Optical constants, dispersion energy parameters and dielectric properties of ultra-smooth nanocrystalline BiVO4 thin films prepared by rf-magnetron sputtering

Solid State Sciences 33 (2014) 58e66

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Optical constants, dispersion energy parameters and dielectric properties of ultra-smooth nanocrystalline BiVO4 thin films prepared by rf-magnetron sputtering S. Sarkar, N.S. Das, K.K. Chattopadhyay* Thin Film and Nanoscience Laboratory, Department of Physics, Jadavpur University, Kolkata 700 032, India

a r t i c l e i n f o

a b s t r a c t

Article history: Received 20 March 2014 Received in revised form 16 April 2014 Accepted 19 April 2014 Available online 28 April 2014

BiVO4 thin films have been prepared through radio frequency (rf) magnetron sputtering of a prefabricated BiVO4 target on ITO coated glass (ITO-glass) substrate and bare glass substrates. BiVO4 target material was prepared through solid-state reaction method by heating Bi2O3 and V2O5 mixture at 800
C for 8 h. The films were characterized by X-ray diffraction, UVeVis spectroscopy, LCR meter, field emission scanning electron microscopy, transmission electron microscopy and atomic force microscopy. BiVO4 thin films deposited on the ITO-glass substrate are much smoother compared to the thin films prepared on bare glass substrate. The rms surface roughness calculated from the AFM images comes out to be 0.74 nm and 4.2 nm for the films deposited on the ITO-glass substrate and bare glass substrate for the deposition time 150 min respectively. Optical constants and energy dispersion parameters of these extra-smooth BiVO4 thin films have been investigated in detail. Dielectric properties of the BiVO4 thin films on ITO-glass substrate were also investigated. The frequency dependence of dielectric constant of the BiVO4 thin films has been measured in the frequency range from 20 Hz to 2 MHz. It was found that the dielectric constant increased from 145 to 343 at 20 Hz as the film thickness increased from 90 nm to 145 nm (deposition time increased from 60 min to 150 min). It shows higher dielectric constant compared to the literature value of BiVO4. Ó 2014 Elsevier Masson SAS. All rights reserved.

Keywords: BiVO4 Thin film Sputtering Dielectric constant Optical constants

1. Introduction Bismuth vanadate (BiVO4) has been attracted more and more attention, not only because it is a non-toxic yellow pigment widely used in the pigment industry [1] but also because of its many other interesting performances, such as, photochromic effect, ionic conductivity, and so on [2e6]. Tucks et al. have investigated its photochromic effect and found impurities like Fe and Pb cause intense photochromism [5,6]. In the recent past BiVO4 material has gained much more attention in the field of photo catalysis because of its good photocatalytic performance for water splitting [7,8], O2 evolution [9,10] and degradation of organic pollutant under visible light irradiation [11,12]. These various interesting properties have forced scientists to focus on the synthesis and characterization of this material. Different wet chemical methods have been developed for the preparation of BiVO4 material, such as chemical vapor deposition [13], hydrothermal treatment [14,15], sonochemical method

* Corresponding author. Tel.: þ91 33 2413 8917; fax: þ91 33 2414 6007. E-mail address: [email protected] (K.K. Chattopadhyay). http://dx.doi.org/10.1016/j.solidstatesciences.2014.04.008 1293-2558/Ó 2014 Elsevier Masson SAS. All rights reserved.

[16], metalorganic decomposition [17], solution combustion synthesis [18], micro-emulsion synthesis [19], and mild hydrothermal method [20]. Properties of BiVO4 are strongly dependent on its morphology and crystal phase. It is commonly believed that the performance of an inorganic material depends on its morphological characteristics, such as shape and size. Different kinds of nano\microstructures [21e25] of BiVO4 have been synthesized and characterized by different groups but there are very few reports on the synthesis and characterization of BiVO4 thin films. Li et al. [26] have prepared BiVO4 thin films by ultrasonic spray pyrolysis and studied its photochemical properties. Xie et al. [27] have synthesized monoclinic BiVO4 thin films by citrate route for its photocatalytic application under visible light. But there are no reports on the synthesis of BiVO4 thin films by sputtering technique and its optical and dielectric properties in thin film form. The rfmagnetron-sputtering method is the major industrial process due to its high deposition rate, high volume, large area uniformity and smoothness of the fabricated films. There has been a lot of interest in bismuth vanadates’s optical and dielectric properties for which good optical quality films are necessary which can be fabricated by rf-magnetron sputtering.

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In the present work, we have fabricated ultra-smooth BiVO4 thin films on ITO-glass substrates by rf-magnetron-sputtering technique for the first time and mainly focused on its optical and dielectric properties. As mentioned earlier, there are very few reports on the preparation on BiVO4 thin films but no report has been made to study the thickness dependent detailed optical and dielectric properties of BiVO4 thin films. Therefore, such a study would be important to develop interesting technological optical devices. In this paper, we report the film thickness dependent changes in structural, optical and dielectric properties. We also have made attempts to provide the in-depth information about various optical and dielectric properties of such an interesting material. 2. Experimental details 2.1. Target preparation for sputtering BiVO4 powder was prepared by means of a conventional solidstate reaction method. As a starting material 3.495 g (0.0075 mol) of Bi2O3 (Finar Regents: purity > 99.9%) was mixed and grinded with 1.365 g (0.0075 mol) of V2O5 (Loba Chemie: purity > 99.9%) in a mortar and pestle for half an hour. The stoichiometric mixture was then heated at 800
C for 8 h in air to obtain the BiVO4 nanocrystalline powder. BiVO4 targets were fabricated by taking a suitable aluminium holder (5 cm diameter) and by compacting polycrystalline BiVO4 powders by applying suitable hydrostatic pressure (z100 kg/cm2). The fabricated targets were placed in the radio frequency magnetron-sputtering chamber for the deposition of nanocrystalline thin films on ITO-glass and bare glass substrates. 2.2. Film synthesis Sputtering is a well-known and one of the most versatile techniques for the deposition of good-quality thin films. Compared with other techniques, the sputtering process produces films with high purity and better controlled composition, provides films with greater adhesive strength and better homogeneity and permits better control of film thickness. Normally for polycrystalline thin film synthesis, sputtering is performed at a lower gas pressure z103 mbar and suitable higher substrate temperature. This would allow the adatoms on the substrate enough mobility for growing bigger crystallites. But for nanocrystalline film synthesis the pressure has been increased to z101 mbar to increase the scattering probability of the ejected target materials with the plasma neutrals, etc. between the electrodes. The films were synthesized at room temperature and the substrates used were ITO-glass substrate and bare glass substrate. Prior to sputtering, the chamber was evacuated by a conventional rotary and a diffusion pump combination to a base pressure of 2  106 mbar. Before starting the actual deposition the target was pre-sputtered in order to remove the surface impurities of the target materials, if any, and the substrates were covered by a movable shutter. The sputtering was performed at different deposition times (60, 105 and 150 min) keeping the other deposition parameters constant as shown in Table 1. For transmission electron microscopic measurements the scratched film was dispersed in ethanol and ultrasonicated for 30 min and then dropwise casted on the carbon coated copper grids.

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Table 1 Deposition parameters used for rf-magnetron sputter deposited BiVO4 thin film. Deposition parameters

Corresponding values

1. 2. 3. 4. 5. 6. 7.

Varied from 60 min to 150 min (180e10) W 3.5 cm Argon (Ar) 0.1 mbar ITO-glass and bare glass S300 K

Deposition time Rf-power (incidentereflected) Electrode distance Sputtering gas Gas pressure Substrates used Substrate temperature

(l ¼ 0.15406 nm), operated at 40 kV and 40 mA. The morphology of the BiVO4 thin films was studied with a field emission scanning electron microscope (FESEM, Hitachi-S4800), while the nanostructures of the films were studied by a transmission electron microscope (HRTEM, JEOL-JEM 2100). UVevis spectrophotometric measurements were performed by using a spectrophotometer (Shimadzu UV-3101 PC) at room temperature. The spectra were recorded by taking a similar ITO-glass as reference and hence the transmission due to the film only was obtained. To study the dielectric properties, thin aluminum film was deposited on the BiVO4 thin films sputtered on ITO-glass substrate. The details of the characterization result are discussed below. 3. Results and discussion 3.1. X-ray diffraction studies X-ray diffraction patterns of the BiVO4 powder (target material) and the BiVO4 thin films sputtered on ITO-glass and bare glass substrates for different time durations are shown in Fig. 1(a) and (b), respectively. It has been reported that three different crystalline phases of BiVO4 can be formed by using different synthesis methods. In our experiment, all the diffraction peaks were indexed to monoclinic BiVO4 (m-BiVO4, JCPDS cards no.75e2480), suggesting the successful single phase synthesis of m-BiVO4 on ITO-glass and bare glass substrates. Our results are consistent with the films prepared by the metalorganic decomposition (MOD) method [28] and hybrid organiceinorganic precursor route [29]. The information on strain (ε) and the particle sizes (L) of the deposited films have been obtained from the following relations [30]:

b cos q 1 ε sin q ¼ þ l l L

(1)

where b is the full-width-at-half-maximum (FWHM) of the diffraction peaks. The slope of the bcosq/l versus sinq/l graph (not shown) depicts the strain values which lie in the range 1.42  102e1.13  102 and the intercept on y-axis gives the crystallite size which lie in the range 5e13 nm. Fig. 1(c) shows the variation of particle size and strain with film thickness (measured from cross-sectional FESEM Images: film thickness 90, 125 and 145 nm is obtained for deposition time 60, 105 and 150 min, respectively) of the BiVO4 thin films. It is clear from the plot that the crystallite strain decreases with the increase in film thickness of the BiVO4 thin films. The particle sizes of 5, 10 and 13 nm were obtained for the BiVO4 films of thickness 90, 125 and 145 nm deposited on ITO-glass substrate for 60, 105 and 150 min, respectively.

2.3. Characterization 3.2. Nanostructural studies The deposited films were characterized by studying mainly structural, optical and dielectric properties. For structural study an X-ray diffractometer (Bruker Advance D8) was used. XRD patterns were measured in 2q range 20e70
using CuKa radiation

FESEM images of the synthesized BiVO4 thin films are shown in Fig. 2(a) and (b). Fig. 2(a) shows the surface topography of the BiVO4 thin films deposited for 150 min on ITO-glass substrate, while

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Fig. 1. X-ray diffraction patterns of BiVO4 thin films sputtered on (a) ITO-glass substrate, (b) bare glass substrate and (c) variation of particle size and strain with film thickness of the BiVO4 thin films on ITO-glass substrate.

Fig. 2(b) shows the morphology of the BiVO4 film deposited on bare glass substrate for 150 min. The BiVO4 film thickness of the rf deposited films on ITO-glass substrates was measured from crosssectional scanning electron microscopy images (not shown here) and average thickness was found in the range 90, 125 and 145 nm for the sputtering deposition time 60, 105 and 150 min, respectively. The nanostructures of the BiVO4 thin films were studied also at room temperature by using a transmission electron microscope

(TEM). The TEM micrographs of BiVO4 thin films on ITO-glass substrate have been shown in Fig. 2(c) and (d). Fig. 2(c) and (d) shows the TEM micrograph of BiVO4 thin films sputtered on ITOglass for 60 and 150 min, respectively. From TEM micrographs we obtained the diameter of the particles lying in the range of 5, 9 and 12 nm for the variation of film thickness 90, 125 and 145 nm, respectively. AFM images are shown in Fig. 3(a) and (b) of the BiVO4 thin films deposited for 150 min on ITO-glass and bare glass

Fig. 2. FESEM images of BiVO4 thin films sputtered on, (a) ITO-glass substrate for 150 min; (b) bare glass substrate for 150 min; TEM images of BiVO4 thin films sputtered on ITOglass substrate for (c) 60 min and (d) 150 min.

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Fig. 3. AFM images of BiVO4 thin films sputtered on, (a) ITO-glass substrate and (b) bare glass substrate for 150 min.

substrate, respectively. The rms surface roughness calculated from the AFM images comes out to be 0.74 nm and 4.2 nm for the films deposited on the ITO-glass substrate and bare glass substrate for the deposition time 150 min respectively, which validates our claim of extra-smooth BiVO4 thin film on ITO-glass substrate. 3.3. Optical absorption and band gap To determine the optical properties, transmittance (T) and reflectance (R) data have been recorded. Fig. 4(a) and (b) represents the spectral variation of transmittance and reflectance of the same films deposited on the ITO-glass substrates. Transmission data has been recorded in the wavelength range of 250e800 nm. Absorption coefficient (a) has been calculated using the relation

a ¼


 1 1R ln d T

(2)

where d is the film thickness. The band gap energies (Eg) of the BiVO4 thin films were determined from the (ahn)1/n versus wavelength traces. The fundamental absorption, which corresponds to electron excitation from the valence band to the conduction band, can be used to determine the nature and value of the optical band gaps. The relation between the absorption coefficient (a) and the incident photon energy (hn) can be written as [31]

  ðahnÞ1=n ¼ A hn  Eg

(3)

where A is a constant, Eg is the band gap energy of the material, and the exponent n depends on the type of the transition. The values of n for direct allowed, indirect allowed and direct forbidden transitions are n ¼ 1/2, 2, and 3/2, respectively. To determine the possible transitions, (ahn)1/n versus hn were plotted, and the corresponding band gaps were obtained by extrapolating the steepest portion of

the graph on the hn axis at (ahn)1/n ¼ 0. Fig. 5(a) shows the (ahn)2 versus hn plots to determine direct band gap energies. The direct band gap energies, lying in the range 3.30e3.41 eV, of the BiVO4 thin films on ITO-glass substrate is higher than that of the reported literature value of band gap energy of BiVO4 microstructures (2.9 eV) [11] due to the smaller particle sizes in the rf sputtered BiVO4 thin films. The indirect band gap energies are obtained from the (ahn)1/2 versus hn plots as shown in Fig. 5(b). The indirect band gap energies lye in the range 2.75e2.82 eV which is also higher than that of the reported literature value of 2.2 eV due to the same reason of smaller particle sizes in the rf sputtered films. The variation of direct and indirect band gap energies of the BiVO4 thin films on ITO-glass substrate with different film thickness is shown in Fig. 6. It is clear from the figure that both the direct and indirect band gap energies increase with the decrease in film thickness (particle size). This may be attributed to the quantum confinement effect put forward by Brus [32] where the size dependency of the band gap of a semiconductor nanoparticle (Eg[nano]) is given by the formula

DE ¼ Eg½nano  Eg½bulk ¼

h2 1:8e2  L 2   L  8m* 2 ε

(4)

2

where DE is the shift of the band gap with respect to the bulk band gap Eg[bulk], L/2 is the radius of the nanoparticles, m* [33] is the reduced mass of electronehole effective masses, and ε is the semiconductor dielectric constant. The first term of the right-handside expression in the equation represents the particle-in-a-box quantum localization energy and has a 1/L2 dependence for both electron and hole. The second term represents the Coulomb energy with an 1/L dependence. Change in band gap energies of different films having different particle sizes have been calculated and the differences in the band gap energies of different films have been tabulated and compared with the experimental value in Table 2.

Fig. 4. Variation of (a) transmission and (b) reflectance with wavelength of BiVO4 thin films of different thickness deposited on ITO-glass substrates.

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Fig. 5. Plot to determine (a) direct band gap and (b) indirect band gap energies of the BiVO4 thin films sputtered on ITO-glass substrates.

where R is the reflectance of the film and l is the wavelength of the incident light wave. Fig. 7(a) shows the film thickness dependent change in refractive index, n of the BiVO4 thin films as a function of wavelength of the incident beam. It is observed that the dispersion curve of refractive index decreases with increasing wavelength. The refractive indices at wavelength of 300 nm are 1.94, 1.96 and 2.03 for the film thickness of 90, 125 and 145 nm, respectively, which are comparable to the reported literature values of 2.1 at 2.95 eV (420 nm) [34]. The variation in extinction coefficient k is shown in Fig. 7(b) as a function of wavelength and the film thickness. The lowest value of extinction coefficient, 3.8  102 for the 90 nm thick BiVO4 film in the visible region indicates the better surface homogeneity of deposited BiVO4 thin films [35]. 3.5. Optical conductivity Fig. 6. Variation of direct and indirect band gaps of BiVO4 thin films of different thickness sputtered on ITO-glass substrates.

3.4. Optical constants It can be mentioned that one of the most important optical constants of a material is refractive index, which generally depends on the wavelength of electromagnetic wave through a relationship called dispersion. In addition to dispersion, an electromagnetic wave propagating through medium experiences attenuation, due to a number of loss mechanisms such as the generation of lattice waves (phonons), free carrier absorption, photo generation and scattering. In these materials, the refractive index turns out to be a complex function of the frequencies of incident light waves. The complex refractive index, denoted by n*, with real part n, and imaginary part k, called the extinction coefficient (total optical losses caused by both the absorption and the scattering wave) can be calculated using the following relations:

n ¼

k ¼

 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  1þR 4R þ  k2 1R ð1  RÞ2

(5)

al

(6)

4p

Table 2 Comparison of calculated and experimental band gap energy shift with particle size.

DE ¼ Eg[5 nm]  Eg[12 nm] DE ¼ Eg[9 nm]  Eg[12 nm]

Calculated shift in band gap energy (meV)

Experimental shift in band gap Direct (meV)

Indirect (meV)

92 58

110 80

70 30

The optical conductivity of a material means the electrical conductivity in the presence of an alternating electric field. The optical conductivity (sop) can be determined using the following relation [31]:

sop ¼

anc 4p

(7)

where c is the velocity of light. The variation in optical conductivity a (sop) as a function of photon energy (hn) is shown in Fig. 7(c). The optical conductivity varies from 4.4  1013 to 1.4  1014 s1 for the BiVO4 film of thickness 145 nm and the values of optical conductivity is lesser for the films of lower thickness at a particular wavelength. As it evident from Fig. 7(c) that the value of optical conductivity is w1013 for all the film thickness, this may be due to the excitation of electrons by photon energy [36]. The optical conductivity of material depends directly on the absorption coefficient and therefore the sop is found to increase sharply for higher energy values due to large absorption coefficient. The similar observation was reported for different materials [37,38], which indicates that the contribution of electron transitions between the valence and conduction bands increases with increasing film thickness of the BiVO4 thin films. 3.6. Electronic polarizability The electronic polarizability ap of BiVO4 thin films can be calculated using the ClausiuseMossotti local-field polarizability model [39] from the relation

  2 n 1 Nr ap ¼ 2 3M n þ2

(8)

where N is the Avogadro’s number, r is the density of BiVO4 material, and M is molecular weight. The dependence of (n2  1)/(n2 þ 2) on

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Fig. 7. Variation of (a) refractive index, (b) extinction coefficient of BiVO4 thin films with film thickness as a function of wavelength; (c) optical conductivity and (d) (n2  1)/(n2 þ 2) of the BiVO4 thin films as a function of photon energy.

incident photon energy is shown in Fig. 7(d). From the extrapolation of linear region towards (n2  1)/(n2 þ 2) axis, the electronic polarizability ap values have been calculated and the values are 1.20  1022,1.28  1022 and 1.30  1022 for the 90,125 and 145 nm thick films. These values obtained for a are quite high compared to the other materials. Generally, polarizability increases as volume occupied by electrons increases. In our case, the electronic polarizability of BiVO4 films increases with increasing deposition time, which may be due to the increase in volume of the electrons. This should be noted that the thickness of deposited film increase with increasing deposition time, which in effect increases the volume and volume available by the electrons of BiVO4 thin films. This is consistent with the evaluation of electronic polarizability.

3.7. Dielectric constants It may be mentioned that the fundamental electron excitation spectrum of thin film is related with the frequency-dependent complex electronic dielectric constant (ε ¼ ε1þiε2). The real part of dielectric constant (ε1) is responsible for slowing down the speed of light in the material, whereas the imaginary part (ε2) is responsible for the energy absorption from electric field due to dipole motion [40]. The real and imaginary parts of electronic dielectric constants, ε1 and ε2 are connected with n and k values and can be calculated using the following equations [41]:

ε1 ¼ n2  k2 ε2 ¼ 2nk

(9) (10)

The dependence of ε1 and ε2 values on wavelength of the incident light is, respectively, shown in Fig. 8(a) and (b). The values of ε1 vary between 3.66 and 4.13 and ε2 from 0.26 to 0.27 for the variation of film thickness from 90 to 145 nm at a wavelength of 280 nm. It is observed from Fig. 8(a) and (b) that the real and imaginary parts of dielectric constants increase with the increase in film thickness indicating the improvement in optical response (i.e., reduction in

the energy dissipative rate of the incident light wave) with film thickness. 3.8. Volume and surface energy loss function It can be mentioned that the characteristic energy losses experienced by the fast moving electrons in passing through a material are due to the excitation of plasma oscillations in the sea of conduction electrons as suggested by Pines and Bohm [42]. The energy loss is related to the optical properties of the material through the dielectric function. The probability that the fast electrons will loss energy when traveling the bulk and the surface of the material is defined as the volume and surface energy loss functions [43]. The energy loss functions: volume energy loss function (VELF) and surface energy loss function (SELF) are related to real and imaginary parts ε1 and ε2 of the complex dielectric constant by the following relations [44]:

VELF ¼

SELF ¼

ε2 ε21 þ ε22 ε2 ðε1 þ 1Þ2 þ ε22

(11)

(12)

The variation of volume and surface energy losses of BiVO4 thin films of different thickness, as a function of photon energy are shown in Fig. 8(c) and (d), respectively. The values of VELF are 1.78  102, 2.13  102 and 2.15  102 for the film thickness of 145, 125 and 90 nm, respectively, at a wavelength of 300 nm. Similarly, the values of SELF are 1.13  102, 1.32  102 and 1.32  102 for the films of thickness 145, 125 and 90 nm, respectively, at a wavelength of 300 nm. Moreover, it is clear from the Fig. 8(c) and (d) that the volume energy loss is greater than the surface energy loss at any incident photon energies. 3.9. Dielectric loss tangent (tand) The variations of tand with frequency are shown in Fig. 9(a). Considering the equivalent circuit shown in the inset of Fig. 9(b),

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Fig. 8. Plot of (a) ε1, (b) ε2, (c) VELF and (d) SELF versus wavelength of BiVO4 thin films with different thickness on ITO-glass substrate.

similar to that proposed by Goswami and Goswami [45], where the equivalent circuit comprises a frequency-dependent capacitive element Cp in parallel with a resistive element Rp, both in series with a low value resistance Rs, and the loss tangent is given by

tan d ¼



   uCp Rp þ uCp Rp 1 þ Rs Rp

(13) 1

In this equation, at low frequencies the term u is dominant and at high frequencies the term u is dominant. Therefore, this

equation predicts a decrease in tand at low frequencies followed by a loss minimum and again an increase in tand at high frequencies. In the present investigation, the observed frequency dependence of tand is quite consistent with those predicted by the equivalent circuit model, described above. The BiVO4 films show minimum of tand at 25, 120 and 400 kHz for the films of thickness 90, 125 and 145 nm, respectively. Abu-Hilal et al. [46] have observed a minimum in tand versus f curves in ZnPc semiconducting thin films. Shihub and Gould [47] have reported decreasing values of tand with

Fig. 9. Dependence of (a) dielectric loss on frequency, (b) ColeeCole plots of Z00 versus Z0 , RC equivalent circuit is shown in the inset. Variation of (c) imaginary impedance, Z00 , (d) real impedance, Z0 with frequency for the BiVO4 thin films of different thickness on ITO-glass substrates.

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frequency 20 Hz for different BiVO4 thin films on ITO-glass substrate. The dielectric constant values are much higher than that of the reported value of dielectric constant 42 in the literature [24]. 4. Conclusions

Fig. 10. Variation of Dielectric Constant with frequency of BiVO4 thin films with different thickness sputtered on ITO-glass substrates.

increasing frequency in CoPc thin films with no indication of a minimum, probably due to the limited frequency range of 100 Hze 20 kHz used. Choudhary and Bhunia [48] have shown a decrease in tand with increasing frequency tending towards a constant value, in case of ACu3Ti4O12 (A ¼ Ca, Sr and Ba). 3.10. Impedance spectroscopy Fig. 9(b) shows the ColeeCole plots of Z0 versus Z00 (where Z0 and Z00 are the real and imaginary parts of the complex impedance, respectively) of the BiVO4 thin films on ITO-glass substrate over the frequency region from 20 Hz to 2 MHz. These plots are single semicircular arcs with their centers lying below the real axis. The finite value of distribution parameter F and a depressed arc are typical for a material with multi-relaxation processes [49]. Also, the arcs have a non-zero intersection with the real axis in the high frequency region. Furthermore, there occurs a reduction in the size of these plots with the decrease in film thickness. Bose et al. [50] have studied the room temperature complex impedance spectra for nanocrystalline SnO2 samples and observed the impedance spectra as depressed single semicircular arcs for different samples corresponding to their grain boundaries. Similar results have also been observed for the spray deposited films of ZnO [51] and the solution grown films of CuInSe2 [52]. A single arc is an indicative of a single parallel RC element [53], as shown in the inset of Fig. 9(b). Here, the small resistance value Rs is attributed to the core of the BiVO4 grains, in accordance with the generally accepted view, while Rp and Cp are attributed to the grain boundary effect. Considering the equivalent circuit model, the values of Z0 and Z00 are given by

Z 0 ¼ Rs þ Rp

.

 1 þ u2 Cp2 R2p

(14)

and

Z 00 ¼ uCp R2p

.

 1 þ u2 Cp2 R2p

(15)

Fig. 9(c) and (d) shows the spectra of Z00 and Z0 versus frequency. The frequency umax at which Z00 is maximum is given by umax ¼ 1/ RPCP ¼ 1/s, where s is the relaxation time. The variation of the dielectric constant as a function of frequency for the BiVO4 thin films with different film thickness on ITO-glass substrate is shown in Fig. 10. It has been observed that the values of the dielectric constant lie in the range 145e343 at

BiVO4 thin films have been synthesized by rf-magnetron sputtering of a BiVO4 target material on ITO-glass substrate and bare glass substrate. X-ray diffraction studies confirmed pure phase synthesis of these BiVO4 thin films on ITO-glass substrate. BiVO4 thin films on ITO-glass substrates are extra smooth with rms surface roughness less than 0.74 nm. Direct and indirect band gap energies were found to vary in the range 3.30e3.41 eV and 2.75e 2.82 eV, respectively, for BiVO4 thin films with different thickness on ITO-glass substrates. Optical constants and energy dispersive parameters have been studied in the entire range of visible light. Dielectric properties of the BiVO4 thin films on ITO-glass substrate were investigated and it was found that the dielectric constants varied from 145 to 343 (at 20 Hz) for the variation of film thickness as well as particle size. Acknowledgment The authors wish to thank the University Grants commission, The Govt. of India (F-1-10/12(NSPE)), for the financial assistance under the ‘University with potential for excellence (UPEII)’ scheme. The authors are also grateful to the Department of Science and Technology, the Govt. of India (SR/S2/CMP-0063/2010) for financial assistance. References [1] M.C. Nevesa, M. Lehockyc, R. Soaresb, L. Lapcik, T. Trindadea, Dyes Pigments 59 (2003) 181e184. [2] J.D. Bierlein, A.W. Sleight, Solid State Commun. 16 (1975) 69e70. [3] A. Pinczuk, B. Welber, F.H. Dacol, Solid State Commun. 29 (1979) 515e518. [4] T.H. Yeom, S.H. Choh, Phys. Rev. B 53 (1996) 3415e3421. [5] A. Tucks, H.P. Beck, J. Solid State Chem. 178 (2005) 1145e1156. [6] A. Tucks, H.P. Beck, Dyes Pigments 72 (2007) 163e177. [7] I. Akihide, H.N. Yun, I. Yoshimi, K. Akihiko, A. Rose, J. Am. Chem. Soc. 133 (2011) 11054e11057. [8] H.N. Yun, I. Akihide, K. Akihiko, A. Rose, J. Phys. Chem. Lett. 1 (2010) 2607e 2612. [9] W. Zhiqiang, L. Wenjun, Y. Shicheng, F. Jianyong, Z. Zongyan, Z. Yisi, L. Zhaosheng, Z. Zhigang, Cryst. Eng. Commun. 13 (2011) 2500e2504. [10] K. Lai, Y. Zhu, J. Lu, Y. Dai, B. Huang, Solid State Sci. 24 (2013) 79e84. [11] Y. Wenzong, W. Wenzhong, Z. Lin, S. Songmei, Z. Ling, J. Hazard. Mater. 173 (2010) 194e199. [12] U.M. García-Pérez, S. Sepúlveda-Guzmán, A. Martínez-de la Cruz, Solid State Sci. 14 (2012) 293e298. [13] A.L. Esther, C. Le, H. Mark, M. Neeka, Y. Lin, J. Ali, W.A. Joel, Phys. Chem. Chem. Phys. 16 (2014) 1651e1657. [14] M. Xue, et al., Mater. Chem. Phys. 125 (2011) 59e65. [15] H. Jiang, H. Dai, J. Deng, Y. Liu, L. Zhang, K. Ji, Solid State Sci. 17 (2013) 21e27. [16] L. Wei, et al., Ultrason. Sonochem. 17 (2010) 669e674. [17] A. Galembeck, O.L. Alves, J. Mater. Sci. 37 (2002) 1923e1927. [18] H.K. Timmaji, W. Chanmanee, D.N.R. Tacconi, K. Rajeshwar, J. Adv. Oxid. Technol. 14 (2011) 93e105. [19] W. Liu, et al., Sci. China Chem. 54 (2011) 724e729. [20] J.B. Liu, H. Wang, S. Wang, H. Yan, Mater. Sci. Eng. B 104 (2003) 36e39. [21] S. Sarkar, K.K. Chattopadhyay, Phys. E 58 (2014) 52e58. [22] H. Fan, D. Wang, L. Wang, H. Li, P. Wang, T. Jiang, T. Xie, Appl. Surf. Sci. 257 (2011) 7758e7762. [23] S. Dong, C. Yu, Y. Li, Y. Li, J. Sun, X. Geng, J. Solid State Chem. 211 (2014) 176e 183. [24] S. Sarkar, K.K. Chattopadhyay, Phys. E 44 (2012) 1742e1746. [25] K. Shantha, K.B.R. Varma, Mater. Sci. Eng. B 56 (1999) 66e75. [26] M. Li, L. Zhao, L.G. Liejin, Int. J. Hydrogen Energy 35 (2010) 7127e7133. [27] B. Xie, C. He, P. Cai, Y. Xiong, Thin Solid Films 518 (2010) 1958e1961. [28] K. Sayama, A. Nomura, T. Arai, T. Sugita, R. Abe, M. Yanagida, T. Oi, Y. Iwasaki, Y. Abe, H. Sugihara, J. Phys. Chem. B 110 (2006) 11352e11360. [29] F. Rullens, A. Laschewsky, M. Devillers, Chem. Mater. 18 (2006) 771e777. [30] S.B. Quadri, E.F. Skelton, D. Hsu, A.D. Dinsmore, J. Yang, H.F. Gray, B.R. Ratna, Phys. Rev. B 60 (1999) 9191e9193.

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