# Electronic Structure and Optical Properties of N/Si-Codoped Anatase TiO2 Evaluated Using First Principles Calculations

Authors: Huey-Jiuan Lin; Hsuan-Chung Wu
Journal: International Journal of Photoenergy
 (2014)

---

## Abstract

First principles calculations were used to evaluate the electronic structure and optical properties of N/Si-monodoped and N/Si-codoped TiO2 to further understand their photocatalytic mechanisms. In accordance with the atomic distance between N and Si dopants, this study considered three N/Si codoping configurations, in which the N dopant had a tendency to bond with the Si dopant. The calculations showed that the bandgaps of the N/Si codoping models were narrow, in the range 3.01–3.05 eV, redshifting the intrinsic absorption edge. The Si 3p orbital of N/Si-codoped TiO2 plays a key role in widening the valence band (VB), thereby increasing carrier mobility. In addition, the N-induced impurity energy level in the forbidden band appears in all three N/Si codoping models, strengthening absorption in the visible region. The bandgap narrowing, VB widening, and impurity energy levels in the forbidden band are beneficial for improving the photocatalytic activity of N/Si-codoped TiO2.


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## Body

## 1. Introduction

Since the pioneering work of Fujishima and Honda in 1972 [1], titanium dioxide (TiO2) has been widely studied as a promising photocatalytic material because of its excellent properties (e.g., it is nontoxic, inexpensive, and chemically stable). However, pure anatase TiO2 has a wide bandgap of 3.2 eV and only absorbs in the UV region (~5%) of solar energy. Therefore, its solar energy use is restricted. Much research has recently been devoted to developing methods of extending the optical absorption of TiO2-based materials into the visible region.Doping TiO2 with various dopants including transition metals such as Mo [2], Co [3], and Au [4] and nonmetals such as N [5–9], Si [10–14], P [15], and S [16] is a popular method of enhancing the characteristics of TiO2. Since the report of Asahi et al. in 2001 [5], N has been considered the most effective nonmetallic elemental dopant and has been studied further [5–9]. Doping with Si is also effective for enhancing the photocatalytic activity of TiO2 [10–14]. Doping TiO2 with two dopants (i.e., codoping) has recently been developed as a method to enhance photocatalytic activity, and promising results have been reported for codoping TiO2 with nitrogen and silicon (N/Si) [17–19]. Ozaki et al. [17, 18] fabricated nitrogen-doped silica-modified TiO2, which showed strong absorption in the 400–500 nm visible region and exhibited high photocatalytic activity toward visible-light-induced acetaldehyde decomposition. They indicated that the amount of Si added significantly increased the amount of N and the visible-light-induced photocatalytic activity. Hou et al. [19] found that N-doped SiO2/TiO2 exhibited higher photocatalytic activity than N-doped TiO2 when the weight ratio of SiO2/TiO2 was in the range 0.05–0.20. Shi et al. [20] performed first principles calculations to evaluate the energies and electronic properties of N/Si-codoped TiO2. The calculated energies indicated that Si doping increases the concentration of N in N/Si-codoped TiO2. The bandgap of Si/N-codoped TiO2 was significantly narrowed to 1.63 eV. However, the calculated bandgap of pure anatase TiO2 (2.18 eV) was underestimated owing to the limitations of standard density functional theory (DFT). A few approaches such as DFT + U (Hubbard U) and hybrid functionals have been used to investigate TiO2-based materials in order to overcome this limitation. Long and English [21] used Heyd-Scuseria-Ernzerhof (HSE06) hybrid DFT calculations to investigate the effects of N/Si codoping on the electronic properties of anatase TiO2. Their calculated bandgap of anatase TiO2 was 3.2 eV, which was consistent with the experimentally obtained bandgaps. The calculated results suggest that double-hole coupling plays a key role in ensuring high photocatalytic activity in the visible region for TiO2-based photocatalysts.The DFT + U is a method of correcting the underestimation of the bandgap and involves adding an orbital-dependent term to the DFT potential; it has previously been used to describe the electronic structures of transition-metal oxides [22–25]. Thus, we used the DFT + U method to more accurately represent the electronic structure and optical properties of N/Si-codoped TiO2. The N/Si codoping system included three N-Si-distance-based models, which were compared with the N-monodoped, Si-monodoped, and pure TiO2 models to further understand the mechanism of N/Si-codoping-induced photocatalytic activity enhancement. The optimized structures and Mulliken charges of the N-, Si-, and N/Si-doped TiO2 were also analyzed and compared with corresponding values in the literature.


## 2. Calculation Models and Methods

Figure1 shows the 2 × 2 × 1 48-atom anatase TiO2 supercell model considered in this study. The N-monodoping and Si-monodoping models were constructed by substituting one O atom (from the O1 site) with one N atom (N
s
(
O
) model) and substituting one Ti atom (from the Ti1 site) with one Si atom (Si
s
(
Ti
) model), respectively. The corresponding concentrations of N and Si were both 2.08 at.% (dopant atoms/total atoms). In addition, we considered three N/Si codoping configurations in which the O1 atom was substituted with one N atom. The Ti1, Ti2, or Ti3 sites were substituted with one Si atom in the N/Si-1, N/Si-2, or N/Si-3 models, respectively. Our calculations showed that the enthalpy of the N/Si-1 model was the lowest (−37865.04 eV), indicating that the N/Si-1 structure was more stable than the N/Si-2 (−37864.71 eV) and N/Si-3 (−37864.73 eV) ones. This implies that the Si in the N/Si codoping model tends to bond with the N (forming Ti-N-Si bonds), which is consistent with the formation energy calculation results in the literature [20].Figure 1
Structural model for pure anatase TiO2 and doping sites. Red and gray spheres represent O and Ti atoms, respectively.CASTEP software was used to perform the first principles calculations [26]. The potentials of ion core and valence electrons were modeled using ultrasoft pseudopotentials in the Vanderbilt form [27]. The valence electron configurations of the atoms were 2s
22p
3 for N, 2s
22p
4 for O, 3s
23p
2 for Si, and 3s
23p
63d
24s
2 for Ti. The wave functions of the valence electrons were expanded through a plane-wave basis set, and the cut-off energy was set to 400 eV. The Monkhorst-Pack-scheme-based K-point grid sampling was set at 4
×
4
×
3 (i.e., <0.04 Å−1) [28]. The convergence threshold for self-consistent iterations was set to 1
×
10
-
6 eV. The optimization parameters were set as follows: energy change = 1
×
10
-
5 eV/atom, maximum force = 0.03 eV/Å, maximum stress = 0.05 GPa, and maximum displacement tolerance = 0.001 Å.We previously used the DFT + U method and the following formalism to describe the exchange and correlation potential [6, 24]:
(1)
E
DFT
+
U
=
E
DFT
+
U
-
J
2
∑
σ
Tr
⁡
[
ρ
σ
-
ρ
σ
ρ
σ
]
,
where ρ
σ denotes the spin (σ)-polarized on-site density matrix. The spherically averaged Hubbard parameter, U, describes the increase in energy caused by placing an extra electron at a particular site, and the parameter J (1 eV) represents the screened exchange energy. The effective Hubbard parameter, U
eff
=
U
-
J, accounts for the on-site Coulomb repulsion for each affected orbital. Here, the effective on-site Coulomb interaction is U
eff
=
8.4 eV for Ti 3d in the DFT + U approach (see Figure S1 in Supplementary Material available online at http://dx.doi.org/10.1155/2014/342132).


## 3. Results and Discussion

### 3.1. Structural Optimization

Table1 summarizes the average optimized bond length and the volume difference ratios of all the doping models and the pure anatase TiO2. In the pure anatase TiO2, each Ti atom is horizontally and vertically surrounded by four and two adjacent O atoms, respectively; the average length of the Ti–O bond is 1.992 Å. When an O atom is substituted with one N atom (N
s
(
O
) model), the Ti–O (1.994 Å) and Ti–N (2.045 Å) bonds were longer than the Ti–O bond in the pure TiO2, expanding the volume. Because the ionic radius and electronegativity of N (1.71 Å for N3− and 3.04) are larger and smaller than those of O (1.32 Å for O2− and 3.44) [29, 30], respectively, the Ti–N bond is longer than the Ti–O one in the N
s
(
O
) model [6]. Conversely, the Ti–O and Si–O bonds in the Si
s
(
Ti
) model are both shorter than the Ti–O bond in the pure anatase TiO2, thereby shrinking the lattice because the Si4+ radius and Si electronegativity (0.40 Å for Si4+ and 1.90) are smaller and higher than those of Ti4+ and Ti (0.61 Å for Ti4+ and 1.54) [30, 31], respectively. This result is consistent with the previously obtained experimental results [10, 11] and theoretical calculations [20].Table 1
Average optimized bond length and volume difference ratio for N/Si-doped TiO2.
Models
Bond length (Å)
Volume difference ratio (%)
Ti–O
Ti–N
Si–O
Si–N
Anatase TiO2
1.992
—
—
—
—
Ns(O)
1.994
2.045
—
—
0.4
Sis(Ti)
1.990
—
1.828
—
−2.0
NSi-1
1.991
2.099
1.818
1.894
−1.5
NSi-2
1.992
2.042
1.830
—
−1.5
NSi-3
1.992
2.042
1.830
—
−1.5In the N/Si-2 and N/Si-3 models, the N-Si distance is longer, weakening the atomic interactions between the N and Si atoms. Therefore, the Ti–N and Si–O bond lengths in the N/Si-2 and N/Si-3 models are closer to those in the monodoping models (N
s
(
O
) and Si
s
(
Ti
)). In the N/Si-1 model, the bond lengths vary in descending order as follows: Ti–N > Ti–O > Si–N > Si–O. The Ti–N bond in the N/Si-1 model (2.099 Å) is longer than that in the N/Si-2 and N/Si-3 models (both = 2.042 Å); the Si–O bond in the N/Si-1 model (1.818 Å) is shorter than that in the N/Si-2 and N/Si-3 models (both = 1.830 Å). Consequently, the volume difference ratios of these three codoping models are almost identical (−1.5%) and are between those of the N
s
(
O
) (0.4%) and Si
s
(
Ti
) (−2.0%) models.


### 3.2. Mulliken Population

Table2 summarizes the average Mulliken atomic and bond populations of each N/Si model. The average atomic populations of the Ti and O atoms in the pure anatase TiO2 are 1.48 and -
0.74
|
e
|, respectively, suggesting that the Ti atoms tend to lose electrons and the O atoms tend to gain them. The Mulliken population of N atoms (-
0.60
|
e
|) is larger than that of O atoms (-
0.74
|
e
|) in the N
s
(
O
) model because of the former’s smaller electronegativity. The atomic population of Si atoms (1.77
|
e
|) is larger than that of Ti atoms (1.50
|
e
|) in the Si
s
(
Ti
) model, indicating that Si atoms transfer more electrons to the surrounding O atoms thereby reducing the average atomic population of O atoms.Table 2
Mulliken atomic population and bond population for N/Si-doped TiO2.
Model
Atomic population (|
e
|)
Bond population (|
e
|)
Ti
O
N
Si
Ti–O
Ti–N
Si–O
Si–N
Anatase TiO2
1.48
−0.74
—
—
0.343
—
—
—
Ns(O)
1.47
−0.74
−0.60
—
0.345
0.337
—
Sis(Ti)
1.50
−0.76
—
1.77
0.342
—
0.410
—
NSi-1
1.49
−0.76
−0.68
1.74
0.343
0.335
0.402
0.500
NSi-2
1.49
−0.76
−0.60
1.77
0.343
0.333
0.408
—
NSi-3
1.49
−0.76
−0.60
1.77
0.342
0.333
0.407
—The atomic population of Si atoms (1.74
|
e
|) in the N/Si-1 model is slightly smaller than that of those in the Si
s
(
Ti
) model because N atoms are less electronegative than O atoms. Further, the atomic population of N atoms in the N/Si-1 model (-
0.68
|
e
|) is smaller than that of N atoms in the N/Si-2 and N/Si-3 models (-
0.60
|
e
|), suggesting that N atoms can gain more electrons from the Si atoms in the N/Si-1 model because the N atoms are directly bonded to the Si atoms. The atomic populations of N atoms (-
0.60
|
e
|) in the N/Si-2 and N/Si-3 models are the same as those in the N
s
(
O
) model, implying that there is, again, almost no interaction between N and Si atoms in the N/Si-2 and N/Si-3 models.The Ti–O bond population was larger than the Ti–N one, indicating that Ti–O bonds are more covalent than Ti–N ones. Further, the Si–N and Si–O bond populations in each model are in the range 0.402–0.500|
e
|, meaning that Si–N and Si–O bonds were more covalent than the Ti–N and Ti–O ones.


### 3.3. Electronic Structure

Figure2 shows the band structures calculated for the N/Si-monodoped and codoped TiO2 models. The Fermi level, indicated by the dotted line, was set to zero. The bandgap obtained for the pure anatase TiO2 was 3.21 eV, as shown in Figure 2(a), and is consistent with experimentally obtained bandgaps. The bandgap in the N
s
(
O
) model (Figure 2(b)) was 3.09 eV, which was less than that of the pure anatase TiO2. An isolated impurity energy level resulting from the empty N-2p orbital above the valence band maximum (VBM) at 1.44 eV caused the TiO2 to absorb in the visible region. The valence band (VB) of the N
s
(
O
) model is 4.6 eV wide, which is slightly wider than that of pure anatase TiO2 (4.5 eV). The bandgap narrowed to 3.05 eV in the Si
s
(
Ti
) model (Figure 2(c)). There is no impurity energy level in the forbidden band because the Si and Ti atoms showed equal valencies. It should be noted that the VB of the Si
s
(
Ti
) model (5.3 eV) is wider than that of pure anatase TiO2 and the N
s
(
O
) model. A wider VB results in higher photogenerated carrier mobility [20]. The bandgaps were narrowed to 3.01–3.05 eV and the VBs were 5.3 eV wide in the N/Si codoping models (Figures 2(d)–2(f)). All three codoping models showed the impurity energy levels; the N/Si-1 model impurity energy level was the highest.Band structures of N/Si-doped TiO2 for (a) pure TiO2, (b) N
s
(
O
), (c) Si
s
(
Ti
), (d) N/Si-1, (e) N/Si-2, and (f) N/Si-3 models.
(a)
(b)
(c)
(d)
(e)
(f)Figure3 shows the total density of states (TDOS) and projected density of states (PDOS) near the Fermi level of N/Si-doped TiO2. They help explain the distribution of each related orbital associated with the constituent elements. The VB mainly consists of the O 2p and a few Ti 3d and N 2p states while the conduction band (CB) comprises the Ti 3d and a few O 2p states in the N
s
(
O
) model (Figure 3(a)). The empty N 2p state mainly contributes to the impurity energy levels in the forbidden band. The Si 3s electrons appear in the range (−7)–(−6.5) eV in the Si
s
(
Ti
) model (Figure 3(b)). The Si 3p orbital mainly contributes to the bottom of the VB, thus significantly widening it. In the N/Si-1 model (Figure 3(c)), the N 2p orbital is hybridized not only with the Si 3s orbital in the range (−7)–(−6.5) eV but also with the Si 3p orbital in the VB. Therefore, the Si–N bond is more covalent than the Ti–N and Ti–O ones, as mentioned in Section 3.2. In addition, adding Si atoms produced a wider VB and a narrower bandgap in the N/Si-1 model than in the N
s
(
O
) one. Figure 3(d) shows the DOS of the N/Si-2 model, which is similar to that of the N/Si-3 one. It should be reemphasized that the Si 3p state, not the N 2p one, contributes to widening the VB; therefore, the Si 3p state played a key role in widening the VB.Density of states of N/Si-doped TiO2 for (a) N
s
(
O
), (b) Si
s
(
Ti
), (c) N/Si-1, and (d) N/Si-2 models.
(a)
(b)
(c)
(d)


### 3.4. Optical Properties

The optical properties of materials can be obtained using the dielectric function,ε
(
ω
)
=
ε
1
(
ω
)
+
i
ε
2
(
ω
), whose imaginary part, ε
2
(
ω
), is calculated using the following expression [32]:
(2)
ε
2
=
2
e
2
π
Ω
ε
0
∑
k
,
v
,
c
|
〈
φ
k
c
|
u
·
r
|
φ
k
v
〉
|
2
δ
(
E
k
c
-
E
k
v
-
ω
)
,
where e, Ω, u, ω, and φ
k
v and φ
k
c represent the electronic charge, unit cell volume, vector defining the polarization of the incident electric field, light frequency, and the wave functions of the conduction and VBs, respectively. Kramers-Kronig relations can be used to calculate the real part of the dielectric function, ε
1
(
ω
), from ε
2
(
ω
). The absorption coefficient, α
(
ω
), can be obtained from ε
1
(
ω
) and ε
2
(
ω
).Figure4 shows the absorption spectra computed for the N/Si-doped TiO2. The pure anatase TiO2 did not show any absorption in the visible region because it shows a wide bandgap of 3.21 eV. Doping the TiO2 with Si narrowed the bandgap, thereby redshifting the intrinsic absorption edge toward higher wavelengths (Figure 4 inset). The N-doped TiO2 showed a redshifted intrinsic absorption edge due to the band gap narrowing and the absorption had extended into the visible and infrared (IR) regions, owing also to the N 2p impurity energy level that occurs in the forbidden band mentioned previously in Section 3.3. The forbidden band contained the N 2p impurity energy level in all three N/Si codoping models. Therefore, the codoping models exhibited stronger absorption than the pure anatase or Si-doped TiO2 in the visible region, thereby enhancing photocatalytic activity. It should be noted that the N/Si-1 model shows the stablest structure of the three codoping models and exhibits the strongest absorption between 400 and 500 nm, which is consistent with the previously reported experimental results [17, 18].Figure 4
Absorption spectra computed for N/Si-doped TiO2.


## 3.1. Structural Optimization

Table1 summarizes the average optimized bond length and the volume difference ratios of all the doping models and the pure anatase TiO2. In the pure anatase TiO2, each Ti atom is horizontally and vertically surrounded by four and two adjacent O atoms, respectively; the average length of the Ti–O bond is 1.992 Å. When an O atom is substituted with one N atom (N
s
(
O
) model), the Ti–O (1.994 Å) and Ti–N (2.045 Å) bonds were longer than the Ti–O bond in the pure TiO2, expanding the volume. Because the ionic radius and electronegativity of N (1.71 Å for N3− and 3.04) are larger and smaller than those of O (1.32 Å for O2− and 3.44) [29, 30], respectively, the Ti–N bond is longer than the Ti–O one in the N
s
(
O
) model [6]. Conversely, the Ti–O and Si–O bonds in the Si
s
(
Ti
) model are both shorter than the Ti–O bond in the pure anatase TiO2, thereby shrinking the lattice because the Si4+ radius and Si electronegativity (0.40 Å for Si4+ and 1.90) are smaller and higher than those of Ti4+ and Ti (0.61 Å for Ti4+ and 1.54) [30, 31], respectively. This result is consistent with the previously obtained experimental results [10, 11] and theoretical calculations [20].Table 1
Average optimized bond length and volume difference ratio for N/Si-doped TiO2.
Models
Bond length (Å)
Volume difference ratio (%)
Ti–O
Ti–N
Si–O
Si–N
Anatase TiO2
1.992
—
—
—
—
Ns(O)
1.994
2.045
—
—
0.4
Sis(Ti)
1.990
—
1.828
—
−2.0
NSi-1
1.991
2.099
1.818
1.894
−1.5
NSi-2
1.992
2.042
1.830
—
−1.5
NSi-3
1.992
2.042
1.830
—
−1.5In the N/Si-2 and N/Si-3 models, the N-Si distance is longer, weakening the atomic interactions between the N and Si atoms. Therefore, the Ti–N and Si–O bond lengths in the N/Si-2 and N/Si-3 models are closer to those in the monodoping models (N
s
(
O
) and Si
s
(
Ti
)). In the N/Si-1 model, the bond lengths vary in descending order as follows: Ti–N > Ti–O > Si–N > Si–O. The Ti–N bond in the N/Si-1 model (2.099 Å) is longer than that in the N/Si-2 and N/Si-3 models (both = 2.042 Å); the Si–O bond in the N/Si-1 model (1.818 Å) is shorter than that in the N/Si-2 and N/Si-3 models (both = 1.830 Å). Consequently, the volume difference ratios of these three codoping models are almost identical (−1.5%) and are between those of the N
s
(
O
) (0.4%) and Si
s
(
Ti
) (−2.0%) models.


## 3.2. Mulliken Population

Table2 summarizes the average Mulliken atomic and bond populations of each N/Si model. The average atomic populations of the Ti and O atoms in the pure anatase TiO2 are 1.48 and -
0.74
|
e
|, respectively, suggesting that the Ti atoms tend to lose electrons and the O atoms tend to gain them. The Mulliken population of N atoms (-
0.60
|
e
|) is larger than that of O atoms (-
0.74
|
e
|) in the N
s
(
O
) model because of the former’s smaller electronegativity. The atomic population of Si atoms (1.77
|
e
|) is larger than that of Ti atoms (1.50
|
e
|) in the Si
s
(
Ti
) model, indicating that Si atoms transfer more electrons to the surrounding O atoms thereby reducing the average atomic population of O atoms.Table 2
Mulliken atomic population and bond population for N/Si-doped TiO2.
Model
Atomic population (|
e
|)
Bond population (|
e
|)
Ti
O
N
Si
Ti–O
Ti–N
Si–O
Si–N
Anatase TiO2
1.48
−0.74
—
—
0.343
—
—
—
Ns(O)
1.47
−0.74
−0.60
—
0.345
0.337
—
Sis(Ti)
1.50
−0.76
—
1.77
0.342
—
0.410
—
NSi-1
1.49
−0.76
−0.68
1.74
0.343
0.335
0.402
0.500
NSi-2
1.49
−0.76
−0.60
1.77
0.343
0.333
0.408
—
NSi-3
1.49
−0.76
−0.60
1.77
0.342
0.333
0.407
—The atomic population of Si atoms (1.74
|
e
|) in the N/Si-1 model is slightly smaller than that of those in the Si
s
(
Ti
) model because N atoms are less electronegative than O atoms. Further, the atomic population of N atoms in the N/Si-1 model (-
0.68
|
e
|) is smaller than that of N atoms in the N/Si-2 and N/Si-3 models (-
0.60
|
e
|), suggesting that N atoms can gain more electrons from the Si atoms in the N/Si-1 model because the N atoms are directly bonded to the Si atoms. The atomic populations of N atoms (-
0.60
|
e
|) in the N/Si-2 and N/Si-3 models are the same as those in the N
s
(
O
) model, implying that there is, again, almost no interaction between N and Si atoms in the N/Si-2 and N/Si-3 models.The Ti–O bond population was larger than the Ti–N one, indicating that Ti–O bonds are more covalent than Ti–N ones. Further, the Si–N and Si–O bond populations in each model are in the range 0.402–0.500|
e
|, meaning that Si–N and Si–O bonds were more covalent than the Ti–N and Ti–O ones.


## 3.3. Electronic Structure

Figure2 shows the band structures calculated for the N/Si-monodoped and codoped TiO2 models. The Fermi level, indicated by the dotted line, was set to zero. The bandgap obtained for the pure anatase TiO2 was 3.21 eV, as shown in Figure 2(a), and is consistent with experimentally obtained bandgaps. The bandgap in the N
s
(
O
) model (Figure 2(b)) was 3.09 eV, which was less than that of the pure anatase TiO2. An isolated impurity energy level resulting from the empty N-2p orbital above the valence band maximum (VBM) at 1.44 eV caused the TiO2 to absorb in the visible region. The valence band (VB) of the N
s
(
O
) model is 4.6 eV wide, which is slightly wider than that of pure anatase TiO2 (4.5 eV). The bandgap narrowed to 3.05 eV in the Si
s
(
Ti
) model (Figure 2(c)). There is no impurity energy level in the forbidden band because the Si and Ti atoms showed equal valencies. It should be noted that the VB of the Si
s
(
Ti
) model (5.3 eV) is wider than that of pure anatase TiO2 and the N
s
(
O
) model. A wider VB results in higher photogenerated carrier mobility [20]. The bandgaps were narrowed to 3.01–3.05 eV and the VBs were 5.3 eV wide in the N/Si codoping models (Figures 2(d)–2(f)). All three codoping models showed the impurity energy levels; the N/Si-1 model impurity energy level was the highest.Band structures of N/Si-doped TiO2 for (a) pure TiO2, (b) N
s
(
O
), (c) Si
s
(
Ti
), (d) N/Si-1, (e) N/Si-2, and (f) N/Si-3 models.
(a)
(b)
(c)
(d)
(e)
(f)Figure3 shows the total density of states (TDOS) and projected density of states (PDOS) near the Fermi level of N/Si-doped TiO2. They help explain the distribution of each related orbital associated with the constituent elements. The VB mainly consists of the O 2p and a few Ti 3d and N 2p states while the conduction band (CB) comprises the Ti 3d and a few O 2p states in the N
s
(
O
) model (Figure 3(a)). The empty N 2p state mainly contributes to the impurity energy levels in the forbidden band. The Si 3s electrons appear in the range (−7)–(−6.5) eV in the Si
s
(
Ti
) model (Figure 3(b)). The Si 3p orbital mainly contributes to the bottom of the VB, thus significantly widening it. In the N/Si-1 model (Figure 3(c)), the N 2p orbital is hybridized not only with the Si 3s orbital in the range (−7)–(−6.5) eV but also with the Si 3p orbital in the VB. Therefore, the Si–N bond is more covalent than the Ti–N and Ti–O ones, as mentioned in Section 3.2. In addition, adding Si atoms produced a wider VB and a narrower bandgap in the N/Si-1 model than in the N
s
(
O
) one. Figure 3(d) shows the DOS of the N/Si-2 model, which is similar to that of the N/Si-3 one. It should be reemphasized that the Si 3p state, not the N 2p one, contributes to widening the VB; therefore, the Si 3p state played a key role in widening the VB.Density of states of N/Si-doped TiO2 for (a) N
s
(
O
), (b) Si
s
(
Ti
), (c) N/Si-1, and (d) N/Si-2 models.
(a)
(b)
(c)
(d)


## 3.4. Optical Properties

The optical properties of materials can be obtained using the dielectric function,ε
(
ω
)
=
ε
1
(
ω
)
+
i
ε
2
(
ω
), whose imaginary part, ε
2
(
ω
), is calculated using the following expression [32]:
(2)
ε
2
=
2
e
2
π
Ω
ε
0
∑
k
,
v
,
c
|
〈
φ
k
c
|
u
·
r
|
φ
k
v
〉
|
2
δ
(
E
k
c
-
E
k
v
-
ω
)
,
where e, Ω, u, ω, and φ
k
v and φ
k
c represent the electronic charge, unit cell volume, vector defining the polarization of the incident electric field, light frequency, and the wave functions of the conduction and VBs, respectively. Kramers-Kronig relations can be used to calculate the real part of the dielectric function, ε
1
(
ω
), from ε
2
(
ω
). The absorption coefficient, α
(
ω
), can be obtained from ε
1
(
ω
) and ε
2
(
ω
).Figure4 shows the absorption spectra computed for the N/Si-doped TiO2. The pure anatase TiO2 did not show any absorption in the visible region because it shows a wide bandgap of 3.21 eV. Doping the TiO2 with Si narrowed the bandgap, thereby redshifting the intrinsic absorption edge toward higher wavelengths (Figure 4 inset). The N-doped TiO2 showed a redshifted intrinsic absorption edge due to the band gap narrowing and the absorption had extended into the visible and infrared (IR) regions, owing also to the N 2p impurity energy level that occurs in the forbidden band mentioned previously in Section 3.3. The forbidden band contained the N 2p impurity energy level in all three N/Si codoping models. Therefore, the codoping models exhibited stronger absorption than the pure anatase or Si-doped TiO2 in the visible region, thereby enhancing photocatalytic activity. It should be noted that the N/Si-1 model shows the stablest structure of the three codoping models and exhibits the strongest absorption between 400 and 500 nm, which is consistent with the previously reported experimental results [17, 18].Figure 4
Absorption spectra computed for N/Si-doped TiO2.


## 4. Conclusions

First principles calculations were performed to study the optimized structure, Mulliken population, electronic structure, and optical properties of N/Si-codoped TiO2 models. The N/Si-1 model exhibited the stablest structure, whose bond lengths are arranged in descending order as follows: Ti–N > Ti–O > Si–N > Si–O. The bandgaps of the N/Si codoping models were narrowed to 3.01–3.05 eV, and the VBs were widened to 5.3 eV; the Si 3p orbital played a key role in extending VB width. All three N/Si codoping models showed the N-induced impurity energy level in the forbidden band; therefore, these models exhibited stronger absorption than the pure anatase TiO2 and the monodoped models in the visible region and thus showed enhanced photocatalytic activity. According to our theoretical calculations, the bandgap narrowing, VB widening, and impurity energy level in the forbidden band all aid in improving the photocatalytic activity of N/Si-codoped TiO2.



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*Source: 342132-2014-04-27.xml*