Interpretation of dc and ac conductivity of Ag2O–SeO2–MoO3 glass-nanocomposite-semiconductor

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Interpretation of dc and ac conductivity of Ag2 O–SeO2 –MoO3 glass-nanocomposite-semiconductor

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Sanjib Bhattacharya a,∗ , Ranadip Kundu a,b , Anindya Sundar Das b,c , Debasish Roy b a

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Department of Engineering Sciences and Humanities, Siliguri Institute of Technology, Darjeeeling 734009, West Bengal, India Department of Mechanical Engineering, Jadavpur University, Jadavpur, Kolkata 700032, India Department of Electronics and Communication Engineering, Regent Education and Research Foundation, Barrackpore, Kolkata 7000121, India

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a r t i c l e

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a b s t r a c t

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Article history: Received 15 August 2014 Received in revised form 13 February 2015 Accepted 18 February 2015 Available online xxx

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Keywords: Glass-nanocomposites Polaron hopping Mott’s model Greave’s model Electrical conductivity

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1. Introduction

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A new type of semiconducting glass-nanocomposites 0.3Ag2 O–0.7 (xMoO3 –(1 − x) SeO2 ) is prepared by melt-quenching route. The formation of Ag2 MoO4 , Ag2 Mo2 O7 and Ag6 Mo10 O33 nanoparticles and SeO3 and SeO4 nanoclusters in glass-nanocomposites has been confirmed from X-ray diffraction (XRD) and field emission scanning electron microscopic (FESEM) studies. Fourier transform infrared (FTIR) spectroscopy is employed to find out Se O stretching vibration as well as stretching vibrations of Mo2 O7 2− ions. The dc conductivity of them is studied on the light of polaron hopping approach in a wide temperature range. At low temperatures, variable range hopping model (Mott’s model) is employed to analyze the conductivity data. Greave’s model is used to predict temperature dependent variable range hopping in the high temperature region. Frequency dependent ac conductivity is well explained on the basis of tunneling. I–V characteristics of the as-prepared samples have also been investigated. © 2015 Published by Elsevier B.V.

Owing to increasing demand of various applications [1–3], oxide glassy systems containing transition metal ions (TMI) are of great interest. It is noted [1–3] that electron-mobility in amorphous semiconducting systems is almost same as ion-mobility in highly conducting solid electrolytes. Therefore, standard band theory cannot be used to describe electronic properties of transition metal oxides. So the electrical measurements data can be analyzed by introducing the concept of small polarons [4]. Small polarons are the confined charge carriers coupled with lattice distortions which, in turn, are responsible for phonon assisted hopping processes [5]. Polaron transport mechanism and glass-structure have been extensively studied by different researchers [1–6] on these semiconducting glassy systems. It is observed from the literature [7] that network modifier plays an important role for the structure of these semiconducting glassy systems. A lot of work [6] is done on vanadate glassy system. But a few is studied so far on other transition metal oxide glassy systems [8,9]. The short-range atomic order in molybdenum–tellurite glassy system is identified from neutron diffraction [10] study. It is also observed that the modifier oxide greatly affects the magnitude of the conductivity and activation

∗ Corresponding author. Tel.: +91 33 24734713. E-mail address: sanjib [email protected] (S. Bhattacharya).

energy of phosphate [6] and tellurite [9] glassy systems containing the same glass forming oxide, MoO3 . Therefore the introduction of Ag2 O in the mixed MoO3 and SeO2 network may affect the electrical properties of the resultant glass-nanocomposite system. The study of dc conductivity on the basis of the classical Boltzmann transport equation as well as quantum mechanical principles [10] reveals the estimation of the order of magnitude of the small polaron drift mobility. The polaron hopping motion of charge carriers must carry with lattice distortion, which imparts additional drag on the motion of the charge carrier. In recent years, the temperature dependent small polaron drift mobility has been computed [10–13] in the two temperature regimes. At low temperatures, the motion of small polaron has been described by Bloch-type band motion while, at higher temperatures, thermally activated hopping controls the polaron motion. However, ac conductivity at low frequency and temperature in amorphous semiconductor shows nearly linear relationship [8]. Although, several theoretical models [1,3,11] based on the electrical relaxation process due to the hopping or tunneling of electrons (polarons) between equilibrium sites have been introduced to explain the frequency and temperature dependence of the ac conductivity. But, still it needs more insight to shed some light on them. Some electrical relaxation data have been analyzed and interpreted using electric modulus formalism [11]. It is observed that ac conductivity [14] show a strong frequency dependence in the high frequency range according to power law. Not much work is reported on the ac conductivity

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studies of ternary glassy nanocomposite systems. The present work, therefore, deals with the study of ac conductivity and the related electrical properties of these Ag2 O–SeO2 –MoO3 glassy nanocomposite systems. The objective of the present paper is to investigate the electrical transport of silver–selenium–molybdate glass-nanocomposites in the framework of small-polaron theory. We also study the ac conductivity of them in a wide frequency and temperature range using existing theoretical models. We have observed the tunneling of polarons as the dominant mechanism for the ac conductivity in these glassy systems. Another aim of the work is to observe that whether the concentration of MoO3 would influence the frequency dependent conductivity of the whole systems or not. 2. Experimental procedure Glass-nanocomposites 0.3Ag2 O–0.7 (xMoO3 –(1 − x) SeO2 ) where x = 0.70, 0.90 and 0.95 were prepared from the reagent grade chemicals AgNO3 , MoO3 and SeO2 . The appropriate amounts of precursor-powders were thoroughly mixed and preheated in an alumina crucible and the mixtures were then melted in an electric furnace in the temperature range from 800 ◦ C to 900 ◦ C depending upon the composition. For sample, x = 0.7, it is observed that melting starts at 750 ◦ C. Next the furnace temperature is fixed at 800 ◦ C to keep the solid state reaction in equilibrium. For x = 0.9 and 0.95, the furnace temperatures become 850 ◦ C and 900 ◦ C respectively due to variation in composition. The melts have been equilibrated for 30 min and quenched between two aluminum plates. Partially transparent glass-nanocomposites of thickness ∼1 mm were collected. XRD patterns of the samples were recorded using a Rich-Seifert X-ray diffractometer (model 3000P) for recording the diffraction traces (2 versus intensity) of the powdered samples. In this instrument, Ni filtered CuK␣ radiation operating at 35 kV and 25 mA in a step scan mode was used. The step size was taken to be of 0.02◦ in 2 and a hold time of 2 s per step. The distribution of Ag2 MoO4 , Ag2 Mo2 O7 and SeO2 nanoparticles has been confirmed from the XRD-peaks and JCPDS data sheet [15]. To explore the microstructure and surface morphology of the prepared glass-nanocomposites, field emission scanning electron micrographs (FESEM) of the polished surfaces of the samples were taken in a field emission scanning electron microscope (JEOL, JSM-7600F). The Fourier transform

infrared (FTIR) spectra of the powdered samples in KBr matrices in transmission mode were recorded in a Nicolate FTIR spectrophotometer (Magna IR-750, Series II) in the wave number range of 400–4000 cm−1 at a temperature 25 ◦ C and humidity at 50–60%. The dc electrical conductivity measurements of the as-prepared samples have been carried out using Metravi made high precision LCR meter at various temperatures. For this, the sample of about 1 mm thickness is used and the measurements have been made by the two-probe method. The ac measurement was carried out using Hioki LCR tester (Model No. 3532-50) in the frequency range 42 Hz–5 MHz at various temperatures. Current–voltage (I–V) characteristic curves of the as-prepared samples were investigated by two-probe [16] method in a specially constructed measuring cell. The measurement system for determining I–V characteristics of the samples consisted of a stabilized dc power supply with a current meter, series load resistor and a Metravi made high precision multimeter. 3. Results and discussion The XRD patterns of 0.3Ag2 O–0.7 (xMoO3 –(1 − x) SeO2 ) glassnanocomposites are presented in Fig. 1. At lower-angle, broad diffuse scattering represents long-range structural disorder. Some crystalline peaks are seen in the amorphous network. It is observed that (0 0 1) peak due to Ag2 Mo2 O7 of P1-space group and (3 1¯ 1) peaks due to Ag6 Mo10 O33 crystal with P1 space group and triclinic symmetry [15,17] respectively. (1 1 0) peaks indicate Ag2 MoO4 crystals [18]. (2 1 0) peak in Fig. 1 is the signature of Ag2 Mo2 O7 nanoparticles [18]. (2 1 0) and (2 0 1) indicate tetragonal P4 space group due to SeO2 crystallites [15] respectively. At higher angles, (2 0 4) peaks indicate that the orthorhombic structure of Ag2 Se [19], confirming the conversion of Ag into Ag2 Se. Fig. 3(a) and (b) represents field emission scanning electron micrographs (FESEM) of as-prepared sample 0.3Ag2 O–0.7 (xMoO3 –(1 − x) SeO2 ) with x = 0.7 and 0.9 respectively. It is observed from surface morphology as shown in Fig. 3 that each sample contains globular like structure [18,20] of Ag2 Mo2 O7 and SeO2 of average size 40 nm and flake like structures [19,20] of Ag2 Se and SeO2 having 2 ␮m in length and 80 nm in breadth respectively. Theses phases were confirmed from XRD studies (Fig. 1). It is also observed that in the lower MoO3 content sample, SeO2 has a prominent tendency of agglomeration and formation of more flakes like

Fig. 1. XRD patterns of 0.3Ag2 O–0.7 (xMoO3 –(1 − x) SeO2 ) glass-nanocomposites (夽 Ag2 Mo2 O7 ,  SeO2 ,  Ag2 MoO4 ,  Ag2 Mo2 O7 , • SeO2 , ♦ SeO2 ).

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Fig. 2. Variation of crystallite-size with MoO3 content of the resultant glassnanocomposites.

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structures of Ag2 Se and SeO2 as shown in Fig. 3(a). As the MoO3 content increases, large particles Ag2 Mo2 O7 and SeO2 are formed due to agglomerates of much smaller particles. FTIR spectra of as-prepared samples are shown in Fig. 4. The readings are taken in transmittance mode at the range of 4000–400 cm−1 . In Fig. 4, the strongest band at 864 cm−l must be assigned as 1 to stretching vibrations of the Se O side groups [21]. It is known that the lateral Se O bonds are attributed to the Se O stretching vibration. As the MoO3 content in the network increases, it gives a flatter response. The bands at 1003 cm−1 and 1115 cm−1 assigned as 2 and 3 which can be stretching vibrations of Mo2 O7 2− ions [22]. Another absorption peak 528 cm−1 may be due to SO2 in the glass network [22]. It is clear from the literatures [19–21] that the structures of selenite glassy systems have a tendency to grow of Se O clusters with the increase in SeO2 content. This structural behavior may restrict the limits of the network-forming region. It is also observed that the formation of SeO3 and SeO4 nanoclusters [19,20] in glassy system containing SeO2 is different from the standard phosphate or borate glassy systems [22]. It is reported that [19] that SeO3 nanocluster takes part in the network-formation at lower SeO2 content. As the SeO2 content increases, it forms chains having isolated Se O bonds [19]. It is also clear from Fig. 1 that change in peak intensities of the several peaks indicates the variation of polycrystalline nature of the samples. It is also noted that the peak intensities are found to decrease with the increase of MoO3 content as well as decrease of SeO2 content. Here, SeO2 may be acting as network former as well as stabilizer and it may urge more and more Ag+ , Se2+ and O2− to take part into the structure. Oxide glassy systems containing transition metal ion “Mo” in more than one valence states Mo+5 and Mo+6 [23]. Mo+6 to Mo+5

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Fig. 4. FTIR spectra for all the compositions.

conversion takes place by releasing charge carriers. The experimental findings have, however, been explained by introducing the concept of small polarons [23] which are charge carriers trapped by self-induced lattice distortions extending over their nearest surroundings. The transport of these quasi-particles consists of phonon assisted hopping processes [23]. As a consequence, Mo6+ contributes to polaron conduction. The interplaner spacings between two successive planes (d-values) have been estimated from XRD analysis. The calculated d-values are also same as those received from JCPDS data sheet [15]. The sizes of Ag2 MoO4 , Ag2 Mo2 O7 and Ag6 Mo10 O33 nanoparticles and SeO3 and SeO4 nanoclusters dispersed in glass-nanocomposites have been determined from Debye–Scherer formula [23] t = 0.89/(ˇ cos ), where t denotes the average grain size of the particles,  stands for the ˚  for the Bragg diffraction angle and ˇ X-ray wavelength (1.54 A), for the peak width in radians at half-height. Fig. 2 describes the variation of particle size with MoO3 content of the resultant glass-nanocomposites. The size of the silver–molybdate nanoparticles is found to be almost same. But that of selenium oxide is found to decrease. At higher SeO2 content the chain structure having isolated Se O bonds exists. As the content of SeO2 decreases (MoO3 increases) the chains of SeO2 are broken into SeO2 nanoclusters, which would take part in the network structure. The dc conductivity for the different MoO3 content is shown in Fig. 5 as a function of reciprocal temperature. The smooth variation of the conductivity with reciprocal temperature, presented in Fig. 5, is the characteristic feature of small polaron-transport [5,6,9,12]. The typical semiconducting behavior has also been observed in the nature of variation of dc conductivity for all the glass-nanocomposites with temperature. However, high temperature and low temperature activation energies (Table 1) have been computed from the slopes of the graphs respectively. It also shows

Fig. 3. FESEM micrographs for (a) x = 0.70 and (b) x = 0.90.

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Table 1 Activation energies at high and low temperatures and density of states at the Fermi level for different compositions of 0.3Ag2 O–0.7 (xMoO3 –(1 − x) SeO2 ) glass-nanocomposites. Compositions x

WH (eV) at high temperature (±0.01)

Wl (eV) at low temperature (±0.01)

N(EF ) (1028 eV−1 cm−3 ) (Mott-model)

N(EF ) (1027 eV−1 cm−3 ) (Grave-model)

0.70 0.90 0.95

1.10 1.00 0.96

0.50 0.49 0.48

3.00 3.89 4.37

3.00 3.60 5.20

Fig. 5. Dc conductivity as a function of reciprocal temperature. I–V characteristic at various temperatures for x = 0.9 is shown in the inset.

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temperature activated nature. Current–voltage (I–V) characteristic for x = 0.90 have been shown in the inset of Fig. 5. These I–V characteristic also show semiconducting nature as the dc conductivity decreases with temperature, indicating small polaron-transport. Fig. 6(a) and (b) shows the composition dependence of the dc conductivity at 303 K and high temperature activation energy, respectively. The data for another semiconducting molybdate system are also included for comparison. It is noteworthy that the conductivity and the activation energy are quite stronger for the present glass-nanocomposites. It may be tacitly understood that the transport properties between the present glass-nanocomposites and the referred molybdate system are different due to the difference in their structure [9]. However, it is observed that the modifier oxide, MoO3 plays an important role in varying the electrical conductivity and corresponding activation energy of phosphate [6] and tellurite [9] glassy systems. So, it is obvious that the modifier oxide (i.e. Ag2 O and SeO2 ) affects the electrical properties of the silver–selenium molybdate glassnanocomposites significantly. It is also noted in Fig. 6 that higher dc conductivity is achieved for those compositions having the lower activation energy. This experimental result may be analyzed with the small polaron hopping theory proposed by Mott [12]. In these glassnanocomposite-semiconductors, optical phonon-assisted hopping of small polarons [11] between localized states is mainly responsible for the conduction process at high temperatures. Above the Debye temperature ( D ), the dc conductivity is given by,

 240

 = 0



e2 C(1 − C) exp(−2˛R) exp kTR

 −W kT

(1)

Fig. 6. Composition dependence of (a) dc conductivity at 303 K and (b) high temperature activation energy.

where 0 is the longitudinal optical phonon frequency, R is the average site separation, ˛ is the inverse localization length, C is the fraction of sites occupied by an electron (or polaron), k is the Boltzmann constant and e is the charge. The value of activation energy (W) in below and above  D given by [5], W

= WH + WD /2

for T > D /2

≈ WD

for T < D /4

(2)

where WH is the polaron hopping energy and WD is the disorder energy. WD is the cause of the variation in the local arrangement of ions. Dc conductivity at a particular temperature versus high temperature activation energy is depicted in Fig. 7. Similar data for the tellurium–molybdate glassy system [9] are also included for comparison. We note that the data for the referred system fall on a straight line. But the present data do not show linear relationship. This result suggests that the conductivity is dependent not only on the thermal activation energy, but also on composition. This result is also pointed toward the difference in structure of these glass-nanocomposites. Low temperature dc conductivity data have been analyzed and interpreted using Mott’s variable range hopping model [24]. The mathematical expression of variable range hopping conductivity is given by,

  0.25  T0

 = Aexp −

T

,

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(3)

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Fig. 7. Dc conductivity at a particular temperature versus high temperature activation energy.

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where A and T0 are constants and T0 is given by

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T0 =

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16˛3 , kN(EF )

(4)

where N(EF ) is the density of states at the Fermi level. The dc conductivity data at low temperature with T−0.25 have been presented in Fig. 8(a). The plot shows linearity over a considerable temperature range, consistent with the variable range-hopping model. Eq. (3) is employed to fit the experimental data as shown in Fig. 6. Here, for localized states ˛−1 is taken to be 10 A˚ [11]. The estimated N(EF ) values are presented in Table 1. N(EF ) is found to increase with x, which confirms dc conductivity data. These results suggest that modifier oxide (Ag2 O and SeO2 ) must play an important role in the conduction process. It is also observed that N(EF ) values of the present system are found to be higher than those of molybdate [9] and vanadate [25] systems due to highly conducting nature. Mott’s model is insignificant for analyzing high temperature dc conductivity data. However Greaves [26] predicted a temperature dependent variable range hopping which is dominant in this region. This model suggests the following expression for the dc conductivity at high temperature range:

 

dc T

1/2



= A exp −

T0 T

1/4

,

(5)

where A and T0 are constants and T0 is given by T 0

=

19.4˛3 kN(EF )

,

Fig. 8. (a) Dc conductivity at low temperatures is plotted against T−0.25 (Mott’s model at low temperature); (b) Temperature dependent variable range hopping conductivity (Greave’s model at high temperature).

to that for other TMI oxide systems [27,28]. At low temperatures,  is found to be greater than  dc and also found to increase with the increase in frequencies. The temperature dependence of  becomes strong at higher temperatures. At high temperature region,  becomes equal to  dc and the frequency-variation

(6)

The experimental data have been presented and fitted to Greave’s model in Fig. 8(b) in the temperature range 750–900 K for different glass-nanocomposites under investigation. Here, we observe that it yields good fits to the data. It should be noted in Table 1 that the values of N(EF ), obtained from two models are almost same though they are operative in different temperature ranges. It is obvious that at high temperatures the phonon assisted polaron hopping takes place and thereby a chance to make collision between phonon and Ag6 Mo10 O33 , Ag2 Mo2 O7 , Ag2 MoO4 , SeO3 and SeO4 nanoparticles and nanoclusters inside the sample under investigation. As a result of this a part of energy is lost, which keeps the values of N(EF ) same. This surprising result may also be explained from their structural point of view. The ac conductivity () data with reciprocal temperature are shown in Fig. 9 at various frequencies. The dc conductivity data are also included for comparison. The nature of the plots is similar

Fig. 9. Ac conductivity with reciprocal temperature at different fixed frequencies. The dc conductivity data are included for comparison.

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Fig. 10. Frequency dependent conductivity   (ω) at different temperatures for a particular glass-nanocomposites, x = 0.7. The solid lines are the least square straight line fits of the ac conductivity data.

becomes insignificant. Here, the polaron-hopping rate may be sufficiently high; consequently high temperature solely controls the 309 conduction process. Similar type of temperature dependence has 310 been observed for other samples. This property of the materials 311 under investigation may be favor of different device applications. 312 Ac conductivity date in semiconducting glassy system contain313 Q4 ing TMI have been analyzed using the following power law [29,30], 314 308

315

(ω) = Aωs

(7)

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where A is a constant dependent on temperature and the power s, is generally equal or less than unity. For the present type of system, linear frequency dependence of (ω) is considered provided the distribution of relaxation times, (), is inversely proportional to relaxation times (). Here,  =  0 exp( ), where is a random variable and  0 is a characteristic relaxation time, which may be taken to be an inverse phonon frequency, 0 −1 . However, the power s may be larger than unity in some cases [31]. In a given ac experiment, the total conductivity  total of the sample has been measured at a particular frequency and temperature in the following manner [29,30]

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total (ω) = (ω) + dc

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(8)

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Here, dc and ac conductivities arise from completely different processes. Fig. 10 shows the conductivity spectra at various temperatures for a particular glass-nanocomposites, x = 0.7. The solid lines indicate the best fitted straight lines of the ac conductivity data. The slopes of the plots provide the value power s as indicated by Eq. (7). The values of power, s with temperatures is presented in Fig. 11. An important feature is also observed in Fig. 11 that s decreases with increasing temperature. This feature predicts the nature of polaron conduction in the glass-nanocomposite-semiconductor. Another important feature is observed that s value increases up to x = 0.90 and it decreases for x = 0.95. This may happen due to low dimensionality and other conduction phenomena, which is still under deep study. To interpret the ac conductivity data and the corresponding power, s different polaron-hopping models regarding quantum mechanical tunneling have been developed. The quantum mechanical tunneling model for power, s has been suggested [5,32,33] as

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s=1−

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346 347 348

4 ln(1/ω0 )

(9)

which shows that s is temperature independent but frequency dependent and thus this model is unable to explain the experimental data presented in Fig. 10.

Fig. 11. Power law exponent‘s’ with temperature. Experimental data has been fitted with HOB model.

Efforts have been made by the researchers [33–35] to develop a model on hopping over barrier (HOB) of charge carriers. A temperature dependent frequency-power can be expressed here in the following fashion (HOB) S = 1 − 6kT/W

(10)

where k is the Boltzmann’s constant and W is the corresponding activation energy. The experimental data in Fig. 10 has been fitted with the HOB model and W values are found to be higher than WH given in Table 1. 4. Conclusion The dc conductivity data for Ag2 O–SeO2 –MoO3 glassy nanocomposite systems have been well explained using polaron hopping theory. It is observed from XRD and FESEM studies that SeO2 has a tendency of agglomeration and formation of more flakes like structures of Ag2 Se and SeO2 . It is clear from FTIR study that the strongest Se O bonds are attributed to the Se O stretching vibration. The smooth variation of the conductivity with temperature reveals the semiconducting nature, which is the characteristic feature of small polaron-transport. I–V characteristics also show semiconducting nature of the as-prepared samples. To analyze the conductivity data in different temperature zone, Mott’s model and Greave’s model have been employed. Polaron hopping as well as quantum mechanical tunneling have been employed to account for the ac conductivity and its frequency exponent. Acknowledgements The financial assistance for the work by the Council of Sci- Q5 entific and Industrial Research (CSIR), India via Sanction No. 03 (1286)/13/EMR-II is thankfully acknowledged. Centre for Research Q6 in Nanoscience and Nanotechnology, Kolkata-700 098, West Bengal, India is also acknowledged for proving FESEM facility. References [1] A. Mekki, G.D. Khattak, P.S. Fodor, L.E. Wenger, J. Non-Cryst. Solids 330 (2003) 156. [2] J. Livage, J.P. Jolivet, E. Trone, J. Non-Cryst. Solids 121 (1990) 35. [3] B. Peng, Z. Fan, X. Qui, L. Jiang, G.H. Tang, H.D. Ford, W. Huang, Adv. Mater. 17 (2005) 857. [4] T. Holstein, Ann. Phys. 8 (1959) 343. [5] I.G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41. [6] M. Sayer, A. Mansingh, Phys. Rev. B 6 (1972) 4629. [7] V. Dimitrov, Y. Dimitiev, M. Arnaudov, D. Topalov, J. Non-Cryst. Solids 57 (1983) 147.

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