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Ab initio calculations of doped TiO2 anatase (101) nanotubes for photocatalytical water splitting applications
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Ab initio calculations of doped TiO2 anatase (101) nanotubes for photocatalytical water splitting applications Oleg Lisovski a, Andrei Chesnokov a, Sergei Piskunov a,n, Dmitry Bocharov a,b, Yuri F. Zhukovskii a, Michael Wessel c, Eckhard Spohr c a
Institute of Solid State Physics, University of Latvia, LV-1063 Riga, Latvia Paul Scherrer Institute, CH-5232 Viligen, Switzerland c Theoretical Chemistry Department, University of Duisburg-Essen, 45141 Essen, Germany b
art ic l e i nf o
a b s t r a c t
Article history: Received 4 May 2015 Received in revised form 11 August 2015 Accepted 2 September 2015
TiO2 (titania) is one of the promising materials for photocatalytic applications. In this paper we report on recently obtained theoretical results for N and S doped, as well as N þS co-doped 6-layer (101) anatase nanotube (NT). First principles calculations in our study have been performed using a modified B3LYP hybrid exchange-correlation functional within density functional theory (DFT). Here we discuss the energy of defect formation mechanism and electronic band structure for nanotubes under study. We also report on influence of dopant concentration on the NT's band structure and discuss the defect–defect interactions. & 2015 Elsevier Ltd. All rights reserved.
Keywords: TiO2 nanotube Atomic structure Electronic structure Hybrid HF-DFT B3LYP calculations
1. Introduction TiO2 (titania) is a promising photocatalyst for water splitting applications. However, bulk titania has low photocatalytic efficiency. It can be improved by making titania into nanotubes (NTs) with large surface area [1–3]. Further improvement of sunlightdriven TiO2 NT catalytical activity is possible through the band gap engineering, e.g. by adding anion dopants. Theoretically, maximal solar energy conversion for a catalyst with a 3.2 eV wide band gap (e.g. TiO2) is approximately 1%, but it can be as high as 15% for a catalyst with a 2.2 eV band gap [4]. Doped TiO2 nanostructures have already shown improved efficiencies as inclusion of dopants leads to narrowing of the band gap from 3.2 eV (pristine material) to 2.0 eV. To shed more light on changes of the electronic structure made by the presence of dopants, we have performed ab initio calculations of TiO2 NTs. In this study we model N and S doped, as well as N þS co-doped anatase NT with (101) morphology, which is reported to be the most stable NT [5]. From our recent calculations on less stable, but more chemically active TiO2 NT rolled up from the (001) nanosheet we know that Nþ S co-doping may result in its visible-light-driven photoresponse enhancement [6]. Therefore from the modeling of the NT rolled-up from the titania nanosheet cut parallel to its (101) surface, we have revealed a n
Corresponding author. Fax: þ 371 67132778. E-mail address: [email protected] (S. Piskunov).
number of dopant sites, and we have observed general trends in the composition of NT's electronic structure as a function of defect concentration in NT's wall.
2. Model and computational details Modeling of S and N co-doped 6-layered (101) TiO2 anatase nanotubes was performed using DFT method with the hybrid exchange-correlation functional (B3LYP having 14% of non-local Fock exchange) as implemented in the CRYSTAL computer code [7]. This computational approach is discussed by us in details elsewhere [6,8,9]. At a first stage of this study a number of undoped 6-layered anatase (101) NTs with chirality indices (n,0) and (0,n) have been modeled and their formation energies have been analyzed. Among them NT with chirality indexes (0,12) has been chosen for further doping. The choice is based on the compromise between a minimal formation energy and a number of atoms in the NT's unit cell. This nanotube consists of 432 atoms (Fig. 1). In the present study we consider NT's consisting of 1 3 and 2 3 periodically repeated “basic” unit cells (Fig. 1). The periodically repeated 1 3 unit cell consists of 36 atoms, while 2 3 one contains 72 atoms, giving dopant concentration of 2.78% (12 dopant per NT unit cell) and 1.39% (6 dopants per NT unit cell), respectively. Moreover we consider four possible dopant sites to substitute the non-equivalent oxygen atoms (Fig. 2). We denote the outermost oxygen
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Fig. 1. 6-layered TiO2 (101) nanotube with chirality indexes (0,12) – (a) front view, (b) side view of 1 3 periodically repeated unit cell and (c) 2 3 unit cell. Periodically repeated units are highlighted. Large balls represent titanium atoms, small balls represent oxygen atoms.
3. Results and discussion 3.1. S doped 6-layer (101) TiO2 nanotubes
Fig. 2. Non-equivalent S or N dopant positions in the NT's wall.
position as the first dopant site, or Position 1, and the innermost the fourth, or the Position 4. The inner atoms follow the sequence as shown in Fig. 2. The dopant formation energies in TiO2 NT were estimated in a following way: tot E Aform = E Atoth/NT + Ehtot − E Atoth − ENT , h
(1)
where E Atot/NT is the calculated total energy of a nanotube conh
taining dopant Ah , Etot h is the total energy of the host atom, which is removed from the nanotube, E Atoth is the total energy calculated for tot the dopant, and ENT stands for the total energy calculated for the perfect nanotube.
Since band structures does not experience essential alterations when doping at different concentrations are considered, we restrict ourselves to displaying only images related to 2.78% defect concentration. In Fig. 3 the band edge positions and defect-induced levels of S doped titania NTs are shown. Solid black lines denote the highest occupied induced levels, in this figure and in the figures below. For the two dopant sites lying closer to the outer surface, sites S1 and S2 (Fig. 2), there is a negative shift in energy for both the bottom of conduction band (CB) and the top of the valence band (VB). In fact, there is no difference between CB/VB positions of the pristine NT and the NTs containing S dopants at the positions S3 and S4. Doping at positions S1 and S4 promotes the highest photocatalytic enhancement, reducing the gap between the lowest unoccupied state and the highest occupied state, from 4.19 eV to 3.14 eV (3.12 eV) and 3.08 eV (3.07 eV) for 1.39% (2.78%) defect concentrations, respectively. It means that S atoms themselves do not provide sufficient rise of photocatalytic activity. S-induced occupied levels are lower at 1.39% concentration. Formation energies are equal for both types of dopants on outer and
Fig. 3. Schematic representation of the band edges and mid-gap states of pristine and S doped TiO2 NTs.
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Table 1 Defect formation energy (in eV) of S and N dopant at 2.78% and 1.39% defect concentrations as calculated by means of Eq. (1). Site
Concentration of defects 1.39%
1 2 3 4
2.78%
S dopant
N dopant
S dopant
N dopant
2.47 2.89 3.43 2.62
3.39 3.49 3.51 3.51
2.47 2.90 3.47 2.62
3.39 4.10 4.15 3.39
inner NT surface, and almost equal for the dopants located in the middle of the nanotube wall. Position S1 is the most favorable, and cost in energy to implement a dopant grows in a row “S1–S4–S2–S3 ” – it is somewhat easier to create a defect on the outer surface than in the middle of a nanotube, which should be ascribed to relatively large size of S atom. At the same time, the S1 site is the most energetically favorable – it requires the lowest formation energy per unit cell/dopant, 2.47 eV for both concentrations (Table 1). As it has been found in all cases the S dopant shows a tendency to be displaced from its initial position. The displacement direction is orthogonal to the tangent line passing through the initial S atom position, and the S atom is protruding out the NT wall. Obviously, it is easier to follow such displacement from initial positions S1 and S4, which explains that the dopant formation energies are lower for these cases. 3.2. N doped 6-layer (101) TiO2 nanotubes Nitrogen dopants do not induce any visible shift in positions of VB top and CB bottom, levels are almost the same as in the case of the pristine structure (Fig. 4). N dopants, however, induce empty states inside the band gap, visualized with dashed black lines. For 2.78% defect concentration these empty states are not always higher than the highest occupied state. As we see in N2 case, the empty state is below an occupied state and is very close to the VB top, which means that in reality it will be easily occupied by electrons with similar energies. In case of N3 structure the highest occupied and the lowest unoccupied levels are located at the same energy level, which means that the empty level will also be occupied. The N3 case exhibits the most advantageous structure among others, but still it is not very promising. In N2 cases the efficiency would be even lower, and in N1 and N4 cases there is an empty level in the target energy interval between 0 and 1.23 eV, which disrupts the
Fig. 5. Possible sites for N dopant if S atom is located in position S1.
whole photocatalytic process. When concentration of N dopant atoms is lowered from 2.78% to 1.39%, i.e., 2 times, a visible difference appears. The lowest induced empty state in N2 and N3 cases is much higher on the energy scale and is slightly above the 1.23 eV level. In the N1 and N4 cases the corresponding level is still approximately 0.5 eV higher than 1.23 eV level. Defect formation energies are given in Table 1. After geometry optimization it becomes obvious that introduction of N dopants does not cause any significant alterations in the structure geometry. 3.3. SþN co-doped 6-layer (101) TiO2 nanotubes In single-atom doping there are only 4 non-equivalent dopant positions. However, after one dopant is introduced, many options for different combinations of dopant positions appear. Due to limited computational resources, we decided to put S dopant in its preferable position, S1. In every modeled co-doped structure the S atom is in position 1, while N dopants are inserted in different positions. Possible positions are assigned by additional indices for identification. “FR” stands for “Front”, “B” for “Between”, “N” for “Near” and “UND” for “Under” (Fig. 5). Electronic structure of six studied N þS co-doped TiO2 NTs with defect concentration of 2.78% is shown in Fig. 6. Note that N3(S1)B and N3(S1)N are identical. The general observation is that improvement in photocatalytic activity of the structures under consideration may be expected. In four cases out of six, the lowest empty state is induced slightly below the 1.23 eV level, and the highest occupied state is between the empty state and the VB top. In two cases the distance between the empty and the occupied induced state is not that large (N1(S1)B and N4(S1)B), which means that it might be relatively easy for electrons to transfer to the empty state and, consequently, to overcome the energy interval between the SHE potential and 1.23 eV potential. This would be more difficult in case of N2(S1)N and N4(S1)UND, where the gap between the highest occupied and lowest empty states is wider. Further, in N3(S1)B case a mixing of the highest occupied and
Fig. 4. Schematic representation of the band edges and mid-gap states of pristine and N doped TiO2 NTs.
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Fig. 6. Schematic representation of the band edges and mid-gap states of pristine and S þN co-doped TiO2 NTs.
lowest induced states is observed at 2.39 eV level which implies a gap between the CB bottom and the highest occupied state of around 3 eV. Finally, in case of N1(S1)FR the lowest empty state is induced within the interval between the SHE and 1.23 eV potential, making the photocatalytic process unrealistic. Edges of bands do not change their positions significantly in N2(S1)N, N3(S1)B and N4(S1)UND cases, and there is a slight negative shift in the rest ones. In N1(S1)B and N4(S1)B cases the lowest empty induced state is now above the 1.23 eV level. In N2(S1)N case this level coincides exactly with the 1.23 eV level. In N3(S1)B model the lowest empty state does not mix with the highest occupied state, being 0.17 eV higher. N3(S1)N and N4(S1)UND models hold the most promising electronic structure, while N1(S1)FR holds the outsider character. A comparison of band edge positions between the 2.78% and 1.39% defect concentration cases shows again that lower dopant concentration produces less prominent alterations in positions of the VB top and the CB bottom. These observations allow us to speculate about possible improvement through modifying the ratio of S and N dopants. If S/N ratio larger than 1 and proper defect concentration is reached, it might be possible to drive the empty level induced by N dopants above the SHE level and to relocate the highest occupied level induced by S dopants closer to 1.23 eV. If this is possible, a fundamental rise of photocatalytic efficiency in water splitting processes can be expected. We also have estimated total energies of investigated systems. No major changes are observed, the difference is in the second or third digit after decimal point. Still, in frame of our simulations this difference is essential for distribution of configurations. In case of 2.78% defect concentration, the most probable configuration is N2(S1), the neighboring value belongs to N1(S1)FR. N4(S1)UND configuration is the least likely to appear. In 1.39% defect concentration case the most probable configuration is N3(S1)N, the neighboring values belong to N2(S1) and N4(S1)UND. The N3(S1)B configuration is the least likely. The general observation is that in most cases S and N atoms have a tendency to be found closer to each other.
4. Conclusions The 6-layered TiO2 (0,12) NT rolled up from the nanosheet cut parallel to the (101) surface is proposed to be the most suitable model for simulations of electronic structure for titania nanotubes. In general, (0,n) nanotubes are found to be more stable than NTs with (n,0) chirality indexes. Electronic structure (band edges positions) of 6-layer (101) anatase NT is similar to the band structure of anatase nanotube made of 9-layer (001) TiO2 nanosheet studied
by us recently [6]. Based on results of our calculations, we predict that lone S or N dopants introduced into the 6-layered TiO2 (0,12) NT cannot result in a significant rise of photocatalytic response. For instance, the N doping may induce empty mid-gap states that can disrupt the photocatalytic process. We found that defect concentration does not have a big impact on the electronic structure of NTs under study; our results show that rise of defect concentration from 1.39% to 2.78% (of doping atoms per unit cell) practically does not shift the band edges and mid-gap states induced by these defects. In this study we show that the S þ N codoping of titania NT can result in enhancement of photocatalytic efficiency, at least qualitatively. At the same time, we have to conclude that changes of TiO2 NT electronic structure induced by co-doping depend on defect concentration.
Acknowledgment This work has been supported by the Alexander von Humboldt Foundation. Support from Latvian National Research Program IMIS2 (2014–2017) is appreciated by us too. D.B. is also grateful for the support through the Latvian National Research Program LATENERGI.
References [1] N.S. Lewis, Toward cost-effective solar energy use, Science 315 (2007) 798–801. [2] T.R. Cook, D.K. Dogutan, S.Y. Reece, Y. Surendranath, T.S. Teets, D.G. Nocera, Solar energy supply and storage for the legacy and nonlegacy worlds, Chem. Rev. 110 (2010) 6474–6502. [3] A. Kudo, Y. Miseki, Heterogeneous photocatalyst materials for water splitting, Chem. Soc. Rev. 38 (2009) 253–278. [4] B.D. Alexander, P.J. Kulesza, I. Rutkowska, R. Solarska, J. Augustynski, Metal oxide photoanodes for solar hydrogen production, J. Mater. Chem. 18 (2008) 2298–2303. [5] M. Lazzeri, A. Vittadini, A. Selloni, Structure and energetics of stoichiometric tio2 anatase surfaces, Phys. Rev. B 63 (2001) 155409, http://dx.doi.org/10.1103/ PhysRevB.63.155409 (URL http://link.aps.org/doi/10.1103/PhysRevB.63.155409). [6] S. Piskunov, O. Lisovski, J. Begens, D. Bocharov, Y.F. Zhukovskii, M. Wessel, E. Spohr, C-, N-, S-, and Fe-doped TiO2 and SrTiO3 nanotubes for visible-lightdriven photocatalytic water splitting: prediction from first principles, J. Phys. Chem. C 119 (2015) 18686–18696, http://dx.doi.org/10.1021/acs.jpcc.5b03691. [7] R. Dovesi, V.R. Saunders, C. Roetti, R. Orlando, C.M. Zicovich-Wilson, F. Pascale, B. Civalleri, K. Doll, N.M. Harrison, I.J. Bush, P. DArco, M. Llunell, M. Caus, Y. Nol, CRYSTAL14 User's Manual, University of Torino, Torino, 2014. [8] O. Lisovski, S. Piskunov, Y.F. Zhukovskii, J. Ozolins, Ab initio modeling of sulphur doped TiO2 nanotubular photocatalyst for water-splitting hydrogen generation, IOP Conf. Ser.: Mater. Sci. Eng. 38 (2012) 012057 (URL http://stacks.iop.org/ 1757-899X/38/i ¼1/a ¼ 012057). [9] Y.F. Zhukovskii, S. Piskunov, J. Begens, J. Kazerovskis, O. Lisovski, First-principles calculations of point defects in inorganic nanotubes, Phys. Status Solidi B 250 (4) (2013) 793–800, http://dx.doi.org/10.1002/pssb.201200817 (URL http://dx. doi.org/10.1002/pssb.201200817).
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Ab initio calculations of doped TiO2 anatase (101) nanotubes for photocatalytical water splitting applications Oleg Lisovski a, Andrei Chesnokov a, Sergei Piskunov a,n, Dmitry Bocharov a,b, Yuri F. Zhukovskii a, Michael Wessel c, Eckhard Spohr c a
Institute of Solid State Physics, University of Latvia, LV-1063 Riga, Latvia Paul Scherrer Institute, CH-5232 Viligen, Switzerland c Theoretical Chemistry Department, University of Duisburg-Essen, 45141 Essen, Germany b
art ic l e i nf o
a b s t r a c t
Article history: Received 4 May 2015 Received in revised form 11 August 2015 Accepted 2 September 2015
TiO2 (titania) is one of the promising materials for photocatalytic applications. In this paper we report on recently obtained theoretical results for N and S doped, as well as N þS co-doped 6-layer (101) anatase nanotube (NT). First principles calculations in our study have been performed using a modified B3LYP hybrid exchange-correlation functional within density functional theory (DFT). Here we discuss the energy of defect formation mechanism and electronic band structure for nanotubes under study. We also report on influence of dopant concentration on the NT's band structure and discuss the defect–defect interactions. & 2015 Elsevier Ltd. All rights reserved.
Keywords: TiO2 nanotube Atomic structure Electronic structure Hybrid HF-DFT B3LYP calculations
1. Introduction TiO2 (titania) is a promising photocatalyst for water splitting applications. However, bulk titania has low photocatalytic efficiency. It can be improved by making titania into nanotubes (NTs) with large surface area [1–3]. Further improvement of sunlightdriven TiO2 NT catalytical activity is possible through the band gap engineering, e.g. by adding anion dopants. Theoretically, maximal solar energy conversion for a catalyst with a 3.2 eV wide band gap (e.g. TiO2) is approximately 1%, but it can be as high as 15% for a catalyst with a 2.2 eV band gap [4]. Doped TiO2 nanostructures have already shown improved efficiencies as inclusion of dopants leads to narrowing of the band gap from 3.2 eV (pristine material) to 2.0 eV. To shed more light on changes of the electronic structure made by the presence of dopants, we have performed ab initio calculations of TiO2 NTs. In this study we model N and S doped, as well as N þS co-doped anatase NT with (101) morphology, which is reported to be the most stable NT [5]. From our recent calculations on less stable, but more chemically active TiO2 NT rolled up from the (001) nanosheet we know that Nþ S co-doping may result in its visible-light-driven photoresponse enhancement [6]. Therefore from the modeling of the NT rolled-up from the titania nanosheet cut parallel to its (101) surface, we have revealed a n
Corresponding author. Fax: þ 371 67132778. E-mail address: [email protected] (S. Piskunov).
number of dopant sites, and we have observed general trends in the composition of NT's electronic structure as a function of defect concentration in NT's wall.
2. Model and computational details Modeling of S and N co-doped 6-layered (101) TiO2 anatase nanotubes was performed using DFT method with the hybrid exchange-correlation functional (B3LYP having 14% of non-local Fock exchange) as implemented in the CRYSTAL computer code [7]. This computational approach is discussed by us in details elsewhere [6,8,9]. At a first stage of this study a number of undoped 6-layered anatase (101) NTs with chirality indices (n,0) and (0,n) have been modeled and their formation energies have been analyzed. Among them NT with chirality indexes (0,12) has been chosen for further doping. The choice is based on the compromise between a minimal formation energy and a number of atoms in the NT's unit cell. This nanotube consists of 432 atoms (Fig. 1). In the present study we consider NT's consisting of 1 3 and 2 3 periodically repeated “basic” unit cells (Fig. 1). The periodically repeated 1 3 unit cell consists of 36 atoms, while 2 3 one contains 72 atoms, giving dopant concentration of 2.78% (12 dopant per NT unit cell) and 1.39% (6 dopants per NT unit cell), respectively. Moreover we consider four possible dopant sites to substitute the non-equivalent oxygen atoms (Fig. 2). We denote the outermost oxygen
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Fig. 1. 6-layered TiO2 (101) nanotube with chirality indexes (0,12) – (a) front view, (b) side view of 1 3 periodically repeated unit cell and (c) 2 3 unit cell. Periodically repeated units are highlighted. Large balls represent titanium atoms, small balls represent oxygen atoms.
3. Results and discussion 3.1. S doped 6-layer (101) TiO2 nanotubes
Fig. 2. Non-equivalent S or N dopant positions in the NT's wall.
position as the first dopant site, or Position 1, and the innermost the fourth, or the Position 4. The inner atoms follow the sequence as shown in Fig. 2. The dopant formation energies in TiO2 NT were estimated in a following way: tot E Aform = E Atoth/NT + Ehtot − E Atoth − ENT , h
(1)
where E Atot/NT is the calculated total energy of a nanotube conh
taining dopant Ah , Etot h is the total energy of the host atom, which is removed from the nanotube, E Atoth is the total energy calculated for tot the dopant, and ENT stands for the total energy calculated for the perfect nanotube.
Since band structures does not experience essential alterations when doping at different concentrations are considered, we restrict ourselves to displaying only images related to 2.78% defect concentration. In Fig. 3 the band edge positions and defect-induced levels of S doped titania NTs are shown. Solid black lines denote the highest occupied induced levels, in this figure and in the figures below. For the two dopant sites lying closer to the outer surface, sites S1 and S2 (Fig. 2), there is a negative shift in energy for both the bottom of conduction band (CB) and the top of the valence band (VB). In fact, there is no difference between CB/VB positions of the pristine NT and the NTs containing S dopants at the positions S3 and S4. Doping at positions S1 and S4 promotes the highest photocatalytic enhancement, reducing the gap between the lowest unoccupied state and the highest occupied state, from 4.19 eV to 3.14 eV (3.12 eV) and 3.08 eV (3.07 eV) for 1.39% (2.78%) defect concentrations, respectively. It means that S atoms themselves do not provide sufficient rise of photocatalytic activity. S-induced occupied levels are lower at 1.39% concentration. Formation energies are equal for both types of dopants on outer and
Fig. 3. Schematic representation of the band edges and mid-gap states of pristine and S doped TiO2 NTs.
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Table 1 Defect formation energy (in eV) of S and N dopant at 2.78% and 1.39% defect concentrations as calculated by means of Eq. (1). Site
Concentration of defects 1.39%
1 2 3 4
2.78%
S dopant
N dopant
S dopant
N dopant
2.47 2.89 3.43 2.62
3.39 3.49 3.51 3.51
2.47 2.90 3.47 2.62
3.39 4.10 4.15 3.39
inner NT surface, and almost equal for the dopants located in the middle of the nanotube wall. Position S1 is the most favorable, and cost in energy to implement a dopant grows in a row “S1–S4–S2–S3 ” – it is somewhat easier to create a defect on the outer surface than in the middle of a nanotube, which should be ascribed to relatively large size of S atom. At the same time, the S1 site is the most energetically favorable – it requires the lowest formation energy per unit cell/dopant, 2.47 eV for both concentrations (Table 1). As it has been found in all cases the S dopant shows a tendency to be displaced from its initial position. The displacement direction is orthogonal to the tangent line passing through the initial S atom position, and the S atom is protruding out the NT wall. Obviously, it is easier to follow such displacement from initial positions S1 and S4, which explains that the dopant formation energies are lower for these cases. 3.2. N doped 6-layer (101) TiO2 nanotubes Nitrogen dopants do not induce any visible shift in positions of VB top and CB bottom, levels are almost the same as in the case of the pristine structure (Fig. 4). N dopants, however, induce empty states inside the band gap, visualized with dashed black lines. For 2.78% defect concentration these empty states are not always higher than the highest occupied state. As we see in N2 case, the empty state is below an occupied state and is very close to the VB top, which means that in reality it will be easily occupied by electrons with similar energies. In case of N3 structure the highest occupied and the lowest unoccupied levels are located at the same energy level, which means that the empty level will also be occupied. The N3 case exhibits the most advantageous structure among others, but still it is not very promising. In N2 cases the efficiency would be even lower, and in N1 and N4 cases there is an empty level in the target energy interval between 0 and 1.23 eV, which disrupts the
Fig. 5. Possible sites for N dopant if S atom is located in position S1.
whole photocatalytic process. When concentration of N dopant atoms is lowered from 2.78% to 1.39%, i.e., 2 times, a visible difference appears. The lowest induced empty state in N2 and N3 cases is much higher on the energy scale and is slightly above the 1.23 eV level. In the N1 and N4 cases the corresponding level is still approximately 0.5 eV higher than 1.23 eV level. Defect formation energies are given in Table 1. After geometry optimization it becomes obvious that introduction of N dopants does not cause any significant alterations in the structure geometry. 3.3. SþN co-doped 6-layer (101) TiO2 nanotubes In single-atom doping there are only 4 non-equivalent dopant positions. However, after one dopant is introduced, many options for different combinations of dopant positions appear. Due to limited computational resources, we decided to put S dopant in its preferable position, S1. In every modeled co-doped structure the S atom is in position 1, while N dopants are inserted in different positions. Possible positions are assigned by additional indices for identification. “FR” stands for “Front”, “B” for “Between”, “N” for “Near” and “UND” for “Under” (Fig. 5). Electronic structure of six studied N þS co-doped TiO2 NTs with defect concentration of 2.78% is shown in Fig. 6. Note that N3(S1)B and N3(S1)N are identical. The general observation is that improvement in photocatalytic activity of the structures under consideration may be expected. In four cases out of six, the lowest empty state is induced slightly below the 1.23 eV level, and the highest occupied state is between the empty state and the VB top. In two cases the distance between the empty and the occupied induced state is not that large (N1(S1)B and N4(S1)B), which means that it might be relatively easy for electrons to transfer to the empty state and, consequently, to overcome the energy interval between the SHE potential and 1.23 eV potential. This would be more difficult in case of N2(S1)N and N4(S1)UND, where the gap between the highest occupied and lowest empty states is wider. Further, in N3(S1)B case a mixing of the highest occupied and
Fig. 4. Schematic representation of the band edges and mid-gap states of pristine and N doped TiO2 NTs.
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4
Fig. 6. Schematic representation of the band edges and mid-gap states of pristine and S þN co-doped TiO2 NTs.
lowest induced states is observed at 2.39 eV level which implies a gap between the CB bottom and the highest occupied state of around 3 eV. Finally, in case of N1(S1)FR the lowest empty state is induced within the interval between the SHE and 1.23 eV potential, making the photocatalytic process unrealistic. Edges of bands do not change their positions significantly in N2(S1)N, N3(S1)B and N4(S1)UND cases, and there is a slight negative shift in the rest ones. In N1(S1)B and N4(S1)B cases the lowest empty induced state is now above the 1.23 eV level. In N2(S1)N case this level coincides exactly with the 1.23 eV level. In N3(S1)B model the lowest empty state does not mix with the highest occupied state, being 0.17 eV higher. N3(S1)N and N4(S1)UND models hold the most promising electronic structure, while N1(S1)FR holds the outsider character. A comparison of band edge positions between the 2.78% and 1.39% defect concentration cases shows again that lower dopant concentration produces less prominent alterations in positions of the VB top and the CB bottom. These observations allow us to speculate about possible improvement through modifying the ratio of S and N dopants. If S/N ratio larger than 1 and proper defect concentration is reached, it might be possible to drive the empty level induced by N dopants above the SHE level and to relocate the highest occupied level induced by S dopants closer to 1.23 eV. If this is possible, a fundamental rise of photocatalytic efficiency in water splitting processes can be expected. We also have estimated total energies of investigated systems. No major changes are observed, the difference is in the second or third digit after decimal point. Still, in frame of our simulations this difference is essential for distribution of configurations. In case of 2.78% defect concentration, the most probable configuration is N2(S1), the neighboring value belongs to N1(S1)FR. N4(S1)UND configuration is the least likely to appear. In 1.39% defect concentration case the most probable configuration is N3(S1)N, the neighboring values belong to N2(S1) and N4(S1)UND. The N3(S1)B configuration is the least likely. The general observation is that in most cases S and N atoms have a tendency to be found closer to each other.
4. Conclusions The 6-layered TiO2 (0,12) NT rolled up from the nanosheet cut parallel to the (101) surface is proposed to be the most suitable model for simulations of electronic structure for titania nanotubes. In general, (0,n) nanotubes are found to be more stable than NTs with (n,0) chirality indexes. Electronic structure (band edges positions) of 6-layer (101) anatase NT is similar to the band structure of anatase nanotube made of 9-layer (001) TiO2 nanosheet studied
by us recently [6]. Based on results of our calculations, we predict that lone S or N dopants introduced into the 6-layered TiO2 (0,12) NT cannot result in a significant rise of photocatalytic response. For instance, the N doping may induce empty mid-gap states that can disrupt the photocatalytic process. We found that defect concentration does not have a big impact on the electronic structure of NTs under study; our results show that rise of defect concentration from 1.39% to 2.78% (of doping atoms per unit cell) practically does not shift the band edges and mid-gap states induced by these defects. In this study we show that the S þ N codoping of titania NT can result in enhancement of photocatalytic efficiency, at least qualitatively. At the same time, we have to conclude that changes of TiO2 NT electronic structure induced by co-doping depend on defect concentration.
Acknowledgment This work has been supported by the Alexander von Humboldt Foundation. Support from Latvian National Research Program IMIS2 (2014–2017) is appreciated by us too. D.B. is also grateful for the support through the Latvian National Research Program LATENERGI.
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Please cite this article as: O. Lisovski, et al., Materials Science in Semiconductor Processing (2015), http://dx.doi.org/10.1016/j. mssp.2015.09.003i