Introduction

Titanium dioxide (TiO2)-based heterostructures make use of a narrow band gap semiconductor and noble metal nanostructures (Chen and Mao 2007; Liu et al. 2010; Wang et al. 2010) to spread the light-response range to the visible region and improve the charge separation and transfer properties of micro-optical devices for photo-electro-catalysis (Lee et al. 2016). These novel heterostructures combine different electronic properties of the constituent materials and promote photo-catalytic efficiency as compared to the single-phase TiO2 photo-catalyst (Baker and Kamat 2009; Tada et al. 2006; Zhang et al. 2008). The TiO2 nanorods show better charge transport properties compared to the TiO2 NP-based mesoporous layer (Kim et al. 2013a). Noble metal nanoparticles (NPs) on the surface of TiO2 nanorods (NRs) can improve the photo-catalytic properties in mainly two ways: (A) the deposited noble metal nanoparticles behaves as an electron trap and enhances electron-hole separation to improve the quantum yield (Lidia et al. 2007; Paramasivam et al. 2008; Zhang et al. 2008), (B) surface plasmon resonance (SPR) effect, which occurs due to the collective and coherent electronic oscillations on the noble metal nanoparticles through visible light irradiation. These effects can enhance the localized electric field in the vicinity of the metal nanoparticles, which helps in the interaction of the localized electric fields with a neighbouring semiconductor and allows the facile formation of electron-hole (e−-h+) pairs in the near-surface region of the semiconductor/metal nanoparticle interface (Awazu et al. 2008; Ingram and Linic 2011; Thimsen et al. 2011; Xu et al. 2010). Recently, the localized surface plasmon resonance (LSPR) effects of Au-NPs and other metal nanostructures have been used to boost the photo-electrochemical properties and attracted wide research attention due to their possible application in micro-optical (Feng et al. 2016; Sun et al. 2015; Zhang et al. 2016) and photo-catalytic devices (Erwin et al. 2016; Huang et al. 2016; Lee et al. 2016). Multi-core flat fibre structure-based surface plasmon resonance sensor has been demonstrated by Rifat et al. (2016), which indicated a possibility of integrated SPR sensor as a lab-on-a-chip for the real-time diagnostic purpose. Awazu and Linic have used the plasmon enhanced photo-catalytic mechanism by isolating Ag NPs using SiO2 and poly (vinylpyrrolidone) (PVP) as shells, respectively (Awazu et al. 2008; Ingram and Linic 2011). Liu et al. (2011) proposed an effective plasmon coupled photo-catalyst for splitting H2O molecules under visible light by integrating Au NPs with doped TiO2 nanotubes. The literature indicates that the plasmon resonance wavelength and intensity strongly depends on the size and shape of NPs, inter-particle spacing, and dielectric property of the surrounding medium (El-Sayed 2001; Feldstein et al. 1997; Feng et al. 2011; Lin et al. 2005; Rycenga et al. 2011).

In recent research, noble metal NPs, such as Pt (Xu et al. 2007a; Zhou et al. 2003), Pd (Liang et al. 2009; Qi et al. 2014), Ag (Fu et al. 2015; Liang et al. 2011) and Au (Chen et al. 2012; Cherevko et al. 2012), exhibited good catalytic activity for electro-oxidation and became the most common catalysts (Jin et al. 2016). Meanwhile, many efforts have been made to improve the activity and stability of noble metal NPs, such as development of NPs with specific surface structure (Cui et al. 2011; Qi et al. 2014; Xu et al. 2007b) and with different alloying contents (Dutta et al. 2011; Oliveira et al. 2011; Wang et al. 2014; Zhu et al. 2012). In addition, photo-electro-catalysis has attracted much attention because of the outstanding LSPR properties, which improve the catalytic activity of noble metal NPs (Hutter and Fendler 2004). The recombination of photo-generated hot electrons and holes reduces the effect of LSPR (Wang et al. 2012; Wu et al. 2011). This recombination can be reduced by combining noble metal NPs with semiconductors to transfer the excited hot electrons into the conduction band (CB) of the adjacent semiconductor, which is defined as plasmon-induced charge separation (Bian et al. 2013; Tian and Tatsuma 2005) and has been proved to be beneficial for electro-oxidation (Murdoch et al. 2011; Tian and Tatsuma 2005; Xu et al. 2011). Since light illumination enhances the electro-oxidation activity, a periodic nanostructure consisting of noble metallic catalysts to enhance the incident light harvesting may be a promising method (Kim et al. 2013b). The vertically aligned titania nanorods (TiO2-NRs) can be more beneficial for plasmon induced photo-catalysis due to one-dimensional facile charge transfer possibility (Raval et al. 2016). However, there are few attempts towards explaining these aspects of the metal nanostructures to enhance the plasmon resonance energy to improve the photo-catalytic activities of semiconductor materials (Long et al. 2017; Yen et al. 2017).

This article reports the hydrothermal synthesis of TiO2-NRs with and without gold nanoparticles on their surface. These samples have been characterized by X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM) and amperometric measurements. It is observed that the Au-NPs significantly improve the photo-catalytic response of TiO2-NRs, which has been explained through a quantum mechanical approach. Theoretical calculations have been done to explore the extinction efficiency of the Au-NPs on TiO2-NRs.

Theoretical description

Band diagram and electron transfer

The charge carriers gain energy through LSPR under visible light irradiation at Au/TiO2 interface and get transferred to the conduction band of TiO2 from the gold NPs as shown in Fig. 1. It can be understood from Fig. 1 that the Au-NPs mainly act as a sensitizer, which absorb incident photons and generate the energetic hot electrons due to the process of the LSPR excitation. The highly energetic hot electrons get injected into the CB of the adjacent TiO2-NRs (Zhang et al. 2012). Resonant Au-NPs exhibit optically induced oscillating electrostatic potential under illumination with respect to the wavelength of incident light (van de Groep et al. 2016). The excess electron density in the conduction band of TiO2-NR plays a role in the photo-response of the TiO2-NR/Au-NP system (Reineck et al. 2016). The transmission probability of generated hot electrons in Au-NPs through the potential barrier of TiO2-NR can be calculated using Eqs. (1–6) (Ghatak 2010) under following assumptions: (1) Junction existing in between Au-NP and TiO2-NR material acts as a potential barrier, (2) Fermi energy levels of Au-NP and TiO2-NR remain aligned during photon interaction with potential barrier.

$$ \frac{\partial^2{\varPsi}_1(x)}{\partial {x}^2}+{k}_1^2{\varPsi}_1(x)=0,x<0\kern0.5em \mathrm{Designated}\ \mathrm{as}\ \mathrm{region}\ 1\ \left(\mathrm{Au}\hbox{-} \mathrm{NP}\right) $$
(1)
$$ \frac{\partial^2{\varPsi}_2(x)}{\partial {x}^2}+{k}_2^2{\varPsi}_2(x)=0,\kern0.5em x>0\kern0.5em \mathrm{Designated}\ \mathrm{as}\ \mathrm{region}\ 2\ \left({\mathrm{TiO}}_2\hbox{-} \mathrm{NR}\right) $$
(2)

where,

$$ {k}_1^2=\frac{2{mE}_0}{{\mathrm{\hslash}}^2},{k}_2^2=\frac{2m\left({E}_0-V\right)}{{\mathrm{\hslash}}^2},\mathrm{m}=9.1\times {10}^{-31}\mathrm{kg},\mathrm{\hslash}=\frac{h}{2\pi }=1.054\times {10}^{-34} Js. $$
Fig. 1
figure 1

Schematic diagram to represent physical processes in Au-NP/TiO2-NR-based device

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The solutions of Eqs. (1) and (2) represent the wave functions of electron on the Au-NP and TiO2-NR side as given by:

$$ {\varPsi}_1={Ae}^{-{jk}_1x}+{Be}^{jk_1x} $$
(3)
$$ {\varPsi}_2={Ce}^{-{jk}_2x} $$
(4)

Under following boundary conditions:

  1. 1)

    The wave function is continuous at the interface, i.e. Ψ1(0) = Ψ2(0), which implies that A + B = C from Eq. (3).

  2. 2)

    The first derivate of the wave function is continuous i.e. \( \frac{\partial }{\partial x}{\varPsi}_1(0)=\frac{\partial }{\partial x}{\varPsi}_2(0) \), which implies that \( \mathrm{A}-\mathrm{B}=\frac{k_2}{k_1}\ C\kern0.5em \)from Eq. (4).

From these expressions transmission (T) and reflection (R) probability of electrons from Au-NPs through the TiO2-NRs potential barrier can be calculated using following equations:

$$ T={\left|\frac{B}{A}\right|}^2={\left|\frac{k_1-{k}_2}{k_1+{k}_2}\right|}^2 $$
(5)
$$ R=\left|\frac{C}{A}\right|\frac{k_2}{k_1}=\frac{4{k}_1{k}_2}{{\left|{k}_1+{k}_2\right|}^2} $$
(6)

Extinction efficiency calculations

The diameter of the particle must be well below the wavelength of light. The scattering and absorption cross section are given by (Bohren and Huffman 2007):

$$ {C}_{scat}=\frac{1}{6\pi }{\left(\frac{2\pi }{\lambda}\right)}^4{\left|\alpha \right|}^2 $$
(7)
$$ {C}_{abs}=\frac{2\pi }{\lambda}\mathit{\operatorname{Im}}\left[\alpha \right] $$
(8)

where, \( \alpha =3V\left[\frac{\upvarepsilon_p/{\upvarepsilon}_m-1}{\upvarepsilon_p/{\upvarepsilon}_m+2}\right] \) denotes polarizability of the particle. Here, V denotes particle volume (a function of particle radius), εp denotes the dielectric function of the particle, and εm denotes the dielectric function of the embedding medium. This expression shows that the scattering cross section depends on the NP size, and as a result, more fraction of light is scattered towards the medium with a higher refractive index. This is clearly observed by enhanced absorption as shown in Fig. 2, the Au-NPs attached TiO2-NR layer is higher as compared to bare TiO2-NRs. However, when the size of Au-NP increases beyond threshold limit, the phase retardation effect dominates (Westcott et al. 2002) and higher order multipole excitation modes (quadrupole, octupole) result in the decreased efficiency of the scattering process(Bing et al. 2010). The size of Au-NP could be optimized by controlling the thickness of the Au thin film during the deposition process and followed by temperature. The extinction efficiency (Qext = Cscat/S + Cabs/S, S being an effective area of scattering particle) of Au-NPs is calculated using Mie theory(Tripathi et al. 2013) and shown in Fig. 3. The plasmon extinction evolves with the increase in the size of Au-NPs, which is in accordance with the existing literature (Huang and El-Sayed 2010; Jain et al. 2006). The increase in particle size leads to an increased contribution from Mie scattering.

Fig. 2
figure 2

Optical characterization of TiO2-NR and Au-NP/TiO2-NR. Inset a Diffuse reflectance of TiO2-NR and Au-NP/TiO2-NR. Inset b Transmittance of Au-NP on glass substrate

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Fig. 3
figure 3

Extinction (Qext) of Au nanoparticles on TiO2-NR

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The incident light is lost through the sample surface by radiative and non-radaitive mechanisms. The scattering efficiency, Qsca quantifies radiative loss and absorption efficiency, Qabs quantifies non-radiative loss. These losses are included in the extinction efficiency, Qext, which effectively includes Qsca and Qabs, and can be calculated for spheres much smaller than the wavelength using the well-known Mie theory (Bohren and Huffman 2007).

Experimental section

Synthesis of materials

Fluorine-doped tin oxide (FTO) coated glass substrate (7 Ω/square, Sigma-Aldrich) substrates were used to grow TiO2-NRs. A stainless steel autoclave of 50 mL capacity with Teflon lining has been used for the hydrothermal synthesis of TiO2 nanorods. In a typical synthesis step, 15 mL of 37% hydrochloric acid was added in the 15 mL of deionized water and sonicated for 5 min. Subsequently, 0.4 mL of titanium (IV) isopropoxide (Ti(OCH(CH3)2)4, 97%, Sigma-Aldrich) was added and further sonication did for 5 min. FTO glass substrates (1.5 cm × 1.5 cm) were placed inside the Teflon (melting point: 326.8 °C) liner with the active layer facing the wall for TiO2-NR deposition. The prepared precursor solution was then poured into an autoclave containing the substrates. The reaction time duration was set to 2 h and the process temperature was 230 °C. After completing the hydrothermal process, the autoclave was left to naturally cool down to room temperature. The substrates were taken out from the autoclave, rinsed thoroughly, and annealed at 300 °C in air prior to use. For depositing Au, a gold target (99.9%) (2-in. diameter, 3 mm thickness) has been used in RF/DC pulsed magnetron (10 kHz, duty cycle: 50%) sputtering system (Millman, Pune). Argon gas was injected with the constant flux of 50 sccm while maintaining working pressure at8 × 10−2 mbar during the entire coating process. The sputtering of Au is done at an applied voltage of 350 V. The process current is measured to be ~ 40 mA for 1-min time duration and temperature was close to 450 °C. All the samples were annealed (1 h), in a vacuum, after film deposition. The samples cooled down freely in vacuum before their removal to room conditions (Raval et al. 2016).

Morphological, structural and optical characterization

The morphological, structural and optical properties of TiO2-NRs were examined by field emission scanning electron microscopy (FE-SEM, ULTRA55, Zeiss), energy dispersive spectrometer (EDS, Model: X-Max, Make: OXFORD), atomic force microscopy (Nanosurf Easycan 2), X-ray diffraction (XRD, X’Pert Pro, PANalytical) in the 2θ range of 20–80° and diffuse reflectance spectroscopy (UV 2600, Shimadzu) respectively.

Electrochemical characterization

For the electrochemical measurements, a working electrode (TiO2-NR with and without Au-NPs in either case) and a platinized FTO as a counter electrode were placed in fixed positions in the testing cell with 0.5 M KOH electrolyte solution. A calibrated LED light source with an intensity of 20 mW/cm2 with an optical chopper was placed between the light source and the photo-electrode for the photocurrent measurement. The photocurrent density was determined with the stable output signals from the test cell connected to the potentiostat (CHI-660D) without any applied bias (See Supplementary Information for more details).

Results and discussion

Structural analysis

Figure 4 shows the X-ray diffraction (XRD) spectrum of the hydrothermally grown TiO2-NRs on FTO glass substrates, where the diffraction peaks are identified as the rutile phase according to JCPDS 21-1276 card. Generally, rutile TiO2 powder containing randomly oriented crystals show a higher (110) diffraction intensity as can be seen in the JCPDS reference of Fig. 4, which is similar to the reported data for the rod-shaped rutile TiO2 nanoparticles (Park et al. 1999). However, in the present case Fig. 4 the (101) diffraction intensity is highest, whereas the (110) peak intensity is comparatively low. This deviation in the intensity for the rutile TiO2-NRs has been confirmed by other researchers also (Kim et al. 2013a). An intense (101) peak along with the enhanced (002) peak for the TiO2-NR layer shows that the rutile crystal grows with (101) plane parallel to the FTO glass substrate and the nanorods are aligned with the (002) direction (Kim et al. 2013a; Nayak et al. 2012; Zhang and Liu 1998). The XRD pattern for the gold nanostructures is shown in Fig. 4, which illustrates prominent peaks corresponding to the (111), (200), (220) planes of face centered cubic (FCC) crystal structure of Au. This result is in agreement with the existing data for gold nanoparticles (JCPDS card number-04-0784) (Zhao et al. 2014). The peak intensity from (111) plane is higher than the other peaks, which confirms the presence of NPs. The preferred orientation in XRD pattern leads to spherical morphology as confirmed from FE-SEM image (Fig. 6) e.

Fig. 4
figure 4

XRD pattern for TiO2-NR on FTO and Au-NPs. JCPDS 77-0452 corresponds to crystallographic planes of FTO. JCPDS 21-1276 corresponds to crystallographic planes of TiO2. JCPDS 04-0784 corresponds to crystallographic planes of Au

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Morphological and elemental analysis

The morphology of the bare TiO2-NRs and Au-NPs incorporated with TiO2-NRs has been investigated by FE-SEM and corresponding images are shown in Fig. 5a. The TiO2 layer prepared by hydrothermal method with subsequent heat treatment at 230 °C for 2 h, exhibit nanometre size NRs morphology. FE-SEM images of Au-NP incorporated TiO2-NRs are shown in Fig. 5b. The TiO2-NR layer has porous morphology, wherein the pores are several hundred nanometres wide as observed in the FE-SEM images top-view of Fig. 5a. The diameter of TiO2-NR is in the range of 80 ± 5 nm Fig. 5a. Figure 5b shows Au-NPs deposited over TiO2-NR layer. The inset of Fig. 5b shows the size distribution of the Au-NPs. Au-NPs of 15 nm size with a variation of ± 10 nm are observed. The cross-sectional image of combined TiO2-NRs and Au-NPs layer deposited on FTO coated glass substrate is shown in Fig. 5c. The thickness of FTO layer is estimated to be 293 ± 10 nm, thickness of TiO2 seed layer is 700 ± 10 nm and thickness of TiO2-NRs layer is 2241 ± 10 nm from Fig. 5c. The EDS of the Au-NPs/TiO2-NRs confirms presence of Au, Ti, O as shown in Fig. S1 in Supplementary Information. The detailed profile elemental analysis was done cross-sectional through EDS for Au-NPs/TiO2-NRs as shown in Fig. 5d. In Fig. 5d, the blue curve shows approximate concentration (in %) of oxygen with respect to the cross sectional thickness, green curve shows approximate concentration (%) of titanium and red curve shows approximate concentration (%) of gold. Region I shows a higher percentage of Au than TiO2 and confirms that the Au-NPs are on the top of each NR as it is also seen in top view in Fig. 5b. In Fig. 5d, region II shows a higher percentage of TiO2 than Au over that thickness range. Au percentage decreases in region II to zero, which confirms that there is no direct contact between FTO layer and Au-NPs. Region III shows titanium rich seed layer. Figure 5d clearly distinguishes different layer concentration over different thickness range. The size distribution of Au-NPs is shown in Fig. 6 (FE-SEM image of Au-NP coated TiO2-NRs). The morphological characterization has been carried out by atomic force microscopy (AFM). The AFM has been performed in the tapping mode using a Nanosurf Easyscan2 system. The AFM images have been recorded at different positions with a scan area of 500 × 500 nm2. The Au NP/TiO2 NR layer morphology is shown in Fig. 6a. Figure 6b shows height distribution of Au-NP decorated on hydrothermally grown TiO2-NR on FTO substrate. The AFM micrograph displayed a uniform distribution of a granular TiO2-NR structure which is consistent with a high-quality and pin-hole free, smooth and crack-free surface as reported by other researchers (Sciancalepore et al. 2008). The histogram of the layer represents the hills corresponding to its average height (nm) distribution. A topographical analysis of the film is also shown in Fig. 6c–d in a 3D view. The 3D view of TiO2-NR and TiO2 NR/Au-NP with a color scale bar shows vertically oriented TiO2-NRs and Au-NPs.

Fig. 5
figure 5

FESEM and EDS characterization. a Top view of the TiO2-NRs. b Au-NPs on TiO2-NRs with size distribution. c Cross-sectional view of the TiO2-NRs. d Elemental cross-sectional profile distribution of Ti, Au, O in Au/TiO2 sample

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Fig. 6
figure 6

Atomic force microscopy of a TiO2-NR/Au-NP morphology. b Height distribution of TiO2-NR/Au-NP. A topographical 3D view of c TiO2-NR and d TiO2-NR/Au-NP. e FE-SEM image of Au-NPs/TiO2-NRs showing the distribution of Au-NPs

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Optical analysis

UV-vis analysis

In Fig. 2, the results of UV-Vis spectroscopic measurements are presented. The absorbance spectra are plotted with respect to the wavelength of incident radiation for a bare TiO2-NR sample and it is compared with TiO2-NR/Au-NP sample. It is seen clearly that TiO2-NR/Au-NP sample has much larger absorption in the visible range (> 400 nm) than the TiO2-NR sample. There are mainly four types of energy-transfer mechanisms in a plasmonic photocatalytic system (Linic et al. 2011) (1) transfer of a hot electron, (2) plasmon induced heating, (3) electromagnetic enhancement through near-field, and (4) resonance in photon scattering. The energy associated with plasmonic heating is significantly lower than the bandgap of TiO2-NR thus it is not a leading mechanism to increase the carrier density in the CB of TiO2-NRs (Liu et al. 2011). The resonant photon-scattering mechanism may not be prevailing mechanism in case of the Au-NP/TiO2-NRs, as it normally occurs for large plasmonic NPs (larger than ∼ 50 nm in diameter) (Burda et al. 2005; Evanoff and Chumanov 2005). Further, electromagnetic enhancement due to near-field is generally observed at wavelengths where the plasmon resonance and semiconductor absorption overlap so this is not a dominant mechanism of the charge transfer (Warren and Thimsen 2012). In the present case, the hot electron are generated by the absorption of incident radiation (hν > 0.9 eV), which is explained in next section. Hot electron transfer mechanism is responsible for the absorption enhancement and is a major contributor to improve the charge concentration in the conduction band of TiO2 which enhances the performance of the Au/TiO2-NRs-based devices under visible light illumination. The broadening of the absorption peak in the visible and near infra-red range is mainly due to the non-uniformity of Au nanoparticle size (Bian et al. 2013). The decrease in the absorbance of Au/TiO2-NRs in ultra-violet region is due to lower exposed surface of the TiO2-NRs as it is covered by Au-NPs. The reflection and transmission measurement of corresponding samples are shown in insert (A) & (B) of Fig. 2. The inset (A) of Fig. 2 shows the reduced reflection of incident radiation due to Au-NPs over TiO2-NRs. The inset (B) of Fig. 2 shows the effect of size of nanoparticles (on glass) on the transmittance of incident radiation. The arrow shows direction of decrease in the size of Au-NPs.

Electrical analysis

Quantum mechanical explanation of the electron transfer from Au-NP to TiO2-NRs

The potential step offered by the conduction band of TiO2-NRs at the Au-NP/TiO2-NR interface is shown in the Fig. 7a. The barrier height (V) is calculated from the difference of gold NP work function (ɸ, varies from 3.6 to 5.1 eV (Zhang et al. 2015) and TiO2 electron affinity (4.5 eV) (Sarkar et al. 2012). The plasmonic oscillations are responsible for an increase in the energy of free electrons of the Au-NP as a function of wavelength of incident radiation. The energy of electron (E0) is calculated in the range of 1.24 to 3.1 eV for the wavelength range of 400–1000 nm. Electron transmission probability with respect to Au-NP size and corresponding work function is shown in Fig. 7b. Due to increase in size of Au-NPs, the work function increases linearly in accordance with the equation: ɸ (eV) = 0.0304 x(nm) + 3.3786 fitted to the data available in reference (Zhang et al. 2015). Figure 7b shows that electron transmission probability increases to small extent with increase in the NPs size till 35 nm. After 35 nm, the transmission probability decreases due to increase in barrier height. Figure 7c shows the transmission probability with respect to the wavelength of incident radiation assuming complete energy transfer from the corresponding photon to the electrons in Au-NPs. With increasing wavelength, the energy associated with the photon decreases thereby decreasing the energy of the electron in Au-NP with a decrease in corresponding transmission probability.

Fig. 7
figure 7

a Excitation of electrons through the incident spectral photons with the mechanism of transfer from Au-NP to TiO2-NR and corresponding Schrodinger wave equations representing the movement of the electrons. b Electron transmission probability with respect to Au-NP size and corresponding work function. c The electron transmission probability with respect to the wavelength of incident radiation assuming complete energy transfer from the corresponding photon to the electrons in Au-NP

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Amperometric current-time analysis

The amperometric (I-t) curves shown in Fig. 8a, for a configuration given in Fig. 1 are recorded at a constant potential of 0 V with the light turning ON/OFF every 30 s. The nature of photocurrent growth and decay due to illumination has been studied with fixed light intensity throughout the experiment (20 mW/cm2). The number of photons with respect to wavelength for incident light is shown in the Fig. 8b. The current increase immediately when the light is turned on and fall back when the light is turned off. During the measurement, light is switched ON after 30th s and remains ON till 60th s, so the photocurrent starts to grow from the dark value. After attaining the highest value, the light is switched OFF at 60th s and the photocurrent instantly starts to decay and almost reaches to the initial dark value. To understand the correlation between LSPR light absorption in TiO2-NR/Au-NP system and correspondingly generated photocurrent density, incident photon-to-current-conversion efficiency (IPCE) measurements have been performed using an equipment from Opto Solar GmbH. Clearly, the TiO2-NR/Au-NP system exhibited obvious photocurrent enhancement as compared to the bare TiO2-NR in the wavelength range of 400–700 nm as shown in Fig. 8c. To analyse the behaviour of the photocurrent, the growth and decay portion of the experimental curve has been analysed separately as shown in Fig. 9. Growth current shown in Fig. 9 clearly indicates the power law relation between current and time which follows following expression (Islam et al. 2012):

$$ I(t)=A\times {\left|t-{t}_c\right|}^{\alpha } $$
(9)
Fig. 8
figure 8

a I-t (current-time) curves of TiO2-NR and Au-NP/TiO2-NR samples from amperometric measurements. b Number of photons with respect to the wavelength of incident light. c IPCE of TiO2-NR & TiO2-NR/Au-NP

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Fig. 9
figure 9

Current growth analysis for TiO2-NR and Au-NP/TiO2-NR

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The experimental data is fitted using Eq. (9) with an acceptable range of R2 from 0.7 to 0.9 as shown in Fig. 9. Here t c value is 38 and t is in time (sec). The Values of α are 0.24 and 0.21, and A is 3.14×10−7 and 7.66×10−8 for the TiO2-Au and TiO2-NR respectively. Under visible light illumination, the catalytic activity of TiO2-NRs is improved by the Au-NP plasmon-induced charge separation, which is indicated by a higher current as compared to the bare TiO2 sample.

Clearly, the TiO2-NR produced little photocurrent density, < 3 μAcm−2, which is just above the background dark current Fig. 9. As expected, a significant photocurrent density enhancement has been observed on the Au-NP/TiO2-NR, with a photocurrent density of ∼ 150 μAcm−2 under otherwise the same conditions, which is 50 times the one with the bare TiO2-NR and is much higher photocurrent density.

The much improved photocurrent density on the Au-NP/TiO2-NR relative to the TiO2-NR is attributed to enhanced electron density in the conduction band of TiO2-NRs, which boosts the catalytic performance under visible light irradiation. The enhanced photocurrent density may be further attributed to the minimization of the thermodynamic free energy of the system, which leads to an electrostatic surface potential on a resonant Au-NP, driven by an increase in the absorption Fig. 2 as a result of electron injection (van de Groep et al. 2016).

A high absorption does not always lead to high photo-catalytic efficiency. A more convincing proof of the plasmonic enhancement is the coincidence of the absorption peak of LSPR with the maximum wavelength region of apparent quantum efficiency according to available literature (Ohtani 2008). In a recent article, Kowalska et al. showed a clear correlation between the absorption spectrum and the quantum efficiency of Au/TiO2 samples (Kowalska et al. 2009; Kowalska et al. 2010). The apparent quantum efficiency is the ratio of the number of consumed electrons to the number of incoming photons (not considering the losses of photons by reflection and transmission). For small noble metal nanoparticles (typically < 60 nm), the Mie scattering is negligible compared to the absorption (Bian et al. 2013; Hodak et al. 2000). Generally, the photons penetrate a few nanometers to a few micrometers into the semiconductor photocatalyst, and thus not all are absorbed effectively. Besides, photons absorbed far below the surface of the semiconductor contribute little to the photoreaction since the generated electrons and holes need to have a long diffusion length and in TiO2 they mostly recombine before reaching the surface. So this study demonstrated the enhancement of the absorption of visible light by Au nanoparticles and its correlation with the observed photocurrent density.

Conclusions

In this work, LSPR and electron transfer behaviour of Au-NPs attached to TiO2-NRs have been studied for their optoelectronic device applications. TiO2-NRs with Au-NPs exhibited a significant photocurrent enhancement as compared to the bare TiO2-NRs. An increase in the photocurrent in amperometric studies has been explained on the basis of excess electron density in the CB of TiO2-NR due to hot electron transfer from the attached Au-NPs. The hybrid nanostructure’s deposition on the transparent substrates demonstrated in this study is suitable for versatile applications.