J. Nig. Soc. Phys. Sci. 1 (2019) 131–137

Journal of the
Nigerian Society

of Physical
Sciences

Original Research

First-principles calculations of Fluorine-doped Titanium dioxide:
A prospective material for solar cells application

A. Shamsudeenb, A. Shuaibua,∗, S. G. Abdua, M. S. Abubakara, Abdullahi lawalb

aDepartment of Physics, Kaduna State University, P. M. B. 2339, Kaduna, Nigeria
bDepartment of Physics, Federal College of Education Zaria, Nigeria

Abstract

This study focuses on the anatase TiO2 doped Fluorine to investigate their structural and electronics properties using Density Functional Theory
(DFT) within generalized gradient approximation (GGA) as implemented in Quantum ESPRESSO (QE). For the anatase TiO2 phase the calculated
electronic band structures of pureTiO2 and TiO2 doped Fluorine nanocrystals are displayed along a high symmetry directions and the energy range
of band structure is plotted from 0.0 eV to 3.9 eV , the energy separation between the bottom of the conduction band and the top of valence band
occurred at the Γ and N points, indicating that anatase T iO2 is an indirect band gap material with an approximate value of 2.30 eV energy gap,
this value is consistent with previous DFT result. When F is added the band structure did not change much because fluorine element doping is
conducive to the generation of Oxygen holes and enhances the mobility of effective electrons which can enhance the conductivity of the adsorbent
substrate and improve the solar cell performance of the fluorine-doped TiO2. The band gap value obtained for F doped TiO2 was found to be
2.11 eV . The dopant formation energy of Fluorine is calculated to be −55.6 Ry which is equivalent to −756.5 eV .

Keywords: DFT, T iO2, Fluorine, electronic properties, solar cells

Article History :
Received: 26 August 2019
Received in revised form: 10 October 2019
Accepted for publication: 11 October 2019
Published: 17 December 2019

c©2019 Journal of the Nigerian Society of Physical Sciences. All rights reserved.
Communicated by: B. J. Falaye

1. Introduction

Engineers and scientists show so much interest in compounds
made of transition metal oxides which have wide band gap,
very good light absorption capability, very good value of heat
formation and other various fascinating properties. This is be-
cause these properties present the potential of use in advanced
applications such as solar cells [1, 2, 3]. Nowadays a lot of
investigations are carried out on oxide materials, especially to
meet industry requirements. This is because material oxides
are used in a lot of art technologies such as magnetic disks,
ICs and solar cells and their likes. A lot of properties sought

∗Corresponding author tel. no: +2348179931945
Email address: alhazikara@gmail.com (A. Shuaibu )

by researchers and the industry, which is driving more research
into the area, include need for economical alternative to current
materials, non-toxic and environmentally friendly, wide avail-
ability and good electrical, magnetic and or optical properties
for use as base materials or doping in optical fibers and sim-
ilar uses. These demands are partly driven by need to meet
energy demand in the future [3, 4, 5]. One of the oxides which
attracted a lot of theoretical and experimental research effort is
TiO2 [6]. This is in order to better understand the optoelectronic
properties of TiO2. Many naturally occurring and engineered
polymorphs of T iO2 exist. These include anatase, baddeleyite,
pyrite, columbite, brookite, fluorite, cotunnite and rutile. Three
of these (i.e. anatase, brookite and rutile) exist naturally while
the rest are manufactured. Due to popular demand and remark-

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Shamsudeen et al. / J. Nig. Soc. Phys. Sci. 1 (2019) 131–137 132

able properties of the naturally occurring polymorphs such as
rutile, for use in production of catalyst, flat panel displays, op-
toelectronic devices, sensors, and solar cell technology and so
on, many of them are often artificially synthesized.

Rutile, as a result of its structure, possesses one of the high-
est stabilities that can be found as compared to others. Anatase
is also thermodynamically stable up to a temperature of about
800 oC. On another hand brookite has a structure that resem-
bles that of rutile, though with less stability at high tempera-
tures [7, 8]. The structure of anatase is the most suitable for
photo catalytic applications. It is one of the reasons for attract-
ing a lot of research interest into the properties of T iO2. Other
properties of T iO2, for which it is held in high regards is its use
in many ceramic materials to add features and capabilities such
as being hydrophilic, photo catalytic, hydrophobic and having
antibacterial features [9], this is aside its good chemical stabil-
ity, nontoxicity and reduced cost. T iO2 is also used for air and
water purification by taking advantage of its antibacterial capa-
bilities. It is used in PVC fabrics, used to make materials with
self-cleaning effects, used for preservation of glass and cultural
heritage [10]. It is also used in de-synthesizing photo cells as a
common photocathode.

The history of T iO2 went as far back as 1971 when the work
of Fushijima and Honda revealed the photo electrochemistry of
the material while using it as an anode in an electrochemical
cell. This application is what gave rise to all the interest that was
generated over the years which led to discovery of a lot of its
other properties [11]. Wang et al.[12] reported that T iO2, when
used to fabricate ultra-violet (UV) photo-detector, shows more
energy efficient operation than other material such as Gallium
Nitride (GaN), Silicon (S i) and Zinc Oxide (ZnO). Its wide
band gap is what limits the usage of T iO2 as a semiconductor
directly used for semiconductor component. This is why it is
mostly used as a substrate for other semiconductor materials
especially in a thin film solar cell technology.

Because of these multiple uses and benefits that can be de-
rived from T iO2, it is obviously of paramount importance, to
areas of harnessing solar energy, optoelectronics, capturing vis-
ible and near visible light, to unveil the full potentials of this
compound and its various forms. This should be done through
tuning the properties of the oxides such as its band gap and
so on. This need is the drive for theoretical and experimen-
tal researches in order to have the comprehensive knowledge
regarding its structure, properties and their relationship to its
performance. A lot of work, especially experimental work is
now available in the research community regarding T iO2, but
theoretical results of research related to the compilation that are
adequate to characterize it are still scarce. Currently most of the
theoretical works are at the level of investigations which were
performed via Density Function Theory (DFT). Since it gives a
simple basis to characterized the quantum properties of various
materials and plays an important role in designing many new
materials. In addition to many experimental studies of T iO2,
is seen by many as a favorable material for many important
high technological applications, a few important first principle
DFT studies are reported in previous work. Furthermore, the
studies discussed and many others, the band gap values of the

materials are either over- or under-estimated. This results in de-
ducting contradictory nature of the band gaps which highlights
the need for more studies. In addition, a lot of the work was
done at different side by side of GGA and LDA, a technique
which underestimate the band gap. Thus, to better understand
the optoelectronic properties of T iO2 such as strong light ab-
sorption, photocurrent sensitivity to the polarization of light it
is essential to use reliable XC approximations to determine its
electronic properties. To utilize the maximum spectral range
in the solar spectrum, the band gap of T iO2 should be tuned,
which will broaden the operational optical window of the T iO2
-based optoelectronic devices.

Nowadays, doping is one of the well-approaches to improve
the properties of materials. Doping can dramatically modify
physical and chemical properties of materials [13]. Therefore,
T iO2 is repeatedly doped with different metals and transition
elements to tune its band gap and enhance its optical, electrical,
and magnetic properties [14, 15, 16, 17, 18]. Non-metal doping
is another approach used to narrow the band gap; in comparison
to metal doping that often forms a donor level in the forbidden
band, non-metal doping usually shifts the valence band edge
upward [18]. Doping with non-metal elements such as F shows
an enhancement in the electronic, optical, and magnetic proper-
ties of narrow-band gap semiconductor materials [19, 20, 21].
The doping by F has also shown higher thermal stability and
conductivity in graphene [22]. The aforesaid reasons motivated
us to study the doping by Fluorine atom, which can significantly
modify/tune the electronic properties T iO2. To the best of our
knowledge, no theoretical studies on F-doped T iO2 exist in lit-
erature. The Fluorine doping approach in T iO2 may open new
paths to non-metal elements doping for various other potential
applications such as infrared detectors, infrared LEDs, lasers,
transistors, and thermo-photovoltaic systems.

2. COMPUTATIONAL DETAILS

2.1. Computational method

The calculations are performed on the 2 × 2 × 2 supercells
relative to the standard primitive unit cell of Fluorine doped
anatase T iO2 within first principle calculation using Quantum
ESPRESSO simulation package [23]. Perdew-Burke-Ernzerhof
generalized gradient approximation (PBE-GGA) exchange-correlation
potential [24] were used for treating electron-electron effects.
For integrals, smearing has been adopted and to be specific
Maxfessel-Paxton smearing method. The brillouin zone inte-
gration is performed using Monkhorst-Pack scheme [25] with
3 × 3 × 2 k-points grids for all the materials. For fluorine
doped T iO2 structure 2 × 2 × 2 supercells relative to the stan-
dard conventional unit cell were used. The supercell consists of
twelve numbers of atoms: four Titanium atom and eight Oxy-
gen atoms. One O atom was replaced by Fluorine atom making
0.25 % occupancy by the dopant. The super cell dimensions
are kept fixed throughout the calculations, while the atomic
positions are fully relaxed for all calculations using Broyden-
Fletcher-Golfarb-Shannon (BFGS) algorithm, until the forces
acting on the atoms are below 0.001 eV/Å.

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3. RESULTS AND DISCUSSION

3.1. Convergence Test

In any DFT calculation using DFT code, it is of paramount
importance to perform a convergence test calculation before
commencing the actual calculation. The results presented be-
low represent the convergence test with respect to plane wave
kinetic energy cut-off and k-points mesh for undoped anatase
T iO2 and Fluorine atom doped T iO2.

3.1.1. Convergence Test Results of undoped T iO2

Figure 1: (A) the convergence of total energy with respect to the kinetic
energy cut-off. (B) The convergence of the total energy with respect to
the k-points grids.

3.1.2. Convergence Test Results of doped Fluorine atom.
It could be seen from Figure 1 that the total energy changes

considerably with the kinetic energy cut-off, until at some en-
ergy cut-off where it becomes almost stable. In all the two
cases, as the total energy decreases, the kinetic energy cut-off
increases from 10 Ry to 40 Ry and becomes almost stable at
40 Ry. That is to say, the total energy remains constant with
any further increases in the kinetic energy cut-off from 40 Ry.
This indicates a well-converged energy cut-off. That is why;

Figure 2: (A) NO HEADING. (B) NO HEADING.

40 Ry was used as the plane wave basis set for the kinetic en-
ergy cut-off of the two cases.

However, Figure 2B and Figure 5B show the variations of
the total energy with respect to the k-points grids. The total
energy changes considerably with the number of k-points at a
certain points, showing a well-converged value. In all the two
cases, the total energy increases from 1×1×2 to 3×3×2 k-point
grids and become almost stable at 3 × 3 × 2. As such, 3 × 3 × 2
k-points have been adopted for the three cases. Furthermore,
Monkhorst and Pack method of selecting k-points is commonly
used in most DFT calculations [25]. Most of the DFT codes
provide ways of choosing k-points using Monkhorst and Pack
method.

3.2. Structural Properties of the Undoped T iO2 and T iO2 doped
F.

In order to explore the structural properties of the anatase
T iO2 with space group 14/amd was simulated in Figure 3. The
anatase structure exhibit tetragonal geometry and have a high
symmetry in which six Oxygen atoms is surrounded to each T i
atom.

From Table 5, it can be observed that, for 12.5 % substitu-
tional doping case, there are eight symmetrically different ap-
proach in which Oxygen (O) atom can be replaced by Fluorine
(F) atom(s). But for this particular study, as shown in tables
above, one configuration (D8 0.125) is considered. No struc-
tural transition is seen; as such the crystal parameters remained

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Table 1: Convergence test of T iO2 total energy with respect to kinetic energy cut-off of the plane wave of undoped T iO2.

S/N Kinetic Energy Cut-Off (Ry) Total Energy (Ry)
1 10 -680.917
2 20 -740.466
3 30 -747.717
4 40 -747.374
5 50 -748.413
6 60 -748.421
7 70 -748.429

Table 2: Convergence of the total energy with respect to the k-points grids of undoped T iO2.

S/N NUMBER OF K-POINTS Total Energy (Ry)
1 1 × 1 × 2 -749.018
2 3 × 3 × 2 -747.670
3 5 × 5 × 2 -747.673
4 7 × 7 × 2 -747.673
5 9 × 9 × 2 -747.672
6 11 × 11 × 2 -747.673
7 13 × 13 × 2 -747.674

Table 3: Convergence test of total energy with respect to the kinetic energy cut-off.

S/N KINETIC ENERGY CUT-OFF (Ry) TOTAL ENERGY (Ry)
1 10 -694.517
2 20 -756.204
3 30 -763.468
4 40 -764.135
5 50 -764.174
6 60 -764.183
7 70 -764.191

Table 4: Convergence of the total energy with respect to the k-points grids of undoped T iO2.

S/N NUMBER OF K-POINTS TOTAL ENERGY (Ry)
1 1 × 1 × 2 -764.697
2 3 × 3 × 2 -763.468
3 5 × 5 × 2 -763.481
4 7 × 7 × 2 -763.478
5 9 × 9 × 2 -763.478
6 11 × 11 × 2 -763.479
7 13 × 13 × 2 -763.480

Table 5: Configurations for substitutional doping of O by F anatase T iO2 material.

Undoped O O O O O O O O
D1 0.125 F O O O O O O O
D2 0.125 O F O O O O O O
D3 0.125 O O F O O O O O
D4 0.125 O O O F O O O O
D5 0.125 O O O O F O O O
D6 0.125 O O O O O F O O
D7 0.125 O O O O O O F O
D8 0.125 O O O O O O O F

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Figure 3: (A): Anatase Structure for undoped T iO2 and (B) T iO2 doped
F.

the same as that for the undoped system. To find the stability
of the structure after Fluorine doping, the dopant formation en-
ergy of the Fluorine atom is estimated using Equation 1 [26].
The dopant formation energy in this context simply refers to
the energy needed to insert one Fluorine atom with a chemical
potential µF into the supercell after removing one Oxygen atom
with chemical potential µF from the same position [27].

E f = Edoped − Eundoped + µo −µF (1)

where, Edoped is the total energy of the anatase T iO2 material;
Eundoped is the total energy of the anatase undoped T iO2 system;
µo is the chemical potential per atom of Oxygen bulk crystal; µF
is the chemical potential per atom of Fluorine bulk crystal.

Following common practice, the chemical potentials were
found as the DFT total energy per atom in the bulk systems.
The dopant formation energy of Fluorine is calculated to be
−55.6 Ry which is equivalent to −756.5 eV . This serves as
the measure of the stability of the doped structure, the lower
value of the formation energy signifies the most stable struc-
ture. From this value of dopant formation energy, this shows
that, the Fluorine doped T iO2 is stable.

3.3. Electronic Properties
Electronic properties calculations are very crucial for de-

scribing the optoelectronic properties of solids. The electronic
properties investigations of T iO2, doped Fluorine covers the
electronic band structure, density of state (DOS) and partial
density of state (PDOS). The main purpose of the ground state,
electronic band structure, DOS and PDOS calculations in this
work is to obtain KS eigenvalues and eigenfunctions as well as
useful information about the electronic properties of the con-
cerned materials. To understand the effect of doping on T iO2,
Fluorine (F) was added in the calculations. The calculated elec-
tronic band structures of pure T iO2 and T iO2 doped Fluorine
thin film are displayed along the eight symmetry (Γ → H →
N → P → Γ → X → M → R) directions and the energy range
of band structure is plotted from 0.0 eV to 3.9 eV . The Fermi

level position on the band structure of these crystals is shown by
the zero on the energy scale. PBE exchange correlation poten-
tials is chosen over LDA, because in several cases GGA-PBE
gives more reliable and accurate results for DFT electronic cal-
culation. The energy separation between the bottom of the con-
duction band and the top of valence band occurred at the Γ and
N points or band structure calculations within PBE which in-
dicate that anatase T iO2 is an indirect band gap material with
value of 2.30 eV energy gap, this value is consistent with pre-
vious DFT result. However, the value is smaller than experi-
mental result of 3.21 eV [28] and this effect is the limitation
of DFT approach due to approximations used in the exchange-
correlation functional. On the other hand, the F-doped T iO2
model was established based on the perfect crystal plane model.
A fluorine atom replaces one of the O atoms on the surface of
the anatase T iO2 perfect crystal plane, and F atom combined
with T i atoms to form T i − F bonds. It can be seen that the
energy band gap did not change much after the fluorine atom
being doped and the value obtained was found to be 2.11 eV .
Furthermore, fluorine element doping is conducive to the gen-
eration of Oxygen holes and enhances the mobility of effective
electrons, which can enhance the conductivity of the adsorbent
substrate and improve the solar cell performance of the fluorine-
doped T iO2.

Figure 4: Band structure of (A) Pure T iO2 (B) F doped T iO2

For more clarification for the nature of the energy gap, we
have also study the total density of state (DOS) of anatase T iO2,
and F doped anatase T iO2. Figure 5 shows a decomposition of
the calculated total DOS of T iO2 and F doped T iO2 in bulk
forms. For pure T iO2 the lowest valence states is dominated
by T i-s orbital and O-p orbital while in the cased of F doped
T iO2 the lowest valence states is dominated by T i-s orbital, O-p
orbital and F-p orbital. The T i-d orbital and O-s orbital con-
tribute much high in the conduction band for pure T iO2 while
T i-d, O-s, O-s orbital as well as F-s orbital contributed slightly
higher in the conduction band. The T i-p and O-p orbitals of
T iO2 contribute a slightly higher in the valence band near the
Fermi level. For F anatase doped T iO2 the main contribution

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Table 6: Calculated energy gap of T iO2 and T iO2 doped F with previous first principle calculations and experimental data.

Material Work Method Band gap Eg(eV ) Nature
Pure T iO2 Our Work PBE-GGA 2.30 Indirect

Other Work PBE-GGA[29] 2.14 Indirect
EV-GGA[29] 2.32 Indirect

PBE-GGA[30] 2.30 Indirect
PBE-GGA[31] 2.30 Indirect
Experiment[32] 3.21 Indirect

F doped T iO2 Our Work PBE-GGA 2.11 Indirect

of valence band near the Fermi level is from T i-p orbital and O-
p orbital. The T i-s, O-s and O-p orbitals contributed the most
near the Fermi level, thus held responsible for the properties of
T iO2. Also, s- and p-orbitals of T i atoms, s- and p-orbitals of
O atoms and s-orbital of F atoms of F doped T iO2 compound
contributed the most near the Fermi level, thus held responsible
for the properties.

Figure 5: Total and partial density of state (A) Pure T iO2 (B) F doped
T iO2.

4. Conclusion

A first principle study was used using PBE XC functional
in Quantum ESPRESSO code. The available results were com-
pared with other experimental values. The electronic properties
density of state, partial density of state and band gap values
were calculated in the ground state properties. It was found that
T iO2 in anatase phase has indirect band gap with a value of
2.30 eV , this value is consistent with previous DFT results. The
obtained band gap value is smaller than experimental result of
3.21 eV and this effect is the limitation of DFT approach due
to approximations used in the exchange-correlation functional.
The Fluorine doped T iO2 model was established based on the
perfect crystal plane model. A fluorine atom replaces one of
the O atoms on the surface of the anatase T iO2 perfect crys-
tal plane, and F atom combined with T i atoms to form T i − F
bonds. It can be seen that the energy band gap did not change

much after the fluorine atom being doped. Furthermore, fluo-
rine element doping is conducive to the generation of Oxygen
holes and enhances the mobility of effective electrons which
can enhance the conductivity of the adsorbent substrate and im-
prove the solar cell performance of the fluorine-doped T iO2.
The dopant formation energy of Fluorine is calculated to be
−55.6 R which is equivalent to −756.5 eV . The formation en-
ergy serves as the measure of the stability of the doped struc-
ture; the lower value of the formation energy signifies the most
stable structures [26]. From this value of dopant formation en-
ergy, this shows that the Fluorine doped anatase T iO2 is stable.

Acknowledgments

We thank the referees for the positive enlightening com-
ments and suggestions, which have greatly helped us in making
improvements to this paper.

References

[1] E. Kabir, P. Kumar, S. Kumar, A. A. Adelodun & K.-H. Kim, ”‘Solar
energy: Potential and future prospects”’, Renewable and Sustainable En-
ergy Reviews 82 (2018) 894.

[2] J. Robertson & B. Falabretti, ”‘Electronic structure of transparent con-
ducting oxides, Handbook of transparent conductors”, Springer (2011)
pp27-50.

[3] K. Nagaveni, M. Hegde, N. Ravishankar, G. Subbanna & G. Madras,
”‘Synthesis and structure of nanocrystalline T iO2 with lower band gap
showing high photocatalytic activity”, Langmuir 20 (2004) 2900.

[4] Y. Xiao, C. Wang, K. K. Kondamareddy, P. Liu, F. Qi, H. Zhang, S. Guo &
X.-Z. Zhao, ”‘Enhancing the performance of hole-conductor free carbon-
based perovskite solar cells through rutile-phase passivation of anatase
T iO2 scaffold”, Journal of Power Sources 422 (2019) 138.

[5] J. Y. Seo, R. Uchida, H. S. Kim, Y. Saygili, J. Luo, C. Moore, J. Ker-
rod, A. Wagstaff, M. Eklund & R. McIntyre, ”‘Boosting the Efficiency of
Perovskite Solar Cells with CsBr-Modified Mesoporous T iO2 Beads as
Electron-Selective Contact”, Advanced Functional Materials 28 (2018)
1705763.

[6] T. Singh, S. Öz, A. Sasinska, R. Frohnhoven, S. Mathur & T. Miyasaka,
”‘Sulfate-Assisted Interfacial Engineering for High Yield and Effi-
ciency of Triple Cation Perovskite Solar Cells with Alkali-Doped T iO2
Electron-Transporting Layers”, Advanced Functional Materials 28 (2018)
1706287.

[7] A. Parameswari, Y. Soujanya & G. N. Sastry, ”‘Functionalized Rutile
T iO2 (110) as a Sorbent To Capture CO2 through Noncovalent Interac-
tions: A Computational Investigation”, The Journal of Physical Chem-
istry C 123 (2019) 3491.

[8] Y. Wang, A. S. Ganeshraja, C. Jin, K. Zhu & J. Wang, “One-pot synthesis
visible-light-active T iO2 photocatalysts at low temperature by peroxotita-
nium complex”, Journal of Alloys and Compounds 765 (2018) 551-559.

136



Shamsudeen et al. / J. Nig. Soc. Phys. Sci. 1 (2019) 131–137 137

[9] O. Çomaklı, M. Yazıcı, H. Kovacı, T. Yetim, A. Yetim & A. Çelik, “Tribo-
logical and electrochemical properties of T iO2 films produced on C p−T i
by sol-gel and SILAR in bio-simulated environment”, Surface and Coat-
ings Technology 352 (2018) 513.

[10] M. Gurbuz, B. Atay & A. Dogan, “Synthesis of High-Temperature-Stable
T iO2 and its Application on Ag+-Activated Ceramic Tile”, International
Journal of Applied Ceramic Technology 12 (2015) 426.

[11] H. Gao, X. Li, J. Lv & G. Liu, “Interfacial charge transfer and en-
hanced photocatalytic mechanisms for the hybrid graphene/anatase T iO2
(001) nanocomposites”, The Journal of Physical Chemistry C 117 (2013)
16022-16027.

[12] W. Wang, C. Shan, H. Zhu, F. Ma, D. Shen, X. Fan & K. Choy, “Metal-
insulator-semiconductor-insulatormetal structured titanium dioxide ultra-
violet photodetector”, Journal of Physics D: Applied Physics 43 (2010)
045102.

[13] A. G. Ilie, M. Scarisoreanu, E. Dutu, F. Dumitrache, A. -M. Banici, C.
T. Fleaca, E. Vasile & I. Mihailescu, “Study of phase development and
thermal stability in as synthesized T iO2 nanoparticles by laser pyrolysis:
ethylene uptake and oxygen enrichment”’, Applied Surface Science 427
(2018) 798.

[14] P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavaz-
zoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni & I. Dabo, “QUAN-
TUM ESPRESSO: a modular and open-source software project for quan-
tum simulations of materials”, Journal of physics: Condensed matter 21
(2009) 395502.

[15] J. P. Perdew, K. Burke & M. Ernzerhof, ”‘Generalized gradient approxi-
mation made simple”’, Physical review letters 77 (1996) 3865.

[16] H. J. Monkhorst & J. D. Pack, “Special points for Brillouin-zone integra-
tions”, Physical Review B 13 (1976) 5188.

[17] X. Fan, F. Wang, Z. Chu, L. Chen, C. Zhang & D. Zou, “Conductive
mesh based flexible dye-sensitized solar cells”, Applied Physics Letters
90 (2007) 073501.

[18] D. S. Parker, F. Zhang, Y. S. Kim, R. I. Kaiser, A. Landera, V. V. Kislov, A.
M. Mebel & A. Tielens, “Low temperature formation of naphthalene and
its role in the synthesis of PAHs (polycyclic aromatic hydrocarbons) in the
interstellar medium”, Proceedings of the National Academy of Sciences
109 (2012) 53.

[19] H. Ali, R. Seidel, A. Bergmann & B. Winter, “Electronic structure of
aqueous-phase anatase titanium dioxide nanoparticles probed by liquid jet
photoelectron spectroscopy”’, Journal of Materials Chemistry A 7 (2019)
6665-6675.

[20] M. Mohamad, B. U. Haq, R. Ahmed, A. Shaari, N. Ali & R. Hussain,

“A density functional study of structural, electronic and optical proper-
ties of titanium dioxide: Characterization of rutile, anatase and brookite
polymorphs”, Materials Science in Semiconductor Processing 31 (2015)
405.

[21] H. Xing-Gang, L. An-Dong, H. Mei-Dong, L. Bin & W. Xiao-Ling,
“First-principles band calculations on electronic structures of Ag-doped
rutile and anatase T iO2”, Chinese Physics Letters 26 (2009) 077106.

[22] R. Faccio, L. Fernández-Werner, H. Pardo & A. W Mombru, “Current
trends in materials for dye sensitized solar cells”, Recent patents on nan-
otechnology 5 (2011) 46.

[23] D. Reyes-Coronado, G. Rodrı́guez-Gattorno, M. Espinosa-Pesqueira, C.
Cab, R.d. de Coss & G. Oskam, “Phase-pure T iO2 nanoparticles: anatase,
brookite and rutile”, Nanotechnology 19 (2008) 145605.

[24] P. J. Perdew, K. Burke & M. Ernzerhof, “Generalized gradient approxi-
mation made simple”, Physical Review Letters18 (1996) 3865.

[25] D. J. Chadi, “Special points for Brillouin-zone integrations”, Physical Re-
view B 16 (1977) 1746.

[26] S. S. Alhassan, A. Shuaibu & M. Y. Onimisi, “Structural and Electronic
Properties of Delafossite CuGa1xMnxO2(X = 0.5) Nanocomposite: A
First Principle Study”,Physics Memoir-Journal of Theoretical & Applied
Physics 1 (2019) 106.

[27] H. Dorian AH, M. H. Assadi, S. Li, A. Yu & C. C. Sorrell, “Ab initio
study of phase stability in doped TiO2”, Computational Mechanics 50
(2012) 185.

[28] M. Mazmira, B. U. Haq, R. Ahmed, A. Shaari, N. Ali & R. Hussain, “A
density functional study of structural, electronic and optical properties of
titanium dioxide: Characterization of rutile, anatase and brookite poly-
morphs”, Materials Science in Semiconductor Processing31 (2015) 405.

[29] S. Raphael, M. Kraft & O. R. Inderwildi, “Electronic and optical proper-
ties of aluminium-doped anatase and rutile T iO2 from ab initio calcula-
tions”, Physical Review B 81 (2010) 075111.

[30] P. Sandeep, A. Abate, P. Ruckdeschel, B. Roose, Karl C. Gödel, Yana
Vaynzof & Aditya Santhala, “Performance and stability enhancement of
dye-sensitized and perovskite solar cells by Al doping of T iO2”, Ad-
vanced Functional Materials 24 (2014) 6046.

[31] L. Min, J. Zhang & Y. Zhang, “First-principles calculation of compen-
sated (2N, W) codoping impacts on band gap engineering in anatase
T iO2”, Chemical Physics Letters 527 (2012) 63.

[32] C. Pawan, P. Basyach & A. Choudhury, “Structural, optical and photo-
catalytic properties of T iO2/S nO2 and S nO2/T iO2 core-shell nanocom-
posites: an experimental and DFT investigation”, Chemical Physics 434
(2014) 1.

137