Correction to: Investigation of growth mechanism for highly oriented TiO2 nanorods: the role of reaction time and annealing temperature

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of TiO 2 nanoparticles with tailorable material properties like sol-gel [28][29][30][31], electrodeposition [32,33], chemical vapor deposition [34], electrochemical anodic oxidation [35], spray pyrolysis [36], template-assisted [33], chemical bath deposition [37], hydrothermal methods [38,39], and many others. Among these methods, the hydrothermal method is commonly used for synthesis of nanocrystalline TiO 2 as it offers the flexibility to attain different particle sizes and morphologies. Large-scale synthesis of TiO 2 nanoparticles with large surface area is also achievable with the hydrothermal method, hence its utilization in industrial-scale synthesis TiO 2 powders and thin films. Anderson et al. [40] reported the preparation of nanosize anatase and rutile TiO 2 by hydrothermal treatment of micro emulsions and investigated their activity for photocatalytic wet oxidation of phenol. Well-dispersed TiO 2 nano-crystals were synthesized by Yang et al. [41] using the hydrothermal methods. Rutile TiO 2 nanorods synthesized on a glass substrate at low temperature under hydrothermal condition was reported by Kakiuchi et al. [42]. Maurya et al. [43]. investigated the effect of temperature on rutile TiO 2 using the hydrolysis method and observed that the crystallinity and density of rutile TiO 2 nanocrystals increases by increasing annealing temperature. The effect of repeated annealing temperature on the TiO 2 thin film and their structural, optical and electrical properties synthesized by dip coating sol-gel method was reported by Pakama et al. [44]. The hydrothermal synthesis of TiO 2 nanocrystals in different basic pHs and their applications in dye sensitized solar cells was reported by Anajafi et al. [45].
In the present work, synthesis of nano-structured TiO 2 thin films was carried out by hydrothermal technique, wherein the influence of different deposition parameters such as growth time, reaction temperature, and the film annealing temperature on the optical, structural and morphological properties have been investigated. The optical, morphological and structural characteristics of the synthesized TiO 2 thin films are studied by using various characterization methods such as X-ray diffraction (XRD), Raman spectroscopy, scanning electron microscopy (SEM) and UV-visible spectroscopy. The goal of the present work is to understand the correlation between the deposition parameters (reaction time and annealing temperature) and the growth mechanism of TiO 2 thin films. The

Synthesis
All chemicals used in this work were analytical grade and used without further purification and treatment. For the synthesis of TiO 2 thin film, titanium (IV) butoxide (Sigma-Aldrich), hydrochloric acid (HCl), ethanol and distilled water were subjected to hydrothermal treatment. Commercially available FTO glass substrate was used for the growth of TiO 2 thin film. Titanium (IV) butoxide (5 g) was added to 10 ml HCl followed by the addition of 15 ml double distilled water. The resulting complex was then stirred at room temperature for half an hour using magnetic stirrer. The solution then transferred into locally fabricated cylindrical autoclave having dimensions 8 cm × 9 cm × 1 cm (height × diameter × thickness). The detailed structure of autoclave is schematically shown in Fig. 1. The FTO glass substrates were initially cleaned ultrasonically with double distilled water and followed by an acetone wash. Then substrates were put in ethanol solution for about 5 min. The substrates were again cleaned with double distilled water and finally given a nitrogen flush for drying. This cleaning procedure permits good adhesion of film to substrates. Then cleaned glass substrate was immersed in the solution in autoclave. After the addition of the reaction complexes and substrates, the autoclave was sealed tightly and placed in an oven at 150 °C for different reaction times ranging from 6 to 24 h for the set-I samples. The autoclave was allowed to cool naturally to room temperature. After cooling the film was taken out from autoclave and annealed at different temperature as shown in Table 1 for an hour. Two sets of films were deposited: in the first set, the TiO 2 thin films were deposited at different reaction times i.e. from 6 to 24 h by keeping other parameters (concentration of the solution, deposition temperature, and annealing temperature) constant, whereas in set-II samples, the depositions was carried out with reaction time of 20 h for all the samples, with the annealing temperature varied from 300 to 600 °C and other deposition parameters were kept constant as listed in Table 1.

Material characterization
The average crystallite size, lattice parameter, inter planner distance, and phase identification of the deposited TiO 2 thin films were carried out using X-ray diffraction (XRD) pattern recorded using (Bruker D8 Advance machine, Germany) diffractometer with Cu Kα (λ = 1.5418 Å) radiation at a grazing angle of 1° and diffraction angle (2θ) ranging from 20° to 80°. Raman spectra were recorded with Raman spectroscope (Jobin-Yvon Horibra LABRAM-HR) in the range of 200-1800 cm −1 . The spectrometer has backscattering geometry for detection of Raman spectrum with a resolution of 1 cm −1 . The excitation source was 632.8 nm line of He-Ne laser. The possibility of laser induced crystallization in the film was avoided by keeping the power of laser beam at < 5 mW. The optical bandgap of the TiO 2 films was estimated from transmittance and reflectance spectra of the films deposited on commercially available FTO glass substrates and were measured using a JASCO, V-670 UV-visible spectrophotometer in the range of 200-1100 nm. The morphological characteristics of the synthesized thin films are studied by a JEOL JSM-6360-LA and Philips XL-30 scanning electron microscope.

Computational details
The density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP) [46,47], a periodic plane wave DFT code  which includes the interactions between the core and valence elections using the Project Augmented Wave (PAW) method [48]. The calculations were performed using the screened hybrid functional as proposed by Heyd-Scuseria-Ernzerhof (HSE06) [49]. A percentage of the exact non-local Fock exchange (α = 0.25) was added to the Perdew, Burke, and Ernzerhof (PBE) functional [50] with a screening of ω = 0.11 bohr −1 applied in order to partition the Coulomb potential into long range (LR) and short range (SR) terms. An energy cut-off of 600 eV, and 9 × 9×3 and 9 × 9×1 Monkhorst-Pack k-point mesh [51], was used to sample the sample the Brillouin zone of TiO 2 bulk and (110) surface, respectively. All calculations were deemed to be converged when the forces on all atoms were less than 0.001 eV/Å. Rutile TiO 2 was modelled in the simple-tetragonal structure ( Fig. 4a) with space group (P4 2 /mnm) [52]. The optimized lattice constants were obtained at a = b = 4.598Å, c = 2.953Å, in close agreement with experimental lattice constants (a = b = 4.594 Å and c = 2.959Å) [52]. The r-TiO 2 (110) surface was created from the optimized bulk material using the METADISE code [53], which ensures the creation of surfaces with zero dipole moment perpendicular to the surface plane [54]. In order to align the energies to the vacuum level, a slab-gap model (slab thickness of 20 Å and vacuum size of 15 Å) was constructed and the corresponding electrostatic potential was averaged along the c-direction, using the Macro Density package [55][56][57], as displayed in Fig. 4(c). The work function ( Φ ), which is the minimum energy needed to remove an electron from the bulk of a material through a surface to a point outside the material was calculated as

Results and discussion
The XRD pattern of the set-I and set-II of TiO 2 thin films as described under the synthesis section are depicted in Fig. 2a,   which is due to the x-ray diffraction occurring from parallel planar layers [62]. The inter planner distance for first order diffraction is 3.26 Å, which is very well matched with the reported values (3.06 Å) in literature [63]. The increased value of inter-planer distance in the present study is attributed to the presence of residual molecules intercalated between the material layers. The estimated lattice constants for the tetragonal structure is a = b=4.6038 Å and c = 2.957 Å, which are in good agreement with the reported values in the literature [50]. The average crystallite size of TiO 2 is calculated by measuring FWHM in radian corresponding to (110) peaks by using the Scherer equation d x-ray = 0.9 cos( ) where, λ is the wavelength of diffracted radiation, θ is the Bragg angle and β is the line width (FWHM) in radians. The crystallite size of TiO 2 was found to be in the range of 23 nm to 34 nm for the film deposited at different deposition time in set I; whereas the maximum crystallite size of 26 nm was observed at 600 °C annealing temperature in set II. In hydrothermal processes, the deposition time and annealing temperature promote the crystallization process. The observed variation in the crystallite size may be due to the non-uniform lattice strain.
The Raman spectroscopy is a resourceful technique used for a fast and non-destructive investigation of a wide-range of Raman active modes of material. Shown in Fig. 3(a, b) are the Raman spectra for both sets of synthesized TiO 2 thin films. Four prominent peaks located at 143.2 cm −1 , 235.6 cm −1 , 447.1 cm −1 and 607.9 cm −1 are evident and can be assigned to Raman active mode with the symmetry of E g for rutile TiO 2 characterized by the tetragonal space group of I41/amd and A 1g , B 1g , and E g which is illustrated by the tetragonal space group of P42/mnm for rutile TiO 2 [64][65][66][67][68][69]. The two prominent maxima peaks located at 447.1 cm −1 (E g ) and 607.9 cm −1 (A 1g ) correspond to O-Ti-O bending vibrations and Ti-O stretching vibrations of monocrystalline rutile TiO 2 phase, respectively [37,67]. The observed prominent Raman shift at 235.6 cm −1 , 443 cm −1 , 610 cm −1 , corresponds to B 1g , E g , A 1g active mode of bulk rutile TiO 2 , as reported by Begun et al. [70]. Raman shift peak positions shown in the Fig. 3 are in good agreement with those reported in the literature, indicating that synthesized TiO 2 is in the rutile phase. The Raman shift peak at 235 cm −1 is attributed to compound vibration peak arising due to multiple phonons scattering process, which is also considered a Raman peak of rutile [71]. There is no observation of Raman active mode for brookite and other organic species impurity phases, which lead us to conclude that the hydrothermal method is the suitable for the synthesis of high-quality rutile TiO 2 thin films for device fabrication.
The optical properties of TiO 2 thin films grown by hydrothermal on FTO glass were investigated from UV-visible spectroscopy. Figure 4 shows the optical absorption spectra of the TiO 2 thin films synthesized using hydrothermal technique at different reaction times and at different annealing temperatures. All the samples synthesized at different reaction times and at different annealing temperatures show sharp absorption edge at 423-430 nm. It also evident from Fig. 4 that the absorption edge shifts towards lower wavelength with increasing reaction times. The shift in the absorption edge towards lower wavelength is attributed to change in the TiO 2 particle size. All the synthesized TiO 2 thin films exhibit very strong and broad UV-visible absorption, similar to the observation by Xie et al. [38,72] This characteristic is in agreement with the photo-protection function of the TiO 2 films thus formed, making them potential candidates for solar photon capture for photo electrochemical applications. The samples however, show a low absorption above 423 nm, which can be attributed to oxygen vacancy defect formation at the surface boundaries of TiO 2 [73] induced by the higher annealing temperatures. It leads to change of shape of the fundamental absorption edge of the material. As can be seen from Fig. 4, the absorption increases exponentially towards shorter wavelengths, similar to previously reported absorption spectra in the literature [74][75][76]. The optical band gap of the thin films was calculated from the dependence of the absorption coefficient (α) on the photon energy (hν) using Tauc relation: where B is Tauc's constant which is a characteristic parameter independent of photon energy, α is the absorption coefficient, h is the Planck's constant, ʋ is photon frequency, and E Tauc is the bandgap of the material. The E Tauc estimate can be deduced by plotting (αE) 2 versus E and extrapolating the linear portion of the plot to the energy axis. Figure 5 shows the (αhν) 2 versus (hν) photon energy plots for the TiO 2 thin films prepared at different reaction times and annealing temperatures. The intercept of the plotted tangent gives a good approximation of the band gap energy for this material. The band gap decreases from 2.9 to 2.8 eV when deposition time increases from 6 to 24 h. It is interesting to note that these values are smaller than the reported values of synthetic TiO 2 thin films [77][78][79]. From the absorption graph, it is confirmed that TiO 2 thin film responds the UV-visible region. The optical absorption of the synthesized sample was found between 423 and 430 nm which corresponds to the band gap of TiO 2 (2.9 eV).
We have employed first-principles DFT calculations to gain insight into the electronic structure and work function of rutile TiO 2 as the field emission properties are strongly dependent on the work function ( Φ ) of the emitter. Shown in Fig. 6 is the crystal structure of r-TiO 2 with the corresponding electronic partial density of state (PDOS). The badgap is predicted at 3.01 eV, which is good agreement with our experimental measurements and previous DFT calculations [80][81][82]. An analysis of PDOS reveals that valence band edge is composed mainly of the O-p whereas the and conduction band edge is composed mainly of Ti-d states, indicating that r-TiO 2 is a O-p-Ti-d charge transfer semiconductor, which agrees with earlier theoretical predictions [80][81][82]. The work function was obtained for the most stable (110) surface of r-TiO 2 , which was cleaved from the geometrically optimized bulk. A vacuum region of length 15 Å was used in the perpendicular direction to the r-TiO 2 (110) plane to avoid spurious interactions with its own periodic image. Figure 6c shows the structure of the r-TiO 2 (110) surface and the corresponding electrostatic potential as a function of coordinate Z (along the c-axis). The work function ( Φ ) is calculated as the difference between the potential energy of one electron between the Fermi level (E f ) and the vacuum level (E v ). The vacuum level is the potential energy, approaching a nearly constant value in the energy distributions in the vacuum region, which is obtained at 6.00 eV in the present study. The work function of the r-TiO 2 (110) surface is predicted at 5.23 eV, in excellent agreement with the values of 5.2-5.5 eV estimated from ultraviolet photoelectron spectroscopy measurements [83][84][85][86][87].
Scanning electron microscopy (SEM) is a convenient method for studying morphology and growth mechanism of the TiO 2 nanorod on the FTO substrates. In the first part, we have investigated the effect of deposition time on growth mechanism of TiO 2 nanorods whiles keeping other deposition parameters constant. Shown in Fig. 7 are the SEM images of TiO 2 films at different reaction time. It is clear from the SEM images that an increase in the reaction time leads to enhancement in the growth of TiO 2 nanorods. The TiO 2 nanorods started to grow on FTO substrate at the initial reaction time (6 h), which increased in density after 12 h and at 24 h reaction time, the growth of the TiO 2 nanorods covers almost the entire surface areas of the FTO substrate. Shown below each SEM image is the schematic of the nature of the growth process, revealing the growth initiation at 6 h, increased density and random growth after 12 h, and nearly full coverage of TiO 2 nanorods on the FTO substrate at 24 h. Although there is clear evidence of enhanced growth of TiO 2 nanorods with increasing reaction times, we could not control preferential growth orientations of TiO 2 nanorods on FTO substrate in hydrothermal synthesis. In the second part, we have focused on the annealing temperature after synthesis of TiO 2 nanorods in the hydrothermal method. The Fig. 8 shows images of TiO 2 nanorods at different annealing temperatures. We observed clear difference in the growth process of the TiO 2 nanorods at annealing temperature as 300 °C, 500 °C, and 600 °C. At 300 °C, the TiO 2 nanorod started growing in FTO substrate in spherical microstructures. The initial stage of the growth process was limited by the premature termination of the growth surface, but with increased annealing temperature, the regularly shaped particles were transformed to onset of nano-rod In schematic diagrams below the SEM images in Fig. 8, we demonstrate how theTiO 2 nanorods grow in uniform shape in a control manner. After the annealing temperature was increased to 500 °C, the TiO 2 nanorod density increased thereby showing the growth of nanorods from a point on the substrate and at 600 °C, the TiO 2 nanorods clearly look like a bunch of flowers. This demonstrates that by varying the annealing temperature we can grow TiO 2 nanorod in a control manner with flower like morphology. The TiO 2 thin films prepared by the hydrothermal technique are without pinholes and provided continuous coverage on the substrate. The uniformly formed rod-like structures of TiO 2 material makes the synthesized thin films better candidates for solar cell (DSSCs) and field emitter arrays applications. The TiO 2 thin films were characterized using AFM technique and shown in Fig. 9 are the 2-dimensional (2D) and 3-dimensional (3D) AFM images of the TiO 2 thin film at 24 h reaction time. The average roughness and root mean square (RMS) roughness for TiO 2 thin film estimated at 418 nm and 518 nm, respectively. The pointed nanorod-likeTiO 2 structures are fascinating structures and may be suitable for several applications including as field emitter arrays. We have thus investigated the field emission properties of the TiO 2 nanorods as shown in Fig. 10: (a) current density (J) versus applied field (E), (b) F-N plot, (c) current stability at 10 µA, and (d) photograph of field emission pattern. The current density (J) is defined J = I/A, where I is the emission current and A is the area of emitter. The applied field (E) is defined as E = V/d, where V is the applied voltage, and d is the separation between the anode and cathode. According Fowler-Nordheim (F-N) theory, in J-E plot, the emission current from surface of emitter varies as exponentially [88]. TiO 2 nanorods J-E plot showing exponential function. The electron emission quantum tunneling turn on and threshold field were found to be 4.06 and 7.06 V/µm at emission current densities of 10 and 100 µA/cm 2 respectively of TiO 2 nanorods. These values suggest that better turn on field of TiO 2 nanorods are recorded as compared to the ones reported in literature [89][90][91]. We have obtained the maximum current density of the TiO 2 nanorods to be 168 µA/cm 2 at an applied field of 7.35 V/µm. The F-N plot of TiO 2 nanorods defined by ln(J/E 2 ) versus 1/E ( Fig. 10(b)) shows a non-linear behavior, which is consistent with the semiconductors nature of the TiO 2 emitter. The emission current stability is very important for practical applications as cold cathode. The emission current (I) versus time (t) plot of the TiO 2 nanorods at 10 µA remained fairly stable for more than 3 h as shown Fig. 10c. The observed fluctuations and spikes in emission current may be due to the adsorption or desorption of residual gas atoms/molecules on the surface of TiO 2 nanorod emitter in the presence of applied field. The field emission of TiO 2 nanorods patterns is shown Fig. 10d with the tiny bright spots representing electron emission from protruding sites of TiO 2 nanorods on the fluorescent screen as electron collector.

Conclusion
Large-area, very dense, and pin-hole free TiO 2 nanorod thin films were successfully synthesized by a simple and cost effective hydrothermal method. The effect of reaction times and annealing temperatures on the growth mechanisms (size and shape) of the TiO 2 nanorods was systematically studied. The TiO 2 nanorods are demonstrated to grow randomly on the FTO substrate with changing reaction times but grow uniformly in a flower-like pattern with increasing annealing temperature. Recorded X-ray diffraction patterns, UV-VIS spectra, and Atomic force microscope images showed that the crystallinity in TiO 2 thin films is significantly affected by increasing annealing temperature. The optical properties investigated experimentally and further corroborated with first-principles density functional theory calculations show the TiO 2 thin films have high absorption coefficient and a direct bandgap in the range 2.8-3.0 eV, which is slightly smaller than the bandgap of bulk rutile TiO 2 . The TiO 2 nanorods exhibit moderate field emission properties and have turn on field of 7.35 V/μm and good field emission stability. These results indicate that TiO 2 nanorods thin films may be promising candidates for applications in electron-emitting nano devices.