CHIN. PHYS. LETT. Vol. 28, No. 7 (2011) 077101
Electronic Structure and Optical Properties of SrBi2 A2 O9 (A=Nb,Ta)
*
ZHAO Na(赵娜), WANG Yue-Hua(王月花)** , ZHAO Xin-Yin(赵新印), ZHANG Min(张旻), GONG Sai(龚赛) Department of Physics, China University of Mining and Technology, Xuzhou 221116
(Received 3 January 2011) The first-principles calculation is performed to investigate the energy band structures, density of states (DOS) and optical properties of SrBi2 A2 O9 (𝐴 = 𝑁 𝑏, 𝑇 𝑎), by using density functional theory (DFT) with the generalized gradient approximation (GGA). The results show that the band-gap of SrBi2 Nb2 O9 is smaller than that of SrBi2 Ta2 O9 , and that there are strong hybridizations of A-O bands, which play very important roles in the electronic properties and optical responses of SrBi2 A2 O9 . SrBi2 Ta2 O9 stimulates much higher photocatalytic activity than SrBi2 Nb2 O9 , which is due to its suitable crystal structure.
PACS: 71.15.Mb, 73.20.At, 78.20.Ci
DOI:10.1088/0256-307X/28/7/077101
In recent years, there has been considerable interest in ferroelectric Aurivillius compounds,[1−4] which are widely used in a new generation of devices. Among these materials, SrBi2 A2 O9 (A = Nb, Ta) are technologically important materials and widely used as nonvolatile ferroelectric memories, nonlinear optical devices and photocatalysts owing to their remarkable characteristics such as high dielectric constant, good retention, low switching fields, low leakage currents and free fatigue.[5,6] The crystal lattice of SrBi2 A2 O9 consists of perovskite-like layers with composition [(SrA2 O7 )2− ]𝑚 interspersed between [(Bi2 O2 )2+ ]𝑚 layers with the divalent Sr cations being located between the corner-sharping AO6 octahedra within the perovskite-like layer.[7] Spontaneous polarization of these materials can be ascribed to the displacement of the A cations as well as a tilting of the AO6 octahedra.[8−10] In addition, photocatalytic splitting of water into H2 and O2 using oxide semiconductor powder is an attractive solution to supply clean and recyclable hydrogen energy. SrBi2 A2 O9 (A = Nb, Ta) have the characteristic layered structures of perovskite and have been demonstrated to be highly active photocatalysts under UV-light irradiation.[11,12] Their interlayer space is used as reaction sites, where electron-hole recombination process can be retarded by the physical separation of electron and hole pairs generated by photoabsorption resulting in the higher photocatalytic activities of these layered photocatalysts for water splitting.[13,14] In order to gain a better understanding of the characteristics of the SrBi2 A2 O9 , it is important to investigate the properties of the compounds. In this Letter, the energy band structures, density of states (DOS), optical properties of SrBi2 A2 O9 (A = Nb, Ta) are calculated, and their photocatalytic properties are also compared. In addition, the dielectric function, absorption coefficient, extinction coefficient, electron energy
loss function, the real part of optical conductivities and refractive index are obtained. The full potential linearized augmented plane wave (FP-LAPW)[15] method with the generalized gradient approximation (GGA) is applied to study the electronic band structure and optical properties of SrBi2 A2 O9 (A = Nb, Ta). The exchange correlation potential can be treated using several approximations in the framework of the GGA. Since GGA has a tendency to enhance electron localization, our calculations are performed without any shape approximations on either potential or electronic charge density.[16] We use the Wien2k implementation, which allows the inclusion of local orbits in the basis, improving linearization and making possible a consistent treatment of semicore and valence states in one energy window, hence ensuring proper orthogonality.[17] The crystal structure of the SrBi2 A2 O9 is orthorhombic, space group 𝐴21 𝑎𝑚. Lattice parameters 𝑎 = 0.5519 nm, 𝑏 = 0.5515 nm, 𝑐 = 2.5112 nm for SrBi2 Nb2 O9 (SBN);[8] and 𝑎 = 0.5527 nm, 𝑏 = 0.5522 nm, 𝑐 = 2.5028 nm for SrBi2 Ta2 O9 (SBT)[7] are relaxed in our calculations. The convergence parameter 𝑅𝐾max , which determines the matrix size in these calculations, is set to be 7.5. Here, the 𝑘-point in the entire Brillouin zone is set to be 150. The selfconsistent calculations are considered to be well converged when the total energy of the system is stable within 0.0001 Ry. The calculated electronic energy band structures along several high symmetry directions in the Brillouin zone are shown in Fig. 1. It is shown that the fundamental band-gap is direct for SrBi2 Nb2 O9 , since the top of the valence band (VB) and the bottom of the conduction band (CB) are all at point Γ(Fig. 1(a)). Our theoretical value is 2.10 eV while the experimental band-gap is 3.43 eV.[11] The fundamental bandgap is indirect for SrBi2 Ta2 O9 , since the valence band
* Supported
by the Fundamental Research Funds for the Central Universities (No 2010LKWL06).
[email protected] © 2011 Chinese Physical Society and IOP Publishing Ltd ** Email:
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CHIN. PHYS. LETT. Vol. 28, No. 7 (2011) 077101
maximum lies at 𝑀 while the conduction band minimum is at point Γ (Fig. 1(b)). Our theoretical value is 2.28 eV while the experimental band-gap is 3.64 eV[12] for SrBi2 Ta2 O9 . The calculated band-gaps are smaller than those obtained experimentally, which come from some flaws in the GGA and have been pointed out as a common feature of DFT calculations.[17,18]
and are similar to each other. The bottom of the CB is formed by Bi 6𝑝, Nb 4𝑑 (Ta 5𝑑) and O 2𝑝 states. The peak height of the Nb 4𝑑 state is 1.729 for SrBi2 Nb2 O9, while the peak of the Ta 5𝑑 state is 1.311 for SrBi2 Ta2 O9 , which shows that the localization characteristic of Nb 4𝑑 electrons is stronger than that of Ta 5𝑑 electrons.
9
A
1 0
6
S r B
2
N
b
2
O
( b )
S r B
9
i
2
T
a
O
2
9
'
B
'
6
C
- 3
S r B
i
S r B
i
2
2
N
b
T
a
2
2
O O
9
9
B
2
i
) ( e V
( a )
0
C D
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4
E
n e r g y
8
3
A
E
- 6
E
' F
F
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G
H
'
H
'
2
- 9
D
Λ
R
∆
Γ
Ζ
X
Μ
Σ
Γ
Λ
R
Γ
∆
Ζ
X
Μ
Σ
Γ
Fig. 1. Calculated band structure of SrBi2 Nb2 O9 and SrBi2 Ta2 O9 along the high symmetry directions in the Brillouin zone. The horizontal dotted lines denote the Fermi level. i
2
N
b
2
O
2
T
a
2
O
3 0 ( e V
4 0
)
Fig. 3. Calculated imaginary parts of the dielectric function for SrBi2 Nb2 O9 and SrBi2 Ta2 O9 along the (100) direction.
t o t
9
9
1
6
S r B
i
S r B
i
2
2
N
b
T
a
2
2
O O
9
9
3 0
S r
5
S r S r
5
4
S r
S r
4
S r
3
1 0 0
0
5
B
i
6
B
i B
B
i
6
i
5
i
6
B
i
1 . 0
0 . 5
0 . 0 3
B
i
)
i
1 . 5
6
2
(
B B
(
)
3
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1
0
6
b
4
2
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N
b
4
N
b
b
4
)
b
T T
a
5
T
a
4
a
5
T
a
5
O
O 2
O
2
2
O
2
10
2
3
)
0 30 O
4
0
4
T
a
(
N N
S O D
i
n e r g y
2 0 0
0 4 3 2 1 0 6
20
S r B
S r
4
4
( b )
t o t
9
2 0 E
S r B
1 0
8
( a )
0
(
100 75 50 25 0 12
0
O
2
1
0
0 O
2
O
2
1 0
2 0
E
n e r g y
3 0
( e V
4 0
)
0 - 30 - 20 - 10 E
0
n e r g y ( e V
10 )
20
- 30 - 20 - 10 E
0
n e r g y ( e V
10
20
)
Fig. 2. Total and partial density of states of SrBi2 Nb2 O9 and SrBi2 Ta2 O9 , showing the energy position of the semicore states.
Figure 2 shows the density states of the ferroelectric phase SrBi2 Nb2 O9 and SrBi2 Ta2 O9 between −35 eV and 20 eV. Here only the majority channels are shown. In order to make small peaks clear, we cut off higher peaks in Fig. 2. The DOS of SrBi2 Nb2 O9 slightly shifts to the lower energy, which favors the structural stabilization of SrBi2 Nb2 O9 . The lower energy bands at about −10 eV consist of Bi 6𝑠 and O 2𝑝 states. The peak heights of the Bi 6𝑠 states are 1.117 for SrBi2 Nb2 O9 and 0.9893 for SrBi2 Ta2 O9 , which indicates the stronger Bi-O hybrid orbital in SrBi2 Nb2 O9 than that in SrBi2 Ta2 O9 . The part between −6 and 0 eV, corresponding to the VB, is made up of Bi 6𝑝, Nb 4𝑑 (Ta 5𝑑) and O 2𝑝 states,
Fig. 4. The calculated optical parameters of SrBi2 Nb2 O9 and SrBi2 Ta2 O9 as a function of the photon energy along the (100) direction: the real part of the dielectric function 𝜀1 (𝑤), the absorption coefficient 𝐼(𝑤), extinction coefficient 𝐾(𝑤), electron energy loss function 𝐿(𝑤), the real part of optical conduction 𝜎𝑟 (𝑤) and refractive index 𝑛(𝑤).
The O 2𝑝 states have admixture with the Bi 6𝑠, Nb 4𝑑 and Sr 3𝑑 states, and the orbital hybridizations of Nb-O bands are much stronger than that of Sr-O and Bi-O bands, as shown in Fig. 2 (a). As shown in Fig. 2 (b), the orbital hybridization of Ta-O bands is stronger than that of Sr-O and Bi-O bands, while it is weaker than that of Nb-O bands in SrBi2 Nb2 O9 , which is derived from the enhancement of the orbital hybridization locality in SrBi2 Nb2 O9 . Strong hybridization between Nb-O bands in SrBi2 Nb2 O9 plays an important role in stable ferroelectricity.[19] The VB maximum value of SrBi2 Nb2 O9 is 0.146 eV and that of SrBi2 Ta2 O9 is 0.159 eV. The CB mini-
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to 9 eV except the shift of the band-gap, but the total density of states of SrBi2 Ta2 O9 is different from that of SrBi2 Nb2 O9 because of the existence of Ta 4𝑓 and Ta 5𝑝 states in the VB. Those at about −18.7 eV mainly arise from Ta 4𝑓 states with a sharp peak due to its strong localization characteristic. The Ta 5𝑝 states are stronger at lower energy than the Nb 4𝑝 states. Our results are in good agreement with the previously calculated result and the experimental result.[19,20]
mum of SrBi2 Nb2 O9 is 1.94 eV and that of SrBi2 Ta2 O9 is 2.12 eV. It is clear that the valence bands of SrBi2 Nb2 O9 are close to that of SrBi2 Ta2 O9 , while the conduction bands move to the lower energy, which is due to the hybridization of the Nb 4𝑑 and O 2𝑝 oribitals. As a result, the energy gap of SrBi2 Nb2 O9 is smaller than that of SrBi2 Ta2 O9 , which is in accordance with the experimental results. The calculated electronic structure of SrBi2 Ta2 O9 is essentially the same as that of SrBi2 Nb2 O9 in the range from −10 Table 1. Electron transition of each peak. SrBi2 Nb2 O9 A (6.2 eV) B (8.86 eV) C (9.9 eV) D (11.4 eV) E (14 eV) F (17 eV) G (20.7 eV) H (35.9 eV) H (35.9 eV)
Electron transition O 2𝑝 (VB) to Nb 4𝑑 (CB) O 2𝑝 (VB) to Sr 3𝑑 (CB) O 2𝑝 (VB) to Nb 4𝑑 (CB) or Sr 3𝑑 (CB) O 2𝑝 (VB) to Nb 4𝑑 (CB) or Sr 4𝑑 (CB) Bi 6𝑠 (VB) to Nb 4𝑑 (CB) Sr 4𝑝 (VB) or O 2𝑠 (VB) to Nb 4𝑑 (CB) Bi 6𝑠 (VB) to Sr 3𝑑 (CB) Bi 5𝑑 (VB) to Sr 3𝑑 (CB) or Sr 5𝑠 (VB) to Nb 4𝑑 (CB)
SrBi2 Ta2 O9 A’ (7.2 eV) B’ (7.8 eV) C’ (9.9 eV) D’ (11.1 eV) E’ (13.6 eV) F’ (17.3 eV) G’ (24.4 eV) H’ (40.4 eV) H’ (40.4 eV)
Electron transition O 2𝑝 (VB) to Ta 5𝑑 (CB) O 2𝑝 (VB) to Sr 3𝑑 (CB) O 2𝑝 (VB) to Ta 5𝑑 (CB) or Sr 3𝑑 (CB) O 2𝑝 (VB) to Ta 5𝑑 (CB) or Sr 4𝑑 (CB) Bi 6𝑠 (VB) to Ta 5𝑑 (CB) Sr 4𝑝 (VB) or O 2𝑠 (VB) to Ta 5𝑑 (CB) O 2𝑠 (VB) to Sr 3𝑑 (CB) Ta 5𝑝 (VB) to Bi 6𝑝 (CB) or Sr 5𝑠 (VB) to Ta 5𝑑 (CB)
Table 2. Photocatalytic activities of SrBi2 Nb2 O9 and SrBi2 Ta2 O9 . Catalyst SrBi2 Nb2 O9
SrBi2 Ta2 O9
Bond angle (A-O-A)/degree
Bond length (A-O)/nm
𝑥𝑜𝑦 plane in middle layer: 155.456 𝑦𝑜𝑧 plane in the middle layer: 164.296 𝑥𝑜𝑦 plane in both ends: 156.618 𝑥𝑜𝑦 plane in the middle layer: 156.772 𝑦𝑜𝑧 plane in the middle layer: 167.773 𝑥𝑜𝑦 plane in both ends: 169.549
0.1887, 0.2245, 0.1861, 0.2001, 0.2145, 0.1943,
The optical properties of SrBi2 A2 O9 are determined by the frequency-dependent dielectric function 𝜀(𝑤) = 𝜀1 (𝑤) + 𝑖𝜀2 (𝑤), which is closely connected with the electronic structures. The imaginary part 𝜀2 (𝑤) of the dielectric function 𝜀(𝑤) is calculated from the momentum matrix elements between the occupied and unoccupied orbitals within selection rules. The real part 𝜀1 (𝑤) of the dielectric function 𝜀(𝑤) can be derived from the imaginary part 𝜀2 (𝑤) using the Kramers–Kronig dispersion equation. The absorption coefficient 𝐼(𝑤), electron energy loss function 𝐿(𝑤), extinction coefficient 𝐾(𝑤), the real part of optical conduction 𝜎𝑟 (𝑤) and refractive index 𝑛(𝑤) can be derived from 𝜀1 (𝑤) and 𝜀2 (𝑤).[17,21] Figure 3 shows the dielectric function of SrBi2 A2 O9 (A=Nb,Ta) along the (100) direction. We emphasize the incident radiation with linear polarization and focus on the imaginary part 𝜀2 (𝑤), which reflects the optical absorbing properties. The peaks of SrBi2 Ta2 O9 move to the higher energy and slightly decrease, which may be attributed to the influence of the density of Ta ions. The corresponding electron transitions are shown in Table 1. The obvious differences in B (8.86 eV) and B’ (7.8 eV) are due to the
0.2213 0.2245 0.2195 0.1978 0.2145 0.1989
band-gap ( eV)
Activity (mmol/h) H2 O2
2.10
0.732
0.106
2.28
2.26
0.12
movement of Sr 3𝑑 electrons (CB). The diversity of peak H (35.9 eV) and H’ (40.4 eV) mainly arises from Ta 4𝑓 states with a sharp peak due to its strong localization characteristic. Intra-band transitions also play an important role on these peaks. The optical property of peaks F, G, H, F’, G’ and H’ are ascribed to transitions of inner electron excitation. Note that every peak of 𝜀2 (𝑤) does not correspond to a single inter-band transition, since many direct or indirect transitions can be found in the band structure with an energy corresponding to the same peak.[17] The real part of the dielectric function 𝜀1 (𝑤), absorption coefficient 𝐼(𝑤), extinction coefficient 𝐾(𝑤), electron energy loss function 𝐿(𝑤), the real part of optical conductivities 𝜎𝑟 (𝑤) and refractive index 𝑛(𝑤) versus photon energy are plotted in Fig. 4. Static dielectric constants are 5.09 and 4.90 for SrBi2 Nb2 O9 and SrBi2 Ta2 O9 , respectively. The static refractive index decreases from 2.26 for SrBi2 Nb2 O9 to 2.21 for SrBi2 Ta2 O9 . The peaks of SrBi2 Ta2 O9 move to the high energy. The photocatalytic activities of SrBi2 Nb2 O9 and SrBi2 Ta2 O9 are shown in Table 2. It is found that SrBi2 Ta2 O9 stimulates much higher photocatalytic
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CHIN. PHYS. LETT. Vol. 28, No. 7 (2011) 077101
activity than SrBi2 Nb2 O9 . First, the bond angle of Ta-O-Ta is closer to 180∘ than that of Nb-O-Nb. The bond angle of A-O-A (A=Nb,Ta) is one of the important factors affecting the photocatalytic properties of the compounds. The closer the bond angle of A-O-A is to the ideal 180∘ , the greater the excitation energy is delocalized. Then the photogenerated electron-hole pairs move more easily. The mobility of electron-hole pairs affects the photocatalysis because it affects the probability of electrons and holes reaching reaction sites on the surface of the photocatalyst.[12] Second, the bond length of A-O is another important factor. The average bond length of SrBi2 Ta2 O9 (0.2033 nm) is shorter than that of SrBi2 Nb2 O9 (0.2108 nm). The shorter the bond length of A-O is, the more stable the electron-hole pairs are, and a shorter bond length favors the creation of more electron-hole pairs. Finally, larger band-gaps are good for stimulating more photocatalytic activity.[22] The band-gap of SrBi2 Nb2 O9 is 2.10 eV while the band-gap of SrBi2 Ta2 O9 is 2.28 eV. In addition, the total densities of states of SrBi2 Nb2 O9 and SrBi2 Ta2 O9 exhibit a sharp rise near the edges of both valence and conduction bands, reflecting a larger number of effective states available for the photoinduced electrons and holes.[23] In summary, the energy band structures, density of states, dielectric function, optical properties and photocatalytic activities of the Aurivillius-type compounds SrBi2 A2 O9 (A = Nb, Ta) have been investigated by using the first principle. The results show that band-gap increases from SrBi2 Nb2 O9 to SrBi2 Ta2 O9 , which is in agreement with the experimental result. A (A = Nb, Ta) 𝑑 states at the conduction band edge have an important influence on the electronic responses and optical properties of
SrBi2 A2 O9 (A = Nb, Ta). The oribital hybridization of Nb-O bands in SrBi2 Nb2 O9 is stronger than that of Ta-O bands in SrBi2 Ta2 O9 , which results in the narrower band-gap in SrBi2 Nb2 O9 . The difference in their photocatalytic activities is ascribed to their special crystal and electronic structure, such as larger bond angle, shorter bond length, larger band-gap and more suitable energy structure.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]
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Aurivillius B 1949 Ark. Kemi. 1 463 Kennedya B J et al 2008 J Solid State Chem. 181 1377 Kennedy B J et al 2003 Solid State Commun. 126 653 Graves P R et al 1995J. Solid State Chem. 114 112 Dhage S R et al 2006 Mater. Chem. Phys. 98 344 Watanabe T and Funakubo H 2005 J. Solid State Chem. 178 64 Macquart R and Kennedy B J 2001 J. Solid State Chem. 160 174 Ismunandar and Kennedy B J 1996 J. Solid State Chem. 126 135 Blake S M et al 1997 J. Mater. Chem. 7 1609 Subbarao E C 1962 J. Phys. Chem. Solids 23 665 Li Y X et al 2010 Int. J. Hydrogen Energy 35 2652 Li Y X et al 2008 J. Solid State Chem. 181 2653 Shimizu K I et al 2004 Phys. Chem. Chem. Phys. 6 1064 Kudo A et al 2000 J. Phys. Chem. B 104 571 Cohen R E and Krakauer H 1990 Phys. Rev. B 42 6416 Sawada H, Hamada N and Terakura K 1997 Physica B 237238 46 Sai G et al 2010 Chin. Phys. Lett. 27 037103 Feng Z B et al 2008 Solid State Commun. 148 472 Stachiotti M G et al 2000 Phys. Rev. B 61 14434 Zhang J, Yin Z and Zhang M S 2002 Appl. Phys. Lett. 81 4778 Saha S and Sinha T P 2000 Phys. Rev. B 62 8828 Wang G Y, Wang Y J and Song B J 2002 J. Hebei University of Technology 31 1 (in Chinese) Hu C C and Teng H 2007 Appl. Catal. A Gen. 331 44
