Abstract. In this research, the structural and electronic properties of N-doped
anatase TiO2 layers were evaluated using the density functional theory (DFT). The
results show that doping positions of N atoms cause different effects on the size
and shape of unit cells of models. Calculated band structures of doped layers show
the appearance of acceptor levels in the band-gaps and the decrease of band-gap
values, corresponds to pure layer values. Density of states (DOS) and projected
density of states (PDOS) of doped layers show that N 2p orbital play the key role in
the appearance of acceptor levels in forbidden bands. Ti 3d and O 2p orbitals still
play the most important roles in the DOS of N-doped TiO2 layers.

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JOURNAL OF SCIENCE OF HNUE
Mathematical and Physical Sci., 2014, Vol. 59, No. 7, pp. 150-156
This paper is available online at
A DFT STUDY ON STRUCTURAL AND ELECTRONIC PROPERTIES
OF N-DOPED ANATASE TiO2 LAYERS
Duong Quoc Van1, Nguyen Minh Thuy1 and Nguyen Huy Viet2
1Faculty of Physics, Hanoi National University of Education
2Institute of Physics, Vietnam Academy of Science and Technology, Hanoi
Abstract. In this research, the structural and electronic properties of N-doped
anatase TiO2 layers were evaluated using the density functional theory (DFT). The
results show that doping positions of N atoms cause different effects on the size
and shape of unit cells of models. Calculated band structures of doped layers show
the appearance of acceptor levels in the band-gaps and the decrease of band-gap
values, corresponds to pure layer values. Density of states (DOS) and projected
density of states (PDOS) of doped layers show that N 2p orbital play the key role in
the appearance of acceptor levels in forbidden bands. Ti 3d and O 2p orbitals still
play the most important roles in the DOS of N-doped TiO2 layers.
Keywords: TiO2 layers, N-doped, DFT, structural properties, electronic structure.
1. Introduction
Thin films have been used in many types of equipments in life, science and
technology. Various materials have been used to prepare thin films such as Si, ZnO,
InGaZnO and more. Doped TiO2 films have been used in many kinds of technical
applications, for example: gas sensors, solar cells, thin-film batteries, gate electrodes
for electronic devices and photocatalysts. In recent years, most studies of doped TiO2
materials have concentrated on their photocatalytic activities, especially for environmental
pollution treatment solutions. Due to its wide band-gap, doped TiO2 film’s photocatalytic
effect is negligible in the range of visible light. Visible photocatalytic effects can be
available if the band-gap of doped TiO2 materials is narrowed. Impurity doping is the
most commonly used method to reduce band-gap and extend the light absorption range of
doped TiO2 materials from the UV to the visible region and N is one of the most effective
Received October 12, 2014. Accepted October 26, 2014.
Contact Duong Quoc Van, e-mail address: vandq@hnue.edu.vn
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A DFT study on structural and electronic properties of N-doped anatase TiO2 layers
dopants [1]. To understand the mechanism of photocatalytic activity in doped TiO2,
ab-initio calculations based on the density-functional theory (DFT) have been performed
[2]. Most of these studies have same disadvantages: they were performed for TiO2 bulk
form properties and they used commercial software such as Materials Studio.
In this paper, our research concentrates on the N-doped TiO2 layers, which can be
consider ideal films. Calculations were performed using Quantum Espresso (QE) [3], an
integrated suite of Open-Source computer code for electronic-structure calculations and
materials modeling at the nanoscale, based on the density-functional theory (DFT), plane
waves and pseudopotentials. This research can serve as a guidance to understand TiO2
thin films properties and can be considered as a first step in the use of Quantum Espresso.
2. Content
2.1. Computational methods
Quantum Espresso, a free and open-source code, was used for calculations.
Generalized Gradient Approximation (GGA) are used for the exchange-correlation
functional and the parametrization of the Perdew-Burke-Ernzerhof (PBE) correlation
potential for homogeneous electron gas was employed [4]. The interaction potentials
between ionic cores and valence electrons (3s23p63d24s2 for Ti, 2s22p4 for O and 2s22p3
for N) are described by the Vanderbilt ultrasoft pseudopotential [5].
All calculations were performed for unit cells of N-doped TiO2 layers which
contains 4 Ti atoms, 7 O atoms and 1 N atom (in different doping positions). A 5 × 5 ×
2 k-point mesh was used in the Brillouin zone sampling for all models [6]. Cutoff energy
for the plane-wave representation of the wavefunctions in the geometry optimization was
set at 40 Rydberg.
2.2. Results and discussions
2.2.1. Structural properties
* Building N-doped TiO2 layers
Unit cells of un-doped TiO2 layers (hereafter referred as TOO-L) were built with
following lattice parameters: a = 3.7893 A˚, b = 9.6072 A˚ and c = 5× 3.7893 A˚ (see Figure
1a). The value of was selected to confirm the convergence of total energy of TOO-L and
to avoid an interaction between two layers in the periodic system [7].
Un-optimized unit cells of N-doped TiO2 layers were received from unit cells of
the un-doped TiO2 layer by replacing one (of eight) O atom with an N atom. There are 8
different O atoms in TOO-L, therefore there are 8 different models, all of them having the
same lattice parameters: a = 3.6704 A˚, b = 9.5102 A˚ and c = 18.9468 A˚.
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Duong Quoc Van, Nguyen Minh Thuy and Nguyen Huy Viet
* Structural properties of N-doped TiO2 layers
Most of the ab-initio calculations started with structural optimization. In this study,
all unit cells of N-doped TiO2 layers were optimized using the variable-cell relaxation
method. All atoms in the unit cell are moved to minimize the forces and stresses on them.
The optimized structures were received when the forces, the stresses of atoms and also
the total energies of unit cells were minimized. To avoid the effect of size limitation in the
z-axis, the value of was kept constant during the relaxation process. After relaxation, 8
optimized unit cells of doped layers are received and denoted TON-L-05 to TON-L-12 (all
of them will be denoted as TON-Ls), due to positions of the doped N atoms, respectively.
Table 1. Lattice parameters of N-doped TiO2 layers before and after optimization
Structural information of doped layers before and after optimization is shown in
Table 1. Depending on their lattice parameters, optimized unit cells can be divided into 2
groups: G1 and G2. The G1 group has 4 unit cells: TON-L-05, TON-L-06, TON-L-09 and
TON-L-10; their lattice parameters have significant changes after optimization. The G2
group has 4 unit cells: TON-L-07, TON-L-08, TON-L-11 and TON-L-12; their lattice
parameters do not change much compared to the un-optimized values. Optimized unit
cells show different changes in their total energies and volumes after optimization. For
the G1 group, both total energy and volume are increase while for the G2 group, the total
energy is increased and the volume is decreased such that structures in the G2 group are
not as stable as those in the G1 group.
Optimized translation units of TOO-L and TON-Ls are shown in Figure 1.The
results show significant distortions in the optimized translation units of the G1 group
(compared to un-doped TiO2) while there is a slightly change in G2. Lattice distortions of
translation units (similar to that of unit cells) can be explained as a consequence of doping.
The atomic radius and the ionic radius of N2− ion and O2− are very close, and this makes
it easy to place N atoms into TiO2 layer lattice but it still causes lattice distortion.
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A DFT study on structural and electronic properties of N-doped anatase TiO2 layers
When N is doped into TiO2, doped layers can transform to different structures but
they will exist in more stable structures. This means that N-doped TiO2 layers tend to
transform to structures in the G1 group. For more evidence, the band structure and DOS
of two groups will be analyzed.
Figure 1. Optimzed translation units of un-doped (a), N-doped TiO2 layers
in G1 group (b-e) and G2 groups (g-i)
2.2.2. Bands structure
Calculated results show that the band structures of G1 are similar as are the
band structures of the G2 group. Figure 2 shows the bands structures of un-doped
TiO2, TON-L-05 and TON-L-08 layers calculated using ab-initio calculations, and the
Generalized Gradient Approximation (GGA) for the xc-functional and the parametrization
of the Perdew-Burke-Ernzerhof (PBE) correlation potential (hereafter referred to as
GGA-PBE).
Figure 2. Band structure of un-doped (a) and N-doped TiO2 layers (b, c)
The bands structures show that un-doped and doped TiO2 are indirect band-gap
semiconductors. A doping effect was shown with the narrowing of band-gap of the
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Duong Quoc Van, Nguyen Minh Thuy and Nguyen Huy Viet
N-doped layers. The band-gap values of G1 are larger than those of G2. The band-gap
energies of G1 layers are around 2.45 eV whereas corresponding values for G2 are
around 2.0 eV, much smaller than the un-doped TiO2 layer value (∼ 2.55 eV [7]).
Recently, Franco et al. [8] estimated that the band-gap of un-doped TiO2 film is around
3.2 eV whereas corresponding values for N-doped TiO2 films depend on the doping
concentration and vary from 2.1 eV to 2.6 eV.Wang et al. [18] proved that those values are
3.2 eV and 2.8 eV, respectively. Wei Quin et al. [9] prepared N-doped TiO2 films using
a micro-plasma oxidation method and showed that the band-gap values of all samples
are around 2.8 eV. Baoshun Liu et al. [10] used a radio frequency reactive magnetron
sputtering method to prepare N-doped TiO2 films, finding the band-gap values of 3.11
eV, 2.90 eV and 2.70 eV for samples with N concentrations of 2.35%, 6.70% and 12.6%.
It is easy to see that our results are in qualitative agreement with these experimental
values. Calculations showed a narrowing of the band-gap of TiO2 layers when N was
doped, and a band-gap value decrease when the doping concentration is increased.
Bands structures of two groups also show the appearance of acceptor levels on the
top of the valence bands. In the G1 group, the separation gap between the acceptor level
and valance bands is about 0.5 eV, in good agreement with our previous results [7]; for
the G2 group, the acceptor levels overlap on the valance bands.
In the band structure of the N-doped TiO2 models, it can be seen the contribution of
N is due to the acceptor level in the top of the valence band. The contribution of this level
in the G1 group differs from that in the G2 group as can be seen on the band structure of
TON-L-05 and TON-L-08.
2.2.3. Density of states
* Density of States
Figure 3. Density of States (DOS) of 1-layer N-doped TiO2 layers
Figure 3 shows the total density of states of un-doped and N-doped TiO2 layers
calculated using GGA-PBE. Changing values of band-gap are easily seen here in addition
to the varying shapes of total DOS.
The contribution of N to the density of states of N-doped TiO2 layers can be seen
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A DFT study on structural and electronic properties of N-doped anatase TiO2 layers
very clearly in Figures 3b and 3c. For layers in G1, acceptor levels are stronger and clearly
separate while in G2 they are weaker and overlap with valence bands.
* Contribution of partial orbitals Figure 3a shows the partial density of states
(PDOS) of un-doped TiO2 layer. Figures 3b and 3c show the PDOS of TON-L-05
(representing G1) and TON-L-08 (representing G2) calculated using GGA-PBE in the
band-gap (the range of energy -5 eV to +5 eV). They show that Ti 3d and O 2p still play the
most important roles in the band structure of TiO2, similar with results for un-doped TiO2
bulk. The upper valence bands and lower conduction bands shows a strong hybridization
of Ti 3d and O 2p electrons. The acceptor levels on the top of the valence bands are
composed predominantly by N 2p orbitals, in agreement with previous results [7].
Figure 4. Contribution of Ti 3d, O 2p and N 2p to total DOS
of 1-layer N-doped TiO2 layers
3. Conclusion
Quantum Espresso has been successfully installed and a detailed setup for ab-initio
calculations using QE has been set. Quantum Espresso has been used to calculate the
structural and electronic properties of N-doped TiO2 layers. The calculated results show
that N doping leads to a change in lattice parameters or a distortion of unit cells.
Band structures of N-doped TiO2 layers show the narrowing band-gap compared to the
un-doped sample, which can be considered to be the effect of acceptor levels which appear
in the top of the valence bands. Calculated PDOSs prove that the contribution of N to band
structures of N-doped TiO2 layers are dominated by the N 2p orbital. The results also show
that Ti 3d and O 2p play the most important role in the creation of a band-gap in TiO2
layers. This work serves as a first step in our theoretical study on optical properties of
N-doped TiO2 thin films using DFT calculations.
Acknowledgments. This work was supported by the Ministry of Education and Training
Grant, No. B2014-17-46.
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Duong Quoc Van, Nguyen Minh Thuy and Nguyen Huy Viet
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