Defect processes in F and Cl doped anatase TiO2

Titanium dioxide represents one of the most widely studied transition metal oxides due to its high chemical stability, non-toxicity, abundance, electron transport capability in many classes of optoelectronic devices and excellent photocatalytic properties. Nevertheless, the wide bang gap of pristine oxide reduces its electron transport ability and photocatalytic activity. Doping with halides and other elements has been proven an efficient defect engineering strategy in order to reduce the band gap and maximize the photocatalytic activity. In the present study, we apply Density Functional Theory to investigate the influence of fluorine and chlorine doping on the electronic properties of TiO2. Furthermore, we present a complete investigation of spin polarized density functional theory of the (001) surface doped with F and Cl in order to elaborate changes in the electronic structure and compare them with the bulk TiO2.

Titanium dioxide represents one of the most widely studied transition metal oxides due to its high chemical stability, non-toxicity, abundance, electron transport capability in many classes of optoelectronic devices and excellent photocatalytic properties. Nevertheless, the wide bang gap of pristine oxide reduces its electron transport ability and photocatalytic activity. Doping with halides and other elements has been proven an efficient defect engineering strategy in order to reduce the band gap and maximize the photocatalytic activity. In the present study, we apply Density Functional Theory to investigate the influence of fluorine and chlorine doping on the electronic properties of TiO 2 . Furthermore, we present a complete investigation of spin polarized density functional theory of the (001) surface doped with F and Cl in order to elaborate changes in the electronic structure and compare them with the bulk TiO 2 .
Transition metal oxides such as titanium dioxide (TiO 2 ) are considered as an extremely important class of materials due to their intense catalytic activity, superior chemical stability, long life cycle and high electrical conductivity [1][2][3][4][5][6][7][8][9][10] . Particularly, anatase TiO 2 has been extensively studied because of its abundance and non-toxicity, high photocatalytic activity and responseto visible light arising from high its absorption coefficient and reflectivity [1][2][3][4][5][6][7][8][9][10] . Moreover, it represents the work-horse photoanode material in dye-sensitized solar cells (DSSCs) [11][12][13][14][15][16] , whereas recently has been widely applied as the device electron transport material in both organic-inorganic halide perovskite (PSC) and organic solar (OSC) cells [17][18][19][20][21][22][23][24][25] . Nevertheless, TiO 2 exhibits a wide band gap of around 3.2 eV 26,27 that limits its absorption in the visible and, especially, in the near infrared (NIR) region 7 . A common way to reduce the band gap of TiO 2 is through doping with appropriate elements which has also significant impact on its electronic structure. A vast variety of literature reports previously demonstrated that by doping TiO 2 with nitrogen (N), halogens such as fluorine (F) and chlorine (Cl), or several transition metal ions such as zinc (Zn) or nickel (Ni), significant changes in its electronic structure are observed [28][29][30][31][32][33][34] . Particularly, the formation of mid gap states resulting in a band gap reduction was evident. For instance, when titanium dioxide is doped with Ni the band gap decreases to 2.57 eV, 33 whereas when it is doped with Cl mid gap states are formed and the band gap decreases to 3 eV 31 . Progress on the photocatalytic performance and heterogeneous catalysis of TiO 2 and other oxides such as ZnO has also been accomplished by the introduction of oxygen vacancies 35,36 combined with metallic doping.
Focusing on other defect related projects regarding the TiO 2 and its application to photocatalysis, it is seen that TiO 2 has a fast recombination of the conduction band electrons and valence band holes and as a result it is not a satisfactory photocatalytic for organic degradation. In order to solve that problem as well as to reduce the large band gap, it is seen in the literature that many doped models of TiO 2 can have improved photocatalysis. For example, N doped TiO 2 37 and Nb doped TiO 2 38 is reported to have better photocatalytic properties than pure TiO 2 .
Although a profound band gap reduction can be beneficial to the material's photocatalytic activity as it results in higher absorption of visible light, it might create mid gap states that usually act as charge traps hence having a negative impact on the performance of organic and perovskite solar cells utilizing TiO 2 exclusively as electron transport/extraction material 39 . In those cases the photocatalytic ability of TiO 2 should be suppressed as it degrades its interface with organic/perovskite semiconductor. The formation of mid gap states upon doping of TiO 2 is therefore undesired in OSCs and PSCs. In the present study, fluorine and chlorine doping of the bulk and surface TiO 2 is studied via Density Functional Theory (DFT) in order to examine the electrical structure before and after doping with F and Cl and investigate the potential improvement in the photocatalytic activity of the TiO 2 . Moreover we investigated many different defect sites for the F and Cl in the bulk system and we also calculated for the first time the interstitial sites and the changes in electrical properties of the (001) TiO 2 surface after the F and Cl doping. Total density of states (DOS) and partial DOS (PDOS) of the energetically minimum sites of the defects are considered in order for the electrical structure changes to be fully understood. A band gap reduction is evident in both cases. Moreover, the formation of mid gap states in all cases is also predicted. Such states are highly beneficial for the photocatalytic applications of TiO 2 though they can be detrimental for

Results and Discussion
Bulk anatase TiO 2 . There are three polymorphs of TiO 2 (rutile, anatase and brookite) with the anatase being the prevalent choice for photovoltaic applications as it has superior photocatalytic properties 40 . The crystal structure for the anatase is tetragonal with space group I4/amd and its experimental structural parameters calculated from neutron diffraction are a = 3.782 Å, b = 3.782 Å and c = 9.502 Å 41 . Our theoretically calculated lattice parameters of the anatase are a = 3.804 Å, b = 3.804 Å and c = 9.729 Å which also agree with other theoretical results 42,43 . The percentage of our dopants was 1 dopant atom per 109 atoms of TiO 2 (0.91% doping). In the surface system we calculated 1 dopant atom per 96 atoms of TiO 2 (1.04% additional doping). As regards the density of F and Cl atoms in the bulk systems, we calculated that for the F interstitial we have a density of 7.863 10 20 cm −3 , for the F substitutional we have a density of 7.872•10 20 cm −3 and lastly for the Cl interstitial and Cl substitutional we have a density of 7.825•10 20 cm −3 and 7.829 10 20 cm −3 respectively. On the other hand, for the surfaces, we calculated a density of 4.451•10 20 cm −3 for the F interstitial and 4.423•10 20 cm −3 for the Cl interstitial. According to our DFT calculations, the F atom is stable either as an oxygen substitutional defect or an interstitial defect in the bulk TiO 2 system. We found that in the case of interstitial, the fluorine atom is located at a distance of 1.983 Å from the nearest oxygen atom (see Figs. 1a and 2a) in agreement with previous studies 33 . Examining thoroughly the various defect formations, we concluded that the minimum energy configuration is when fluorine occupies an oxygen site displacing the oxygen to an interstitial site, as seen in Figs. 1b and 2b. Moreover, the simple substitution of an O atom with F has also been examined (Figs. 1c, 2c). Concerning Cl atom doping of bulk TiO 2 , we show that the Cl can either substitute an oxygen atom or relax in a substitutional position, at a distance of 2.15 Å from the nearest oxygen atom (Figs. 1d,e and 2d,e).
For each supercell, we calculated the DOS (Fig. 3(a)-(f)) and, in Fig. 3a, the total DOS of the pure TiO 2 is shown as a reference. Our calculations were performed with DFT + U model with the Hubbard-U parameter equal to 8.2 eV 33,34 . We calculated the band gap at 3.14 eV, in agreement with previous theoretical studies 33,34,44 , which show a band gap narrowing from 3 to 3.16 eV and close to the experimental value of 3.2 eV.
As we show in Fig. 3b, the F interstitial in the bulk TiO 2 gives rise to a small peak inside the band gap at approximately 0.98 eV above the valence band (VB) and it also decreases the band gap to 3.04 eV. When an oxygen atom is replaced by a fluorine, the mid-gap impurity band is shifted towards the conduction band (Fig. 3d). Figure 4(a)-(d) represents the PDOS of doped and undoped bulk TiO 2 . In order to fully understand the emergence of the mid-gap peak in the case of the F interstitial, we calculated the partial DOS which is shown in Fig. 4a. Figure 5(a)-(f) examines in more detail the PDOS and the orbital contribution to the mid gap rise. There, one can www.nature.com/scientificreports www.nature.com/scientificreports/ see that the conduction band is mainly attributed to Ti while the valence band to O. In more detail,in Fig. 5a, it is shown that the main contributions to the valence and the conduction bands are attributed mainly to the O-2p and Ti-3d respectively. As far as the rise of mid-gap states (Fig. 5b) is concerned, we found that it is mainly attributed to the O-2p and F-2p orbitals. Concerning the minimum energy configuration with a fluorine replacing an oxygen which is displaced to an interstitial, two mid-gap levels emerge, one at 0.48 eV and one at 2.02 eV above the VB maximum. Moreover, it is seen that the band gap decreases by approximately 0.10 eV, reaching a value of 3.04 eV. To shed more light on these mid-gap peaks, a PDOS calculation was conducted again and presented in Fig. 4b. As one can see in Fig. 5d, the main contributions to these mid-gap levels come from O-2p and Ti-3d with and only a minimal contribution originates from fluorine, unlike the previous case of the F interstitial (Fig. 5b). A similar DFT research was conducted by Valentin and Pacchioni 45 and they calculated that when F is inserted as a substitutional defect, the band gap is reduced to 3.08 eV which is also in a good agreement with the present results. Samsudin and Hamid 46 have done an important experimental work on the band gap engineering of anion doped TiO 2 and they calculated that the band gap of TiO 2 is significantly decreased to 3.02 eV, which is again consistent with the present DFT work.
For the bulk Cl:TiO 2 , in the case of a Cl interstitial, the DOS (Fig. 3d) shows peaks at 0.19 eV and 1.38 eV above the conduction band minimum and, in addition, the band gap of the bulk TiO 2 is significantly reduced to 2.89 eV. Looking at the PDOS of the bulk with Cl interstitial, we see that the valence and the conduction bands mainly consist of Ti-3d and O-2p and the mid-gap peak of O-2p and Cl-2p states. For the case of Cl substituting an O, one can see that a mid-gap peak appears again, at 1.77 eV, while the band gap is reduced to 2.84 eV (Figs. 1d  and 2f). Focusing on the experimental work of Sun et al. 47 it is seen that the band gap of the Cl:TiO 2 reaches a value of 2.98 eV. This experimental work is also in agreement with our calculations, therefore it is suggested that band gap engineering of TiO 2 can be used to a number of applications such as photocatalysis.
Surface of anatase tio 2 . In order to develop better photocatalytic materials with visible light response and high activity, such as TiO 2 , more attention should be paid to surface doping with atoms or molecules. However, theoretical investigations of the effect of the surface doping on the surface electronic structure of TiO 2 are at present scarce compared to the studies concerning the bulk system 48 . The aim of this section is to investigate the structural and electronic properties of the F-and Cl-doped TiO 2 surface by using a DFT + U, in spin polarized calculations. We calculated the interatomic distances and angles, the electronic density of states of the undoped and doped TiO 2 surface, as well as the changes of the band gap when the system is doped. For the simulation of the surfacewe used a slab model with a vacuum of 14 Å thickness vertical to the (001) plane and with periodic boundary conditions in the other directions. In our surface system, the top 4 layers were fully relaxed while the bottom 4 layers were kept fixed in order to simulate the bulk area. We chose this particular surface because it is a common choice in other studies concerning the absorption of different atoms and molecules, like CO 2 49 , but the www.nature.com/scientificreports www.nature.com/scientificreports/ interstitial-doping with fluorine or chlorine atoms has never been studied before. Instead, the (101) surface has mostly been considered for fluorine and chlorine doping 50 . However, the (001) TiO 2 surface is considered one of the most highly energetic surfaces of the TiO 2 and, as a result, it often plays the role of the active site in photocatalytic reactions [51][52][53][54][55] . Τo the best of our knowledge only Zhou p. et al. 56 have studied the TiO 2 (001) surface in the case of F doping as a substitution of an O atom. The undoped configuration is shown in Fig. 6a while the minimum energy structures for F and Cl doped TiO 2 (001) surfaces are shown in Fig. 6b,c respectively.
According to our DFT calculations, when fluorine is inserted in the (001) surface as an interstitial (Fig. 7a), it is located at a distance of 2.00 Å from the nearest oxygen while Cl (Fig. 7b) at 2.18 Å. Looking at the DOS for each supercell, in Fig. 8a it is seen that the F interstitial at the surface produces a small impurity band peak at approximately 0.35 eV above the VB. On the other hand, as it is seen in Fig. 8b, when the surface is doped with a Cl atom, two mid-gap peaks arise, which are observed at approx. 0.55 eV and 0.93 eV above the valence band. Concerning the band gap, when the TiO 2 surface is doped with F, the band gap is predicted at a value of 2.24 eV whereas for the Cl-doped surface, the calculated band gap reaches a value of 2.31 eV. The band gap of the undoped TiO 2 surface calculated at 2.37 eV (Fig. 8c) in agreement with other theoretical studies concerning (001) TiO 2 surfaces 57 . Therefore, the insertion of F or Cl on the (001) surface, has a minor effect on the band gap of the TiO 2 system. www.nature.com/scientificreports www.nature.com/scientificreports/ conclusions DFT calculations were performed for fluorine and chlorine-doped anatase TiO 2 bulk and surface structures in order to evaluate the effect this kind of doping on the band gap and the electronic structure of TiO 2 . Both substitutional and interstitial halogen defects were predicted. In all cases, occupied mid-gap states attributed to a hybridization of O-2p with halogen 1 s orbitals were also predicted. Although such states are beneficial for the oxide's photocatalytic activity as they significantly reduce the optical band gap with respect to that of undoped TiO 2 , they might be detrimental for its application as electron transport material in other classes of photovoltaic devices such as organic and perovskite solar cells.

Methods
Computational methodology. We performed periodic DFT calculations using the CASTEP program 58,59 .
The Perdew, Burke and Ernzerhof (PBE) 60 generalized gradient approximation (GGA) functional was employed for the exchange and correlation interactions with ultrasoftpseudopotentials 61 . The cut-off Energy was chosen at 480 eV and a 3 × 3 × 1 Monkhorst-Pack (MP) 62 k-points mesh while supercells of 108 atoms were adopted for www.nature.com/scientificreports www.nature.com/scientificreports/ the bulk system.The structure was optimized with the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method. To consider the effects of electronlocalization, the DFT + U method was employed for spin-polarized calculations with on-site Coulomb repulsions of 8.2 eV for the 3d orbitals of Ti. Finally, for the DOS calculations, a 3 × 3 × 3 k-points mesh of was adopted while for the PDOS a 7 × 7 × 7. The efficacy of the present approach has been demonstrated in recent studies 10,11 . For the surface structures, a supercell consisting of 96 atoms was used, with an energy cut off of 480 eV and a MP k-point mesh of 2 × 2 × 1. Finally, for the density of states, we chose a 7 × 7 × 7 k-point mesh.