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Structural and electronic properties of Mg and Mg-Nb co-doped TiO2 (101) anatase surface
Accepted Manuscript Title: Structural and electronic properties of Mg and Mg-Nb co-doped TiO2 (101) anatase surface: Author: Alireza Sasani Ardeshir Baktash Kavoos Mirabbaszadeh Bahram Khoshnevisan PII: DOI: Reference:
S0169-4332(16)31048-0 http://dx.doi.org/doi:10.1016/j.apsusc.2016.05.040 APSUSC 33233
To appear in:
APSUSC
Received date: Revised date: Accepted date:
20-1-2016 18-4-2016 7-5-2016
Please cite this article as: Alireza Sasani, Ardeshir Baktash, Kavoos Mirabbaszadeh, Bahram Khoshnevisan, Structural and electronic properties of Mg and Mg-Nb co-doped TiO2 (101) anatase surface:, Applied Surface Science http://dx.doi.org/10.1016/j.apsusc.2016.05.040 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Structural and electronic properties of Mg and Mg-Nb co-doped TiO2 (101) anatase surface:
2
Alireza Sasania, Ardeshir Baktashb, Kavoos Mirabbaszadehc*, Bahram Khoshnevisan b
3 4 5 6 7 8
a
Department of Science, Karaj Islamic Azad University, Karaj, Alborz, P.O. Box 31485-313, Iran. b
Institute of Nano Science and Nano Technology, University of Kashan, Kashan, P.O. Box 87317-51167, Iran
c Department
of Energy Engineering and Physics, Amirkabir University of Technology, Tehran, P. O. Box 15875-4413 Iran
9
Email: [email protected]
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*Corresponding author, Tel: +982164545248.
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Graphical abstract
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1
1 2 3 4 5 6 7 8
Highlights
Formation energy of Mg and Mg-Nb co-doped TiO2 anatase surface (101) is studied Effect of Mg defect to the TiO2 anatase (101) surface and bond length distribution of the surface is studied and it is shown that Mg defects tend to stay far from each other. Effect of Mg and Nb to the bond length distribution of the surface studied and it is shown that these defects tend to stay close to each other. Effects of Mg and Mg-Nb defects on DSSCs using TiO2 anatase hosting these defects are studied.
9 10 11
Abstract:
12
In this paper, by using density functional theory, Mg and Nb-Mg co-doping of TiO2 anatase (101)
13
surfaces are studied. By studying the formation energy of the defects and the bond length
14
distribution of the surface, it is shown that Mg defects tend to stay as far as possible to induce least 2
1
possible lattice distortion while Nb and Mg defects stay close to each other to cause less stress to
2
the surface. By investigating band structure of the surface and changes stemmed from the defects,
3
potential effects of Mg and Mg-Nb co-doping of TiO2 surface on dye-sensitized solar cells are
4
investigated. In this study, it is shown that the Nb-Mg co-doping could increase JSC of the surface
5
while slightly decreasing VOC compared to Mg doped surface, which might result in an increase
6
in efficiency of the DSSCs compared to Nb or Mg doped surfaces.
7
Key Words: Density functional theory, Mg doped TiO2, Mg-Nb Co-doped anatase TiO2, Surface
8
properties and Electronic Structure.
9
1. Introduction
10
Having characteristics such as low cost, non-toxicity, high chemical and thermal stability and
11
catalytic activity, Titanium dioxide (TiO2), or Titania as a semiconductor photo-catalysts, has been
12
extensively studied experimentally and theoretically. Aforementioned distinguishing qualities of
13
TiO2 have made it very suitable for a wide range of environmental applications [1, 2] and
14
inexpensive Dye Synthesized Solar Cells (DSSCs) [3, 4].
15
Doping TiO2 to tune its properties according to our needs has been put into practice extensively.
16
In Particular, to improve the low conversion efficiency of dye sensitized solar cells, doping TiO2
17
anode using different metal ion dopants examined experimentally and this method has been shown
18
to have promising results [5]. Magnesium (Mg) is one of the investigated metal dopants which is
19
shown to enhance the open circuit voltage (Voc) of DSSCs compared to pristine TiO2 [6, 7, 8].
20
However, reduction in Voc due to Mg doping is also reported [9]. It is shown that Mg doping into
21
TiO2 shifts the CB downward and results in higher short-current density (JSC) in DSSCs, this
3
1
behavior is explained by the enlargement in the difference of LUMO of the dye and the conduction
2
band (CB) of TiO2 [9, 10].
3
Several research groups have examined Niobium (Nb) doped TiO2 films with different doping
4
levels [5-10]. Previous results show that a doping level of about 6% of Nb into the anatase TiO2
5
leads to excellent conductivity and transparency [11-23]. Lee et al. used 6% of Nb doped TiO2 as
6
a compact layer in dye sensitized solar cells (DSSCs). They found that the use of Nb-doped TiO2
7
increases the photocurrent density (JSC) [14]. Hasin et al. used Pt supported Nb-doped TiO2 as
8
counter electrodes for DSSCs and found lower charge transfer resistance and larger exchange
9
current density [24].
10
Huang and coworkers prepared nanocrystals of Nb-doped TiO2 for the application in DSSCs and
11
observed that the photoelectric conversion efficiency of DSSCs with Nb-doped TiO2 is higher
12
compared to DSSCs with pure TiO2 [25]. While incorporation of many transition metals in TiO2
13
leads to narrowing its band gap and influence the gap states, Nb doping of anatase TiO2 does not
14
lead to significant gap narrowing and does not affect the gap states [26].
15
Moreover, Nb doping in TiO2 anatase positively affects carrier density (up to 10 21 cm-2) and
16
consequently electrical conductivity (over 103- 10 4 Ω-1. cm-2)[27]. For highly Nb-doped TiO2,
17
however, metal-like behavior was observed [11], which makes it unfavorable for electrochemical
18
applications because of high electron recombination rate [28].
19
Furthermore, recently low Nb doped TiO2 has been used as an electrode to control the junction
20
characteristics and enhance the charge transport in dye synthesized solar cells at the interface with
21
dye molecules and the electrolytes [26].
4
1
Considering the different properties of Mg and Nb doped TiO2, it could be predicted that co-doping
2
of Nb and Mg into the TiO2 surface could have superior properties compared to Mg or Nb doped
3
surfaces. To the best of our knowledge, there are no experimental or theoretical reports regarding
4
the investigation of the co-doped Mg and Nb in TiO2. Goals of this study are as follow, to
5
investigate the properties of Mg and Nb-Mg co-doped TiO2 surface, understand how Nb-Mg co-
6
doping changes surface properties, how these changes differ from those of Mg doped surface and
7
finally to study effects of these changes on DSSC.
8 9 10
2. Computational method
11
In this paper, by using density functional theory (DFT) implemented in the SIESTA code [29], the
12
effects of introducing Magnesium and Niobium atoms on the surface structure and electrical
13
properties of the TiO2 anatase surface are studied. For this purpose, two different defects sites
14
(Ti5c, Ti6c) in Oxygen poor and Oxygen rich conditions, were compared. In order to understand
15
defect concentration effects on the formation of these defects, two different structural forms are
16
studied. The generalized gradient approximation (GGA) with the Perdew–Becke–Erzenhof (PBE)
17
[30] functional is chosen as exchange-correlation (XC) functional. We used a double zeta
18
polarization (DZP) basis set for all atoms. Optimization was carried out with a force tolerance of
19
0.025 eV Å−1 also a 200 Ry mesh cutoff was used. A confinement radius corresponding to an
20
energy shift of 0.01 eV is used. Periodic boundary conditions were used to model a surface layer
21
of anatase TiO2 (101) with 96 atoms (Ti32O64). Anatase TiO2 (101) surface modeled by a four
22
atomic layer periodic slab and all the atoms were allowed to relax throughout our simulations. 5
1 2
3. Results and discussions 3.1. Analysis of Pure TiO2 Structure:
3
The TiO2 anatase structure can be described by a coordination of octahedral TiO6 (Figure 1 (a)) in
4
which the two octahedral layers stacking alternatively along c axis (Figure 1 (b)). For this structure,
5
it is shown that the empty room and soft bonds along c axis result in lower elastic constants in this
6
direction in comparison with other directions [31].
7
The bond lengths of octahedral TiO6 are shown in Figure 1 (a), which shows higher bond lengths
8
along c direction compared to a and b directions. To study the interaction of Ti and O in each
9
direction, crystal orbital occupation population (COOP) of each of the bonds is calculated [32].
10
Figure 2 shows the interaction of Ti and O atoms (Ti-O curve). In this curve, positive COOP shows
11
bonding state, zero COOP shows non-bonding state and the negative one is an indicator of the
12
anti-bonding state. By projecting these interactions to each of the bonds, a stronger bonding for Ti
13
and Oxygen atoms along a and b axis (B-1, B-2) compared to Ti-O bond interaction along c axis
14
(B-3) can be observed (Figure 2). The COOP curves along with empty rooms in c direction can be
15
used to assess elastic constants of this structure. Lower COOP density for bonds along c axis is an
16
indicator of lower bond strength and hence lower elastic constant in c direction which is in
17
agreement with the literature [31].
18
To study doping of TiO2, a two-dimensional slab of the anatase (101) surface used, because it has
19
been shown that nanoparticles prepared under acidic conditions expose mainly (101) surface [33,
20
34]. Anatase TiO2 (101) surface modeled by a four atomic layer periodic slab and all the layers
21
allowed to relax throughout our simulations. To study structural changes due to crystal termination
22
boundary, bond length distribution of this structure is plotted. Crystal termination for this surface
6
1
has caused a big change in its bond length distribution compared to the bulk structure. Figure 3 (a)
2
shows bond length distribution of the (101) anatase surface which has 8 different peaks each of
3
which corresponding to one bond and Figure 3 (b) shows each of these bonds. In this surface, there
4
are two different Ti sites, namely Ti5c and Ti6c.These two sites have different coordination
5
numbers. The Ti5c atoms have 5 neighboring oxygen atoms while the other one have 6 neighboring
6
oxygen atoms. These results in 11 bonding of which some are equal, so resulting in 8 different
7
bond lengths for this surface.
8
For the Bulk structure, there are two directions with strong bonding and bonding along c direction
9
is softer in comparison with other directions. While, for the surface the changes have caused
10
altering the bonding of Ti with O atom in different directions. The crystal growth direction is along
11
one of the directions of Bulk structure (direction b) while making 45 degrees with c axis and the
12
other direction (direction a). To investigate the changes in Ti-O interaction along each direction,
13
COOP curves of Ti5c and Ti6c atoms with their neighboring Oxygen atoms are studied.
14
In Figure 3 (a) all bonds of Ti5c and Ti6c are labeled and Figure 4 (a) and (b) show COOP curves
15
corresponding to each of the labeled bonds and here, only the filled states lower than Fermi level
16
are plotted, most of which are bonding states. According to Figure 4 bonding along the c direction
17
has changed to two different bonding strength for Ti5c and Ti6c and each of these sites has a strong
18
bonding (Bond 11, Bond 6) and a weak bonding (Bond 9, Bond 2) in c direction which results in
19
a change in elastic constant of the surface compared to Bulk one for the surface. For direction a,
20
the crystal is terminated and has caused longer bond lengths for Ti6c sites and lower bond length
21
for Ti5c with the lower layer and for both of these bonds a strong coupling between Ti and O (Bond
22
5, Bond 10) can be seen which makes this bond most stiff bond. Ti5c and Ti6c have different
7
1
bonding along direction b (growth direction of the surface) and bonding of Ti6c (Bond 3, Bond 4)
2
is much stronger compared to Ti5c (Bond 7, Bond 8).
3
In order to study the bonding of Oxygen atoms with their neighboring Ti atoms COOP curves for
4
5 different Oxygen atom sites are calculated. Figure 5 (a) shows 5 different oxygen sites and Figure
5
5 (b) shows their corresponding COOP curves. According to these curves oxygen 2 (O-2) has the
6
weakest interaction with the surface so this Oxygen might be the most probable missing Oxygen
7
resulting in Oxygen vacancy and the Oxygen 4 (O-4) is the second most probable missing Oxygen
8
resulting in Oxygen vacancies, but the other 3 different sites show stronger bonding with surface.
9 10
3.2. Mg doped TiO2 Surface:
11
To investigate the properties of Mg substitutional (Mgsub) defects in TiO2 host surface and its
12
effects on the surface, one Ti atom was substituted by a Mg atom. Defect formation energy was
13
calculated using the following expression:
14
Eform (Mgsub-TiO2) = Etot (Mg sub - TiO2) - Etot (TiO2 (host)) + N*μTi – P*μMg
15
In the above formula, Etot (Mg sub - TiO2) is the total energy of the surface with Mgsub defect in it
16
and Etot (TiO2 surface) is the total energy of the defect-free host surface. N represents the number
17
of removed Ti atoms to be replaced by P, Mg atoms. Two extreme conditions were used to compute
18
Mgsub defect formation energy. In the Oxygen rich condition, the oxygen chemical potential was
19
calculated
20
μTi=Etot(TiO2(anatase)-2μO and Mg chemical potential was calculated using magnesium hexagonal
21
close packed (hcp) bulk structure i.e μMg=μMg(metal). On the other extreme condition, i.e. Oxygen
as
μO=Etot(O2)/2,
the
Titanium
8
chemical
potential
was
calculated
as
1
poor condition, Titanium chemical potential calculated from Titanium hcp bulk metal structure i.e
2
μTi=μTi(metal), oxygen chemical potential was calculated as μO=(Etot(TiO2(anatase))- μ Ti)/2 and
3
the Mg chemical potential was calculated just like O-rich condition.
4
For Mgsub defect, there are two different possible sites to substitute Ti atom, i.e Ti5c and Ti6c.
5
Formation energy of both of these sites is computed and according to our results Ti5c sites are more
6
stable in terms of formation energy by 0.18 eV compared to Ti6c sites. The change in formation
7
energy of Ti5c as a function of Oxygen chemical potential is plotted in Figure 6. For all the
8
following calculations the Ti5c site is used as preferred defect position.
9
Doping Mg into TiO2 could result in lattice expansion which is due to the higher ionic radius of
10
Mg2+ (0.065nm) compared to Ti4+ (0.0605nm) [35]. Comparing COOP curves of two sites i.e.
11
Ti5c, Ti6c, this could be concluded that due to softer bonds and being free in 101 direction Ti5c site
12
could accept bigger atoms while Ti6c site has two stiff bonds in lattice growth direction (Bond 3,
13
4) and is bounded from upside (Bond 1) which makes Mgsub defect in this site less probable
14
energetically compared to Ti5c positions.
15
To study the effect of Mg sub defect on surface structure, bond length distribution of the surface
16
with an Mgsub defect in it is plotted (Figure 7). As Figure 7 shows all the bonds of the surface has
17
distributed in a wider range compared to the pristine surface. Table 1 shows the average value and
18
standard deviation of each of bonds.
19
By studying average bond length and standard deviation of bond length distribution, it can be
20
observed that all the bonds have expanded while Bond 5 and Bond 6 have diminished compared
21
to the pristine surface and Bond 10 and 11 are the Bonds that spread in the widest range.
9
1
It has been shown that increasing stress along directions a and b increases the band gap of TiO2
2
while increasing stress along c direction reduces the gap [36]. Bonds 2, 6, 9 and Bond 11 are along
3
c direction and their expansion causes a reduction in Band gap (which is compensated with empty
4
rooms in c direction) while other bonds are in directions a and b, hence, their expansion causes
5
the band gap widening.
6
3.3. Higher density Mg defects into anatase TiO2:
7
To study the higher density of defect, two different structural forms, Figure 8 (a) (C-structure) and
8
Figure 8 (b) (F-structure), are studied. To study the formation energy of these structures, two Ti
9
atoms are substituted with two Mg atoms (at yellow colored atom sites). Figure 7 shows formation
10
energy of F-structure in O-rich and O-poor conditions. According to our calculations, the F-
11
structure (Figure 8 (b)) is more stable by 0.2 eV compared to C-structure.
12
To investigate the reason behind the higher stability of F-structure, bond length distribution of
13
each of the forms is extracted. Table.2 shows bond length average and standard deviation of bond
14
distribution for each of these forms. The average standard deviation for F-structure and for C-
15
structure are 0.042 and 0.049 respectively which indicates that bonds in F-structure are spread in
16
a narrower range around mean value of the bond compared to C-structure. So this could be inferred
17
that the C-structure has caused more changes in crystal structure as a result of higher stress, hence
18
causing less stable structure.
19
When the surface is doped with one Mg atom, its defect distances are 10.521 Angstroms while in
20
F-structure and C-structure their distances are 7.765 and 3.869 Angstroms respectively. Due to the
21
reduction in formation energy that is caused by increase in Mg atom distances, it could be
10
1
concluded that these defects tend to stay as far as possible to induce least lattice distortion. So,
2
these defects tend to be more stable in a lower concentration of Mg impurity.
3
3.4. Mg-Nb co-doped anatase TiO2 :
4
To study the Nb doping effect on the lattice, the bond length distribution of Nb doped surface is
5
investigated. Comparing lattice distortion of Nb doped surface and that of Mg doped surface, and
6
studying bond length average and standard deviation of their bond length distribution, Nb due to
7
lower ionic radius has caused less stress to the lattice hence causing more stable defect compared
8
to the Mg defected structure.
9
To study Mg-Nb co-doping and their interactions, Mg-Nb doping is studied in two different forms
10
that are shown in Figure 8 (a) (MN-C) and (b) (MN-F) in which one Nb atom and one Mg atom
11
are substituted by Ti atoms (yellow colored atoms). Figure 9 shows formation energy of MN-C
12
structure. According to our calculations, these defects are more stable when they are closer (MN-
13
C structure) to each other by 0.1 eV.
14
Table 3 shows standard deviation and bond length distribution of the both structures (MN-C and
15
MN-F). Mean value of standard deviation for MN-C and MN-B structures are 0.040 and 0.043 and
16
these standard deviations and their mean values show that when these defects are closer to each
17
other, lattice distortions are less, so the defect formation energies are less. Hence, Nb and Mg when
18
co-doped tend to stay close to each other to induce least lattice distortions.
19
3.5. Effects of Mg and Mg-Nb doping on DSSCs:
20
By studying density of states (DOS) of Mg doped surface and projected density of states (PDOS)
21
on Mg atom (Figure 11 (a)) no states can be seen on conduction band edge due to the existence of
11
1
Mg, hence, the shift in conduction band edge could be explained by using the distortion caused by
2
higher ionic radius of Mg+2 substitution in surface which is in agreement with literature [36].
3
To study effects of Nb-Mg co-doping on DSSCs, DOS of the doped surfaces are studied. Figure
4
11 (b) shows DOS of the surface and PDOS of Mg and Nb which indicates that there is no
5
contribution to the band edges due to the Mg while d-orbital of Nb contributes to the conduction
6
band edge.
7
Table 4 shows Fermi energy, valence band and conduction band edges of the surface and doped
8
surfaces in their stable forms. As Table 4 shows the biggest shift in conduction band edge belongs
9
to the higher density of Mg doping (Mg-F structure) which is due to the more exerted stress to the
10
surface due to the Mg atoms and this shift could result in improvement in VOC of the solar cell.
11
However, this also could result in a reduction of the short current density which is in agreement
12
with the literature [6- 8].
13
Nb doping in the TiO2 surface is shown to improve short current while slightly reducing its open
14
circuit voltage [26]. As Table 4 shows Nb and Mg co-doping has almost the same conduction band
15
edge as Mg doped surface which shows that Nb doping does not change conduction band edge
16
while introducing this defect could result in a higher crystalline order of the surface and it also
17
reduce oxygen vacancy defects [26]. Introducing this defect into the surface raises electron density
18
which is apparent from the increase in Fermi level of the surface, hence improves electron mobility
19
of the surface [27]. So, its incorporation into the surface improves the short current density of the
20
DSSC.
21
Based on our calculation, it is predicted that Mg-Nb co-doping could result in higher open circuit
22
voltage and higher short current density in DSSCs compared to pristine TiO2. Due to the 12
1
improvement of VOC and JSC of the cell in the co-doped surface, it is predicted that DSSC made
2
with Mg-Nb co-doped TiO2 surface anode could have higher efficiency compared to Mg or Nb
3
doped surfaces.
4
4. Conclusion:
5
In this paper using first principles, Mg doping and Mg-Nb co-doping of TiO2 (101) surfaces are
6
investigated. Using bond length distributions, structural changes due to doping is investigated and
7
it is shown that Mg defects resulted in more stress to the surface when they are closer to each other
8
while Mg and Nb defect results in higher lattice distortion when they are far from each other. By
9
studying changes in the electronic band structure of the surface and doped structures, it is shown
10
that Nb doping into Mg doped surface could cause a raise in conversion efficiency with increasing
11
Jsc.
12 13 14 15 16 17 18 19
13
1 2 3 4 5 6 7 8 9
References
10
[1] A. Fujishima and K. Honda, Electrochemical photolysis of water at a semiconductor electrode,
11
Nature (London), 238 (1972) 37- 8.
12
[2] M. Ni, M. K. H. Leung, D. Y. C. Leung and K. Sumathy, A review and recent developments
13
in photocatalytic water-splitting using TiO2 for hydrogen production, Renew. Sustain. Ener. Rev.
14
11 (2007) 401-425.
15
[3] O. Regan and M. Gratzel, A low-cost, high-efficiency solar cell based on dye-sensitized
16
colloidal TiO2 films, Nature, 353 (1991) 737-740.
17
[4] A. Kay and M. Gratzel, Low cost photovoltaic modules based on dye sensitized nanocrystalline
18
titanium dioxide and carbon powder, Sol. Energy Mater. Sol. Cells, 44 (1996) 99-117.
14
1
[5] T. Ma, M. Akiyama, E. Abe, I. Imai, High-efficiency dye-sensitized solar cell based on a
2
nitrogen-doped nanostructured titania electrode, Nano Letter 5 (2005) 2543.
3
[6] C. Zhang, S. Chen, L.e. Mo, Y. Huang, H. Tian, L. Hu, Z. Huo, S. Dai, F. Kong, X. Pan, Charge
4
Recombination and Band-Edge Shift in the Dye-Sensitized Mg2+-Doped TiO2 Solar Cells, The
5
Journal of Physical Chemistry C, 115 (2011) 16418-16424.
6
[7] S. Iwamoto, Y. Sazanami, M. Inoue, T. Inoue, T. Hoshi, K. Shigaki, M. Kaneko, A.
7
Maenosono, Fabrication of Dye-Sensitized Solar Cells with an Open-Circuit Photovoltage of 1V,
8
ChemSusChem, 1 (2008) 401-403.
9
[8] K. Kakiage, T. Tokutome, S. Iwamoto, T. Kyomen, M. Hanaya, Fabrication of a dye-sensitized
10
solar cell containing a Mg-doped TiO2 electrode and a Br3-/Br- redox mediator with a high open-
11
circuit
12
[9] Q. Liu, Photovoltaic Performance Improvement of Dye-Sensitized Solar Cells Based on Mg-
13
Doped TiO2 Thin Films, Electrochimica Acta, 129 (2014) 459-462.
14
[10] N.J. Cherepy, G.P. Smestad, M. Gratzel, J.Z. Zhang, Ultrafast Electron Injection: Implications
15
for a Photoelectrochemical Cell Utilizing an Anthocyanin Dye-Sensitized TiO2 Nanocrystalline
16
Electrode, J. Phys. Chem. B 101 (1997) 9342.
17
[11] Y. Furubayashi, H. Hitosugi, Y. Yamamoto, K. Inaba, G. Kinoda, Y. Hirose, T. Shimada and
18
T. Hasegawa, A transparent metal: Nb-doped anatase TiO2, Appl. Phys. Lett. 86 (2005) Art No
19
252101.
photovoltage
of
1.21
V,
Chemical
15
Communications,
49
(2013)
179-180.
1
[12] M. S. Dabney, M. F.A.M. van Hest, C. W. Teplin, S. P. Arenkiel, J. D. Perkins and D. S.
2
Ginley, Pulsed laser deposited Nb doped TiO 2 as a transparent conducting oxide, Thin Solid
3
Films, 516 (2008) 4133-4138.
4
[13] T. Hitosugi, A. Ueda, S. Nakao, N. Yamada, Y. Furubayashi, Y. Hirose, T, Shimada and T.
5
Hasegawa, Fabrication of highly conductive Ti1-xNb xO2 polycrystalline films on glass substrates
6
via crystallization of amorphous phase grown by pulsed laser deposition, Appl. Phys. Lett. 90
7
(2007) 212106.
8
[14] S. Lee, J. H. Noh, H. S. Han, D. K. Yim, D. H. Kim, J. K. Lee, J. T. Kim, H. S. Jung, and K.
9
S. Hong, A new compact layer material for TiO2 dye-sensitized solar cells, J. Phys. Chem. C 113
10
(2009) 6878- 6882.
11
[15] Y. Sato, H. Akizuki, T. Kamiyama and Y. Shigesato, Transparent conductive Nb-doped TiO2
12
films deposited by direct-current magnetron sputtering using a TiO2−x target, Thin Solid Films,
13
516 (2008) 5758- 5762.
14
[16] N. Yamada, T. Hitosugi, J. Kasai, N. L. H. Hoang, S. Nakao, Y. Hirose, T. Shimada and T.
15
Hasegawa, Transparent conducting Nb-doped anatase TiO2 (TNO) thin films sputtered from
16
various oxide targets, Thin Solid Films, 518 (2010) 3101- 3104.
17
[17] M. A. Gillispie, M. F. A. M. Van Hest, M. S. Dabney, J. D. Perkins and D. S. Ginley, rf
18
magnetron sputter deposition of transparent conducting Nb-doped TiO2 films on SrTiO 3, J. Appl.
19
Phys. 101 (2007) 033125.
16
1
[18] M. A. Gillispie, M. F. A. M. Van Hest, M. S. Dabney, J. D. Perkins and D. S. Ginley, Sputtered
2
Nb-and Ta-doped TiO2 transparent conducting oxide films on glass, J. Mater. Res. 22 (2007)
3
2832-2837.
4
[19] T. Hitosugi, N. Yamada, N. L. H. Hoang, J. Kasai, S. Nakao, T. Shimada and T.
5
Hasegawa, Fabrication of TiO 2-based transparent conducting oxide on glass and polyimide
6
substrates, Thin Solid Films, 517 (2009) 3106-3186.
7
[20] N. L. H. Hoang, N. Yamada, T. Hitosugi, J. Kasai, S. Nakao, T. Shimada and T.
8
Hasegawa, Low-temperature fabrication of transparent conducting anatase Nb-doped TiO2 films
9
by sputtering, Appl. Phys. Express, 1 (2008) 115001.
10
[21] S. X. Zhang, D. C. Kundaliya, W. Yu, S. Dhar, S. Y. Young, L. G. Salamanca#Riba, S. B.
11
Ogale, R. D. Vispute and T. Venkatesan, Nb Doped TiO2: Intrinsic Transparent Metallic Anatase
12
Versus Highly Resistive Rutile Phase, J. Appl. Phys. 102 (2007) 013701.
13
[22] D. Kurita, S. Ohta, K. Sugiura, H. Ohta and K. Koumoto, Carrier generation and transport
14
properties of heavily Nb-doped anatase TiO2 epitaxial films at high temperatures, J. Appl. Phys.
15
100 (2006) 096105.
16
[23] S. X. Zhang, S. Dhar, W. Yu, H. Xu, S. B. Ogale and T. Venkatesan, Growth parameter-
17
property phase diagram for pulsed laser deposited transparent oxide conductor anatase Nb: TiO2,
18
Appl. Phys. Lett. 91 (2007) 112113.
19
[24] B. J. Morgan, D. O. Scanlon, and G. W. Watson, Small polarons in Nb- and Ta-doped rutile
20
and anatase TiO2, J. Mater. Chem. 19 (2009) 5175-5178.
17
1
[25] X. Lu, X. Mou, J. Wu, D. Zhang, L. Zhang, F. Huang, F. Xu and S. Huang, , Improved-
2
Performance Dye-Sensitized Solar Cells Using Nb-Doped TiO2Electrodes: Efficient Electron
3
Injection and Transfer, Adv. Funct. Mater. 20 (2010) 509-515.
4
[26] Tsvetkov Nikolay, Liudmila Larina, Oleg Shevaleevskiy Byung Tae Ahn, Electronic
5
structure study of lightly Nb-doped TiO2electrode for dye-sensitized solar cells, Energy Environ.
6
Sci. 4 (2011) 1480-1484.
7
[27] I. Hamberg and C. G. Granqvist, Evaporated Sn-doped In2O3 films: Basic optical properties
8
and applications to energy-efficient windows, J. Appl. Phys. 60 (1986) R123-R160.
9
[28] I. Hamberg and C. G. Granqvist, Evaporated Sn-doped In2O3 films: Basic optical properties
10
and applications to energy-efficient windows, J. Appl. Phys. 60 (1986) R123-R160.
11
[29] José M Soler, Emilio Artacho, Julian D Gale, Alberto García, Javier Junquera, Pablo Ordejón
12
and Daniel Sánchez-Portal, The SIESTA method for ab initio order-N materials simulation, J.
13
Phys. Cond. Matt. 14, (2002) 2745-2779.
14
[30] John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Generalized Gradient Approximation
15
Made Simple, Phys. Rev. Lett., 77 (1996) 3865.
16
[31] Wan-Jian Yin,Shiyou Chen, Ji-Hui Yang, Xin-Gao Gong, Yanfa Yan and Su-Huai Wei,
17
Effective band gap narrowing of anatase TiO2 by strain along a soft crystal direction, Appl.
18
Phys.Lett. 96 (2010) 221901.
19
[32] R. Hoffmann, Angew., How Chemistry and Physics Meet in the Solid State, Chem. Int. Ed.
20
Engl. 26 (1987) 846-878.
18
1
[33] C. J. Barbe, F. Arendse, P. Comte, M. Jirousek, F. Lenzmann, V. Shklover, M. Gratzel,
2
Nanocrystalline titanium oxide electrodes for photovoltaic applications, J. Am. Ceram. Soc. 80
3
(1997),3157.
4
[34] A. Zaban, S. T. Aruna, S. Tirosh, B. A. Gregg, Y. Mastai, The Effect of the Preparation
5
Condition of TiO2 Colloids on Their Surface Structures, J. Phys.Chem. B 104 (2000), 4130.
6
[35] R. D. Shannon., Revised effective ionic radii and systematic studies of interatomic distances
7
in halides and chalcogenides , Acta Cryst A 32 (1976) 751-767.
8
[36] Lukas Thulin and John Guerra, Calculations of strain-modified anatase TiO2 band structures,
9
Physical Review B 77 (2008) 195112.
10 11 12 13 14 15 16
Figure Captions:
17
Figure 1. (a) Coordination of octahedral TiO6 in directions a, b and c (b) Two octahedral layers
18
stacking along c direction.
19
Figure 2. COOP curves for Bulk structure in different directions
20
Figure 3. (a) Bond length distribution for surface and (b) different bonds in (101) direction
21
Figure 4. COOP curves for (a) bonds 1-6 of the surface (b) bonds 7-11 of the surface
19
1
Figure 5. (a) Different oxygen sites for anatase TiO2 (101) surface and (b) COOP curves for each
2
of the oxygen sites
3
Figure 6. Formation energy of Mg defect as a function of oxygen chemical potential
4
Figure 7. Bond length distribution of Mg doped TiO2 surface
5
Figure 8. Two impurities doped into the structure and (a) close together (C-structure), (b) far from
6
each other (F-structure).
7
Figure 9. Formation energy of higher density Mg defect as a function of oxygen chemical potential
8
Figure 10. Formation energy of Mg-Nb defect as a function of oxygen chemical potential
9
Figure 11. Density of states of doped surfaces and PDOS on Mg and Nb atoms
10 11 12 13
Table Captions:
20
1
Table 1: Bond length average (BL) and standard deviation (SD) of the bond length distribution of
2
Mg doped surface (Mg-D).
3
Table 2: Bond length average (BL) and standard deviation (SD) of bond length distribution of F-
4
structure and C-structure doped surface (F and C).
5
Table 3: Bond length average (BL) and standard deviation (SD) of bond length distribution of MN-
6
F and MN-C structure doped surface.
7
Table 4: Fermi energy (Ef),valence band edge (Ev) and conduction band edge (Ec) of the Mg
8
doped F structure (Mg-F), Mg-Nb doped C structures (MN-C) and pritine surface (surf).
9 10 11 12 13 14 15 16 17 18 19 20 21
Table 1 surf-(BL)
Mg-D(BL)
21
Surf-(SD)
Mg-D(SD)
Bond 1 Bond 2 Bond 3,4 Bond 5 Bond 6 Bond 7,8 Bond 9 Bond 10 Bond 11
1.847 2.058 1.934 2.167 2.046 1.983 2.066 1.815 1.861
1.861 2.080 1.938 2.132 2.025 1.987 2.067 1.833 1.867
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Table 2
22
0.000 0.001 0.000 0.001 0.001 0.001 0.001 0.000 0.000
0.019 0.023 0.020 0.032 0.021 0.033 0.015 0.068 0.055
Bond 1 Bond 2 Bond 3,4 Bond 5 Bond 6 Bond 7,8 Bond 9 Bond 10 Bond 11
C-BL 1.875 2.069 1.944 2.114 2.027 1.989 2.089 1.845 1.884
F-(BL) 1.873 2.073 1.940 2.118 2.021 1.986 2.085 1.848 1.877
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Table 3 23
C-(SD) 0.027 0.064 0.013 0.051 0.046 0.036 0.042 0.080 0.083
F-(SD) 0.023 0.044 0.022 0.045 0.034 0.037 0.013 0.084 0.076
Bond 10 Bond 1 Bond 11 Bond 3,4 Bond 7,8 Bond 6 Bond 2 Bond 5 Bond 9
MN-C (BL)
MN-F(BL)
MN-C (SD)
MN-F (SD)
1.837 1.867 1.867 1.939 1.993 2.035 2.071 2.128 2.079
1.837 1.869 1.868 1.939 1.991 2.033 2.069 2.134 2.093
0.055 0.030 0.059 0.022 0.043 0.035 0.048 0.045 0.030
0.055 0.036 0.061 0.025 0.033 0.039 0.057 0.053 0.031
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Table 4 24
Surf Mg Mg-F MN-C
Ef -6.759 -8.202 -8.330 -7.961
Ev -8.408 -8.402 -8.414 -8.299
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
25
Ec -5.699 -5.691 -5.686 -5.690
Bg 2.710 2.711 2.728 2.609
1 2
Figure 1 (a)
Figure 1 (b)
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
26
1 2
Figure 2
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
27
1
2 3
Figure 3 (a)
Figure 3 (b)
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
28
1 2
3 4
Figure 4 (a)
Figure 4 (b)
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
29
1 2 3 4 5 6 7 8 9
Figure 5 (a)
Figure 5 (b)
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
30
1 2
3 4
Figure 6
5 6 7 8 9 10 11 12 13 14 15 16 17 18
31
1 2 3
4 5
Figure 7
6 7 8 9 10 11 12 13 14 15 16 17 18
32
1 2 3
4 5
Figure 8 (a)
Figure 8 (b)
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
33
1
2 3
Figure 9
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
34
1 2 3
4 5
Figure 10
6 7 8 9 10 11 12 13 14 15 16 17
35
1 2
Figure 11
36
S0169-4332(16)31048-0 http://dx.doi.org/doi:10.1016/j.apsusc.2016.05.040 APSUSC 33233
To appear in:
APSUSC
Received date: Revised date: Accepted date:
20-1-2016 18-4-2016 7-5-2016
Please cite this article as: Alireza Sasani, Ardeshir Baktash, Kavoos Mirabbaszadeh, Bahram Khoshnevisan, Structural and electronic properties of Mg and Mg-Nb co-doped TiO2 (101) anatase surface:, Applied Surface Science http://dx.doi.org/10.1016/j.apsusc.2016.05.040 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
1
Structural and electronic properties of Mg and Mg-Nb co-doped TiO2 (101) anatase surface:
2
Alireza Sasania, Ardeshir Baktashb, Kavoos Mirabbaszadehc*, Bahram Khoshnevisan b
3 4 5 6 7 8
a
Department of Science, Karaj Islamic Azad University, Karaj, Alborz, P.O. Box 31485-313, Iran. b
Institute of Nano Science and Nano Technology, University of Kashan, Kashan, P.O. Box 87317-51167, Iran
c Department
of Energy Engineering and Physics, Amirkabir University of Technology, Tehran, P. O. Box 15875-4413 Iran
9
Email: [email protected]
10
*Corresponding author, Tel: +982164545248.
11
Graphical abstract
12
1
1 2 3 4 5 6 7 8
Highlights
Formation energy of Mg and Mg-Nb co-doped TiO2 anatase surface (101) is studied Effect of Mg defect to the TiO2 anatase (101) surface and bond length distribution of the surface is studied and it is shown that Mg defects tend to stay far from each other. Effect of Mg and Nb to the bond length distribution of the surface studied and it is shown that these defects tend to stay close to each other. Effects of Mg and Mg-Nb defects on DSSCs using TiO2 anatase hosting these defects are studied.
9 10 11
Abstract:
12
In this paper, by using density functional theory, Mg and Nb-Mg co-doping of TiO2 anatase (101)
13
surfaces are studied. By studying the formation energy of the defects and the bond length
14
distribution of the surface, it is shown that Mg defects tend to stay as far as possible to induce least 2
1
possible lattice distortion while Nb and Mg defects stay close to each other to cause less stress to
2
the surface. By investigating band structure of the surface and changes stemmed from the defects,
3
potential effects of Mg and Mg-Nb co-doping of TiO2 surface on dye-sensitized solar cells are
4
investigated. In this study, it is shown that the Nb-Mg co-doping could increase JSC of the surface
5
while slightly decreasing VOC compared to Mg doped surface, which might result in an increase
6
in efficiency of the DSSCs compared to Nb or Mg doped surfaces.
7
Key Words: Density functional theory, Mg doped TiO2, Mg-Nb Co-doped anatase TiO2, Surface
8
properties and Electronic Structure.
9
1. Introduction
10
Having characteristics such as low cost, non-toxicity, high chemical and thermal stability and
11
catalytic activity, Titanium dioxide (TiO2), or Titania as a semiconductor photo-catalysts, has been
12
extensively studied experimentally and theoretically. Aforementioned distinguishing qualities of
13
TiO2 have made it very suitable for a wide range of environmental applications [1, 2] and
14
inexpensive Dye Synthesized Solar Cells (DSSCs) [3, 4].
15
Doping TiO2 to tune its properties according to our needs has been put into practice extensively.
16
In Particular, to improve the low conversion efficiency of dye sensitized solar cells, doping TiO2
17
anode using different metal ion dopants examined experimentally and this method has been shown
18
to have promising results [5]. Magnesium (Mg) is one of the investigated metal dopants which is
19
shown to enhance the open circuit voltage (Voc) of DSSCs compared to pristine TiO2 [6, 7, 8].
20
However, reduction in Voc due to Mg doping is also reported [9]. It is shown that Mg doping into
21
TiO2 shifts the CB downward and results in higher short-current density (JSC) in DSSCs, this
3
1
behavior is explained by the enlargement in the difference of LUMO of the dye and the conduction
2
band (CB) of TiO2 [9, 10].
3
Several research groups have examined Niobium (Nb) doped TiO2 films with different doping
4
levels [5-10]. Previous results show that a doping level of about 6% of Nb into the anatase TiO2
5
leads to excellent conductivity and transparency [11-23]. Lee et al. used 6% of Nb doped TiO2 as
6
a compact layer in dye sensitized solar cells (DSSCs). They found that the use of Nb-doped TiO2
7
increases the photocurrent density (JSC) [14]. Hasin et al. used Pt supported Nb-doped TiO2 as
8
counter electrodes for DSSCs and found lower charge transfer resistance and larger exchange
9
current density [24].
10
Huang and coworkers prepared nanocrystals of Nb-doped TiO2 for the application in DSSCs and
11
observed that the photoelectric conversion efficiency of DSSCs with Nb-doped TiO2 is higher
12
compared to DSSCs with pure TiO2 [25]. While incorporation of many transition metals in TiO2
13
leads to narrowing its band gap and influence the gap states, Nb doping of anatase TiO2 does not
14
lead to significant gap narrowing and does not affect the gap states [26].
15
Moreover, Nb doping in TiO2 anatase positively affects carrier density (up to 10 21 cm-2) and
16
consequently electrical conductivity (over 103- 10 4 Ω-1. cm-2)[27]. For highly Nb-doped TiO2,
17
however, metal-like behavior was observed [11], which makes it unfavorable for electrochemical
18
applications because of high electron recombination rate [28].
19
Furthermore, recently low Nb doped TiO2 has been used as an electrode to control the junction
20
characteristics and enhance the charge transport in dye synthesized solar cells at the interface with
21
dye molecules and the electrolytes [26].
4
1
Considering the different properties of Mg and Nb doped TiO2, it could be predicted that co-doping
2
of Nb and Mg into the TiO2 surface could have superior properties compared to Mg or Nb doped
3
surfaces. To the best of our knowledge, there are no experimental or theoretical reports regarding
4
the investigation of the co-doped Mg and Nb in TiO2. Goals of this study are as follow, to
5
investigate the properties of Mg and Nb-Mg co-doped TiO2 surface, understand how Nb-Mg co-
6
doping changes surface properties, how these changes differ from those of Mg doped surface and
7
finally to study effects of these changes on DSSC.
8 9 10
2. Computational method
11
In this paper, by using density functional theory (DFT) implemented in the SIESTA code [29], the
12
effects of introducing Magnesium and Niobium atoms on the surface structure and electrical
13
properties of the TiO2 anatase surface are studied. For this purpose, two different defects sites
14
(Ti5c, Ti6c) in Oxygen poor and Oxygen rich conditions, were compared. In order to understand
15
defect concentration effects on the formation of these defects, two different structural forms are
16
studied. The generalized gradient approximation (GGA) with the Perdew–Becke–Erzenhof (PBE)
17
[30] functional is chosen as exchange-correlation (XC) functional. We used a double zeta
18
polarization (DZP) basis set for all atoms. Optimization was carried out with a force tolerance of
19
0.025 eV Å−1 also a 200 Ry mesh cutoff was used. A confinement radius corresponding to an
20
energy shift of 0.01 eV is used. Periodic boundary conditions were used to model a surface layer
21
of anatase TiO2 (101) with 96 atoms (Ti32O64). Anatase TiO2 (101) surface modeled by a four
22
atomic layer periodic slab and all the atoms were allowed to relax throughout our simulations. 5
1 2
3. Results and discussions 3.1. Analysis of Pure TiO2 Structure:
3
The TiO2 anatase structure can be described by a coordination of octahedral TiO6 (Figure 1 (a)) in
4
which the two octahedral layers stacking alternatively along c axis (Figure 1 (b)). For this structure,
5
it is shown that the empty room and soft bonds along c axis result in lower elastic constants in this
6
direction in comparison with other directions [31].
7
The bond lengths of octahedral TiO6 are shown in Figure 1 (a), which shows higher bond lengths
8
along c direction compared to a and b directions. To study the interaction of Ti and O in each
9
direction, crystal orbital occupation population (COOP) of each of the bonds is calculated [32].
10
Figure 2 shows the interaction of Ti and O atoms (Ti-O curve). In this curve, positive COOP shows
11
bonding state, zero COOP shows non-bonding state and the negative one is an indicator of the
12
anti-bonding state. By projecting these interactions to each of the bonds, a stronger bonding for Ti
13
and Oxygen atoms along a and b axis (B-1, B-2) compared to Ti-O bond interaction along c axis
14
(B-3) can be observed (Figure 2). The COOP curves along with empty rooms in c direction can be
15
used to assess elastic constants of this structure. Lower COOP density for bonds along c axis is an
16
indicator of lower bond strength and hence lower elastic constant in c direction which is in
17
agreement with the literature [31].
18
To study doping of TiO2, a two-dimensional slab of the anatase (101) surface used, because it has
19
been shown that nanoparticles prepared under acidic conditions expose mainly (101) surface [33,
20
34]. Anatase TiO2 (101) surface modeled by a four atomic layer periodic slab and all the layers
21
allowed to relax throughout our simulations. To study structural changes due to crystal termination
22
boundary, bond length distribution of this structure is plotted. Crystal termination for this surface
6
1
has caused a big change in its bond length distribution compared to the bulk structure. Figure 3 (a)
2
shows bond length distribution of the (101) anatase surface which has 8 different peaks each of
3
which corresponding to one bond and Figure 3 (b) shows each of these bonds. In this surface, there
4
are two different Ti sites, namely Ti5c and Ti6c.These two sites have different coordination
5
numbers. The Ti5c atoms have 5 neighboring oxygen atoms while the other one have 6 neighboring
6
oxygen atoms. These results in 11 bonding of which some are equal, so resulting in 8 different
7
bond lengths for this surface.
8
For the Bulk structure, there are two directions with strong bonding and bonding along c direction
9
is softer in comparison with other directions. While, for the surface the changes have caused
10
altering the bonding of Ti with O atom in different directions. The crystal growth direction is along
11
one of the directions of Bulk structure (direction b) while making 45 degrees with c axis and the
12
other direction (direction a). To investigate the changes in Ti-O interaction along each direction,
13
COOP curves of Ti5c and Ti6c atoms with their neighboring Oxygen atoms are studied.
14
In Figure 3 (a) all bonds of Ti5c and Ti6c are labeled and Figure 4 (a) and (b) show COOP curves
15
corresponding to each of the labeled bonds and here, only the filled states lower than Fermi level
16
are plotted, most of which are bonding states. According to Figure 4 bonding along the c direction
17
has changed to two different bonding strength for Ti5c and Ti6c and each of these sites has a strong
18
bonding (Bond 11, Bond 6) and a weak bonding (Bond 9, Bond 2) in c direction which results in
19
a change in elastic constant of the surface compared to Bulk one for the surface. For direction a,
20
the crystal is terminated and has caused longer bond lengths for Ti6c sites and lower bond length
21
for Ti5c with the lower layer and for both of these bonds a strong coupling between Ti and O (Bond
22
5, Bond 10) can be seen which makes this bond most stiff bond. Ti5c and Ti6c have different
7
1
bonding along direction b (growth direction of the surface) and bonding of Ti6c (Bond 3, Bond 4)
2
is much stronger compared to Ti5c (Bond 7, Bond 8).
3
In order to study the bonding of Oxygen atoms with their neighboring Ti atoms COOP curves for
4
5 different Oxygen atom sites are calculated. Figure 5 (a) shows 5 different oxygen sites and Figure
5
5 (b) shows their corresponding COOP curves. According to these curves oxygen 2 (O-2) has the
6
weakest interaction with the surface so this Oxygen might be the most probable missing Oxygen
7
resulting in Oxygen vacancy and the Oxygen 4 (O-4) is the second most probable missing Oxygen
8
resulting in Oxygen vacancies, but the other 3 different sites show stronger bonding with surface.
9 10
3.2. Mg doped TiO2 Surface:
11
To investigate the properties of Mg substitutional (Mgsub) defects in TiO2 host surface and its
12
effects on the surface, one Ti atom was substituted by a Mg atom. Defect formation energy was
13
calculated using the following expression:
14
Eform (Mgsub-TiO2) = Etot (Mg sub - TiO2) - Etot (TiO2 (host)) + N*μTi – P*μMg
15
In the above formula, Etot (Mg sub - TiO2) is the total energy of the surface with Mgsub defect in it
16
and Etot (TiO2 surface) is the total energy of the defect-free host surface. N represents the number
17
of removed Ti atoms to be replaced by P, Mg atoms. Two extreme conditions were used to compute
18
Mgsub defect formation energy. In the Oxygen rich condition, the oxygen chemical potential was
19
calculated
20
μTi=Etot(TiO2(anatase)-2μO and Mg chemical potential was calculated using magnesium hexagonal
21
close packed (hcp) bulk structure i.e μMg=μMg(metal). On the other extreme condition, i.e. Oxygen
as
μO=Etot(O2)/2,
the
Titanium
8
chemical
potential
was
calculated
as
1
poor condition, Titanium chemical potential calculated from Titanium hcp bulk metal structure i.e
2
μTi=μTi(metal), oxygen chemical potential was calculated as μO=(Etot(TiO2(anatase))- μ Ti)/2 and
3
the Mg chemical potential was calculated just like O-rich condition.
4
For Mgsub defect, there are two different possible sites to substitute Ti atom, i.e Ti5c and Ti6c.
5
Formation energy of both of these sites is computed and according to our results Ti5c sites are more
6
stable in terms of formation energy by 0.18 eV compared to Ti6c sites. The change in formation
7
energy of Ti5c as a function of Oxygen chemical potential is plotted in Figure 6. For all the
8
following calculations the Ti5c site is used as preferred defect position.
9
Doping Mg into TiO2 could result in lattice expansion which is due to the higher ionic radius of
10
Mg2+ (0.065nm) compared to Ti4+ (0.0605nm) [35]. Comparing COOP curves of two sites i.e.
11
Ti5c, Ti6c, this could be concluded that due to softer bonds and being free in 101 direction Ti5c site
12
could accept bigger atoms while Ti6c site has two stiff bonds in lattice growth direction (Bond 3,
13
4) and is bounded from upside (Bond 1) which makes Mgsub defect in this site less probable
14
energetically compared to Ti5c positions.
15
To study the effect of Mg sub defect on surface structure, bond length distribution of the surface
16
with an Mgsub defect in it is plotted (Figure 7). As Figure 7 shows all the bonds of the surface has
17
distributed in a wider range compared to the pristine surface. Table 1 shows the average value and
18
standard deviation of each of bonds.
19
By studying average bond length and standard deviation of bond length distribution, it can be
20
observed that all the bonds have expanded while Bond 5 and Bond 6 have diminished compared
21
to the pristine surface and Bond 10 and 11 are the Bonds that spread in the widest range.
9
1
It has been shown that increasing stress along directions a and b increases the band gap of TiO2
2
while increasing stress along c direction reduces the gap [36]. Bonds 2, 6, 9 and Bond 11 are along
3
c direction and their expansion causes a reduction in Band gap (which is compensated with empty
4
rooms in c direction) while other bonds are in directions a and b, hence, their expansion causes
5
the band gap widening.
6
3.3. Higher density Mg defects into anatase TiO2:
7
To study the higher density of defect, two different structural forms, Figure 8 (a) (C-structure) and
8
Figure 8 (b) (F-structure), are studied. To study the formation energy of these structures, two Ti
9
atoms are substituted with two Mg atoms (at yellow colored atom sites). Figure 7 shows formation
10
energy of F-structure in O-rich and O-poor conditions. According to our calculations, the F-
11
structure (Figure 8 (b)) is more stable by 0.2 eV compared to C-structure.
12
To investigate the reason behind the higher stability of F-structure, bond length distribution of
13
each of the forms is extracted. Table.2 shows bond length average and standard deviation of bond
14
distribution for each of these forms. The average standard deviation for F-structure and for C-
15
structure are 0.042 and 0.049 respectively which indicates that bonds in F-structure are spread in
16
a narrower range around mean value of the bond compared to C-structure. So this could be inferred
17
that the C-structure has caused more changes in crystal structure as a result of higher stress, hence
18
causing less stable structure.
19
When the surface is doped with one Mg atom, its defect distances are 10.521 Angstroms while in
20
F-structure and C-structure their distances are 7.765 and 3.869 Angstroms respectively. Due to the
21
reduction in formation energy that is caused by increase in Mg atom distances, it could be
10
1
concluded that these defects tend to stay as far as possible to induce least lattice distortion. So,
2
these defects tend to be more stable in a lower concentration of Mg impurity.
3
3.4. Mg-Nb co-doped anatase TiO2 :
4
To study the Nb doping effect on the lattice, the bond length distribution of Nb doped surface is
5
investigated. Comparing lattice distortion of Nb doped surface and that of Mg doped surface, and
6
studying bond length average and standard deviation of their bond length distribution, Nb due to
7
lower ionic radius has caused less stress to the lattice hence causing more stable defect compared
8
to the Mg defected structure.
9
To study Mg-Nb co-doping and their interactions, Mg-Nb doping is studied in two different forms
10
that are shown in Figure 8 (a) (MN-C) and (b) (MN-F) in which one Nb atom and one Mg atom
11
are substituted by Ti atoms (yellow colored atoms). Figure 9 shows formation energy of MN-C
12
structure. According to our calculations, these defects are more stable when they are closer (MN-
13
C structure) to each other by 0.1 eV.
14
Table 3 shows standard deviation and bond length distribution of the both structures (MN-C and
15
MN-F). Mean value of standard deviation for MN-C and MN-B structures are 0.040 and 0.043 and
16
these standard deviations and their mean values show that when these defects are closer to each
17
other, lattice distortions are less, so the defect formation energies are less. Hence, Nb and Mg when
18
co-doped tend to stay close to each other to induce least lattice distortions.
19
3.5. Effects of Mg and Mg-Nb doping on DSSCs:
20
By studying density of states (DOS) of Mg doped surface and projected density of states (PDOS)
21
on Mg atom (Figure 11 (a)) no states can be seen on conduction band edge due to the existence of
11
1
Mg, hence, the shift in conduction band edge could be explained by using the distortion caused by
2
higher ionic radius of Mg+2 substitution in surface which is in agreement with literature [36].
3
To study effects of Nb-Mg co-doping on DSSCs, DOS of the doped surfaces are studied. Figure
4
11 (b) shows DOS of the surface and PDOS of Mg and Nb which indicates that there is no
5
contribution to the band edges due to the Mg while d-orbital of Nb contributes to the conduction
6
band edge.
7
Table 4 shows Fermi energy, valence band and conduction band edges of the surface and doped
8
surfaces in their stable forms. As Table 4 shows the biggest shift in conduction band edge belongs
9
to the higher density of Mg doping (Mg-F structure) which is due to the more exerted stress to the
10
surface due to the Mg atoms and this shift could result in improvement in VOC of the solar cell.
11
However, this also could result in a reduction of the short current density which is in agreement
12
with the literature [6- 8].
13
Nb doping in the TiO2 surface is shown to improve short current while slightly reducing its open
14
circuit voltage [26]. As Table 4 shows Nb and Mg co-doping has almost the same conduction band
15
edge as Mg doped surface which shows that Nb doping does not change conduction band edge
16
while introducing this defect could result in a higher crystalline order of the surface and it also
17
reduce oxygen vacancy defects [26]. Introducing this defect into the surface raises electron density
18
which is apparent from the increase in Fermi level of the surface, hence improves electron mobility
19
of the surface [27]. So, its incorporation into the surface improves the short current density of the
20
DSSC.
21
Based on our calculation, it is predicted that Mg-Nb co-doping could result in higher open circuit
22
voltage and higher short current density in DSSCs compared to pristine TiO2. Due to the 12
1
improvement of VOC and JSC of the cell in the co-doped surface, it is predicted that DSSC made
2
with Mg-Nb co-doped TiO2 surface anode could have higher efficiency compared to Mg or Nb
3
doped surfaces.
4
4. Conclusion:
5
In this paper using first principles, Mg doping and Mg-Nb co-doping of TiO2 (101) surfaces are
6
investigated. Using bond length distributions, structural changes due to doping is investigated and
7
it is shown that Mg defects resulted in more stress to the surface when they are closer to each other
8
while Mg and Nb defect results in higher lattice distortion when they are far from each other. By
9
studying changes in the electronic band structure of the surface and doped structures, it is shown
10
that Nb doping into Mg doped surface could cause a raise in conversion efficiency with increasing
11
Jsc.
12 13 14 15 16 17 18 19
13
1 2 3 4 5 6 7 8 9
References
10
[1] A. Fujishima and K. Honda, Electrochemical photolysis of water at a semiconductor electrode,
11
Nature (London), 238 (1972) 37- 8.
12
[2] M. Ni, M. K. H. Leung, D. Y. C. Leung and K. Sumathy, A review and recent developments
13
in photocatalytic water-splitting using TiO2 for hydrogen production, Renew. Sustain. Ener. Rev.
14
11 (2007) 401-425.
15
[3] O. Regan and M. Gratzel, A low-cost, high-efficiency solar cell based on dye-sensitized
16
colloidal TiO2 films, Nature, 353 (1991) 737-740.
17
[4] A. Kay and M. Gratzel, Low cost photovoltaic modules based on dye sensitized nanocrystalline
18
titanium dioxide and carbon powder, Sol. Energy Mater. Sol. Cells, 44 (1996) 99-117.
14
1
[5] T. Ma, M. Akiyama, E. Abe, I. Imai, High-efficiency dye-sensitized solar cell based on a
2
nitrogen-doped nanostructured titania electrode, Nano Letter 5 (2005) 2543.
3
[6] C. Zhang, S. Chen, L.e. Mo, Y. Huang, H. Tian, L. Hu, Z. Huo, S. Dai, F. Kong, X. Pan, Charge
4
Recombination and Band-Edge Shift in the Dye-Sensitized Mg2+-Doped TiO2 Solar Cells, The
5
Journal of Physical Chemistry C, 115 (2011) 16418-16424.
6
[7] S. Iwamoto, Y. Sazanami, M. Inoue, T. Inoue, T. Hoshi, K. Shigaki, M. Kaneko, A.
7
Maenosono, Fabrication of Dye-Sensitized Solar Cells with an Open-Circuit Photovoltage of 1V,
8
ChemSusChem, 1 (2008) 401-403.
9
[8] K. Kakiage, T. Tokutome, S. Iwamoto, T. Kyomen, M. Hanaya, Fabrication of a dye-sensitized
10
solar cell containing a Mg-doped TiO2 electrode and a Br3-/Br- redox mediator with a high open-
11
circuit
12
[9] Q. Liu, Photovoltaic Performance Improvement of Dye-Sensitized Solar Cells Based on Mg-
13
Doped TiO2 Thin Films, Electrochimica Acta, 129 (2014) 459-462.
14
[10] N.J. Cherepy, G.P. Smestad, M. Gratzel, J.Z. Zhang, Ultrafast Electron Injection: Implications
15
for a Photoelectrochemical Cell Utilizing an Anthocyanin Dye-Sensitized TiO2 Nanocrystalline
16
Electrode, J. Phys. Chem. B 101 (1997) 9342.
17
[11] Y. Furubayashi, H. Hitosugi, Y. Yamamoto, K. Inaba, G. Kinoda, Y. Hirose, T. Shimada and
18
T. Hasegawa, A transparent metal: Nb-doped anatase TiO2, Appl. Phys. Lett. 86 (2005) Art No
19
252101.
photovoltage
of
1.21
V,
Chemical
15
Communications,
49
(2013)
179-180.
1
[12] M. S. Dabney, M. F.A.M. van Hest, C. W. Teplin, S. P. Arenkiel, J. D. Perkins and D. S.
2
Ginley, Pulsed laser deposited Nb doped TiO 2 as a transparent conducting oxide, Thin Solid
3
Films, 516 (2008) 4133-4138.
4
[13] T. Hitosugi, A. Ueda, S. Nakao, N. Yamada, Y. Furubayashi, Y. Hirose, T, Shimada and T.
5
Hasegawa, Fabrication of highly conductive Ti1-xNb xO2 polycrystalline films on glass substrates
6
via crystallization of amorphous phase grown by pulsed laser deposition, Appl. Phys. Lett. 90
7
(2007) 212106.
8
[14] S. Lee, J. H. Noh, H. S. Han, D. K. Yim, D. H. Kim, J. K. Lee, J. T. Kim, H. S. Jung, and K.
9
S. Hong, A new compact layer material for TiO2 dye-sensitized solar cells, J. Phys. Chem. C 113
10
(2009) 6878- 6882.
11
[15] Y. Sato, H. Akizuki, T. Kamiyama and Y. Shigesato, Transparent conductive Nb-doped TiO2
12
films deposited by direct-current magnetron sputtering using a TiO2−x target, Thin Solid Films,
13
516 (2008) 5758- 5762.
14
[16] N. Yamada, T. Hitosugi, J. Kasai, N. L. H. Hoang, S. Nakao, Y. Hirose, T. Shimada and T.
15
Hasegawa, Transparent conducting Nb-doped anatase TiO2 (TNO) thin films sputtered from
16
various oxide targets, Thin Solid Films, 518 (2010) 3101- 3104.
17
[17] M. A. Gillispie, M. F. A. M. Van Hest, M. S. Dabney, J. D. Perkins and D. S. Ginley, rf
18
magnetron sputter deposition of transparent conducting Nb-doped TiO2 films on SrTiO 3, J. Appl.
19
Phys. 101 (2007) 033125.
16
1
[18] M. A. Gillispie, M. F. A. M. Van Hest, M. S. Dabney, J. D. Perkins and D. S. Ginley, Sputtered
2
Nb-and Ta-doped TiO2 transparent conducting oxide films on glass, J. Mater. Res. 22 (2007)
3
2832-2837.
4
[19] T. Hitosugi, N. Yamada, N. L. H. Hoang, J. Kasai, S. Nakao, T. Shimada and T.
5
Hasegawa, Fabrication of TiO 2-based transparent conducting oxide on glass and polyimide
6
substrates, Thin Solid Films, 517 (2009) 3106-3186.
7
[20] N. L. H. Hoang, N. Yamada, T. Hitosugi, J. Kasai, S. Nakao, T. Shimada and T.
8
Hasegawa, Low-temperature fabrication of transparent conducting anatase Nb-doped TiO2 films
9
by sputtering, Appl. Phys. Express, 1 (2008) 115001.
10
[21] S. X. Zhang, D. C. Kundaliya, W. Yu, S. Dhar, S. Y. Young, L. G. Salamanca#Riba, S. B.
11
Ogale, R. D. Vispute and T. Venkatesan, Nb Doped TiO2: Intrinsic Transparent Metallic Anatase
12
Versus Highly Resistive Rutile Phase, J. Appl. Phys. 102 (2007) 013701.
13
[22] D. Kurita, S. Ohta, K. Sugiura, H. Ohta and K. Koumoto, Carrier generation and transport
14
properties of heavily Nb-doped anatase TiO2 epitaxial films at high temperatures, J. Appl. Phys.
15
100 (2006) 096105.
16
[23] S. X. Zhang, S. Dhar, W. Yu, H. Xu, S. B. Ogale and T. Venkatesan, Growth parameter-
17
property phase diagram for pulsed laser deposited transparent oxide conductor anatase Nb: TiO2,
18
Appl. Phys. Lett. 91 (2007) 112113.
19
[24] B. J. Morgan, D. O. Scanlon, and G. W. Watson, Small polarons in Nb- and Ta-doped rutile
20
and anatase TiO2, J. Mater. Chem. 19 (2009) 5175-5178.
17
1
[25] X. Lu, X. Mou, J. Wu, D. Zhang, L. Zhang, F. Huang, F. Xu and S. Huang, , Improved-
2
Performance Dye-Sensitized Solar Cells Using Nb-Doped TiO2Electrodes: Efficient Electron
3
Injection and Transfer, Adv. Funct. Mater. 20 (2010) 509-515.
4
[26] Tsvetkov Nikolay, Liudmila Larina, Oleg Shevaleevskiy Byung Tae Ahn, Electronic
5
structure study of lightly Nb-doped TiO2electrode for dye-sensitized solar cells, Energy Environ.
6
Sci. 4 (2011) 1480-1484.
7
[27] I. Hamberg and C. G. Granqvist, Evaporated Sn-doped In2O3 films: Basic optical properties
8
and applications to energy-efficient windows, J. Appl. Phys. 60 (1986) R123-R160.
9
[28] I. Hamberg and C. G. Granqvist, Evaporated Sn-doped In2O3 films: Basic optical properties
10
and applications to energy-efficient windows, J. Appl. Phys. 60 (1986) R123-R160.
11
[29] José M Soler, Emilio Artacho, Julian D Gale, Alberto García, Javier Junquera, Pablo Ordejón
12
and Daniel Sánchez-Portal, The SIESTA method for ab initio order-N materials simulation, J.
13
Phys. Cond. Matt. 14, (2002) 2745-2779.
14
[30] John P. Perdew, Kieron Burke, and Matthias Ernzerhof, Generalized Gradient Approximation
15
Made Simple, Phys. Rev. Lett., 77 (1996) 3865.
16
[31] Wan-Jian Yin,Shiyou Chen, Ji-Hui Yang, Xin-Gao Gong, Yanfa Yan and Su-Huai Wei,
17
Effective band gap narrowing of anatase TiO2 by strain along a soft crystal direction, Appl.
18
Phys.Lett. 96 (2010) 221901.
19
[32] R. Hoffmann, Angew., How Chemistry and Physics Meet in the Solid State, Chem. Int. Ed.
20
Engl. 26 (1987) 846-878.
18
1
[33] C. J. Barbe, F. Arendse, P. Comte, M. Jirousek, F. Lenzmann, V. Shklover, M. Gratzel,
2
Nanocrystalline titanium oxide electrodes for photovoltaic applications, J. Am. Ceram. Soc. 80
3
(1997),3157.
4
[34] A. Zaban, S. T. Aruna, S. Tirosh, B. A. Gregg, Y. Mastai, The Effect of the Preparation
5
Condition of TiO2 Colloids on Their Surface Structures, J. Phys.Chem. B 104 (2000), 4130.
6
[35] R. D. Shannon., Revised effective ionic radii and systematic studies of interatomic distances
7
in halides and chalcogenides , Acta Cryst A 32 (1976) 751-767.
8
[36] Lukas Thulin and John Guerra, Calculations of strain-modified anatase TiO2 band structures,
9
Physical Review B 77 (2008) 195112.
10 11 12 13 14 15 16
Figure Captions:
17
Figure 1. (a) Coordination of octahedral TiO6 in directions a, b and c (b) Two octahedral layers
18
stacking along c direction.
19
Figure 2. COOP curves for Bulk structure in different directions
20
Figure 3. (a) Bond length distribution for surface and (b) different bonds in (101) direction
21
Figure 4. COOP curves for (a) bonds 1-6 of the surface (b) bonds 7-11 of the surface
19
1
Figure 5. (a) Different oxygen sites for anatase TiO2 (101) surface and (b) COOP curves for each
2
of the oxygen sites
3
Figure 6. Formation energy of Mg defect as a function of oxygen chemical potential
4
Figure 7. Bond length distribution of Mg doped TiO2 surface
5
Figure 8. Two impurities doped into the structure and (a) close together (C-structure), (b) far from
6
each other (F-structure).
7
Figure 9. Formation energy of higher density Mg defect as a function of oxygen chemical potential
8
Figure 10. Formation energy of Mg-Nb defect as a function of oxygen chemical potential
9
Figure 11. Density of states of doped surfaces and PDOS on Mg and Nb atoms
10 11 12 13
Table Captions:
20
1
Table 1: Bond length average (BL) and standard deviation (SD) of the bond length distribution of
2
Mg doped surface (Mg-D).
3
Table 2: Bond length average (BL) and standard deviation (SD) of bond length distribution of F-
4
structure and C-structure doped surface (F and C).
5
Table 3: Bond length average (BL) and standard deviation (SD) of bond length distribution of MN-
6
F and MN-C structure doped surface.
7
Table 4: Fermi energy (Ef),valence band edge (Ev) and conduction band edge (Ec) of the Mg
8
doped F structure (Mg-F), Mg-Nb doped C structures (MN-C) and pritine surface (surf).
9 10 11 12 13 14 15 16 17 18 19 20 21
Table 1 surf-(BL)
Mg-D(BL)
21
Surf-(SD)
Mg-D(SD)
Bond 1 Bond 2 Bond 3,4 Bond 5 Bond 6 Bond 7,8 Bond 9 Bond 10 Bond 11
1.847 2.058 1.934 2.167 2.046 1.983 2.066 1.815 1.861
1.861 2.080 1.938 2.132 2.025 1.987 2.067 1.833 1.867
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Table 2
22
0.000 0.001 0.000 0.001 0.001 0.001 0.001 0.000 0.000
0.019 0.023 0.020 0.032 0.021 0.033 0.015 0.068 0.055
Bond 1 Bond 2 Bond 3,4 Bond 5 Bond 6 Bond 7,8 Bond 9 Bond 10 Bond 11
C-BL 1.875 2.069 1.944 2.114 2.027 1.989 2.089 1.845 1.884
F-(BL) 1.873 2.073 1.940 2.118 2.021 1.986 2.085 1.848 1.877
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Table 3 23
C-(SD) 0.027 0.064 0.013 0.051 0.046 0.036 0.042 0.080 0.083
F-(SD) 0.023 0.044 0.022 0.045 0.034 0.037 0.013 0.084 0.076
Bond 10 Bond 1 Bond 11 Bond 3,4 Bond 7,8 Bond 6 Bond 2 Bond 5 Bond 9
MN-C (BL)
MN-F(BL)
MN-C (SD)
MN-F (SD)
1.837 1.867 1.867 1.939 1.993 2.035 2.071 2.128 2.079
1.837 1.869 1.868 1.939 1.991 2.033 2.069 2.134 2.093
0.055 0.030 0.059 0.022 0.043 0.035 0.048 0.045 0.030
0.055 0.036 0.061 0.025 0.033 0.039 0.057 0.053 0.031
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Table 4 24
Surf Mg Mg-F MN-C
Ef -6.759 -8.202 -8.330 -7.961
Ev -8.408 -8.402 -8.414 -8.299
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
25
Ec -5.699 -5.691 -5.686 -5.690
Bg 2.710 2.711 2.728 2.609
1 2
Figure 1 (a)
Figure 1 (b)
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
26
1 2
Figure 2
3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
27
1
2 3
Figure 3 (a)
Figure 3 (b)
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
28
1 2
3 4
Figure 4 (a)
Figure 4 (b)
5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
29
1 2 3 4 5 6 7 8 9
Figure 5 (a)
Figure 5 (b)
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
30
1 2
3 4
Figure 6
5 6 7 8 9 10 11 12 13 14 15 16 17 18
31
1 2 3
4 5
Figure 7
6 7 8 9 10 11 12 13 14 15 16 17 18
32
1 2 3
4 5
Figure 8 (a)
Figure 8 (b)
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
33
1
2 3
Figure 9
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
34
1 2 3
4 5
Figure 10
6 7 8 9 10 11 12 13 14 15 16 17
35
1 2
Figure 11
36