Structural, electronic and optical properties of La, C-codoped TiO2 investigated by first principle calculations

Journal of Physics and Chemistry of Solids 132 (2019) 121–129

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Structural, electronic and optical properties of La, C-codoped TiO2 investigated by first principle calculations

T

Yuzhen Fanga,∗, Ting Xua, Yuting Zhanga, Xiangjin Konga, Junhai Liua, Shouxin Cuib, Dongting Wanga a b

School of Chemistry and Chemical Engineering, Liaocheng University, Liaocheng, 252059, PR China School of Physics Science and Information Technology, Liaocheng University, Liaocheng, 252059, PR China

A R T I C LE I N FO

A B S T R A C T

Keywords: Electronic structure Band gap Optical properties Doped TiO2 Visible photo-catalytic activity

The electronic structures and optical properties of La, C-codoped TiO2 were investigated by the first-principles plane-wave ultrasoft pseudopotential method. Our calculations suggest that the micro-structures of La-C codoped system is different from that of TiO2, and the hole effective mass is increased by La-doping, which can create holes in the valence band; Nonmetal C doping can narrow the band gap of TiO2 and enhance the photocatalytic activity by the formation of localized mid-gap state originated from C 2p states above the top of the valence band; Metal La and nonmetal C co-doping could induce a synergistic effect, the doping of La atoms leads the redistribution of C 2p states in C atoms, which provide more electrons to participate into the 3d states of Ti atoms. The charge compensation effects between Ti 3d and C 2p produce impurity levels, which reduce the band gaps and enhance the carrier concentration, meanwhile La ions are not easy to enter the lattice of TiO2, which may form hetero-junction structure of La2O3-TiO2 with better dispersion in the bulk phase of TiO2 to limit the recombination of photo-generated electron hole pairs. The calculated results of optical properties show that CTiO2 and La-C-TiO2 systems exhibit good visible absorption and the doping is beneficial to the propagation of light in the doped TiO2.

1. Introduction Titanium dioxide has a wide application in solving the energy crisis and environmental pollution due to its high oxidation efficiency, nontoxicity, cheap, high photo-stability, chemical inertness, and excellent self-cleaning [1]. A large number of TiO2-based photo-catalysts have been explored for a variety of reactions, such as reduction of carbon dioxide [2], degradation of environmental pollutants [3], removal of volatile organic compounds in gas phase [4], generating solar fuels from photo-splitting of water [5] et al. However, the band-gap (Eg) of titanium dioxide is wide, such as, Eg = 3.20 eV for the anatase structure and 3.00 eV for the rutile structure, and it absorbs very little visible light [6], which prevents its wide application in the visible region. To utilize solar light adequately, it is necessary to enhance the visible optical absorption of TiO2. Therefore, research about reducing the band gap of TiO2 has become one of the most important goals in photo-catalyst studies [7]. The typical approaches to extend the spectral response to visible light region are either cations or anions impurities doping of TiO2. For example, the doping of carbon (C) [8,9], nitrogen (N) [10,11], sulfur (S) [12,13], ∗

iodine (I) [14] and boron (B) [15] in TiO2 can be an effective method to produce energy levels above the valence band to lead a narrowed bandgap and an additional absorption in the visible-light region. Shen and co-workers [16] reported that C-doped TiO2 was efficient to degrade trichloroacetic acid under visible light irradiation than pure TiO2. Doping nitrogen into titania changes the refraction index, hardness, electrical conductivity, elastic modulus, and the photocatalytic activity toward visible light absorption [17]. The doping of S into the TiO2 distorts the crystal lattice because the ionic radius of S is greater than that of O [18]. The incorporation of S 3p bands are above the valence band and ensures higher photo-catalytic efficiency. Further more, rareearth metal ions doping (such as Sc, V [19,20], Y, Ce [21], Gd [22] La, Sm [23], Ho [24], Co [15], Cu [25]) is another effective approaches, the lower crystallite size of the photo-catalyst can be prepared by metal ions doping, which increases the specific surface area, promotes the separation of photo-generated electrons and holes, and thus can improve the inter-facial charge transfer efficiency [26,27]. Nonmetals-doped TiO2 has been found to be inactivated by the loss of N during the oxidation of 2-propanediol under visible irradiation [28]. This major drawback of nonmetallic anions for doping TiO2 can

Corresponding author. E-mail address: [email protected] (Y. Fang).

https://doi.org/10.1016/j.jpcs.2019.04.017 Received 29 December 2018; Received in revised form 18 March 2019; Accepted 12 April 2019 Available online 19 April 2019 0022-3697/ © 2019 Elsevier Ltd. All rights reserved.

Journal of Physics and Chemistry of Solids 132 (2019) 121–129

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broaden the visible light response of the catalyst, we choose the C doping sites to narrow the band gap, and the band gap of this model in Fig. 1 was found to be the lowest; The doping position of La atom is selected according to the low doping concentration in photo-catalyst, and the substitutional La at center site in the periodic structure has the lowest doping concentration. As a result, the doping sites of C and La atoms in this paper are the best. To study the electronic, structural, band gap and optical properties of different doped TiO2, the first principle ultrasoft pseudopotential method has been used DFT with generalized gradient approximation (GGA) [37] put forward by Perdew-Burke-Ernzerhof (PBE) [38] as implemented in the CASTEP code. The cutoff kinetic energy of the electron wave function were set to 340 eV and 420 eV, and the k-point sampling set 7 × 7 × 3 division of the reciprocal unit cell based on the Monkhorst-Pack scheme was found to be converged. Geometrical optimization is conducted using the convergence of thresholds of 1 × 10−6 eV/atom for the total energy, all forces on atoms were converged to less than 0.01 eV/Å, the maximum ionic displacement was within 0.0001 Å and the total stress tensor was reduced to the order of 0.02 GPa. The basis set of the valence electronic states are taken as: 5s25p65d16s2, 3s23p63d24s2, 2s22p4, and 2s22p2 for La, Ti, O, and C atoms respectively, and the other orbital electrons are core electrons. The band gap calculated by GGA-PBE is lower than the experimental value, which has also been accepted internationally for the result of the function itself, and it can not be used to make accurate calculation of the absolute energy [39]. In order to calculate the energy band more accurately, the band gap values were calculated by norm-conversing pseudopotentia method using HSE06 in the property of band gap to confirm the results being reliable [40].

be compensated by the coupling of cation and anion ions co-doped TiO2. In the work of Chen et al. [29], La/N co-doped TiO2 supported on diatomite can enhance the photocatalytic activity under visible light during the degradation of rhodamine B (RhB). Lei et al. reported that [30] the La and C co-doped TiO2 nano-materials exhibited the higher activity for Cr (VI) photocatalytic reduction under visible light irradiation than single doping. The results of experimental research [31] and theoretical research [32] both confirmed that C, Mo-codoping could enhance the photocatalytic activity of TiO2. The co-doping could produce a synergistic effect to exhibit excellent photocatalytic activity [33]. However, a clear mechanistic view of the dopant role in photocatalysis is far from being established, and a detailed theoretical investigation is also necessary. As we all know, TiO2 has three crystalline phases, which are rutile, anatase, and brookite. Anatase and rutile are the two most common crystalline phases. And anatase is generally considered to have higher photocatalytic activity than rutile [34–36], thus, we conceived the influence of co-doping configurations on the electronic structure and optical properties of anatase TiO2, and the first principles calculations were carried. A systematic analysis of the electronic and optical properties of different doping configurations in anatase TiO2 were given, which provide that nonmetal C doping can narrow the band gap of anatase TiO2 and increase the utilization efficiency of visible light, while La doping can enhance the carrier concentration, and the La-C codoped TiO2 is a kind of potential visible photocatalytic materials. 2. Theoretical methodology To calculate the electronic structures and optical properties of pure and C, La-codoped anatase TiO2, a supercell contained 12 atoms was used. For the C, La doped or codoped TiO2, two O atoms were replaced with two C atoms, and one Ti atom was replaced with a La atom. Substitution models were formed with configurations of Ti4O8, LaTi3O8, C2-Ti4O6 and C2La-Ti3O6, which are presented in Fig. 1. The other doping sites of La and C have also been considered. In order to

3. Results and discussion 3.1. Optimized structures The optimized geometrical configurations and partial bonds length

Fig. 1. The theoretical models of TiO2, La-TiO2, C-TiO2 and C-La-TiO2 (Blue represents the La atom, dark gray represents the C atom, light gray represents the Ti atom, and red represents the O atom). 122

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Fig. 2. Optimized geometrical configurations with the supercell of 4 × 4 × 1 and partial bonds length for (a) TiO2, (b) La-TiO2, (c) C-TiO2 and (d) La-C-TiO2 systems. Table 1 Bond length, crystal lattice parameters, and binding energy of TiO2, La-TiO2, C-TiO2 and La-C-TiO2 calculated by GGA-PBE with cutoff = 340 eV. Structures

TiO2 La-TiO2 C-TiO2 La-C-TiO2

Bond length (Å)

La-O

Ti-O

Ti-C

1.927, 1.983 1.891 1.921 1.845

—— —— 1.908, 2.099 2.168

La-C

—— 2.602, 2.107 —— 2.172

—— —— —— 3.984

Binding energy (eV)

a=b

c

3.776 3.776 3.776 3.776

9.486 9.486 9.486 9.486

26.239 24.000 24.043 22.719

La-C-TiO2 may be in relation to La coordination with O atoms without bonding to adjacent C atoms, the reason is that the La-C bond length 3.984 Å and Ti-C bond length 2.168 Å in La-C-TiO2 are much longer than its standard value 2.46 Å and corresponding value 1.908 Å in CTiO2, and the La-O bonds length were 2.602 Å and 2.107 Å close to its standard value 2.35 Å. The C atoms may form other carboxides with adjacent O, and La-C codoped arrangements the local microstructures, which will be better to reduce the frequent recombination of the photogenerated electron-hole pairs. The diffraction patterns of pure TiO2 and doped TiO2 were calculated by reflex module shown in Fig. 3, and patterns (PDF-# 73–1764) of anatase phases were found in all structures. Compared to the XRD pattern of TiO2, the additional diffraction peaks of La-TiO2 and La-CTiO2 are ascribed to La2O3 (PDF-# 74–1144). This is because the radii of La3+ (1.016 Å) ion is too large to replace the Ti4+ (0.68 Å) ion in the TiO2 matrix [41], whereas C atoms can easily enter the TiO2 matrix under synthesis conditions. The Lanthanum precursor (earth salts) may form oxides La2O3 during the preparation of La doped TiO2 catalyst, as reported by wang et al. [42], heterogeneous La2O3/TiO2 interfaces can supply an ideal space for charge accumulation and electric energy storage. In La-C-TiO2 system, the presence of small and isolated clusters of lanthanide oxide that are well dispersed in the titania matrix or on the surface of TiO2 can form the heterojunction La2O3-TiO2 to limit the recombination of photogenerated electron hole pairs leading to enhanced photocatalytic activity.

for pure TiO2 and doped TiO2 systems are shown in Fig. 2, and the bond length, crystal lattice parameters, and binding energies calculated by GGA-PBE are listed in Table 1. The binding energy of TiO2 can be obtained according formula (1):

ΔETiO2 = ETi + 2EO − ETiO2

Lattice parameters (Å)

(1)

In which ΔETiO2 was the binding energy of TiO2, ETiO2 is the total energy of anatase TiO2, ETi and EO were total energy for the free Ti and O atom, and so on, we can also get other binding energy according to the above formula. The values of binding energy are important parameter to characterize the bond strength and relative stability between atoms, which were 26.239, 24.000, 24.043 and 22.719 eV for TiO2, La-TiO2, C-TiO2 and La-C-TiO2, respectively. The relative lower value of binding energy means less stability, as a result, the stability is in the order of La-CTiO2 < La-TiO2 < C-TiO2 < TiO2. From Table 1, it can be found that crystal lattice parameters has no changes, however, the bond length of Ti-O, Ti-C, La-O, La-C changed significantly. To see the optimized micro-structure more intuitively, we chose the supercell of 4 × 4 × 1 based on the theoretical models. As reported in Fig. 2a and b, the lengths of six La-O bonds in La-TiO2 formed by the substitutional La and adjacent six O atoms are 2.602, 2.602, 2.107, 2.107, 2.107 and 2.107 Å, resulting in structural distortion in comparison to the original Ti-O bond lengths (1.983, 1.983, 1.927, 1.927, and 1.927 Å) in pure TiO2, due to the larger ionic radius of La3+ ion vis-avis Ti4+ ion. For the C-substituted case (Fig. 2c), the length of Ti-O bond was 1.921 Å comparison to the original value of 1.927 Å, and the length of Ti-C bond were 2.099 Å and 1.908 Å comparison to the original value of 1.983 Å and 1.927 Å, substitutional C slightly affect the structure. From the Fig. 2d, we find that the lowest binding energy for

3.2. Band structure and partial density of states To calculated the TDOS, PDOS and band structures more accurately, we have tested the cutoff energy, as shown in Fig. 4, and the tested 123

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Fig. 3. The X ray powder diffraction pattern of TiO2, La-TiO2, C-TiO2 and La-C-TiO2 by first principle calculactions.

similar to those reported in the literature [45,46]. Therefore, under the selected calculation conditions, the band gap values are credible. As we known, the impurity states in the band gaps can reduce the electronic transition energy of specimen. For a comparison, the band gap of La or C doped TiO2 and La-C codoped TiO2 are well investigated. In Fig. 5b, three impurity energy levels hybridized by the orbits of La 5d, Ti 3d and O 2p are found, which lies on the top of the VBM of pure TiO2, and the band gap is reduced to the value of 1.7222 eV in La-TiO2. Besides in Fig. 5c, we can see that the band gap of the C-TiO2 system decreases to 0.3548 eV, and a series of impurity energy levels originated from C 2p states appear in the forbidden gap, and all of the impurity energy levels are located above the valence band maximum (VBM) and below the conduction band minimum (CBM). When the C atom doping in TiO2 matrix, the impurity energy levels would overlap with O 2p as the top of valence band to decrease the band gap of TiO2, which will reduce the transiting energy for the electrons form the valence band to the conduction band, eventually improve the photo-catalytic activity of TiO2. The impurity states located in the band gap are not only related to the location of the impurity atom, but also depend on the chemical environment around the impurity atom. For La/C-TiO2 in Fig. 5d, the calculated band gap is 0.5376 eV, however, the distributing regulations and the relative positions of the C 2p, Ti 3d and O 2p states are different from that in C-TiO2, and their electron density of states decreases obviously, as well as the Ti 3d state and O 2p state shift downward by the value of −1.9499 eV and −2.4875 eV, respectively. It can be seen that the doping of La atoms leads to re-distributions of C 2p states, which provide more electrons to participate into the 3d states of Ti atoms, which are located at the bottom of the conduction band. The charge compensation effects between Ti 3d and C 2p produce impurity levels, which reduce the band gaps and enhance the absorption of visible light in La/C-TiO2.

Fig. 4. The total energy of anatase TiO2 with different cutoff.

result shows that 340 eV is smaller. At last, we choose the value of cutoff = 420 eV to calculate the TDOS, PDOS and band structures of pure TiO2, La-TiO2, C-TiO2, La-C co-doped TiO2 and La2O3 by the GGAPBE method, and the results are plotted in Fig. 5a–e. The maximum value of the valence band (VBM) and the minimum value of the conduction band (CBM) and the band gaps (Eg) calculated by PBE and HSE06 are listed in Table 2. The HSE06 method used in this paper is based on the structural relaxation of GGA-PBE, and only the band structure is calculated by HSE06. As seen in Table 2 and Fig. 5a, the band structure of undoped TiO2 displays a indirect band gap of 2.109 eV, its valence band (VB) mainly consists of O 2p states, and the conduction band (CB) mainly consists of Ti 3d states. As shown in Fig. 5e, the band gap of pure La2O3 is 3.7989 eV. Based on its valence band (VB), the state of O 2p was dominant, and it was also hybridized with the orbit of La 5d and La 5p. On the other hand, according to its conduction band (CB), the state of La 5d would be dominant. The values of EgPBE = 2.1090 eV and EgHSE06 = 2.219 eV is lower than the experimental value for the PBE function itself, to get a band gap similar to the lab value, the DFT + U calculations are necessary [43,44]. However, the band gap values were

3.3. Electron density and electron density difference To further understand the electronic characteristic, we calculated the electron density and electron density difference properties, the results for different samples are shown in Fig. 6. As seen in Fig. 6a–d (below), the average mulliken charges of O and Ti in the pure TiO2 are −0.670 e and 1.330 e, which are differently 124

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Fig. 5. The band structures and partial density of states (PDOS) GGA-PBE with cutoff = 420 eV. (a) TiO2; (b) La-TiO2; (c) C-TiO2; (d) La-C-TiO2; (e) La2O3. Table 2 The top of the valence band (VBM), the bottom of the conduction band (CBM), band width calculated by GGA-PBE (EgPBE) and HSE06 (EgHSE06) for different structures (unit: eV). Cutoff = 340 eV

CBM VBM EgPBE EgHSE06

Cutoff = 420 eV

TiO2

La-TiO2

C-TiO2

La-C-TiO2

TiO2

La-TiO2

C-TiO2

La-C-TiO2

2.1090 0 2.1090 2.219

2.0767 0.3545 1.7222 1.8546

1.2019 0.8470 0.3549 0.5024

−1.9499 −2.4875 0.5376 0.5847

2.1368 0 2.1368

2.0386 0.3441 1.6945

1.1075 0.8127 0.2948

−1.8616 −2.3456 0.4840

respectively. The mulliken charges of La, Ti, C and O atoms are 0.670 e, 0.320 e, −0.070 e and −0.380 e in La-C-TiO2, respectively. The mulliken populations of Ti atoms in doped TiO2 are lower than that of 1.33 in pure TiO2, implying the increase of electron density and enhancement in reducibility of Ti atoms in doped TiO2, some Ti 3d states at the

from their normal ion charges (−2 e and +4 e). The mulliken charges of La, Ti are 1.950 e and 1.130 e in La-TiO2, while the charges for O atoms are −0.630 e, −0.730 e and −0.610 e, respectively. The mulliken charges of Ti, C are 1.200 (1.320) e and −0.500 e in C-TiO2, while the charges for O atoms are −0.630 e, −0.640 e and −0.650 e, 125

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Fig. 6. The electron density (below) and electron density difference (above) at the slice of best fit. (a) TiO2; (b) La-TiO2; (c) C-TiO2; (d) La-C-TiO2.

Of which, ni is the carrier concentration, mn∗ is the effective mass of the electron, and mp∗ is the effective mass of the hole. Combined with the calculated band structure, effective mass of holes (mp∗), electrons (mn∗) and the carrier concentration (ni: cm−3) nearby the valence band top or the conduction band bottom in the band structures of TiO2 and doped TiO2 are shown in Table 3. The corresponding effective mass of holes is: -0.2746 m0, -0.3156 m0, -0.0714 m0 and -0.1545 m0, and the effective electron mass is: 0.0878 m0, 0.0878 m0, 0.0858 m0 and 0.1880 m0 for pure TiO2, La-TiO2, C-TiO2 and La-CTiO2, respectively. The hole effective mass increases after La substitute for Ti in the case of La-TiO2, La3+ cations have lower oxidation state than Ti4+, to keep the electroneutrality, the electrons could be removed from the valence band, and then create holes in the valence band of the system and increases the hole effective mass. In La-C codoped system, electron migration between C 2p and Ti 3d orbitals at the bottom of conduction band increases the effective mass of electrons. When the temperature T is 300 K, the carrier concentration is 1.5305 × 1018 cm−3, 1.6999 × 1018 cm−3, 5.4947 × 1017 cm−3, and 1.7644 × 1018 for TiO2, La-TiO2, C-TiO2 and La-C-TiO2, respectively, and the carrier concentration is the larger in La-TiO2 and La-C-TiO2 systems. This indicates that the La doping is beneficial to increase the carrier concentration. In C-TiO2 system, the carrier concentration is low while the band gap is narrow. Because the carrier concentration is not only related to the band gap, but also to the band structure. The effective mass of electrons and holes are calculated by fitting the curvature of the minimum or maximum point of the conduction band or valence band in band structure. When C replaces the O atom in the TiO2 lattice, the bending degree at the top maximum of the valence band increases obviously, the effective mass of the hole decreases, and this decreasing effect of the effective mass of the hole dominates. As a

bottom of conduction bands are occupied by the electrons, as a result, the Ti4+ ions are reduced to the Ti3+ ions, especially in the structure of La-C-TiO2. The above analysis on the band gaps and density of states also exhibits similar results. As seen in the electron density difference results in Fig. 6a–d (above), the covalent bonding is clearly visible in La-TiO2 and in La-CTiO2. In La-C-TiO2 system, the substitutional La and C atoms bonding with the adjacent O or Ti atom are major covalent-like bonding interactions by common electron clouds, and there are some charges transferring between the substitutional C and Ti atoms. On the contrary, the electron transfer is relatively clear in TiO2 and C-TiO2, which indicates that the bonds in these two structures are obviously less than a general covalent bond. 3.4. Carrier concentration One of the most important physical quantities to measure the photocatalytic activity is the carrier concentration, which can be calculated using the effective mass of the hole or electron based on band structures by the band E (k)-k relation model as shown in formula (2) [47]. Here, m is the effective mass of the carrier, h is the Planck's constant, E(k) is the conduction band bottom or valance-band maximum and k is the wave vector.

1 1 ∂2E (k ) = 2 m h ∂k 2

(2)

The effective mass the effective mass of holes and electrons can be obtained according to formula (3). The values of X0 can be obtained by the second derivative of the energy band curves near the valence band top or the conduction band bottom, a is the calculated lattice parameter, and m0 is the mass of electron.

(

6.626 × 10−34

)

a × 10−10 m∗ = m0 X0 × 1.6 × 10−19 × 9.109 × 10−31

Table 3 Effective mass of holes (mp∗ ), electrons (mn∗ ) and the carrier concentration (ni:

(3)

cm−3) calculated by GGA-PBE with cutoff = 340 eV.

Finally, the carrier concentration can be calculated by formula (4) as follows [48]: 3

3

∗ m ∗ mp ⎞ 4 T 2 − E ⎞ e 2T ni (2.510 × 1019) ⎜⎛ n ⎟ ⎛ ⎝ m 0 m 0 ⎠ ⎝ 300 ⎠

(4) 126

Structures

TiO2

La-TiO2

C-TiO2

La-C-TiO2

mp∗/m0

−0.2746

−0.3156

−0.0714

−0.1545

mn∗ /m0 ni

0.0878

0.0878

0.0858

0.1880

1.5305E+18

1.6999E+18

5.4947E+17

1.7644E+18

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0.27 eV, 4.29 eV, 6.62 eV and 8.53 eV for La-TiO2, 0.17 eV and 4.00 eV for C-TiO2, 1.87 eV, 4.38 eV and 7.44 eV for La-C-TiO2 from the ε2 (ω) curve, respectively. The optical transition peak of 4.33 eV in pure TiO2, 4.29 eV for the La-TiO2, 4.00 eV for C-TiO2 system and 1.87 eV for the La-C-TiO2 system are corresponding to the transition of the O 2p electrons to the Ti 3d conduction band. The red shift of the optical transition was due to the decreased band gaps in the doped systems, which was in good agreement with the result of band structures above. Moreover, the optical transition peaks around 0.27 eV and 0.17 eV could be observed for the La and C-doped TiO2 systems, the peak of 0.27 eV could be caused by the transition of the O 2p electrons to the Ti 3d conduction bands as well as from the O 2p electrons into the La-5d conduction bands. The peak of 0.17 eV could be due to the transition of the C 2p electrons to the Ti 3d conduction bands as well as from the C 2p electrons into the O 2p valence bands. It is well known that, visible light region is in the range of 1.64-3.19 eV or 740-370 nm. The peak of 1.87 eV indicated that La-C codoping could induce a visible optical transition. It was found that C and La codoping could produce a synergistic effect which could further increase the visible absorption compared with single doping. The relationship between the complex refractive index and the incident photon energy is shown in Fig. 7 (b), the refractive index n or pure TiO2 increases with the increase of photon energy, when the photon energy is 3.28 eV, n reaches the maximum, and then decreases gradually. The values of n (0) for pure TiO2, La-TiO2, C-TiO2 and La-CTiO2 are 2.28, 4.66, 18.99 and 5.77, respectively, C and La doping or codoping can greatly increase the static refractive index. Comparing with the refractive index n and extinction coefficient k, we can also see that the energy range of k > n decreases after doping, which further shows that doping is beneficial to the propagation of light in the doped TiO2. The loss function and refractivity properties can be obtained from the dielectric function, and the results are shown in Fig. 8. The electron energy-loss functions can behave as a gauge to measure how an incident electron loses its energy after emerging from the compounds under study. It is generally considered that the loss peak is caused by plasma excitation, the energy loss curve generally has a sharp peaks near the plasma frequency, which are 10.91 eV, 12.57 eV and 12.99 eV for pure TiO2, La-TiO2 and La-C-TiO2, respectively, where the longitudinal charge fluctuation occurs. The peak of the energy loss function is associated with the abrupt reduction in the reflectivity curve. Meanwhile, a flat peak of loss function in C-TiO2 is situated at approximately 12.37 eV, corresponding to a gently reduction in its reflective curve. The absorption spectrum of the pure and doped TiO2 systems are

result, the carrier concentration of C-TiO2 decreases. 3.5. Optical properties It is well-known that optical property is one of the most important properties of TiO2. In this section, material optical response caused by the interaction of the incident photon with the atoms is described in terms of complex dielectric constant ε(ω) = ε1(ω)+iε2(ω), where real part of dielectric constant ε1(ω) represents the polarization of light, and the imaginary part of dielectric constant ε2(ω) represent the absorption of light by the material. The imaginary part ε2(ω) commonly depends on the real transition between the occupied and unoccupied electric states, and the intraband and interband transition both contributes to ε2(ω) as seen in formula (5) [49].

4π 2e 2 ε2 (ω) = ⎛ 2 2 ⎞ ⎝m ω ⎠ ⎜

⎟

∑ ∫k 〈i M j〉2 fi (1 − fi ) δ (Ej,k − Ei,k − ω) d3k i, j

(5)

Here, i and j are the initial and final states respectively, M is the dipole matrix, fi is the fermi distribution function for the i-th state, and Ei, k is the energy of electron in the i-th state with the crystal wave vector k. The real part of the dielectric function can be derived according to the Kramers-Kroning relation shown in formula (6) [50].

ε1 (ω) = 1 +

2 p π

∫0

∞

ω′ε2 (ω′) dω′ ω′2 − ω2

(6)

The relations between the complex refractive index and the complex dielectric function are ε1 = n2-k2 and ε2 = 2nk. The calculated values of the complex dielectric function (ε1(ω) and ε2(ω)) and the complex refractive index (n and k) are shown in Fig. 7. The dielectric functions are shown in Fig. 7 (a), we have determined the static dielectric constants ε1 (0) with 5.22, 21.36, 350.01 and 33.13 for TiO2, La-TiO2, C-TiO2 and La-C-TiO2 from the ε1(ω) curve, respectively, the ε1 (0) value of C doped TiO2 is the most significant. The curve of ε1 (ω) keeps at negative in the higher energy region of 4.8710.91 eV, 7.03-12.54 eV, 3.78-12.18 eV and 4.79-12.97 eV for TiO2, LaTiO2, C-TiO2 and La-C-TiO2, respectively, which show that the reflection of light falling on the material surface and materials become metallic. The imaginary part of ε2 (ω) is important for describing the optical properties of any material. Optical transition peaks correspond to optical transitions between two states, and the intensity of the peaks is proportional to the density of states. The peak values of the imaginary part of dielectric function ε2 were 4.33 eV and 7.46 eV for TiO2,

Fig. 7. The calculated complex dielectric constant and refractive index. (a) the complex dielectric function of ε1(ω) and ε2(ω); (b) the complex refractive index of n and k. 127

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Fig. 8. The properties of (a) loss function and (b) refractivity.

C codoping could produce an obvious synergistic effect for its narrower band gap than La-TiO2 and higher carrier concentration than C-TiO2. For La-C-codoped system, the absorption of visible-light are greatly enhanced at the range of 405 nm-542 nm, which is because the synergistic effect of La and C co-doping can lead to a decrease of the photon excitation energy in view of the electronic structure. The relative values of refractive index n and extinction coefficient k further shows that doping is beneficial to the propagation of light in the doped TiO2. Therefore, it is conceivable that La, C-codoped TiO2 would be useful for visible photoactivity. Acknowledgment This work was financial supported by Natural Science Foundation of Shandong Province, China (Grant No. ZR2015PB015, ZR2015BM014, ZR2018LB032) and National Natural Science Foundation of China, China (Grant No. 21406103). Fig. 9. The absorption spectrum of the pure and doped TiO2 systems.

References

calculated and shown in Fig. 9. In the pure anatase TiO2, it is found that TiO2 and La-TiO2 can only respond to ultraviolet-light, which shows nearly no absorption response in the visible-light region. For C-TiO2 and La-C-TiO2 systems, they exhibit good optical absorption property in the visible-light region. Because the doped C atoms have impurity levels of C 2p in the forbidden gap, which leads to the higher optical absorption performance than pure TiO2 system in the long wave length range, the results are also consistent with the experimental optical absorption spectrum [51]. For La-C-codoped system, it is interesting that the absorption of visible-light are greatly enhanced at the range of 405 nm-542 nm, which is because the synergistic effect of La and C codoping can lead to a decrease of the photon excitation energy in view of the electronic structure.

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