Introduction

From electronics, communications, optoelectronics, sensors and a host of other applications, semiconductors have become a part and parcel of the modern society. It is difficult to conceive a thriving technology without their ubiquitous presence. Most semiconductor devices deploy some kind of band structure engineering in order to modify the properties of the constituent materials. Doping TiO2 with a variety of cations, anions, metals, and transition metals, have been implemented in order to improve its efficiency for absorbing in the visible range by either decreasing the bandgap or by introducing intra-bandgap states [10, 13]. Further, the photocatalytic performance of TiO2 is reported to increase by inhibiting the recombination of holes and electrons, when doped with noble metals like Au, Ag, and Pt. Among TiO2 polymorphs, anatase with a wide bandgap of 3.2 eV has been proven to have a superior photocatalytic activity due to its longer electron–hole pair lifetime [21]. Other approaches like doping with transition metals too have been adopted to modify it to absorb in the visible range. For instance Wang et al. have reported the doping in TiO2 with various transition metals [23]. They have reported that doping with Cr, Co, and Ni are energetically more favored at Ti site than O site. They have studied that the transition metal doping improves the photocatalytic activity of TiO2 by narrowing down the bandgap to visible region. Doping with lanthanides have been reported to effectively enhance photocatalytic activity in visible region [4]. A few metals as such have also been studied as dopants and proved to be effective for band gap narrowing [16]. In general, noble metals are known to retard the carrier recombination and enhance photocatalytic activity. Recently, Alotaibi et al. [1] have reported that multifunctional thin films of TiO2 doped with Cu show enhanced photocatalytic and antibacterial activity. In a similar work on Cr-doped TiO2 photoanodes, Song et al. attributed Cr 3d orbitals and Oxygen vacancies which produced a synergistic effect to increase visible light activity of Cr-doped TiO2 [22].

Jensen et al. [12] have studied Ni-doped TiO2 with H2O molecules and deduced that Ni indeed reduces the bandgap of TiO2 and enhances visible light photoactivity. Doping with Ni changes the phase composition and optical absorption range of TiO2 film gradually expands and shifts to the red with increasing dosages enhancing the light utilization according to Yao et al. [24].

In this study, we too have studied the doping of Ni into TiO2 and using first principles studies investigated the optical properties to ascertain the change in electronic structure caused by Ni. The absorption too has been noted to be enhanced by Ni doping in the visible region with a higher absorption coefficient in the visible region.

Numerous methods have been tried to modify TiO2 as a visible light photocatalyst such as cation doping, anion doping [8], transition metals [23], lanthanides [4], etc. Noble metals like Pt, Au, Pd, and Ag have been routinely used in TiO2 doping to enhance charge carrier separation. The noble metals have higher work functions but lower Fermi energy level compared to TiO2. Thus, they enable electrons to be transferred from the CB of TiO2 by means of the Schottky barriers to get trapped by these noble metals [11]. Hence, they promote ample separation of charges while minimizing charge carrier recombination, thereby improving photocatalytic activity of TiO2.

In our earlier paper [7], we had envisaged using first principles DFT calculations how the electronic and optical properties of anatase TiO2 are effectively tuned by controlled concentrations of Pt and Ag as dopants. The modified electronic structures end up in successful operation of the optical and electronic properties in the favorable visible region.

Bai et al. [2] have studied the Pd-doped flower-like structures anatase TiO2 with exposed (001) facets. They synthesized Pd/TiO2 nanocomposite catalysts which exhibited strong absorption in the desirable visible light and remarkable photocatalytic activity for BPA degradation under UV and visible light compared to bare TiO2. Dong Li et al. [15] have successfully prepared a visible light active Pd/C–N–S–TiO2 NS photoelectrode which can function as a viable visible light based photocatalyst. Studies also show Pd-doped TiO2 nanofibers can be utilized as highly sensitive gas sensors [17, 18].

Our DFT studies on electronic structures prove that increasing concentrations Pd dopants [5] and Ni [6] dopants result in successive narrowing of band gap in TiO2. In this paper, we have also compared the modified optical properties for bulk TiO2 system to the 4.17% Pd-doped TiO2 and also with 4.17% Ni-doped TiO2. The optical properties hold promise to the efficient photocatalytic applications of Pd /Ni doping in TiO2.

Computational methods

To examine the impacts of doping with Pd on the electronic structure of TiO2, the calculations were performed using the VASP [14] code based on first principles density functional theory. The ground-state structure optimization and the corresponding electronic properties calculations were performed based on the Perdew–Burke–Ernzhof (PAW-PBE) exchange–correlation functional [20] under the Generalized Gradient Approximation (GGA) [3]. For calculations, cutoff energy for the plane-wave basis set was set to be 550 eV after convergence analysis. The ground-state structure optimization for the Brillouin zone of the supercell was performed by a (3 × 3 × 3) Monkhorst–Pack K-point mesh whereas for electronic properties calculation a higher mesh of (5 × 5 × 5) and were used. The optical programs were carried out separately with (6 × 6 × 6) K-Points. As shown in Fig. 1, we have used a (2 × 1 × 1) anatase supercell of TiO2 consisting of 8 Platinum and 16 Oxygen atoms to construct the doped structures, where one Ti atom is replaced by one, Pd/Ni atoms, corresponding to a doping concentration of about 4.17% to study the optical properties of the doped TiO2. To explicitly treat the valence electrons of Ti (3d2 4s2), O (2s2 2p4), Pd (5s04d10) and Ni (3d8,4s2), the projected augmented wave (PAW) method is used. Both pristine Ti8O16 and substitutional doped Ti8−xO16Pd/Nix (x = 1) structures along with lattice parameters and ionic positions were fully relaxed so that energies and forces reached convergence values. The criterion of electronic convergence in the self-consistent field was 10–7 eV and the force convergence was set to be 0.001 eV/Å.

Fig. 1
figure 1

The optimized structures of Ti8O16 supercell with impurity of 4.17% Ni. Colour: Blue: Ti, Red: Oxygen, Violet: Ni

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Optical properties

To evaluate optical properties of Pd- and Ni-doped supercells of TiO2, the dielectric tensor is calculated following Kubo–Greenwood type formula, where the imaginary part of the dielectric tensor is the sum over occupied and unoccupied bands of the dipole matrix elements, neglecting local field effects [9].

The frequency-dependent dielectric matrix is calculated after the electronic ground state has been determined. The dielectric function which is sum of the real and imaginary part can be expressed as,

$$\varepsilon \left( \omega \right) = \varepsilon_{1} \left( \omega \right) + i\varepsilon_{2} \left( \omega \right),$$
(1)

where \(\varepsilon_{1} \left( \omega \right)\) and \(\varepsilon_{2} \left( \omega \right)\) are the real and imaginary parts of the complex dielectric function.

The imaginary part \({\varepsilon }_{2},\) is derived by summing over conduction bands as,

$$\varepsilon _{{\alpha \beta }}^{2} \left( \omega \right) = \frac{{4\pi ^{2} e^{2} }}{\Omega }\lim _{{q \to 0}} \frac{1}{{q^{2} }}\sum\limits_{{c,v,k}} {2\omega _{k} } \delta \left( {\varepsilon _{{ck}} - \varepsilon _{{vk}} - \omega } \right)\left\langle {{u_{{ck + e_{{\alpha q}} }} }} \mathrel{\left | {\vphantom {{u_{{ck + e_{{\alpha q}} }} } {u_{{vk}} }}} \right. \kern-\nulldelimiterspace} {{u_{{vk}} }} \right\rangle \left\langle {{u_{{ck + e_{{\beta q}} }} }} \mathrel{\left | {\vphantom {{u_{{ck + e_{{\beta q}} }} } {u_{{vk}} }}} \right. \kern-\nulldelimiterspace} {{u_{{vk}} }} \right\rangle ^{*} .$$
(2)

Here, c and v refer to conduction and valence band. \({u}_{ck}\, {\mathrm{and}\, u}_{vk}\) are the cell periodic parts at k-point \(k\). E is the electronic charge \(.\Omega\) is the unit cell volume and \(\omega\) the plasma frequency. \(\varepsilon\) k is the single particle energy. The factor 2 comes from the summation over the spin. The \({e}_{\alpha q,}\, \mathrm{and}\, {e}_{\beta q}\) vectors are unit vectors for the three Cartesian directions. ωk is weight of k-Point vector.

From the imaginary part of the dielectric tensor component, the corresponding real part which is obtained from Kramers–Kronig relation can be expressed as,

$$\varepsilon_{\alpha \beta }^{1} \left( \omega \right) = 1 + \frac{2}{\pi }P\int\limits_{0}^{\infty } {\frac{{\varepsilon_{\alpha \beta }^{2} \left( {\omega^{^{\prime}} } \right)\omega }}{{\omega^{^{\prime}2} - \omega^{2} + i\eta }}} {\text{d}}\omega^{^{\prime}} ,$$
(3)

where P is the principal value of the integral.

Then, other energy-dependent optical parameters can be determined using these obtained values of \({\varepsilon }_{1}(\omega )\) and \({\varepsilon }_{2}\left(\omega \right).\) The reflectivity \(R\left(\omega \right),\) absorption coefficient \(\alpha \left(\omega \right),\) refractive index \(\eta \left(\omega \right),\) energy loss spectrum \(L\left(\omega \right),\) and extinction coefficient \(\kappa (w)\) are evaluated as,

$$R\left( \omega \right) = \left| {\frac{{\sqrt {\varepsilon_{1} \left( \omega \right) + j\varepsilon_{2} \left( \omega \right)} - 1}}{{\sqrt {\varepsilon_{1} \left( \omega \right) + j\varepsilon_{2} \left( \omega \right)} + 1}}} \right|^{2}$$
(4)
$$\alpha \left( \omega \right) = \sqrt 2 \, \omega \left[ {\sqrt {\varepsilon_{1}^{2} \left( \omega \right) + \varepsilon_{2}^{2} \left( \omega \right)} - \varepsilon_{1} \left( \omega \right)} \right]^{\frac{1}{2}}$$
(5)
$$\eta \left( \omega \right) = \frac{{\left[ {\sqrt {\varepsilon_{1}^{2} \left( \omega \right) + \varepsilon_{2}^{2} \left( \omega \right)} + \varepsilon_{1} \left( \omega \right)} \right]^{\frac{1}{2}} }}{\sqrt 2 }$$
(6)
$${\text{L}}\left( \omega \right) = \frac{{\varepsilon_{2} \left( \omega \right)}}{{\left[ {\varepsilon_{1}^{2} \left( \omega \right) + \varepsilon_{2}^{2} \left( \omega \right)} \right]}}$$
(7)
$$\kappa \left( \omega \right) = \left[ {\frac{{\sqrt {\varepsilon_{1}^{2} \left( \omega \right) + \varepsilon_{2}^{2} \left( \omega \right)} - \varepsilon_{1} \left( \omega \right)}}{2}} \right]^{\frac{1}{2}} .$$
(8)

Results and discussion

It has been studied that Pd doping shows steady decrease of bandgap as dopant concentration increases, while Ni doping shows metallic nature developing as Ni dopant concentration increases.

In this section, we discuss the various electronic and optical studies of Ni-doped TiO2. Figures 1 and 2 show the optimized tetragonal structures of TiO2 doped with 1Ni atom and 1 Pd atom, respectively. In the following discussion, we report the electronic structures of these doped structures.

Fig. 2
figure 2

Optimized structures of (2 × 1 × 1) Supercell of TiO2 doped with 4.17% Pd atom. Colour: Blue: Ti, Red: Oxygen, Violet: Pd

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Electronic Structure of Ni-doped TiO2

The electronic density of states for 4.17% doped TiO2 [Ti7O16 Ni] [6] shows a distinct valence band consisting of predominantly O 2p orbitals and the conduction band dominated by Ti 3d orbitals. The Fermi level is closer to the valence band and there is a distinct band gap seen. The conduction band shows presence of Ni 3d orbitals in the 1 eV region well hybridizing with the O 2p and Ti 3d orbitals. The peaks are distinct and the orbitals are far apart.

Electronic structure of Pd-doped TiO2

The tetragonal shaped anatase TiO2 belongs to the space group I41/amd (141). In the anatase structure, every Ti atom is octahedrally bonded to six O atoms where four Ti–O bonds are shorter at 1.93 Å, while the other two Ti–O bonds are longer at 1.98 Å [19]. The Total density of states of the Pd-doped TiO2 supercells have been reported [5]. It was shown that as doping Pd atoms increase in the TiO2 supercell, the band gap narrowing occurs.

Optical properties of Ni and Pd-doped TiO2.

Both Pd and Ni doping cause absorbance edge to be shifted to the visible region compared to the pure TiO2.

Absorption coefficient

In Fig. 3, we have compared optical properties of 4.17% Pd-doped TiO2, Ni-doped TiO2 and pure TiO2. We know the pure TiO2 form mostly absorbs in the UV range of the spectrum and its spectra here begins from 2 eV as seen in the figure.

Fig. 3
figure 3

Absorption spectra of TiO2 doped with 1Pd/1Ni and Pure TiO2

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Upon doping with Pd, the absorption edge is being shifted toward the visible region and the doped structure show significant peaks in the visible spectrum. The maximum absorption in the visible region is around 1.2 × 105 cm−1 in the energy region 0.5–1.5 eV predicting that photocatalytic properties of Pd-doped TiO2 will prevail in the visible region. Though the absorption coefficient for pure system is higher in UV region compared to the visible region, the Ni-doped TiO2 shows high absorption of 1 × 105 cm−1 in the visible region also. Hence we can state that visible light absorption is enhanced with Ni doping in TiO2 although the intensity is lower than that of pure TiO2 in UV region.

Electron energy loss spectra of Ni- and Pd-doped TiO2

The electron-energy loss spectrum as in Fig. 4 shows interesting details regarding the intensities of the Plasmon peaks at around 30 eV. The Ni-doped TiO2 shows much decreased intensity compared to Pd-doped TiO2, whereas pure TiO2 shows maximum intensity.

Fig. 4
figure 4

Electron-energy spectrum of Ni, Pd and Pure TiO2

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Hence, we conclude that Ni-doped TiO2 is more dense and crystalline in structure or metallic compared to Pd-doped and pure TiO2 structures.

Extinction coefficient of Ni- and Pd-doped TiO2

From Fig. 5, we see that extinction coefficients are lower for the doped Ni- and Pd-doped TiO2 compared to the bulk TiO2, indicating that pure TiO2 has lower light absorption. Doping with Ni and Pd increases the light absorption or reduces decay of light.

Fig. 5
figure 5

Extinction coefficient of Ni, Pd and Pure TiO2

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Reflectivity of Ni- and Pd-doped TiO2

The reflective properties of the TiO2 structures are given in Fig. 6. The pure TiO2 shows better reflectivity in the region around10eV. However, in UV–Visible regions (< 6 eV), all three structures show similar reflectivity. The Ni-doped TiO2 shows a slightly higher reflectivity than the Pd-doped and pure TiO2. In the higher energy 15–50 eV range, the reflectivity are greatly lowered.

Fig. 6
figure 6

Reflectivity of Ni, Pd and Pure TiO2

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Refractivity of Ni- and Pd-doped TiO2

The refractive indices are illustrated in Fig. 7. The Ni-doped TiO2 shows a slightly higher refractive index of around 3 compared to the Pd-doped and pure TiO2, indicating that Ni-doped TiO2 has greater thickness compared to other structures.

Fig. 7
figure 7

Refractive Index of Ni, Pd and Pure TiO2

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Conclusions

Pd-doped TiO2 has higher absorption coefficient compared to pure TiO2 in the visible region. We predict that optimum Pd doping concentration has successfully altered the electronic and optical properties of TiO2 to yield an efficient visible light photocatalyst. The optical properties affirm that Ni doping enhances absorption in visible region although with lower intensity compared to that of pure TiO2 in UV region. Ni-doped TiO2 exhibit higher reflectivity and refractivity than Pd-doped TiO2. Hence, we conclude the enhancement in visible light photocatalytic activity and conduction ability of Ni-doped TiO2 which can have many photocatalytic and optoelectronic applications.