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Local vibrational modes of Zn–H–As defects in GaAs, ZnSe and ZnTe
Computational Materials Science 33 (2005) 145–147 www.elsevier.com/locate/commatsci
Local vibrational modes of Zn–H–As defects in GaAs, ZnSe and ZnTe V.J.B. Torres b
a,*
, J. Coutinho a, P.R. Briddon
b
a Department of Physics, University of Aveiro, 3810 Aveiro, Portugal School of Natural Sciences, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, United Kingdom
Abstract The hydrogenation of the zinc acceptor in GaAs (ZnGa), and As acceptor in ZnSe (AsSe) and in ZnTe (AsTe), is studied by computer modeling using an ab initio pseudopotential density-functional method. We found that the lowest energy location for hydrogen is nearly bond-centered (closer to As) between Zn and As atoms. Also for GaAs:ZnH, ZnSe:AsH and ZnTe:AsH, antibonding As–H units were found to be metastable by 0.4, 0.5 and 0.7 eV, respectively. The calculated local vibrational modes and deuterium isotopic shifts agree within less than 4% of the experimental data. The correct ordering of the As–H stretch modes in GaAs and ZnSe is only reproduced when anharmonic effects are taken into account. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction The effects that arise from the incorporation of hydrogen into semiconductors have been at the center of many research activities. For example, hydrogen is well known to interact effectively with dopant impurities, by often removing or displacing their electrical levels [1]. Zinc in GaAs is known to act as an acceptor after replacing a gallium atom. In the presence of hydrogen, the appearance of an *
Corresponding author. Tel.: +351 234 370278; fax: +351 234 424965. E-mail address: vtorres@fis.ua.pt (V.J.B. Torres).
absorption band at 2146.9 cm1 has been linked to a vibration at a ZnH complex [2]. Arsenic has also been proposed as a source of p-type conductivity in ZnSe, and it is believed to sit at a Se site. Here, H was also found to interact with the dopants, and an infrared line at 2165.6 cm1 was assigned to a local vibrational mode at a AsH complex [3]. In ZnTe, As is assumed to sit at a Te site and to be an acceptor. An infrared line at 2014 cm1 was measured in As,H codoped ZnTe [4], and assigned to a As–H stretch vibrational mode. The closeness of these bands led to the suggestion that similar Zn–H–As structures occur in all GaAs:ZnH and ZnSe:AsH and ZnTe:AsH complexes [3]. A bond
0927-0256/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2004.12.055
146
V.J.B. Torres et al. / Computational Materials Science 33 (2005) 145–147
center position between Zn and As atoms in ZnSe:AsH has been proposed by previous ab initio calculations [5], but modeling studies of Zn–H–As complexes in other materials is still lacking in the literature. The aim of this paper is to model, in a comparative way, the vibrational properties of Zn–H–As structures that occur in GaAs:ZnH, ZnSe:AsH and ZnTe:AsH complexes.
˚ displacing the Zn, H and As atoms by 0.005 A along all six Cartesian directions, and (ii) anharmonic, with the H atom vibrating along a h1 1 1i axis between Zn and As atoms, where the total energy was calculated at 20 points. The three lowest vibrational states were determined numerically using the shooting method [12], allowing us to estimate the fundamental and overtone absorptions associated to this local mode.
2. Theoretical method
3. Results
We use a pseudopotential density-functional supercell code (AIMPRO) [6], along with the exchange-correlation parameterized by Pewdew and Wang [7]. The pseudopotentials by Troullier and Martins are used [8], with the zinc 3d electrons considered in valence states. Khon–Sham orbitals are expanded by using atom-centered s, p and d Cartesian–Gaussians functions. Further details on the method may be found elsewhere [9]. Calculations were performed using 64 atom cubic shaped supercells, and 8 reducible special kpoints to sample the Brillouin zone [10]. Lattice parameters and bulk modulus (shown in Table 1), were obtained according to the Murnaghan equation of state [11]. All atoms in the defective supercells were allowed to relax until the forces ˚. at each atom were less than 0.03 eV/A The Zn–H–As stretching mode frequencies reported here are (i) quasi-harmonic, where a dynamical matrix is obtained from the forces after
Hydrogen was placed around the impurity atoms, i.e., ZnGa in GaAs, and AsVI in ZnSe and ZnTe, on several sites. These sites are shown in Fig. 1 for the case of ZnSe and ZnTe hosts, and are labelled according to the usual notation. We found that in the ground state of all GaAs:ZnH, ZnSe:AsH and ZnTe:AsH complexes, hydrogen sits in a nearly bond-centered position between ˚ zinc and arsenic atoms, forming a bond (1.54 A length) with the As atom. Details of their geometries are shown in Table 1. We also found that structures where H is antibonding with respect to As atoms, are metastable by 0.4, 0.5 and 0.7 eV in GaAs:ZnH, ZnSe:AsH and ZnTe:AsH, respectively. The antibonding location to the Zn atom is metastable by at least 1 eV. The calculated quasi-harmonic stretching frequencies (xQH) for the bond centered configuration are shown in
Table 1 Calculated lattice parameter (a0), bulk modulus (B) of GaAs, ZnSe and ZnTe crystals, and atomic distances (r) for the Zn–H– As defects GaAs a0 Expt. Calc. B Expt. Calc. r (As–H) r (Zn–H) r (Zn–As)
ZnSe
5.65 5.606 74.8 76.4
5.67 5.675 62.5 66.5
1.528 1.814 3.342
˚ and B in GPa. All distances are in A
1.539 1.792 3.331
ZnTe 6.09 6.108 50.9 52.6 1.545 1.889 3.434
Fig. 1. Projection of a ZnSe (ZnTe) crystal on the plane. Substitutional As is indicated by the large black circle at the center. Hydrogen is located at sites represented by small black circles labeled according to the usual notation. For example, BC stands for the bond centered position. Zn and Se (Te) are represented as large open and small gray circles, respectively.
V.J.B. Torres et al. / Computational Materials Science 33 (2005) 145–147 Table 2 Local vibrational stretching modes (cm1) of the bond centered Zn–H–As and Zn–D–As defects in GaAs, ZnSe and ZnTe GaAs H–As
ZnSe
147
wag modes at 396 cm1 and at 465 cm1 for ZnSe:AsH and ZnTe:AsH complexes.
ZnTe
4. Conclusions
x20 Expt. Calc. x10 Expt. Calc. xQH
4216.7 4162 2146.9 2189 2207
2165.6 2218 2179
2014 2006 2035
D–As
x10 Expt. Calc. xQH
1549.1 1552 1567
1557 1572 1547
NA 1425 1446
Isotopic shifts
Dx10 Expt. Calc. DxQH
597.9 637 639
608.6 646 632
NA 581 589
x20, x10 and xQH stand for the overtone, the fundamental transition and quasi-harmonic frequencies, respectively. NA stands for not available.
Table 2. These differ by only 3% when compared to the experimental fundamental transition frequencies for GaAs:ZnH [2], and less than 1% for ZnSe:AsH [3] and ZnSe:AsH [4], respectively. The isotopic shifts obtained after replacing hydrogen by deuterium are also reproduced within less than 4% with respect to the experimental data. Despite the good agreement, the relative ordering of the stretch modes in GaAs:ZnH and ZnSe:AsH is not reproduced. This is only achieved when we consider anharmonic effects. Accordingly, the fundamental transition frequencies, x10, are at most 2% away from the experimental values, and the same kind of agreement is obtained for the deuterium– arsenic stretch mode and respective isotopic shifts. From Table 1 we note that the Zn–H distance follows the same trend of the stretching vibrational modes, i.e., the shortest Zn–H distance and higher frequency occur in ZnSe. We believe that the Zn– H coupling is better accounted for when anharmonicity is considered, where the H atom is displaced along longer distances. After inspection of the stretching-mode potential energies, we find these very similar for both complexes in ZnSe and GaAs near the equilibrium and compressed As–H regions. However, for As–H distances greater than ˚ the potential in ZnSe grows faster. In 0.05 A addition to the stretch frequencies, we also predict
We have explored several atomic configurations of H nearby the Zn acceptor in GaAs, and the As acceptor in ZnSe and ZnTe, by using an ab initio density-functional method. The lowest energy configurations are those where H sits near the Zn–As bond center sites, with H bonded to As. The local vibrational modes agree well with experimental data. The larger As–H stretching frequency in ZnSe is attributed to the shorter Zn–H distance in this center. This effect is essentially anharmonic, since this feature is not reproduced by the quasiharmonic calculation.
Acknowledgements This work was supported by the FCT and FEDER in Portugal (Grants ref. SFRH/BPD/ 5735/2001 and POCTI/CTM/40979/2001).
References [1] S.J. Pearton, J.W. Corbett, M. Stavola, Hydrogen in Crystalline Semiconductors, Springer-Verlag, Berlin, 1992. [2] R. Darwich, B. Pajot, B. Rose, D. Robein, B. Theys, R. Rahbi, C. Porte, F. Gendron, Phys. Rev. B 48 (1993) 17776. [3] M.D. McCluskey, E.E. Haller, F.X. Zach, E.D. BorretCourchesne, Appl. Phys. Lett. 68 (1996) 3476. [4] L. Svob, Y. Marfaing, B. Clerjaud, D. Cote, D. Balllutaud, B. Yheys, R. Druilhe, W. Kuhn, H. Stanzl, W. Gebhardt, Mat. Sci. Forum 143–147 (1994) 447. [5] V.J.B. Torres, J. Coutinho, P.R. Briddon, Physica B 340– 342 (2003) 272. [6] P.R. Briddon, R. Jones, Phys. Status Solidi B 207 (2000) 131. [7] J.P. Perdew, Y. Wang, Phys. Rev. B 43 (1992) 13244. [8] N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993. [9] J. Coutinho, V.J.B. Torres, P.R. Briddon, Phys. Rev. B 67 (2003) 35205. [10] M.D. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [11] F.D. Murnaghan, Proc. Natl. Acad. Sci. USA 30 (1944) 244. [12] T. Pang, An Introduction to Computational Physics, Cambridge University Press, Cambridge, 1997.
Local vibrational modes of Zn–H–As defects in GaAs, ZnSe and ZnTe V.J.B. Torres b
a,*
, J. Coutinho a, P.R. Briddon
b
a Department of Physics, University of Aveiro, 3810 Aveiro, Portugal School of Natural Sciences, University of Newcastle upon Tyne, Newcastle upon Tyne, NE1 7RU, United Kingdom
Abstract The hydrogenation of the zinc acceptor in GaAs (ZnGa), and As acceptor in ZnSe (AsSe) and in ZnTe (AsTe), is studied by computer modeling using an ab initio pseudopotential density-functional method. We found that the lowest energy location for hydrogen is nearly bond-centered (closer to As) between Zn and As atoms. Also for GaAs:ZnH, ZnSe:AsH and ZnTe:AsH, antibonding As–H units were found to be metastable by 0.4, 0.5 and 0.7 eV, respectively. The calculated local vibrational modes and deuterium isotopic shifts agree within less than 4% of the experimental data. The correct ordering of the As–H stretch modes in GaAs and ZnSe is only reproduced when anharmonic effects are taken into account. Ó 2004 Elsevier B.V. All rights reserved.
1. Introduction The effects that arise from the incorporation of hydrogen into semiconductors have been at the center of many research activities. For example, hydrogen is well known to interact effectively with dopant impurities, by often removing or displacing their electrical levels [1]. Zinc in GaAs is known to act as an acceptor after replacing a gallium atom. In the presence of hydrogen, the appearance of an *
Corresponding author. Tel.: +351 234 370278; fax: +351 234 424965. E-mail address: vtorres@fis.ua.pt (V.J.B. Torres).
absorption band at 2146.9 cm1 has been linked to a vibration at a ZnH complex [2]. Arsenic has also been proposed as a source of p-type conductivity in ZnSe, and it is believed to sit at a Se site. Here, H was also found to interact with the dopants, and an infrared line at 2165.6 cm1 was assigned to a local vibrational mode at a AsH complex [3]. In ZnTe, As is assumed to sit at a Te site and to be an acceptor. An infrared line at 2014 cm1 was measured in As,H codoped ZnTe [4], and assigned to a As–H stretch vibrational mode. The closeness of these bands led to the suggestion that similar Zn–H–As structures occur in all GaAs:ZnH and ZnSe:AsH and ZnTe:AsH complexes [3]. A bond
0927-0256/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2004.12.055
146
V.J.B. Torres et al. / Computational Materials Science 33 (2005) 145–147
center position between Zn and As atoms in ZnSe:AsH has been proposed by previous ab initio calculations [5], but modeling studies of Zn–H–As complexes in other materials is still lacking in the literature. The aim of this paper is to model, in a comparative way, the vibrational properties of Zn–H–As structures that occur in GaAs:ZnH, ZnSe:AsH and ZnTe:AsH complexes.
˚ displacing the Zn, H and As atoms by 0.005 A along all six Cartesian directions, and (ii) anharmonic, with the H atom vibrating along a h1 1 1i axis between Zn and As atoms, where the total energy was calculated at 20 points. The three lowest vibrational states were determined numerically using the shooting method [12], allowing us to estimate the fundamental and overtone absorptions associated to this local mode.
2. Theoretical method
3. Results
We use a pseudopotential density-functional supercell code (AIMPRO) [6], along with the exchange-correlation parameterized by Pewdew and Wang [7]. The pseudopotentials by Troullier and Martins are used [8], with the zinc 3d electrons considered in valence states. Khon–Sham orbitals are expanded by using atom-centered s, p and d Cartesian–Gaussians functions. Further details on the method may be found elsewhere [9]. Calculations were performed using 64 atom cubic shaped supercells, and 8 reducible special kpoints to sample the Brillouin zone [10]. Lattice parameters and bulk modulus (shown in Table 1), were obtained according to the Murnaghan equation of state [11]. All atoms in the defective supercells were allowed to relax until the forces ˚. at each atom were less than 0.03 eV/A The Zn–H–As stretching mode frequencies reported here are (i) quasi-harmonic, where a dynamical matrix is obtained from the forces after
Hydrogen was placed around the impurity atoms, i.e., ZnGa in GaAs, and AsVI in ZnSe and ZnTe, on several sites. These sites are shown in Fig. 1 for the case of ZnSe and ZnTe hosts, and are labelled according to the usual notation. We found that in the ground state of all GaAs:ZnH, ZnSe:AsH and ZnTe:AsH complexes, hydrogen sits in a nearly bond-centered position between ˚ zinc and arsenic atoms, forming a bond (1.54 A length) with the As atom. Details of their geometries are shown in Table 1. We also found that structures where H is antibonding with respect to As atoms, are metastable by 0.4, 0.5 and 0.7 eV in GaAs:ZnH, ZnSe:AsH and ZnTe:AsH, respectively. The antibonding location to the Zn atom is metastable by at least 1 eV. The calculated quasi-harmonic stretching frequencies (xQH) for the bond centered configuration are shown in
Table 1 Calculated lattice parameter (a0), bulk modulus (B) of GaAs, ZnSe and ZnTe crystals, and atomic distances (r) for the Zn–H– As defects GaAs a0 Expt. Calc. B Expt. Calc. r (As–H) r (Zn–H) r (Zn–As)
ZnSe
5.65 5.606 74.8 76.4
5.67 5.675 62.5 66.5
1.528 1.814 3.342
˚ and B in GPa. All distances are in A
1.539 1.792 3.331
ZnTe 6.09 6.108 50.9 52.6 1.545 1.889 3.434
Fig. 1. Projection of a ZnSe (ZnTe) crystal on the plane. Substitutional As is indicated by the large black circle at the center. Hydrogen is located at sites represented by small black circles labeled according to the usual notation. For example, BC stands for the bond centered position. Zn and Se (Te) are represented as large open and small gray circles, respectively.
V.J.B. Torres et al. / Computational Materials Science 33 (2005) 145–147 Table 2 Local vibrational stretching modes (cm1) of the bond centered Zn–H–As and Zn–D–As defects in GaAs, ZnSe and ZnTe GaAs H–As
ZnSe
147
wag modes at 396 cm1 and at 465 cm1 for ZnSe:AsH and ZnTe:AsH complexes.
ZnTe
4. Conclusions
x20 Expt. Calc. x10 Expt. Calc. xQH
4216.7 4162 2146.9 2189 2207
2165.6 2218 2179
2014 2006 2035
D–As
x10 Expt. Calc. xQH
1549.1 1552 1567
1557 1572 1547
NA 1425 1446
Isotopic shifts
Dx10 Expt. Calc. DxQH
597.9 637 639
608.6 646 632
NA 581 589
x20, x10 and xQH stand for the overtone, the fundamental transition and quasi-harmonic frequencies, respectively. NA stands for not available.
Table 2. These differ by only 3% when compared to the experimental fundamental transition frequencies for GaAs:ZnH [2], and less than 1% for ZnSe:AsH [3] and ZnSe:AsH [4], respectively. The isotopic shifts obtained after replacing hydrogen by deuterium are also reproduced within less than 4% with respect to the experimental data. Despite the good agreement, the relative ordering of the stretch modes in GaAs:ZnH and ZnSe:AsH is not reproduced. This is only achieved when we consider anharmonic effects. Accordingly, the fundamental transition frequencies, x10, are at most 2% away from the experimental values, and the same kind of agreement is obtained for the deuterium– arsenic stretch mode and respective isotopic shifts. From Table 1 we note that the Zn–H distance follows the same trend of the stretching vibrational modes, i.e., the shortest Zn–H distance and higher frequency occur in ZnSe. We believe that the Zn– H coupling is better accounted for when anharmonicity is considered, where the H atom is displaced along longer distances. After inspection of the stretching-mode potential energies, we find these very similar for both complexes in ZnSe and GaAs near the equilibrium and compressed As–H regions. However, for As–H distances greater than ˚ the potential in ZnSe grows faster. In 0.05 A addition to the stretch frequencies, we also predict
We have explored several atomic configurations of H nearby the Zn acceptor in GaAs, and the As acceptor in ZnSe and ZnTe, by using an ab initio density-functional method. The lowest energy configurations are those where H sits near the Zn–As bond center sites, with H bonded to As. The local vibrational modes agree well with experimental data. The larger As–H stretching frequency in ZnSe is attributed to the shorter Zn–H distance in this center. This effect is essentially anharmonic, since this feature is not reproduced by the quasiharmonic calculation.
Acknowledgements This work was supported by the FCT and FEDER in Portugal (Grants ref. SFRH/BPD/ 5735/2001 and POCTI/CTM/40979/2001).
References [1] S.J. Pearton, J.W. Corbett, M. Stavola, Hydrogen in Crystalline Semiconductors, Springer-Verlag, Berlin, 1992. [2] R. Darwich, B. Pajot, B. Rose, D. Robein, B. Theys, R. Rahbi, C. Porte, F. Gendron, Phys. Rev. B 48 (1993) 17776. [3] M.D. McCluskey, E.E. Haller, F.X. Zach, E.D. BorretCourchesne, Appl. Phys. Lett. 68 (1996) 3476. [4] L. Svob, Y. Marfaing, B. Clerjaud, D. Cote, D. Balllutaud, B. Yheys, R. Druilhe, W. Kuhn, H. Stanzl, W. Gebhardt, Mat. Sci. Forum 143–147 (1994) 447. [5] V.J.B. Torres, J. Coutinho, P.R. Briddon, Physica B 340– 342 (2003) 272. [6] P.R. Briddon, R. Jones, Phys. Status Solidi B 207 (2000) 131. [7] J.P. Perdew, Y. Wang, Phys. Rev. B 43 (1992) 13244. [8] N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993. [9] J. Coutinho, V.J.B. Torres, P.R. Briddon, Phys. Rev. B 67 (2003) 35205. [10] M.D. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188. [11] F.D. Murnaghan, Proc. Natl. Acad. Sci. USA 30 (1944) 244. [12] T. Pang, An Introduction to Computational Physics, Cambridge University Press, Cambridge, 1997.