Jie Ma and Lin-Wang Wang Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA. Abstract

Transcription

1 The role of the isolated s states in BiO on the electronic and atomic structures Jie Ma and Lin-Wang Wang Lawrence Berkeley National Laboratory, Berkeley, California 90, USA Abstract BiO is one of the most promising photoanodes for water-splitting applications. Similar to many d 0 materials, where the full-shell d electrons are not directly involved in the bonding, the Bi s electrons form isolated low-energy bands in BiO. By systematically altering the energy of the Bi s states, we find direct evidences that the isolated s states, through the s-p coupling, affect the BiO properties, including valence band maximum position, charge density, and atomic structural distortion. We find that many good properties of BiO for water splitting are related to the s-p coupling due to the existence of Bi s states. Based on this understanding, we propose that alloying Bi with Sb can enhance these properties, and hence improve the water-splitting efficiency.

2 Water-splitting, which uses solar energy to generate hydrogen gas from water, is a promising way to produce renewable fuel. Finding good light-absorbing electrode materials for photoelectrochemical cell is an actively pursued research area [ ]. Besides single lightabsorbing material systems, such as TiO [], GaN/ZnO alloy [], and TaON compounds [], one can also find photoanode and photocathod materials separately. The requirements for a good photoanode material include: good light-absorption with a band gap smaller than e, a relatively high conduction band minimum (CBM) level, good carrier mobility, and corrosion resistance. The monoclinic BiO (BO) is one of the promising candidates for photoanode [ 9]. Compared to other oxides like WO [0], it has higher CBM, hence better onset potential. It is relatively stable in base condition. Its hole minority carrier mobility is relatively large, and its optical band gap is. e. Although relatively good, BO is not a perfect photoanode material, especially its band gap is a little bit too large. It is thus critical to understand what determines its band gap and other properties, and how to improve them. Bi atom in BO is in its + state, which leaves its two s electrons alone in the lower part of the valence bands. This situation is similar to the d electrons in d 0 materials, such as ZnO, Cu S, etc. In those d 0 materials, although the d electrons are not directly involved in the bonding process, they can significantly affect many material properties, such as the band gap, band alignment, formation energy, effective mass, and spin-orbit coupling through the p-d coupling []. Some previous studies of BO [ ] pointed out that the isolated Bi s band might affect the band structure and effective mass through the coupling between Bi s electron and the O p electron. However, those claims are made solely based on the partial density of state plot. A systematic and quantitative estimation of the effects of the s-p coupling is still lacking, in particular, not only on the electronic structures, but also on the atomic structures. According to the X-ray diffraction (XRD) experiments, there exist significant distortions around Bi atoms from the ideal scheelite structure where all Bi-O bond lengths are similar []. In the monoclinic BO, the longest Bi-O bonds are 0. Å longer than the shortest ones []. Such a structural distortion is important for its electronic structures, but cannot be reproduced by direct density functional theory (DFT) calculations [ ]. On the other hand, the DFT calculations seem to give a band gap close to the experimental value. Resolving these issues is important in order to fully understand the properties and behaviors of BO, and to propose ways to improve them for

3 water-splitting applications. In this work, by applying an auxiliary external potential on the Bi s states, we have systematically modified the energy of the Bi s states, and observed the change in its electronic and atomic structures. In this way, we can directly study the effects of the Bi s states on the BO properties. We find that: () the Bi s states couple with O p state, and affect the position of valence band maximum (BM) and sub-band charge densities; () the s-p coupling is the source of the Bi atomic distortion from the ideal scheelite structure; () conventional DFT methods, including generalized gradient approximation (GGA) and hybrid functional (HSE0) [], underestimate the s-p coupling, and by increasing the s-p coupling, we can reproduce the experimentally observed atomic distortion; () the apparent good agreement of the GGA calculated band gap of BO is a result of the overestimation of the d state energy, which is an common feature in DFT calculations. Our calculations were based on DFT [8] within GGA formulated by Perdew, Burke, and Ernzerhof (PBE) [9] or HES0 [] as implemented in the ienna Ab-initio Simulation Package (ASP) [0]. The electron wave functions were described by the projected augmented wave (PAW) method [] with an energy cutoff of 00 e. We employed the primitive cell of BO, which contains atoms. The k-point mesh was employed for the Brillouin zone (BZ) integration. To adjust the energy of the isolated Bi s level, we adopted an auxiliary external potential on the Bi s states, following the method in Ref. []. We first discuss the effect of the isolated Bi s states on the band structure of BO. The band structures of BO calculated under various external potentials are displayed in Fig.. When the external potential is zero ( = 0), it is the regular PBE calculation. In this case, both the BM and CBM are located at the M L line, with an indirect band gap of. e. The direct band gap at the A point is. e. The top valence band at the Γ point is 0. e lower in energy than that at the A point. These results are in good agreement with previous publications [ ]. When we shift the Bi s state energy up by applying a positive external potential (denoted as = + e), the conduction band does not change much, but the top valence band changes significantly. The indirect band gap decreases to.0 e with the BM located along the L line, and the top valence band energy difference between the A point and the Γ point increases to 0.9 e. All these changes can be explained by the increased coupling between the O p states and the Bi s states due to their reduced energy difference. This coupling pushes up the O p states, which are the main component of the

4 top valence state, so the BM energy increases and the band gap decreases. Due to the symmetry, the s-p couplings at low-symmetry points are stronger than that at the Γ point. Hence the top valence band at the A point rises much faster than that at the Γ point. The bottom conduction band of BO is mainly the d state, which does not couple strongly with the Bi s states, so there is no change in the conduction band. Reversely, when we apply a negative potential to lower the Bi s energy ( = e) (hence reduce the s-p coupling), we see the opposite effect in the band structure: the indirect band gap increases to. e, and the top valence band energy different between the A point and the Γ point decreases to 0.0 e. When we further lower the Bi s energy ( = e), the band gap increases to.9 e, and the BM moves to the Γ point. Through this study, we reveal the direct evidence for the influence of the Bi s states on the electronic structure of BO. Without the s-p coupling, the BO band gap will increase at least 0. e. The s-p coupling can also be observed from the charge densities of the valence bands, as shown in Fig.. The valence bands of BO are consist of several distinct sub-bands (Fig. ). The upper sub-band is mainly consist of the O p states, and the lower one is mainly consist of Bi s states (the O s and core states are not shown). The differences of the charge densities between the = + and = 0 e calculations of two sub-bands are shown in Fig. (a) and (b), respectively. At = + e, the charge density of the upper sub-band decreases around O atoms and increases around Bi atoms compared to the = 0 case; oppositely, the charge density of the lower sub-band increases around O atoms and decreases around Bi atoms. These are direct consequences of the increased s-p coupling at = + e. We next discuss the effect of the isolated Bi s states on the structure of BO. The monoclinic BO has a distorted scheelite structure, where every Bi atom forms eight Bi O bonds. According to the XRD data [], there are significant distortions of these Bi O bonds. While in the ideal scheelite structure all the Bi O bonds have the similar bond lengths, in monoclinic BO the longest Bi O bond is 0. Å longer than the shortest Bi O bond. However, in DFT calculations, for both PBE and HSE0 functionals, no large distortion has been observed. According to our PBE (HSE0) calculations, the longest Bi O bond is only 0.0 Å ( 0. Å) longer than the shortest one. We find that the bond length distortion is strongly correlated with the s-p coupling. As the Bi s energy is increased by = + e in PBE calculations, the bond length difference also increases to 0. Å. One reason is that

5 as the s-p coupling increases, the BM level rises, which can increase the driving force for atomic distortions to lower the BM energy and hence to lower the electronic energy. Thus, we believe the absence of this distortion in PBE calculation is due to the underestimation of the s-p coupling. However, the = + e shift in the s energy will raise the s level too high compared to the experimental X-ray photoelectron spectroscopy (XPS) measurements of the Bi s level []. We do note that, the s-p coupling not only depends on their original energy difference, but also depends on their coupling constant ψ s H ψ p. This coupling constant might depend on the functional. In HSE0 calculations, after adding a = + e external potential, the bond length distortion is 0. Å, which agrees with the experiments. In this HSE0 calculation, the s levels are close to the experimentally measured XPS data, although still slightly higher, as shown in Fig.. If we increase the mixing parameter of the exact-exchange in HSE0 from 0. to 0., the Bi s level will further decrease 0. e. Thus, we believe, in PBE, and even HSE0 calculation, the s energy is incorrect, and the s-p coupling is too weak. We note that in HSE0 calculations the band gap of BO becomes e, which is much larger than the experimental value of. e. In contrast, the original PBE provides a band gap of. e, in better agreement with the experiment. However, we would like to point out that this good agreement is just accidental due to the erroneous PBE d energy. The BO conduction band is consisted of empty d states. It is well known that the PBE and HSE0 predicts such d state too high in energy. Thus, if this d level is lower down as suggested in Ref. [], PBE will produce a much smaller band gap than the experiments, which is a common PBE phenomena. On the other hand, the HSE0 calculation may predict a band gap close to the experiment. Thus, in order to describe correctly both the BO electronic and atomic structures, one should raise its Bi s level and lower its d level in HSE0 calculations. Finally, based on the above understanding of the important role of Bi s level, we can suggest ways to reduce the band gap of BO. One simple option is to replace the Bi by Sb. This is because the s level of Sb is much higher in energy than the s level of Bi, and the stronger s-p coupling can pushes up the BM energy. If the structure of SbO is forced to stay in the scheelite derived structure, after atomic relaxation, we found that the SbO band gap is.9 e as calculated by PBE, compared to the BO band gap of. e calculated by the same method. The band structure is shown in Fig.. However, the

6 true ground state of SbO is a rutile-type structure []. We thus propose an alloying of Sb into BiO. At low Sb concentrations, the alloy should be stable in the scheelite derived structure. We found that Bi x Sb x O with x =.% can lower the band gap by 0. e, due to the large bowing effect. In summary, we present a systematic study and quantitative evidence for how the existence of Bi s state and its coupling with O p state can change the electronic structure and atomic distortions of BO. We found that the PBE and HSE0 calculated s-p coupling is too weak. By raising the HSE0 calculated Bi s level, and lower the d level, we can account for the observed BO electronic properties and atomic structures. Based on this understanding, we also propose to alloy Bi with Sb, which can reduce the band gap of BO. Acknowledgments The authors are grateful to J. Cooper, L. Chen, I. Sharp, and J. Ager for helpful discussions. This material is based upon work performed by the Joint Center for Artificial Photosynthesis, a DOE Energy Innovation Hub, supported through the Office of Science of the U.S. Department of Energy under Award No. DE-SC Computations are performed using resources of the National Energy Research Scientific Computing Center (NERSC) at the LBNL that are supported by the Office of Science of the U.S. Department of Energy under Contracts No. DE-AC0-0CH. [] M. D. Hernandez-Alonso, F. Fresno, S. Suarez, and J. M. Coronado, Energy Environ. Sci., (009). [] A. Kudo and Y. Miseki, Chem. Soc. Rev. 8, (009). [] Z. Zou, J. Ye, K. Satama, and H. Arakawa, Science, (00). [] A. Fujishima and K. Honda, Nature 8, (9). [] T. Ohno, L. Bai, T. Hisatomi, K. Maeda, and K. Domen, J. Am. Chem. Soc., 8 (0). [] M. Higashi, K. Domen, and R. Abe, J. Am. Chem. Soc., 98 (0). [] A. Kudo, K. Omori, and H. Kato, J. Am. Chem. Soc., 9 (999). [8] K. Sayama, A. Nomura, T. Arai, T. Sugita, R. Abe, M. Yanagida, T. Oi, Y. Iwasaki, Y. Abe,

7 and H. Sigihara, J. Phys. Chem. B 0, (00). [9] H. Luo, A. H. Mueller, T. M. McCleskey, A. K. Burrel, E. Bauer, and Q. X. Jia, J. Phys. Chem. C, 099 (008). [0] K. Sivula, F. L. Formal, and M. Gratzel, Chem. Mater., 8 (009). [] S. H. Wei and A. Zunger, Phys. Rev. B, 898 (988). [] A. Walsh, Y. Yan, M. N. Huda, M. M. Al-Jassim, and S. H. Wei, Chem. Mater., (009). [] W. J. Yin, S. H. Wei, M. M. Al-Jassim, J. Turner, and Y. Yan, Phys. Rev. B 8, 0 (0). [] Z. Zhao, Z. Li, and Z. Zou, Phys. Chem. Chem. Phys., (0). [] J. K. Cooper, S. Gul, F. M. Toma, L. Chen, P.-A. Glans, J. Guo, J. W. Ager, J. Yano, and I. D. Sharp, Chem. Mater., (0). [] A. W. Sleight, H. Y. Chen, A. Ferretti, and D. E. Cox, Mater. Res. Bull, (99). [] J. Paier, M. Marsman, K. Hummer, G. Kresse, I. C. Gerber, and J. G. Ángyán, J. Chem. Phys., 09 (00). [8] W. Kohn and L. J. Sham, Phys. Rev. 0, A (9). [9] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett., 8 (99). [0] G. Kresse and J. Furthmuller, Phys. Rev. B, 9 (99). [] G. Kresse and D. Joubert, Phys. Rev. B 9, 8 (999). [] S. Lany, H. Raebiger, and A. Zunger, Phys. Rev. B, 0(R) (008). [] S. Lany, Phys. Rev. B 8, 08 (0). [] A. R. Landa-Canovas, F. J. Garcia-Garcia, and S. Hansen, Catalysis Today 8, (00).

8 =0 =+ =- =- FIG. : The band structures of BO calculated under various external potentials. = 0 is the regular PBE calculation. Negative lowers the Bi s energy and vice versa. 8

9 (a) (b) FIG. : The charge density difference between the = e and = 0 calculations of the O p-band (a) and Bi s-band (b). The cyan and yellow colors indicate the charge decrease and increase in the = calculation compared to the = 0 calculation, respectively. The big balls represent Bi, medium ones represent, and small ones represent O atoms, respectively. 9

10 HSE0 HSE0+ XPS DOS FIG. : The comparison between the calculated DOS and the experimental XPS data taken from Ref. [] of the valence bands. The HSE0+ denotes the HSE0 calculation with the = + e external potential. 0

11 Z A M L FIG. : The band structure of SbO in the BO derived structure. The indirect band gap is.9 e.

12 =0 =+ =- =-

13 (a) (b)

14 HSE0 HSE0+ XPS DOS

15 Z A M L