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Electronic structure and optical properties of CdWO4 with oxygen vacancy studied from first principles
Solid State Communications 150 (2010) 5–8
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Electronic structure and optical properties of CdWO4 with oxygen vacancy studied from first principlesI Xiuwen Zhou a , Tingyu Liu a,b,∗ , Qiren Zhang a , Fang Cheng a , Hailing Qiao a a
College of Science, University of Shanghai for Science and Technology, 516 JunGong Road, Shanghai 200093, China
b
Shanghai Key Laboratory of Contemporary Optics System, China
article
info
Article history: Received 22 May 2009 Received in revised form 27 August 2009 Accepted 15 October 2009 by J. Zhu Available online 18 October 2009 PACS: 71.20.Ps 77.22.Ej 78.20.Bh Keywords: A. CdWO4 crystal C. Oxygen vacancy D. Electronic structure D. Optical properties
abstract The electronic structures, dielectric functions and absorption coefficient of both perfect CdWO4 crystal (CWO) and the CWO crystal containing oxygen vacancy (CWO:VO ) have been studied using the CASTEP code with the lattice structure optimized. The calculated total density of states (TDOS) of CWO:VO indicates that the oxygen vacancy would introduce a new electronic state within the band gap compared with that of perfect CWO. The dielectric functions are calculated since the imaginary part of the dielectric function can reduce the optical absorption of a certain crystal, and then the absorption coefficient is calculated. The calculated absorption spectra show that CWO:VO exhibits two absorption bands in the ultraviolet and visible region, peaking at about 3.0 eV (413 nm) and 3.5 eV (354 nm), respectively, which are in agreement with the experimental results showing that the yellow CWO has two optical absorption bands in this region peaking at around 350 nm and 400 nm respectively. It can be concluded that oxygen vacancy causes these two absorption bands. The calculations also indicate that the optical properties of CWO exhibit anisotropy, and can be explained by the anisotropy of the crystal lattice. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Cadmium tungstate (CdWO4 ) single crystal is a commercially viable scintillator because of its excellent properties such as high light yield, short radiation length, high density and the radiation stability with varied temperature [1–3]. The scintillating emission from CdWO4 crystal (CWO) is intrinsic and peaks around 490 nm [2]. This spectral range allows this scintillator to be coupled to both photomultiplier tube and photo diodes. With these features, CWO is considered for X-ray computer tomography (CT) and introscope [1], high-energy nuclear spectroscopy [4], and oil well logging [5] applications. However, defects may deteriorate the light yield and decrease the transmissivity of the crystal, which are formed during the
I Supported by the Scientific Development Foundation of Shanghai Municipal Education Committee, China (Grant No. 09YZ210) and the Shanghai Leading Academic Discipline Project (S30502) and the Programs (No. 07DZ22026) from Shanghai Committee of Science & Technology. ∗ Corresponding author at: College of Science, University of Shanghai for Science and Technology, 516 JunGong Road, Shanghai 200093, China. Tel.: +86 021 55272483; fax: +86 021 55274057. E-mail addresses: [email protected], [email protected] (T. Liu).
0038-1098/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2009.10.019
process of crystal growth or after the irradiation of high-energy rays. Sabharwal and Sangeeta [6] supposed that the optical absorption of CWO in the region of 325–500 nm was relevant to the structural defects based on the fact that CdO was easier to evaporate than WO3 . Robertson et al. [7] reported that both the spectra of pale yellow and orange CWO showed two absorption bands peaking at about 350 nm and 400 nm, respectively. They predicted that the 350 nm band was caused by a structural defect and the 400 nm band resulted from a metallic ion impurity. Bondar et al. [8] also suggested the absorption bands in their optical spectra were associated with the oxygen-related structural defects. All these experiments suggest that the color of undoped CWO may be caused by the intrinsic defects in the crystal. Thus, it is important to understand the intrinsic defects in the crystal and how they affect the optical properties of CWO. However, there are few theoretical studies on these defects, of which the electronic structure and optical properties remain unclear. In this work, we focus on the oxygen vacancy (VO ) in CWO. The electronic structures and optical properties, such as the density of states (DOS), dielectric functions and absorption spectra under polarized light for both the perfect CWO and the CWO crystal containing oxygen vacancy (CWO:VO ), are theoretically studied by the Cambridge Serial Total Energy Package (CASTEP) code [9].
6
X. Zhou et al. / Solid State Communications 150 (2010) 5–8
Cd O1
Crystal parameter
W O1
O2
Table 1 Crystal parameters and atomic positions (x; y; z ) used in the present calculations.
a = 5.026 Å b = 5.867 Å c = 5.078 Å β = 91.47◦
O
O2 O2 b O2
O1
c O1
β a
Fig. 1. Lattice structure of CWO.
2. Computational model and methods 2.1. Computational model CWO has the wolframite-type structure [10], which is in the monoclinic class and has the space group of P2/c (No. 13), as illustrated in Fig. 1. In this structure, each W and Cd is surrounded by six Os. The resultant WO6 octahedra form a chain by edge sharing, so that there are two energetically distinct O positions in the lattice. Type 1 (O1 ) forms a bond to one tungsten atom with a very short bond length. Type 2 (O2 ) connects to two different W atoms with longer bond lengths. The crystal parameters and atomic positions (x, y, z ) used in the present calculations are listed in Table 1 [11]. The calculating model for CWO:VO is a super-cell (2 × 2 × 2 unit cell) with an O atom removed. According to our calculation, the total energy for the 95-atom-system with an O1 vacancy and an O2 vacancy are −707.786 eV and −707.269 eV, respectively. The formation energy of an O2 vacancy is 0.517 eV less than that of an O1 vacancy. Thus, the former is more energetically favorable than the latter in the crystal. Therefore, an O2 atom is removed from the super-cell to simulate CWO:VO . 2.2. Computational methods The approach used in this work is density functional theory (DFT) using the generalized gradient approximation in the form of Perdew-Wang-91 (GGA-PW91) combined with nonlocal, ultra-soft pseudopotentials and plane wave expansions in the CASTEP program [12,13]. For the ground-state electronic structure calculations, the valence electronic configurations are 4d10 5s2 for Cd, 5d4 6s2 for W and 2s2 2p4 for O. The GGA calculations use Brillouin-zone sampling with 2×2×2 grid of Monkhorst–Pack kpoints and plane-wave cutoff energies of 340 eV; fast Fourier transform (FFT) grid dimensions are 60 × 60 × 64 and space representation is reciprocal. Self-consistent field (SCF) tolerance is 1.0 × 10−6 eV/atom. Lattice optimization is necessary for calculation in order to obtain believable results. In every case, the geometrical optimization is made and convergence is assumed when: the forces on the lattice ions are less than 0.5 eV/nm; the changes of energy per atom are less than 0.00001 eV; and the atomic displacements are less than 0.0001 nm. The dielectric function of an anisotropic crystal is a complex second-order tensor describing the linear response of an electronic system to an applied external electric field. The imaginary part of the dielectric tensor directly relates to the band structure of a material and can be computed from the knowledge of singleparticle orbital and energy approximated by the solutions of
Atomic positions (fractional coordinates) Atom
x
y
z
Cd W O1 O2
0.5 0 0.189 0.250
0.75 0.25 0.454 0.393
0.302 0.1784 0.901 0.360
the Kohn–Sham equations. However, it is well known that DFT calculations underestimate the band gap. Therefore, a ‘‘scissors operator’’ [14–16] is used for correction. The scissors operator allows a shift of the bands situated above the valence band and then rescales the matrix elements to fit the band gap to the real value. It is computationally shown (in comparison of the GW and LDA band structures) that most of the differences between Kohn–Sham eigenvalues and the true excitation energies can be accounted by a upward rigid shift of the conduction band with respect to the valence band [17]. Assuming the one-electron rigidband approximation, and neglecting the electron polarization effects (Koopmans’ approximation), in the limit of linear optics and of the visible–ultraviolet range, the imaginary part of dielectric function εi is given by [18,19]
εi (ω) =
e2 π 2
ε0 m2 (ω − ∆C /h¯ )2 X Z 2dK 2 × | a · M | δ[ E ( K ) + ∆ c − E ( K ) − h ω] (1) ¯ v, c c v 3 BZ (2π ) V ,C
where a is the unit vector of potential A; Mv,c is the matrix of dipole transition; C is the conduction band; V is the valence band. BZ denotes the Brillouin zone; ∆c is the shifting value of the scissors operator; e is the electron charge; ε0 is the dielectric constant in vacuum; m is the mass of free electron; ω is the frequency of the incident wave; h is Planck’s constant; K is the wave vector. Our calculated band gap of CWO is 2.3 eV; that is less than the experimental value. Here we use the scissor approximation to fit the calculated absorption edge to the experimental value of 3.8 eV [6,20–25]. Therefore, the scissor operator of 1.5 eV is chosen for the optical properties calculation. The absorption coefficient is obtained from the following equation [18]:
α = ωεi (ω)/n(ω)c (2) where α is the absorption coefficient, n is the refractive index, c is the speed of light in vacuum. 3. Results and discussion 3.1. Electronic structures Fig. 2 shows the calculated total density of states (TDOS) of perfect CWO (dotted lines) and CWO:VO (solid lines) ranged from −25 eV to 10 eV, and Fig. 3 illustrates the partial density of states (PDOS) of CWO:VO . The main features of our calculated TDOS of perfect CWO are consistent with previous theoretical results [19]. The O 2p state distributes not only in the valence band but also in the conduction band, and the W 5d state also distributes in both the conduction band and the valence band. That is, O would share the valence electrons with W instead of wholly trapping them because of the covalent bond between O and W. The TDOS of CWO:VO is quite similar to that of perfect CWO. However, an extra state is introduced within the band gap. From analyzing the PDOS of CWO:VO , we learn that this new state is mainly contributed to by W 5d state and partly by O 2p state and Cd 5s state. The existence of VO causes significant lattice distortion around it, and then changes the ligand field for the neighboring ions. As a result, the outmost states of those ions split and introduce the new level within the band gap.
X. Zhou et al. / Solid State Communications 150 (2010) 5–8
7
Imaginary part of dielectric function/arb.units
10 calculated values val ues ex experimental perim entalvalues values
1 8 1 6
4
2 3
2
2
4
3 4
0 0
Fig. 2. TDOS of perfect CWO (dotted lines) and CWO:VO (solid lines). The inset shows the new introduced state peak within the forbidden band on an expanded scale.
5
10
15 20 Energy/eV
25
30
Fig. 4. Calculated values (scattered dots) and experimental values (solid lines) of the imaginary part of dielectric function of the perfect CWO for E k a.
9
a
Imaginary part of dielectric function/arb.units
6 3 0
b
9 6 3 0
c
9 6 3
Fig. 3. The PDOS of CWO:VO . The inset shows the PDOS of the new introduced state on an expanded scale.
0 0
5
3.2. Imaginary part of the dielectric function The TDOS and PDOS of CWO:VO indicate that the existence of VO would introduce a new state peak within the band gap which may cause optical absorptions. In order to study the optical absorption properties of CWO:VO , the imaginary part of dielectric function and the absorption coefficient of CWO:VO are discussed, respectively. The imaginary part of the dielectric function is calculated for the electric vector of incident light along [0.9996710 − 0.02565], [0 1 0] or [0 0 1] direction, which is parallel to a axis (E k a), b axis (E k b) or c axis (E k c) of the crystal respectively. Fig. 4 compares our calculated result of for E k a with experimental result [24] in the case of perfect CWO. As shown in Fig. 4, our calculated values agree with the experimental values satisfactorily. Those peaks marked with the same number are located at almost the same region, although the experimental values shift a little to high-energy. Fig. 5 shows our calculated εi of perfect CWO and CWO:VO . The structures in the spectra of εi of perfect CWO exhibit remarkable polarization dependence, which reflects the anisotropy of the lattice structure of CWO. What is more, the spectra of εi of CWO:VO have two new additional structures in the range of about 2.6–3.8 eV, compared with those of the perfect CWO. These additional structures are caused by the oxygen vacancy and new optical absorption would occur in the absorption spectra of the crystal.
10 15 Energy/eV
20
25
Fig. 5. Calculated values of the imaginary part of the dielectric function of perfect CWO (dotted lines) and CWO:VO (solid lines) for (a) E k a, (b) E k b, (c) E k c.
3.3. Absorption spectra The calculated absorption spectra of perfect CWO and CWO:VO for E k a, E k b and E k c are shown in Fig. 6. The spectra of CWO:VO appear as two new absorption bands peaking at about 3.1 eV (413 nm) and 3.5 eV (354 nm), respectively. The new absorption bands are caused by VO that causes a new state within the band gap of the crystal. As mentioned in Section 1, the yellow CWO presents two absorption bands peaking at 400 nm and 350 nm in Ref. [7]. Thus our calculated absorption spectra are in agreement with the experimental results. We therefore conclude that the existence of VO in the CWO would cause the 400 nm and 350 nm absorption bands. 4. Conclusion The electronic structures, dielectric functions and absorption spectra under the polarized light for perfect CWO and CWO:VO have been calculated using CASTEP code. The optical properties of CWO exhibit anisotropic. Our calculated results indicate that the perfect CWO does not show optical absorption in the visible and near-ultraviolet range. However, CWO:VO exhibits two additional absorption bands in this region, which agree with the experimental
8
X. Zhou et al. / Solid State Communications 150 (2010) 5–8
a
15 10
Absorption coefficient/arb.units
5 0 20
b
15 10 5 0
c
15 10 5 0
0
5
10 15 Energy/eV
20
25
Fig. 6. Absorption spectra of perfect CWO (dotted lines) and CWO:VO (solid lines). The insets show the absorption in the region of 2.4–4.0 eV for CWO:VO on an expanded scale, under the incident light with (a) E k a, (b) E k b, (c) E k c.
results. A conclusion is drawn that oxygen vacancy in CWO would cause the 350 nm and 400 nm absorption bands. References [1] M.R. Farukhi, IEEE Trans. Nucl. Sci. NS-29 (1982) 1237–1251. [2] B.C. Grabmaier, IEEE Trans. Nucl. Sci. NS-31 (1984) 372–376.
[3] D.R. Kinloch, W. Novak, P. Raby, I. Toepke, IEEE Trans. Nucl. Sci. 41 (1994) 752–754. [4] L.L. Nagornaya, O.V. Zelenskaya, S.V. Budakovsky, Y.A. Chichikalyuk, IEEE Trans. Nucl. Sci. 43 (1996) 1284–1286. [5] C.L. Melcher, R.A. Manente, J.S. Schweitzer, IEEE Trans. Nucl. Sci. 36 (1989) 1188–1192. [6] S.C. Sabharwal, Sangeeta, J. Cryst. Growth 200 (1999) 191–198. [7] D.S. Robertson, I.M. Young, J. Mater. Sci. 14 (1979) 2967–2974. [8] V.G. Bondara, S.F. Burachasa, K.A. Katrunova, V.P. Martinova, V.D. Ryzhikov, V.I. Mankob, H.H. Gutbrod, G. Tamulaitisd, Nuclear Instrum. Methods A 411 (1998) 376–382. [9] M. Segall, J.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark, M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717–2743. [10] M. Itoh, N. Fujita, Y. Inabe, J. Phys. Soc. Japan 75 (2006) 084705. [11] M. Daturi, M.M. Borel, A. Leclaire, P. Piaggios, J. Phys. Chem. B 101 (1997) 4358–4369. [12] M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias, J.D. Joannopoulos, Rev. Modern Phys. 64 (1992) 1045–1097. [13] V. Milman, B. Winkler, Int. J. Inorg. Mater. 1 (1999) 273–279. [14] R.D. Sole, R. Girlanda, Phys. Rev. B 48 (1993) 11789–11795. [15] C. Ambrosch-Draxl, R. Abt, Synth. Met. 85 (1997) 1099–1100. [16] Z.H. Levine, D.C. Allan, Phys. Rev. Lett. 63 (1989) 1719–1722. [17] R.W. Godby, Top. Appl. Phys. 69 (1992) 51–88. [18] R.C. Fang, Spectroscopy of solid, University of Science and Technology of China, Hefei, 2001 (in Chinese). [19] Y. Abraham, N.A.W. Holzwarth, R.T. Williams, Phys. Rev. B 62 (2000) 1733–1741. [20] K. Tanaka, T. Miyajima, N. Shirai, Q. Zhuang, R. Nakata, J. Appl. Phys. 77 (1995) 6581–6587. [21] R.H. Gillette, Rev. Sci. Instrum. 21 (1950) 294–301. [22] M.M. Chirila, K.T. Stevensa, H.J. Murphyb, N.C. Gilesa, J. Phys. Chem. Solids 61 (2000) 675–681. [23] L. Nagornaya, G. Onyshchenko, E. Pirogov, N. Starzhinskiy, I. Tupitsyna, V. Ryzhikov, Y. Galich, Y. Vostretsov, S. Galkin, E. Voronkin, Nuclear Instrum. Methods A 537 (2005) 163–167. [24] M. Fujita, M. Itoh, T. Katagiri, D. Iri, M. Kitaura, V.B. Mikhailik, Phys. Rev. B 77 (2008) 155118. [25] H.P. Xiao, H.B. Chen, F. Xua, C.Y. Jiang, P.Z. Yang, J. Cryst. Growth 310 (2008) 521–524.
Contents lists available at ScienceDirect
Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Electronic structure and optical properties of CdWO4 with oxygen vacancy studied from first principlesI Xiuwen Zhou a , Tingyu Liu a,b,∗ , Qiren Zhang a , Fang Cheng a , Hailing Qiao a a
College of Science, University of Shanghai for Science and Technology, 516 JunGong Road, Shanghai 200093, China
b
Shanghai Key Laboratory of Contemporary Optics System, China
article
info
Article history: Received 22 May 2009 Received in revised form 27 August 2009 Accepted 15 October 2009 by J. Zhu Available online 18 October 2009 PACS: 71.20.Ps 77.22.Ej 78.20.Bh Keywords: A. CdWO4 crystal C. Oxygen vacancy D. Electronic structure D. Optical properties
abstract The electronic structures, dielectric functions and absorption coefficient of both perfect CdWO4 crystal (CWO) and the CWO crystal containing oxygen vacancy (CWO:VO ) have been studied using the CASTEP code with the lattice structure optimized. The calculated total density of states (TDOS) of CWO:VO indicates that the oxygen vacancy would introduce a new electronic state within the band gap compared with that of perfect CWO. The dielectric functions are calculated since the imaginary part of the dielectric function can reduce the optical absorption of a certain crystal, and then the absorption coefficient is calculated. The calculated absorption spectra show that CWO:VO exhibits two absorption bands in the ultraviolet and visible region, peaking at about 3.0 eV (413 nm) and 3.5 eV (354 nm), respectively, which are in agreement with the experimental results showing that the yellow CWO has two optical absorption bands in this region peaking at around 350 nm and 400 nm respectively. It can be concluded that oxygen vacancy causes these two absorption bands. The calculations also indicate that the optical properties of CWO exhibit anisotropy, and can be explained by the anisotropy of the crystal lattice. © 2009 Elsevier Ltd. All rights reserved.
1. Introduction Cadmium tungstate (CdWO4 ) single crystal is a commercially viable scintillator because of its excellent properties such as high light yield, short radiation length, high density and the radiation stability with varied temperature [1–3]. The scintillating emission from CdWO4 crystal (CWO) is intrinsic and peaks around 490 nm [2]. This spectral range allows this scintillator to be coupled to both photomultiplier tube and photo diodes. With these features, CWO is considered for X-ray computer tomography (CT) and introscope [1], high-energy nuclear spectroscopy [4], and oil well logging [5] applications. However, defects may deteriorate the light yield and decrease the transmissivity of the crystal, which are formed during the
I Supported by the Scientific Development Foundation of Shanghai Municipal Education Committee, China (Grant No. 09YZ210) and the Shanghai Leading Academic Discipline Project (S30502) and the Programs (No. 07DZ22026) from Shanghai Committee of Science & Technology. ∗ Corresponding author at: College of Science, University of Shanghai for Science and Technology, 516 JunGong Road, Shanghai 200093, China. Tel.: +86 021 55272483; fax: +86 021 55274057. E-mail addresses: [email protected], [email protected] (T. Liu).
0038-1098/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ssc.2009.10.019
process of crystal growth or after the irradiation of high-energy rays. Sabharwal and Sangeeta [6] supposed that the optical absorption of CWO in the region of 325–500 nm was relevant to the structural defects based on the fact that CdO was easier to evaporate than WO3 . Robertson et al. [7] reported that both the spectra of pale yellow and orange CWO showed two absorption bands peaking at about 350 nm and 400 nm, respectively. They predicted that the 350 nm band was caused by a structural defect and the 400 nm band resulted from a metallic ion impurity. Bondar et al. [8] also suggested the absorption bands in their optical spectra were associated with the oxygen-related structural defects. All these experiments suggest that the color of undoped CWO may be caused by the intrinsic defects in the crystal. Thus, it is important to understand the intrinsic defects in the crystal and how they affect the optical properties of CWO. However, there are few theoretical studies on these defects, of which the electronic structure and optical properties remain unclear. In this work, we focus on the oxygen vacancy (VO ) in CWO. The electronic structures and optical properties, such as the density of states (DOS), dielectric functions and absorption spectra under polarized light for both the perfect CWO and the CWO crystal containing oxygen vacancy (CWO:VO ), are theoretically studied by the Cambridge Serial Total Energy Package (CASTEP) code [9].
6
X. Zhou et al. / Solid State Communications 150 (2010) 5–8
Cd O1
Crystal parameter
W O1
O2
Table 1 Crystal parameters and atomic positions (x; y; z ) used in the present calculations.
a = 5.026 Å b = 5.867 Å c = 5.078 Å β = 91.47◦
O
O2 O2 b O2
O1
c O1
β a
Fig. 1. Lattice structure of CWO.
2. Computational model and methods 2.1. Computational model CWO has the wolframite-type structure [10], which is in the monoclinic class and has the space group of P2/c (No. 13), as illustrated in Fig. 1. In this structure, each W and Cd is surrounded by six Os. The resultant WO6 octahedra form a chain by edge sharing, so that there are two energetically distinct O positions in the lattice. Type 1 (O1 ) forms a bond to one tungsten atom with a very short bond length. Type 2 (O2 ) connects to two different W atoms with longer bond lengths. The crystal parameters and atomic positions (x, y, z ) used in the present calculations are listed in Table 1 [11]. The calculating model for CWO:VO is a super-cell (2 × 2 × 2 unit cell) with an O atom removed. According to our calculation, the total energy for the 95-atom-system with an O1 vacancy and an O2 vacancy are −707.786 eV and −707.269 eV, respectively. The formation energy of an O2 vacancy is 0.517 eV less than that of an O1 vacancy. Thus, the former is more energetically favorable than the latter in the crystal. Therefore, an O2 atom is removed from the super-cell to simulate CWO:VO . 2.2. Computational methods The approach used in this work is density functional theory (DFT) using the generalized gradient approximation in the form of Perdew-Wang-91 (GGA-PW91) combined with nonlocal, ultra-soft pseudopotentials and plane wave expansions in the CASTEP program [12,13]. For the ground-state electronic structure calculations, the valence electronic configurations are 4d10 5s2 for Cd, 5d4 6s2 for W and 2s2 2p4 for O. The GGA calculations use Brillouin-zone sampling with 2×2×2 grid of Monkhorst–Pack kpoints and plane-wave cutoff energies of 340 eV; fast Fourier transform (FFT) grid dimensions are 60 × 60 × 64 and space representation is reciprocal. Self-consistent field (SCF) tolerance is 1.0 × 10−6 eV/atom. Lattice optimization is necessary for calculation in order to obtain believable results. In every case, the geometrical optimization is made and convergence is assumed when: the forces on the lattice ions are less than 0.5 eV/nm; the changes of energy per atom are less than 0.00001 eV; and the atomic displacements are less than 0.0001 nm. The dielectric function of an anisotropic crystal is a complex second-order tensor describing the linear response of an electronic system to an applied external electric field. The imaginary part of the dielectric tensor directly relates to the band structure of a material and can be computed from the knowledge of singleparticle orbital and energy approximated by the solutions of
Atomic positions (fractional coordinates) Atom
x
y
z
Cd W O1 O2
0.5 0 0.189 0.250
0.75 0.25 0.454 0.393
0.302 0.1784 0.901 0.360
the Kohn–Sham equations. However, it is well known that DFT calculations underestimate the band gap. Therefore, a ‘‘scissors operator’’ [14–16] is used for correction. The scissors operator allows a shift of the bands situated above the valence band and then rescales the matrix elements to fit the band gap to the real value. It is computationally shown (in comparison of the GW and LDA band structures) that most of the differences between Kohn–Sham eigenvalues and the true excitation energies can be accounted by a upward rigid shift of the conduction band with respect to the valence band [17]. Assuming the one-electron rigidband approximation, and neglecting the electron polarization effects (Koopmans’ approximation), in the limit of linear optics and of the visible–ultraviolet range, the imaginary part of dielectric function εi is given by [18,19]
εi (ω) =
e2 π 2
ε0 m2 (ω − ∆C /h¯ )2 X Z 2dK 2 × | a · M | δ[ E ( K ) + ∆ c − E ( K ) − h ω] (1) ¯ v, c c v 3 BZ (2π ) V ,C
where a is the unit vector of potential A; Mv,c is the matrix of dipole transition; C is the conduction band; V is the valence band. BZ denotes the Brillouin zone; ∆c is the shifting value of the scissors operator; e is the electron charge; ε0 is the dielectric constant in vacuum; m is the mass of free electron; ω is the frequency of the incident wave; h is Planck’s constant; K is the wave vector. Our calculated band gap of CWO is 2.3 eV; that is less than the experimental value. Here we use the scissor approximation to fit the calculated absorption edge to the experimental value of 3.8 eV [6,20–25]. Therefore, the scissor operator of 1.5 eV is chosen for the optical properties calculation. The absorption coefficient is obtained from the following equation [18]:
α = ωεi (ω)/n(ω)c (2) where α is the absorption coefficient, n is the refractive index, c is the speed of light in vacuum. 3. Results and discussion 3.1. Electronic structures Fig. 2 shows the calculated total density of states (TDOS) of perfect CWO (dotted lines) and CWO:VO (solid lines) ranged from −25 eV to 10 eV, and Fig. 3 illustrates the partial density of states (PDOS) of CWO:VO . The main features of our calculated TDOS of perfect CWO are consistent with previous theoretical results [19]. The O 2p state distributes not only in the valence band but also in the conduction band, and the W 5d state also distributes in both the conduction band and the valence band. That is, O would share the valence electrons with W instead of wholly trapping them because of the covalent bond between O and W. The TDOS of CWO:VO is quite similar to that of perfect CWO. However, an extra state is introduced within the band gap. From analyzing the PDOS of CWO:VO , we learn that this new state is mainly contributed to by W 5d state and partly by O 2p state and Cd 5s state. The existence of VO causes significant lattice distortion around it, and then changes the ligand field for the neighboring ions. As a result, the outmost states of those ions split and introduce the new level within the band gap.
X. Zhou et al. / Solid State Communications 150 (2010) 5–8
7
Imaginary part of dielectric function/arb.units
10 calculated values val ues ex experimental perim entalvalues values
1 8 1 6
4
2 3
2
2
4
3 4
0 0
Fig. 2. TDOS of perfect CWO (dotted lines) and CWO:VO (solid lines). The inset shows the new introduced state peak within the forbidden band on an expanded scale.
5
10
15 20 Energy/eV
25
30
Fig. 4. Calculated values (scattered dots) and experimental values (solid lines) of the imaginary part of dielectric function of the perfect CWO for E k a.
9
a
Imaginary part of dielectric function/arb.units
6 3 0
b
9 6 3 0
c
9 6 3
Fig. 3. The PDOS of CWO:VO . The inset shows the PDOS of the new introduced state on an expanded scale.
0 0
5
3.2. Imaginary part of the dielectric function The TDOS and PDOS of CWO:VO indicate that the existence of VO would introduce a new state peak within the band gap which may cause optical absorptions. In order to study the optical absorption properties of CWO:VO , the imaginary part of dielectric function and the absorption coefficient of CWO:VO are discussed, respectively. The imaginary part of the dielectric function is calculated for the electric vector of incident light along [0.9996710 − 0.02565], [0 1 0] or [0 0 1] direction, which is parallel to a axis (E k a), b axis (E k b) or c axis (E k c) of the crystal respectively. Fig. 4 compares our calculated result of for E k a with experimental result [24] in the case of perfect CWO. As shown in Fig. 4, our calculated values agree with the experimental values satisfactorily. Those peaks marked with the same number are located at almost the same region, although the experimental values shift a little to high-energy. Fig. 5 shows our calculated εi of perfect CWO and CWO:VO . The structures in the spectra of εi of perfect CWO exhibit remarkable polarization dependence, which reflects the anisotropy of the lattice structure of CWO. What is more, the spectra of εi of CWO:VO have two new additional structures in the range of about 2.6–3.8 eV, compared with those of the perfect CWO. These additional structures are caused by the oxygen vacancy and new optical absorption would occur in the absorption spectra of the crystal.
10 15 Energy/eV
20
25
Fig. 5. Calculated values of the imaginary part of the dielectric function of perfect CWO (dotted lines) and CWO:VO (solid lines) for (a) E k a, (b) E k b, (c) E k c.
3.3. Absorption spectra The calculated absorption spectra of perfect CWO and CWO:VO for E k a, E k b and E k c are shown in Fig. 6. The spectra of CWO:VO appear as two new absorption bands peaking at about 3.1 eV (413 nm) and 3.5 eV (354 nm), respectively. The new absorption bands are caused by VO that causes a new state within the band gap of the crystal. As mentioned in Section 1, the yellow CWO presents two absorption bands peaking at 400 nm and 350 nm in Ref. [7]. Thus our calculated absorption spectra are in agreement with the experimental results. We therefore conclude that the existence of VO in the CWO would cause the 400 nm and 350 nm absorption bands. 4. Conclusion The electronic structures, dielectric functions and absorption spectra under the polarized light for perfect CWO and CWO:VO have been calculated using CASTEP code. The optical properties of CWO exhibit anisotropic. Our calculated results indicate that the perfect CWO does not show optical absorption in the visible and near-ultraviolet range. However, CWO:VO exhibits two additional absorption bands in this region, which agree with the experimental
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X. Zhou et al. / Solid State Communications 150 (2010) 5–8
a
15 10
Absorption coefficient/arb.units
5 0 20
b
15 10 5 0
c
15 10 5 0
0
5
10 15 Energy/eV
20
25
Fig. 6. Absorption spectra of perfect CWO (dotted lines) and CWO:VO (solid lines). The insets show the absorption in the region of 2.4–4.0 eV for CWO:VO on an expanded scale, under the incident light with (a) E k a, (b) E k b, (c) E k c.
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