Figure 1 shows the room temperature X-ray diffraction pattern of BaSnO₃ powder prepared by wet chemical method. The XRD pattern shows peaks due to cubic perovskite structure only without any impurity peak. We have performed the Reitveld refinement on structural data using PDXL software with pseudo-Voight band profile in order to get the reliable estimate of the cubic cell parameters. Table 1 presents the Lattice parameter, unit cell volume and goodness of fitting using Reitveld refinement technique. Accordingly, the value of cell parameter obtained is 4.11933 Å which is very close to the literature value and the fitting parameters are also quite satisfactory. The fitting matches very well with

ICDD DB card No. 04-007-8719 and observed d-values shown in the table are also very close to the reference data. The formation of single phase material is confirmed as no extra XRD lines due to precursor oxides or minor secondary phases are traceable within the detection limit. The theoretical density of the unit cell was calculated from XRD data and density of the pellets was measured using Archimedes technique. Accordingly, the densification of ceramics is 91.7%. We also obtained the percentage density by simply weighing the pellets and measuring its volume which also comes out to be around 90%. The average crystallite size calculated using Scherer method is ~42 nm. Small crystallite size may be the reason while higher densification is observed at relatively lower temperature.

The surface morphology was studied by scanning electron microscopy (Zeiss, EVO® MA 10). The surface microstructure is an important factor that controls the electrical properties through inter-grain connectivity. The SEM micrographs of the BSO powder synthesized by wet chemical route are shown is Figure 2(a). Random grain growth is clearly visible with agglomeration of smaller particles forming the grains. Average grains size is estimated from linear intercept method using five different lines on the micrographs each having roughly 15 grains.

The average grain size is ≈2 μm with loosely interconnected grains. The average grain size in the sintered pellets remains same with homogeneous grain distribution. The elemental analysis and the chemical uniformity over the surface have been probed using EDAX spectra. The representative EDAX spectra are shown in Figure 2(b) from a section. Similar EDAX signals have been studied from various selected region over the surface. Elemental percentage in BaSnO₃ sample are estimated from EDAX using standards SiO₂ for O; Sn for Sn and BaF₂ for Ba as shown in Table 2. The estimated values of Ba, Sn and oxygen atoms are very close to the stoichiometric composition. There is no significant difference in the elemental percentage obtained from different regions.

Raman spectroscopic studies of cubic perovskites have been extensively reported and spectral features are understood quite well [43] [44] [45] [46] . In the cubic phase (space group Pm-3 m), group theoretical analysis allows 12 optical modes (3F_1u and 1F_2u) that are Raman forbidden. Despite the fact that there are no allowed phonons in cubic perovskite phase, reported Raman spectra of BSO show a number of peaks coming from the first order Raman activity [47] . There are contradictory interpretations regarding the origin of these peaks [47] [48] . Recently, we have made an attempt to resolve the controversy and attributed the observed Raman activity due to local structural symmetry change induced by defects in the system [49] . This results into folding of Γ-point of Brillion zone (Zone Centre) into M- and or R-point (zone boundary), as suggested by DFT based calculations also [47] . Thus, Raman spectroscopy could be used to track the local structural changes occurring in the material during processing as first order Raman activity is forbidden in cubic phase. On the other hand, three optical phonons are active in IR viz. TO₁, TO₂ and TO₃; the LO-TO splitting is expected due to ionic character of bonds.

The unpolarised room temperature Raman spectrum for the composition is shown in Figure 3. Raman modes due to BSO are observed at 135 and 241 cm⁻¹. The band appearing at 152 cm⁻¹ is probably due to BaCO₃which may be formed if defects are present as reported earlier [50] . Non-observance of higher frequency modes in compositions is due to large background scattering suppressing these modes probably due to the presence of moisture. Appearance of modes

at 135 and 241 cm⁻¹ assigned to BSO means the local symmetry structure is distorted from cubic symmetry.

The room temperature FTIR spectrum of BSO composition in the range 500 cm⁻¹ to 4000 cm⁻¹ is shown in Figure 4. The observed bands are also marked in the figure. The broad band appearing in the O-H stretching range (3000 - 3500 cm⁻¹) as well as those coming from ambient gases (1700 - 2300 cm⁻¹) appears clearly reflecting the presence of moisture in the composition. This may be due to porous nature of sample. The transverse optical modes of BSO in IR appears at 135, 244 and 668 cm⁻¹, whereas corresponding longitudinal phonons are expected at 154, 421 and 723 cm⁻¹ as reported from IR reflectivity data [47] . Based on this, the strong band appearing at 668 cm⁻¹ could be assigned to BSO TO mode. The low frequency modes could not be observed due to experimental limitations in our experiment. Two bands appearing at 865 and 1446 cm⁻¹ could be associated with BaCO₃ vibrational modes [51] and indicate the presence of small amount of BaCO₃ in the samples below the detection limit of XRD. A shoulder around 421 cm⁻¹ is also visible in compositions assigned to LO mode clearly indicating that the LO-TO splitting is present and local structure is distorted from cubic symmetry as evident from Raman spectra also.

The optical (UV-Vis) absorption spectrum for the BSO powder has been measured using Shimadzu UV 1700 Pharma spec spectrophotometer in the absorption mode. The spectrum is shown in Figure 5. Strong absorption bands around 250 nm and 430 nm are mainly due to optical transitions from valence band to conduction band involving O²⁻: 2p and Sn⁴⁺: 5s orbitals. An absorption tail towards NIR region is also observed. Theoretically, for direct band semiconductors, the absorption coefficient follows the relation [52]

α ( h ω ) α h ω − E g / h ω (1)

This leads to the Tauc relation given as

( α h ν ) 2 = A ( h ν − E g ) (2)

Here α is the absorption coefficient, hw is the photon energy, A is a constant. Thus, the optical band gap energy (E_g) can be calculated by plotting the graph between (αhν)² vs. (hν). Band gap (E_g) can be obtained by extrapolating the linear portion of the plot to the x axis, where (αhν)² = 0. The Tauc plot is shown in Figure 6(a). The calculated band gap energy is 2.85 eV, which is albeit smaller to those reported earlier [53] . The smaller value of optical band gap in comparison to the known band gap of ≈3.1 eV may be due to local states formation near the band edge. It is well known that band gap measurements using the Tauc plot require the precise determination of absorption coefficient (α) in order to get correct value of band gap. However, for this, it is necessary to perform corrections to the absorption due to reflection. We have therefore, used an alternate procedure called absorption spectra fitting (ASF) to calculate the band gap [54] .

The absorption spectra fitting procedure (ASF) has advantage over Tauc plot method as the optical band gap can be determined directly from absorbance data and without having the need to measure the thickness of the sample and is not affected by local states due to disorder.

ASF procedure has been a simple modification of Tauc plot method. This could be done by rewriting Equation (1) as α ( λ ) = A ( h c ) m − 1 λ [ 1 λ − 1 λ g ] m , and substituting α ( λ ) = 2.303 × A b s ( λ ) d using Beer’s Lambert law gives

A b s ( λ ) = A 1 λ [ 1 λ − 1 λ g ] m + A 2 (3)

where A₁ and A₂ being constants. The value of parameter λ_g can be obtained by extrapolating the ( A b s λ ) 1 m   vs .   1 λ plot linearly at ( A b s λ ) 1 m = 0 . The optical band gap energy (E_g, in electron volt), can be calculated as E g = 1239.83 λ g . The

least square fitting of the absorption data has best fitting for m = 1/2. The plot

( A b s λ ) 1 m   vs .   1 λ is shown in Figure 6(b). The value of E_g (2.97 eV) is quite close to the reported values ranging from 3.1 - 3.4 eV.

Figure 7 shows the variation of d. c. electrical conductivity as a function of temperature. DC electrical conductivity increases with increase in temperature for all compositions showing typical semiconductor-like behavior. The observed value of dc electrical conductivity at room temperature is ≈10⁻³ (Ω×cm)⁻¹ which increases and approaches 10⁻² (Ω×cm)⁻¹ at 200˚C. The observed high value of DC electrical conductivity approaching to those reported in perovskite electronic conductors [55] .

DC electrical conductivity in n-type semiconductors is generally found to be thermally activated with Arrhenius form. The Arrhenius type plot (logσ_dc Vs. 1000/T) (Figure 7) show non-linear variation and could be fitted into linear form in different temperature ranges with varying slope. This means that different thermally activated processes operative in different temperature ranges either involve different charge species or charge transport is being governed by hopping rather than being thermally activated. The activation energies are calculated using the relation σ = σ 0 exp ( − E a / k T ) where σ₀, E_a and k are the pre-exponential factor, activation energy of the mobile charge carriers and

Boltzmann constant respectively. The calculated values of activation energies in different temperature ranges are shown in Table 3. The activation barrier energy varies significantly in different temperature range. It may be noted that the values of activation energies in the temperature range (35˚C - 150˚C), and (150˚C - 200˚C) are 0.08, and 0.44 eV respectively. This means different charge species are involved in the conduction process at low temperatures (35˚C - 150˚C) and high temperatures (150˚C - 200˚C). The typical values of activation energy at least in the lower temperature range are very small than the activation energy required for O²⁻ vacancies (typically 0.5 eV) in the conduction process indicating that oxygen ion vacancies are not involved in dc conduction process up to 150˚C.

It seems that low temperature conductivity mechanism may be Mott-type variable range hopping, whereas, at higher temperature, it may be thermally activated Arrhenius type. To get a clear picture of conductivity mechanism and to understand the transport behavior, the role of electronic structure of the doping becomes crucial [56] . However, in pure material, defects (intrinsic) generated during synthesis may modify Sn structure partially reducing Sn⁴⁺ into Sn²⁺, increasing charge career density and also creating disorder in the octahedral (SnO₆) units restricting the long range motion of charge species. Thus, conduction may occur due to hopping of electron between equivalent sites. As per the Mott’s variable range hopping (VRH) model, the electrical conductivity in bulk due to hopping can be expressed as [57]

σ ( T ) = σ 0 exp − ( T 0 T ) 1 / 4 (4)

Here T₀ is the Mott’s characteristic temperature which depends on density of states in the vicinity of Fermi energy and localization length “a” given as [58]

T 0 = 18 k B N ( E F ) a 3 (5)

The mean hopping distance R_h(T) and hopping energy E_h(T) at a given temperature T could also be estimated in terms of T₀ and localization length as given by [59]

R h ( T ) = 3 8 a ( T 0 T ) 1 / 4 (6)

And

E h ( T ) = 1 4 k B T 3 / 4 T 0 1 / 4 (7)

We fitted the temperature dependent dc electrical conductivity data using Mott’s VRH model (Equation (4)) as shown in Figure 8(a). The plots reveal that the range of temperature in which data could be fitted with VRH model is restricted only at higher temperatures. This means that the conduction mechanism is dominantly governed by the disorder induced localization of charges at elevated temperatures.

Some reports have also indicated the role of small polaron in the conduction in alkali earth stannates [60] . A small polaron may be formed when an excess of charge carriers moves slowly and stays at some atomic position so as to allow the coordinate ion to adjust its position due to the presence of the carrier. The conduction may take place by diffusion of electrons at localized sites. In fact, in La-substituted SrSnO₃, it is suggested that conduction occurs through low polaron hopping of electrons between localized ions Sn⁴⁺/Sn²⁺.

In order to confirm the nature of hopping conduction, we use Mott-Davis small polaron hopping model [61] which has been found successful in many rare earth transition metal oxide systems at high temperature including Fe-substituted SrSnO₃ [62] . According to small polaron hopping, the temperature dependent electrical conductivity can be expressed as

σ T = σ k exp ( E p k B T ) (8)

where E_p is the activation energy, k_B is the Boltzmann constant and T is absolute temperature. In order to estimate the polaron hopping energy, we plotted the ln(σT) vs. 1000/T in Figure 8(b). The activation energy is related to polaron hopping energy (W_H) and disorder energy (W_D) in the temperature range given by [63]

E p = { W H + W D / 2         ( T > θ D / 2 ) W D                                 ( T < θ D / 4 ) (9)

Here θ_D is Debye temperature. The plot(logsT vs. 1000/T) deviates from straight line at certain value of temperature denoted by θ_D/2 in Figure 8(b). The slope of high temperature side (above θ_D/2) has been used to estimate the activation energy of polaron (E_p), which comes out to be 0.08 eV. Analysis clearly reveals that oxygen vacancies are not the dominant defects involved in charge transport and probably protonic type of conduction takes place with small polaron formation being evident at higher temperatures.

Figure 9 shows the frequency variation of ac conductivity (σ_ac) at different temperatures. The ac conductivity was calculated from the impedance data using the relation σ a c = ω ε 0 ε r ( tan δ ) . The conductivity spectra at different temperatures show some typical behavior; no dispersion has been observed in the low frequency range of measurements with almost frequency independent low frequency plateau observed up to 250˚C. However, a. c. conductivity shows significant increase at 300˚C. Further, in the high frequency region dispersion is observed with the conductivity variation becoming non-linear at higher temperature. The frequency independent region shows a general trend; the region shifts towards higher frequency side with increase in temperature. These results indicate the existence of multiple relaxation processes and thermally activated charge species in the materials. The frequency at which change in slope of the of the

pattern occurs is known as hopping frequency (ω_p) suggesting that the electrical conduction occurs via hopping mechanism governed by Jonscher’s power law [64] .

The frequency dependence of a. c. conductivity may arise due to free as well as bound charge carriers. In case of conduction being due to free carriers the conductivity showed decrease with increase in frequency [65] . In our case, a. c. conductivity remains frequency independent and increases with frequency only after a certain frequency; therefore, bound charges trapped in the materials seems to be mainly responsible for conduction. Energy required for the relaxation/orientational process is lower than that required for mobility of charge carriers over a long distance. The observed almost frequency independent ac activation energy at lower frequencies indicates that contribution due to long range charge mobility is insignificant in the material.

The frequency dependence of conductivity is fitted with Jonscher’s power law relation [64] ,

σ ( ω ) = σ d c + A ω n (10)

where σ_dc is the frequency independent conductivity and the coefficient A and exponent n are temperature and material dependent. The term Aωⁿ contains ac dependence and characterizes all dispersion phenomena. The exponent n show different dependence with temperature in different systems i.e. remains constant, decreasing with temperature, increasing with temperature but always varies between 0 < n < 1. The variation of ac conductivity (σ_ac) with frequency at different temperatures, along with the fitting with Jonscher’s relation, is shown in Figure 9. From the theoretical fit (lines in the plot) it is evident that ac electrical conductivity spectrumobeys Jonscher’s power law at all frequencies; hence electrical conduction of the materials is thermally activated process at these frequencies. According to Jonscher [64] , the origin of the frequency dependent conductivity lies in the motion of mobile charge carriers. When a mobile charge carrier hops to a new site from its original position, it remains in a state of displacement between two potential energy minima. After a sufficiently long time, the defect could relax until the two minima of lattice potential energy coincide with the lattice site.