis, A. Janotti, C. Ro¨dl, F. Bechstedt, M. Scheffler, and C. G. Van de Walle, First-Principles Optical Spectra for F Centers in MgO, Phys. Rev. Lett. 108, 126404 (2012).
52. A. Alkauskas, J. L. Lyons, D. Steiauf, and C. G. Van de Walle, First-Principles Calculations of Luminescence Spectrum Line Shapes for Defects in Semiconductors: The Example of GaN and ZnO, Phys. Rev. Lett. 109, 267401 (2012).