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First-principles study on electronic and optical properties of Cu-doped LiF with Li vacancy
Physica B 407 (2012) 2458–2461
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
First-principles study on electronic and optical properties of Cu-doped LiF with Li vacancy Y.K. Sun a,b, J.H. Zhang a, J.W. Ding a,b,n, X.H. Yan a a b
College of Electronic Science Engineering, Nanjing University of Post & Telecommunication, 211106 Nanjing, China Department of Physics & Institute for Nanophysics and Rare-earth Luminescence, Xiangtan University, Xiangtan, 411105 Hunan, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 January 2012 Received in revised form 15 March 2012 Accepted 16 March 2012 Available online 23 March 2012
Taken into account the presences of Li vacancy (VLi), we calculate the formation energy, electronic structure and optical properties of Cu doped LiF (LiF:Cu) by using the density functional theory. The presence of VLi leads to a decrease of the formation energies of Cu, in favor of Cu doping into LiF. Due to Cu doping, an impurity band of Cu-3d states is formed at the Fermi level, which is then split by the introduction of VLi. A wide absorption band and some new absorption peaks are obtained in LiF:Cu with an adjacent VLi to Cu. There appears an absorption peak at 9.3 eV, which is consistent with the experiment observation (133 nm). The results are useful for understanding of the optical properties of the doped systems. & 2012 Elsevier B.V. All rights reserved.
Keywords: LiF:Cu Li vacancy Electronic structures Optical properties
1. Introduction Lithium fluoride (LiF) has been widely used in various technological applications such as in x-ray monochromators, as a filter for ultraviolet radiation [1], and in thermoluminescent (TL) dosimetry. Owing to its highest sensitivity [2], especially, LiF codoped with Mg, Cu and P stimulated extensive interest in the radiation dosimetry in the past decades [3,4]. However, its performance of ultrasensitivity is easily lost in the heat treatment of above 240 1C [2]. To keep high sensitivity and thermal stability, a variety of dopants in LiF have been successfully explored, such as LiF:Mg,Cu,Na, LiF:Mg,Cu,Na,Si and LiF:Mg,Cu,Si [5]. The impurities of Cu and Mg were inferred to be more favorable to improve the TL properties of the co-doped systems. It has been well identified [6–8] that the high TL sensitivity is closely associated with the Mg-related defects. As for Cu impurity, its ion size ˚ is larger than that of Li þ (0.68 A). ˚ It was usually thought (0.96 A) that LiF cannot be doped with Cu þ [9–11], while such a substitution needs no charge compensation. In fact, Cu doped LiF crystal (LiF:Cu) had been prepared by Scacco et al. [12]. Especially, there are some conflicting arguments on the role of Cu impurity on TL sensitivity. For example, some authors proposed that Cu acts as a luminescent center [13,14], while others take the opposite view [3,9]. n Corresponding author at: Department of Physics & Institute for Nanophysics and Rare-earth Luminescence, Xiangtan University, Xiangtan, Hunan 411105, China. Tel.: þ 86 731 58292329; fax: þ86 731 58292468. E-mail address: [email protected] (J.W. Ding).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.03.046
Under g irradiation, on the other hand, there exists a common defect of Li vacancy (VLi), and thus a complex defect of Cu–VLi dipole may be introduced in the doped system. The complex defects may play an important modulation role on TL sensitivity, different from isolated substitution defects. Such an effect had been experimentally observed [15]. Recently, Scacco and Furette studied the g irradiated LiF:Cu crystals and deduced that Cu2 þ –VLi dipole is the emission center [12]. Davidson et al. demonstrated that impurity-VLi dipole can enhance the emission of alkali halides [16]. How about the influence of the Cu–VLi dipole on the structural and optical properties of LiF:Cu? This is still an open subject. To explore luminescence mechanism, the absorption of LiF dosimetry materials has been investigated [17–19]. Experimentally, the effect of VLi on the luminescent properties is hardly concerned [19]. Theoretically, the effect of VLi can be considered in determining the crystal structure and electrical properties of the doped system by first-principle calculations. Also, the optical properties can be further obtained from their electronic structures of the doped systems, which will be useful for the understanding of experimental findings. In this paper, we present a detailed investigation on LiF:Cu in the presence of VLi by using the first-principles method. The defect structure has been determined from the formation energy. It is shown that the presence of VLi leads to a decrease of the formation energies of Cu, in favor of Cu doping into LiF. The electronic structure and optical properties of the doped systems were systematically studied, which can be largely modulated by VLi. A new absorption peak appears at 9.3 eV in LiF:Cu with an
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adjacent VLi to Cu, which is in good agreement with experimental observation.
2. Computational details The calculations were performed with the CASTEP code, based on the density functional theory using a plane-wave pseudopotential method. The valence electronic configurations for the lithium, fluorine and copper atoms are 1s22s1, 2s22p5 and 3d104s1, respectively. The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) scheme was used for treating the exchange and correlation potential [20]. The Brillouin zone sampling mesh parameters for the k point set were 3 3 3. The plane-wave energy cutoff was set to be 330 eV. Both pure and Cudoped LiF calculations were performed with 2 2 2 supercell. For the Cu-doped case, one Li atom at center of the supercell was replaced by one Cu atom. In the presence of VLi, it is located at the position from the nearest to the fifth nearest neighbor to Cu. The lattice constants of pure cubic LiF before optimization are chosen ˚ The atomic geometries were fully optimized as a ¼b¼c ¼4.028 A. by using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) force on atoms and stresses on the supercell [21]. Convergence thresholds for geometry optimization were 1.0 10 5 eV atom 1 for total energy variation, 0.03 eV A˚ 1 for maximum force on each atom, 0.05 GPa for the unit cell stress and 0.001 A˚ for the maximum atomic displacement. The optical properties of LiF, LiF:Cu and LiF:CuþVLi were then calculated from the complex dielectric function of e(o)¼ e1(o)þ ie2(o). The imaginary part e2(o) of the dielectric function is calculated in CASTEP numerically by evaluating the matrix elements connecting the occupied and unoccupied electronic states. The real part e1(o) of e(o) is calculated then using the Kramers– Kroning transform [22]. In order to obtain comparable results with the experiment of optical properties, in calculations we used unpolarized models and scissors operators.
3. Results and discussion By optimizing the pure cubic LiF supercell, we got the lattice parameters as follows: a¼b ¼c¼4.13 A˚ with a space group of Pm3m, which are in good agreement with experimental results of a ¼b¼c¼ 3.99 A˚ [23], a ¼ b ¼ g ¼ 901. The result shows that the calculation methods are reasonable.
The formation energy of impurity indicates the relative degree of difficulty for Cu doping into LiF [24]. For lower formation energy, the doping substitution would be energetically more favorable. In the absence of VLi, the formation energy (Ef) of impurity Cu in LiF:Cu is defined as [9,10] ð1Þ
where ELiF and ELiF:Cu are total energies of pure LiF and LiF:Cu with the same size supercell. Ecu and ELi are the energies of Cu and Li atoms in the elementary substance. In the presence of VLi, the formation energy Ef of impurity Cu in LiF with a VLi (LiF:VLi) can be calculated by Ef ¼ ELiF:Cu þ V Li ELiF:V Li ECu þ ELi
Table 1 Formation energies of LiF:Cuþ VLi with different Cu–VLi distances. Sample
LiF:Cu
S1
S2
S3
S4
S5
Ef (eV)
3.01
1.1
0.72
0.34
0.44
0.12
The calculated formation energies have been listed in Table 1. In the absence of VLi, we obtain a positive formation energy, Ef ¼ 3.01 eV, showing that Cu doping into LiF is very difficult [9,10]. In the presence of VLi, we obtain Ef ¼ 1.1, 0.72, 0.34, 0.44, and 0.12 eV for the five various configurations of S1, S2, , S5. The negative formation energy of Cu shows that the presence of VLi is in favor of Cu doping into LiF, while it is difficult for doping an isolate Cu into LiF [9]. The result agrees well with the experimental observation [25]. Also from Table 1, it is found that the formation energy of Cu in LiF:VLi decreases with decreasing the Cu–VLi distance. This means that the impurity Cu is in favor of staying closer to VLi in LiF:Cuþ VLi. In the latter calculations, therefore, we will consider only the S1 configuration with the shortest Cu–VLi distance. 3.2. Electronic structures
3.1. Formation energies
Ef ¼ ELiF:Cu ELiF ECu þ ELi
Fig. 1. Possible positions of Cu substitution in LiF:VLi with different Cu–VLi distance, marked by S1, S2,y, S5.
ð2Þ
ELiF:V Li and ELiF:Cu þ V Li are the total energies of LiF:VLi and Cu doped LiF:VLi (LiF:CuþVLi) supercell. For LiF:CuþVLi system, various configurations are considered, having different VLi–Cu distances for Cu from VLi, which are marked in Fig. 1 by S1, S2,y, S5.
We calculated the electronic properties of pure LiF, LiF:Cu and LiF:CuþVLi. For the pure LiF, the top of the valence band (VB) is mainly composed of F-2p states with band width of 3.1 eV, while the bottom of the conduction band (CB) is dominated by Li-1 s states. A direct band gap of 8.46 eV exists at along G–X of the Brillouin zone, consistent with other theoretical calculation [26]. The band gap is still underestimated, less than the experimental value of 13.6–14.2 eV [27], which is due to the choice of exchangecorrelation energy. In order to overcome such a discrepancy, the so-called scissor operator [25] is introduced to eliminate the difference between the theoretical and experimental gap values by means of a simple rigid shift of the unoccupied CB with respect to VB. The value of the scissor operator is about 5.0 eV, which was applied in the previous study of LiF [26]. Fig. 2(a) shows the TDOS and PDOS of LiF:Cu. It can be seen that the top of VB and the bottom of CB for LiF:Cu are still contributed mainly by F-2p states and Li-1 s states. However, the TDOS of LiF:Cu moves to the deep energy, compared with that of perfect LiF. The Li-1 s states dominate the energy range from
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100
total
total
50 0 Cu-s Cu-p Cu-3d
DOS (states/eV)
10 5
Cu-s Cu-p Cu-3d
0 100
F-2p
F-2p
50 0 10
Li- s
Li- s
5 0 -10
-5
0
5
10 -5
5
0
10
15
Energy (eV) Fig. 2. PDOS of LiF:Cu (a) in the absence and (b) in the presence of VLi. The vertical dashed lines indicate the Fermi level.
3.3. Optical properties Based on the obtained electronic band structures, the optical absorption spectra of LiF, LiF:Cu and LiF:CuþVLi were calculated in Fig. 3 under 5.0 eV scissors operation. For pure LiF, the absorption only exists at above 13 eV, consistent with the experimental measurements [12]. For LiF:Cu, there is no absorption in visible region of below 8 eV, while there exists only absorption in vacuum ultraviolet (UV) region above 8 eV. Thus, the sample should be transparent crystals. Due to the existence of IB in LiF:Cu, interestingly, a wide absorption band with a few peaks is obtained in the region of 9–12 eV, while there newly
3.0 LiF
Absorption coefficient (105cm-1)
3.5 eV to 9.2 eV, while the F-2p states locate mainly at the energy range from 7.9 eV to 4.5 eV. Due to Cu substitution, the Fermi level is shifted from the top of VB to about the middle of band gap. Especially, an impurity band (IB) of Cu-3d states is formed with a band width of 1.7 eV, which is across the Fermi energy and partially occupied. As a result, an electron in LiF:Cu can transit from VB to IB and then to unoccupied CB states with lower energy. Also, the band gap is narrowed due to the introduction of impurity states, which would result in the shift of absorption edge to the low-energy region. Some new optical properties can be expected in such doped systems. To explore the effect of VLi on the electronic structures of LiF:Cu, Fig. 2(b) shows the TDOS and PDOS of LiF:CuþVLi. It is seen that the top of VB of LiF:CuþVLi is mainly contributed by F-2p states and the bottom of CB mainly by Li-1s states, of which the shapes are hardly influenced by VLi. The F-2p states are scattered in the energy range from 1 eV to 5 eV, while the Li-1s states locate mainly in the energy range from 5 eV to 12.5 eV. Due to the Cu–VLi interactions, interestingly, the energy range of Cu-3d states is broader than that of LiF:Cu. And the impurity bands of Cu-3d states are split into two sub-bands, different from that of LiF:Cu. One sub-band lies just across the Fermi energy with a band width of 1 eV, which is partially occupied. The other locates at below the Fermi energy from 0.5 to 5 eV. Compared with LiF:Cu, the energy gap between VB and the Fermi energy is about 1.5 eV, while Cu-3d states just lies within the energy gap. The transition of an electron from VB to unoccupied states needs even lower energy in LiF:CuþVLi than that in LiF:Cu. This means that the optical properties of LiF:Cu can be largely modulated by the presence of VLi.
LiF:Cu
2.5
LiF:Cu+VLi
2.0 1.5 1.0 0.5 0.0
6
8
10
12
14
16
18
Energy (eV) Fig. 3. Optical absorption spectra of pure LiF, LiF:Cu, and LiF:Cuþ VLi.
appear some absorption peaks beside the host peak, located at near 11 eV and 12.5 eV. For LiF:Cuþ VLi, especially, the absorption band is obtained in the region of 7–12 eV, which is largely broaden due to the presence of VLi. The two absorption peaks are obtained, shifted to about 10 eV and 13 eV, due to the split IB by Cu–VLi interactions. In addition, there appears an absorption peak at about 9.3 eV within the absorption band, which had been observed in experiment. Therefore, the optical properties of the LiF:Cu sample have been largely modulated by the presence of VLi, which should be taken into account for understanding the luminescence mechanism of the doped system.
4. Conclusion We have performed first-principles calculations on the geometry, electronic structures, and optical properties of LiF, LiF:Cu and LiF:CuþVLi. The formation energy of Cu impurity is decreased in the presence of VLi, and Cu is preferred to stay closer to VLi, forming a Cu–VLi dipole structure. Due to Cu substitution, an impurity band of Cu-3d states are formed in the middle of band gap and partially occupied. Furthermore, the impurity bands of
Y.K. Sun et al. / Physica B 407 (2012) 2458–2461
Cu-3d states are split into two sub-bands by the Cu–VLi interactions. A wide absorption band is obtained in LiF:CuþVLi, there appearing some new absorption peaks, while no absorption in the visible region for both pure LiF and LiF:Cu systems. The absorption peak appearing at 9.3 eV is consistent with the experimental observation (133 nm). The results are useful for understanding of the optical properties of the doped systems.
Acknowledgments This work was supported by Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant no. 200726), Hunan Provincial Innovation Foundation for Postgraduate (Grant no. CX2011B247), and partially by PCSIRT (IRT1080). References [1] K. Teegarden, G. Baldini, Phys. Rev. 155 (1967) 896. [2] B. Yang, L. Wang, P.D. Townsend, H. Gao, Nucl. Instrum. Methods B 266 (2008) 2581. [3] S.W.S. McKeever, J. Phys. D: Appl. Phys. 24 (1991) 988. [4] T.C. Chen, T.G. Stoebe, Radiat. Prot. Dosim. 78 (1998) 101. [5] J.I. Lee, J.L. Kim, A.S. Pradhan, B.H. Kim, Radiat. Meas. 43 (2008) 303.
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[6] P. Bilski, M. Budzanowski, P. Olko, Radiat. Prot. Dosim. 69 (1997) 187. [7] J.I. Lee, J.L. Kim, S.Y. Chang, K.S. Chung, H.S. Choe, Radiat. Prot. Dosim. 115 (2005) 340. [8] P. Bilski, M. Budzanowski, P. Olko, Radiat. Prot. Dosim. 65 (1996) 195. [9] K. Kurt, V.K. Mathur, S.W.S. McKeever, P.D. Townsend, L. Valberg, Radiat. Prot. Dosim. 119 (2006) 134. [10] D.S. Mcclure, S.C. Weaver, J. Phys. Chem. Solids 52 (1991) 81. [11] V.K. Mathur, P.K. Bandyopadhyay, J.H. Barkyoumb, G.G. Cai, Radiat. Meas. 100 (2002) 103. [12] A. Scacco, C. Furetta, C. Sanipoli, Nucl. Instrum. Methods B 116 (1996) 545. [13] R.R. Patil, S.V. Moharil, J. Phys.: Condens. Matter 7 (1995) 9925. [14] S.S. Shinde, B.S. Dhabekar, T.K.G. Rao, J. Phys. D: Appl. Phys. 34 (2001) 2683. [15] W. Shen, K. Tang, H. Zhu, B. Liu, Radiat. Prot. Dosim. 100 (2002) 357. [16] A.T. Davidson, A.G. Kozakiewicz, T.E. Derry, J.D. Comins, M. Suszynska, Phys. Status Solidi C 4 (2007) 1044. [17] S. McKeever, J. Appl. Phys. 68 (1990) 724. [18] G.C. Crittenden, P.D. Townsend, S.E. Townshend, J. Phys. D: Appl. Phys. 7 (1974) 2397. [19] J.L. Landreth, S.W.S. McKeever, J. Phys. D: Appl. Phys. 18 (1985) 1919. [20] J.E. Jaffe, J.A. Snyder, Z. Lin, A.C. Hess, Phys. Rev. B 62 (2000) 1660. [21] B.G. Pfrommer, M. Cˆote´, S.G. Louie, M.L. Cohen, J. Comput. Phys. 131 (1997) 233. [22] M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias, J.D. Joannopoulos, Rev. Mod. Phys. 64 (1992) 1045. [23] R.W.G. Wyckoff, 2nd ed.,Crystal Structures, vol. 1, Wiley, New York, 1986. [24] X.Y. Cui, J.E. Medvedeva, B. Delley, A.J. Freeman, N. Newman, C. Stampfl, Phys. Rev. Lett. 95 (2005) 1. [25] M.R. Pederson, B.M. KIein, Phys. Rev. B 37 (1988) 10319. [26] D.J. Mickish, A.B. Kunz, T.C. Collins, Phys. Rev. B 9 (1974) 4461. [27] Z.H. Levine, D.C. Allan, Phys. Rev. B 43 (1991) 4187.
Contents lists available at SciVerse ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
First-principles study on electronic and optical properties of Cu-doped LiF with Li vacancy Y.K. Sun a,b, J.H. Zhang a, J.W. Ding a,b,n, X.H. Yan a a b
College of Electronic Science Engineering, Nanjing University of Post & Telecommunication, 211106 Nanjing, China Department of Physics & Institute for Nanophysics and Rare-earth Luminescence, Xiangtan University, Xiangtan, 411105 Hunan, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 4 January 2012 Received in revised form 15 March 2012 Accepted 16 March 2012 Available online 23 March 2012
Taken into account the presences of Li vacancy (VLi), we calculate the formation energy, electronic structure and optical properties of Cu doped LiF (LiF:Cu) by using the density functional theory. The presence of VLi leads to a decrease of the formation energies of Cu, in favor of Cu doping into LiF. Due to Cu doping, an impurity band of Cu-3d states is formed at the Fermi level, which is then split by the introduction of VLi. A wide absorption band and some new absorption peaks are obtained in LiF:Cu with an adjacent VLi to Cu. There appears an absorption peak at 9.3 eV, which is consistent with the experiment observation (133 nm). The results are useful for understanding of the optical properties of the doped systems. & 2012 Elsevier B.V. All rights reserved.
Keywords: LiF:Cu Li vacancy Electronic structures Optical properties
1. Introduction Lithium fluoride (LiF) has been widely used in various technological applications such as in x-ray monochromators, as a filter for ultraviolet radiation [1], and in thermoluminescent (TL) dosimetry. Owing to its highest sensitivity [2], especially, LiF codoped with Mg, Cu and P stimulated extensive interest in the radiation dosimetry in the past decades [3,4]. However, its performance of ultrasensitivity is easily lost in the heat treatment of above 240 1C [2]. To keep high sensitivity and thermal stability, a variety of dopants in LiF have been successfully explored, such as LiF:Mg,Cu,Na, LiF:Mg,Cu,Na,Si and LiF:Mg,Cu,Si [5]. The impurities of Cu and Mg were inferred to be more favorable to improve the TL properties of the co-doped systems. It has been well identified [6–8] that the high TL sensitivity is closely associated with the Mg-related defects. As for Cu impurity, its ion size ˚ is larger than that of Li þ (0.68 A). ˚ It was usually thought (0.96 A) that LiF cannot be doped with Cu þ [9–11], while such a substitution needs no charge compensation. In fact, Cu doped LiF crystal (LiF:Cu) had been prepared by Scacco et al. [12]. Especially, there are some conflicting arguments on the role of Cu impurity on TL sensitivity. For example, some authors proposed that Cu acts as a luminescent center [13,14], while others take the opposite view [3,9]. n Corresponding author at: Department of Physics & Institute for Nanophysics and Rare-earth Luminescence, Xiangtan University, Xiangtan, Hunan 411105, China. Tel.: þ 86 731 58292329; fax: þ86 731 58292468. E-mail address: [email protected] (J.W. Ding).
0921-4526/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physb.2012.03.046
Under g irradiation, on the other hand, there exists a common defect of Li vacancy (VLi), and thus a complex defect of Cu–VLi dipole may be introduced in the doped system. The complex defects may play an important modulation role on TL sensitivity, different from isolated substitution defects. Such an effect had been experimentally observed [15]. Recently, Scacco and Furette studied the g irradiated LiF:Cu crystals and deduced that Cu2 þ –VLi dipole is the emission center [12]. Davidson et al. demonstrated that impurity-VLi dipole can enhance the emission of alkali halides [16]. How about the influence of the Cu–VLi dipole on the structural and optical properties of LiF:Cu? This is still an open subject. To explore luminescence mechanism, the absorption of LiF dosimetry materials has been investigated [17–19]. Experimentally, the effect of VLi on the luminescent properties is hardly concerned [19]. Theoretically, the effect of VLi can be considered in determining the crystal structure and electrical properties of the doped system by first-principle calculations. Also, the optical properties can be further obtained from their electronic structures of the doped systems, which will be useful for the understanding of experimental findings. In this paper, we present a detailed investigation on LiF:Cu in the presence of VLi by using the first-principles method. The defect structure has been determined from the formation energy. It is shown that the presence of VLi leads to a decrease of the formation energies of Cu, in favor of Cu doping into LiF. The electronic structure and optical properties of the doped systems were systematically studied, which can be largely modulated by VLi. A new absorption peak appears at 9.3 eV in LiF:Cu with an
Y.K. Sun et al. / Physica B 407 (2012) 2458–2461
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adjacent VLi to Cu, which is in good agreement with experimental observation.
2. Computational details The calculations were performed with the CASTEP code, based on the density functional theory using a plane-wave pseudopotential method. The valence electronic configurations for the lithium, fluorine and copper atoms are 1s22s1, 2s22p5 and 3d104s1, respectively. The generalized gradient approximation (GGA) with the Perdew–Burke–Ernzerhof (PBE) scheme was used for treating the exchange and correlation potential [20]. The Brillouin zone sampling mesh parameters for the k point set were 3 3 3. The plane-wave energy cutoff was set to be 330 eV. Both pure and Cudoped LiF calculations were performed with 2 2 2 supercell. For the Cu-doped case, one Li atom at center of the supercell was replaced by one Cu atom. In the presence of VLi, it is located at the position from the nearest to the fifth nearest neighbor to Cu. The lattice constants of pure cubic LiF before optimization are chosen ˚ The atomic geometries were fully optimized as a ¼b¼c ¼4.028 A. by using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) force on atoms and stresses on the supercell [21]. Convergence thresholds for geometry optimization were 1.0 10 5 eV atom 1 for total energy variation, 0.03 eV A˚ 1 for maximum force on each atom, 0.05 GPa for the unit cell stress and 0.001 A˚ for the maximum atomic displacement. The optical properties of LiF, LiF:Cu and LiF:CuþVLi were then calculated from the complex dielectric function of e(o)¼ e1(o)þ ie2(o). The imaginary part e2(o) of the dielectric function is calculated in CASTEP numerically by evaluating the matrix elements connecting the occupied and unoccupied electronic states. The real part e1(o) of e(o) is calculated then using the Kramers– Kroning transform [22]. In order to obtain comparable results with the experiment of optical properties, in calculations we used unpolarized models and scissors operators.
3. Results and discussion By optimizing the pure cubic LiF supercell, we got the lattice parameters as follows: a¼b ¼c¼4.13 A˚ with a space group of Pm3m, which are in good agreement with experimental results of a ¼b¼c¼ 3.99 A˚ [23], a ¼ b ¼ g ¼ 901. The result shows that the calculation methods are reasonable.
The formation energy of impurity indicates the relative degree of difficulty for Cu doping into LiF [24]. For lower formation energy, the doping substitution would be energetically more favorable. In the absence of VLi, the formation energy (Ef) of impurity Cu in LiF:Cu is defined as [9,10] ð1Þ
where ELiF and ELiF:Cu are total energies of pure LiF and LiF:Cu with the same size supercell. Ecu and ELi are the energies of Cu and Li atoms in the elementary substance. In the presence of VLi, the formation energy Ef of impurity Cu in LiF with a VLi (LiF:VLi) can be calculated by Ef ¼ ELiF:Cu þ V Li ELiF:V Li ECu þ ELi
Table 1 Formation energies of LiF:Cuþ VLi with different Cu–VLi distances. Sample
LiF:Cu
S1
S2
S3
S4
S5
Ef (eV)
3.01
1.1
0.72
0.34
0.44
0.12
The calculated formation energies have been listed in Table 1. In the absence of VLi, we obtain a positive formation energy, Ef ¼ 3.01 eV, showing that Cu doping into LiF is very difficult [9,10]. In the presence of VLi, we obtain Ef ¼ 1.1, 0.72, 0.34, 0.44, and 0.12 eV for the five various configurations of S1, S2, , S5. The negative formation energy of Cu shows that the presence of VLi is in favor of Cu doping into LiF, while it is difficult for doping an isolate Cu into LiF [9]. The result agrees well with the experimental observation [25]. Also from Table 1, it is found that the formation energy of Cu in LiF:VLi decreases with decreasing the Cu–VLi distance. This means that the impurity Cu is in favor of staying closer to VLi in LiF:Cuþ VLi. In the latter calculations, therefore, we will consider only the S1 configuration with the shortest Cu–VLi distance. 3.2. Electronic structures
3.1. Formation energies
Ef ¼ ELiF:Cu ELiF ECu þ ELi
Fig. 1. Possible positions of Cu substitution in LiF:VLi with different Cu–VLi distance, marked by S1, S2,y, S5.
ð2Þ
ELiF:V Li and ELiF:Cu þ V Li are the total energies of LiF:VLi and Cu doped LiF:VLi (LiF:CuþVLi) supercell. For LiF:CuþVLi system, various configurations are considered, having different VLi–Cu distances for Cu from VLi, which are marked in Fig. 1 by S1, S2,y, S5.
We calculated the electronic properties of pure LiF, LiF:Cu and LiF:CuþVLi. For the pure LiF, the top of the valence band (VB) is mainly composed of F-2p states with band width of 3.1 eV, while the bottom of the conduction band (CB) is dominated by Li-1 s states. A direct band gap of 8.46 eV exists at along G–X of the Brillouin zone, consistent with other theoretical calculation [26]. The band gap is still underestimated, less than the experimental value of 13.6–14.2 eV [27], which is due to the choice of exchangecorrelation energy. In order to overcome such a discrepancy, the so-called scissor operator [25] is introduced to eliminate the difference between the theoretical and experimental gap values by means of a simple rigid shift of the unoccupied CB with respect to VB. The value of the scissor operator is about 5.0 eV, which was applied in the previous study of LiF [26]. Fig. 2(a) shows the TDOS and PDOS of LiF:Cu. It can be seen that the top of VB and the bottom of CB for LiF:Cu are still contributed mainly by F-2p states and Li-1 s states. However, the TDOS of LiF:Cu moves to the deep energy, compared with that of perfect LiF. The Li-1 s states dominate the energy range from
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100
total
total
50 0 Cu-s Cu-p Cu-3d
DOS (states/eV)
10 5
Cu-s Cu-p Cu-3d
0 100
F-2p
F-2p
50 0 10
Li- s
Li- s
5 0 -10
-5
0
5
10 -5
5
0
10
15
Energy (eV) Fig. 2. PDOS of LiF:Cu (a) in the absence and (b) in the presence of VLi. The vertical dashed lines indicate the Fermi level.
3.3. Optical properties Based on the obtained electronic band structures, the optical absorption spectra of LiF, LiF:Cu and LiF:CuþVLi were calculated in Fig. 3 under 5.0 eV scissors operation. For pure LiF, the absorption only exists at above 13 eV, consistent with the experimental measurements [12]. For LiF:Cu, there is no absorption in visible region of below 8 eV, while there exists only absorption in vacuum ultraviolet (UV) region above 8 eV. Thus, the sample should be transparent crystals. Due to the existence of IB in LiF:Cu, interestingly, a wide absorption band with a few peaks is obtained in the region of 9–12 eV, while there newly
3.0 LiF
Absorption coefficient (105cm-1)
3.5 eV to 9.2 eV, while the F-2p states locate mainly at the energy range from 7.9 eV to 4.5 eV. Due to Cu substitution, the Fermi level is shifted from the top of VB to about the middle of band gap. Especially, an impurity band (IB) of Cu-3d states is formed with a band width of 1.7 eV, which is across the Fermi energy and partially occupied. As a result, an electron in LiF:Cu can transit from VB to IB and then to unoccupied CB states with lower energy. Also, the band gap is narrowed due to the introduction of impurity states, which would result in the shift of absorption edge to the low-energy region. Some new optical properties can be expected in such doped systems. To explore the effect of VLi on the electronic structures of LiF:Cu, Fig. 2(b) shows the TDOS and PDOS of LiF:CuþVLi. It is seen that the top of VB of LiF:CuþVLi is mainly contributed by F-2p states and the bottom of CB mainly by Li-1s states, of which the shapes are hardly influenced by VLi. The F-2p states are scattered in the energy range from 1 eV to 5 eV, while the Li-1s states locate mainly in the energy range from 5 eV to 12.5 eV. Due to the Cu–VLi interactions, interestingly, the energy range of Cu-3d states is broader than that of LiF:Cu. And the impurity bands of Cu-3d states are split into two sub-bands, different from that of LiF:Cu. One sub-band lies just across the Fermi energy with a band width of 1 eV, which is partially occupied. The other locates at below the Fermi energy from 0.5 to 5 eV. Compared with LiF:Cu, the energy gap between VB and the Fermi energy is about 1.5 eV, while Cu-3d states just lies within the energy gap. The transition of an electron from VB to unoccupied states needs even lower energy in LiF:CuþVLi than that in LiF:Cu. This means that the optical properties of LiF:Cu can be largely modulated by the presence of VLi.
LiF:Cu
2.5
LiF:Cu+VLi
2.0 1.5 1.0 0.5 0.0
6
8
10
12
14
16
18
Energy (eV) Fig. 3. Optical absorption spectra of pure LiF, LiF:Cu, and LiF:Cuþ VLi.
appear some absorption peaks beside the host peak, located at near 11 eV and 12.5 eV. For LiF:Cuþ VLi, especially, the absorption band is obtained in the region of 7–12 eV, which is largely broaden due to the presence of VLi. The two absorption peaks are obtained, shifted to about 10 eV and 13 eV, due to the split IB by Cu–VLi interactions. In addition, there appears an absorption peak at about 9.3 eV within the absorption band, which had been observed in experiment. Therefore, the optical properties of the LiF:Cu sample have been largely modulated by the presence of VLi, which should be taken into account for understanding the luminescence mechanism of the doped system.
4. Conclusion We have performed first-principles calculations on the geometry, electronic structures, and optical properties of LiF, LiF:Cu and LiF:CuþVLi. The formation energy of Cu impurity is decreased in the presence of VLi, and Cu is preferred to stay closer to VLi, forming a Cu–VLi dipole structure. Due to Cu substitution, an impurity band of Cu-3d states are formed in the middle of band gap and partially occupied. Furthermore, the impurity bands of
Y.K. Sun et al. / Physica B 407 (2012) 2458–2461
Cu-3d states are split into two sub-bands by the Cu–VLi interactions. A wide absorption band is obtained in LiF:CuþVLi, there appearing some new absorption peaks, while no absorption in the visible region for both pure LiF and LiF:Cu systems. The absorption peak appearing at 9.3 eV is consistent with the experimental observation (133 nm). The results are useful for understanding of the optical properties of the doped systems.
Acknowledgments This work was supported by Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant no. 200726), Hunan Provincial Innovation Foundation for Postgraduate (Grant no. CX2011B247), and partially by PCSIRT (IRT1080). References [1] K. Teegarden, G. Baldini, Phys. Rev. 155 (1967) 896. [2] B. Yang, L. Wang, P.D. Townsend, H. Gao, Nucl. Instrum. Methods B 266 (2008) 2581. [3] S.W.S. McKeever, J. Phys. D: Appl. Phys. 24 (1991) 988. [4] T.C. Chen, T.G. Stoebe, Radiat. Prot. Dosim. 78 (1998) 101. [5] J.I. Lee, J.L. Kim, A.S. Pradhan, B.H. Kim, Radiat. Meas. 43 (2008) 303.
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