PCCP View Article Online
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
PAPER
Cite this: DOI: 10.1039/c5cp02441b
View Journal
The synergistic effect between effective mass and built-in electric field for the transfer of carriers in nonlinear optical materials Mengmeng Li, Ying Dai,* Xiangchao Ma, Zhujie Li and Baibiao Huang Recent experiments have demonstrated that the typical nonlinear optical material K3B6O10Br can be an excellent photocatalyst under ultraviolet (UV) light irradiation. To understand the origin of the photocatalytic activity and further improve its photocatalytic efficiency to develop alternative photocatalysts, the built-in electric field and the electron effective mass and their synergistic effect on transfer and the separation of carriers in K3B6O10X (X = Br, Cl) were investigated by means of first-principles calculations. Our results show that the built-in electric field and the smallest effective mass of holes in K3B6O10Br are both along the [001] direction. In contrast, the effective masses of electrons are isotropic because of the spherically symmetric s orbitals at the conduction band minimum (CBM). Therefore, the electric field can promote efficient transfer and separation of the photogenerated carriers along the [001] direction. As a consequence, the synergistic
Received 27th April 2015, Accepted 6th June 2015
effect of built-in electric field and the isotropy of the electron effective mass results in the {001} surface, to
DOI: 10.1039/c5cp02441b
also be obtained for a K3B6O10Cl crystal considering the analogous structure with that of K3B6O10Br. The present study may provide theoretical insight to develop the photocatalytic performance of nonlinear optical
www.rsc.org/pccp
materials.
which most of the carriers will accumulate, showing the highest photocatalytic activity. Similar results can
Introduction In recent years, photocatalysis has attracted intense attention for its potential to overcome environmental and energy problems. Researchers have focused on searching for optimal photocatalytic materials with high solar energy absorption efficiencies and high quantum efficiencies. Previous works have mainly focused on increasing the solar energy absorption efficiency, by doping,1–3 localized surface plasmon resonance,4–6 and solid solution materials,7,8 and much progress has been made. The absorption of solar light has been extended into the visible and even the near infrared regions,9–11 which dominate sunlight. Recently, researchers have shown increasing interest in the enhancement of quantum efficiency. It is thought that the separation of photogenerated carriers is one of the most crucial factors affecting quantum efficiency. In an attempt to promote the separation of photogenerated carriers, different approaches, such as heterojunction structuring12,13 and metal particle deposition14 have been adopted. Meanwhile, it has been found that the built-in electric field due to the regular alignment of dipole moments can always have the potential to enhance electron–hole separation upon photoexcitation.15 Therefore, some nonlinear optical School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, People’s Republic of China. E-mail: [email protected]
This journal is © the Owner Societies 2015
materials with intrinsic dipole moments have gained researchers’ attention.16–18 Recently, a typical nonlinear optical material, K3B6O10Br, has been proven to show a higher photocatalytic activity than that of commercial P25 TiO2 under UV light irradiation.18 Recent studies proposed that the presence of an internal polar electric field may enhance the separation of photogenerated charge carriers and thus the photocatalytic activity.17 It is believed that the electric dipole moments within the material contribute to the excellent photocatalytic performance.19 However, the alignment of electric dipole moments and the direction of the built-in electric field for such systems are still unclear. Considering there is a considerable discrepancy over the direction of built-in electric field between the previous calculation18 and the elementary symmetry analysis, we examined the local dipole moments and determine the direction of built-in electric field by means of valence-bond theory. Simultaneously, it is known that the effective masses of photogenerated electrons and holes can not only reflect the transfer nature of carriers, but also affect the separation of photogenerated carriers through the simplicity of transferring them along specific directions.20,21 Therefore, it is interesting to know if there is a synergistic effect between the built-in electric field and the effective mass distribution for the separation of carriers in K3B6O10X (X = Br, Cl) structures and how one can obtain optimal photocatalytic performance for the synthesized
Phys. Chem. Chem. Phys.
View Article Online
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
Paper
sample by using such synergistic effect to improve the photocatalytic efficiency. On the other hand, the existence of the nonequivalent metal–oxygen polyhedra linked by corner-sharing is another structural feature which may enhance the separation of carriers besides the built-in electric field, as mentioned in Lou’s paper.17 Whether the enhancement mechanism is available for the nonequivalent B–O units in K3B6O10X (X = Br, Cl) is also worthy of studying to understand its photocatalytic activity. Therefore, in the present work, the effective masses of photogenerated electrons and holes, density of states, charge density and energy band structure are also investigated using first-principles calculations. Our results show that the built-in electric field and the smallest effective mass of holes for K3B6O10Br are both along [001] direction and the effective masses of electrons are isotropic. Therefore, the net electric field and the carriers with small effective masses can promote the easy transfer of electrons to the (001) surface and the easiest transfer of holes to the (001% ) surface, thus making the {001} surface show the best photocatalytic performance. Meanwhile, the presence of nonequivalent B–O polyhedra is conducive to the separation of carriers in some extent due to the small but different contribution from [BO3] and [BO4] to the conduction band minimum (CBM). The same synergistic effect is also found in K3B6O10Cl, a similar nonlinear optical material with K3B6O10Br.
Computational details All our calculations were based on density functional theory using the Vienna ab initio simulation package (VASP).22,23 The projectoraugmented wave (PAW) potential was used to describe electron–ion interactions,24 and the generated gradient approximation (GGA) in the form of the Perdew–Burke–Ernzerhof (PBE) was used for the electron exchange–correlation functional.25,26 Though the GGA calculation can lead to the underestimation of the band gap, compared with the GW and GGA + U, the dispersion of the band edge generally depends weakly on the functional used.27–29 Therefore, the calculated effective masses based on the conduction band and valence band edges will not be significantly affected by the GW correction. The calculation of electric dipole moments depends on the geometry structure, which is also not influenced by the GW correction. Combining the analysis above, we believe that present results will not be significantly affected by the GW corrections. The experimental lattice constants were used with a = b = 10.115 Å, c = 8.8592 Å for K3B6O10Br30 and a = b = 10.062 Å, c = 8.836 Å for K3B6O10Cl.31 The valence configuration of the pseudopotentials were 2s2p1 for B, 2s22p4 for O, 3s23p64s2 for K and 4s24p5 for Br, 3s23p5 for Cl. The electronic wave functions were expanded into a basis set of plane waves with an energy cutoff of 400 eV. The Brillouin zone was represented by a set of 2 2 2 k points for both geometry optimizations and the static total energy calculations for K3B6O10Br and K3B6O10Cl. All of the atoms’ positions were fully relaxed until the atomic forces converged to 0.05 eV Å1. The total and projected densities of states were calculated at the equilibrium volume using Gaussian smearing with a smearing parameter of 0.05 eV.
Phys. Chem. Chem. Phys.
PCCP
Results and discussion 1. Crystal structure K3B6O10Br, a nonlinear optical material, was first synthesized by Al-Ama et al.32 in 2006 and belongs to the trigonal crystal system with a R3m space group, and its crystal structure is shown in Fig. 1. As we can see, there are two types of B atoms in K3B6O10Br, one bonded to three adjacent O atoms forming a [BO3] unit, and the other bonded to four O atoms forming a [BO4] unit. Three [BO3] triangles and three [BO4] tetrahedrons are corner-shared with O atoms, constituting a hexaborate [B6O13] unit. Each K atom is bonded by six O atoms and two Br atoms, forming a [KBr2O6] polyhedron. The [B6O13] unit is inserted in the three-dimensional network formed by K atoms bonding to Br atoms,33 as shown in Fig. 1. 2. The dipole moments Given that nonlinear optical materials have a macroscopic polarization due to the different centers of symmetry of the positive and negative charges, the electric dipole moments in K3B6O10Br were calculated first. Combining the analysis above, the K3B6O10Br structure can be divided into three units, [BO3], [BO4] and [KBr2O6]. For convenience, the O atoms shared by both [BO3] and [BO4] in the [B6O13] unit are marked as O1, the O atoms bonding to two adjacent [B6O13] units are marked as O2 and the O atoms shared by three [BO4] in the [B6O13] unit are marked as O3. The B atoms in [BO4] and [BO3] units are marked as B1 and B2, respectively. Based on the optimized bond lengths and bond angles, bond valences of the [B6O13] and [KBr2O6] unit were calculated using the following equation: Sij ¼
X
exp R0 Rij B
(1)
j
where B = 0.37 and R0 is an empirical constant depending on the bonding atoms (R0 = 1.371 for B–O bond,34 R0 = 2.132 for K–O bond34 and R0 = 2.66 for K–Br bond35), Rij is the bond length between the central cation i and the anion j, Sij is the valence of the bond ‘‘ij’’.36 The calculated results of bond valences are listed in Table 1, which are consistent with previous calculations in general.33
Fig. 1 Crystal structure for K3B6O10Br. Purple, olive, red and brown balls denote K, B, O and Br atoms, respectively.
This journal is © the Owner Societies 2015
View Article Online
PCCP
Paper
Table 1
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
B1 B2 K
Bond valence (Sij) and bond valence sum of B and K
O1
O2
O3
Br
Br
Sum
1.004 2 0.769 2 0.166 2
0.978 0.794 0.174 2
— 0.650 0.147 2
— — 0.172
— — 0.170
2.986 2.982 1.316
Fig. 2 Structure of [B6O13] and [K3Br4O15]. The color marks of the atoms are the same as in Fig. 1.
Through the Debye equation m = neR (n represents the total number of electrons, e is the electron charge, R is the difference between the ‘‘centroids’’ of positive and negative charge and m is the net dipole moment in Debye),37 the net dipole moments were determined to be 1.502, 0.687, and 4.744 Debye (D) for the [BO3], [BO4], and [KBr2O6] units, respectively. Given that each [B6O13] unit is composed of three [BO4] units and three [BO3] units and it has a C3 symmetry with the c axis as the symmetrical axis (Fig. 2(a)), the dipole moments of the three [BO3] and [BO4] units in the [B6O13] unit will be offset in the a–b plane. So there is only a remaining dipole moment along the c axis with a value of 1.653 D for the [B6O13] unit. In the same way, the [K3Br4O15] unit, as shown in Fig. 2(b), also has a net dipole moment along the c axis direction. Since each cell is composed of three [B6O13] units and three [K3Br4O15] units, there is a total dipole moment with a value of 19.107 D along the c axis. Therefore, the transfer of photogenerated carriers can be promoted along the c axis by the net dipole moments in K3B6O10Br. Detailed data for the calculated electric dipole moments are listed in Table 2.
on the basis of the parabolic approximation of the conduction band minimum (CBM) and valence band maximum (VBM): m ¼ h2
2 1 d Ek dk2
where k is the wave-vector and Ek is the energy corresponding to the wave vector k. Here, the effective masses of carriers along three representative directions ([100], [010] and [001]) are examined. The effective masses of carriers along other directions can be obtained qualitatively from the following analysis of three-dimensional (3D) band structures. According to the calculated energy band structure (Fig. 3), we can see that the gap is direct at the G point with a band gap of 5.29 eV, which is smaller than the experimental band gap (6.4 eV),38 owing to the well-known deficiency of the GGA functional. The valance band edge is much flatter compared to the conduction band edge, suggesting that the effective masses of electrons are much smaller than those of the holes. The results of the calculated effective masses of carriers are listed in Table 3. It was found that electrons showed almost the same effective masses along the three selected directions, 0.52, 0.52 and 0.49 me, for the [100], [010] and [001] directions, respectively. They are only half that of the effective mass of electrons in TiO2 (about 1.0 me).39 While the effective masses of holes show quite different properties, with the smallest effective mass along the [001] direction, with a value of 3.735 me. Along
3. Effective mass and band structure In view of the fact that the effective masses of the photogenerated electrons and holes dominate the carriers’ ability to transfer from bulk to the surface reactive sites and thus play an important role in determining the photocatalytic activity,20,21 the effective masses of electrons (me*) and holes (mh*) are calculated
Table 2
Fig. 3 Calculated electronic band structure of K3B6O10Br. The Fermi level is set to zero.
Electric dipole moments in K3B6O10Br
mx [BO3] [BO4] [B6O13]
my
mz
0.471 0.302 0.0
0.818 0.003 0.0
1.168 0.617 1.653
[KBr2O6] [K3Br4O15]
0.260 0.0
0.449 0.0
4.716 14.148
[K9B18O30Br3]
0.0
0.0
19.107
This journal is © the Owner Societies 2015
Table 3 Effective masses of electrons (me*) and holes (mh*) in the unit of free-electron mass for K3B6O10Br along the [100], [010] and [001] direction in the reciprocal space
me* mh*
[100]
[010]
[001]
0.52 —
0.52 —
0.49 3.735
Phys. Chem. Chem. Phys.
View Article Online
Paper
conduction and valance band edge dispersion in certain reciprocal lattice planes (the kx–ky plane, ky–kz plane and kz–kx plane) were examined. The projections corresponding to the six threedimensional band structures are shown in Fig. 4. It can be seen that the projections of the 3D band structure on the kx–ky plane, ky–kz plane and kz–kx plane for the lowest conduction
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
the [100] and [010] direction, effective masses of holes are very large for the extremely small band dispersion at the valence bond edge. In the analysis above, the effective masses of electrons and holes along three particular directions are examined. To quantify the effective masses of carriers along other directions, both the
PCCP
Fig. 4 The projections of three-dimensional (3D) band structure of K3B6O10Br for the lowest conduction band (LCB) (the left columns) and for the highest valence band (HVB) (the right columns) in the kx–ky (a, b), ky–kz (c, d) and kz–kx plane (e, f). The constant-energy contour references are given on the right of the corresponding projections.
Phys. Chem. Chem. Phys.
This journal is © the Owner Societies 2015
View Article Online
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
PCCP
band (LCB) (Fig. 4(a), (c) and (e)) show the same distribution and are circle-like, which indicates that the effective masses of electrons are isotropic. Combined with the calculation of the effective masses of electrons above, small effective masses of about 0.5 me for electrons along every direction in the kx–ky, ky–kz and kz–kx planes can be obtained. Therefore, in K3B6O10Br, electrons can transfer to each surface rapidly because of their small effective masses along these directions. For the projection of the highest valence band (HVB) on the kx–ky plane (Fig. 4(b)), shown as irregular hexagons, there is only a relatively small energy difference, about 0.006 eV in the selected area, which manifests itself by the very large effective masses of holes in the kx–ky plane. Then the transfer of holes along directions in the kx–ky plane is very difficult. Furthermore, in Fig. 4(d) and (f), the projections of HVB on the ky–kz plane and kz–kx plane show the similar ellipses. Hence the effective masses of holes in the ky–kz plane and kz–kx plane are anisotropic, with the smallest value along the [001] direction (corresponding to the short axis of the ellipses) and the largest value along the [100] and [010] directions (corresponding to the long axis of the ellipses). Therefore, the transfer of holes along the [001] direction is much easier than that along other directions
Paper
in the ky–kz and kz–kx planes due to the smallest effective mass along the [001] direction. 4. Density of states and charge density In order to understand the different properties of the effective masses shown by electrons and holes along different directions, the total density of states (DOS) and partial density of states (PDOS) of K3B6O10Br are calculated and shown in Fig. 5. It can be seen that the VBM is mainly composed of Br 4p states, while O 2p states mainly occupy the valence band in the energy range between 3.3 eV and 0.6 eV. Thus the main contribution from the p states, which are anisotropic, can result in the different effective masses of holes along different directions. On the other hand, the CBM is mainly formed by the s states of the O, K and Br atoms. Because the s states are isotropic, similar effective masses of electrons along different directions can be understood. Overall, the results are in good agreement with the calculated effective masses of carriers above. Considering that the nonequivalent metal–oxygen polyhedra linked by corner-sharing can enhance the separation of photogenerated carriers,17 the possible enhancement effect for the separation of carriers in the similar B–O polyhedra ([BO3] and
Fig. 5 Calculated total density of states (TDOS) and partial density of states (PDOS) of K3B6O10Br at the VBM (a) and CBM (b, c), respectively. The Fermi level is set to zero.
This journal is © the Owner Societies 2015
Phys. Chem. Chem. Phys.
View Article Online
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
Paper
[BO4]) was also investigated. From the PDOS in Fig. 5(c), the s and p states of both B1 and B2 have contributions to the CBM, while the contribution from B1 in [BO4] is more than that from B2 in [BO3], resulting in an accumulation of electrons in the [BO4] units by the B2–O–B1 bridges. On the other hand, combining the TDOS (Fig. 5(b)), it can be seen that the contribution from the B atoms is smaller than that of the K, O and Br atoms. Therefore the nonequivalent B–O units in K3B6O10Br can promote the separation of photogenerated charge carriers but the effect is limited. In addition, to further determine the orientation of the smallest effective mass of holes and the isotropic properties of the small effective masses of electrons, we calculated the charge density near the VBM and CBM and show this in Fig. 6. It’s clear that the charges mainly accumulate in the Br p states for the VBM, which is in good accordance with the analysis from the DOS. It can also be seen that the lobes of the Br p states are mainly along the [001] direction and thus electron transfer to the neighboring atoms along the [001] direction will be easier, which shows the smallest effective mass of holes. The charge density of the CBM is somewhat complicated, but it can be seen that the electrons occupy the spherically symmetric s orbitals of the O, K and Br atoms, showing an isotropic distribution. All of the results are consistent with the analysis of the effective masses of electrons and holes above, and also prove the smallest effective mass of holes along the [001] direction. In principle, the highest photocatalytic activity of K3B6O10Br can be obtained once the direction of the built-in electric field is consistent with the direction along which carriers can transfer most easily. From the results, it can be seen that the built-in electric field induced by the electric dipole moments is along the [001] direction in K3B6O10Br. Meanwhile, the smallest effective mass of holes is also along the [001] direction and the small effective masses of electrons distribute isotropically.
Fig. 6 The charge density of K3B6O10Br for the bottom of the conduction band (a) in the range of 5.29 to 5.32 eV and for the top of the valence band (b) in the range of 0.05 to 0 eV. The color marks of the atoms are the same as Fig. 1.
Phys. Chem. Chem. Phys.
PCCP
Therefore, the built-in electric field can further promote the transfer of the photogenerated electrons along the [001] direction and holes along the opposite direction, resulting in the accumulation of electrons to the (001) surface and holes to the (001% ) surface. So if K3B6O10Br mainly exposes the {001} surface, it will show the best photocatalytic activity. However, the samples of K3B6O10Br synthesized and applied to the dechlorination experiment mainly expose the (211) surface, as shown in the XRD pattern and the photograph of the sample.18,33 Thus it can be inferred that the photocatalytic activity is limited by the less exposed {001} surface to some extent. Of course, there is still a projection of the built-in electric field along the direction perpendicular to the (211) surface. Therefore, the built-in electric field can promote the transfer and separation of photogenerated carriers to some extent, although this will not have greatest effect. Based on the analysis above, we can propose that the K3B6O10Br with more exposed {001} surface may have the highest photocatalytic efficiency.
5. K3B6O10Cl Meanwhile, an examination of nonlinear optical material K3B6O10Cl with a similar structure to K3B6O10Br was also performed. It shows the same synergistic effect between the built-in electric field and the effective mass for the transfer and separation of photogenerated carriers as shown in K3B6O10Br. The similar geometric structure generates a similar polarization along the c axis in K3B6O10Cl.31 Fig. 7 shows its charge density with the composition of VBM and CBM, similar to that of K3B6O10Br. The p states in VBM ensure the easiest transfer along the c axis for holes and the isotropic contribution from the s states in CBM indicates the isotropic transfer ability of the electrons. Therefore, the internal electric field in K3B6O10Cl can also promote the transfer of carriers along the [001] direction
Fig. 7 The charge density of K3B6O10Cl for the bottom of the conduction band (a) and for the top of the valence band (b). Purple, olive, red and green balls denote K, B, O and Cl atoms, respectively.
This journal is © the Owner Societies 2015
View Article Online
PCCP
synergistically with the intrinsic transfer nature of electrons and holes.
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
Conclusion The properties of carrier transfer and separation in K3B6O10Br were investigated by examining both the intrinsic built-in electric field and the effective masses of the photogenerated electrons and holes along different directions. The corresponding energy band structure, density of states and charge density were also investigated to further understand the different properties exhibited by the effective masses of electrons and holes along different directions. Our results show that the built-in electric field in K3B6O10Br is along the [001] direction. The effective masses of electrons, about 0.5 me, are isotropic along different directions, because of the spherically symmetric s orbitals of the O, K and Br atoms contributing to the CBM. Furthermore, the smallest effective mass of holes is about 3.74 me, along the [001] direction, which is consistent with the direction of the builtin electric field induced by the electric dipole moments, while the effective masses of holes are very large along all directions perpendicular to the built-in field, due to the anisotropic properties of the p states contributing to the VBM. Therefore, the built-in electric field in K3B6O10Br can show a synergistic effect with the intrinsic transfer ability of carriers imposed by their small effective masses along the [001] direction. However, the K3B6O10Br synthesized in the experiment mainly exposes the (211) surface, which limits its higher photocatalytic activity to some extent. Taken together, our results suggest that K3B6O10Br, exposing more of the {001} surface, will show a higher photocatalytic activity. Meanwhile, there is a slight enhancement effect due to the nonequivalent B–O units for the separation of electrons and holes. Similarly, K3B6O10Cl shows the same synergistic effect for the transfer of carriers and thus can be a potential photocatalyst. This work may provide some proposals for the design and synthesis of nonlinear materials with higher efficiencies of separation of photogenerated electrons and holes.
Acknowledgements This work is supported by the National Basic Research Program of China (973 program, 2013CB632401), National Natural Science foundation of China under Grant 11374190, 21333006, and the Fund for Doctoral Program of National Education 20120131110066, 111 Project B13029. We also thank the National Supercomputer Center in Jinan for providing high performance computation.
References 1 A. Xu, Y. Gao and H. Liu, J. Catal., 2002, 207, 151–157. 2 G. Liu, Y. Zhao, C. Sun, F. Li, G. Lu and H. Cheng, Angew. Chem., Int. Ed., 2008, 47, 4516–4520. 3 R. Asahi, T. Morikawa, T. Ohwaki, K. Aoki and Y. Taga, Science, 2001, 293, 269–271.
This journal is © the Owner Societies 2015
Paper
4 P. Wang, B. Huang, X. Qin, X. Zhang, Y. Dai, J. Wei and M.-H. Whangbo, Angew. Chem., Int. Ed., 2008, 47, 7931–7933. 5 X. Ma, Y. Dai, L. Yu and B. Huang, Sci. Rep., 2014, 4, 3986. 6 X. Ma, Y. Dai, L. Yu, Z. Lou, B. Huang and M.-H. Whangbo, J. Phys. Chem. C, 2014, 118, 12133–12140. 7 K. Maeda, T. Takata, M. Hara, N. Saito, Y. Inoue, H. Kobayashi and K. Domen, J. Am. Chem. Soc., 2005, 127, 8286–8287. 8 A. Kudo, I. Tsuji and H. Kato, Chem. Commun., 2002, 1958–1959. 9 X. Zhang, Y. Zhu, X. Yang, S. Wang, J. Shen, B. Lin and C. Li, Nanoscale, 2013, 5, 3359–3366. 10 G. Wang, B. Huang, X. Ma, Z. Wang, X. Qin, X. Zhang, Y. Dai and M.-H. Whangbo, Angew. Chem., Int. Ed., 2013, 52, 4810–4813. 11 T. Jing, Y. Dai, W. Wei, X. Ma and B. Huang, Phys. Chem. Chem. Phys., 2014, 16, 18596–18604. 12 T. Xie, C. Liu, L. Xu, J. Yang and W. Zhou, J. Phys. Chem. C, 2013, 117, 24601–24610. 13 H. Wang, L. Zhang, Z. Chen, J. Hu, S. Li, Z. Wang, J. Liu and X. Wang, Chem. Soc. Rev., 2014, 43, 5234–5244. 14 M. Murdoch, G. I. N. Waterhouse, M. A. Nadeem, J. B. Metson, M. A. Keane, R. F. Howe, J. Llorca and H. Idriss, Nat. Chem., 2011, 3, 489–492. 15 J. L. Giocondi and G. S. Rohrer, J. Phys. Chem. B, 2001, 105, 8275–8277. 16 W. Wang, B. Huang, X. Ma, Z. Wang, X. Qin, X. Zhang, Y. Dai and M.-H. Whangbo, Chem. – Eur. J., 2013, 19, 14777–14780. 17 R. Zhang, Y. Dai, Z. Lou, Z. Li, Z. Wang, Y. Yang, X. Qin, X. Zhang and B. Huang, CrystEngComm, 2014, 16, 4931–4934. 18 X. Fan, L. Zang, M. Zhang, H. Qiu, Z. Wang, J. Yin, H. Jia, S. Pan and C. Wang, Chem. Mater., 2014, 26, 3169–3174. 19 L. Li, P. A. Salvador and G. S. Rohrer, Nanoscale, 2014, 6, 24–42. 20 N. Umezawa, S. Ouyang and J. Ye, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 83, 035202. 21 X. Ma, Y. Dai, M. Guo and B. Huang, ChemPhysChem, 2012, 13, 2304–2309. ¨ller, Comput. Mater. Sci., 1996, 6, 22 G. Kresse and J. Furthmu 15–50. ¨ller, Phys. Rev. B: Condens. Matter 23 G. Kresse and J. Furthmu Mater. Phys., 1996, 54, 11169–11186. ¨chl, Phys. Rev. B: Condens. Matter Mater. Phys., 1994, 24 P. E. Blo 50, 17953–17979. 25 J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh and C. Fiolhais, Phys. Rev. B: Condens. Matter Mater. Phys., 1992, 46, 6671–6687. 26 J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868. 27 H. Jiang, J. Phys. Chem. C, 2012, 116, 7664–7671. 28 A. Yamasaki and T. Fujiwara, Phys. Rev. B: Condens. Matter Mater. Phys., 2002, 66, 245108. 29 P. S. Yadav, R. K. Yadav, S. Agrawal and B. K. Agrawal, Physica E, 2007, 36, 79–85. 30 M. Zhang, X. Su, S. Pan, Z. Wang, H. Zhang, Z. Yang, B. Zhang, L. Dong, Y. Wang, F. Zhang and Y. Yang, J. Phys. Chem. C, 2014, 118, 11849–11856.
Phys. Chem. Chem. Phys.
View Article Online
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
Paper
31 H. Wu, S. Pan, K. R. Poeppelmeier, H. Li, D. Jia, Z. Chen, X. Fan, Y. Yang, J. M. Rondinelli and H. Luo, J. Am. Chem. Soc., 2011, 133, 7786–7790. 32 G. Al-Ama, E. L. Belokoneva, S. Y. Stefanovich, O. V. Dimitrova and N. N. Mochenova, Crystallogr. Rep., 2006, 51, 225–230. 33 M. Zhang, S. Pan, X. Fan, Z. Zhou, K. R. Poeppelmeier and Y. Yang, CrystEngComm, 2011, 13, 2899–2903. 34 I. D. Brown and D. Altermatt, Acta Crystallogr., Sect. B: Struct. Sci., 1985, 41, 244–247.
Phys. Chem. Chem. Phys.
PCCP
35 N. E. Brese and M. O’Keeffe, Acta Crystallogr., Sect. B: Struct. Sci., 1991, 47, 192–197. 36 Z. Li, Y. Dai, X. Ma, Y. Zhu and B. Huang, Phys. Chem. Chem. Phys., 2014, 16, 3267–3273. 37 P. A. Maggard, T. S. Nault, C. L. Stern and K. R. Poeppelmeier, J. Solid State Chem., 2003, 175, 27–33. 38 B. Zhang, M.-H. Lee, Z. Yang, Q. Jing, S. Pan, M. Zhang, H. Wu, X. Su and C.-S. Li, Appl. Phys. Lett., 2015, 106, 031906. 39 D. Kurita, S. Ohta, K. Sugiura, H. Ohta and K. Koumoto, J. Appl. Phys., 2006, 100, 096105.
This journal is © the Owner Societies 2015
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
PAPER
Cite this: DOI: 10.1039/c5cp02441b
View Journal
The synergistic effect between effective mass and built-in electric field for the transfer of carriers in nonlinear optical materials Mengmeng Li, Ying Dai,* Xiangchao Ma, Zhujie Li and Baibiao Huang Recent experiments have demonstrated that the typical nonlinear optical material K3B6O10Br can be an excellent photocatalyst under ultraviolet (UV) light irradiation. To understand the origin of the photocatalytic activity and further improve its photocatalytic efficiency to develop alternative photocatalysts, the built-in electric field and the electron effective mass and their synergistic effect on transfer and the separation of carriers in K3B6O10X (X = Br, Cl) were investigated by means of first-principles calculations. Our results show that the built-in electric field and the smallest effective mass of holes in K3B6O10Br are both along the [001] direction. In contrast, the effective masses of electrons are isotropic because of the spherically symmetric s orbitals at the conduction band minimum (CBM). Therefore, the electric field can promote efficient transfer and separation of the photogenerated carriers along the [001] direction. As a consequence, the synergistic
Received 27th April 2015, Accepted 6th June 2015
effect of built-in electric field and the isotropy of the electron effective mass results in the {001} surface, to
DOI: 10.1039/c5cp02441b
also be obtained for a K3B6O10Cl crystal considering the analogous structure with that of K3B6O10Br. The present study may provide theoretical insight to develop the photocatalytic performance of nonlinear optical
www.rsc.org/pccp
materials.
which most of the carriers will accumulate, showing the highest photocatalytic activity. Similar results can
Introduction In recent years, photocatalysis has attracted intense attention for its potential to overcome environmental and energy problems. Researchers have focused on searching for optimal photocatalytic materials with high solar energy absorption efficiencies and high quantum efficiencies. Previous works have mainly focused on increasing the solar energy absorption efficiency, by doping,1–3 localized surface plasmon resonance,4–6 and solid solution materials,7,8 and much progress has been made. The absorption of solar light has been extended into the visible and even the near infrared regions,9–11 which dominate sunlight. Recently, researchers have shown increasing interest in the enhancement of quantum efficiency. It is thought that the separation of photogenerated carriers is one of the most crucial factors affecting quantum efficiency. In an attempt to promote the separation of photogenerated carriers, different approaches, such as heterojunction structuring12,13 and metal particle deposition14 have been adopted. Meanwhile, it has been found that the built-in electric field due to the regular alignment of dipole moments can always have the potential to enhance electron–hole separation upon photoexcitation.15 Therefore, some nonlinear optical School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, People’s Republic of China. E-mail: [email protected]
This journal is © the Owner Societies 2015
materials with intrinsic dipole moments have gained researchers’ attention.16–18 Recently, a typical nonlinear optical material, K3B6O10Br, has been proven to show a higher photocatalytic activity than that of commercial P25 TiO2 under UV light irradiation.18 Recent studies proposed that the presence of an internal polar electric field may enhance the separation of photogenerated charge carriers and thus the photocatalytic activity.17 It is believed that the electric dipole moments within the material contribute to the excellent photocatalytic performance.19 However, the alignment of electric dipole moments and the direction of the built-in electric field for such systems are still unclear. Considering there is a considerable discrepancy over the direction of built-in electric field between the previous calculation18 and the elementary symmetry analysis, we examined the local dipole moments and determine the direction of built-in electric field by means of valence-bond theory. Simultaneously, it is known that the effective masses of photogenerated electrons and holes can not only reflect the transfer nature of carriers, but also affect the separation of photogenerated carriers through the simplicity of transferring them along specific directions.20,21 Therefore, it is interesting to know if there is a synergistic effect between the built-in electric field and the effective mass distribution for the separation of carriers in K3B6O10X (X = Br, Cl) structures and how one can obtain optimal photocatalytic performance for the synthesized
Phys. Chem. Chem. Phys.
View Article Online
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
Paper
sample by using such synergistic effect to improve the photocatalytic efficiency. On the other hand, the existence of the nonequivalent metal–oxygen polyhedra linked by corner-sharing is another structural feature which may enhance the separation of carriers besides the built-in electric field, as mentioned in Lou’s paper.17 Whether the enhancement mechanism is available for the nonequivalent B–O units in K3B6O10X (X = Br, Cl) is also worthy of studying to understand its photocatalytic activity. Therefore, in the present work, the effective masses of photogenerated electrons and holes, density of states, charge density and energy band structure are also investigated using first-principles calculations. Our results show that the built-in electric field and the smallest effective mass of holes for K3B6O10Br are both along [001] direction and the effective masses of electrons are isotropic. Therefore, the net electric field and the carriers with small effective masses can promote the easy transfer of electrons to the (001) surface and the easiest transfer of holes to the (001% ) surface, thus making the {001} surface show the best photocatalytic performance. Meanwhile, the presence of nonequivalent B–O polyhedra is conducive to the separation of carriers in some extent due to the small but different contribution from [BO3] and [BO4] to the conduction band minimum (CBM). The same synergistic effect is also found in K3B6O10Cl, a similar nonlinear optical material with K3B6O10Br.
Computational details All our calculations were based on density functional theory using the Vienna ab initio simulation package (VASP).22,23 The projectoraugmented wave (PAW) potential was used to describe electron–ion interactions,24 and the generated gradient approximation (GGA) in the form of the Perdew–Burke–Ernzerhof (PBE) was used for the electron exchange–correlation functional.25,26 Though the GGA calculation can lead to the underestimation of the band gap, compared with the GW and GGA + U, the dispersion of the band edge generally depends weakly on the functional used.27–29 Therefore, the calculated effective masses based on the conduction band and valence band edges will not be significantly affected by the GW correction. The calculation of electric dipole moments depends on the geometry structure, which is also not influenced by the GW correction. Combining the analysis above, we believe that present results will not be significantly affected by the GW corrections. The experimental lattice constants were used with a = b = 10.115 Å, c = 8.8592 Å for K3B6O10Br30 and a = b = 10.062 Å, c = 8.836 Å for K3B6O10Cl.31 The valence configuration of the pseudopotentials were 2s2p1 for B, 2s22p4 for O, 3s23p64s2 for K and 4s24p5 for Br, 3s23p5 for Cl. The electronic wave functions were expanded into a basis set of plane waves with an energy cutoff of 400 eV. The Brillouin zone was represented by a set of 2 2 2 k points for both geometry optimizations and the static total energy calculations for K3B6O10Br and K3B6O10Cl. All of the atoms’ positions were fully relaxed until the atomic forces converged to 0.05 eV Å1. The total and projected densities of states were calculated at the equilibrium volume using Gaussian smearing with a smearing parameter of 0.05 eV.
Phys. Chem. Chem. Phys.
PCCP
Results and discussion 1. Crystal structure K3B6O10Br, a nonlinear optical material, was first synthesized by Al-Ama et al.32 in 2006 and belongs to the trigonal crystal system with a R3m space group, and its crystal structure is shown in Fig. 1. As we can see, there are two types of B atoms in K3B6O10Br, one bonded to three adjacent O atoms forming a [BO3] unit, and the other bonded to four O atoms forming a [BO4] unit. Three [BO3] triangles and three [BO4] tetrahedrons are corner-shared with O atoms, constituting a hexaborate [B6O13] unit. Each K atom is bonded by six O atoms and two Br atoms, forming a [KBr2O6] polyhedron. The [B6O13] unit is inserted in the three-dimensional network formed by K atoms bonding to Br atoms,33 as shown in Fig. 1. 2. The dipole moments Given that nonlinear optical materials have a macroscopic polarization due to the different centers of symmetry of the positive and negative charges, the electric dipole moments in K3B6O10Br were calculated first. Combining the analysis above, the K3B6O10Br structure can be divided into three units, [BO3], [BO4] and [KBr2O6]. For convenience, the O atoms shared by both [BO3] and [BO4] in the [B6O13] unit are marked as O1, the O atoms bonding to two adjacent [B6O13] units are marked as O2 and the O atoms shared by three [BO4] in the [B6O13] unit are marked as O3. The B atoms in [BO4] and [BO3] units are marked as B1 and B2, respectively. Based on the optimized bond lengths and bond angles, bond valences of the [B6O13] and [KBr2O6] unit were calculated using the following equation: Sij ¼
X
exp R0 Rij B
(1)
j
where B = 0.37 and R0 is an empirical constant depending on the bonding atoms (R0 = 1.371 for B–O bond,34 R0 = 2.132 for K–O bond34 and R0 = 2.66 for K–Br bond35), Rij is the bond length between the central cation i and the anion j, Sij is the valence of the bond ‘‘ij’’.36 The calculated results of bond valences are listed in Table 1, which are consistent with previous calculations in general.33
Fig. 1 Crystal structure for K3B6O10Br. Purple, olive, red and brown balls denote K, B, O and Br atoms, respectively.
This journal is © the Owner Societies 2015
View Article Online
PCCP
Paper
Table 1
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
B1 B2 K
Bond valence (Sij) and bond valence sum of B and K
O1
O2
O3
Br
Br
Sum
1.004 2 0.769 2 0.166 2
0.978 0.794 0.174 2
— 0.650 0.147 2
— — 0.172
— — 0.170
2.986 2.982 1.316
Fig. 2 Structure of [B6O13] and [K3Br4O15]. The color marks of the atoms are the same as in Fig. 1.
Through the Debye equation m = neR (n represents the total number of electrons, e is the electron charge, R is the difference between the ‘‘centroids’’ of positive and negative charge and m is the net dipole moment in Debye),37 the net dipole moments were determined to be 1.502, 0.687, and 4.744 Debye (D) for the [BO3], [BO4], and [KBr2O6] units, respectively. Given that each [B6O13] unit is composed of three [BO4] units and three [BO3] units and it has a C3 symmetry with the c axis as the symmetrical axis (Fig. 2(a)), the dipole moments of the three [BO3] and [BO4] units in the [B6O13] unit will be offset in the a–b plane. So there is only a remaining dipole moment along the c axis with a value of 1.653 D for the [B6O13] unit. In the same way, the [K3Br4O15] unit, as shown in Fig. 2(b), also has a net dipole moment along the c axis direction. Since each cell is composed of three [B6O13] units and three [K3Br4O15] units, there is a total dipole moment with a value of 19.107 D along the c axis. Therefore, the transfer of photogenerated carriers can be promoted along the c axis by the net dipole moments in K3B6O10Br. Detailed data for the calculated electric dipole moments are listed in Table 2.
on the basis of the parabolic approximation of the conduction band minimum (CBM) and valence band maximum (VBM): m ¼ h2
2 1 d Ek dk2
where k is the wave-vector and Ek is the energy corresponding to the wave vector k. Here, the effective masses of carriers along three representative directions ([100], [010] and [001]) are examined. The effective masses of carriers along other directions can be obtained qualitatively from the following analysis of three-dimensional (3D) band structures. According to the calculated energy band structure (Fig. 3), we can see that the gap is direct at the G point with a band gap of 5.29 eV, which is smaller than the experimental band gap (6.4 eV),38 owing to the well-known deficiency of the GGA functional. The valance band edge is much flatter compared to the conduction band edge, suggesting that the effective masses of electrons are much smaller than those of the holes. The results of the calculated effective masses of carriers are listed in Table 3. It was found that electrons showed almost the same effective masses along the three selected directions, 0.52, 0.52 and 0.49 me, for the [100], [010] and [001] directions, respectively. They are only half that of the effective mass of electrons in TiO2 (about 1.0 me).39 While the effective masses of holes show quite different properties, with the smallest effective mass along the [001] direction, with a value of 3.735 me. Along
3. Effective mass and band structure In view of the fact that the effective masses of the photogenerated electrons and holes dominate the carriers’ ability to transfer from bulk to the surface reactive sites and thus play an important role in determining the photocatalytic activity,20,21 the effective masses of electrons (me*) and holes (mh*) are calculated
Table 2
Fig. 3 Calculated electronic band structure of K3B6O10Br. The Fermi level is set to zero.
Electric dipole moments in K3B6O10Br
mx [BO3] [BO4] [B6O13]
my
mz
0.471 0.302 0.0
0.818 0.003 0.0
1.168 0.617 1.653
[KBr2O6] [K3Br4O15]
0.260 0.0
0.449 0.0
4.716 14.148
[K9B18O30Br3]
0.0
0.0
19.107
This journal is © the Owner Societies 2015
Table 3 Effective masses of electrons (me*) and holes (mh*) in the unit of free-electron mass for K3B6O10Br along the [100], [010] and [001] direction in the reciprocal space
me* mh*
[100]
[010]
[001]
0.52 —
0.52 —
0.49 3.735
Phys. Chem. Chem. Phys.
View Article Online
Paper
conduction and valance band edge dispersion in certain reciprocal lattice planes (the kx–ky plane, ky–kz plane and kz–kx plane) were examined. The projections corresponding to the six threedimensional band structures are shown in Fig. 4. It can be seen that the projections of the 3D band structure on the kx–ky plane, ky–kz plane and kz–kx plane for the lowest conduction
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
the [100] and [010] direction, effective masses of holes are very large for the extremely small band dispersion at the valence bond edge. In the analysis above, the effective masses of electrons and holes along three particular directions are examined. To quantify the effective masses of carriers along other directions, both the
PCCP
Fig. 4 The projections of three-dimensional (3D) band structure of K3B6O10Br for the lowest conduction band (LCB) (the left columns) and for the highest valence band (HVB) (the right columns) in the kx–ky (a, b), ky–kz (c, d) and kz–kx plane (e, f). The constant-energy contour references are given on the right of the corresponding projections.
Phys. Chem. Chem. Phys.
This journal is © the Owner Societies 2015
View Article Online
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
PCCP
band (LCB) (Fig. 4(a), (c) and (e)) show the same distribution and are circle-like, which indicates that the effective masses of electrons are isotropic. Combined with the calculation of the effective masses of electrons above, small effective masses of about 0.5 me for electrons along every direction in the kx–ky, ky–kz and kz–kx planes can be obtained. Therefore, in K3B6O10Br, electrons can transfer to each surface rapidly because of their small effective masses along these directions. For the projection of the highest valence band (HVB) on the kx–ky plane (Fig. 4(b)), shown as irregular hexagons, there is only a relatively small energy difference, about 0.006 eV in the selected area, which manifests itself by the very large effective masses of holes in the kx–ky plane. Then the transfer of holes along directions in the kx–ky plane is very difficult. Furthermore, in Fig. 4(d) and (f), the projections of HVB on the ky–kz plane and kz–kx plane show the similar ellipses. Hence the effective masses of holes in the ky–kz plane and kz–kx plane are anisotropic, with the smallest value along the [001] direction (corresponding to the short axis of the ellipses) and the largest value along the [100] and [010] directions (corresponding to the long axis of the ellipses). Therefore, the transfer of holes along the [001] direction is much easier than that along other directions
Paper
in the ky–kz and kz–kx planes due to the smallest effective mass along the [001] direction. 4. Density of states and charge density In order to understand the different properties of the effective masses shown by electrons and holes along different directions, the total density of states (DOS) and partial density of states (PDOS) of K3B6O10Br are calculated and shown in Fig. 5. It can be seen that the VBM is mainly composed of Br 4p states, while O 2p states mainly occupy the valence band in the energy range between 3.3 eV and 0.6 eV. Thus the main contribution from the p states, which are anisotropic, can result in the different effective masses of holes along different directions. On the other hand, the CBM is mainly formed by the s states of the O, K and Br atoms. Because the s states are isotropic, similar effective masses of electrons along different directions can be understood. Overall, the results are in good agreement with the calculated effective masses of carriers above. Considering that the nonequivalent metal–oxygen polyhedra linked by corner-sharing can enhance the separation of photogenerated carriers,17 the possible enhancement effect for the separation of carriers in the similar B–O polyhedra ([BO3] and
Fig. 5 Calculated total density of states (TDOS) and partial density of states (PDOS) of K3B6O10Br at the VBM (a) and CBM (b, c), respectively. The Fermi level is set to zero.
This journal is © the Owner Societies 2015
Phys. Chem. Chem. Phys.
View Article Online
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
Paper
[BO4]) was also investigated. From the PDOS in Fig. 5(c), the s and p states of both B1 and B2 have contributions to the CBM, while the contribution from B1 in [BO4] is more than that from B2 in [BO3], resulting in an accumulation of electrons in the [BO4] units by the B2–O–B1 bridges. On the other hand, combining the TDOS (Fig. 5(b)), it can be seen that the contribution from the B atoms is smaller than that of the K, O and Br atoms. Therefore the nonequivalent B–O units in K3B6O10Br can promote the separation of photogenerated charge carriers but the effect is limited. In addition, to further determine the orientation of the smallest effective mass of holes and the isotropic properties of the small effective masses of electrons, we calculated the charge density near the VBM and CBM and show this in Fig. 6. It’s clear that the charges mainly accumulate in the Br p states for the VBM, which is in good accordance with the analysis from the DOS. It can also be seen that the lobes of the Br p states are mainly along the [001] direction and thus electron transfer to the neighboring atoms along the [001] direction will be easier, which shows the smallest effective mass of holes. The charge density of the CBM is somewhat complicated, but it can be seen that the electrons occupy the spherically symmetric s orbitals of the O, K and Br atoms, showing an isotropic distribution. All of the results are consistent with the analysis of the effective masses of electrons and holes above, and also prove the smallest effective mass of holes along the [001] direction. In principle, the highest photocatalytic activity of K3B6O10Br can be obtained once the direction of the built-in electric field is consistent with the direction along which carriers can transfer most easily. From the results, it can be seen that the built-in electric field induced by the electric dipole moments is along the [001] direction in K3B6O10Br. Meanwhile, the smallest effective mass of holes is also along the [001] direction and the small effective masses of electrons distribute isotropically.
Fig. 6 The charge density of K3B6O10Br for the bottom of the conduction band (a) in the range of 5.29 to 5.32 eV and for the top of the valence band (b) in the range of 0.05 to 0 eV. The color marks of the atoms are the same as Fig. 1.
Phys. Chem. Chem. Phys.
PCCP
Therefore, the built-in electric field can further promote the transfer of the photogenerated electrons along the [001] direction and holes along the opposite direction, resulting in the accumulation of electrons to the (001) surface and holes to the (001% ) surface. So if K3B6O10Br mainly exposes the {001} surface, it will show the best photocatalytic activity. However, the samples of K3B6O10Br synthesized and applied to the dechlorination experiment mainly expose the (211) surface, as shown in the XRD pattern and the photograph of the sample.18,33 Thus it can be inferred that the photocatalytic activity is limited by the less exposed {001} surface to some extent. Of course, there is still a projection of the built-in electric field along the direction perpendicular to the (211) surface. Therefore, the built-in electric field can promote the transfer and separation of photogenerated carriers to some extent, although this will not have greatest effect. Based on the analysis above, we can propose that the K3B6O10Br with more exposed {001} surface may have the highest photocatalytic efficiency.
5. K3B6O10Cl Meanwhile, an examination of nonlinear optical material K3B6O10Cl with a similar structure to K3B6O10Br was also performed. It shows the same synergistic effect between the built-in electric field and the effective mass for the transfer and separation of photogenerated carriers as shown in K3B6O10Br. The similar geometric structure generates a similar polarization along the c axis in K3B6O10Cl.31 Fig. 7 shows its charge density with the composition of VBM and CBM, similar to that of K3B6O10Br. The p states in VBM ensure the easiest transfer along the c axis for holes and the isotropic contribution from the s states in CBM indicates the isotropic transfer ability of the electrons. Therefore, the internal electric field in K3B6O10Cl can also promote the transfer of carriers along the [001] direction
Fig. 7 The charge density of K3B6O10Cl for the bottom of the conduction band (a) and for the top of the valence band (b). Purple, olive, red and green balls denote K, B, O and Cl atoms, respectively.
This journal is © the Owner Societies 2015
View Article Online
PCCP
synergistically with the intrinsic transfer nature of electrons and holes.
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
Conclusion The properties of carrier transfer and separation in K3B6O10Br were investigated by examining both the intrinsic built-in electric field and the effective masses of the photogenerated electrons and holes along different directions. The corresponding energy band structure, density of states and charge density were also investigated to further understand the different properties exhibited by the effective masses of electrons and holes along different directions. Our results show that the built-in electric field in K3B6O10Br is along the [001] direction. The effective masses of electrons, about 0.5 me, are isotropic along different directions, because of the spherically symmetric s orbitals of the O, K and Br atoms contributing to the CBM. Furthermore, the smallest effective mass of holes is about 3.74 me, along the [001] direction, which is consistent with the direction of the builtin electric field induced by the electric dipole moments, while the effective masses of holes are very large along all directions perpendicular to the built-in field, due to the anisotropic properties of the p states contributing to the VBM. Therefore, the built-in electric field in K3B6O10Br can show a synergistic effect with the intrinsic transfer ability of carriers imposed by their small effective masses along the [001] direction. However, the K3B6O10Br synthesized in the experiment mainly exposes the (211) surface, which limits its higher photocatalytic activity to some extent. Taken together, our results suggest that K3B6O10Br, exposing more of the {001} surface, will show a higher photocatalytic activity. Meanwhile, there is a slight enhancement effect due to the nonequivalent B–O units for the separation of electrons and holes. Similarly, K3B6O10Cl shows the same synergistic effect for the transfer of carriers and thus can be a potential photocatalyst. This work may provide some proposals for the design and synthesis of nonlinear materials with higher efficiencies of separation of photogenerated electrons and holes.
Acknowledgements This work is supported by the National Basic Research Program of China (973 program, 2013CB632401), National Natural Science foundation of China under Grant 11374190, 21333006, and the Fund for Doctoral Program of National Education 20120131110066, 111 Project B13029. We also thank the National Supercomputer Center in Jinan for providing high performance computation.
References 1 A. Xu, Y. Gao and H. Liu, J. Catal., 2002, 207, 151–157. 2 G. Liu, Y. Zhao, C. Sun, F. Li, G. Lu and H. Cheng, Angew. Chem., Int. Ed., 2008, 47, 4516–4520. 3 R. Asahi, T. Morikawa, T. Ohwaki, K. Aoki and Y. Taga, Science, 2001, 293, 269–271.
This journal is © the Owner Societies 2015
Paper
4 P. Wang, B. Huang, X. Qin, X. Zhang, Y. Dai, J. Wei and M.-H. Whangbo, Angew. Chem., Int. Ed., 2008, 47, 7931–7933. 5 X. Ma, Y. Dai, L. Yu and B. Huang, Sci. Rep., 2014, 4, 3986. 6 X. Ma, Y. Dai, L. Yu, Z. Lou, B. Huang and M.-H. Whangbo, J. Phys. Chem. C, 2014, 118, 12133–12140. 7 K. Maeda, T. Takata, M. Hara, N. Saito, Y. Inoue, H. Kobayashi and K. Domen, J. Am. Chem. Soc., 2005, 127, 8286–8287. 8 A. Kudo, I. Tsuji and H. Kato, Chem. Commun., 2002, 1958–1959. 9 X. Zhang, Y. Zhu, X. Yang, S. Wang, J. Shen, B. Lin and C. Li, Nanoscale, 2013, 5, 3359–3366. 10 G. Wang, B. Huang, X. Ma, Z. Wang, X. Qin, X. Zhang, Y. Dai and M.-H. Whangbo, Angew. Chem., Int. Ed., 2013, 52, 4810–4813. 11 T. Jing, Y. Dai, W. Wei, X. Ma and B. Huang, Phys. Chem. Chem. Phys., 2014, 16, 18596–18604. 12 T. Xie, C. Liu, L. Xu, J. Yang and W. Zhou, J. Phys. Chem. C, 2013, 117, 24601–24610. 13 H. Wang, L. Zhang, Z. Chen, J. Hu, S. Li, Z. Wang, J. Liu and X. Wang, Chem. Soc. Rev., 2014, 43, 5234–5244. 14 M. Murdoch, G. I. N. Waterhouse, M. A. Nadeem, J. B. Metson, M. A. Keane, R. F. Howe, J. Llorca and H. Idriss, Nat. Chem., 2011, 3, 489–492. 15 J. L. Giocondi and G. S. Rohrer, J. Phys. Chem. B, 2001, 105, 8275–8277. 16 W. Wang, B. Huang, X. Ma, Z. Wang, X. Qin, X. Zhang, Y. Dai and M.-H. Whangbo, Chem. – Eur. J., 2013, 19, 14777–14780. 17 R. Zhang, Y. Dai, Z. Lou, Z. Li, Z. Wang, Y. Yang, X. Qin, X. Zhang and B. Huang, CrystEngComm, 2014, 16, 4931–4934. 18 X. Fan, L. Zang, M. Zhang, H. Qiu, Z. Wang, J. Yin, H. Jia, S. Pan and C. Wang, Chem. Mater., 2014, 26, 3169–3174. 19 L. Li, P. A. Salvador and G. S. Rohrer, Nanoscale, 2014, 6, 24–42. 20 N. Umezawa, S. Ouyang and J. Ye, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 83, 035202. 21 X. Ma, Y. Dai, M. Guo and B. Huang, ChemPhysChem, 2012, 13, 2304–2309. ¨ller, Comput. Mater. Sci., 1996, 6, 22 G. Kresse and J. Furthmu 15–50. ¨ller, Phys. Rev. B: Condens. Matter 23 G. Kresse and J. Furthmu Mater. Phys., 1996, 54, 11169–11186. ¨chl, Phys. Rev. B: Condens. Matter Mater. Phys., 1994, 24 P. E. Blo 50, 17953–17979. 25 J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh and C. Fiolhais, Phys. Rev. B: Condens. Matter Mater. Phys., 1992, 46, 6671–6687. 26 J. P. Perdew, K. Burke and M. Ernzerhof, Phys. Rev. Lett., 1996, 77, 3865–3868. 27 H. Jiang, J. Phys. Chem. C, 2012, 116, 7664–7671. 28 A. Yamasaki and T. Fujiwara, Phys. Rev. B: Condens. Matter Mater. Phys., 2002, 66, 245108. 29 P. S. Yadav, R. K. Yadav, S. Agrawal and B. K. Agrawal, Physica E, 2007, 36, 79–85. 30 M. Zhang, X. Su, S. Pan, Z. Wang, H. Zhang, Z. Yang, B. Zhang, L. Dong, Y. Wang, F. Zhang and Y. Yang, J. Phys. Chem. C, 2014, 118, 11849–11856.
Phys. Chem. Chem. Phys.
View Article Online
Published on 08 June 2015. Downloaded by University of Pennsylvania Libraries on 18/06/2015 05:34:26.
Paper
31 H. Wu, S. Pan, K. R. Poeppelmeier, H. Li, D. Jia, Z. Chen, X. Fan, Y. Yang, J. M. Rondinelli and H. Luo, J. Am. Chem. Soc., 2011, 133, 7786–7790. 32 G. Al-Ama, E. L. Belokoneva, S. Y. Stefanovich, O. V. Dimitrova and N. N. Mochenova, Crystallogr. Rep., 2006, 51, 225–230. 33 M. Zhang, S. Pan, X. Fan, Z. Zhou, K. R. Poeppelmeier and Y. Yang, CrystEngComm, 2011, 13, 2899–2903. 34 I. D. Brown and D. Altermatt, Acta Crystallogr., Sect. B: Struct. Sci., 1985, 41, 244–247.
Phys. Chem. Chem. Phys.
PCCP
35 N. E. Brese and M. O’Keeffe, Acta Crystallogr., Sect. B: Struct. Sci., 1991, 47, 192–197. 36 Z. Li, Y. Dai, X. Ma, Y. Zhu and B. Huang, Phys. Chem. Chem. Phys., 2014, 16, 3267–3273. 37 P. A. Maggard, T. S. Nault, C. L. Stern and K. R. Poeppelmeier, J. Solid State Chem., 2003, 175, 27–33. 38 B. Zhang, M.-H. Lee, Z. Yang, Q. Jing, S. Pan, M. Zhang, H. Wu, X. Su and C.-S. Li, Appl. Phys. Lett., 2015, 106, 031906. 39 D. Kurita, S. Ohta, K. Sugiura, H. Ohta and K. Koumoto, J. Appl. Phys., 2006, 100, 096105.
This journal is © the Owner Societies 2015
