Doping effects on catechol functionalized anatase TiO2(101) surface for dye-sensitized solar cells

Doping effects of Al, Mg and Cr on the structural and photoelectric properties of catechol functionalized anatase TiO2(101) surface (CFAS) have been studied using density-functional theory. The results indicate that the adsorption processes of CFAS and catechol functionalized doped anatase TiO2(101) surfaces (CFDAS) are all exothermic and these adsorption systems are quite stable. The relative lower formation energy of Al-doped TiO2 means that it is energetically favorable structure under Ti-rich conditions. For band structure of catechol-Cr-doped-TiO2, the electron transition energy will be reduced, and visible light absorption will be extended on account of the decreased band gap and widespread impurity states. The positive Fermi energy shift of Cr-doped TiO2 suggests that it is beneficial to increase the open circuit voltage compared with pure TiO2 under the same conditions. When catechol as a model organic sensitizer functionalizing the pure and Al, Mg and Cr doped TiO2 (101) surfaces, a positive shift of the Fermi energies is observed in comparison with those materials without catechol functionalization. Compared with the optical properties of CFDAS, Cr doping has a greater effect on the optical properties of anatase TiO2 (101) surface than that of Al or Mg doping. The results show that Cr doped anatase TiO2 (101) surface is a better photoanode material and can be applied in Dye-Sensitized Solar Cells.


Introduction
Dye-sensitized solar cells (DSSCs) have drawn enormous attention because of their low manufacturing cost, high efficiencies, environmental-friendliness, and so on [1,2]. Several efforts have been made to enhance the performance of DSSCs by improving the properties of sensitizers [3][4][5][6], counter electrode materials [7,8], electrolytes [9] and the photoanode materials [10,11], especially TiO 2 . To date, various TiO 2 modification methods including metal (Al, Mg, Zr, Nb, Cr, W) doping have been utilized to construct DSSCs with high energy-conversion efficiency [10][11][12][13][14][15][16][17][18]. Recently, Khosravi et al have revealed that Al-doped TiO 2 thin films prepared by spray pyrolysis method exhibited potential photovoltaic applications [16]. Janoha et al have demonstrated that Mg-doped nanostructure TiO 2 electrode increased the power conversion efficiency from 6.26% to 7.36% [17]. Nguyen et al reported that Cr doped TiO 2 nanotubes enhanced the photocurrent intensity to improve performance of DSSCs [18]. Besides, the interaction between dyes and the surface of TiO 2 has attracted increasing attention [19][20][21][22]. Meanwhile, catechol functionalized TiO 2 as a prototypical model for DSSCs has also received much attention [23][24][25]. The strength of optical absorption in the visible region plays an essential role in photovoltaic efficiency of catechol-TiO 2 interfaces [23]. Li et al [24,25] have studied the Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. adsorption behaviors of catechol on anatase (101) surface and rutile TiO 2 (110) surface. Risplendi et al [26] have found that the performance of DSSCs employed by catechol as an anchoring group is better than that of isonicotinic acid. Liu et al [27] have pointed that bidentate adsorption mode for catechol on the anatase TiO 2 (101) surface is essentially immobile. Lin et al [28] have showed that the thermal fluctuations of catechol on the anatase TiO 2 (101) surfaces enhance the absorption spectrum. Li et al [29,30] have selected catechol-TiO 2 inteface as a research object for electron injection process to investigate the effects of Zn and W dopant in TiO 2 by density functional calculations. As far as we know, many studies have been focused on the doped nanostructure TiO 2 or the interplay between catechol and TiO 2 surfaces [31,32]. However, the detail mechanism of metal doping effects for catechol functionalized anatase (101) surface (CFAS) remains to be elucidated. To obtain the mechanism of doping effects of Al, Mg, and Cr on CFAS, we examined the formation energies of doped TiO 2 systems, adsorption energies, band structures, density of states, shifts of Fermi energy and optical properties of doped configurations by performing first-principles DFT calculations. In this paper, catechol-TiO 2 , catechol-Al-doped-TiO 2 , catechol-Mg-doped-TiO 2 and catechol-Cr-doped-TiO 2 represent catechol functionalized pure and doped TiO 2 (101) surfaces, respectively. This work may provide insight into highly efficient of DSSCs by metal doped TiO 2 .

Computational methods
Plane wave DFT calculations were performed within VASP code in MedeA software [33,34]. The cutoff energy was 400 eV. 2×2×2 Monkhorst-Pack k-point mesh [35] were used for geometry optimization and 4×4×4 for electronic and optical properties calculations. Exchange-correlation functional was described by the Perdew-Burke-Ernzerhof (PBE) [36], and a Hubbard U term of 6 eV to both O (2p) and Ti (3d) states [37,38] was employed. A force convergence tolerance on the atoms of<0.02 eV Å −1 was set for geometry optimizations. The calculated anatase bulk lattice parameters are a=3.776 Å and c=9.486 Å, which are consistent with the experimental values (a=3.782 Å and c=9.502 Å) [39]. The anatase TiO 2 (101) surface was built from a 3×3 108-atom supercell. The slab model included four TiO 2 trilayers (O-Ti-O) thick, with a vacuum layer of 15 Å. In order to mimic the bulk effects, atomic positions at the bottom of two O-Ti-O trilayers were fixed.

Results and discussion
3.1. Adsorption energy and formation energy of doped configurations 3.1.1. Adsorption energy Take the factor of stability into account, the bidentate adsorption mode is chosen to study the doping effects on CFAS [27]. The optimized configuration of CFAS is shown in figure 1. To further study the doping effects for adsorption configuration, Ti (1) represents the substitutive Ti atom for Al, Mg and Cr atoms, respectively. To reveal the stability of doped systems, the adsorption energy (E ads ) is estimated according to )and E catechol ( )are the energies of adsorption system, mutually independent TiO 2 (101) surface and catechol molecule, respectively. According to this definition, a negative value of E ads indicates the doped system is stable.
The adsorption energies for adsorption systems are listed in table 1. The calculated adsorption energy for catechol-TiO 2 is −1.24 eV, and its absolute value is closer to the calculated value of 1.25 eV by Liu et al [27]. It's worth noting that our definition of the adsorption energy is contrary to that of Liu et al The adsorption energy value (−3.47 eV) of catechol-Mg-doped-TiO 2 in table 1 is the lowest of all adsorption systems. The relative lower adsorption energy means that the adsorption system possesses better structural stability. Table 1 also demonstrates that the adsorption energies of all adsorption systems are negative. The above results reveal that the adsorption processes of catechol on pure and doped TiO 2 (101) surfaces are exothermic and the adsorption systems are quite stable.

The formation energy of doped configurations
The concentration c of point defects in thermodynamic equilibrium can be expressed as follows: [40].
Here, E f is the defect formation energy, and the lower formation energies of defects, the more likely to form. By exploring possibility, stability and optimal growth conditions of doping, one can study the dopant formation energies, according to the following equation [41] [42]. From figures S1-S2 and table 3, it can be seen that the band gaps of Al and Mg-doped TiO 2 (3.02 eV and 2.95 eV, respectively) are a little bit lower than that of pure TiO 2 (3.04 eV). The result reveals doped Al or Mg atoms could reduce the band gaps of pure TiO 2 , resulting in a small redshift of the optical absorption of TiO 2 , and the theoretical prediction for the redshift of the optical absorption of Al-doped TiO 2 is in accordance  with the experimental report [43]. In addition, compared with pure TiO 2 , the Fermi levels for Al and Mg-doped TiO 2 (see figures S1-S2) shift downward to valence band. Figure 3 gives the band structure of Cr-doped TiO 2 . The valence band maximum (VBM), the conduction band minimum (CBM), CBM+1, CBM+2 and CBM+3 are labeled in figure 3. The calculated band gap of Cr-doped TiO 2 (2.06 eV) is narrower than that of pure TiO 2 (3.04 eV, see table 3). The electrons in VBM can also transit to CBM+1 or CBM+2 or CBM+3. The transition energies of E VBM, CBM+1 (2.08 eV) , E VBM, CBM+2 (2.25 eV) and E VBM, CBM+3 (2.98 eV) are also lower than the band gap of pure TiO 2 . For these results, the appearance of these new energy levels cause Fermi level of Cr-doped TiO 2 to shift upward to conduction band and optical spectrum to red-shift compared with pure TiO 2 . Figure 4 shows the band structure of catechol-TiO 2 , and the corresponding VBM-3, VBM-2, VBM-1, VBM, CBM, and CBM+1 are labeled. Figure 4 demonstrates three impurity energy levels in the energy range are between −2.3 and 0 eV, ascribing to the catechol functionalized. From table 3, it is found that the calculated band gap of catechol-TiO 2 (1.17 eV) is narrower than that of pure TiO 2 . Open-circuit voltage (V oc ) and the short-circuit current (I sc ) have good relevance to the band gap of solar cell's material [44,45]. The narrower the band gap of the solar cell, the lower the V oc , and the higher the I sc of corresponding solar cell. This implies that introduction of impurity energy levels will red shift of optical absorption edge of catechol-TiO 2 , promote the recombination of photogenerated carriers and increase the I sc . Figures S3-S4 show the band structure of catechol-Al-doped TiO 2 and catechol-Mg-doped TiO 2 , respectively. The results of figures S3-S4 show that some impurity energy levels of catechol enter into the valance band. From figures S3-S4 and table 3, the band gaps of catechol-Al-doped TiO 2 and catechol-Mg-doped TiO 2 are 1.69 eV and 0.33 eV, respectively. According to exhibits the band structure of catechol-Cr-doped TiO 2 shown in figure S5, the three impurity energy levels (−2 eV-0 eV) derive from catechol adsorption, and other impurity energy levels (0 eV-1 eV) mainly originate from introduction of Cr. From table 3, the band gap of catechol-Cr-doped TiO 2 is 0.32 eV, which decreases significantly compared with that of pure TiO 2 . The reduced

Electron injection mechanism
To trace the electron injection mechanism, the partial charge densities of catechol-TiO 2 are displayed in figure 5. Figure 5 shows that the electronic density from VBM is predominately located on the catechol adsorbed on the TiO 2 (101) surface, while the electronic densities from CBM and CBM+1 are basically located on the Ti (3d) orbitals of TiO 2 (101) surface. It is found that other partial charge densities from the VBM-1 and VBM-2 are mainly dominated by π-conjugated orbitals of the catechol and the adsorption interface, and the partial charge densities for VBM-3 mainly reside in TiO 2 (101) surface, suggesting that the catechol and TiO 2 (101) surface could interact with each other. The electrons are excited from the photoexcited catechol to the conduction band of TiO 2 directly, which proves a direct injection mechanism [46]. The partial charge densities of catechol-Al-doped-TiO 2 , catechol-Mg-doped-TiO 2 and catechol-Cr-doped-TiO 2 are displayed in figures S6-S8, respectively. Figure S6 shows that the electronic density from VBM mainly consists of π-conjugated orbitals of the catechol, while the electronic densities from CBM and CBM+1 mainly reside in the Ti (3d) orbitals of TiO 2 (101) surface. It is obvious that some partial charge density of VBM-2 exists in the nearby doped Al atom. Figure S7 presents that the electronic density from VBM mainly resides in the nearby doped Mg atom of TiO 2 (101) surface, while the electronic density from CBM mainly consists of π-conjugated orbitals of the catechol. Figure S8 shows that the electronic densities from VBM and CBM mainly reside in the nearby doped Cr atom of TiO 2 (101) surface, while the electronic densities from VBM-2 and VBM-3 mainly consist of π-conjugated orbitals of the catechol. From figures S6-S8, it can be seen that the introduction of Al, Mg and Cr have a large impact on the partial charge densities of catechol adsorbed doped TiO 2 (101) systems for the Γ point of specific bands and optical properties of catechol adsorbed doped TiO 2 (101) systems.

The effect of Fermi energy
As we know, TiO 2 (101) surface has attracted much interest in DSSCs [47][48][49]. Figure 6 shows the Fermi energy of pure, doped TiO 2 (101), and catechol adsorbed pure and doped TiO 2 (101) systems. For DSSCs, V oc is  Then we further analyzed the electronic structures of the TiO 2 (101) surface under the influence of the functionalizing molecules. Figure 9 shows the total density of states (TDOS) of CFAS and catechol, respectively. It can be observed that catechol exerts a key influence on electronic properties of pure TiO 2 (101) surface. The adsorbed catechol gives rise to narrow band gap in the electronic properties of pure TiO 2 (101) surface, hence optical adsorption margin of CFAS moves to longer wavelength. Besides, adsorbed catechol produces three impurity states in the range of −2.5 eV-0 eV in figure 9. It is clear that there are delocalization and strong hybridization between occupied states and the top of the original valence band of CFAS. Therefore, it reveals that there is an interaction between catechol and pure TiO 2 (101) surface. Three impurity states promote charge carriers transition from valence band (or conduction band) to impurity states.
To explore the constituent of the impurity energy levels due to catechol functionalized, the TDOS of catechol functionalized pure and doped TiO 2 (101) systems are illustrated in figure 10. The energy bands of TDOS of catechol-Al-doped-TiO 2 shift wholly to the higher energy region compared with that of catechol-TiO 2 (see figures 10(a) and (b)). From figure 10(b), we can see clearly that only one impurity peak appears near the Fermi energy in TDOS of catechol-Al-doped-TiO 2 and impurity states caused by catechol functionalized mainly overlap with the valence band. As shown in figure 10(c), energy band also moves to the higher energy region and catechol functionalized generates the impurity states which overlapped with the valence band for catechol-Mg-doped-TiO 2 . From figure 10(d), it can be seen that for catechol functionalized Cr-doped TiO 2 (101) surface, impurity states mainly contributed by catechol and Cr-doped appear localized between valence band and conduction band in the range from −2 eV─1 eV. Hence, the conductance of this system increases remarkably by reason that electrons of the valence band can enter into impurity states.

Optical properties
Absorption of photon describes optical properties, which provides detail information about the density of states and electronic band structure of a semiconductor [51]. Usually, the optical absorption coefficient is correlated with the imaginary part of the dielectric constant. The optical absorption spectrum of pure TiO 2 (101), doped TiO 2 (101) surfaces, and catechol adsorbed pure and doped TiO 2 (101) systems are plotted in figure 11. We take visible-light optical absorption into consideration. From figure 11, it is obvious that all doped TiO 2 (101) systems induce the enhancement of visible light absorption, in comparison with that of pure TiO 2 . After catechol adsorbed pure and doped TiO 2 (101) systems, the adsorbed systems can harvest longer-wavelength visible-light. For optical absorption spectrum of Mg, Cr, and Al doped TiO 2 (101) surface, the intensity of absorption peak of Mg-doped TiO 2 located at the range of 0-1.5 eV is the largest one. Moreover, the intensity of absorption peak of Cr-doped TiO 2 located at the range of 1.5-3 eV is the largest one. For catechol adsorbed pure and doped TiO 2 (101) systems, the intensity of absorption peak of catechol adsorbed Cr-doped TiO 2 located at the range of 1-3 eV is the largest one. That is because that the impurity energy levels in doped systems benefit the light absorption. As a bridge, the impurity energy levels will benefit the electron transition [52]. Therefore, compared with pure TiO 2 , the light absorption abilities of catechol-Cr-doped-TiO 2 are enhanced in longer  wavelengths regions. In brief, Cr-doped TiO 2 exhibits a more efficient material for DSSCs, these results agrees well with the recent experiment [18].

Conclusions
In this work, we report a theoretical investigation of doping effects of CFAS. According to our study, the negative adsorption energies of CFDAS reveal that the processes of catechol adsorbed on pure and doped anatase TiO 2 (101) surfaces are exothermic. Catechol-Mg-doped-TiO 2 possesses the most stability due to the lowest adsorption energy value (−1.20 eV). The calculations of dopant formation energies show that the configuration of Al-doped TiO 2 is thermodynamically favorable under Ti-rich conditions. The substitution of Al, Mg and Cr for Ti in anatase TiO 2 (101) surface would decrease band gap due to the gap states. Catechol functionalization introduces three impurity energy levels in the range of −2.5 −0 eV. Compared with the Fermi energy of pure TiO 2 , Cr-doped TiO 2 moves to the positive direction. The results indicate that Cr-doped TiO 2 is beneficial to increase the open circuit voltage. Furthermore, catechol adsorbed Cr-doped TiO 2 will cause narrow band gap, superior absorption in the visible light region. The results demonstrate that Cr-doped TiO 2 is a potential candidate as a photoanode material of DSSCs field application.