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Defect levels in d-electron containing systems: Comparative study of CdTe using LDA and LDA + U

Yuan Yin1, 2, , Yu Wang1, Guangde Chen2 and Yelong Wu2

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 Corresponding author: Yuan Yin, E-mail: yinyuan8008@126.com

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Abstract: The defect properties in d-electron containing materials will be strongly influenced by the non-negligible on-site Coulomb interactions. However, this has been omitted in the current widely adopted standard first-principles calculations, such as LDA, leading to a large deviation of calculated results. Therefore, as a comparative case study, in this paper the defects of CdTe are investigated by first-principles calculations including standard LDA and LDA + U, and we find that LDA + U gives more accurate formation energies of the neutral point defects than the standard LDA. The same trend can be found in transition energies of the charged state defects as well. These comparative analyses show that LDA + U gives better results for the defects of CdTe than the standard LDA and requires less computing resource than LAPW, indicating it should have huge potential to model supercells with large number of atoms and strong electron interactions. Moreover, a new anion interstitial defect structure is found to be more stable than the well-known tetrahedron central anion interstitial defect structure ${\rm{Te}}_i^a$.

Key words: defectsLDALDA + Uformation energytransition energyfirst-principles



[1]
Neumark G F. Defects in wide band gap II–VI crystals. Mater Sci Eng, 1997, 21, 1 doi: 10.1016/S0927-796X(97)00008-9
[2]
Koizumi S. Ultraviolet emission from a diamond pn junction. Science, 2001, 292, 1899 doi: 10.1126/science.1060258
[3]
Isberg J, Hammersberg J, Johansson E, et al. High carrier mobility in single-crystal plasma-deposited diamond. Science, 2002, 297, 1670 doi: 10.1126/science.1074374
[4]
Teukam Z, Chevallier J, Saguy C, et al. Shallow donors with high n-type electrical conductivity in homoepitaxial deuterated boron-doped diamond layers. Nat Mater, 2003, 2, 482 doi: 10.1038/nmat929
[5]
Chevallier J, Teukam Z, Saguy C, et al. Shallow donor induced n-type conductivity in deuterated boron-doped diamond. Phys Status Solidi A, 2004, 201, 2444 doi: 10.1002/pssa.200405180
[6]
Takeuchi T, Takeuchi H, Sota S, et al. Optical properties of strained AlGaN and GaInN on GaN. Jpn J Appl Phys, 1997, 36, 5393 doi: 10.1143/JJAP.36.5393
[7]
Nakamura S, Mukai T, Senoh M. Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes. Appl Phys Lett, 1994, 64, 1687 doi: 10.1063/1.111832
[8]
Huang M H. Room-temperature ultraviolet nanowire nanolasers. Science, 2001, 292, 1897 doi: 10.1126/science.1060367
[9]
Wei S H, Zhang S B. Chemical trends of defect formation and doping limit in II–VI semiconductors: The case of CdTe. Phy Rev B, 2002, 66, 5211 doi: 10.1103/PhysRevB.66.155211
[10]
Look D C, Claflin B, Alivov Y I, et al. The future of ZnO light emitters. Phys Status Solidi A, 2004, 201, 2203 doi: 10.1002/pssa.200404803
[11]
Tsukazaki A O A, Onuma T, Ohtani M, et al. Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO. Nat Mater, 2005, 4, 42 doi: 10.1038/nmat1284
[12]
Tsukazaki M K A, Ohtomo A, Onuma T, et al. Blue light-emitting diode based on ZnO. Jpn J Appl Phys, 2005, 44, 643 doi: 10.1143/JJAP.44.L643
[13]
Taniyasu M K Y, Makimoto T. An aluminium nitride light-emitting diode with a wavelength of 210 nanometres. Nature, 2006, 441, 325 doi: 10.1038/nature04760
[14]
Dhere R G. Study of the CdS/CdTe interface and its relevance to solar cell properties: University of Colorado, 1997
[15]
Lyahovitskaya V, Chernyak L, Greenberg J, et al. n- and p-type post-growth self-doping of CdTe single crystals. J Cryst Growth, 2000, 214, 1155 doi: 10.1016/S0022-0248(00)00294-3
[16]
Wei S H, Krakauer H. Local-density-functional calculation of the pressure-induced metallization of BaSe and BaTe. Phy Rev Lett, 1985, 55, 1200 doi: 10.1103/PhysRevLett.55.1200
[17]
Singh D J, Nordstrom L. Planewaves, pseudopotentials and the LAPW method. Boston: Kluwer, 1994
[18]
Roy D P. S-wave K-N scattering by the ND method. Phys Rev, 1964, 136, B804 doi: 10.1103/PhysRev.136.B804
[19]
Kohn W, Sham L J. Self-consistent equations including exchange and correlation effects. Phys Rev, 1965, 140, A1133 doi: 10.1103/PhysRev.140.A1133
[20]
Joseph M, Tabata H, Kawai T. p-type electrical conduction in ZnO thin films by Ga and N codoping. Jpn J Appl Phys, 1999, 38, 1205 doi: 10.1143/JJAP.38.L1205
[21]
Miller A. Landolt-bornstein: numerical data and functional relationships in science and technology. Opt Acta, 1982, 32, 507 doi: 10.1080/713821754
[22]
Anisimov V I, Zaanen J, Andersen O K. Band theory and mott insulators: Hubbard U instead of stoner I. Phy Rev B, 1991, 44, 943 doi: 10.1103/PhysRevB.44.943
[23]
Hubbard J. Electron correlations in narrow energy bands. Proceedings of the Royal Society of London, 1963, 276, 238
[24]
Dudarev S L, Botton G A, Savrasov S Y, et al. Electronic structure and elastic properties of strongly correlated metal oxides from first principles: LSDA + U, SIC-LSDA and EELS study of UO2 and NiO. Phys Status Solidi A, 1998, 166, 429 doi: 10.1002/(SICI)1521-396X(199803)166:1<429::AID-PSSA429>3.0.CO;2-F
[25]
Berding M A. Native defects in CdTe. Phy Rev B, 1999, 60, 8943 doi: 10.1103/PhysRevB.60.8943
[26]
Stampfl C, Van de Walle C G. Theoretical investigation of native defects, impurities, and complexes in aluminum nitride. Phy Rev B, 2002, 65, 155212 doi: 10.1103/PhysRevB.65.155212
[27]
Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B, 1990, 41, 7892 doi: 10.1103/PhysRevB.41.7892
[28]
Kresse G. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phy Rev B, 1996, 54, 11169 doi: 10.1103/PhysRevB.54.11169
[29]
Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phy Rev B, 1999, 59, 1758 doi: 10.1103/PhysRevB.59.1758
[30]
Wei S H. Overcoming the doping bottleneck in semiconductors. Comput Mater Sci, 2004, 30, 337 doi: 10.1016/j.commatsci.2004.02.024
[31]
Yan Y F, Wei S H. Doping asymmetry in wide-bandgap semiconductors: Origins and solutions. Phys Status Solidi B, 2008, 245, 641 doi: 10.1002/pssb.200743334
[32]
Wu Y, Chen G, Zhu Y, et al. LDA + U/GGA + U calculations of structural and electronic properties of CdTe: Dependence on the effective U parameter. Comput Mater Sci, 2014, 98, 18 doi: 10.1016/j.commatsci.2014.10.051
[33]
Lany S, Zunger A. Anion vacancies as a source of persistent photoconductivity in II–VI and chalcopyrite semiconductors. Phy Rev B, 2005, 72, 035215 doi: 10.1103/PhysRevB.72.035215
[34]
Yin Y, Chen G, Ye H, et al. A novel anion interstitial defect structure in zinc-blende materials: A first-principles study. Europhys Lett, 2016, 114, 36001 doi: 10.1209/0295-5075/114/36001
Fig. 1.  (Color online) (a) The stable structure is that the Te atom is at the center of the tetrahedron, and (b) a more stable structure is that the anion atom Te and two cation atom Cds are almost in a line.

Fig. 2.  (Color online) The acceptor defect (q < 0) transition energy level positions of native defects in CdTe, calculated by LDA, LDA + U and LAPW, respectively.

Fig. 3.  (Color online) The donor defect (q > 0) transition energy level positions of native defects in CdTe, calculated by LDA, LDA + U and LAPW, respectively.

Table 1.   Calculated defect formation energy $\Delta H\left( {\alpha ,q} \right)$ [through Eq. (1)] of point defects for tetrahedron structure at neutral charge state $\left( {q = 0} \right)$ and μi = 0, the unit of defect formation energies is eV.

DefectLAPW[9]LDALDA + UDefectLAPW[9]LDALDA + U
VCd2.672.422.80CdTe3.923.303.63
VTe3.242.943.13TeCd3.703.423.55
Teia3.522.072.00Cdia2.262.052.10
Teic3.413.733.68Cdic2.041.771.76
NaCd0.450.250.48AlCd1.170.881.10
CuCd1.311.251.51GaCd1.231.011.17
AgCd1.321.241.48InCd1.230.971.14
AuCd1.301.401.64FTe–0.08–0.84–0.95
NTe2.622.882.83ClTe0.480.230.22
PTe1.831.961.66BrTe0.620.270.29
AsTe1.681.371.55ITe0.991.041.11
SbTe1.721.541.77Cuia2.142.052.07
BiTe1.961.862.04Cuic2.242.272.30
Naia0.600.210.34Naic0.450.080.21
DownLoad: CSV

Table 2.   Calculated acceptor defect (q < 0) transition energies of tetrahedron CdTe. The unit of transition energy is eV.

Defect stateLAPW[9]LDALDA + U
Teia(0/–2)0.571.7951.993
VCd(0/–1)0.130.0910.173
VCd(–1/–2)0.21–0.3130.446
CuCd(0/–1)0.220.0940.177
AuCd(0/–1)0.200.1940.282
AgCd(0/–1)0.150.0930.170
NaCd(0/–1)0.020.0410.114
BiTe(0/–1)0.300.2870.378
SbTe(0/–1)0.230.1880.245
AsTe(0/–1)0.100.0450.115
PTe(0/–1)0.05–0.0340.060
NTe(0/–1)0.01–0.0580.013
DownLoad: CSV

Table 3.   Calculated donor defect (q > 0) transition energy levels for tetrahedron native defects. The unit of transition energies is eV.

Defect stateLAPW[9]LDALDA + U
CdTe(+2/0)0.100.010.05
TeCd(+1/0)0.340.3450.625
TeCd(+2/+1)0.590.347–0.917
Cdic(+2/0)0.450.4680.572
VTe(+2/0)0.710.8900.662
AlCd(+1/0)< 0.03-0.028–0.038
InCd(+1/0)< 0.050.3530.347
ITe(+1/0)0.050.3660.293
GaCd(+1/0)0.240.1070.316
BrTe(+1/0)> 0.240.4010.341
ClTe(+1/0)0.350.4220.371
FTe(+1/0)0.870.6700.739
Cuia(+1/0)–0.01–0.127–0.032
Naic(+1/0)0.01–0.078–0.006
DownLoad: CSV
[1]
Neumark G F. Defects in wide band gap II–VI crystals. Mater Sci Eng, 1997, 21, 1 doi: 10.1016/S0927-796X(97)00008-9
[2]
Koizumi S. Ultraviolet emission from a diamond pn junction. Science, 2001, 292, 1899 doi: 10.1126/science.1060258
[3]
Isberg J, Hammersberg J, Johansson E, et al. High carrier mobility in single-crystal plasma-deposited diamond. Science, 2002, 297, 1670 doi: 10.1126/science.1074374
[4]
Teukam Z, Chevallier J, Saguy C, et al. Shallow donors with high n-type electrical conductivity in homoepitaxial deuterated boron-doped diamond layers. Nat Mater, 2003, 2, 482 doi: 10.1038/nmat929
[5]
Chevallier J, Teukam Z, Saguy C, et al. Shallow donor induced n-type conductivity in deuterated boron-doped diamond. Phys Status Solidi A, 2004, 201, 2444 doi: 10.1002/pssa.200405180
[6]
Takeuchi T, Takeuchi H, Sota S, et al. Optical properties of strained AlGaN and GaInN on GaN. Jpn J Appl Phys, 1997, 36, 5393 doi: 10.1143/JJAP.36.5393
[7]
Nakamura S, Mukai T, Senoh M. Candela-class high-brightness InGaN/AlGaN double-heterostructure blue-light-emitting diodes. Appl Phys Lett, 1994, 64, 1687 doi: 10.1063/1.111832
[8]
Huang M H. Room-temperature ultraviolet nanowire nanolasers. Science, 2001, 292, 1897 doi: 10.1126/science.1060367
[9]
Wei S H, Zhang S B. Chemical trends of defect formation and doping limit in II–VI semiconductors: The case of CdTe. Phy Rev B, 2002, 66, 5211 doi: 10.1103/PhysRevB.66.155211
[10]
Look D C, Claflin B, Alivov Y I, et al. The future of ZnO light emitters. Phys Status Solidi A, 2004, 201, 2203 doi: 10.1002/pssa.200404803
[11]
Tsukazaki A O A, Onuma T, Ohtani M, et al. Repeated temperature modulation epitaxy for p-type doping and light-emitting diode based on ZnO. Nat Mater, 2005, 4, 42 doi: 10.1038/nmat1284
[12]
Tsukazaki M K A, Ohtomo A, Onuma T, et al. Blue light-emitting diode based on ZnO. Jpn J Appl Phys, 2005, 44, 643 doi: 10.1143/JJAP.44.L643
[13]
Taniyasu M K Y, Makimoto T. An aluminium nitride light-emitting diode with a wavelength of 210 nanometres. Nature, 2006, 441, 325 doi: 10.1038/nature04760
[14]
Dhere R G. Study of the CdS/CdTe interface and its relevance to solar cell properties: University of Colorado, 1997
[15]
Lyahovitskaya V, Chernyak L, Greenberg J, et al. n- and p-type post-growth self-doping of CdTe single crystals. J Cryst Growth, 2000, 214, 1155 doi: 10.1016/S0022-0248(00)00294-3
[16]
Wei S H, Krakauer H. Local-density-functional calculation of the pressure-induced metallization of BaSe and BaTe. Phy Rev Lett, 1985, 55, 1200 doi: 10.1103/PhysRevLett.55.1200
[17]
Singh D J, Nordstrom L. Planewaves, pseudopotentials and the LAPW method. Boston: Kluwer, 1994
[18]
Roy D P. S-wave K-N scattering by the ND method. Phys Rev, 1964, 136, B804 doi: 10.1103/PhysRev.136.B804
[19]
Kohn W, Sham L J. Self-consistent equations including exchange and correlation effects. Phys Rev, 1965, 140, A1133 doi: 10.1103/PhysRev.140.A1133
[20]
Joseph M, Tabata H, Kawai T. p-type electrical conduction in ZnO thin films by Ga and N codoping. Jpn J Appl Phys, 1999, 38, 1205 doi: 10.1143/JJAP.38.L1205
[21]
Miller A. Landolt-bornstein: numerical data and functional relationships in science and technology. Opt Acta, 1982, 32, 507 doi: 10.1080/713821754
[22]
Anisimov V I, Zaanen J, Andersen O K. Band theory and mott insulators: Hubbard U instead of stoner I. Phy Rev B, 1991, 44, 943 doi: 10.1103/PhysRevB.44.943
[23]
Hubbard J. Electron correlations in narrow energy bands. Proceedings of the Royal Society of London, 1963, 276, 238
[24]
Dudarev S L, Botton G A, Savrasov S Y, et al. Electronic structure and elastic properties of strongly correlated metal oxides from first principles: LSDA + U, SIC-LSDA and EELS study of UO2 and NiO. Phys Status Solidi A, 1998, 166, 429 doi: 10.1002/(SICI)1521-396X(199803)166:1<429::AID-PSSA429>3.0.CO;2-F
[25]
Berding M A. Native defects in CdTe. Phy Rev B, 1999, 60, 8943 doi: 10.1103/PhysRevB.60.8943
[26]
Stampfl C, Van de Walle C G. Theoretical investigation of native defects, impurities, and complexes in aluminum nitride. Phy Rev B, 2002, 65, 155212 doi: 10.1103/PhysRevB.65.155212
[27]
Vanderbilt D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys Rev B, 1990, 41, 7892 doi: 10.1103/PhysRevB.41.7892
[28]
Kresse G. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phy Rev B, 1996, 54, 11169 doi: 10.1103/PhysRevB.54.11169
[29]
Kresse G, Joubert D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phy Rev B, 1999, 59, 1758 doi: 10.1103/PhysRevB.59.1758
[30]
Wei S H. Overcoming the doping bottleneck in semiconductors. Comput Mater Sci, 2004, 30, 337 doi: 10.1016/j.commatsci.2004.02.024
[31]
Yan Y F, Wei S H. Doping asymmetry in wide-bandgap semiconductors: Origins and solutions. Phys Status Solidi B, 2008, 245, 641 doi: 10.1002/pssb.200743334
[32]
Wu Y, Chen G, Zhu Y, et al. LDA + U/GGA + U calculations of structural and electronic properties of CdTe: Dependence on the effective U parameter. Comput Mater Sci, 2014, 98, 18 doi: 10.1016/j.commatsci.2014.10.051
[33]
Lany S, Zunger A. Anion vacancies as a source of persistent photoconductivity in II–VI and chalcopyrite semiconductors. Phy Rev B, 2005, 72, 035215 doi: 10.1103/PhysRevB.72.035215
[34]
Yin Y, Chen G, Ye H, et al. A novel anion interstitial defect structure in zinc-blende materials: A first-principles study. Europhys Lett, 2016, 114, 36001 doi: 10.1209/0295-5075/114/36001
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    Received: 15 December 2019 Revised: 01 January 2020 Online: Accepted Manuscript: 03 March 2020Uncorrected proof: 05 March 2020Published: 01 October 2020

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      Yuan Yin, Yu Wang, Guangde Chen, Yelong Wu. Defect levels in d-electron containing systems: Comparative study of CdTe using LDA and LDA + U[J]. Journal of Semiconductors, 2020, 41(10): 102701. doi: 10.1088/1674-4926/41/10/102701 Y Yin, Y Wang, G D Chen, Y L Wu, Defect levels in d-electron containing systems: Comparative study of CdTe using LDA and LDA + U[J]. J. Semicond., 2020, 41(10): 102701. doi: 10.1088/1674-4926/41/10/102701.Export: BibTex EndNote
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      Yuan Yin, Yu Wang, Guangde Chen, Yelong Wu. Defect levels in d-electron containing systems: Comparative study of CdTe using LDA and LDA + U[J]. Journal of Semiconductors, 2020, 41(10): 102701. doi: 10.1088/1674-4926/41/10/102701

      Y Yin, Y Wang, G D Chen, Y L Wu, Defect levels in d-electron containing systems: Comparative study of CdTe using LDA and LDA + U[J]. J. Semicond., 2020, 41(10): 102701. doi: 10.1088/1674-4926/41/10/102701.
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      Defect levels in d-electron containing systems: Comparative study of CdTe using LDA and LDA + U

      doi: 10.1088/1674-4926/41/10/102701
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      • Corresponding author: E-mail: yinyuan8008@126.com
      • Received Date: 2019-12-15
      • Revised Date: 2020-01-01
      • Published Date: 2020-10-04

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