Abstract

Employing first-principles combined with hybrid functional calculations, the electronic and optical properties of GaAs alloyed with isovalent impurities Bi and N are investigated. As GaAsBiN alloy is a quaternary alloy, the band gap and the lattice constant of the alloy can be individually tuned. Both impurities are important to the valence band and conduction band of the alloy, with the band gap of the alloy being dramatically reduced by Bi 6p states and N localized 2s states. Interestingly, the calculated optical properties of the quaternary alloy are similar to those of undoped GaAs except that the absorption edge has a redshift toward lower energy. These results suggest potential interest in the long-wavelength applications of GaAsBiN alloy.

© 2014 Optical Society of America

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References

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    [Crossref] [PubMed]
  3. J. Gu, F. Zhou, K. T. Wan, T. K. Lim, S. C. Tam, Y. L. Lam, D. Xu, and Z. Cheng, “Q-switching of a diode-pumped Nd: YVO4 laser with GaAs nonlinear output coupler,” Opt. Lasers Eng. 35(5), 299–307 (2001).
    [Crossref]
  4. D. G. Thomas, J. J. Hopfield, and C. J. Frosch, “Isoelectronic traps due to nitrogen in gallium phosphide,” Phys. Rev. Lett. 15(22), 857–860 (1965).
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    [Crossref] [PubMed]
  6. C. Wang, D. Shiau, and A. Lin, “Preparation of GaSb substrates for GaSb and GaInAsSb growth by organometallic vapor phase epitaxy,” J. Cryst. Growth 261(2-3), 385–392 (2004).
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  7. S. Francoeur, S. Tixier, E. Young, T. Tiedje, and A. Mascarenhas, “Bi isoelectronic impurities in GaAs,” Phys. Rev. B 77(8), 085209 (2008).
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
  21. W. Shan, W. Walukiewicz, J. Ager, E. Haller, J. Geisz, D. Friedman, J. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloys,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
    [Crossref]
  22. L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
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    [Crossref]
  25. V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Origin of band gap bowing in dilute GaAs1-xNx and GaP1-xNx alloys: A real-space view,” Phys. Rev. B 88(3), 035204 (2013).
    [Crossref]
  26. D. C. Li, M. Yang, S. Zhao, Y. Cai, and Y. Feng, “First principles study of bismuth alloying effects in GaAs saturable absorber,” Opt. Express 20(10), 11574–11580 (2012).
    [Crossref] [PubMed]
  27. Y. Zhang, A. Mascarenhas, and L. W. Wang, “Similar and dissimilar aspects of III-V semiconductors containing Bi versus N,” Phys. Rev. B 71(15), 155201 (2005).
    [Crossref]
  28. V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Modeling Bi-induced changes in the electronic structure of GaAs1-xBix alloys,” Phys. Rev. B 88, 235201 (2013).
    [Crossref]
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    [Crossref]

2013 (2)

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Origin of band gap bowing in dilute GaAs1-xNx and GaP1-xNx alloys: A real-space view,” Phys. Rev. B 88(3), 035204 (2013).
[Crossref]

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Modeling Bi-induced changes in the electronic structure of GaAs1-xBix alloys,” Phys. Rev. B 88, 235201 (2013).
[Crossref]

2012 (4)

D. C. Li, M. Yang, S. Zhao, Y. Cai, and Y. Feng, “First principles study of bismuth alloying effects in GaAs saturable absorber,” Opt. Express 20(10), 11574–11580 (2012).
[Crossref] [PubMed]

D. C. Li, M. Yang, Y. Cai, S. Zhao, and Y. Feng, “First principles study of the ternary complex model of EL2 defect in GaAs saturable absorber,” Opt. Express 20(6), 6258–6266 (2012).
[Crossref] [PubMed]

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Hybrid functional study of band structures of GaAs1−xN x and GaSb1−xNx alloys,” Phys. Rev. B 85(8), 085134 (2012).
[Crossref]

R. Lewis, M. Masnadi-Shirazi, and T. Tiedje, “Growth of high Bi concentration GaAs1−xBix by molecular beam epitaxy,” Appl. Phys. Lett. 101(8), 082112 (2012).
[Crossref]

2010 (2)

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

H. X. Deng, J. Li, S. S. Li, H. Peng, J. B. Xia, L. W. Wang, and S. H. Wei, “Band crossing in isovalent semiconductor alloys with large size mismatch: First-principles calculations of the electronic structure of Bi and N incorporated GaAs,” Phys. Rev. B 82(19), 193204 (2010).
[Crossref]

2009 (1)

J. Wróbel, K. J. Kurzydłowski, K. Hummer, G. Kresse, and J. Piechota, “Calculations of ZnO properties using the Heyd-Scuseria-Ernzerhof screened hybrid density functional,” Phys. Rev. B 80(15), 155124 (2009).
[Crossref]

2008 (1)

S. Francoeur, S. Tixier, E. Young, T. Tiedje, and A. Mascarenhas, “Bi isoelectronic impurities in GaAs,” Phys. Rev. B 77(8), 085209 (2008).
[Crossref]

2005 (1)

Y. Zhang, A. Mascarenhas, and L. W. Wang, “Similar and dissimilar aspects of III-V semiconductors containing Bi versus N,” Phys. Rev. B 71(15), 155201 (2005).
[Crossref]

2004 (1)

C. Wang, D. Shiau, and A. Lin, “Preparation of GaSb substrates for GaSb and GaInAsSb growth by organometallic vapor phase epitaxy,” J. Cryst. Growth 261(2-3), 385–392 (2004).
[Crossref]

2003 (2)

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 118(18), 8207–8215 (2003).
[Crossref]

J. Li and L. W. Wang, “Energy levels of isoelectronic impurities by large scale LDA calculations,” Phys. Rev. B 67(3), 033102 (2003).
[Crossref]

2002 (1)

A. Janotti, S. H. Wei, and S. Zhang, “Theoretical study of the effects of isovalent coalloying of Bi and N in GaAs,” Phys. Rev. B 65(11), 115203 (2002).
[Crossref]

2001 (1)

J. Gu, F. Zhou, K. T. Wan, T. K. Lim, S. C. Tam, Y. L. Lam, D. Xu, and Z. Cheng, “Q-switching of a diode-pumped Nd: YVO4 laser with GaAs nonlinear output coupler,” Opt. Lasers Eng. 35(5), 299–307 (2001).
[Crossref]

1999 (1)

W. Shan, W. Walukiewicz, J. Ager, E. Haller, J. Geisz, D. Friedman, J. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloys,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[Crossref]

1996 (4)

T. T. Kajava and A. L. Gaeta, “Q switching of a diode-pumped Nd:YAG laser with GaAs,” Opt. Lett. 21(16), 1244–1246 (1996).
[Crossref] [PubMed]

L. Bellaiche, S. H. Wei, and A. Zunger, “Localization and percolation in semiconductor alloys: GaAsN vs GaAsP,” Phys. Rev. B Condens. Matter 54(24), 17568–17576 (1996).
[Crossref] [PubMed]

G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Phys. Rev. B Condens. Matter 54(16), 11169–11186 (1996).
[Crossref] [PubMed]

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77(18), 3865–3868 (1996).
[Crossref] [PubMed]

1994 (3)

J. Kuznia, J. Yang, Q. Chen, S. Krishnankutty, M. A. Khan, T. George, and J. Frietas., “Low pressure metalorganic chemical‐vapor deposition of cubic GaN over (100) GaAs substrates,” Appl. Phys. Lett. 65(19), 2407–2409 (1994).
[Crossref]

G. Ramírez-Flores, H. Navarro-Contreras, A. Lastras-Martínez, R. C. Powell, and J. E. Greene, “Temperature-dependent optical band gap of the metastable zinc-blende structure β -GaN,” Phys. Rev. B Condens. Matter 50(12), 8433–8438 (1994).
[Crossref] [PubMed]

P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B Condens. Matter 50(24), 17953–17979 (1994).
[Crossref] [PubMed]

1992 (1)

Z. Zhang, L. Qian, D. Fan, and X. Deng, “Gallium arsenide: A new material to accomplish passively mode‐locked Nd: YAG laser,” Appl. Phys. Lett. 60(4), 419–421 (1992).
[Crossref]

1983 (1)

D. Aspnes and A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27(2), 985–1009 (1983).
[Crossref]

1965 (1)

D. G. Thomas, J. J. Hopfield, and C. J. Frosch, “Isoelectronic traps due to nitrogen in gallium phosphide,” Phys. Rev. Lett. 15(22), 857–860 (1965).
[Crossref]

1921 (1)

L. Vegard, “The constitution of mixed crystals and the space occupied by atoms,” Z. Phys. 5, 17–26 (1921).
[Crossref]

Ager, J.

W. Shan, W. Walukiewicz, J. Ager, E. Haller, J. Geisz, D. Friedman, J. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloys,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[Crossref]

Aspnes, D.

D. Aspnes and A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27(2), 985–1009 (1983).
[Crossref]

Bellaiche, L.

L. Bellaiche, S. H. Wei, and A. Zunger, “Localization and percolation in semiconductor alloys: GaAsN vs GaAsP,” Phys. Rev. B Condens. Matter 54(24), 17568–17576 (1996).
[Crossref] [PubMed]

Blöchl, P. E.

P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B Condens. Matter 50(24), 17953–17979 (1994).
[Crossref] [PubMed]

Burke, K.

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77(18), 3865–3868 (1996).
[Crossref] [PubMed]

Cai, Y.

Chen, Q.

J. Kuznia, J. Yang, Q. Chen, S. Krishnankutty, M. A. Khan, T. George, and J. Frietas., “Low pressure metalorganic chemical‐vapor deposition of cubic GaN over (100) GaAs substrates,” Appl. Phys. Lett. 65(19), 2407–2409 (1994).
[Crossref]

Cheng, Z.

J. Gu, F. Zhou, K. T. Wan, T. K. Lim, S. C. Tam, Y. L. Lam, D. Xu, and Z. Cheng, “Q-switching of a diode-pumped Nd: YVO4 laser with GaAs nonlinear output coupler,” Opt. Lasers Eng. 35(5), 299–307 (2001).
[Crossref]

Dähne, M.

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

Deng, H. X.

H. X. Deng, J. Li, S. S. Li, H. Peng, J. B. Xia, L. W. Wang, and S. H. Wei, “Band crossing in isovalent semiconductor alloys with large size mismatch: First-principles calculations of the electronic structure of Bi and N incorporated GaAs,” Phys. Rev. B 82(19), 193204 (2010).
[Crossref]

Deng, X.

Z. Zhang, L. Qian, D. Fan, and X. Deng, “Gallium arsenide: A new material to accomplish passively mode‐locked Nd: YAG laser,” Appl. Phys. Lett. 60(4), 419–421 (1992).
[Crossref]

Ebert, P.

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

Eisele, H.

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

Ernzerhof, M.

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 118(18), 8207–8215 (2003).
[Crossref]

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77(18), 3865–3868 (1996).
[Crossref] [PubMed]

Fahy, S.

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

Fan, D.

Z. Zhang, L. Qian, D. Fan, and X. Deng, “Gallium arsenide: A new material to accomplish passively mode‐locked Nd: YAG laser,” Appl. Phys. Lett. 60(4), 419–421 (1992).
[Crossref]

Feng, Y.

Francoeur, S.

S. Francoeur, S. Tixier, E. Young, T. Tiedje, and A. Mascarenhas, “Bi isoelectronic impurities in GaAs,” Phys. Rev. B 77(8), 085209 (2008).
[Crossref]

Friedman, D.

W. Shan, W. Walukiewicz, J. Ager, E. Haller, J. Geisz, D. Friedman, J. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloys,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[Crossref]

Frietas, J.

J. Kuznia, J. Yang, Q. Chen, S. Krishnankutty, M. A. Khan, T. George, and J. Frietas., “Low pressure metalorganic chemical‐vapor deposition of cubic GaN over (100) GaAs substrates,” Appl. Phys. Lett. 65(19), 2407–2409 (1994).
[Crossref]

Frosch, C. J.

D. G. Thomas, J. J. Hopfield, and C. J. Frosch, “Isoelectronic traps due to nitrogen in gallium phosphide,” Phys. Rev. Lett. 15(22), 857–860 (1965).
[Crossref]

Furthmüller, J.

G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Phys. Rev. B Condens. Matter 54(16), 11169–11186 (1996).
[Crossref] [PubMed]

Gaeta, A. L.

Geelhaar, L.

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

Geisz, J.

W. Shan, W. Walukiewicz, J. Ager, E. Haller, J. Geisz, D. Friedman, J. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloys,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[Crossref]

George, T.

J. Kuznia, J. Yang, Q. Chen, S. Krishnankutty, M. A. Khan, T. George, and J. Frietas., “Low pressure metalorganic chemical‐vapor deposition of cubic GaN over (100) GaAs substrates,” Appl. Phys. Lett. 65(19), 2407–2409 (1994).
[Crossref]

Greene, J. E.

G. Ramírez-Flores, H. Navarro-Contreras, A. Lastras-Martínez, R. C. Powell, and J. E. Greene, “Temperature-dependent optical band gap of the metastable zinc-blende structure β -GaN,” Phys. Rev. B Condens. Matter 50(12), 8433–8438 (1994).
[Crossref] [PubMed]

Gu, J.

J. Gu, F. Zhou, K. T. Wan, T. K. Lim, S. C. Tam, Y. L. Lam, D. Xu, and Z. Cheng, “Q-switching of a diode-pumped Nd: YVO4 laser with GaAs nonlinear output coupler,” Opt. Lasers Eng. 35(5), 299–307 (2001).
[Crossref]

Haller, E.

W. Shan, W. Walukiewicz, J. Ager, E. Haller, J. Geisz, D. Friedman, J. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloys,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[Crossref]

Havu, V.

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Modeling Bi-induced changes in the electronic structure of GaAs1-xBix alloys,” Phys. Rev. B 88, 235201 (2013).
[Crossref]

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Origin of band gap bowing in dilute GaAs1-xNx and GaP1-xNx alloys: A real-space view,” Phys. Rev. B 88(3), 035204 (2013).
[Crossref]

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Hybrid functional study of band structures of GaAs1−xN x and GaSb1−xNx alloys,” Phys. Rev. B 85(8), 085134 (2012).
[Crossref]

Heyd, J.

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 118(18), 8207–8215 (2003).
[Crossref]

Hopfield, J. J.

D. G. Thomas, J. J. Hopfield, and C. J. Frosch, “Isoelectronic traps due to nitrogen in gallium phosphide,” Phys. Rev. Lett. 15(22), 857–860 (1965).
[Crossref]

Hummer, K.

J. Wróbel, K. J. Kurzydłowski, K. Hummer, G. Kresse, and J. Piechota, “Calculations of ZnO properties using the Heyd-Scuseria-Ernzerhof screened hybrid density functional,” Phys. Rev. B 80(15), 155124 (2009).
[Crossref]

Ivanova, L.

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

Janotti, A.

A. Janotti, S. H. Wei, and S. Zhang, “Theoretical study of the effects of isovalent coalloying of Bi and N in GaAs,” Phys. Rev. B 65(11), 115203 (2002).
[Crossref]

Kajava, T. T.

Khan, M. A.

J. Kuznia, J. Yang, Q. Chen, S. Krishnankutty, M. A. Khan, T. George, and J. Frietas., “Low pressure metalorganic chemical‐vapor deposition of cubic GaN over (100) GaAs substrates,” Appl. Phys. Lett. 65(19), 2407–2409 (1994).
[Crossref]

Kresse, G.

J. Wróbel, K. J. Kurzydłowski, K. Hummer, G. Kresse, and J. Piechota, “Calculations of ZnO properties using the Heyd-Scuseria-Ernzerhof screened hybrid density functional,” Phys. Rev. B 80(15), 155124 (2009).
[Crossref]

G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Phys. Rev. B Condens. Matter 54(16), 11169–11186 (1996).
[Crossref] [PubMed]

Krishnankutty, S.

J. Kuznia, J. Yang, Q. Chen, S. Krishnankutty, M. A. Khan, T. George, and J. Frietas., “Low pressure metalorganic chemical‐vapor deposition of cubic GaN over (100) GaAs substrates,” Appl. Phys. Lett. 65(19), 2407–2409 (1994).
[Crossref]

Kurtz, S. R.

W. Shan, W. Walukiewicz, J. Ager, E. Haller, J. Geisz, D. Friedman, J. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloys,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[Crossref]

Kurzydlowski, K. J.

J. Wróbel, K. J. Kurzydłowski, K. Hummer, G. Kresse, and J. Piechota, “Calculations of ZnO properties using the Heyd-Scuseria-Ernzerhof screened hybrid density functional,” Phys. Rev. B 80(15), 155124 (2009).
[Crossref]

Kuznia, J.

J. Kuznia, J. Yang, Q. Chen, S. Krishnankutty, M. A. Khan, T. George, and J. Frietas., “Low pressure metalorganic chemical‐vapor deposition of cubic GaN over (100) GaAs substrates,” Appl. Phys. Lett. 65(19), 2407–2409 (1994).
[Crossref]

Lam, Y. L.

J. Gu, F. Zhou, K. T. Wan, T. K. Lim, S. C. Tam, Y. L. Lam, D. Xu, and Z. Cheng, “Q-switching of a diode-pumped Nd: YVO4 laser with GaAs nonlinear output coupler,” Opt. Lasers Eng. 35(5), 299–307 (2001).
[Crossref]

Lastras-Martínez, A.

G. Ramírez-Flores, H. Navarro-Contreras, A. Lastras-Martínez, R. C. Powell, and J. E. Greene, “Temperature-dependent optical band gap of the metastable zinc-blende structure β -GaN,” Phys. Rev. B Condens. Matter 50(12), 8433–8438 (1994).
[Crossref] [PubMed]

Lenz, A.

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

Lewis, R.

R. Lewis, M. Masnadi-Shirazi, and T. Tiedje, “Growth of high Bi concentration GaAs1−xBix by molecular beam epitaxy,” Appl. Phys. Lett. 101(8), 082112 (2012).
[Crossref]

Li, D. C.

Li, J.

H. X. Deng, J. Li, S. S. Li, H. Peng, J. B. Xia, L. W. Wang, and S. H. Wei, “Band crossing in isovalent semiconductor alloys with large size mismatch: First-principles calculations of the electronic structure of Bi and N incorporated GaAs,” Phys. Rev. B 82(19), 193204 (2010).
[Crossref]

J. Li and L. W. Wang, “Energy levels of isoelectronic impurities by large scale LDA calculations,” Phys. Rev. B 67(3), 033102 (2003).
[Crossref]

Li, S. S.

H. X. Deng, J. Li, S. S. Li, H. Peng, J. B. Xia, L. W. Wang, and S. H. Wei, “Band crossing in isovalent semiconductor alloys with large size mismatch: First-principles calculations of the electronic structure of Bi and N incorporated GaAs,” Phys. Rev. B 82(19), 193204 (2010).
[Crossref]

Lim, T. K.

J. Gu, F. Zhou, K. T. Wan, T. K. Lim, S. C. Tam, Y. L. Lam, D. Xu, and Z. Cheng, “Q-switching of a diode-pumped Nd: YVO4 laser with GaAs nonlinear output coupler,” Opt. Lasers Eng. 35(5), 299–307 (2001).
[Crossref]

Lin, A.

C. Wang, D. Shiau, and A. Lin, “Preparation of GaSb substrates for GaSb and GaInAsSb growth by organometallic vapor phase epitaxy,” J. Cryst. Growth 261(2-3), 385–392 (2004).
[Crossref]

Mascarenhas, A.

S. Francoeur, S. Tixier, E. Young, T. Tiedje, and A. Mascarenhas, “Bi isoelectronic impurities in GaAs,” Phys. Rev. B 77(8), 085209 (2008).
[Crossref]

Y. Zhang, A. Mascarenhas, and L. W. Wang, “Similar and dissimilar aspects of III-V semiconductors containing Bi versus N,” Phys. Rev. B 71(15), 155201 (2005).
[Crossref]

Masnadi-Shirazi, M.

R. Lewis, M. Masnadi-Shirazi, and T. Tiedje, “Growth of high Bi concentration GaAs1−xBix by molecular beam epitaxy,” Appl. Phys. Lett. 101(8), 082112 (2012).
[Crossref]

Navarro-Contreras, H.

G. Ramírez-Flores, H. Navarro-Contreras, A. Lastras-Martínez, R. C. Powell, and J. E. Greene, “Temperature-dependent optical band gap of the metastable zinc-blende structure β -GaN,” Phys. Rev. B Condens. Matter 50(12), 8433–8438 (1994).
[Crossref] [PubMed]

O’Reilly, E. P.

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

Olson, J.

W. Shan, W. Walukiewicz, J. Ager, E. Haller, J. Geisz, D. Friedman, J. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloys,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[Crossref]

Peng, H.

H. X. Deng, J. Li, S. S. Li, H. Peng, J. B. Xia, L. W. Wang, and S. H. Wei, “Band crossing in isovalent semiconductor alloys with large size mismatch: First-principles calculations of the electronic structure of Bi and N incorporated GaAs,” Phys. Rev. B 82(19), 193204 (2010).
[Crossref]

Perdew, J. P.

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77(18), 3865–3868 (1996).
[Crossref] [PubMed]

Piechota, J.

J. Wróbel, K. J. Kurzydłowski, K. Hummer, G. Kresse, and J. Piechota, “Calculations of ZnO properties using the Heyd-Scuseria-Ernzerhof screened hybrid density functional,” Phys. Rev. B 80(15), 155124 (2009).
[Crossref]

Powell, R. C.

G. Ramírez-Flores, H. Navarro-Contreras, A. Lastras-Martínez, R. C. Powell, and J. E. Greene, “Temperature-dependent optical band gap of the metastable zinc-blende structure β -GaN,” Phys. Rev. B Condens. Matter 50(12), 8433–8438 (1994).
[Crossref] [PubMed]

Puska, M. J.

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Origin of band gap bowing in dilute GaAs1-xNx and GaP1-xNx alloys: A real-space view,” Phys. Rev. B 88(3), 035204 (2013).
[Crossref]

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Modeling Bi-induced changes in the electronic structure of GaAs1-xBix alloys,” Phys. Rev. B 88, 235201 (2013).
[Crossref]

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Hybrid functional study of band structures of GaAs1−xN x and GaSb1−xNx alloys,” Phys. Rev. B 85(8), 085134 (2012).
[Crossref]

Qian, L.

Z. Zhang, L. Qian, D. Fan, and X. Deng, “Gallium arsenide: A new material to accomplish passively mode‐locked Nd: YAG laser,” Appl. Phys. Lett. 60(4), 419–421 (1992).
[Crossref]

Ramírez-Flores, G.

G. Ramírez-Flores, H. Navarro-Contreras, A. Lastras-Martínez, R. C. Powell, and J. E. Greene, “Temperature-dependent optical band gap of the metastable zinc-blende structure β -GaN,” Phys. Rev. B Condens. Matter 50(12), 8433–8438 (1994).
[Crossref] [PubMed]

Riechert, H.

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

Schumann, O.

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

Scuseria, G. E.

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 118(18), 8207–8215 (2003).
[Crossref]

Shan, W.

W. Shan, W. Walukiewicz, J. Ager, E. Haller, J. Geisz, D. Friedman, J. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloys,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[Crossref]

Shiau, D.

C. Wang, D. Shiau, and A. Lin, “Preparation of GaSb substrates for GaSb and GaInAsSb growth by organometallic vapor phase epitaxy,” J. Cryst. Growth 261(2-3), 385–392 (2004).
[Crossref]

Studna, A.

D. Aspnes and A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27(2), 985–1009 (1983).
[Crossref]

Tam, S. C.

J. Gu, F. Zhou, K. T. Wan, T. K. Lim, S. C. Tam, Y. L. Lam, D. Xu, and Z. Cheng, “Q-switching of a diode-pumped Nd: YVO4 laser with GaAs nonlinear output coupler,” Opt. Lasers Eng. 35(5), 299–307 (2001).
[Crossref]

Thomas, D. G.

D. G. Thomas, J. J. Hopfield, and C. J. Frosch, “Isoelectronic traps due to nitrogen in gallium phosphide,” Phys. Rev. Lett. 15(22), 857–860 (1965).
[Crossref]

Tiedje, T.

R. Lewis, M. Masnadi-Shirazi, and T. Tiedje, “Growth of high Bi concentration GaAs1−xBix by molecular beam epitaxy,” Appl. Phys. Lett. 101(8), 082112 (2012).
[Crossref]

S. Francoeur, S. Tixier, E. Young, T. Tiedje, and A. Mascarenhas, “Bi isoelectronic impurities in GaAs,” Phys. Rev. B 77(8), 085209 (2008).
[Crossref]

Timm, R.

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

Tixier, S.

S. Francoeur, S. Tixier, E. Young, T. Tiedje, and A. Mascarenhas, “Bi isoelectronic impurities in GaAs,” Phys. Rev. B 77(8), 085209 (2008).
[Crossref]

Tuomisto, F.

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Modeling Bi-induced changes in the electronic structure of GaAs1-xBix alloys,” Phys. Rev. B 88, 235201 (2013).
[Crossref]

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Origin of band gap bowing in dilute GaAs1-xNx and GaP1-xNx alloys: A real-space view,” Phys. Rev. B 88(3), 035204 (2013).
[Crossref]

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Hybrid functional study of band structures of GaAs1−xN x and GaSb1−xNx alloys,” Phys. Rev. B 85(8), 085134 (2012).
[Crossref]

Vaughan, M.

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

Vegard, L.

L. Vegard, “The constitution of mixed crystals and the space occupied by atoms,” Z. Phys. 5, 17–26 (1921).
[Crossref]

Virkkala, V.

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Origin of band gap bowing in dilute GaAs1-xNx and GaP1-xNx alloys: A real-space view,” Phys. Rev. B 88(3), 035204 (2013).
[Crossref]

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Modeling Bi-induced changes in the electronic structure of GaAs1-xBix alloys,” Phys. Rev. B 88, 235201 (2013).
[Crossref]

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Hybrid functional study of band structures of GaAs1−xN x and GaSb1−xNx alloys,” Phys. Rev. B 85(8), 085134 (2012).
[Crossref]

Walukiewicz, W.

W. Shan, W. Walukiewicz, J. Ager, E. Haller, J. Geisz, D. Friedman, J. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloys,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[Crossref]

Wan, K. T.

J. Gu, F. Zhou, K. T. Wan, T. K. Lim, S. C. Tam, Y. L. Lam, D. Xu, and Z. Cheng, “Q-switching of a diode-pumped Nd: YVO4 laser with GaAs nonlinear output coupler,” Opt. Lasers Eng. 35(5), 299–307 (2001).
[Crossref]

Wang, C.

C. Wang, D. Shiau, and A. Lin, “Preparation of GaSb substrates for GaSb and GaInAsSb growth by organometallic vapor phase epitaxy,” J. Cryst. Growth 261(2-3), 385–392 (2004).
[Crossref]

Wang, L. W.

H. X. Deng, J. Li, S. S. Li, H. Peng, J. B. Xia, L. W. Wang, and S. H. Wei, “Band crossing in isovalent semiconductor alloys with large size mismatch: First-principles calculations of the electronic structure of Bi and N incorporated GaAs,” Phys. Rev. B 82(19), 193204 (2010).
[Crossref]

Y. Zhang, A. Mascarenhas, and L. W. Wang, “Similar and dissimilar aspects of III-V semiconductors containing Bi versus N,” Phys. Rev. B 71(15), 155201 (2005).
[Crossref]

J. Li and L. W. Wang, “Energy levels of isoelectronic impurities by large scale LDA calculations,” Phys. Rev. B 67(3), 033102 (2003).
[Crossref]

Wei, S. H.

H. X. Deng, J. Li, S. S. Li, H. Peng, J. B. Xia, L. W. Wang, and S. H. Wei, “Band crossing in isovalent semiconductor alloys with large size mismatch: First-principles calculations of the electronic structure of Bi and N incorporated GaAs,” Phys. Rev. B 82(19), 193204 (2010).
[Crossref]

A. Janotti, S. H. Wei, and S. Zhang, “Theoretical study of the effects of isovalent coalloying of Bi and N in GaAs,” Phys. Rev. B 65(11), 115203 (2002).
[Crossref]

L. Bellaiche, S. H. Wei, and A. Zunger, “Localization and percolation in semiconductor alloys: GaAsN vs GaAsP,” Phys. Rev. B Condens. Matter 54(24), 17568–17576 (1996).
[Crossref] [PubMed]

Wróbel, J.

J. Wróbel, K. J. Kurzydłowski, K. Hummer, G. Kresse, and J. Piechota, “Calculations of ZnO properties using the Heyd-Scuseria-Ernzerhof screened hybrid density functional,” Phys. Rev. B 80(15), 155124 (2009).
[Crossref]

Xia, J. B.

H. X. Deng, J. Li, S. S. Li, H. Peng, J. B. Xia, L. W. Wang, and S. H. Wei, “Band crossing in isovalent semiconductor alloys with large size mismatch: First-principles calculations of the electronic structure of Bi and N incorporated GaAs,” Phys. Rev. B 82(19), 193204 (2010).
[Crossref]

Xu, D.

J. Gu, F. Zhou, K. T. Wan, T. K. Lim, S. C. Tam, Y. L. Lam, D. Xu, and Z. Cheng, “Q-switching of a diode-pumped Nd: YVO4 laser with GaAs nonlinear output coupler,” Opt. Lasers Eng. 35(5), 299–307 (2001).
[Crossref]

Yang, J.

J. Kuznia, J. Yang, Q. Chen, S. Krishnankutty, M. A. Khan, T. George, and J. Frietas., “Low pressure metalorganic chemical‐vapor deposition of cubic GaN over (100) GaAs substrates,” Appl. Phys. Lett. 65(19), 2407–2409 (1994).
[Crossref]

Yang, M.

Young, E.

S. Francoeur, S. Tixier, E. Young, T. Tiedje, and A. Mascarenhas, “Bi isoelectronic impurities in GaAs,” Phys. Rev. B 77(8), 085209 (2008).
[Crossref]

Zhang, S.

A. Janotti, S. H. Wei, and S. Zhang, “Theoretical study of the effects of isovalent coalloying of Bi and N in GaAs,” Phys. Rev. B 65(11), 115203 (2002).
[Crossref]

Zhang, Y.

Y. Zhang, A. Mascarenhas, and L. W. Wang, “Similar and dissimilar aspects of III-V semiconductors containing Bi versus N,” Phys. Rev. B 71(15), 155201 (2005).
[Crossref]

Zhang, Z.

Z. Zhang, L. Qian, D. Fan, and X. Deng, “Gallium arsenide: A new material to accomplish passively mode‐locked Nd: YAG laser,” Appl. Phys. Lett. 60(4), 419–421 (1992).
[Crossref]

Zhao, S.

Zhou, F.

J. Gu, F. Zhou, K. T. Wan, T. K. Lim, S. C. Tam, Y. L. Lam, D. Xu, and Z. Cheng, “Q-switching of a diode-pumped Nd: YVO4 laser with GaAs nonlinear output coupler,” Opt. Lasers Eng. 35(5), 299–307 (2001).
[Crossref]

Zunger, A.

L. Bellaiche, S. H. Wei, and A. Zunger, “Localization and percolation in semiconductor alloys: GaAsN vs GaAsP,” Phys. Rev. B Condens. Matter 54(24), 17568–17576 (1996).
[Crossref] [PubMed]

Appl. Phys. Lett. (3)

Z. Zhang, L. Qian, D. Fan, and X. Deng, “Gallium arsenide: A new material to accomplish passively mode‐locked Nd: YAG laser,” Appl. Phys. Lett. 60(4), 419–421 (1992).
[Crossref]

R. Lewis, M. Masnadi-Shirazi, and T. Tiedje, “Growth of high Bi concentration GaAs1−xBix by molecular beam epitaxy,” Appl. Phys. Lett. 101(8), 082112 (2012).
[Crossref]

J. Kuznia, J. Yang, Q. Chen, S. Krishnankutty, M. A. Khan, T. George, and J. Frietas., “Low pressure metalorganic chemical‐vapor deposition of cubic GaN over (100) GaAs substrates,” Appl. Phys. Lett. 65(19), 2407–2409 (1994).
[Crossref]

J. Chem. Phys. (1)

J. Heyd, G. E. Scuseria, and M. Ernzerhof, “Hybrid functionals based on a screened Coulomb potential,” J. Chem. Phys. 118(18), 8207–8215 (2003).
[Crossref]

J. Cryst. Growth (1)

C. Wang, D. Shiau, and A. Lin, “Preparation of GaSb substrates for GaSb and GaInAsSb growth by organometallic vapor phase epitaxy,” J. Cryst. Growth 261(2-3), 385–392 (2004).
[Crossref]

Opt. Express (2)

Opt. Lasers Eng. (1)

J. Gu, F. Zhou, K. T. Wan, T. K. Lim, S. C. Tam, Y. L. Lam, D. Xu, and Z. Cheng, “Q-switching of a diode-pumped Nd: YVO4 laser with GaAs nonlinear output coupler,” Opt. Lasers Eng. 35(5), 299–307 (2001).
[Crossref]

Opt. Lett. (1)

Phys. Rev. B (11)

J. Wróbel, K. J. Kurzydłowski, K. Hummer, G. Kresse, and J. Piechota, “Calculations of ZnO properties using the Heyd-Scuseria-Ernzerhof screened hybrid density functional,” Phys. Rev. B 80(15), 155124 (2009).
[Crossref]

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Hybrid functional study of band structures of GaAs1−xN x and GaSb1−xNx alloys,” Phys. Rev. B 85(8), 085134 (2012).
[Crossref]

A. Janotti, S. H. Wei, and S. Zhang, “Theoretical study of the effects of isovalent coalloying of Bi and N in GaAs,” Phys. Rev. B 65(11), 115203 (2002).
[Crossref]

S. Francoeur, S. Tixier, E. Young, T. Tiedje, and A. Mascarenhas, “Bi isoelectronic impurities in GaAs,” Phys. Rev. B 77(8), 085209 (2008).
[Crossref]

Y. Zhang, A. Mascarenhas, and L. W. Wang, “Similar and dissimilar aspects of III-V semiconductors containing Bi versus N,” Phys. Rev. B 71(15), 155201 (2005).
[Crossref]

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Modeling Bi-induced changes in the electronic structure of GaAs1-xBix alloys,” Phys. Rev. B 88, 235201 (2013).
[Crossref]

D. Aspnes and A. Studna, “Dielectric functions and optical parameters of Si, Ge, GaP, GaAs, GaSb, InP, InAs, and InSb from 1.5 to 6.0 eV,” Phys. Rev. B 27(2), 985–1009 (1983).
[Crossref]

L. Ivanova, H. Eisele, M. Vaughan, P. Ebert, A. Lenz, R. Timm, O. Schumann, L. Geelhaar, M. Dähne, S. Fahy, H. Riechert, and E. P. O’Reilly, “Direct measurement and analysis of the conduction band density of states in diluted GaAs1−xNx alloys,” Phys. Rev. B 82(16), 161201 (2010).
[Crossref]

J. Li and L. W. Wang, “Energy levels of isoelectronic impurities by large scale LDA calculations,” Phys. Rev. B 67(3), 033102 (2003).
[Crossref]

H. X. Deng, J. Li, S. S. Li, H. Peng, J. B. Xia, L. W. Wang, and S. H. Wei, “Band crossing in isovalent semiconductor alloys with large size mismatch: First-principles calculations of the electronic structure of Bi and N incorporated GaAs,” Phys. Rev. B 82(19), 193204 (2010).
[Crossref]

V. Virkkala, V. Havu, F. Tuomisto, and M. J. Puska, “Origin of band gap bowing in dilute GaAs1-xNx and GaP1-xNx alloys: A real-space view,” Phys. Rev. B 88(3), 035204 (2013).
[Crossref]

Phys. Rev. B Condens. Matter (4)

L. Bellaiche, S. H. Wei, and A. Zunger, “Localization and percolation in semiconductor alloys: GaAsN vs GaAsP,” Phys. Rev. B Condens. Matter 54(24), 17568–17576 (1996).
[Crossref] [PubMed]

G. Ramírez-Flores, H. Navarro-Contreras, A. Lastras-Martínez, R. C. Powell, and J. E. Greene, “Temperature-dependent optical band gap of the metastable zinc-blende structure β -GaN,” Phys. Rev. B Condens. Matter 50(12), 8433–8438 (1994).
[Crossref] [PubMed]

P. E. Blöchl, “Projector augmented-wave method,” Phys. Rev. B Condens. Matter 50(24), 17953–17979 (1994).
[Crossref] [PubMed]

G. Kresse and J. Furthmüller, “Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set,” Phys. Rev. B Condens. Matter 54(16), 11169–11186 (1996).
[Crossref] [PubMed]

Phys. Rev. Lett. (3)

J. P. Perdew, K. Burke, and M. Ernzerhof, “Generalized gradient approximation made simple,” Phys. Rev. Lett. 77(18), 3865–3868 (1996).
[Crossref] [PubMed]

D. G. Thomas, J. J. Hopfield, and C. J. Frosch, “Isoelectronic traps due to nitrogen in gallium phosphide,” Phys. Rev. Lett. 15(22), 857–860 (1965).
[Crossref]

W. Shan, W. Walukiewicz, J. Ager, E. Haller, J. Geisz, D. Friedman, J. Olson, and S. R. Kurtz, “Band anticrossing in GaInNAs alloys,” Phys. Rev. Lett. 82(6), 1221–1224 (1999).
[Crossref]

Z. Phys. (1)

L. Vegard, “The constitution of mixed crystals and the space occupied by atoms,” Z. Phys. 5, 17–26 (1921).
[Crossref]

Other (1)

O. Madelung, Semiconductors–Basic Data (Springer-Verlag, 1996).

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Figures (5)

Fig. 1
Fig. 1 (a)The band structures and the total DOS of GaAs1-xNx (x = 3.125%). (b) The band decomposed charge density of defect band, isosurfaces correspond to 0.0002 e/Å3.
Fig. 2
Fig. 2 (a)The band structures and the total DOS of GaAs1-x-yBixNy (x = 6.25%, y = 3.125%). (b) The band decomposed charge density of defect band, isosurfaces correspond to 0.007 e/Å3
Fig. 3
Fig. 3 Partial density of states of GaAs1-x-yBixNy (x = 6.25%, y = 3.125%).
Fig. 4
Fig. 4 The band gap of GaAs1-x-yBixNy with different size of cell, the concentrations of Bi and N are: (32) 12.5% and 6.25%; (64) 6.25% and 3.125%; (96) 4.17% and 2.08%; (128) 3.125% and 1.57%
Fig. 5
Fig. 5 (a) The imaginary part ε2 of the dielectric function and (b) absorption coefficient of GaAs and GaAs1-x-yBixNy (x = 6.25%, y = 3.125%)

Tables (1)

Tables Icon

Table 1 Calculated lattice constants a and band gap Eg for the zinc-blende phase GaAs, GaN, GaBi, both by PBE and HSE.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

a ( x , y ) = ( 1 x y ) a G a A s + x a G a B i + y a G a N
y = 0.58 x
α ( ω ) = 2 [ ε 1 2 ( ω ) + ε 2 2 ( ω ) ε 1 ( ω ) ] 1 2

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