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Investigations of the EPR parameters and substitutional sites of Ni3+ ions in CuGaS2 and AgGaS2 ternary semiconductors
Materials Science and Engineering B 130 (2006) 273–276
Investigations of the EPR parameters and substitutional sites of Ni3+ ions in CuGaS2 and AgGaS2 ternary semiconductors Zheng Wen-Chen a,c,d,∗ , Wu Xiao-Xuan a,b,c , Zhou Qing a , He Lv a a
Department of Material Science, Sichuan University, Chengdu 610064, People’s Republic of China Department of Physics, Civil Aviation Flying Institute of China, Guanghan 618307, People’s Republic of China c International Centre for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, People’s Republic of China d Surface Physics Laboratory (National Key Lab), Fudan University, Shanghai 200433, People’s Republic of China b
Received 21 November 2005; received in revised form 23 February 2006; accepted 19 March 2006
Abstract The electronic paramagnetic resonance (EPR) parameters (g factors g// , g⊥ and zero-field splitting D) of Ni3+ ions at both M+ (M = Cu, Ag) and Ga3+ sites in MGaS2 ternary semiconductors are calculated from the high-order perturbation formulas based on the two spin-orbit (SO) coupling parameter model for 3d7 ions in tetragonal symmetry. The calculated results suggest that Ni3+ ions replace the monovalent M+ ions in MGaS2 crystals. This point is contrary to the previous assumption that Ni3+ ions substitute for the isovalent Ga3+ ions to attain the charge neutrality. The reasonableness of the suggestion is discussed. © 2006 Elsevier B.V. All rights reserved. Keywords: Defect formation; Electron paramagnetic resonance; Nickel; Crystal-field theory; Semiconductors
1. Introduction Ternary semiconductors with the chalcopyride structure and formula IB -III-VI2 (e.g., CuGaS2 and AgGaS2 ) are important materials for blue and green LED [1], solar cell [2], second harmonic generators [2,3] and room-temperature ferromagnetic semiconductors [4]. There are two tetragonal (D2d ) cationic sites, IB group ion and III-group ion sites, in this type of semiconductors [5]. When a transition-metal (3dn ) impurity ion enters these crystals, the determination of the substitutional site of impurity is difficult because of the similarity of the first anionic shells in IB -group and III-group cationic sites. However, for technical applications, it is necessary to understand the nature and the substitutional site of impurity incorporated in these semiconductors because the impurity centers have great influence on the electric, magnetic and optical properties of semiconductors. The defect model of a paramagnetic impurity center in crystals was often studied by electronic paramagnetic resonance (EPR) measurement. So many EPR spectra were made for 3dn ions in IB -III-VI2 semiconductors [6–9]. For example, the EPR spectra
∗
Corresponding author. Fax: +86 28 85416050. E-mail address: [email protected] (Z. Wen-Chen).
0921-5107/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2006.03.009
of Ni3+ (3d7 ) ions in MGaS2 (M = Cu, Ag) crystals were measured and their EPR parameters (g factors g// , g⊥ and zero-field splitting D) were given [9]. May be considering that the charge and size [10] of impurity Ni3+ are very close to those of the replaced host ion Ga3+ , Kaufmann et al. [9] assumed that Ni3+ ions occupy the isovalent Ga3+ sites in MGaS2 crystals. In order to check the assumption and also to explain reasonably the EPR parameters of MGaS2 : Ni3+ crystals, in this paper, we calculate the EPR parameters for Ni3+ at both M+ and Ga3+ sites of MGaS2 crystals by using the high-order perturbation formulas based on the two spin-orbit (SO) coupling parameter model for the EPR parameters of 3d7 ions in tetragonal symmetry. From the calculations, the contrary assumption (i.e., Ni3+ ions at M+ sites rather than Ga3+ sites in MGaS2 crystals) is suggested. The results are discussed. 2. Calculation For a 3dn ion in semiconductors, the admixture of d electrons of 3dn ion and the p electrons of ligands via covalence effects should be considered in the studies of EPR parameters. So, the high-order perturbation formulas of EPR parameters based on the two-SO-parameter model (where not only the contribution to EPR parameter from the SO coupling parameter of 3dn ion, but
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Z. Wen-Chen et al. / Materials Science and Engineering B 130 (2006) 273–276
also that of ligands via covalence effects are included [11,12]) are preferable to those based on the one-SO-parameter model (in which only the contribution from the SO coupling parameter of 3dn ion in the conventional crystal-field theory is considered). Ni3+ ion at M+ or Ga3+ site forms the tetragonal (NiS4 )5− cluster. For 3d7 ion in tetragonal tetrahedra, from the one-electron basis functions based on the LCAO molecular orbital (MO) and the Macfarlane’s perturbation-loop methods [13,14], the high-order perturbation formulas of EPR parameters based on the two-SOparameter model are derived as [15] 1 Dt 35B4 ζζ Dt 1 2 D = 35ζ − − 2 , 2 9 E1 E3 E2 E32 g// = gs + +
8k ζ 2ζ (2k ζ − kζ + 2gs ζ ) − 3E1 9E12
4ζ 2 (k − 2gs ) 2ζ 2 (k + gs ) − 9E32 3E22
140k ζ Dt 1 1 1 − + 4k ζ ζ − + , 9E1 E3 3E1 E2 3E2 E3 9E12
210k ζ Dt , 9E12
g⊥ = g// + with
(1)
(λπ )2 0 ζ = (Nt ) + 2λπ λσ − ζp , 2 λ π λσ (λπ )2 0 0 ζ = Nt · N e ζ d + √ + ζp , 2 2 2 √ (λ ) π k = (Nt )2 1− + 2λπ λσ + 2λσ Sdp (σ) + 2λπ Sdp (π) , 2 (λπ )2 λ π λσ k = Nt · Ne 1 − + √ + 4λπ Sdp (π) + λσ Sdp (σ) , 2 2 2
ζd0
√
B4 = Nt3 Ne B0
(2)
in which gs (≈2.0023) is the free-electron value; E1 , E2 and E3 the zero-order energy separations between the ground level
4A
3 e4 )
and the excited states 4 T2 (t2 4 e3 ), 2 T2a (t2 3 e4 ) and respectively. Dt is the tetragonal field parameter. 2b (t2 N␥ (␥ = eg or t2g ) and λα (α = π orσ) are the normalization factor and the orbital mixing coefficient in the one-electron basis functions. ζd0 and ζp0 are, respectively, the SO coupling parameter of the 3d7 ion and that of ligands in free state. Sdp (α) is the group overlap integral. B0 (and C0 ) are the Racah parameters of 3d7 ions in free state. For the studied MGaS2 : Ni3+ crystals, B0 (Ni3+ ) ≈ 1195 cm−1 , C0 (Ni3+ ) ≈ 4808 cm−1 , ζd0 (Ni3+ ) ≈ 749 cm−1 [16], ζp0 (S2− ) ≈ 365 cm−1 [17]. The group overlap integrals can be calculated from the Slater-type SCF functions [18,19] and the metal–ligand distance R. For Ni3+ at both M+ and Ga3+ sites of MGaS2 crystals, the distances R [5,20,21] and the calculated Sdp (π) and Sdp (σ) are shown in Table 1. The parameters Nt, Ne and the effective cubic field parameter ∆eff (which is close to the cubic field parameter 10Dq when the difference between Nt and Ne is small) can be obtained from the optical spectra of the studied system by the use of a modified Nt , Ne and ∆eff scheme [11,12]. No optical spectral data of MGaS2 : Ni3+ were reported, we estimate reasonably the parameters Nt , Ne and ∆eff of Ni3+ in MGaS2 from the optical spectra of the isoelectronic 3d7 ion Co2+ in the same crystals. The estimations are based on the following points: (i) the parameters Nt , and Ne are also called the covalence reduction factors which decrease with the increasing covalence of the studied 3dn clusters. (ii) For the isoelectronic 3dn series in the same crystal, the parameter Dq and the covalence of 3dn clusters increase (and hence the parameters Nt and Ne decrease) with the increasing atomic number [22]. Thus, from the optical spectra of MGaS2 : Co2+ [23,24], we estimate for CuGaS2 : Ni3+ , 2T
2 (t2
4 e3 ),
Nt ≈ 0.8320,
Ne ≈ 0.8340,
∆eff ≈ 630 cm−1 ,
(3)
∆eff ≈ 385 cm−1 .
(4)
and for AgGaS2 : Ni3+ , Nt ≈ 0.8550,
Ne ≈ 0.8580,
These estimated parameters can be supported by the following fact. For the iron-group ion Mn+ in a crystal, the cubic crystal-field parameter Dq (≈∆eff /10) increases with the increasing valence state n [21,25]. From the optical spectral studies, Kaufmann [26] obtained Dq ≈ 325 and 263 cm−1 for Ni+ ion in CuGaS2 and AgGaS2 crystals, respectively. These values are smaller than the corresponding values for Ni3+ in CuGaS2 and
Table 1 The structural data, the group overlap integrals, the orbital mixing coefficients, the spin-orbit coupling parameters and the orbital reduction factors for Ni3+ at M+ and Ga3+ sites in MGaS2 (M = Cu, Ag) crystals ˚ R (A)
θ (◦ )
Sdp (σ)
Sdp (π)
λσ
λπ
ζ (cm−1 )
ζ (cm−1 )
k
k
CuGaS2 Cu+ Ga3+
2.34a 2.26a
56.01a 54.66a
−0.0275 −0.0321
0.0074 0.0092
0.5747 0.5796
−0.3894 −0.3913
419.3 418.1
498.8 498. 5
0.3947 0.3865
0.6177 0.6128
AgGaS2 Ag+ Ga3+
2.605b 2.235b
60.40b 54.84b
−0.0159 −0.0336
0.0036 0.0098
0.5145 0.5332
−0.3493 −0.3556
463.5 459.1
531.8 530.5
0.4869 0.4576
0.6754 0.6583
a The angle θ depends strongly upon the anion position parameter χ. For CuGaS , the errors of the measured values of χ are relatively great [5], we use the mean 2 observed value χ ≈ 0.263 (1), which is consistent with the theoretical value [5] and the value obtained by use of Ni+ ion probe [21]. b Ref. [20].
Z. Wen-Chen et al. / Materials Science and Engineering B 130 (2006) 273–276
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Table 2 The EPR parameters g// , g (=g// − g⊥ ) and D for Ni3+ at M+ and Ga3+ sites of MGaS2 (M = Cu, Ag) crystals CuGaS2 : Ni3+
AgGaS2 : Ni3+
Calculation Cu+ g// g D (cm−1 )
Experiment [9] Ga3+
site
2.1154 −0.0129 1.486
Ag+
site
2.1234 0.0008 −0.084
2.1158(15) −0.0152(35) 1.276(1)
AgGaS2 crystals given above. So, the above estimated values can be regarded as reasonable. The orbital mixing coefficients λα are calculated from N␥ by using the normalization relations [11,15] −1/2
Ne = [1 + 3(λσ )2 + 6λπ Sdp (π)]
Calculation
, −1/2
Nt = [1 + (λσ )2 + (λπ )2 + 2λσ Sdp (σ) + 2λπ Sdp (π)]
(5)
The results for both sites in MGaS2 : Ni3+ are collected in Table 1. Based on these, the parameters in Eq. (2) for Ni3+ at both sites of MGaS2 crystals are calculated and the results are also collected in Table 1. The tetragonal field parameter Dt can be calculated from the superposition model [27], i.e., 4 ¯ A4 (R)[7 sin θ 4 + (35 cos4 θ − 30 cos2 θ + 3)] (6) 21 ¯ 4 (R) is the intrinsic parameter. For 3dn MX4 clusters, where A ¯ 4 (R) = (27/16)Dq [12,27]. θ is the angle between we have A the direction of R and C4 axis. The angles θ for both cationic sites of MGaS2 crystals are obtained from the crystallographic data [5,20,21] and are shown in Table 1. Substituting all these parameters into the above formulas, the EPR parameters g// , g and D for Ni3+ at both M+ and Ga3+ sites of MGaS2 crystals are calculated. The results are compared with the experimental values in Table 2. Dt =
3. Discussion From the above studies, one can find that the calculated EPR parameters g// , g and D for Ni3+ at M+ sites of MGaS2 crystals appear to be similar to the corresponding experimental values, whereas the calculated EPR parameters (in particular, the g and D) for Ni3+ at Ga3+ sites do not (see Table 2). So, contrary to the assumption in Ref. [9], we suggest that Ni3+ ions in MGaS2 crystals substitute for M+ ions rather than Ga3+ ions. Considering that for Ni3+ in MGaS2 crystals, the impurity Ni3+ and the host ion Ga3+ (rather than M+ ) have the same charge (which can attain the charge neutrality of the system) and the close ionic radius [10], the above suggestion seems to be astonishing. The following points support our suggestion: (i) As is known, the g-anisotropy g and zero-field splitting D for a 3d7 ion in tetragonally tetrahedral crystals depend strongly upon the tetragonal distortion θ − θ 0 , (where θ 0 ≈ 54.74◦ , the angle in cubic tetrahedron, in fact,
site
2.146 −0.124 15.2
Experiment [9] Ga3+
site
2.220 −0.002 0.26
2.142(2) −0.130(6) 15(2)
if θ − θ 0 ≈ 0 or θ = θ 0 , we have Dt = 0 and hence g = D = 0 as in the case of cubic ZnS: Ni3+ [28]). The observed EPR parameters g and D for Ni3+ in AgGaS2 are much greater than those for Ni3+ in CuGaS2 , pointing to the tetragonal distortion θ − θ 0 for Ni3+ center in AgGaS2 being much larger than that in CuGaS2 . However, the distortions θ − θ 0 at the Ga3+ sites in AgGaS2 and CuGaS2 crystals are close to each other, whereas the distortion θ − θ 0 at Ag+ site of AgGaS2 is much larger than that at Cu+ site of CuGaS2 (see Table 1). So, our suggestion is reasonable because it can explain the large difference of g and D between AgGaS2 : Ni3+ and CuGaS2 : Ni3+ crystals. (ii) Similar cases that the trivalent 3dn ions in IB -III-VI2 semiconductors MBX2 replace the IB group ion M+ rather than the isovalent III-group ion B3+ were reported. For example, from the hyperfine structures arising from hyperfine interaction with the nuclear magnetic moment of 51 V, Aksenov and Sato [29] suggested that V3+ in CuAlS2 substitutes for Cu+ ion rather than the isovalent Al3+ ion. The suggestion is confirmed by the theoretical calculations of the EPR parameters for V3+ in both cationic sites [30]. In addition, by studying the fine structures of photoluminescence spectra in Fe-doped single crystal of CuAl1−x Gax S2 , Sato et al. [31] concluded that Fe3+ ion replaces the Cu+ ion, contrary to the commonly accepted concept that the Fe3+ may replace Ga3+ or Al3+ to attain the charge neutrality. In fact, as pointed out in Refs. [4,32], the substitutional sites of impurity ions in some IB -III-VI2 semiconductors depend strongly upon the technology of the material preparation (including physical and chemical treatments), for instance, in the Cr-doped CuAlS2 crystal, Cr2+ replaces Al3+ ion in Al-deficient crystal and Cr2+ replaces Cu+ ion in Cudeficient crystal [32]; and in the Mn-doped CuBX2 (B = Al, Ga, In; X = S, Se, Te) semiconductors, the first-principles calculations suggest that Mn (Mn0 or Mn+ ) prefers the B3+ site under Cu-rich and Cu+ site under B-rich condition [4]. So, it is possible that the trivalent 3dn ions in IB -III-VI2 semiconductors (including Ni3+ in MGaS2 ) substitute for the IB -group cations. Acknowledgements This project was supported by the National Natural Science Foundation of China (Grant No.10274054) and the CAAC Scientific Research Base of Civil Aviation Flight Technology and Safety.
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References [1] I. Aksenov, K. Sato, Appl. Phys. Lett. 61 (1992) 1063. [2] J.L. Shay, J.H. Wernick, Ternary Chalcopyrite Semiconductor: Growth, Electronic Properties and Applications, Pergamon Press, New York, 1975. [3] R.L. Byer, M.M. Choy, R.L. Herbst, D.S. Chemla, R.S. Feigelson, Appl. Phys. Lett. 24 (1974) 65. [4] Y.J. Zhao, A. Zunger, Phys. Rev. B69 (2004) 075208. [5] J.E. Jaffe, A. Zunger, Phys. Rev. B29 (1984) 1882. [6] K. Sato, I. Aksenov, N. Nishikawa, Jpn. J. Appl. Phys. 32 (Suppl.) (1993) 841. [7] N. Nishikawa, I. Aksenov, T. Shinzato, T. Sakamoto, K. Sato, Jpn. J. Appl. Phys. 34 (1995) L975. [8] K. Stevens, N.Y. Garces, L. Bai, N.C. Giles, L.E. Halliburton, S.D. Setzier, P.G. Schunemann, T.M. Pollak, R.K. Route, R.S. Feigelson, J. Phys.: Condens. Matter 16 (2004) 2593. [9] U. Kaufmann, A. Rauber, J. Schneider, Solid State Commun. 15 (1974) 1881. [10] R.D. Shannon, Acta Cryst. A 32 (1976) 751. [11] M.L. Du, C. Rudowicz, Phys. Rev. B 46 (1992) 8974. [12] W.C. Zheng, S.Y. Wu, J. Zi, Semicond. Sci. Technol. 17 (2002) 493. [13] R.M. Macharlane, J. Chem. Phys. 47 (1967) 2066. [14] R.M. Macharlane, Phys. Rev. B1 (1970) 989. [15] W.C. Zheng, S.Y. Wu, J. Phys. Chem. Solids 60 (1999) 1725.
[16] P.H.M. Uylings, A.J.J. Raassen, J.F. Wyart, J. Phys. B17 (1984) 4103. [17] S. Fraga, K.M.S. Saxena, J. Karwowski, Handbook of Atomic Data, Elsevier, New York, 1970. [18] E. Clementi, D.L. Raimondi, J. Chem. Phys. 38 (1963) 2686. [19] E. Clementi, D.L. Raimondi, W.P. Reinhardt, J. Chem. Phys. 47 (1967) 1300. [20] H.W. Spiess, V. Hacberin, G. Brandt, A. Runber, J. Schneider, Phys. Status Solidi B 62 (1974) 183. [21] X.X. Wu, W.C. Zheng, S. Tang, J. Zi, Mater. Sci. Eng. B107 (2004) 186. [22] J.A. Lever, Inorganic Electronic Spectroscopy, Elsevier, Amsterdam, 1984. [23] K. Sato, T. Kawakami, T. Teranishi, T. Kambara, K. Gondaira, J. Phys. Soc. Jpn. 41 (1976) 937. [24] Y. Park, H. Kim, I. Hwang, J.E. Kim, H.Y. Park, M.S. Jin, S.K. Oh, W.T. Kim, Phys. Rev. B 53 (1996) 15604. [25] K.H. Karisson, T. Perander, Chem. Scr. 3 (1973) 201. [26] U. Kaufmann, Phys. Rev. B11 (1975) 2478. [27] D.J. Newman, B. Ng, Rep. Prog. Phys. 52 (1989) 699. [28] W.C. Holton, J. Schneider, T.L. Estle, Phys. Rev. 133 (1964) A1638. [29] I. Aksenov, K. Sato, Jpn. J. Appl. Phys. 31 (1992) L527. [30] W.C. Zheng, S.Y. Wu, J. Phys. Chem. Solids 60 (1999) 599. [31] K. Sato, K. Tanaka, K. Ishii, S. Matsuda, J. Cryst. Growth 99 (1990) 772. [32] I. Aksenov, K. Sato, Jpn. J. Appl. Phys. 31 (1992) 2352.
Investigations of the EPR parameters and substitutional sites of Ni3+ ions in CuGaS2 and AgGaS2 ternary semiconductors Zheng Wen-Chen a,c,d,∗ , Wu Xiao-Xuan a,b,c , Zhou Qing a , He Lv a a
Department of Material Science, Sichuan University, Chengdu 610064, People’s Republic of China Department of Physics, Civil Aviation Flying Institute of China, Guanghan 618307, People’s Republic of China c International Centre for Materials Physics, Chinese Academy of Sciences, Shenyang 110016, People’s Republic of China d Surface Physics Laboratory (National Key Lab), Fudan University, Shanghai 200433, People’s Republic of China b
Received 21 November 2005; received in revised form 23 February 2006; accepted 19 March 2006
Abstract The electronic paramagnetic resonance (EPR) parameters (g factors g// , g⊥ and zero-field splitting D) of Ni3+ ions at both M+ (M = Cu, Ag) and Ga3+ sites in MGaS2 ternary semiconductors are calculated from the high-order perturbation formulas based on the two spin-orbit (SO) coupling parameter model for 3d7 ions in tetragonal symmetry. The calculated results suggest that Ni3+ ions replace the monovalent M+ ions in MGaS2 crystals. This point is contrary to the previous assumption that Ni3+ ions substitute for the isovalent Ga3+ ions to attain the charge neutrality. The reasonableness of the suggestion is discussed. © 2006 Elsevier B.V. All rights reserved. Keywords: Defect formation; Electron paramagnetic resonance; Nickel; Crystal-field theory; Semiconductors
1. Introduction Ternary semiconductors with the chalcopyride structure and formula IB -III-VI2 (e.g., CuGaS2 and AgGaS2 ) are important materials for blue and green LED [1], solar cell [2], second harmonic generators [2,3] and room-temperature ferromagnetic semiconductors [4]. There are two tetragonal (D2d ) cationic sites, IB group ion and III-group ion sites, in this type of semiconductors [5]. When a transition-metal (3dn ) impurity ion enters these crystals, the determination of the substitutional site of impurity is difficult because of the similarity of the first anionic shells in IB -group and III-group cationic sites. However, for technical applications, it is necessary to understand the nature and the substitutional site of impurity incorporated in these semiconductors because the impurity centers have great influence on the electric, magnetic and optical properties of semiconductors. The defect model of a paramagnetic impurity center in crystals was often studied by electronic paramagnetic resonance (EPR) measurement. So many EPR spectra were made for 3dn ions in IB -III-VI2 semiconductors [6–9]. For example, the EPR spectra
∗
Corresponding author. Fax: +86 28 85416050. E-mail address: [email protected] (Z. Wen-Chen).
0921-5107/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2006.03.009
of Ni3+ (3d7 ) ions in MGaS2 (M = Cu, Ag) crystals were measured and their EPR parameters (g factors g// , g⊥ and zero-field splitting D) were given [9]. May be considering that the charge and size [10] of impurity Ni3+ are very close to those of the replaced host ion Ga3+ , Kaufmann et al. [9] assumed that Ni3+ ions occupy the isovalent Ga3+ sites in MGaS2 crystals. In order to check the assumption and also to explain reasonably the EPR parameters of MGaS2 : Ni3+ crystals, in this paper, we calculate the EPR parameters for Ni3+ at both M+ and Ga3+ sites of MGaS2 crystals by using the high-order perturbation formulas based on the two spin-orbit (SO) coupling parameter model for the EPR parameters of 3d7 ions in tetragonal symmetry. From the calculations, the contrary assumption (i.e., Ni3+ ions at M+ sites rather than Ga3+ sites in MGaS2 crystals) is suggested. The results are discussed. 2. Calculation For a 3dn ion in semiconductors, the admixture of d electrons of 3dn ion and the p electrons of ligands via covalence effects should be considered in the studies of EPR parameters. So, the high-order perturbation formulas of EPR parameters based on the two-SO-parameter model (where not only the contribution to EPR parameter from the SO coupling parameter of 3dn ion, but
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Z. Wen-Chen et al. / Materials Science and Engineering B 130 (2006) 273–276
also that of ligands via covalence effects are included [11,12]) are preferable to those based on the one-SO-parameter model (in which only the contribution from the SO coupling parameter of 3dn ion in the conventional crystal-field theory is considered). Ni3+ ion at M+ or Ga3+ site forms the tetragonal (NiS4 )5− cluster. For 3d7 ion in tetragonal tetrahedra, from the one-electron basis functions based on the LCAO molecular orbital (MO) and the Macfarlane’s perturbation-loop methods [13,14], the high-order perturbation formulas of EPR parameters based on the two-SOparameter model are derived as [15] 1 Dt 35B4 ζζ Dt 1 2 D = 35ζ − − 2 , 2 9 E1 E3 E2 E32 g// = gs + +
8k ζ 2ζ (2k ζ − kζ + 2gs ζ ) − 3E1 9E12
4ζ 2 (k − 2gs ) 2ζ 2 (k + gs ) − 9E32 3E22
140k ζ Dt 1 1 1 − + 4k ζ ζ − + , 9E1 E3 3E1 E2 3E2 E3 9E12
210k ζ Dt , 9E12
g⊥ = g// + with
(1)
(λπ )2 0 ζ = (Nt ) + 2λπ λσ − ζp , 2 λ π λσ (λπ )2 0 0 ζ = Nt · N e ζ d + √ + ζp , 2 2 2 √ (λ ) π k = (Nt )2 1− + 2λπ λσ + 2λσ Sdp (σ) + 2λπ Sdp (π) , 2 (λπ )2 λ π λσ k = Nt · Ne 1 − + √ + 4λπ Sdp (π) + λσ Sdp (σ) , 2 2 2
ζd0
√
B4 = Nt3 Ne B0
(2)
in which gs (≈2.0023) is the free-electron value; E1 , E2 and E3 the zero-order energy separations between the ground level
4A
3 e4 )
and the excited states 4 T2 (t2 4 e3 ), 2 T2a (t2 3 e4 ) and respectively. Dt is the tetragonal field parameter. 2b (t2 N␥ (␥ = eg or t2g ) and λα (α = π orσ) are the normalization factor and the orbital mixing coefficient in the one-electron basis functions. ζd0 and ζp0 are, respectively, the SO coupling parameter of the 3d7 ion and that of ligands in free state. Sdp (α) is the group overlap integral. B0 (and C0 ) are the Racah parameters of 3d7 ions in free state. For the studied MGaS2 : Ni3+ crystals, B0 (Ni3+ ) ≈ 1195 cm−1 , C0 (Ni3+ ) ≈ 4808 cm−1 , ζd0 (Ni3+ ) ≈ 749 cm−1 [16], ζp0 (S2− ) ≈ 365 cm−1 [17]. The group overlap integrals can be calculated from the Slater-type SCF functions [18,19] and the metal–ligand distance R. For Ni3+ at both M+ and Ga3+ sites of MGaS2 crystals, the distances R [5,20,21] and the calculated Sdp (π) and Sdp (σ) are shown in Table 1. The parameters Nt, Ne and the effective cubic field parameter ∆eff (which is close to the cubic field parameter 10Dq when the difference between Nt and Ne is small) can be obtained from the optical spectra of the studied system by the use of a modified Nt , Ne and ∆eff scheme [11,12]. No optical spectral data of MGaS2 : Ni3+ were reported, we estimate reasonably the parameters Nt , Ne and ∆eff of Ni3+ in MGaS2 from the optical spectra of the isoelectronic 3d7 ion Co2+ in the same crystals. The estimations are based on the following points: (i) the parameters Nt , and Ne are also called the covalence reduction factors which decrease with the increasing covalence of the studied 3dn clusters. (ii) For the isoelectronic 3dn series in the same crystal, the parameter Dq and the covalence of 3dn clusters increase (and hence the parameters Nt and Ne decrease) with the increasing atomic number [22]. Thus, from the optical spectra of MGaS2 : Co2+ [23,24], we estimate for CuGaS2 : Ni3+ , 2T
2 (t2
4 e3 ),
Nt ≈ 0.8320,
Ne ≈ 0.8340,
∆eff ≈ 630 cm−1 ,
(3)
∆eff ≈ 385 cm−1 .
(4)
and for AgGaS2 : Ni3+ , Nt ≈ 0.8550,
Ne ≈ 0.8580,
These estimated parameters can be supported by the following fact. For the iron-group ion Mn+ in a crystal, the cubic crystal-field parameter Dq (≈∆eff /10) increases with the increasing valence state n [21,25]. From the optical spectral studies, Kaufmann [26] obtained Dq ≈ 325 and 263 cm−1 for Ni+ ion in CuGaS2 and AgGaS2 crystals, respectively. These values are smaller than the corresponding values for Ni3+ in CuGaS2 and
Table 1 The structural data, the group overlap integrals, the orbital mixing coefficients, the spin-orbit coupling parameters and the orbital reduction factors for Ni3+ at M+ and Ga3+ sites in MGaS2 (M = Cu, Ag) crystals ˚ R (A)
θ (◦ )
Sdp (σ)
Sdp (π)
λσ
λπ
ζ (cm−1 )
ζ (cm−1 )
k
k
CuGaS2 Cu+ Ga3+
2.34a 2.26a
56.01a 54.66a
−0.0275 −0.0321
0.0074 0.0092
0.5747 0.5796
−0.3894 −0.3913
419.3 418.1
498.8 498. 5
0.3947 0.3865
0.6177 0.6128
AgGaS2 Ag+ Ga3+
2.605b 2.235b
60.40b 54.84b
−0.0159 −0.0336
0.0036 0.0098
0.5145 0.5332
−0.3493 −0.3556
463.5 459.1
531.8 530.5
0.4869 0.4576
0.6754 0.6583
a The angle θ depends strongly upon the anion position parameter χ. For CuGaS , the errors of the measured values of χ are relatively great [5], we use the mean 2 observed value χ ≈ 0.263 (1), which is consistent with the theoretical value [5] and the value obtained by use of Ni+ ion probe [21]. b Ref. [20].
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Table 2 The EPR parameters g// , g (=g// − g⊥ ) and D for Ni3+ at M+ and Ga3+ sites of MGaS2 (M = Cu, Ag) crystals CuGaS2 : Ni3+
AgGaS2 : Ni3+
Calculation Cu+ g// g D (cm−1 )
Experiment [9] Ga3+
site
2.1154 −0.0129 1.486
Ag+
site
2.1234 0.0008 −0.084
2.1158(15) −0.0152(35) 1.276(1)
AgGaS2 crystals given above. So, the above estimated values can be regarded as reasonable. The orbital mixing coefficients λα are calculated from N␥ by using the normalization relations [11,15] −1/2
Ne = [1 + 3(λσ )2 + 6λπ Sdp (π)]
Calculation
, −1/2
Nt = [1 + (λσ )2 + (λπ )2 + 2λσ Sdp (σ) + 2λπ Sdp (π)]
(5)
The results for both sites in MGaS2 : Ni3+ are collected in Table 1. Based on these, the parameters in Eq. (2) for Ni3+ at both sites of MGaS2 crystals are calculated and the results are also collected in Table 1. The tetragonal field parameter Dt can be calculated from the superposition model [27], i.e., 4 ¯ A4 (R)[7 sin θ 4 + (35 cos4 θ − 30 cos2 θ + 3)] (6) 21 ¯ 4 (R) is the intrinsic parameter. For 3dn MX4 clusters, where A ¯ 4 (R) = (27/16)Dq [12,27]. θ is the angle between we have A the direction of R and C4 axis. The angles θ for both cationic sites of MGaS2 crystals are obtained from the crystallographic data [5,20,21] and are shown in Table 1. Substituting all these parameters into the above formulas, the EPR parameters g// , g and D for Ni3+ at both M+ and Ga3+ sites of MGaS2 crystals are calculated. The results are compared with the experimental values in Table 2. Dt =
3. Discussion From the above studies, one can find that the calculated EPR parameters g// , g and D for Ni3+ at M+ sites of MGaS2 crystals appear to be similar to the corresponding experimental values, whereas the calculated EPR parameters (in particular, the g and D) for Ni3+ at Ga3+ sites do not (see Table 2). So, contrary to the assumption in Ref. [9], we suggest that Ni3+ ions in MGaS2 crystals substitute for M+ ions rather than Ga3+ ions. Considering that for Ni3+ in MGaS2 crystals, the impurity Ni3+ and the host ion Ga3+ (rather than M+ ) have the same charge (which can attain the charge neutrality of the system) and the close ionic radius [10], the above suggestion seems to be astonishing. The following points support our suggestion: (i) As is known, the g-anisotropy g and zero-field splitting D for a 3d7 ion in tetragonally tetrahedral crystals depend strongly upon the tetragonal distortion θ − θ 0 , (where θ 0 ≈ 54.74◦ , the angle in cubic tetrahedron, in fact,
site
2.146 −0.124 15.2
Experiment [9] Ga3+
site
2.220 −0.002 0.26
2.142(2) −0.130(6) 15(2)
if θ − θ 0 ≈ 0 or θ = θ 0 , we have Dt = 0 and hence g = D = 0 as in the case of cubic ZnS: Ni3+ [28]). The observed EPR parameters g and D for Ni3+ in AgGaS2 are much greater than those for Ni3+ in CuGaS2 , pointing to the tetragonal distortion θ − θ 0 for Ni3+ center in AgGaS2 being much larger than that in CuGaS2 . However, the distortions θ − θ 0 at the Ga3+ sites in AgGaS2 and CuGaS2 crystals are close to each other, whereas the distortion θ − θ 0 at Ag+ site of AgGaS2 is much larger than that at Cu+ site of CuGaS2 (see Table 1). So, our suggestion is reasonable because it can explain the large difference of g and D between AgGaS2 : Ni3+ and CuGaS2 : Ni3+ crystals. (ii) Similar cases that the trivalent 3dn ions in IB -III-VI2 semiconductors MBX2 replace the IB group ion M+ rather than the isovalent III-group ion B3+ were reported. For example, from the hyperfine structures arising from hyperfine interaction with the nuclear magnetic moment of 51 V, Aksenov and Sato [29] suggested that V3+ in CuAlS2 substitutes for Cu+ ion rather than the isovalent Al3+ ion. The suggestion is confirmed by the theoretical calculations of the EPR parameters for V3+ in both cationic sites [30]. In addition, by studying the fine structures of photoluminescence spectra in Fe-doped single crystal of CuAl1−x Gax S2 , Sato et al. [31] concluded that Fe3+ ion replaces the Cu+ ion, contrary to the commonly accepted concept that the Fe3+ may replace Ga3+ or Al3+ to attain the charge neutrality. In fact, as pointed out in Refs. [4,32], the substitutional sites of impurity ions in some IB -III-VI2 semiconductors depend strongly upon the technology of the material preparation (including physical and chemical treatments), for instance, in the Cr-doped CuAlS2 crystal, Cr2+ replaces Al3+ ion in Al-deficient crystal and Cr2+ replaces Cu+ ion in Cudeficient crystal [32]; and in the Mn-doped CuBX2 (B = Al, Ga, In; X = S, Se, Te) semiconductors, the first-principles calculations suggest that Mn (Mn0 or Mn+ ) prefers the B3+ site under Cu-rich and Cu+ site under B-rich condition [4]. So, it is possible that the trivalent 3dn ions in IB -III-VI2 semiconductors (including Ni3+ in MGaS2 ) substitute for the IB -group cations. Acknowledgements This project was supported by the National Natural Science Foundation of China (Grant No.10274054) and the CAAC Scientific Research Base of Civil Aviation Flight Technology and Safety.
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