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First Principles Calculations of Electronic Band Structure and Optical Properties of Cr-Doped ZnO Luyan Li,† Weihua Wang,† Hui Liu,*,† Xindian Liu,‡ Qinggong Song,§ and Shiwei Ren⊥ Department of Electronics, Nankai UniVersity, Tianjin 300071, China, Department of Physics, Tianjin UniVersity, Tianjin 300072, China, College of Science, CiVil AViation UniVersity of China, Tianjin 300300, China, and Department of Applied Physics, Hebei UniVersity of Science and Technology, Shijiazhuang 050018, Hebei ProVince, China ReceiVed: December 31, 2008; ReVised Manuscript ReceiVed: February 27, 2009
Electronic band structure and optical properties of Cr-doped ZnO were studied using the density functional method within the generalized-gradient approximation. Three configurations with the substitution of Zn by one and two Cr atoms in different positions were considered. For the pure ZnO, the Fermi level locates at the valence band maximum, while it shifts to the conduction band and exhibits metal-like characteristic after Cr atoms are introduced into the ZnO supercell. The calculated optical properties indicate that the optical energy gap is increased after Cr doping. More importantly, strong absorption in the visible-light region is found, which originates from the intraband transition of the Cr 3d bands and the conduction bands. Our calculations provide electronic structure evidence that, in addition to usage as short-wavelength optoelectronic devices, the Cr-doped ZnO system could be a potential candidate for photoelectrochemical application due to the increase in its photocatalytic activity. 1. Introduction Since the discovery of the photoinduced decomposition effect of water on TiO2 electrodes,1 semiconductor-based photocatalytic reactions have attracted intensive attention. Photocatalysis is a complicate progress which originates from the generation of electrons and holes caused by the photoexcitation of semiconductors. Up to now, many efforts have been focused on the search for new photocatalytic materials based on TiO2, ZnO, NaBiO3, and ZnS.2-7 Among them, ZnO-based photocatalysts have been paid much attention because of its excellent properties, such as high chemical stabilizations, nontoxicity, abundance in nature, a wide direct band gap of 3.3 eV, and a large exciton binding energy of 60 meV,8,9 which make ZnO an attractive versatile material applied in short-wavelength optoelectronics devices, transparent conducting layers for displays, photocatalysts, etc.4,10,11 It has been well-documented now that ZnO is superior over other semiconductors such as TiO2 in producing hydrogen peroxide, which allows ZnO-based photocatalysts to be more efficient in photodegradation of organic acid and sterilization of bacteria and viruses.12-16 It is known that ultraviolet (UV) light accounts for a small fraction of the solar energy (∼5%), whereas visible light accounts for a large fraction of it (∼45%).17 However, as a potential photocatalyst for the degradation of various environmental pollutants in air or water, the large band gap (∼3.3 eV) of pure ZnO makes it exhibit photocatalytic activity only under the UV-light region. Therefore, to fulfill the application of ZnO as a photocatalytic material, the greatest challenge is to achieve a higher absorption coefficient in the visible region for the effective utilization of sunlight. Recently, research works have proved that intentional impurity doping with C, S, N, and Mg * Corresponding author. E-mail:
[email protected]. † Nankai University. ‡ Tianjin University. § Civil Aviation University of China. ⊥ Hebei University of Science and Technology.
would manipulate the optical and electrical properties of the ZnO host,12,18,19 and it has been proven that impurity doping is a good method for realization of photocatalytic activity under the visible light region. For example, Chen et al.18 found that high-temperature calcined N-, S-, and C-doped ZnO showed strong visible light absorption, and an appropriate amount of dopants would reduce the recombination of electron-hole pairs and raise the photocatalytic activity under UV and visible light illumination. Li et al.19 indicated that the photocatalytic performance of the sprayed N-doped ZnO powder was superior to that of a pure ZnO sample under visible light irradiation. The experimental and calculation results by Qiu et al.12 also showed that Mg-doped ZnO samples exhibited enhanced photocatalytic activity. However, compared with the well-studied TiO2 system, reports on the photocatalytic properties of ZnO are scarce. Theoretical investigation of the electronic band structure and optical properties based on ZnO system is important for better understanding the photocatalytic mechanism of these photocatalysts to promote study of their applications. In this paper, we report our theoretical study of Cr-doped ZnO systems using first principles calculations based on density function theory (DFT). Four different structure configurations, which correspond to a Cr concentrations of x ) 0, 6.25, and 12.5% were employed to investigate the doping effect of Cr. The electronic band structure, the density of states (DOS), and the optical properties of Cr-doped ZnO systems were systematically studied. Finally, the possible reasons for the significantly improved photocatalytic activity in the visible-light region were investigated. To the best of our knowledge, few theoretical studies have been reported on the optical properties in the UV-visible light regions of Crdoped ZnO system. 2. Calculation Models and Method On the basis of the wurtzite ZnO unit cell, the 2 × 2 × 2 supercell containing 32 atoms is adopted for pure ZnO, as shown
10.1021/jp811507r CCC: $40.75 2009 American Chemical Society Published on Web 04/20/2009
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Figure 1. The schematic 32-atom supercell used in the calculations. Big green (1, 2, and 3), gray, and small red spheres designate Cr, Zn, and O ions respectively.
in Figure 1. Three other different configurations based on this supercell are considered for Cr-doped ZnO to study the effect of doping concentration on the electronic structure. One model is obtained by replacing one Zn with a Cr atom (at site 2 shown in Figure 1), which corresponds to x ) 6.25%. For the concentration with x ) 12.5%, two different positions of Cr atoms (at sites 1, 2 and 1, 3 separately, as illustrated in Figure 1) are considered following the research work of Jia et al.:20 the “near” configuration, in which the Cr atoms in the same unit cell are separated by a single O, and the “far” configuration, in which they are connected via -O-Zn-O- bond. All calculations are performed with the CASTEP code21 of plane wave and ultrasoft pseudopotentials.22 The generalized gradient approximation with the Perdew-Burke-Ernzerhof scheme23 is adopted for the exchange-correlation potential. The electron wave function is expanded in plane waves with a cutoff energy of 370 eV, and a monkhorst-pack grid24 with parameters of 4 × 4 × 2 is used for irreducible Brillouin zone sampling. The total energy is converged to lower than 2 × 10-5 eV/atom. The crystal structure and the atomic coordinates are fully relaxed without any restriction using the Broyden-FletcherGoldfarb-Shanno method25 until the force on each atom converges to less than 0.05 eV/Å. The test calculations with higher cutoff energies and denser k-point grids are also performed, and the overall results remain unchanged. Then the electronic structures and optical properties are calculated on the basis of the optimized supercells. From the viewpoint of quantum mechanics, the interaction of a photon with an electron in the system is described in terms of time-dependent perturbations of the ground electronic state. Transitions between occupied and unoccupied states are caused by the photon absorption or emission. The spectra resulting from excitations can be thought of as a joint DOS between the conduction band and the valence band. The imaginary part (ε2(ω)) of the dielectric function can be written as
ε2(q f Ouˆ , hω) )
2πe2 |〈ψc |u · r|ψkv 〉|2δ(E kc - Ekv - E) Ωε0 k,v,c k
∑
(1) where u is the vector defining the polarization of the incident electric field; k is the reciprocal lattice vector; the superscripts c and v represent the conduction band and valence band, respectively; and ω is the frequency of the incident photon. Since the dielectric function shows a causal response, the real part (ε1) of the dielectric function can be obtained from the imaginary
Figure 2. (a) Band structure and (b) DOS for pure ZnO. The Fermi level is set to 0. The dashed olive lines are guides to the eye.
part with the Kramers-Kroning relations. Then the other optical spectra, such as absorption coefficient (R(ω)), reflectivity (R(ω)), refractivity index (n(ω)), and energy-loss (L(ω)) can be gained by ε1(ω) and ε2(ω):26
R(ω) ) √2ω[√ε21(ω) + ε22(ω) - ε1(ω)]1 ⁄ 2
(2)
√ε1(ω) + jε2(ω) - 1 2 √ε1(ω) + jε2(ω) + 1
(3)
R(ω) )
|
|
n(ω) ) √ε12(ω) + ε22(ω) + ε1(ω)
[
L(ω) ) ε2(ω) ⁄ [ε12(ω) + ε22(ω)]
1⁄2
]
⁄ √2
(4) (5)
3. Results and Discussion The optimized lattice constants are a ) 3.283 Å and c ) 5.311 Å for pure ZnO, which are in good agreement with the JCPDS file of ZnO (a ) 3.253 Å, c ) 5.213 Å). The band structure and DOS near the Fermi energy of the 32-atom supercell of pure ZnO are presented in Figure 2(a, b) as standard references. The optimized structure is triclinic, and the high symmetry points are G ) (0, 0, 0), F ) (0, 1/2, 0), Q ) (0, 1/2, 1/2), and Z ) (0, 0, 1/2). It can be seen from Figure 2(a) that the valence band maximum and the conduction band minimum locate at the same G point, indicating that the pure ZnO is a direct band gap semiconductor. Compared with the experimental value of 3.3 eV, the calculated band gap is underestimated to be 0.76 eV, which is attributed to the wellknown intrinsic factor of DFT. It can be seen from the DOS in Figure 2(b) that the valence band consists of two groups with a bandwidth of 5.8 eV. The upper valence band from -4 to 0 eV originates mainly from the O 2p states, and the lower valence band from -5.8 to -4 eV is derived from the Zn 3d states. In addition, the lowest conduction band is dominated by Zn 4s states. These characteristics are consistent with the previous calculations presented by Ren et al.27 To investigate the doping effect of Cr on the electronic structures, the band structure and DOS are calculated for replacing one Zn site with a Cr atom, which corresponds to x ) 6.25%, as shown in Figure 3(a, b). Compared with the undoped ZnO, the remarkable feature in the energy band for Cr-doped ZnO is that the Fermi level shifts upward into the conduction band, which indicates that the material is n-type metallic. The O 2p states are the most dominant in the energy range between -6 and -1.8 eV, and the Zn 3d states locate mainly in the energy range between -8 and -6 eV. The
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Figure 3. (a) Band structure and (b) DOS for Cr-doped ZnO with x ) 6.25%. The Fermi level is set to 0. The dashed olive lines are guides to the eye.
Figure 4. DOS for two Cr-doped ZnO in the (a) “near” and (b) “far” configurations. The Fermi level is set to 0. The dashed olive lines are guides to the eye.
impurity bands of Cr 3d states are separated into two bands: One lies just across the Fermi energy, which is partially occupied with a bandwidth of 2.34 eV. The other locates above the Fermi energy in the energy range from 1.68 to 3.44 eV. Note that the energy difference between the occupied impurity bands minimum and the Fermi energy level is 1.61 eV. In addition, there are some occupied levels introduced into the Zn 4s states below the Fermi energy. In this situation, the electronic intraband transition from the occupied bands to the unoccupied ones would occur under irradiation, which may induce intense absorption in the long wavelength visible region. On the other hand, the energy difference between valence band maximum and the Fermi level is about 2 eV, which is much larger than the band gap of pure ZnO (0.76 eV here). As a result, the transition of an electron from valence band to unoccupied states will need more energy in Cr-doped ZnO, and the optical absorption edge of Cr-doped ZnO will shift to the high-energy region compared with pure ZnO, which will be discussed carefully below. Figure 4(a, b) shows the DOS of replacing two Zn sites with Cr atoms in the “near” and “far” configurations, respectively. It can be seen from Figure 4(a) that although the Cr 3d states are still partially occupied, they become more delocalized than that of one Cr doping; that is, the impurity energy band becomes wider. Meanwhile, the Cr 3d states are enhanced with increased x. The energy difference between the valence band maximum and the Fermi level is increased to 2.17 eV. These two characters
Li et al.
Figure 5. Imaginary part of the dielectric function of Cr-doped ZnO with x ) 0, 6.25, and 12.5% in different configurations.
confirm that the visible light absorption would increase and the optical absorption edge would further shift to the high energy region. Comparing with the results presented in Figure 4(a, b), the “far” configuration makes the Cr 3d states more localized and strong, and the energy difference between the valence band maximum and the Fermi level becomes larger than the “near” configuration, which proves that different configurations will affect the physical properties of the system with the same x. In the following part of this paper, the optical properties of Cr-doped ZnO systems will be systematically discussed on the basis of the dielectric function, absorption coefficient, reflectivity, refractivity index, and energy-loss spectrum. Components of the optical properties corresponding to the polarization vectors perpendicular to the c axis (E ⊥ c) have been considered. Figure 5 shows the imaginary part of the dielectric function (ε2(ω)), which is the pandect of the optical properties for the four different configurations of the ZnO systems. For pure ZnO, there are three major peaks located at 1.51, 6.50, and 10.5 eV, which correspond to three intrinsic plasma frequencies. The peak at 1.51 eV originates from the electronic transition between the O 2p states in the upper valence band and the Zn 4s states in the lowest conduction band (Figure 2), which value is close to the calculated band gap (0.76 eV). The peak at 6.50 eV may be due to the transition between Zn 3d and O 2p states in the valence band. The transition between Zn 3d and O 2s states (which are not plotted in the electronic structure) results in the weak peak at 10.5 eV. For ZnO doped with one Cr atom, two main peaks exist at 0.68 and 6.41 eV. The same number of peaks is also observed for two Cr-doped ZnO systems in both “near” and “far” configurations, which locate at 0.76 and 6.40 eV, 0.59 and 6.60 eV, respectively. The peak at around 6.40-6.60 eV originates mainly from the transition between Zn 3d and O 2p states (Figures 3 and 4). The peak in the low region (0.59-0.76 eV) comes from the electronic intraband transition of impurity Cr 3d states and Zn 4s states in the conduction band, where the shift of the position corresponds to the localized degree of the impurity band as discussed in the electronic property, above. It can also be seen from Figure 5 that the line shape is almost the same for all the ZnO systems in the high energy range. These properties indicate that the different configurations of Cr dopant affect mainly the optical properties in the low energy range. Because the calculated band gaps of pure ZnO (0.76 eV) is much smaller than the experimental value (3.3 eV), the scissor approximation with the value of 2.54 eV is used for the calculated absorption edge to fit the experimental value. Figure 6 presents the absorption spectrum of the ZnO systems with
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