Photoelectrochemical and theoretical investigation of the photocatalytic activity of TiO₂ : N

Abstract

Electrochemical and photoelectrochemical techniques have been employed to investigate the electronic energy level modification of N-doped TiO₂ and to elucidate its properties and roles, particularly the electron transfer rate and influence on recombination, in a simple and facile manner. However, the results obtained cannot be easily interpreted and they need comparisons with theoretical calculations. In this study, photoelectrochemical measurements were conducted to investigate the effect of N-doping on TiO₂ nanomaterials, and the results obtained were compared with theoretical calculations. Band-gap values calculated by diffuse reflectance UV-vis spectroscopy were used together with photoelectrochemical measurements of TiO₂ and TiO₂ : N flat-band potentials to create a scheme of the energy-level band edges. In addition, this method confirmed the creation of energetic inter-levels by the N-doping process, as predicted by theoretical calculations. The replacement of an oxygen atom by nitrogen atom in the anatase structure shows a modification of the energetic levels, caused by a shift of the upper energy level; this shift was caused by local structural disorder. From the photoelectrochemical results, it is possible to confirm that the electron concentration in the TiO₂ photoelectrode is higher than that in the TiO₂ : N photoelectrode; due to an increase in the recombination of electrons and holes because of the creation of inter-levels in the TiO₂ : N band-gap. In addition, theoretical analysis indicated a possibility of direct transfer of electrons into the band-gap of TiO₂ : N. This combined approach was useful for interpreting many unclear results with respect to the photocatalytic activity of TiO₂ : N.

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1 Introduction

In semiconductor materials, photoexcitation is a beneficial process in oxidative reactions because of generation of electron–hole pairs, which migrate to the surface and catalyze these reactions.^1–7 Materials such as ZnO, ZnS, and TiO₂ exhibit these desirable characteristics conductive for photocatalysis due to large band-gaps ranging from 2.0 eV to 3.5 eV.^8–11 However, the photocatalytic behavior associated with these materials is limited to the high-energy ultraviolet (UV) region of the sunlight spectrum. Meanwhile, one method for modifying the electronic properties of these materials is to dope them with metals and/or nonmetals during semiconductor synthesis.^12–19 This strategy has been reported to improve the energy absorption range by reducing the band-gap or creating donor–acceptor levels in the band-gap. Although it is reasonable to hypothesize the generation of extra energy levels between the conduction (CB) and valence (VB) bands in TiO₂-doped nanoparticles (energetic inter-levels), it is not well understood if these levels can increase electronic recombination, and consequently, effectively alter photocatalytic activity.

The TiO₂ : N doping process is categorized as anion doping, which is different from the typical cation doping process.^20,21 Anion doping alters the negative charge balance in the semiconductor by forming interstitial inclusions or substitutional dopants (where O²⁻ in the network is replaced by N³⁻). Although defects and dopants in TiO₂ are typically paramagnetic, electron paramagnetic resonance (EPR) spectroscopy is one of the methods employed to identify their effect.²² X-ray photoelectron spectroscopy (XPS) is also useful for identifying interstitial or substitutional N-doping in TiO₂.²³ However, both these methods are expensive and may be not adequate for analysis. Therefore, it is imperative to develop alternative techniques to characterize these catalysts.

In this regard, electrochemical and photoelectrochemical techniques have been applied to evaluate the actual N-doping effect, which generates new energy levels between the CB and VB in the band-gap of TiO₂. These techniques exhibit advantages of possible direct evaluation of the transfer of electrons during the photocatalytic process as well as the characterization of important features such as the quasi-Fermi level of doped oxides.²⁴ Mott–Schottky plots are representative of these techniques and are determined by impedance spectroscopy. With these plots, it is possible to determine the so-called flat-band potential (V_fb) of a bulk semiconductor electrode.²⁴

When the interface between a semiconductor and an electrolyte is illuminated with energy higher than its band-gap energy, electron–hole pairs are generated at the electrode surface. The junction of the semiconductor/electrolyte interface, caused when the semiconductor is in contact with an electrolyte, determines the electron hole separation kinetics. To reach the equilibrium condition, the junction in a redox electrolyte causes a change in the electrochemical potential, which allows the flow of charge from one phase to another. Generally, this shift of electrochemical potential promotes bending in the energy edges (conduction and valence band) and the region where there is bending is called the space charge layer. The space charge layer is characterized by the accumulation of electrons or holes at the surface, depending the semiconductor type (n or p-type) and the redox potential of the electrolyte. When the potential across the space charge region approaches zero, the resultant charge transferred is zero. This potential is known as the flat-band potential and is an important parameter for bulk semiconductor photoelectrodes.²⁴ Other examples are the relation between the incident photon-to-current efficiency (IPCE) and the absorption wavelength²⁵ and the Mott–Schottky plots, which are typically used for the characterization of dye- and quantum-dot-sensitized solar cells. However, it is essential to interpret the results obtained by photoelectrochemical measurements, and it is desirable to compare these results with those from theoretical calculations as ab initio methods can aid in the understanding of the possible processes during charge photogeneration.

Thus, this study investigates the modification of N-doped TiO₂’s electronic energy levels and elucidates its properties and roles, particularly the electron transfer rate and influence on charge recombination, in a simple and facile manner. For this purpose, photoelectrochemical measurements were conducted in a manner similar to measurements conducted for dye- and quantum-dot-sensitized solar cells. Cyclic voltammetry was employed to determine the quasi-Fermi level potential of TiO₂ and TiO₂ : N embedded in carbon paste solid electrodes, and diffuse reflectance spectroscopy (DRS) was employed together with V_fb results to obtain a simplified scheme of the energy edges. An electrochemical model was applied to determine the concentration of electrons in each electrode as well as the electron transfer rate. To understand the photoelectrochemical results, theoretical calculations of the density of states (DOS) and effective band-gaps were performed for a comparative analysis. This work is not intended for a direct comparison between the absolute results derived from theoretical calculations and those obtained from characterization measurements but for a tentative evaluation between the results and the relative Fermi levels with the nitrogen content variation. This combined approach is a useful, fast, and easy tool for understanding the influence of the generation of energy levels on the photocatalytic behavior of these doped materials. In addition, this approach can also be applied to future research on other anion-doped TiO₂ materials.

2 Materials and methods

2.1 TiO₂ nanoparticle synthesis

Titanium(IV) resins were prepared using a polymeric precursor method. First, titanium tetraisopropoxide (Merck) was dissolved in an aqueous citric acid solution (Merck) at 75 °C in a molar ratio of 1 : 3. After complete dissolution and homogenization using a magnetic stirring bar, the titanium citrate was polymerized by the addition of ethylene glycol (Merck). Nitrogen-doped resins were prepared by the same route, except for the addition of 2% urea (weight equivalent TiO₂) before heat treatment, which was carried out for all samples, as previously reported by Soares et al.¹⁵ Diffuse reflectance UV-Vis spectra were recorded on an ultraviolet-visible-near-infrared (UV-Vis-NIR) Cary 5G spectrophotometer. Prior to each measurement, the substrate spectrum was taken as the baseline. UV-Vis spectra were obtained in diffuse-reflectance mode (R) and transformed to a magnitude proportional to the extinction coefficient (K) by the Kubelka–Munk model, which relates the extinction coefficient and scattering (S) with the reflectance (K/S = (1 − R)²/2R). For comparison, all spectra were arbitrarily normalized at an intensity of 1.0. The band-gap values obtained for TiO₂ and TiO₂ : N were 2.99 eV and 2.87 eV, respectively.¹⁵

2.2 Preparation and characterization of the composite electrodes

For electrochemical characterization, carbon paste electrodes were packed in 1 mL syringes. Different amounts of TiO₂ (15% and 60%) (w/w) were vigorously mixed in a mortar with graphite powder (Dinamica), and the resultant powder was suspended in mineral oil (3.0 mg : 0.3 mL of graphite powder : mineral oil). Voltammetric experiments were performed using a potentiostat–galvanostat (Autolab PGSTAT 30). The carbon paste electrodes were characterized by cyclic voltammetry (CV) using a K₃Fe(CN)₆ solution (Merck) (0.05 mol L⁻¹) as the electrolyte and three electrodes: a saturated calomel electrode (SCE), platinum wire, and TiO₂ carbon paste as the reference, counter, and working photoelectrodes, respectively. The set up used to conduct the voltammetric measurements was similar to that proposed by our previously work.²⁶

2.3 Computational details

The structural and electronic properties of both pure and doped TiO₂ anatase were investigated by first principles calculations based on Density Functional Theory (DFT) using the B3LYP hybrid functional^27,28 augmented with a Long-Range Dispersion correction (B3LYP+D)²⁹ and all calculations were performed using the CRYSTAL09 package.³⁰ First of all, the experimental unit cell for pure TiO₂ was fully-relaxed (cell parameters and atomic positions) as a function of the total energy of the system. Substitutional paramagnetic (N²) and diamagnetic (N³⁻) doping on bulk anatase was modelled by replacing one and two oxygen atoms in a 2 × 2 × 1 supercell (48 atoms), respectively. Furthermore, the diamagnetic scenario requires the creation of oxygen vacancies, which was modelled by removing one oxygen atom of the supercell, as presented in Fig. 1b. Otherwise, in order to take the surface effects on the nitrogen doping process into account, a (001) periodic slab was cleaved from the optimized anatase unit cell consisting of a slab thickness of 18-layers, where one outermost oxygen (2c) atom was replaced by N² (Fig. 1c). Theoretical reports suggest that both anionic and cationic doping processes located on the surface layer are more favorable than those at subsurface ones.^31,32 It is important to clarify that only substitutional nitrogen species were considered due to the similarity between the electronic structures obtained with substitutional/interstitial species, as reported by other theoretical studies.^33–35 The optimization process was controlled by mono- and bielectronic integrals converged with pre-defined criteria in 10⁻⁸ Hartree. Thresholds for convergence on the RMS gradient, RMS displacement, maximum gradient and maximum displacement were set to 3 × 10⁻⁵, 1.2 × 10⁻⁴, 4.5 × 10⁻⁵ and 1.8 × 10⁻⁵ a.u., respectively. Diagonalization of the matrix density was carried out using a grid of k points in reciprocal space according to the Monkhorst–Pack method³⁶ and the shrink factor was set to 8 × 8 (Gilat Web) corresponding to 59, 170 and 34 independent points, k, in the Brillouin zone for the pure, supercell N-doped and slab N-doped TiO₂, respectively. The level of accuracy in evaluating the Coulomb and exchange series was controlled by five thresholds, for which values 10⁻⁷, 10⁻⁷, 10⁻⁷, 10⁻⁷ and 10⁻¹⁴, are suggested for magnetic materials.³⁷ The Ti, O and N atoms were described by the all-electron atom-centered Gaussian-type basis sets 8-6411(31d)G, 8-411(1d)G and 6-31d1G, respectively.^38,39

Fig. 1 Periodic models for pure and doped anatase TiO₂. (a) Crystallographic unit cell. (b) 2 × 2 × 1 supercell doped with nitrogen at a three-fold coordinated anionic site. (c) 001-surface oriented 18-layer periodic slab, 18-layers doped with nitrogen at the two-coordinated outermost oxygens. Blue, red and green balls represent the titanium, oxygen and nitrogen atoms, respectively.

3 Results and discussion

3.1 Electroanalytical characterization

The electron transfer ability of the obtained photoelectrodes was evaluated in the presence of the Fe(CN)₆^(3−/4−) redox system, which is globally employed as a standard system to obtain information about heterogeneous electron transfer rates.^26,40 Fig. 2 shows the current–potential characteristics for the carbon paste electrode with and without TiO₂ (15% w/w) and TiO₂ : N (15% w/w), in the dark and under UVC radiation at 20 mV s⁻¹ in N-purged 0.05 M K₃Fe(CN)₆, pH 7.0. The thickness of the electrodes was 50 mm, and the geometric area of the electrode surface was 7.1 mm².

Fig. 2 CVs of different carbon paste electrodes in the dark and with UVC illumination (a) 15% TiO₂/carbon paste electrode and carbon paste electrode, (b) 15% N (2%) : TiO₂/carbon paste electrode and 15% TiO₂/carbon paste electrode. Scan rate = 20 mV s⁻¹; electrolyte solution: (K₃Fe(CN)₆), 0.05 mol L⁻¹, under N-purged atmosphere, at ambient temperature.

As shown in Fig. 2a, the carbon paste photoelectrode without TiO₂ also presented an electrochemical response for the Fe(CN)₆^(3−/4−) redox system, and the photoelectrode containing TiO₂ (Fig. 2b) exhibited an anodic current density lower than that of the electrode without TiO₂. Electron transfer kinetics are significantly influenced by the electrode surface arrangement and some defects or deformation in the photoelectrode surface could modify the electron transfer process.⁴⁰ Considering a semiconductor material (TiO₂) dispersed in a conductive matrix (carbon paste electrode) will present surface polarization under an external electrical field, the resulting material may have some deviations due to OH⁻ charges on TiO₂, related to the number of interfaces (TiO₂/carbon contact). The presence of TiO₂ in the carbon paste matrix diminished the contact points for conduction, decreasing the resultant peak current with respect to the carbon paste electrode.²⁶

Under UVC illumination, the maximum photocurrent increased in both cases for the TiO₂-free carbon paste (Fig. 2a) and TiO₂/carbon paste photoelectrodes (Fig. 2b). The TiO₂-free carbon paste electrode (Fig. 2a) exhibits a photocurrent under UVC illumination probably caused by the photoelectric effect.²⁶ However, this increase was clearly more significant for the TiO₂-containing electrode (Fig. 2b), indicating a positive synergistic effect on the specific capacitance of the electrode. The presence of TiO₂ in the matrix electrode clearly modifies the electron transfer mechanism on the electrode surface and this process could be interfered with by electronic transfer kinetics and electronic diffusion in the electrolyte solution, considering a mixed-control regime.⁴¹ Under illumination, the TiO₂/carbon paste electrode provides better electronic conductivity compared to that without illumination.

Fig. 2c presents the behavior of the TiO₂ : N/carbon paste photoelectrode and, in this case, should highlight the alteration in the photoelectrode characteristics only by the embedded different material’s characteristics as a doped semiconductor, confirming the difference between pristine TiO₂ and N doped TiO₂. This difference is promoted especially by defects in the TiO₂ lattice induced during the doping process, as oxygen vacancies, which influence in the final conductivity.

It is evident that the presence of TiO₂ in the carbon paste electrode modifies the conduction properties of carbon paste, as confirmed by the voltammetric data shown in Fig. 2. The peak-to-peak separation (ΔE) between the reduction and oxidation signals in Fig. 2 can provide the heterogeneous electron transfer rate constant (ψ) by the Nicholson method and then, the rate of electron transfer can be obtained (k₀).⁴⁰ From Fig. 2, it is possible to observe that the TiO₂/carbon paste photoelectrode shows the largest ΔE (978 mV vs. SCE), followed by the SCE : N/carbon paste photoelectrode (329 mV vs. SCE). The carbon paste electrode displays the smallest ΔE (278 mV vs. SCE). The diffusion coefficients used for the calculations were D_O = D_R = 7.26 × 10⁻⁶ cm² s⁻¹.⁴² Comparing the three electrodes, the carbon paste electrode offered the fastest electron transfer (k₀ = 3.39 × 10⁻⁴ cm s⁻¹), as expected. In the presence of TiO₂ nanoparticles, the rate constant of electron transfer is reduced to 6.46 × 10⁻⁵ cm s⁻¹ and for TiO₂ : N, k₀ shows a slightly decrease compared with the carbon paste electrode (2.66 × 10⁻⁴ cm s⁻¹), indicating the N-doping influence on electron transfer in the photoelectrodes.

Some important defining aspects of semiconductor electrochemistry should be highlighted, such as the Fermi level which is defined as the occupation description of energy levels in a semiconductor at thermodynamic equilibrium. However, the thermodynamic equilibrium situation is not always satisfied, especially when electrons and holes are in excess under semiconductor illumination or injected under electric bias. For this reason, the electron and hole densities in the conduction and valence bands are defined by a quasi-Fermi level of electrons and quasi-Fermi level of holes. When a photon reaches the semiconductor’s surface, creating a charge pair electron–hole, the density of majority carriers (electrons, in the case of TiO₂) does not expressly increase upon illumination and the quasi-Fermi level of electrons is almost the same compared with the Fermi level at thermodynamic equilibrium. On the other hand, the density of minority carriers (holes) increases by many orders of magnitude, and this leads to a shift of the quasi-Fermi level of holes. Only for heavily doped n-type metal oxides like TiO₂, is the lower conduction band edge (E_CB) practically unified with the quasi-Fermi level of electrons.

Now, consider the introduction of an electrode in a photoelectrochemical system, with an electrode surface in contact with an electrolyte solution. After contact of the semiconductor surface (electrode) with the electrolyte, thermodynamic equilibrium is established on both sides by adjustment of the Fermi level of the semiconductor with the Fermi level of the electrolyte (E_F,redox). As E_F,redox is considered constant, to reach the equilibrium, electron transfer should occur across the interface, resulting in space charge layer formation (a depletion layer). In the case of an n-type semiconductor, electron transfer creates an excess of positive charges on the semiconductor surface. Consequently, negative charges are located in the electrolyte solution. In this situation, the electric field of the negative charges on the electrolyte obstructs electron transfer until thermodynamic equilibrium is reached. As a result, no net charge flow happens and this condition is known as the flat band potential (V_fb).^24,43 So, in a thermodynamic equilibrium between the electrode surface and electrolyte, V_fb has the same energy value as the quasi-Fermi level of electrons in TiO₂, or the same value as E_CB.

As a consequence, the conduction and valence bands are bent upwards. However, the bent bands only apply to thin compact highly doped TiO₂ films. In the context of nanomaterials, as presented in this case for TiO₂ nanoparticles (crystallite size = 10 nm) and TiO₂ : N (crystallite size = 7 nm), and in an exceedingly porous nanocrystalline electrode such as carbon paste electrodes, the space-charge layer formation does not occur due to the small crystallite size of the semiconductor.⁴³ In this case, the small TiO₂ crystal does not contain enough electrons in order to create an effective space-charge layer.

With the support of the Buttler equation²⁰ is possible to determine the flat band potential of each semiconductor:

where j is the photocurrent density, q is the transferred charge per ion, ε is the permittivity of the surroundings, ε₀ is the vacuum permittivity, I₀ is the current density difference, α is the optic absorption coefficient, N_d is the number of charge donors, V is the potential, and V_fb is the flat band potential. The flat band potential may thus be regarded as the potential for the onset of the square photocurrent obtained in Fig. 3.^21,44 In this way, Fig. 3 is derived from Fig. 2, and shows the V_fb for the TiO₂ composite photoelectrode of 0.112 V vs. SCE and for the TiO₂ : N composite photoelectrode of 0.049 V vs. SCE, in 0.05 M K₃Fe(CN)₆, pH 7.0. The values of V_fb are important to obtain direct information on the position of the CB edge in n-type semiconductor materials, since it could be assumed that the difference between V_fb and E_CB is insignificant. In this way, measurement of V_fb shows the conduction band edge determination of thin compact TiO₂ electrodes.⁴³ The obtained values of E_CB are −0.132 V vs. NHE and −0.195 V vs. NHE for the TiO₂ composite electrode and the TiO₂ : N composite electrode, respectively. It is important to highlight that these values are presented for Fe(CN)₆^(3−/4−) solution in pH = 7 and are also dependent on material characteristics which are related to the synthesis method.

Fig. 3 Square of the anodic photo-current shown in Fig. 2 of the different carbon paste electrodes (TiO₂ and N (2%) : TiO₂) with UVC illumination.

Spadavecchia et al.³³ present an extensive comparison between the determination of V_fb by the Mott–Schottky plot and photovoltage/photocurrent method/spectroelectrochemistry of TiO₂ and TiO₂ : N different electrodes. It is important to note that the V_fb variation is dependent on the electrolyte pH and material synthesis methods used, showing a large deviation in values. In this way, the results presented here are in accordance with those reported by Spadavecchia et al.³³ Typically, the V_fb value shifts in the negative direction for the TiO₂ : N electrode.^45,46 For instance, as described by Xiang et al.,⁴⁵ for a mesoporous nitrogen-doped TiO₂ sphere used in quasi-solid-state dye-sensitized solar cells, the doped structure exhibits a shift of 0.13 V vs. SCE for more negative values as compared to the undoped structure.

Fig. 4 shows the energy scheme with the E_CB and E_VB values relative to the hydrogen standard electrode potential, for the TiO₂ and TiO₂ : N photoelectrodes shown in Fig. 2 and 3. The determination of the E_CB often explains the measurement of the position of the quasi-Fermi level of electrons in the TiO₂ photoelectrodes. Once this is known, the E_VB values can be simply calculated by adding the value of band-gap energy that is presented in Section 2.1 of a paper by Soares et al.¹⁵ to obtain V_fb for each of the photoelectrodes. Because N-doping causes a decrease in the band-gap values of the semiconductor, an electric field is necessary to maintain the separation of the photogenerated charges.⁴⁷

Fig. 4 Conduction and valence bands schematic of the photoelectrodes with semiconductors TiO₂ and TiO₂ : N in pH = 7 (H⁺/H₂ redox potential = 0.414 V (pH 7.0), O₂/H₂O redox potential = 1.109 V, Fe(CN)₆³⁻/Fe(CN)₆⁴⁻ redox potential = 0.770 V in pH 7.0). This figure takes the electrochemical convention energy scale into consideration.

As shown in Fig. 3, the E_CB values of the TiO₂ and TiO₂ : N photoelectrodes were −0.132 V and −0.195 V vs. NHE, respectively. The potential values shifted to more negative values after doping, and together with the results shown in Fig. 4, these results indicate that N-doping actually creates new energy levels between the CB and VB, known as inter-levels, in the TiO₂ band-gap.⁴⁶ Some authors have termed these new energy levels between the CB and VB of TiO₂ as intralevels; however, this name is not representative of the location of the new energy levels.^13,17 The variation in V_fb after doping was in accordance with other dopants such as F and is due to the higher abundance of electrons in the doped nanoparticles.⁴⁸ Consequently, the deformation of the energy level caused by N doping decreased the effective energy amount required for excitation of an electron in the VB to the CB in the case of surface photoexcitation.⁴⁹ Beranek et al. have observed similar behavior²⁵ by employing capacitive spectral-resolved surface photovoltage and IPCE measurements, affirming that recombination becomes more efficient as the band-gap reaches low values. However, the shift of V_fb induced by N doping is not only an effect of the presence of nitrogen on the TiO₂ lattice; it is well known that the visible activity of TiO₂ : N is caused due to diverse factors such as the presence of oxygen vacancies caused by the doping methods, the electron–hole recombination rate and morphological/structural properties of the material. The presence of N in a TiO₂ lattice could be considered as being in an interstitial or substitutional way, in other words, in space sites or in O sites in the TiO₂ lattice. In both ways, there is a charge compensation, causing O vacancies. It is possible to describe the TiO₂ photoexcitation based on the clusters model, in which [TiO₆]^x is associated with neutral , mono-ionized or di-ionized oxygen vacancies. First of all, the creation of a hole-pair is required as:

Subsequently, the hydroxyl radical (OH*) (eqn (3) and (4)) and superoxide radical (O₂H*) (eqn (5)–(7)) occur, with water and molecular oxygen adsorbed on the surface of the material, respectively.

In the case of the TiO₂ : N material, there are more reactions involved in the mechanism. First, [TiO₆]^x is associated with a neutral oxygen vacancy in the presence of an N source (N_source).

The resulting [TiO₆N]′ presents a negative charge characteristic and should stabilize the creation of more oxygen vacancies compared with the undoped TiO₂ material, promoting a modification in radical production and then in the surface material characteristics. The differences in the E_CB and E_VB values observed in Fig. 4 between the doped and undoped TiO₂ seem to be small, however it should be noted that a small shift in these values could produce a change in energy level of tens of millivolts, enabling some applications of TiO₂ : N that are not possible for the TiO₂ material.

One of the most important parameters related to the efficiency of charge recombination is electron lifetime, which can be calculated by intensity-modulated photovoltage spectroscopy; however, it is not useful for elements that exhibit a significant potential difference at the open circuit. To avoid this limitation, two parameters can be employed: open-circuit voltage decay (OCVD) and charge extraction. However, these parameters are only applicable for solar cell structures. Meanwhile, for photoelectrocatalysis, the method suggested by Monllor-Satoca and Gomez⁵⁰ can be employed to obtain the pseudo-first-order velocity (inverse lifetime) for the charge recombination and transfer processes using a thin film electrode. However, no studies have reported the methodology using a solid electrode. This method is based on cyclic voltammetry without illumination (Fig. 5a) and the open-circuit voltage (V_oc) versus time relaxation decay after switching off illumination. This method considers an equilibrium between the free and trapped electrons and the open-circuit voltage (OCP, V_oc) versus time relaxation decay after switching off illumination. Under these conditions, the chronoamperometry results for each photoelectrode are reported in Fig. 5c, for two conditions – A in the dark, before turning on the illumination (before illumination) and B in the dark, after turning off the illumination (after illumination). A solid electrode was used instead of a thin film electrode; Fig. 5c shows V_oc versus time. When the V_oc after illumination is more negative than it is in the dark, holes are preferentially transferred to solution, and the photoelectrode presents photoanodic behavior. Conversely, when V_oc under illumination is more positive than it is in the dark, the electrons are preferentially transferred to solution (photocathode). The first condition is adequate for the TiO₂ and TiO₂ : N photoelectrodes, as confirmed in Fig. 5c. In this way, ferricyanide/ferricyanide is an adequate electrolyte to obtain the photoelectrochemical characterization of solid electrodes.

Fig. 5 (a) Cyclic voltammetry with the photoelectrodes of TiO₂ and TiO₂ : N (15%), 20 mV s⁻¹, K₃Fe(CN)₆, 0.05 mol L⁻¹, without UV-C illumination, (b) insert from (a) of the region used for electron density calculations, (c) circuit open potential before and after UVC illumination for the photoelectrodes, K₃Fe(CN)₆, 0.05 mol L⁻¹, (d) relation between n_ph vs. time for the photoelectrodes with TiO₂ and TiO₂ : N (15%).

The concentration of electrons during decay (n_ph(E)) after switching off illumination can be obtained by integration of the voltammogram (Fig. 5b) between the potential steady state or stationary potential in the dark (V_oc) and the potential at a certain time (in this case, defined as 1.0 V vs. SCE) during decay as follows:⁵⁰

here, A is the geometric area of the electrode, I is the voltammogram current, v is the cyclic voltammetric scan velocity, and d is the film thickness. As a solid electrode is used in this study, d represents the thickness of the carbon paste electrode. This fit probably changes the final value of the electron concentration compared with that obtained using thin film electrodes; however, this difference will not interfere with the results because the goal is to compare the TiO₂ and TiO₂ : N photoelectrodes and to investigate whether N-doping interferes with photocatalytic efficiency.²⁴

The V_oc (open potential circuit potential) values of the TiO₂ and TiO₂ : N photoelectrodes were 0.208 V and 0.439 V vs. SCE, respectively (Fig. 5b). The concentration of electrons during decay (n_ph(E)) was 7.108 × 10²⁰ cm⁻³ and 6.253 × 10²⁰ cm⁻³ for the TiO₂ and TiO₂ : N photoelectrodes, respectively (Fig. 5d). As shown in Fig. 5d, the TiO₂ photoelectrode had a higher concentration of electrons than the TiO₂ : N photoelectrode at different decay times. Xiang et al.⁴⁵ have also reported an increase in the efficiency of charge collection after doping TiO₂ with N by intensity-modulated photocurrent spectroscopy.

For photocatalysis to occur, at least two chemical processes must occur simultaneously on the catalyst: oxidation based on the transfer of the photogenerated holes and reduction involving the photogenerated electrons. Both processes are based on a precise charge balance. If the catalyst is present as particles or agglomerates, there will be interference from other processes such as the recombination of electrons and holes and/or relaxation of electrons and holes to lower energy states. In this regard, recombination is not desirable because it negatively affects electronic transfer, or in extreme cases, the overall processes could be inhibited. Also, in photocatalysis or photoelectrocatalysis, the visible activity of a semiconductor is important, caused by the increase in the activation of its wavelength, and consequently, recombination could occur, as the effective energy barrier is smaller. The main reason for the previously obtained result, i.e., a lower concentration of electrons in TiO₂ : N than in TiO₂, is an increase in the recombination of electrons and holes or the relaxation of electrons and holes to lower energy states, as N-doping creates inter-levels in the band-gap of TiO₂ : N. Hence, the effective energy barrier for electron concentration is smaller.

The principal question is whether the decrease in the effective energy barrier causes an inhibition of the overall process. Hence, the results obtained here are important since they demonstrate that although TiO₂ : N may have lower energy barriers for the generation of electrons and holes, recombination may improve because of the same factor. The results of n_ph vs. time were similar to those observed in previous studies using thin film electrodes, confirming the perfect fit of this mathematical model with the experimental results.⁵⁰

The relationship between the rate of transfer of electrons to acceptors, v_e, can be determined in relation to the electron concentration by:⁵⁰

Fig. 6 shows the relationship between dn_ph/dt and n_ph and between k and n_ph for both electrodes. In the absence of effective oxidants (e⁻ acceptors), k denotes the recombination of the accumulated electrons or intermediate molecules in photooxidation. However, in the presence of an oxidant, as in this case, the constant mainly refers to the velocity of the transfer of electrons to the acceptors.⁵⁰ Notably, a remarkable difference can be observed between the electrodes, i.e., the electron transfer in the TiO₂ : N electrode was significantly faster than that in the TiO₂ electrode.

Fig. 6 Relation between dn_ph/dt (a) and k vs. n_ph (b) for the photoelectrodes with TiO₂ and TiO₂ : N.

The n_ph(E) values are similar to the densities of donors, calculated by the Nyquist plot from electrochemical impedance spectroscopy. As reported by Kang et al.,⁵¹ the donor densities for pristine TiO₂ arrays are higher than those observed for TiO₂ arrays reduced by NaBH₄ (8.93 × 10¹⁷ and 2.06 × 10¹⁸ cm⁻³, respectively).⁵¹ They have attributed the observed increase in the donor densities to the generation of surface oxygen vacancies, which serve as electron donors, promoting a shift in the TiO₂ Fermi level toward the CB. Consequently, charge separation at the semiconductor electrode interface easily occurs by increasing the degree of bending of the band at the TiO₂ surface.⁵¹

In the case of the (n_ph(E)) values, surface oxygen vacancies do not increase after doping as compared to those of the undoped electrode, resulting in a shift in the TiO₂ : N Fermi level toward the VB. This shift in the Fermi level permits the transfer of charge in the space charge region, thereby preventing efficient charge separation at the semiconductor electrode interface.

This result confirms that doping actually creates energy inter-levels in the TiO₂ band-gap with a decrease in the effective energy barrier for electron transfer. However, these effects cause a consequent increase in the rate of electron transfer, confirming an undesirable doping effect, i.e., the recombination rate of electrons increases, thereby decreasing the photocatalytic efficiency.

3.2 DFT calculations

In this section, we carry out a theoretical evaluation of the N-doping effect on the structural and electronic properties of the bulk and surface TiO₂ anatase focused on the photocatalytic behavior. Such results are useful for understanding the intrinsic effects of doping in semiconductors and infer the properties associated with bulk/surface charge migration, which is important in the overall process. Firstly, the optimized lattice parameters at the B3LYP + D level of theory (a = 3.783, c = 9.570 and µ = 0.208) show excellent agreement with the experimental results.⁵² For the (N²⁻)-doped model, an expansion of the unit cell that can be related to the increase in the Ti–N and Ti–O bond lengths in the axial and equatorial planes was observed, as presented in Fig. 7b. This expansion induces a large distortion in comparison to the pure TiO₆ cluster (Fig. 7a), resulting in local structural disorder associated with the electronic distribution of the paramagnetic N²⁻ species (2s² 2p⁵), which induces a large spin localization on the p_z orbital inducing elongation around the axial plane. On the other hand, diamagnetic doping (N³⁻) induces a contraction of the unit cell volume, which is related to the reduced Ti–N and Ti–O bond lengths attributed to the presence of oxygen vacancies (Fig. 7c). In this case, the structural distortion is related to the presence of a negatively charged [TiO₆N]′ cluster that induces the formation of oxygen vacancies , resulting in a reduced Ti³⁺ species. Since this structural disorder is associated with the titanium 3d orbitals, the corresponding electronic state must be located above the valence band maximum resulting in several changes in the electronic structure, as reported by other theoretical analyses.^34,35,53,54 Thus, the electronic structures of TiO₂ : N and TiO₂ were analyzed from density of states (DOS) and the band structure profiles presented in Fig. 8.

Fig. 7 Optimized local geometry and Ti–(O, N) bond distances for (a) TiO₂ (b) paramagnetic (N²⁻) and (c) diamagnetic (N³⁻) nitrogen doped TiO₂ anatase. Blue, red, green, purple and orange balls represent the Ti, O, N²⁻, N³⁻ and O_vac species, respectively.

Fig. 8 Atom-resolved density of states (DOS) and band structure profiles for the (a) pure, (b) paramagnetic (N²⁻) and (c) diamagnetic (N³⁻) nitrogen doped anatase TiO₂. Black, red and blue lines in the DOS correspond to the titanium, oxygen and nitrogen electronic states, respectively. The green lines in the DOS correspond to the electronic states due to vacancies. In all cases the Fermi Level was set to zero. The arrows represent up and down spin states.

It was observed from the DOS results for pure TiO₂ (Fig. 8a) that the valence band (VB) is mainly composed of oxygen 2p states, whereas the conduction band (CB) is based on 3d (Ti) electronic states. Band structure profiles show an indirect band-gap between the Y–Γ points at around 3.80 eV, in agreement with experimental reports (3.20–3.60 eV) and similar to other theoretical deviations.^55–58 The electronic results for paramagnetic (N²⁻)-doped TiO₂ (Fig. 8b) indicates a perturbation in both the VB and CB energy levels through the introduction of the nitrogen electronic states in the midgap region resulting in a narrowing band-gap of 2.44 eV. On the other hand, considering the diamagnetic (N³⁻) scenario (Fig. 8c), it was observed that the main effects related to the doping process are associated with the creation of midgap states near to the valence band maximum (VBM), resulting in narrowing band-gap of 3.26 eV. These midgap states are mainly composed of 2p states of N and O atoms associated with 3d orbitals from the Ti³⁺ species, in excellent agreement with theoretical data reported by Spadavecchia and co-workers.³³ Such results are in agreement with the experimental observations for the shifted VB and flat-band potential in the N-doped TiO₂ samples (Fig. 3) suggesting improved sunlight-driven photocatalytic behavior. In addition to the band-gap reduction, to favor the creation of electron–hole pairs, the recombination process plays a fundamental role in the photocatalytic activity. The photocatalytic behavior of anatase TiO₂ is strictly related to the indirect nature of the band-gap excitation due to the higher charge carrier lifetime compared with that of direct band-gap semiconductors.⁵⁹ However, the band structure profiles for both the paramagnetic (N²⁻) and diamagnetic (N³⁻) doped TiO₂ scenarios (Fig. 8b and c) indicate that both the VBM and CBM were shifted from their Y and Γ points, respectively. In the first case, the creation of midgap states associated with the paramagnetic N²⁻ species modifies the band distribution resulting in a quite small energy difference between the direct (2.46 eV X–X; 2.48 eV Σ–Σ) and indirect (2.44 eV Y–X; 2.43 eV Y–Σ) band-gap values (Fig. 8b). Otherwise, for diamagnetic doping (N³⁻) the CBM remains similar to that of the pure TiO₂, while the VBM is shifted from the Y point behaving as a flat band, where the energy differs between the direct (3.26 eV Γ–Γ) and indirect (3.27 eV Y–Γ; 3.28 eV Σ–Γ) band-gap values (Fig. 8c). Therefore, the electronic structures of both nitrogen doped TiO₂ scenarios are more susceptible to electron–hole recombination than pure TiO₂ (Fig. 8a) due to having the smallest direct band-gap. These data support the experimental observation presented in Fig. 6, which suggests a higher electron-recombination rate for the N-doped samples in comparison to the pure anatase. Furthermore, despite the difference between the mechanism associated with the doping of both paramagnetic and diamagnetic nitrogen atoms, theoretical results indicate that both species act in the band-gap region, which becomes narrowed and direct, resulting in an extended electron–hole pair recombination.

In order to compare the N-doping process on the bulk and surface-oriented TiO₂ nanoparticles, periodic slab models were simulated at the DFT/B3LYP + D level of theory considering a 001-oriented supercell with an 18-layer slab thickness (36 atoms). The calculated surface energy for the pure anatase (001) surface (1.56 J m⁻²) exhibits good agreement with other theoretical reports.^60,61 In this case, only the paramagnetic (N²⁻) scenario was considered due to the huge computational cost of diamagnetic doping, which consists of substitutional N³⁻ species summed to the number of oxygen vacancies. Further studies considering this scenario are in progress. However, paramagnetic and diamagnetic nitrogen doping in bulk anatase TiO₂ induces a similar effect on the electronic structure considering the photocatalytic efficiency, as discussed above, indicating that N²⁻ doped 001-oriented TiO₂ nanoparticles are useful for predicting the main effect behind the photocatalytic behavior.

Electronic density of state and band structure profiles for the pure and N-doped anatase (001) surfaces are presented in Fig. 9. The electronic occupations at the valence and conduction bands for the 001-oriented anatase (Fig. 9a) shows the same pattern of distribution observed in the bulk (Fig. 8a) with an indirect band-gap around 2.96 eV between the M–Γ points. Regarding the N-doping process (Fig. 9b), DOS results reveal the creation of midgap states, mainly on the top of the valence band, composed of nitrogen (2p) states. It is important to note that the doping mechanisms at the bulk/surface exhibit different electronic structures because nitrogen replacement on the two-coordinated outermost oxygen surface keeps the dangling bonds at an anionic site resulting in a higher amount of spin-density (0.996 a.u.) in comparison to the three-fold coordinated site in the bulk (0.885 a.u.). Such an effect induces a smallest band-gap of around 1.84 eV; however, the nature of the electronic transition was modified to a direct excitation between N–N points suggesting a higher electron recombination rate in comparison to the pure 001-oriented TiO₂. Therefore, despite the band-gap reduction, the bulk and surface nitrogen doping mechanism also induces a large electron–hole recombination rate reducing the photocatalytic efficiency.

Fig. 9 Atom-resolved density of state and band structure profiles for the (a) pure and (b) (N²⁻)-doped 001-surface oriented TiO₂ anatase. Black, red and blue lines in the DOS correspond to the titanium, oxygen and nitrogen electronic states, respectively. For the band structures, the Fermi level was set to zero. The arrows represent up and down spin states.

Besides the band-gap nature, photocatalytic efficiency is also affected by the mobility of photoinduced electrons and holes. In this context, the effective mass of electrons and holes plays a fundamental role in the diffusion (D) of free charge carriers, as follows:

where µ corresponds to the mobility, which is linked to effective mass (m*) and the collision time (τ) of the charge carrier. Therefore, D increases if the effective mass of the photogenerated carriers becomes lighter, reflective of enhanced photocatalytic efficiency. Furthermore, the ratio between the effective mass of electrons and holes is a powerful tool to predict the electron/hole pair stability with respect to the recombination process. In this case, a larger effective mass difference induces distinct mobilities, which reduce the electron–hole pair recombination increasing the photocatalytic efficiency.^62–64

In order to explain the photocatalytic performance of both the pure and N-doped TiO₂ anatase, the effective masses of electrons and holes were calculated (Table 1) by fitting parabolic functions considering a small region near the CBM and VBM.^62–64

Table 1 Effective mass of electrons (m^*_e) and holes (m^*_h) for the pure and N-doped TiO₂ anatase at the CBM and VBM along a specific direction in reciprocal space. TiO₂ : (N²⁻) and TiO₂ : (N³⁻) correspond to the paramagnetic and diamagnetic nitrogen doped models, while m_o is the standard electron rest mass

Models		Direction
Bulk	TiO2	Y–Γ	0.46	0.14
	TiO2 : (N^2−)	X–X	0.56	0.44
		Y–Σ	0.53	0.49
	TiO2 : (N^3−)	Γ–Γ	0.25	0.17
		Y–Γ	0.21	0.17
Surface	TiO2	M–Γ	0.84	0.13
	TiO2 : (N^2−)	N–N	0.80	0.23

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Theoretical results for pure TiO₂ show that the effective mass of holes is sensitive to crystal growth, in agreement with the different bands’ dispersion near the CBM for the bulk and 001-surface models (Fig. 8a and 9a). In this case, the electron mobility is higher in the bulk, indicating that photoinduced charge carriers can easily migrate to the surface to participate in the photocatalytic process. Furthermore, the higher suggests that, once localized on the surface, the electron mobility is reduced while the hole remains stable, which is beneficial for reducing the recombination process.

Regarding the paramagnetic nitrogen (N²⁻) doping process into anatase TiO₂, similar behavior was observed for the bulk and surface models. In both cases, theoretical results indicate that the electron and hole effective masses increase with doping, reducing the which is reflective of a higher electron–hole pair recombination rate in accordance with experimental results. The main differences between the results were assigned to the nitrogen effect at the effective mass of holes in both models, which can be associated with the bands’ dispersion related to the two-fold and three-fold coordinated N²⁻ species. Further, considering the N³⁻ scenario, it can be seen that diamagnetic nitrogen doping also significantly reduces the ratio, increasing the electron–hole pair recombination, which can be associated with the creation of vacancies, resulting in a Ti³⁺ species that acts as an electron-trap. Therefore, in all cases, the nitrogen doping process reduces the ratio making it difficult for the separation of photogenerated electrons from their associated holes, increasing the probability of their recombination. Despite the differences from the experimental measurements (caused by limitations of calculations in environments other than a vacuum), these results confirm the analysis of photoelectrochemical measurements, where a similar tendency is shown, supporting our hypothesis.

4 Conclusions

This study reports the electronic structure and the effect of TiO₂ : N nanoparticles on a photoactivated process. This investigation, based on experimental and theoretical results, confirmed the creation of inter-levels by N-doping. The replacement of an oxygen atom by nitrogen in the anatase structure modified the energy levels, which reduces the band-gap by 1 eV due to a shift in upper energy level. In addition, theoretical analysis showed a possible direct band-gap in both the paramagnetic and diamagnetic TiO₂ : N models, which would imply an increase in the generation of charges, albeit with faster recombination. This combined approach was notably useful for interpreting the electron–hole recombination process on photocatalytic activity using TiO₂ : N. Therefore, N-doped TiO₂ anatase is a self-consistent system because it supports the photocatalysis process through a highly decreased band-gap; however, it increases electron–hole pair recombination from the ratio under UVC illumination.

Acknowledgements

The authors acknowledge Fapesp, CNPq, Finep, Capes, Projeto MP1 Rede Agronano - Embrapa, and the Araucaria Foundation for financial support.

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