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First-principles calculations of electronic structures and absorption spectra of YAlO3 crystals with F center
Computational Materials Science 46 (2009) 225–228
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
First-principles calculations of electronic structures and absorption spectra of YAlO3 crystals with F center Jianyu Chen a,b, Guangjun Zhao a,*, Dunhua Cao a,b, Hongjun Li a, Shengming Zhou a a
Key Laboratory of Material Science and Technology for High Power Lasers, Shanghai Institute of Optical and Fine Mechanics, Chinese Academy of Sciences, Jia Ding, Shanghai 201800, People’s Republic of China b Graduate School of the Chinese Academy of Sciences, Beijing 100039, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 2 November 2008 Received in revised form 22 February 2009 Accepted 24 February 2009 Available online 26 March 2009 PACS: 61.72.y 71.15.Mb 71.20.b
a b s t r a c t The electronic structures and absorption spectra of perfect YAlO3 crystal and YAlO3 crystal containing F center (oxygen vacancy V2þ O catching two electrons) with lattice structure optimized were calculated using density functional theory code CASTEP. The calculated electronic structures of YAlO3 crystal containing F center appear new density of states in forbidden band compared with that of perfect YAlO3 crystal and the calculated absorption spectra of the YAlO3 containing F center along three lattice parameter directions exhibit absorption bands in the range from 200 to 300 nm which are in agreement with experimental values. These new absorption bands are caused by separated F center in YAlO3 crystal. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: YAlO3 crystal Electronic structures F centers Absorption spectra
1. Introduction Yttrium orthoaluminate single crystal, YAlO3 (YAP), is a host material exhibiting high thermal conductivity and hardness [1]. YAP single crystals doped with rare-earth and transition metal ions are prospective materials for laser engineering, scintillators, holographic recording, data storage and substrate materials for thin films of high-temperature superconductors [2–11]. As laser crystals, Nd, Tm, Ho etc. rare-earth ions doped YAP crystals have advantages of the line polarized laser output and high laser efficiency compared with the same rare-earth ions doped wellknown YAG host [4–6]; Ce:YAP single crystal characterized by relatively high light yield and very short decay time is an excellent scintillator which can be employed in various gamma ray and light particle detections [7,8]; Mn doped YAP crystal is a promising material for using in holographic recording and optical data storage [9–11].
* Corresponding author. E-mail addresses: [email protected], [email protected] (G. Zhao). 0927-0256/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2009.02.029
However, intrinsic defects (thermally generated) will be produced in YAP during different crystal growing process. These defects produce additional absorptions or electron traps in band gap and they will affect the properties of the YAP crystal dramatically [12,13], thus restrict the YAP crystal application as excellent host material for laser, scintillation and data-recording applications. The as-grown YAP crystals are colorless. They turn salmon pink in air gradually and the color will deeper after annealing in air atmosphere or by UV irradiation. The photo-chromic effect is reversible, annealing in H2 atmosphere indeed restore the crystals to their original states. It is suggested that oxygen ions are active and moveable in perovskite structure oxides [14]. The color changes of the YAP after annealing treatments are related to the change of concentration of oxygen vacancies center and electron trap [15,16]. However, the model was deduced indirectly owning to shortage of direct experimental evidence and hence are not widely accepted. There are a large number of successful simulations on electronic structures and optical properties of crystals using the powerful code of CASTEP [17,18]. In this paper, the electronic structures and absorption spectra of both perfect YAP crystal and YAP crystal containing F center with lattice structure optimized are calculated using the CASTEP code.
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J. Chen et al. / Computational Materials Science 46 (2009) 225–228
shift of the bands situated above the valence band and a rescaling of the matrix elements. Most of the difference between Kohn-Sham eigenvalues and the true excitation energies can be accounted for by a rigid shift of the conduction band upwards with respect to the valence band [20]. Under Koopmans’ approximation (one-electron rigid-band approximation with the electron polarization effects neglected) and the limitation of linear optics within the visible and UV range, the imaginary part of dielectric function ei is given by [21,22]
ei ðxÞ ¼
e 2 p2
e0
x Dc=hÞ2
m2 ð
( X Z V;C
Fig. 1. The structure of YAP unit cell.
2. The cluster models and calculation methods 2.1. The cluster models The YAP crystal crystallizes the orthorhombically distorted perovskite structure (a = 5.330 Å, b = 7.375 Å, c = 5.180 Å; space group Pnma-D16 2h ) [19]. The YAP’s conventional unit cell contains four formula units per unit cell and can be conveniently presented as a grid of tilted AlO6 octahedra with the Y ions occupying holes between them. The Al cations are located in the center of a practically regular octahedral. The unit cell of the crystal structure is featured in Fig. 1. The perfect YAP cluster model used here consists of 16 Y, 16 Al and 48 O centered at Al3+. The YAP super-cell containing F center substitutes the oxygen ions O2 nearest to the centered Al ion by V2þ O and the total charge of super-cell are set zero which will form the F center in the calculation. 2.2. The calculation methods The lattice optimization for YAP containing F center is performed by using CASTEP code. We use ultra-soft pseudo-potentials for the Y, Al and O atoms and a plane-wave cut-off of 340 eV. Optimal atomic positions are determined until satisfying the conditions: (1) the maximal force on them is smaller than 0.5 eV/nm; (2) the maximal change of energy per atom is smaller than 0.00001 eV; (3) the maximal displacement is smaller than 0.0001 nm. All other calculations are performed on the basis of the lattice structure optimized. For the ground-state electronic structure, calculations based on the density functional theory (DFT) within generalized gradient approximations (GGA) were performed using the CASTEP code. The DFT is a ground-state theory which is not able to describe excited states. In setting up the CASTEP run, basic parameters are chosen as follows: kinetic energy cut-off = 340 eV; fast Fourier transform (FFT) grid dimensions = 60 60 64; space representation = reciprocal; SCF tolerance = 1.0 106 eV/atom. The optical absorption spectrum arises from two factors: the interband transitions and the Lorentz terms. Here we focus on the interband transitions because the structural transform occurs in interband channel. The dielectric function of an anisotropic material is a complex symmetric second-order tensor describing the linear response of an electronic system to an applied external electric filed. The imaginary part of the dielectric tensor is directly related to band structure of a solid so that it can be computed based on the knowledge of single-particle orbital and energy approximated by the solution of the Kohn-Sham equation. However, it is well known that DFT calculations within GGA underestimate the band gap. To take this into account, a ‘‘scissors operator” is used, allowing a
BZ
) i 2d~ K ~ 2 h ~ ~ ~ ; a M d E ð KÞ þ D c E ð KÞ h x V;C C V ð2pÞ3
~ V;C is the matrix of dipole where ~ a is the unit vector potential ~ A. M transition. C and V denote the conduction band and valence band, respectively. BZ denotes the Brillouin zone. Dc is the modifying value of the ‘scissors operator’, e is the electron charge. e0 is the dielectric constant in vacuum. m is the mass of a free electron. x is the frequency and ~ K is wave vector of the incident wave, and h is the Planck constant. The Kramers-Kronig relation which links the real and the imaginary part of the dielectric function is used to obtain the real part er ðxÞ of the dielectric function with smearing factor of 0.10 eV. The ‘scissors operator’ Dc is chosen as 2.0 eV, which originates from the fact that the calculated bad gap of the perfect YAP crystal is 6.0 eV while the experimental value is 8.0 eV [23,24]. The BZ integration over 64 independent k-points is chosen for YAP crystal. 3. Results and discussion 3.1. Structure optimization The distance between F center and its closer ions for pre-optimized and that for optimized structures are listed in Table 1. Compared with perfect YAP structure, the optimized lattice structures of YAP containing F center show the following characteristics: (1) 2þ the Al3+ cations nearby V2þ O move slightly away from VO ; (2) the 2þ move slightly towards V Y3+ and O2 ions nearby V2þ O O . The ions around V2þ O keep moving until the electrical and mechanical potential reach new balance. The distortion on lattice structure will affect the electronic structures and optical properties of YAP crystal containing F center formed by V2þ O significantly. 3.2. Electronic structures Total density of states (DOS) and partial DOS (PDOS) of perfect YAP crystal are calculated in the range from 45 eV to 15 eV, as shown in Fig. 2. The regions below the Fermi level can be divided into four regions. The bottom-most valence band (VB) region with energy located at around 40.0 eV is composed of Y-4s states. The Table 1 The distance between V2þ O and its closer ions for pre-optimized and that for optimized structures. System
Structures Y–V2þ O (Å)
Al–V2þ O (Å)
O–V2þ O (Å)
Pre-optimized
2.237 2.306 3.010 3.119 2.194 2.277 2.974 3.100
1.901
2.666 2.681 2.724 2.725 2.649 2.664 2.697 2.751
Optimized
1.927
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J. Chen et al. / Computational Materials Science 46 (2009) 225–228
Density of States (electrons/eV)
80
120
Total
0 80
O
O 2p
O 2s
40 0
Al
6
Al 3s+3p
Al 3s+3p
4 Al 3s+3p
2 0
Y
80
Total
80
40
Y 4p
Density of Satates (electrons/eV)
120
40 0 15
Y
10 5 0 15
Al
10 5 0 15
O
10
Y 4s
40
Y 4d
Y 4d
5 0
0 -40
-30
-20
-10
0
-50
10
-40
-30
Energy (eV)
120
Total Density of States (electrons/eV)
Perfect YAP 80
40
0
YAP:F center 80
40
0 -30
-20
-10
0
10
Energy (eV)
Fig. 3. The TDOS of perfect YAP and YAP crystal containing F center.
Absorption coefficient (a.u.)
Y-4p states dominate the bands at about 20.0 eV. The bands ranging from 18.0 to 15.2 eV mostly originate from O-2s, Al-3s and Al-3p states. The highest VB region arises from the O-2p states with a small mixing of Al-3s, Al-3p and Y-4d states. The conduction band (CB) above Fermi level is mostly dominated by Y-4d states. The Total DOS (TDOS) of perfect YAP and YAP containing F center are given in Fig. 3. Their TDOS are very similar. The top of VB of YAP containing F center are still mainly contributed by O-2p states and the bottom of the CB are mainly contributed by Y-4d states, however, the TDOS of YAP containing F center move about 2.5 eV to deeper energy level. The whole shift of DOS of YAP containing F center is caused by the total charge set on the cluster. The bigger difference between the TDOS of perfect YAP and that of YAP containing F center is that a small density of state occurs in the forbidden band at zero energy level. These mean that V2þ O will produce great influence on the electrons of ions around it and will affect optical properties of YAP significantly. The V2þ O is positive divalent and requires negative charges to compensate its positive charges to form F center. We give the PDOS of YAP crystal containing F center in Fig. 4 in order to confirm the origin of the small DOS in forbidden band. From the PDOS, we can find that the Y-4d, Al-3p and O-2p are almost equal contributions to the small DOS. The small DOS is the donor lever in forbidden band because it locates at the Fermi level and the electrons on it could jump to CB when they are excited by high energy. The V2þ O forms F+ color center if catching an electron and it forms F color
-40
-10
0
10
Fig. 4. The TDOS and PDOS of YAP crystal containing F center.
Fig. 2. The TDOS and PDOS of perfect YAP crystal.
-50
-20 Energy (eV)
35 30 25 20 15 10 5 0 30 25 20 15 10 5 0 30 25 20 15 10 5 0
k//a
k//b
k//c
0
100
200
300
400
500
600
Wavelength (nm)
700
800
900
1000
Fig. 5. Absorption spectra of perfect YAP (dotted lines) and YAP containing F center (solid lines) under k//a, k//b and k//c.
center if catching two electrons. F and F+ energy level locate in forbidden band. Our calculated results are in agreement with the results of other oxide crystals [25,26]. 3.3. Absorption spectra The absorption coefficient follows the relationship a ¼ xei =nc: The absorption spectra that light incidence directions along lattice parameter a, b and c (k//a, k//b and k//c) were calculated for perfect YAP and YAP containing F center, as shown in Fig. 5. There are no absorption bands in visible region and the absorption bands only exist below 300 nm in UV region for both perfect YAP and YAP containing F center. Compared with the absorption spectra of perfect YAP shown in Fig. 5 (dotted line), absorption spectra under k//a, k//b and k//c for YAP containing F center exhibit two characteristics as follows: (1) the absorption spectra are very similar to the absorption spectra of perfect YAP below 200 nm which show slight anisotropy along different incidence directions and (2) the absorption spectra of YAP containing F center appear new absorption bands in region from 200 to 300 nm. These absorption bands obtained in our calculation are in agreement with experimental measurements [15]. The new appeared absorption spectra along different incident directions k//a, k//b and k//c in the range from 200 to 300 nm of YAP containing F center are shown in Fig. 6. These absorption
Absorption coefficient (a.u.)
228
J. Chen et al. / Computational Materials Science 46 (2009) 225–228 8 7 6 5 4 3 2 1 0 7
244 nm
F center with lattice structure optimized have been calculated using the density function theory code CASTEP. The calculated results show that F center in YAP crystal lead to the appearance of little density of state peak in forbidden band and new absorption bands in the range from 200 to 300 nm in UV region. The color changes of YAP crystal after different atmosphere annealing treatments have nothing to do with F center formed by oxygen vacancy.
k//a
k//b
6
244 nm
5
Acknowledgments
261 nm
4 3 2
The authors appreciate the financial support from the National Science Foundation of China (Grant No. 60607015) and Shanghai Supercomputer Center of China for the support of computation.
227 nm
1 0 7
k//c
6 5
References
261 nm
4
237 nm
3 2
250 nm
1 0 200
210
220
230
240
250
260
Wavelength (nm)
270
280
290
300
Fig. 6. The absorption spectra of YAP containing F center in the range from 200 to 300 nm under k//a, k//b and k//c (solid lines) and its fitting to Gaussian bands (dotted line).
spectra show some anisotropy obviously and they are decomposed into Gaussian bands. It can be seen that the absorption spectra under k//a exhibit only one band peaking at 244 nm, while the absorption spectra under k//b exhibit three bands peaking at 224, 244 and 261 nm and the absorption spectra under k//c exhibit three bands peaking at 237, 250 and 261 nm, respectively. All these absorption bands are caused by the existence of F center. The orthorhombic system YAP crystal is biaxial crystal and the symmetric second-order tensors eij (dielectric coefficient) meet the relation e11 –e22 –e33 : So we consider the anisotropy of absorption spectra of YAP under k//a, k//b and k//c are decided by the anisotropy of the lattice structure (a–b–c). The absorption bands of YAP located in the UV region range from 200 to 300 nm are caused by F center and they have nothing to do with the color changes of YAP crystal after different annealing treatments. 4. Conclusion The electronic structures and absorption spectra under k//a, k//b and k//c for a perfect YAP crystal and a YAP crystal containing
[1] J. Kvapil, J. Kvapil, J. Kubelka, R. Autrata, Cryst. Res. Technol. 18 (1983) 127. [2] D.M. Bercha, K.Z. Rushchanskii, M. Sznajder, A. Matkovskii, P. Potera, Phys. Rev. B 66 (2002) 195203. [3] P. Potera, L. Grigorjeva, A. Matkovskii, D. Millers, T. Lukasiewicz, Z. Galazka, T. Wojciechowski, Radiat. Measur. 38 (2004) 371. [4] C.K. Duan, P.A. Tanner, V.N. Makhov, M. Kirm, Phys. Rev. B 75 (2007) 195130. [5] N. Garnier, R. Moncorge, H. Manaa, E. Descroix, P. Laporte, Y. Guyot, J. Appl. Phys. 79 (1996) 4323. [6] B.Q. Yao, X.M. Duan, L.L. Zheng, Y.L. Ju, Y.Z. Wang, G.J. Zhao, Q. Dong, Opt. Express 16 (2008) 14668. [7] S. Baccaro, K. Blazek, F. de Notaristefani, P. Maly, J.A. Marser, R. Pani, R. Pellegrini, A. Soluri, Nucl. Instr. Meth. Phys. Res. A 361 (1995) 209. [8] M. Kapusta, J. Pawelke, M. Moszynski, Nucl. Instr. Meth. Phys. Res. A 404 (1998) 413. [9] G.B. Loutts, M. Warren, L. Taylor, R.R. Rakhimov, H.R. Ries, G. Miller, M.A. Noginov, M. Curley, N. Noginova, N. Kukhtarev, H.J. Caulfield, P. Venkateswarlu, Phys. Rev. B 57 (1998) 3706. [10] M.A. Noginov, G.B. Loutts, J. Opt. Soc. Am. B 16 (1999) 3. [11] M.A. Noginov, G.B. Loutts, M. Warren, J. Opt. Soc. Am. B 16 (1999) 475. [12] Z.J. Qu, C.Y. Yu, W.Z. Li, Y.X. Chen, Acta Phys.-Chim. Sinica 10 (1994) 796. [13] C.R. Stanek, K.J. McClellan, M.R. Levy, R.W. Grimes, J. Appl. Phys. 99 (2006) 113518. [14] D.J. Singh, Phys. Rev. B 76 (2007) 214115. [15] X.H. Zeng, G.J. Zhao, J. Xu, X.M. He, J. Appl. Phys. 95 (2004) 749. [16] T. Li, G.J. Zhao, X.M. He, J. Xu, S.K. Pan, J. Synth. Cryst. 31 (2002) 465. [17] X.P. Yang et al., Phys. Rev. B 69 (2004) 193401. [18] J.F. Wan, J.N. Wang, Phys. B 355 (2005) 172. [19] R. Diehl, G. Brandt, Mater. Res. Bull. 10 (1975) 85. [20] X.G. Xu, X. Ding, Q. Chen, L.-M. Peng, Phys. Rev. B 73 (2006) 165403. [21] R.C. Fan, Spectroscopy of Solids, University of Science and Technology of China Press, 2001 (in Chinese). [22] Y. Abraham et al., Phys. Rev. B 64 (2000) 245109. [23] T. Tomiki, F. Fukudome, M. Kaminao, M. Fujisawa, Y. Tanahara, J. Phys. Soc. Japan 55 (1986) 2090. [24] T. Tomiki, F. Fukudome, M. Kaminao, M. Fujisawa, Y. Tanahara, T. Futemna, J. Lumin. 40–41 (1988) 379. [25] T.Y. Liu, Q.R. Zhang, S.L. Zhuang, Phys. Lett. A 333 (2004) 473. [26] Z.X. Shao, Q.R. Zhang, T.Y. Liu, J.Y. Chen, Comput. Mater. Sci. 43 (2008) 1018.
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
First-principles calculations of electronic structures and absorption spectra of YAlO3 crystals with F center Jianyu Chen a,b, Guangjun Zhao a,*, Dunhua Cao a,b, Hongjun Li a, Shengming Zhou a a
Key Laboratory of Material Science and Technology for High Power Lasers, Shanghai Institute of Optical and Fine Mechanics, Chinese Academy of Sciences, Jia Ding, Shanghai 201800, People’s Republic of China b Graduate School of the Chinese Academy of Sciences, Beijing 100039, People’s Republic of China
a r t i c l e
i n f o
Article history: Received 2 November 2008 Received in revised form 22 February 2009 Accepted 24 February 2009 Available online 26 March 2009 PACS: 61.72.y 71.15.Mb 71.20.b
a b s t r a c t The electronic structures and absorption spectra of perfect YAlO3 crystal and YAlO3 crystal containing F center (oxygen vacancy V2þ O catching two electrons) with lattice structure optimized were calculated using density functional theory code CASTEP. The calculated electronic structures of YAlO3 crystal containing F center appear new density of states in forbidden band compared with that of perfect YAlO3 crystal and the calculated absorption spectra of the YAlO3 containing F center along three lattice parameter directions exhibit absorption bands in the range from 200 to 300 nm which are in agreement with experimental values. These new absorption bands are caused by separated F center in YAlO3 crystal. Ó 2009 Elsevier B.V. All rights reserved.
Keywords: YAlO3 crystal Electronic structures F centers Absorption spectra
1. Introduction Yttrium orthoaluminate single crystal, YAlO3 (YAP), is a host material exhibiting high thermal conductivity and hardness [1]. YAP single crystals doped with rare-earth and transition metal ions are prospective materials for laser engineering, scintillators, holographic recording, data storage and substrate materials for thin films of high-temperature superconductors [2–11]. As laser crystals, Nd, Tm, Ho etc. rare-earth ions doped YAP crystals have advantages of the line polarized laser output and high laser efficiency compared with the same rare-earth ions doped wellknown YAG host [4–6]; Ce:YAP single crystal characterized by relatively high light yield and very short decay time is an excellent scintillator which can be employed in various gamma ray and light particle detections [7,8]; Mn doped YAP crystal is a promising material for using in holographic recording and optical data storage [9–11].
* Corresponding author. E-mail addresses: [email protected], [email protected] (G. Zhao). 0927-0256/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.commatsci.2009.02.029
However, intrinsic defects (thermally generated) will be produced in YAP during different crystal growing process. These defects produce additional absorptions or electron traps in band gap and they will affect the properties of the YAP crystal dramatically [12,13], thus restrict the YAP crystal application as excellent host material for laser, scintillation and data-recording applications. The as-grown YAP crystals are colorless. They turn salmon pink in air gradually and the color will deeper after annealing in air atmosphere or by UV irradiation. The photo-chromic effect is reversible, annealing in H2 atmosphere indeed restore the crystals to their original states. It is suggested that oxygen ions are active and moveable in perovskite structure oxides [14]. The color changes of the YAP after annealing treatments are related to the change of concentration of oxygen vacancies center and electron trap [15,16]. However, the model was deduced indirectly owning to shortage of direct experimental evidence and hence are not widely accepted. There are a large number of successful simulations on electronic structures and optical properties of crystals using the powerful code of CASTEP [17,18]. In this paper, the electronic structures and absorption spectra of both perfect YAP crystal and YAP crystal containing F center with lattice structure optimized are calculated using the CASTEP code.
226
J. Chen et al. / Computational Materials Science 46 (2009) 225–228
shift of the bands situated above the valence band and a rescaling of the matrix elements. Most of the difference between Kohn-Sham eigenvalues and the true excitation energies can be accounted for by a rigid shift of the conduction band upwards with respect to the valence band [20]. Under Koopmans’ approximation (one-electron rigid-band approximation with the electron polarization effects neglected) and the limitation of linear optics within the visible and UV range, the imaginary part of dielectric function ei is given by [21,22]
ei ðxÞ ¼
e 2 p2
e0
x Dc=hÞ2
m2 ð
( X Z V;C
Fig. 1. The structure of YAP unit cell.
2. The cluster models and calculation methods 2.1. The cluster models The YAP crystal crystallizes the orthorhombically distorted perovskite structure (a = 5.330 Å, b = 7.375 Å, c = 5.180 Å; space group Pnma-D16 2h ) [19]. The YAP’s conventional unit cell contains four formula units per unit cell and can be conveniently presented as a grid of tilted AlO6 octahedra with the Y ions occupying holes between them. The Al cations are located in the center of a practically regular octahedral. The unit cell of the crystal structure is featured in Fig. 1. The perfect YAP cluster model used here consists of 16 Y, 16 Al and 48 O centered at Al3+. The YAP super-cell containing F center substitutes the oxygen ions O2 nearest to the centered Al ion by V2þ O and the total charge of super-cell are set zero which will form the F center in the calculation. 2.2. The calculation methods The lattice optimization for YAP containing F center is performed by using CASTEP code. We use ultra-soft pseudo-potentials for the Y, Al and O atoms and a plane-wave cut-off of 340 eV. Optimal atomic positions are determined until satisfying the conditions: (1) the maximal force on them is smaller than 0.5 eV/nm; (2) the maximal change of energy per atom is smaller than 0.00001 eV; (3) the maximal displacement is smaller than 0.0001 nm. All other calculations are performed on the basis of the lattice structure optimized. For the ground-state electronic structure, calculations based on the density functional theory (DFT) within generalized gradient approximations (GGA) were performed using the CASTEP code. The DFT is a ground-state theory which is not able to describe excited states. In setting up the CASTEP run, basic parameters are chosen as follows: kinetic energy cut-off = 340 eV; fast Fourier transform (FFT) grid dimensions = 60 60 64; space representation = reciprocal; SCF tolerance = 1.0 106 eV/atom. The optical absorption spectrum arises from two factors: the interband transitions and the Lorentz terms. Here we focus on the interband transitions because the structural transform occurs in interband channel. The dielectric function of an anisotropic material is a complex symmetric second-order tensor describing the linear response of an electronic system to an applied external electric filed. The imaginary part of the dielectric tensor is directly related to band structure of a solid so that it can be computed based on the knowledge of single-particle orbital and energy approximated by the solution of the Kohn-Sham equation. However, it is well known that DFT calculations within GGA underestimate the band gap. To take this into account, a ‘‘scissors operator” is used, allowing a
BZ
) i 2d~ K ~ 2 h ~ ~ ~ ; a M d E ð KÞ þ D c E ð KÞ h x V;C C V ð2pÞ3
~ V;C is the matrix of dipole where ~ a is the unit vector potential ~ A. M transition. C and V denote the conduction band and valence band, respectively. BZ denotes the Brillouin zone. Dc is the modifying value of the ‘scissors operator’, e is the electron charge. e0 is the dielectric constant in vacuum. m is the mass of a free electron. x is the frequency and ~ K is wave vector of the incident wave, and h is the Planck constant. The Kramers-Kronig relation which links the real and the imaginary part of the dielectric function is used to obtain the real part er ðxÞ of the dielectric function with smearing factor of 0.10 eV. The ‘scissors operator’ Dc is chosen as 2.0 eV, which originates from the fact that the calculated bad gap of the perfect YAP crystal is 6.0 eV while the experimental value is 8.0 eV [23,24]. The BZ integration over 64 independent k-points is chosen for YAP crystal. 3. Results and discussion 3.1. Structure optimization The distance between F center and its closer ions for pre-optimized and that for optimized structures are listed in Table 1. Compared with perfect YAP structure, the optimized lattice structures of YAP containing F center show the following characteristics: (1) 2þ the Al3+ cations nearby V2þ O move slightly away from VO ; (2) the 2þ move slightly towards V Y3+ and O2 ions nearby V2þ O O . The ions around V2þ O keep moving until the electrical and mechanical potential reach new balance. The distortion on lattice structure will affect the electronic structures and optical properties of YAP crystal containing F center formed by V2þ O significantly. 3.2. Electronic structures Total density of states (DOS) and partial DOS (PDOS) of perfect YAP crystal are calculated in the range from 45 eV to 15 eV, as shown in Fig. 2. The regions below the Fermi level can be divided into four regions. The bottom-most valence band (VB) region with energy located at around 40.0 eV is composed of Y-4s states. The Table 1 The distance between V2þ O and its closer ions for pre-optimized and that for optimized structures. System
Structures Y–V2þ O (Å)
Al–V2þ O (Å)
O–V2þ O (Å)
Pre-optimized
2.237 2.306 3.010 3.119 2.194 2.277 2.974 3.100
1.901
2.666 2.681 2.724 2.725 2.649 2.664 2.697 2.751
Optimized
1.927
227
J. Chen et al. / Computational Materials Science 46 (2009) 225–228
Density of States (electrons/eV)
80
120
Total
0 80
O
O 2p
O 2s
40 0
Al
6
Al 3s+3p
Al 3s+3p
4 Al 3s+3p
2 0
Y
80
Total
80
40
Y 4p
Density of Satates (electrons/eV)
120
40 0 15
Y
10 5 0 15
Al
10 5 0 15
O
10
Y 4s
40
Y 4d
Y 4d
5 0
0 -40
-30
-20
-10
0
-50
10
-40
-30
Energy (eV)
120
Total Density of States (electrons/eV)
Perfect YAP 80
40
0
YAP:F center 80
40
0 -30
-20
-10
0
10
Energy (eV)
Fig. 3. The TDOS of perfect YAP and YAP crystal containing F center.
Absorption coefficient (a.u.)
Y-4p states dominate the bands at about 20.0 eV. The bands ranging from 18.0 to 15.2 eV mostly originate from O-2s, Al-3s and Al-3p states. The highest VB region arises from the O-2p states with a small mixing of Al-3s, Al-3p and Y-4d states. The conduction band (CB) above Fermi level is mostly dominated by Y-4d states. The Total DOS (TDOS) of perfect YAP and YAP containing F center are given in Fig. 3. Their TDOS are very similar. The top of VB of YAP containing F center are still mainly contributed by O-2p states and the bottom of the CB are mainly contributed by Y-4d states, however, the TDOS of YAP containing F center move about 2.5 eV to deeper energy level. The whole shift of DOS of YAP containing F center is caused by the total charge set on the cluster. The bigger difference between the TDOS of perfect YAP and that of YAP containing F center is that a small density of state occurs in the forbidden band at zero energy level. These mean that V2þ O will produce great influence on the electrons of ions around it and will affect optical properties of YAP significantly. The V2þ O is positive divalent and requires negative charges to compensate its positive charges to form F center. We give the PDOS of YAP crystal containing F center in Fig. 4 in order to confirm the origin of the small DOS in forbidden band. From the PDOS, we can find that the Y-4d, Al-3p and O-2p are almost equal contributions to the small DOS. The small DOS is the donor lever in forbidden band because it locates at the Fermi level and the electrons on it could jump to CB when they are excited by high energy. The V2þ O forms F+ color center if catching an electron and it forms F color
-40
-10
0
10
Fig. 4. The TDOS and PDOS of YAP crystal containing F center.
Fig. 2. The TDOS and PDOS of perfect YAP crystal.
-50
-20 Energy (eV)
35 30 25 20 15 10 5 0 30 25 20 15 10 5 0 30 25 20 15 10 5 0
k//a
k//b
k//c
0
100
200
300
400
500
600
Wavelength (nm)
700
800
900
1000
Fig. 5. Absorption spectra of perfect YAP (dotted lines) and YAP containing F center (solid lines) under k//a, k//b and k//c.
center if catching two electrons. F and F+ energy level locate in forbidden band. Our calculated results are in agreement with the results of other oxide crystals [25,26]. 3.3. Absorption spectra The absorption coefficient follows the relationship a ¼ xei =nc: The absorption spectra that light incidence directions along lattice parameter a, b and c (k//a, k//b and k//c) were calculated for perfect YAP and YAP containing F center, as shown in Fig. 5. There are no absorption bands in visible region and the absorption bands only exist below 300 nm in UV region for both perfect YAP and YAP containing F center. Compared with the absorption spectra of perfect YAP shown in Fig. 5 (dotted line), absorption spectra under k//a, k//b and k//c for YAP containing F center exhibit two characteristics as follows: (1) the absorption spectra are very similar to the absorption spectra of perfect YAP below 200 nm which show slight anisotropy along different incidence directions and (2) the absorption spectra of YAP containing F center appear new absorption bands in region from 200 to 300 nm. These absorption bands obtained in our calculation are in agreement with experimental measurements [15]. The new appeared absorption spectra along different incident directions k//a, k//b and k//c in the range from 200 to 300 nm of YAP containing F center are shown in Fig. 6. These absorption
Absorption coefficient (a.u.)
228
J. Chen et al. / Computational Materials Science 46 (2009) 225–228 8 7 6 5 4 3 2 1 0 7
244 nm
F center with lattice structure optimized have been calculated using the density function theory code CASTEP. The calculated results show that F center in YAP crystal lead to the appearance of little density of state peak in forbidden band and new absorption bands in the range from 200 to 300 nm in UV region. The color changes of YAP crystal after different atmosphere annealing treatments have nothing to do with F center formed by oxygen vacancy.
k//a
k//b
6
244 nm
5
Acknowledgments
261 nm
4 3 2
The authors appreciate the financial support from the National Science Foundation of China (Grant No. 60607015) and Shanghai Supercomputer Center of China for the support of computation.
227 nm
1 0 7
k//c
6 5
References
261 nm
4
237 nm
3 2
250 nm
1 0 200
210
220
230
240
250
260
Wavelength (nm)
270
280
290
300
Fig. 6. The absorption spectra of YAP containing F center in the range from 200 to 300 nm under k//a, k//b and k//c (solid lines) and its fitting to Gaussian bands (dotted line).
spectra show some anisotropy obviously and they are decomposed into Gaussian bands. It can be seen that the absorption spectra under k//a exhibit only one band peaking at 244 nm, while the absorption spectra under k//b exhibit three bands peaking at 224, 244 and 261 nm and the absorption spectra under k//c exhibit three bands peaking at 237, 250 and 261 nm, respectively. All these absorption bands are caused by the existence of F center. The orthorhombic system YAP crystal is biaxial crystal and the symmetric second-order tensors eij (dielectric coefficient) meet the relation e11 –e22 –e33 : So we consider the anisotropy of absorption spectra of YAP under k//a, k//b and k//c are decided by the anisotropy of the lattice structure (a–b–c). The absorption bands of YAP located in the UV region range from 200 to 300 nm are caused by F center and they have nothing to do with the color changes of YAP crystal after different annealing treatments. 4. Conclusion The electronic structures and absorption spectra under k//a, k//b and k//c for a perfect YAP crystal and a YAP crystal containing
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