Dielectric relaxation and current conduction mechanism of Tb and Mn codoped bismuth ferrite grafted poly (vinyl alcohol) nanocomposite film

Investigation on current conduction mechanism through Tb and Mn codoped Bismuth Ferrite grafted polyvinyl alcohol (BTFMO-PVA)nanocomposite filmabove room temperature (300 K – 415 K) is reported here in detail. A detailed study on dielectric properties of the sample is done over a wide temperature range in a frequency range of 20Hz 2MHz. The conduction is attributed to correlated barrier hoppingmodel. Bipolaronhoppingdominates over single-polaron hopping in this system. Complex electric modulus spectra and complex modulus spectra are well explained by suitable models to understand the effective dielectric response. The sample responds to the externally applied magnetic field exhibiting negative magnetocapacitance at room temperature.


Introduction
Research on the development and the characterization of polymer composites with ferro-, pyro-, piezo-electric properties are very much in trend for showing unique electromagnetic responses [1]. The inclusion of nano-sized fillers in a polymer matrix element can enhance the multifunctional properties of the host polymer. A proper combination of nanofiller and polymer improves the physical, optical, electrical, and magnetic properties [2]. For the enhancement in the charge conduction mechanism of the polymer nanocomposite system, semiconductor type ma-terials are generally used. Due to the accumulation of charge at the grain boundaries, interfacial polarisation plays a role in controlling the charge conduction mechanism of the composite system. Under suitable conditions, nanocomposite films prepared by drop-casting or sol-gel processes show better molecular interaction between the nanofiller and the polymer [3]. Out of many polymers, polyvinyl alcohol (PVA) is a widely used matrix element due to its non-toxicity, significant electrical properties, flexibility, reasonable tensile strength, and functional charge storage capacity [4]. In this work, we have focused on multiferroic-polymer nanocomposite. Recently many researchers are going on with this type of composite due to its multifunctionalities [5]. The dielectric/magnetodielectric response, charge conduction mechanism in the polymer matrix can be significantly affected by the insertion of multiferroic nanofiller. In our previous work, we have discussed the current conduction mechanism of BiFeO 3 (BFO) nanofiller inserted PVA nanocomposite film [6]. Enhancement in current conduction was achieved in BFO-PVA film than the pristine PVA film. Bismuth Ferrite is a very relevant multiferroic as it simultaneously exhibits ferroelectric and antiferromagnetic properties at room temperature [7]. Here, Tb and Mn codoped BiFeO 3 (BTFMO) nanoparticles are dispersed in PVA matrix. Enhancement of electrical, magnetic properties has been reported with the doping of other ions at A or B site of Bismuth ferrite [7]. Meanwhile, the space charge polarisation induced by the dopants can act as additional dipoles [8].
The present article reports the charge conduction mechanism and dielectric relaxation, magneto-dielectric response, the interfacial polarisation of the film sample in the temperature range between 300 K to 415 K. Here, frequency-dependent electrical modulus spectroscopy, complex admittance spectroscopy, and complex impedance spectroscopy of the sample are studied to get the idea about the charge conduction mechanism through the materials. Variation of current with the application of voltage is also considered. These spectroscopic studies of the conduction mechanism is first time reported for the present nanocomposite film.

Experimental Details
2.0 wt% of BTFMO (Bi 0.95 Tb 0.05 Fe 0.95 Mn 0.05 O 3 ) nanofillers are grafted in prepared polyvinyl alcohol (PVA) solution. DI water is taken as a solvent for PVA solution. By the drop-casting method, the solvent is evenly poured on a clean glass petri dish at room temperature. After natural drying for 7 days, the thin nanocomposite film is achieved by detaching it from the substrate (petri dish). For achieving a thin uniform film thickness (< 100 µm), little amount (15 ml) of BTFMO-PVA solution is poured on an even surface. In the present work, the wet film thickness was~600 µm which produced 95 µm thick dry thin film (measured from FESEM image). The detailed experimental procedure is reported earlier [9].
The film sample is morphologically examined usinf field emission scanning electron microscopy (ZEISS EVO-MA 10). Before testing, the sample is coated with a thin layer of gold to avoid the electrical charging during the examination. Here, the current conduction mechanism of the film is studied elaborately in the temperature range 300 K -415 K. For measuring the electrical properties, a parallel plate configuration is prepared by pasting silver (Acheson Colloiden B. V Holland) electrodes on both sides of a small square portion (average thickness 0.095±0.001 mm and area 10×10 mm 2 ) of the film sample. The temperaturedependent AC electrical measurements and dielectric response are studied in the frequency range 20 Hz -2 MHz with Agilent E 4980A precision LCR meter using a furnace fitted with 8502 Eurotherm temperature controller cryostat in temperature range 300 K -415 K. Room temperature magneto-dielectric response is measured using an electromagnet (EM-250). The current-voltage (I-V) characteristics are measured with a two-probe system of Keithley 2450 source measure unit (SMU) equipped with KickStart software.

Results and Discussions
The digital image of the thin nanocomposite film is given in Figure 1   given in Figure 1 (c). It is observed that the nanocomposite displays a homogeneous and smooth surface morphology quite similar to the pristine PVA film [ Figure 1 (b)]. Only the nanofillers appear to be rougher and containg bigger grains out of the PVA matrix. It can be also demonstrated that the nanocomposite possesses a good degree of dispersion of the nanofiller. The overall surface roughness is very low showing crack/kink free smooth surface. Figure 2 (a) presents the Arrhenius fittings of the temperature dependence of AC electrical conductivity [log of (σac) versus 1000/T at different frequencies (500 KHz, 800 KHz, 1M Hz, 1.5 MHz, & 2 MHz). These plots show that at lower temperatures, electrical conductivity increases with increasing frequency. In PVA, dielectric α-transition occurs as the existing flexible polar groups rotate with frequency. From the literature survey, it is observed that dielectric behaviour of PVA undergoes α-relaxation process at~360 K. The dielectric α-transition associates with the glass transition temperature, Tg. In the present investigated film sample, the glass transition temperature (Tg) is found to be around 348 K. Here, micro-Brownian motion along the main chain in the amorphous regions and the segmental motion within the crystalline phase of PVA nanocomposite occur [10,11]. Due to the change in the chemical composition and the formation of chargetransfer-complexes (CTCs) in PVA chains, the electrical conductivity enhances [12]. As the temperature rises, the conductivity dispersion region is reduced. The temperature dependence of σac is stronger at low frequencies than at relatively higher frequencies. This suggests that the conductivity is a thermally activated charge transport process from different localised states. This properties of a material is governed by Arrhenius equation as follows, where σ 0 is a conductivity exponential factor, E A is the AC activation energy for mobile ions, and k B is the Boltzmann's constant. The activation energy values are listed in Table 1. The existence of multiple activation energies from each curve indicates different current conduction mechanisms inside the sample. Multiple activation energies for the conduction and the relaxation may be due to the fact that the relaxation process involves only the hopping energy of the carriers between the localised states, but the conduction mechanism involves the hopping energy as well as the disorder and binding energy of polarons [13]. At lower temperature regions, the activation energy decreases with the increase in frequency. Lower values of the obtained activation energy confirm the applicability of hopping conduction mechanism in the nanocomposite system [14]. Further, we have studied the variation of total measured conductivity with frequency. The total conductivity obeys Jonscher's power law named as Universal Dielectric Response (UDR) as follows [15,16], where σ dc is the DC conductivity, α is a temperaturedependent constant which depends on the intrinsic properties of a material, and S is a power law exponent. S represents the measure of correlation between the nanofiller particles and the polymer matrix. For UDR, S ≤ 1. The values of S are ascertained from the linear variation of ln σ ′ (f , T) vs. ln f plot [shown in Figure 2 (b)]. With increasing temperature, frequency independent behaviour is found to be dominant. At higher frequency, long range movement of mobile charge carriers is dominant. The deviation from σac value in low frequency region is due to the electrode polarisation. The dispersion of σac at lower temperature possibly suggests the accumulation of space charge in the material and it vanishes at higher temperature and frequency. The value of σ dc increases with the increase in temperature because the thermally activated drift mobility of ions increases according to the hopping conduction mechanism. The values of 'S' as a function is shown in the inset of Figure 2 (b). Different models have been proposed to explain the conduction mechanism on the basis of the parameter S. If S is temperature independent, quantum mechanical tunnelling (QMT) model is expected. If S increases with temperature, then small polaron hopping (SPH) model is predominant. If S initially decreases with temperature reaching a minimum value and then increases, then the overlapping large-polaron (OLP) model is the most probable mechanism. Here S is independent of frequency but decreases as the temperature increases [17]. This result reveals that correlated barrier  hopping (CBH) conduction model is the most suitable representation to characterise the electrical conduction [18]. In this model, conduction of carriers takes place through the hopping between the localised states separating by barrier. In CBH model also, two kind of conduction can occur between two defect sites (D + and D − ): 1. single polaron hopping and 2. bipolaron hopping. The ac conductivity can be expressed as follows, where N is the density of localised states where carriers exist, N P is the density of localised states to which carriers hop, n = 2 and n = 1 for bipolaron and single polaron hopping, Rω is the hopping distance [19]. Figure 3 shows the plots of the contributions for single polaron (S) and bipolaron (B) hopping processes and their sum (S+B) by fitting the above Eq. 3 with the experimental data of conductivity at 100 kHz frequency. It is clear from the figure that single polaron hopping contribution is much smaller and hence the conduction mechanism mostly occurs via bipolaron hopping. The complex admittance spectroscopy is very important tool to understand the interfacial charge carrier motion in the interlayer of electrode-semiconductor material [20]. Total AC electrical data acquired in the form of the admittance over frequency range 20 Hz -2 MHz are used to represent the best meaning of the dispersion.  of the film at different experimental temperatures. The admittance measurements show the evidence of a narrow distribution of trap states near the BTFMO-PVA interface. The peak structure in the frequency dependent imaginary admittance (Y ′′ ) plot arises due to the defect states/traps at the barrier interface of the nanocomposite [21].
The effective dielectric response in an inhomogeneous system can be further explained by Complex impedance spectroscopy. This study offers an insight of the electrical processes taking place within the system and their correlation with the sample when modelled in terms of its equivalent circuit. This observation is capable to to study the electrical properties like grain resistance (Rg), grain boundary resistance (︀ R gb )︀ and electrode interface under the influence of applied frequency range [22]. The expression of the complex impedence is given as follows [23], Where Rg and are the grain resistance and grain boundary resistance respectively. Cg and C gb are the grain capacitance and grain boundary capacitance respectively. ωg and ω gb are the angular frequencies at the peak of the grain and grain boundary semicircles respectively. Maxwell-Wagner capacitor model is taken here to under-

Figure 5:
The equivalent circuit diagram (R-C circuit) for the Impedance spectra. stand the complex impedance of the sample. Nyquist plots ) of the film sample at selective temperatures are shown in Figure 5. The equivalent electrical circuit (parallel R-C circuit) model diagram is shown in Figure 6 that is fitted with the experimental data to evaluate the parameters (listed in Table 2). The plots exhibit semicircular arc in the high frequencies. A semicircular arc having a trend to form two semicircular arcs tells about both grain and grain boundary contribution to the electric conductivity. At low temperatures (350 K and 360 K), the plot consists of one region over the whole frequency range i.e. the grain effect only. Here semicircle with the center lying below the real axis exhibits non-Debe type behavior [24]. Furthermore, the relxation time for grain and grain boundary can be expressed using the relations, and τ gb = 1 ⧸︀ ω gb and the calculated values of relaxation time are listed in Table 2.
The temperature variation of the real part [︀ ε ′ (f ) ]︀ and the imaginary part [︀ ε ′′ (f ) ]︀ of the dielectric constant at different frequencies are shown in Figure 7. At a particular frequency, the value of the dielectric constant increases thoroughly with temperature. Further, the temperature variation of the dielectric constant is more prominent in lower frequency than that of higher one. At high frequency, dipoles get opposed in orienting themselves along the applied field. For the mutual movement of dipoles and charges, an electric relaxation arises. The dielectric relaxation behaviour is the result of the combination of two polarisation mechanisms (interfacial polarisation and space charge polarisation) that depend on the physical movement of the charges responsible for the dipoles and on the length of time required for the displacement [25].
Electric modulus spectroscopy is studied to understand the space charge relaxation behavior in the sample.The real part [︀ M ′ ]︀ and the imaginary part [︀ M ′′ ]︀ of complex electric modulus spectra of the sample are shown in Figure 8 (a) -(b), respectively. M ′ goes to zero at lower frequencies due to the absence of electrode polarization. With the increase in frequency, the spectra show a step function dependence on frequency. This type of behavior gives rise to the well-defined loss peak in the M ′′ spectra. With increasing temperature, the peaks appear to shift systematically towards higher frequency. These spectra tell about two apparent relaxation zones. The peak shift exhibit the thermally activated nature of relaxation time. The left side of the asymmetric peak indicates the conduction mechanism of charge carriers over a long-range while the right portion corresponds to the charges confined to a potential well [26]. Modified Kohlrausch-Williams-Watts (KWW) function is required here to account for the asymetric distribution of the characteristic peak. The imaginary electric modulus can be formulated as follows [27], where 'a' and 'b' are shape parameters describing the symmetric and asymmetric broadening of the relaxation curve and their obtained values are given in Table 3.
To avoid the ambiguity arising out of the presence of grain or grain boundary effect at different temperatures, the impedance data are plotted in the complex modulus plane. Further, the modulus spectra [ Figure 8 (c)] show a change in its size and shape with the rise in temperature. It suggests a probable change in the values of capacitance as a function of temperature. The semicircular arc indicates the conductivity relaxation [28]. The plot has a tendency of two deformed semicircles indicating the occurance of both grain and grain boundary contributions in the nanocomposite film. The centre of the circles lying below the ordinate. It indicates non-Debye type relaxation of the sample. Figure 9 shows the variation of magnetocapacitance with the applied magnetic field at different frequencies (20 kHz and 50 kHz) at room temperature. Magnetocapacitance is stated as follows [29], where ε ′ (H) and ε ′ (0) are the dielectric constants at the magnetic field H and zero, respectively. The plot shows the negative magnetocapacitance effect of the sample. The magnetocapacitance value increases with the increase in the applied magnetic field. Maxwell-Wagner type polarisa-   Figure 9: Magnetocapacitance of the sample with the applied magnetic field at rom temperature at selective frequencies.
tion in the sample is the responsible factor for this type of behavior. Figure 10 (a) shows the non-linearity of currentvoltage (I-V) characteristics curve at different experimental temperatures within the applied voltage range ± 30 V. It shows good rectifying property of the sample. The curves display strong temperature dependence behavior. The Schottky Emission (SE) model can explain the current conduction mechanism in the nanocomposite system. According to this model, thermally activated electrons gain sufficient energy to overcome a potential barrier at the electrode-semiconductor interface to produce current [30]. Current density can be written as, where A * is a constant, φ B is the zero-field junction barrier height, q is electronic charge, ε 0 and εr are the free space dielectric constant and dynamic dielectric constant respectively. In Figure 10 (b), ln J vs. E 1/2 plot of I-V experimental data of the sample is shown at different experimental temperatures. Extracted values of φ B and εr are given in Table 4. Both the values of Schottky barrier height and op- tical dielectric constant decrease with increasing temperature.

Conclusion
We report a detailed investigation on the charge conduction mechanism in BTFMO-PVA nanocomposite film system. The existence of multiple activation energies implies different current conduction mechanisms at different tem-perature regions. Correlated barrier hopping model explains the electrical transport mechanism through the polymeric matrix. Non-Debye type relaxation process is also observed which has been further demonstrated by the modified Kohlrausch-Williams-Watts (KWW) model. Complex impedance spectroscopy of the nanocomposite film clearly shows the grain and grain boundary contributions. Negative magnetocapacitance arises in the sample due to the Maxwell-Wagner type polarization at the interface. The film exhibits charge storage ability that may be potentially applicable in the electronic world. As the nanocomposite film responds well with temperature as well as ecternal magnetic field, this film has potential applicabilities in thermistor, magnetic field sensors.