Resolution of the Band Gap Prediction Problem for Materials Design

Crowley, Jason M.; Tahir-Kheli, Jamil; Goddard, III, William A.

doi:10.1021/acs.jpclett.5b02870

Title: Resolution of the Band Gap Prediction Problem for Materials Design

Abstract

An important property with any new material is the band gap. Standard density functional theory methods grossly underestimate band gaps. This is known as the band gap problem. Here in this paper, we show that the hybrid B3PW91 density functional returns band gaps with a mean absolute deviation (MAD) from experiment of 0.22 eV over 64 insulators with gaps spanning a factor of 500 from 0.014 to 7 eV. The MAD is 0.28 eV over 70 compounds with gaps up to 14.2 eV, with a mean error of -0.03 eV. To benchmark the quality of the hybrid method, we compared the hybrid method to the rigorous GW many-body perturbation theory method. Surprisingly, the MAD for B3PW91 is about 1.5 times smaller than the MAD for GW. Furthermore, B3PW91 is 3-4 orders of magnitude faster computationally. Hence, B3PW91 is a practical tool for predicting band gaps of materials before they are synthesized and represents a solution to the band gap prediction problem.

Authors:

Crowley, Jason M. ^[1]; Tahir-Kheli, Jamil ^[1]; Goddard, III, William A. ^[1]

Materials and Process Simulation Center, MC139-74, California Institute of Technology, Pasadena, California 91125, United States

Publication Date:: Wed Mar 16 00:00:00 EDT 2016

Research Org.:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE; National Science Foundation (NSF)

OSTI Identifier:: 1328820

Alternate Identifier(s):: OSTI ID: 1436091

Grant/Contract Number:: SC0004993

Resource Type:: Published Article

Journal Name:: Journal of Physical Chemistry Letters

Additional Journal Information:: Journal Name: Journal of Physical Chemistry Letters Journal Volume: 7 Journal Issue: 7; Journal ID: ISSN 1948-7185

Publisher:: American Chemical Society

Country of Publication:: United States

Language:: English

Subject:: 36 MATERIALS SCIENCE

Citation Formats


                    Crowley, Jason M., Tahir-Kheli, Jamil, and Goddard, III, William A. Resolution of the Band Gap Prediction Problem for Materials Design.  United States: N. p., 2016. 
Web.  doi:10.1021/acs.jpclett.5b02870.

Copy to clipboard


                    Crowley, Jason M., Tahir-Kheli, Jamil, & Goddard, III, William A. Resolution of the Band Gap Prediction Problem for Materials Design.  United States.  https://doi.org/10.1021/acs.jpclett.5b02870

Copy to clipboard


                    Crowley, Jason M., Tahir-Kheli, Jamil, and Goddard, III, William A. Wed .  
"Resolution of the Band Gap Prediction Problem for Materials Design".  United States.  https://doi.org/10.1021/acs.jpclett.5b02870.

Copy to clipboard


                    
@article{osti_1328820,

  title        = {Resolution of the Band Gap Prediction Problem for Materials Design},

  author       = {Crowley, Jason M. and Tahir-Kheli, Jamil and Goddard, III, William A.},

  abstractNote = {An important property with any new material is the band gap. Standard density functional theory methods grossly underestimate band gaps. This is known as the band gap problem. Here in this paper, we show that the hybrid B3PW91 density functional returns band gaps with a mean absolute deviation (MAD) from experiment of 0.22 eV over 64 insulators with gaps spanning a factor of 500 from 0.014 to 7 eV. The MAD is 0.28 eV over 70 compounds with gaps up to 14.2 eV, with a mean error of -0.03 eV. To benchmark the quality of the hybrid method, we compared the hybrid method to the rigorous GW many-body perturbation theory method. Surprisingly, the MAD for B3PW91 is about 1.5 times smaller than the MAD for GW. Furthermore, B3PW91 is 3-4 orders of magnitude faster computationally. Hence, B3PW91 is a practical tool for predicting band gaps of materials before they are synthesized and represents a solution to the band gap prediction problem.},

  doi          = {10.1021/acs.jpclett.5b02870},

  journal      = {Journal of Physical Chemistry Letters},

  number       = 7,

  volume       = 7,

  place        = {United States},

  year         = {Wed Mar 16 00:00:00 EDT 2016},

  month        = {Wed Mar 16 00:00:00 EDT 2016}

}

Copy to clipboard

Journal Article:

Free Publicly Available Full Text

Publisher's Version of Record
https://doi.org/10.1021/acs.jpclett.5b02870

Other availability

Search WorldCat to find libraries that may hold this journal

Citation Metrics:

Cited by: 182 works

Citation information provided by
Web of Science

Figures / Tables:

Figure 1: Calculated B3PW (hybrid DFT), GW (many-body perturbation), and PBE (standard DFT) band gaps versus lowtemperature experiment. A list of the compounds studied may be found in Figures 2 and 3 and Tables S1−S3. (a) B3PW, (b) PBE, (c) GW results (G₀W₀ and post-G₀W₀) versus experiment for compounds withmore »

All figures and tables (3 total)

Save / Share:

Export Metadata

Save to My Library

Works referenced in this record:

Generalized Gradient Approximation Made Simple
journal, October 1996

Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
DOI: 10.1103/PhysRevLett.77.3865

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

Improved semiconductor lattice parameters and band gaps from a middle-range screened hybrid exchange functional
journal, March 2012

Lucero, M. J.; Henderson, T. M.; Scuseria, G. E.
Journal of Physics: Condensed Matter, Vol. 24, Issue 14
DOI: 10.1088/0953-8984/24/14/145504

Efficient implementation of the $G W$ approximation within the all-electron FLAPW method
journal, March 2010

Friedrich, Christoph; Blügel, Stefan; Schindlmayr, Arno
Physical Review B, Vol. 81, Issue 12
DOI: 10.1103/PhysRevB.81.125102

Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post- d group 16–18 elements
journal, December 2003

Peterson, Kirk A.; Figgen, Detlev; Goll, Erich
The Journal of Chemical Physics, Vol. 119, Issue 21
DOI: 10.1063/1.1622924

Electronic phase transitions of bismuth under strain from relativistic self-consistent $G W$ calculations
journal, March 2015

Aguilera, Irene; Friedrich, Christoph; Blügel, Stefan
Physical Review B, Vol. 91, Issue 12
DOI: 10.1103/PhysRevB.91.125129

Density-functional exchange-energy approximation with correct asymptotic behavior
journal, September 1988

Becke, A. D.
Physical Review A, Vol. 38, Issue 6
DOI: 10.1103/PhysRevA.38.3098

Influence of the exchange screening parameter on the performance of screened hybrid functionals
journal, December 2006

Krukau, Aliaksandr V.; Vydrov, Oleg A.; Izmaylov, Artur F.
The Journal of Chemical Physics, Vol. 125, Issue 22
DOI: 10.1063/1.2404663

Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional
journal, November 2005

Heyd, Jochen; Peralta, Juan E.; Scuseria, Gustavo E.
The Journal of Chemical Physics, Vol. 123, Issue 17
DOI: 10.1063/1.2085170

Antiferromagnetic band structure of ${La}_{2} {CuO}_{4} :$ Becke-3–Lee-Yang-Parr calculations
journal, March 2001

Perry, Jason K.; Tahir-Kheli, Jamil; Goddard, William A.
Physical Review B, Vol. 63, Issue 14
DOI: 10.1103/PhysRevB.63.144510

Density-based mixing parameter for hybrid functionals
journal, January 2011

Marques, Miguel A. L.; Vidal, Julien; Oliveira, Micael J. T.
Physical Review B, Vol. 83, Issue 3
DOI: 10.1103/PhysRevB.83.035119

On the prediction of band gaps from hybrid functional theory
journal, July 2001

Muscat, J.; Wander, A.; Harrison, N. M.
Chemical Physics Letters, Vol. 342, Issue 3-4
DOI: 10.1016/S0009-2614(01)00616-9

Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction
journal, April 2008

Mori-Sánchez, Paula; Cohen, Aron J.; Yang, Weitao
Physical Review Letters, Vol. 100, Issue 14
DOI: 10.1103/PhysRevLett.100.146401

Band-edge positions in $G W$ : Effects of starting point and self-consistency
journal, October 2014

Chen, Wei; Pasquarello, Alfredo
Physical Review B, Vol. 90, Issue 16
DOI: 10.1103/PhysRevB.90.165133

Relativistic energy-consistent pseudopotentials?Recent developments
journal, April 2002

Stoll, Hermann; Metz, Bernhard; Dolg, Michael
Journal of Computational Chemistry, Vol. 23, Issue 8
DOI: 10.1002/jcc.10037

Quasiparticle band structure of thirteen semiconductors and insulators
journal, June 1991

Zhu, Xuejun; Louie, Steven G.
Physical Review B, Vol. 43, Issue 17
DOI: 10.1103/PhysRevB.43.14142

Accurate Ab Initio Quantum Mechanics Simulations of Bi ₂ Se ₃ and Bi ₂ Te ₃ Topological Insulator Surfaces
journal, September 2015

Crowley, Jason M.; Tahir-Kheli, Jamil; Goddard, William A.
The Journal of Physical Chemistry Letters, Vol. 6, Issue 19
DOI: 10.1021/acs.jpclett.5b01586

Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies
journal, October 1986

Hybertsen, Mark S.; Louie, Steven G.
Physical Review B, Vol. 34, Issue 8, p. 5390-5413
DOI: 10.1103/PhysRevB.34.5390

Accurate Band Gaps for Semiconductors from Density Functional Theory
journal, January 2011

Xiao, Hai; Tahir-Kheli, Jamil; Goddard, William A.
The Journal of Physical Chemistry Letters, Vol. 2, Issue 3
DOI: 10.1021/jz101565j

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation
journal, September 1992

Perdew, John P.; Chevary, J. A.; Vosko, S. H.
Physical Review B, Vol. 46, Issue 11
DOI: 10.1103/PhysRevB.46.6671

Band-edge levels in semiconductors and insulators: Hybrid density functional theory versus many-body perturbation theory
journal, July 2012

Chen, Wei; Pasquarello, Alfredo
Physical Review B, Vol. 86, Issue 3
DOI: 10.1103/PhysRevB.86.035134

Predicted roles of defects on band offsets and energetics at CIGS (Cu(In,Ga)Se ₂ /CdS) solar cell interfaces and implications for improving performance
journal, September 2014

Goddard, William A.
The Journal of Chemical Physics, Vol. 141, Issue 9
DOI: 10.1063/1.4893985

Core polarization in solids: Formulation and application to semiconductors
journal, September 1997

Shirley, Eric L.; Zhu, Xuejun; Louie, Steven G.
Physical Review B, Vol. 56, Issue 11
DOI: 10.1103/PhysRevB.56.6648

Quasiparticle energies in GaAs and AlAs
journal, March 1987

Godby, R.; Schlüter, M.; Sham, L.
Physical Review B, Vol. 35, Issue 8
DOI: 10.1103/PhysRevB.35.4170

Self-interaction correction to density-functional approximations for many-electron systems
journal, May 1981

Perdew, J. P.; Zunger, Alex
Physical Review B, Vol. 23, Issue 10, p. 5048-5079
DOI: 10.1103/PhysRevB.23.5048

All-Electron Self-Consistent $G W$ Approximation: Application to Si, MnO, and NiO
journal, September 2004

Faleev, Sergey V.; van Schilfgaarde, Mark; Kotani, Takao
Physical Review Letters, Vol. 93, Issue 12
DOI: 10.1103/PhysRevLett.93.126406

Ab Initio Prediction of Conduction Band Spin Splitting in Zinc Blende Semiconductors
journal, March 2006

Chantis, Athanasios N.; van Schilfgaarde, Mark; Kotani, Takao
Physical Review Letters, Vol. 96, Issue 8
DOI: 10.1103/PhysRevLett.96.086405

Accurate Quasiparticle Spectra from Self-Consistent GW Calculations with Vertex Corrections
journal, December 2007

Shishkin, M.; Marsman, M.; Kresse, G.
Physical Review Letters, Vol. 99, Issue 24
DOI: 10.1103/PhysRevLett.99.246403

Definitive Band Gaps for Single-Wall Carbon Nanotubes
journal, September 2010

Matsuda, Yuki; Tahir-Kheli, Jamil; Goddard, William A.
The Journal of Physical Chemistry Letters, Vol. 1, Issue 19
DOI: 10.1021/jz100889u

Photoemission from Rare-Gas Solids: Electron Energy Distributions from the Valence Bands
journal, March 1975

Schwentner, N.; Himpsel, F. -J.; Saile, V.
Physical Review Letters, Vol. 34, Issue 9
DOI: 10.1103/PhysRevLett.34.528

Analysis of the Heyd-Scuseria-Ernzerhof density functional parameter space
journal, May 2012

Moussa, Jonathan E.; Schultz, Peter A.; Chelikowsky, James R.
The Journal of Chemical Physics, Vol. 136, Issue 20
DOI: 10.1063/1.4722993

Quasiparticle band structures of the antiferromagnetic transition-metal oxides MnO, FeO, CoO, and NiO
journal, June 2009

Rödl, C.; Fuchs, F.; Furthmüller, J.
Physical Review B, Vol. 79, Issue 23
DOI: 10.1103/PhysRevB.79.235114

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

Chen, Wei; Pasquarello, Alfredo
Physical Review B, Vol. 88, Issue 11
DOI: 10.1103/PhysRevB.88.115104

Spin-orbit splittings and energy band gaps calculated with the Heyd-Scuseria-Ernzerhof screened hybrid functional
journal, August 2006

Peralta, Juan E.; Heyd, Jochen; Scuseria, Gustavo E.
Physical Review B, Vol. 74, Issue 7
DOI: 10.1103/PhysRevB.74.073101

Semiconductors: Data Handbook
book, January 2004

Madelung, Otfried
DOI: 10.1007/978-3-642-18865-7

Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities
journal, November 1983

Perdew, John P.; Levy, Mel
Physical Review Letters, Vol. 51, Issue 20
DOI: 10.1103/PhysRevLett.51.1884

Figures / Tables found in this record:

Figure 1 (p. 2)

Figure 2 (p. 3)

Figure 3 (p. 4)

Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.

Similar Records in DOE PAGES and OSTI.GOV collections:

Towards predictive band gaps for halide perovskites: Lessons from one-shot and eigenvalue self-consistent GW

Journal Article Leppert, Linn ; Rangel, Tonatiuh ; Neaton, Jeffrey B. - Physical Review Materials

Hmore »« less
https://doi.org/10.1103/physrevmaterials.3.103803

Full Text Available
Predicting Band Gaps with Hybrid Density Functionals

Journal Article Garza, Alejandro J. ; Scuseria, Gustavo E. - Journal of Physical Chemistry Letters

We look at the ability of four popular hybrid density functionals (B3LYP, B3PW91, HSE, and PBE0) for predicting band gaps of semiconductors and insulators over a large benchmark set using a consistent methodology. We observe no significant statistical difference in their overall performance, although the screened hybrid HSE is more accurate for typical semiconductors. HSE can improve its accuracy for large band gap materials—without affecting that of semiconductors—by including a larger portion of Hartree–Fock exchange in its short-range. Given that screened hybrids are computationally much less expensive than their global counterparts, we conclude that they are a better option formore » the black box prediction of band gaps.« less
Cited by 271
https://doi.org/10.1021/acs.jpclett.6b01807

Full Text Available
Predicted roles of defects on band offsets and energetics at CIGS (Cu(In,Ga)Se ₂ /CdS) solar cell interfaces and implications for improving performance

Journal Article Goddard, William A. - Journal of Chemical Physics

The laboratory performance of CIGS (Cu(In,Ga)Se₂) based solar cells (20.8% efficiency) makes them promising candidate photovoltaic devices. However, there remains little understanding of how defects at the CIGS/CdS interface affect the band offsets and interfacial energies, and hence the performance of manufactured devices. To determine these relationships, we use density functional theory with the B3PW91 hybrid functional that we validate to provide very accurate descriptions of the band gaps and band offsets. This confirms the weak dependence of band offsets on surface orientation observed experimentally. We predict that the conduction band offset (CBO) of perfect CuInSe2/CdS interface is large, 0.79more »« less
Cited by 22
https://doi.org/10.1063/1.4893985

Full Text Available
Predicting band gaps and band-edge positions of oxide perovskites using density functional theory and machine learning

Journal Article Li, Wei ; Wang, Zigeng ; Xiao, Xia ; ... - Physical Review. B

Density functional theory (DFT) within the local or semilocal density approximations, i.e., the local density approximation (LDA) or generalized gradient approximation (GGA), has become a workhorse in the electronic structure theory of solids, being extremely fast and reliable for energetics and structural properties, yet remaining highly inaccurate for predicting band gaps of semiconductors and insulators. The accurate prediction of band gaps using first-principles methods is time consuming, requiring hybrid functionals, quasiparticle GW, or quantum Monte Carlo methods. Efficiently correcting DFT-LDA/GGA band gaps and unveiling the main chemical and structural factors involved in this correction is desirable for discovering novel materialsmore »« less
https://doi.org/10.1103/physrevb.106.155156

Full Text Available
Wannier–Koopmans method calculations for transition metal oxide band gaps

Journal Article Weng, Mouyi ; Pan, Feng ; Wang, Lin-Wang - npj Computational Materials

The widely used density functional theory (DFT) has a major drawback of underestimating the band gaps of materials. Wannier–Koopmans method (WKM) was recently developed for band gap calculations with accuracy on a par with more complicated methods. WKM has been tested for main group covalent semiconductors, alkali halides, 2D materials, and organic crystals. Here we apply the WKM to another interesting type of material system: the transition metal (TM) oxides. TM oxides can be classified as either with d⁰ or d¹⁰ closed shell occupancy or partially occupied open shell configuration, and the latter is known to be strongly correlated Mottmore »« less
Cited by 7
https://doi.org/10.1038/s41524-020-0302-0

Full Text Available

Similar Records

Title: Resolution of the Band Gap Prediction Problem for Materials Design

Abstract

Citation Formats

Figures / Tables:

Generalized Gradient Approximation Made Simple journal, October 1996

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

Improved semiconductor lattice parameters and band gaps from a middle-range screened hybrid exchange functional journal, March 2012

Efficient implementation of the G W approximation within the all-electron FLAPW method journal, March 2010

Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post- d group 16–18 elements journal, December 2003

Electronic phase transitions of bismuth under strain from relativistic self-consistent G W calculations journal, March 2015

Density-functional exchange-energy approximation with correct asymptotic behavior journal, September 1988

Influence of the exchange screening parameter on the performance of screened hybrid functionals journal, December 2006

Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional journal, November 2005

Antiferromagnetic band structure of La 2 CuO 4 : Becke-3–Lee-Yang-Parr calculations journal, March 2001

Density-based mixing parameter for hybrid functionals journal, January 2011

On the prediction of band gaps from hybrid functional theory journal, July 2001

Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction journal, April 2008

Band-edge positions in G W : Effects of starting point and self-consistency journal, October 2014

Relativistic energy-consistent pseudopotentials?Recent developments journal, April 2002

Quasiparticle band structure of thirteen semiconductors and insulators journal, June 1991

Accurate Ab Initio Quantum Mechanics Simulations of Bi 2 Se 3 and Bi 2 Te 3 Topological Insulator Surfaces journal, September 2015

Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies journal, October 1986

Accurate Band Gaps for Semiconductors from Density Functional Theory journal, January 2011

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation journal, September 1992

Band-edge levels in semiconductors and insulators: Hybrid density functional theory versus many-body perturbation theory journal, July 2012

Predicted roles of defects on band offsets and energetics at CIGS (Cu(In,Ga)Se 2 /CdS) solar cell interfaces and implications for improving performance journal, September 2014

Core polarization in solids: Formulation and application to semiconductors journal, September 1997

Quasiparticle energies in GaAs and AlAs journal, March 1987

Self-interaction correction to density-functional approximations for many-electron systems journal, May 1981

All-Electron Self-Consistent G W Approximation: Application to Si, MnO, and NiO journal, September 2004

Ab Initio Prediction of Conduction Band Spin Splitting in Zinc Blende Semiconductors journal, March 2006

Accurate Quasiparticle Spectra from Self-Consistent GW Calculations with Vertex Corrections journal, December 2007

Definitive Band Gaps for Single-Wall Carbon Nanotubes journal, September 2010

Photoemission from Rare-Gas Solids: Electron Energy Distributions from the Valence Bands journal, March 1975

Analysis of the Heyd-Scuseria-Ernzerhof density functional parameter space journal, May 2012

Quasiparticle band structures of the antiferromagnetic transition-metal oxides MnO, FeO, CoO, and NiO journal, June 2009

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

Spin-orbit splittings and energy band gaps calculated with the Heyd-Scuseria-Ernzerhof screened hybrid functional journal, August 2006

Semiconductors: Data Handbook book, January 2004

Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities journal, November 1983

Generalized Gradient Approximation Made Simple
journal, October 1996

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

Improved semiconductor lattice parameters and band gaps from a middle-range screened hybrid exchange functional
journal, March 2012

Efficient implementation of the $G W$ approximation within the all-electron FLAPW method
journal, March 2010

Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post- d group 16–18 elements
journal, December 2003

Electronic phase transitions of bismuth under strain from relativistic self-consistent $G W$ calculations
journal, March 2015

Density-functional exchange-energy approximation with correct asymptotic behavior
journal, September 1988

Influence of the exchange screening parameter on the performance of screened hybrid functionals
journal, December 2006

Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional
journal, November 2005

Antiferromagnetic band structure of ${La}_{2} {CuO}_{4} :$ Becke-3–Lee-Yang-Parr calculations
journal, March 2001

Density-based mixing parameter for hybrid functionals
journal, January 2011

On the prediction of band gaps from hybrid functional theory
journal, July 2001

Localization and Delocalization Errors in Density Functional Theory and Implications for Band-Gap Prediction
journal, April 2008

Band-edge positions in $G W$ : Effects of starting point and self-consistency
journal, October 2014

Relativistic energy-consistent pseudopotentials?Recent developments
journal, April 2002

Quasiparticle band structure of thirteen semiconductors and insulators
journal, June 1991

Accurate Ab Initio Quantum Mechanics Simulations of Bi ₂ Se ₃ and Bi ₂ Te ₃ Topological Insulator Surfaces
journal, September 2015

Electron correlation in semiconductors and insulators: Band gaps and quasiparticle energies
journal, October 1986

Accurate Band Gaps for Semiconductors from Density Functional Theory
journal, January 2011

Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation
journal, September 1992

Band-edge levels in semiconductors and insulators: Hybrid density functional theory versus many-body perturbation theory
journal, July 2012

Predicted roles of defects on band offsets and energetics at CIGS (Cu(In,Ga)Se ₂ /CdS) solar cell interfaces and implications for improving performance
journal, September 2014

Core polarization in solids: Formulation and application to semiconductors
journal, September 1997

Quasiparticle energies in GaAs and AlAs
journal, March 1987

Self-interaction correction to density-functional approximations for many-electron systems
journal, May 1981

All-Electron Self-Consistent $G W$ Approximation: Application to Si, MnO, and NiO
journal, September 2004

Ab Initio Prediction of Conduction Band Spin Splitting in Zinc Blende Semiconductors
journal, March 2006

Accurate Quasiparticle Spectra from Self-Consistent GW Calculations with Vertex Corrections
journal, December 2007

Definitive Band Gaps for Single-Wall Carbon Nanotubes
journal, September 2010

Photoemission from Rare-Gas Solids: Electron Energy Distributions from the Valence Bands
journal, March 1975

Analysis of the Heyd-Scuseria-Ernzerhof density functional parameter space
journal, May 2012

Quasiparticle band structures of the antiferromagnetic transition-metal oxides MnO, FeO, CoO, and NiO
journal, June 2009

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

Spin-orbit splittings and energy band gaps calculated with the Heyd-Scuseria-Ernzerhof screened hybrid functional
journal, August 2006

Semiconductors: Data Handbook
book, January 2004

Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities
journal, November 1983