Analysis of Indium Oxidation State on the Electronic Structure and Optical Properties of TiO2

Due to the high formation energy of Indium interstitial defect in the TiO2 lattice, the most probable location for Indium dopant is substitutional sites. Replacing Ti by In atom in the anatase TiO2 shifted the absorption edge of TiO2 towards visible regime. Indium doping tuned the band structure of TiO2 via creating In 5p states. The In 5p states are successfully coupled with the O 2p states reducing the band gap. Increasing In doping level in TiO2 improved the visible light absorption. Compensating the charge imbalance by oxygen vacancy provided compensated Indium doped TiO2 model. The creation of oxygen vacancy widened the band gap, blue shifted the absorption edge of TiO2 and declined the UV light absorption. The 2.08% In in TiO2 is the optimal Indium doping concentration, providing suitable band structure for the photoelectrochemical applications and stable geometrical configuration among the simulated models. Our results provide a reasonable explanation for the improved photoactivity of Indium doped TiO2.


Introduction
Environmental pollution and energy crises are the major problems attracting considerable attention from researchers. A semiconductor like Titanium dioxide (TiO 2 ) could be used for environmental cleanup and renewable energy sources [1,2]. However, the wide band gap limits the efficiency of TiO 2 in photoelectrochemical applications. With the help of Plasmonic nanoparticles, the limited absorption of TiO 2 can be resolved [3,4]. However, for most practical applications, the usage of expensive metal nano-particles is not economically feasible. Doping foreign atoms in the network of TiO 2 could be a suitable way to tune the band gap utilizing majors part of the solar spectrum [5,6]. The proper oxidation state of the dopant atoms can favorably stabilize the system and tailor the band structure. Inducing dopant atoms in any semiconductor materials disturbs the structure of the bulk material and the modification depends upon the difference in the ionic radii of bulk and dopant ions. Wide functionalities of the TiO 2 could be induced by selecting a dopant with the proper oxidation state. Thus, the band structure of TiO 2 could be tuned to utilize a major part of the solar energy with minimum structure distortion [7][8][9][10].
Introducing foreign atoms into the bulk of TiO 2 either creates states in the forbidden region or mixes with the valence or conduction band modifying the electronic band structure [11,12]. Doping non-metal extended the absorption edge of TiO 2 towards a visible regime by creating impurity states (in the forbidden region) or narrowing the band gap [13][14][15]. The states due to nitrogen (N) appeared above the valence band maximum which might annihilate the photo-generated carriers [16]. The efficiency of transition metals doped TiO 2 is also limited due to the existence of localized d states and the recombination centers [17]. Existence of the isolated states in the band gap effect the optical absorption spectra and photo-activity of TiO 2 . Unoccupied isolated states often act as an electron trap, promoting the electron-hole pair recombination [18,19]. Removing the unoccupied states from the band gap or mixing it with the valence or conduction band would increase the lifetime of the photo-excited carriers, thereby improving the photo-activity.
Mixing the oxide of Indium (In) with TiO 2 and improving the photo-activity are widely reported in literature. Nanocrystalline TiO 2 -In 2 O 3 powders with different Ti/In ratios are prepared by sol-gel method and the photodegradation response is evaluated. Mixing In 2 O 3 with TiO 2 improved the photoelectrochemical properties of TiO 2 [20]. The photoactive In 2 O 3 -TiO 2 mixed oxides are extensively studied by Gonzalez et al. [21] and the photocatalytic activity are explored. The Indium oxide (In 2 O 3 ) in combination with the silver improved the photoactivity of TiO 2 [22]. Wang et al. [23] prepared Indium doped TiO 2 by the sol-gel method and evaluated the photo-activity under visible light illuminations. Doping Indium in the TiO 2 lattice improved the activity for the degradation of 4-chlorophenol under visible light irradiations. The topic of mixing the In 2 O 3 with TiO 2 or doping Indium in the structure of TiO 2 is experimentally investigated. However, the alterations in the band structure and lattice of TiO 2 due to Indium doping are rarely reported. To elucidate the effect of Indium doping on the geometrical structure, band structure and photo-response, it is suggested to perform some ab-initio calculations.
This work report DFT based calculations for Indium (In) doped TiO 2 with different In doping level. Charge neutralization is made by generating oxygen vacancy and the electronic band structure and optical properties are evaluated.

Method of Calculations
With Materials Studio 8.0, the calculations are performed based on the plane wave method of DFT. The generalized gradient approximation (GGA) parameterized by PBE is utilized as an exchange correlation potential [24]. Keeping the maximum energy equal to 400 eV and k-mesh of 2 × 2 × 2, the electrons wave functions are expanded (in plane waves). The simulation environment is the ideal environment which is relaxed using some constraints for optimizing the simulated models. Using the BFGS minimization scheme [25], the maximum displacement was set to 5.0 × 10 −4 Å, while the convergence limit for self-consistent tolerance was 2.0 × 10 −6 eV/atom. Anatase TiO 2 supercell is made from the replication of 2 × 2 × 1 TiO 2 unitcell. Low concentration of Indium in anatase TiO 2 are possible by increasing the size of the supercell. Indium (In) doped models are constructed by replacing the lattice Ti atoms by In atoms. Doping single In atom at Ti sites have the In doping level of 2.08% represented by Ti 16-1 In 1 O 32 . The doping concentration of In is increased to 4.16% and this system is named as Ti 16-2 In 2 O 32 . The effect of oxygen vacancy on the band structure is evaluated by creating one oxygen vacancy along with two In atoms at Ti sites and it is represented by Ti 16-2 In 2 O 31 . Figure 1 displays the atomic configuration of anatase TiO 2 having substitutional In (at Ti site) and oxygen vacancy. As a standard model, a defect free bare TiO 2 is also simulated. absorption spectra and photo-activity of TiO2. Unoccupied isolated states often act as an electron trap, promoting the electron-hole pair recombination [18,19]. Removing the unoccupied states from the band gap or mixing it with the valence or conduction band would increase the lifetime of the photo-excited carriers, thereby improving the photo-activity.
Mixing the oxide of Indium (In) with TiO2 and improving the photo-activity are widely reported in literature. Nanocrystalline TiO2-In2O3 powders with different Ti/In ratios are prepared by sol-gel method and the photodegradation response is evaluated. Mixing In2O3 with TiO2 improved the photoelectrochemical properties of TiO2 [20]. The photoactive In2O3-TiO2 mixed oxides are extensively studied by Gonzalez et al. [21] and the photocatalytic activity are explored. The Indium oxide (In2O3) in combination with the silver improved the photoactivity of TiO2 [22]. Wang et al. [23] prepared Indium doped TiO2 by the sol-gel method and evaluated the photo-activity under visible light illuminations. Doping Indium in the TiO2 lattice improved the activity for the degradation of 4-chlorophenol under visible light irradiations. The topic of mixing the In2O3 with TiO2 or doping Indium in the structure of TiO2 is experimentally investigated. However, the alterations in the band structure and lattice of TiO2 due to Indium doping are rarely reported. To elucidate the effect of Indium doping on the geometrical structure, band structure and photo-response, it is suggested to perform some ab-initio calculations.
This work report DFT based calculations for Indium (In) doped TiO2 with different In doping level. Charge neutralization is made by generating oxygen vacancy and the electronic band structure and optical properties are evaluated.

Method of Calculations
With Materials Studio 8.0, the calculations are performed based on the plane wave method of DFT. The generalized gradient approximation (GGA) parameterized by PBE is utilized as an exchange correlation potential [24]. Keeping the maximum energy equal to 400 eV and k-mesh of 2 × 2 × 2, the electrons wave functions are expanded (in plane waves). The simulation environment is the ideal environment which is relaxed using some constraints for optimizing the simulated models. Using the BFGS minimization scheme [25], the maximum displacement was set to 5.0 × 10 −4 Å, while the convergence limit for self-consistent tolerance was 2.0 × 10 −6 eV/atom. Anatase TiO2 supercell is made from the replication of 2 × 2 × 1 TiO2 unitcell. Low concentration of Indium in anatase TiO2 are possible by increasing the size of the supercell. Indium (In) doped models are constructed by replacing the lattice Ti atoms by In atoms. Doping single In atom at Ti sites have the In doping level of 2.08% represented by Ti16-1In1O32. The doping concentration of In is increased to 4.16% and this system is named as Ti16-2In2O32. The effect of oxygen vacancy on the band structure is evaluated by creating one oxygen vacancy along with two In atoms at Ti sites and it is represented by Ti16-2In2O31. Figure 1 displays the atomic configuration of anatase TiO2 having substitutional In (at Ti site) and oxygen vacancy. As a standard model, a defect free bare TiO2 is also simulated.

Results and Discussion
The calculated lattice parameters for pure TiO 2 (anatase) are; a = 3.81 Å and c = 9.71 Å, compared to the reported theoretical (a = 3.81 Å and c = 9.48 Å) [26] and experimental data (a = 3.78 Å and c = 9.49 Å) [27]. The bond lengths of the optimized systems are averaged and shown in Table 1.
The O-Ti and O-O bonds are 1.9651 and 2.7034 Å, respectively. The Dmol 3 based calculated Ti-O bond length for pure TiO 2 is reported to be 1.930 Å [28]. Treacy et al. [29] studied the structural features of anatase TiO 2 (101) with surface x-ray diffraction (SXRD) and then compared the results with the calculations based on density functional theory (DFT). It is found that the Ti-O bond length fluctuates between 1.89 ± 0.01 Å and 2.08 ± 0.01 Å [29]. Inducing defects modified the averaged bond lengths of the optimized TiO 2 . The bonds of Ti 16 [30,31]. Comparing the relative changes induced in the bond lengths due to different doping configuration, the Ti 16-1 In 1 O 32 modelled system provided minimum structure distortion in reference to bare TiO 2 . This system might improve the stability of the doped TiO 2 system and further improve the efficiency of In-doped in photoelectrochemical applications. The electronic band structure of the simulated models is depicted in Figure 2. The DFT based theoretically calculated electronic band gap is associated with the photoemission data. Similarly, the optical gap in the form of direct band gap could be linked with the spectrum of excitonic effects. The absorption spectrum of the TiO 2 has a relationship with the optical band gap. Therefore, the spectrum of the TiO 2 can be tuned by doping various elements, which create states in band gap or mix with valence or conduction band [5,32,33]. The calculated band gap of pure TiO 2 (2.13 eV) is underestimated relative to the 3.20 eV. The underestimation is a drawback of GGA based calculations [34]. In case of known exact exchange-correlation potential, the DFT can only have access to the ground state properties. To deal with this problem, the electronic excitations modeled by Kohn-Sham equations should be substituted by the Dyson equation. Thus, the unknown exchange-correlation potential is modeled by an operator depending on the self-energy. The utilization of the Hubbard model along with DFT is one of the ways to deal with the underestimated band gap [10,35,36]. We consider the current study as a relative study that describes the relative changes induced due to different doping/defect configurations. So, the underestimation would not affect our results. Replacing the lattice Ti atom by In atom (Ti 16-1 In 1 O 32 ), the band gap is reduced to 2.113 eV. The reduction in the band gap would be helpful in shifting the absorption regime towards visible light. Moreover, the Fermi level is moved slightly upwards in the forbidden region. The location of the Fermi level and the band edge positions of different models are summarized in Table 2. At gamma point, the band gap of Ti 16-2 In 2 O 32 is 2.65 eV. Though the band gap seems to be extended, some humps are present at the conduction band maximum and it may help in migrating the electrons from valence to conduction band. Creating oxygen vacancy widens the band gap and the band gap for Ti  In 2 O 31 is 2.483 eV. The widening of the band gap due to oxygen vacancy in TiO 2 is consistent with literature and this increase might be explained by the localized states [37,38].   The band structure modifications are further investigated and densities of states are calculated. Figure 3 displays the density of states of the simulated models. Doping In atoms modified the band structure of TiO2 and the In 5p states are coupled with the host O 2p and Ti 3d states. Increasing the In doping level from 2.08% to 4.16% has no considerable effect on the band gap. Figure 3b demonstrates the partial density of states (PDOS) of the models. It is clarified that the valence band of bare TiO2 comprises of O 2p states while the Ti 3d contribute (predominantly) to the conduction band. Adding In atoms at Ti sites induced In 5p states which are coupled with the O 2p states, modifying the valence band of TiO2. In the Ti16-2In2O32 model, the Indium doping concentration is increased to 4.16% and the density of In 5p states near the valence band is enhanced. Moreover, some In 5p also contribute to modifying the conduction band. The intensity of In 5p states in the Ti16-2In2O31 model remains the same. However, the In 5p states are smoothened compare to the non-compensated systems. The In 5p states in the band structure would be supportive in migrating the visible light photons from valence to conduction band. The band structure modifications are further investigated and densities of states are calculated. Figure 3 displays the density of states of the simulated models. Doping In atoms modified the band structure of TiO 2 and the In 5p states are coupled with the host O 2p and Ti 3d states. Increasing the In doping level from 2.08% to 4.16% has no considerable effect on the band gap. Figure 3b demonstrates the partial density of states (PDOS) of the models. It is clarified that the valence band of bare TiO 2 comprises of O 2p states while the Ti 3d contribute (predominantly) to the conduction band. Adding In atoms at Ti sites induced In 5p states which are coupled with the O 2p states, modifying the valence band of TiO 2 . In the Ti 16-2 In 2 O 32 model, the Indium doping concentration is increased to 4.16% and the density of In 5p states near the valence band is enhanced. Moreover, some In 5p also contribute to modifying the conduction band. The intensity of In 5p states in the Ti  In 2 O 31 model remains the same. However, the In 5p states are smoothened compare to the non-compensated systems. The In 5p states in the band structure would be supportive in migrating the visible light photons from valence to conduction band.   Figure 4 depicts the optical absorption spectra of the simulated systems. Tuning the band structure modifies the optical absorption properties of the semiconductor materials. For evaluating the optical properties, the underestimated band gap is updated to the experimental value of the band gap (3.20 eV) with scissor approximation [12]. The spectrum of bare TiO2 displays absorption in the UV region only because the wide band gap deprives it from utilizing the major part of the solar energy. The UV light absorption corresponds to the excitations of electron between O 2p and Ti 3d states. The In doping in the anatase TiO2 network shifted the absorption range towards the visible regime. It is clarified from Figure 4 that with the UV absorption, the Ti16-1In1O32 model also exhibits visible light absorption. The In 5p states are responsible for shifting the absorption threshold towards visible light region. In this case, the electron undergoes step wise transition from O 2p to Ti 3d states via In 5p states. Thus, it indirectly modifies the absorption spectra. Increasing the Indium doping level improved the absorption in the visible regime. The shifting of the absorption edge of TiO2 towards visible regime due to In doping is consistent with the reported data [23]. Inducing oxygen vacancy in the Indium doped TiO2 model made the absorption peak disappear in the visible light region. In addition, the Ti16-2In2O31 model only absorbs UV light, confirming the findings of band structure analysis. Furthermore, the UV light absorption is also reduced compared to bare TiO2. The Ti16-2In2O31 blue shifted the absorption regime of the TiO2. Stable structure, favorable band structure and improved optical response of In-doped TiO2 would improve its efficiency in photoelectrochemical applications.   In this case, the electron undergoes step wise transition from O 2p to Ti 3d states via In 5p states. Thus, it indirectly modifies the absorption spectra. Increasing the Indium doping level improved the absorption in the visible regime. The shifting of the absorption edge of TiO 2 towards visible regime due to In doping is consistent with the reported data [23]. Inducing oxygen vacancy in the Indium doped TiO 2 model made the absorption peak disappear in the visible light region. In addition, the Ti 16-2 In 2 O 31 model only absorbs UV light, confirming the findings of band structure analysis. Furthermore, the UV light absorption is also reduced compared to bare TiO 2 . The Ti 16-2 In 2 O 31 blue shifted the absorption regime of the TiO 2 . Stable structure, favorable band structure and improved optical response of In-doped TiO 2 would improve its efficiency in photoelectrochemical applications.   Figure 4 depicts the optical absorption spectra of the simulated systems. Tuning the band structure modifies the optical absorption properties of the semiconductor materials. For evaluating the optical properties, the underestimated band gap is updated to the experimental value of the band gap (3.20 eV) with scissor approximation [12]. The spectrum of bare TiO2 displays absorption in the UV region only because the wide band gap deprives it from utilizing the major part of the solar energy. The UV light absorption corresponds to the excitations of electron between O 2p and Ti 3d states. The In doping in the anatase TiO2 network shifted the absorption range towards the visible regime. It is clarified from Figure 4 that with the UV absorption, the Ti16-1In1O32 model also exhibits visible light absorption. The In 5p states are responsible for shifting the absorption threshold towards visible light region. In this case, the electron undergoes step wise transition from O 2p to Ti 3d states via In 5p states. Thus, it indirectly modifies the absorption spectra. Increasing the Indium doping level improved the absorption in the visible regime. The shifting of the absorption edge of TiO2 towards visible regime due to In doping is consistent with the reported data [23]. Inducing oxygen vacancy in the Indium doped TiO2 model made the absorption peak disappear in the visible light region. In addition, the Ti16-2In2O31 model only absorbs UV light, confirming the findings of band structure analysis. Furthermore, the UV light absorption is also reduced compared to bare TiO2. The Ti16-2In2O31 blue shifted the absorption regime of the TiO2. Stable structure, favorable band structure and improved optical response of In-doped TiO2 would improve its efficiency in photoelectrochemical applications.

Conclusions
Substitutional In doping at Ti sites reduced the band gap of anatase TiO 2 and shifted the absorption edge toward the visible regime. Along with the absorption in the visible light region, the absorption in UV regime is also improved in reference to pure TiO 2 . The band structure of TiO 2 is modified due to the creation of In 5p states in the band structure. The defect states associated with In are successfully mixed with the O 2p states without creating isolated states in the band gap. Increasing In doping level induced no substantial change in the absorption spectra. The creation of oxygen vacancy in the Indium doped TiO 2 blue shifted the absorption edge and declined the UV light absorption. The experimentally observed improved photoactivity of In-TiO 2 could be reasonably explained by the 2.08% In doped TiO 2 model, which exhibits stable configuration, and reduced band gap. The proper oxidation state of In dopant stabilized the TiO 2 system while inducing visible light absorption spectrum. Stabilizing the visible light active In doped TiO 2 would improve its efficiency in photoelectrochemical applications.
Author Contributions: M.K., Z.L., and Y.Z. conceived and designed the models; M.K. performed calculations and finalized the paper.