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AC conductivity behaviour and charge carrier concentrations of some vanadate glassy system
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Physics Letters A ••• (••••) ••••••
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AC conductivity behaviour and charge carrier concentrations of some vanadate glassy system Sanjib Bhattacharya Department of Engineering Sciences and Humanities, Siliguri Institute of Technology, Darjeeeling-734009, West Bengal, India
a r t i c l e
i n f o
Article history: Received 4 November 2019 Received in revised form 5 January 2020 Accepted 8 February 2020 Available online xxxx Communicated by M. Wu
a b s t r a c t The investigation of wide range of temperature and frequency dependent conductivity of some semiconducting glassy system reveals DC conductivity, crossover frequency and frequency exponent. The composition dependence of AC conduction activation energy and the permissible energy of polaron migration have also been computed. The Nernst-Einstein relation proves that the concentration of mobile charge carriers does not undertake a substantial part in electrical conduction. © 2020 Published by Elsevier B.V.
Keywords: Amorphous materials Electrical properties Vanadate semiconducting glassy system AC conductivity and frequency exponent (n) Power law exponent (s) Mobile charge carrier concentrations
1. Introduction Transition metal oxide (TMO) such as V2 O5 doped glassy materials usually exhibit semiconducting behaviour [1], which make them important for various applications such as electrochromic devices, optical devices, switching, and memory switching devices, etc. [2,3]. In glassy system containing vanadium pentoxide (V2 O5 ) as a glass network former, the electrical conduction may arise for hopping conduction of unpaired 3d1 electron between V4+ and V5+ valence states [4,5]. These unpaired electrons are supposed to start polarization about vanadium ions to form a quasi-particle, known as polaron [4,5]. The transparent conducting oxide (TCO) ZnO has been broadly used as touch panels, window electrodes for flat panel displays, and in solar cells as they reveal excellent electrical and optical properties [6]. Moreover, it has also been typically used in varistors, piezoelectric transducers, optical waveguides, and gas sensor [7]. “AC conductivity” can be considered as a significant feature to retrieve confirmation of the occurrence of defect states in the glassy system and can be utilized to discriminate the conduction process [8]. Certain models, for instance, quantum-mechanical tunnelling model (QMT) [8], non-overlapping small polaron tunnelling model (NSPT) [8] etc have been predicted by many researchers to exhibit AC conduction mechanism owing to hopping or tunnelling of electrons or polarons. But till date, no concrete explanation on this conduction process has been revealed.
E-mail address: [email protected]. https://doi.org/10.1016/j.physleta.2020.126324 0375-9601/© 2020 Published by Elsevier B.V.
So, the study of AC conductivity of semiconducting glassy system is essential for material researchers not only for practical applications but also for academic interest. In the present communication, the AC conductivity of a semiconducting glassy system has been investigated in a wide frequency and temperature range. The electrical measurements data have been analyzed using some theoretical models to elucidate conduction mechanism, power law exponent and charge carrier concentration. 2. Experimental TMO-doped semiconducting glassy system, xV2 O5 –(1-x) (0.05 SeO2 –0.95 ZnO) with x = 0.35, 0.55, 0.75 and 0.95 have been prepared using melt quenching route from reagent grade chemicals. To conduct electrical measurements, both sides of the as-prepared glassy samples are coated with conducting silver paste to serve as the electrode. Electrical measurements of the as-prepared samples have been measured using HIOKI (model no. 3532-50) made programmable high precision LCR meter at various temperatures and in the frequency window 42 Hz to 5 MHz. The microstructures of as-prepared samples have been performed using a JEOL made Scanning Electron Microscopic (SEM) studies. 3. Results and discussions AC conductivity spectra for x = 0.35 is presented in Fig. 1(a) at various temperatures, which reveal two distinct regions: (i) almost
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Fig. 1. (a): Real part of conductivity spectra at different temperature for x = 0.35; (b) Imaginary part of conductivity spectra at different temperature for x = 0.35; (c) SEM micrograph for a particular sample, x = 0.35; (d) The histogram of particle-distribution within the glassy matrix for x = 0.35.
flat or plateau region and (ii) dispersion region. At lower frequency, the flat region is recognized where conductivity (σ (ω )) is almost frequency independent, and the width of the plateau region rises with a rise in temperature. However, dispersion commences at higher frequency region, which reveals frequency dependent conductivity in terms of introduction to power-law [8,9]. The width of dispersion region (high frequency range) is found to reduce with temperature. The real part of AC conductivity of amorphous materials exhibits the power-law dependency, suggested by AlmondWest [9]
σ (ω) = σdc 1 +
ω ωH
Table 1 The values of hopping frequency (ωH ) at 493 K, activation energy for hopping frequency (EH ), DC conductivity (σ dc ) at 493 K, average frequency exponent (n) from Almond West Power Law. x
Log ωH (rad s−1 ) at 493 K
EH (±0.002 eV)
Log σ dc (−1 cm−1 ) at 493 K
Average value of n
0.35 0.55 0.75 0.95
6.134 6.448 7.535 8.549
0.148 0.324 0.267 0.264
-7.271 -6.264 -5.201 -4.421
0.872 0.756 0.536 1.146
n (1)
where, σ dc is DC conductivity, ωH is hopping or crossover frequency from DC region (plateau region) to the dispersion region and n is the frequency exponent. The values of σ dc , ωH and n are obtained from the non-linear best fitted curve fitting of conductivity spectra using Eq. (1) as presented in Fig. 1(a) by solid lines. The values of σ dc and ωH at temperature 493 K and the average values of n are estimated and included in Table 1. Here, ωH shows thermally activated nature, which follows similar nature of DC conductivity. Hopping of polaron can be the best-suited process for AC conduction in all as-prepared samples [10]. In Almond-West formalism, n is associated with diffusion of charge carriers in random charge conducting paths in term of dimensionality of conduction pathways [8]. It may be put forward that the dispersion in the AC conductivity is influenced by the dimensionality of the charge carrier, which is evidenced by the numerical values of frequency exponent (n) [8]. The frequency dependent conductivity may re-
late to hopping of polaron in a bit of short distances concerning adjacent sites, separated by energy barriers of varying heights. If polaron hopping in the present glassy system appears suddenly between randomly distributed localized charge states, n value lies between 0.7 and 1 (Table 1). The lower value of n usually arises in multiple hops, while the higher value of n ensues for single hop and it indicates a strong drift of polarons [8]. It is pointed out from Table 1 that the value of n is highest of the sample for x = 0.95 that denotes strong polaron drift, thus, exhibiting highest conductivity. It can be concluded that in consequence of the morphological dispersion, the inter-site potential energy barrier should be significantly altered, which contribute to an excessive growth in the degree of polaron hopping. Papathanassiou et al. [11] successfully developed a model based on the aspect of the distribution of the length of conduction paths regarding the universal powerlaw dispersive AC conductivity, observed in polymer networks and, generally, in disordered matter. Larger values of power law ex-
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S. Bhattacharya / Physics Letters A ••• (••••) ••••••
ponent (>1) are physically acceptable within this model, which should be restricted by an upper frequency limit. For complete understanding of the conductivity, imaginary part of conductivity [12] is also studied. Fig. 1(b) presents the imaginary part of conductivity spectra for a particular sample, x = 0.35. At higher frequencies, a gradual increase of conductivity is observed in Fig. 1(b). As the frequency is decreased, conductivity is found to decrease up to certain frequency, below which it shows an increasing nature. It is also noted that electrode polarization becomes significant at lower frequencies. To shed more light on the nature of conductivity spectra as shown in Fig. 1(a), Emin-model [13] has been considered, which indicates that there are two sources of the frequency-dependence for polaron-hopping conductivity’s. Firstly, the jump rate for a polaron hop increases with applied frequency (except at exceptionally high temperatures) as per Eq. (94) and curve b of Fig. 7 in Ref. [13]. Secondly, the conductivity of carriers confined within spatial regions by disorder rises as the applied frequency is increased [13]. The second effect [13] generates the very lowtemperature (< 10 K) AC conductivity of charge carriers that hop between especially close pairs of impurity states of very lightly doped compensated covalent semiconductors [14]. However, the major issue is to explain of such an effect, which should dominate the high-temperature hopping of high densities of polarons in the present glassy system. To shed some light on this issue, microstructural investigation of the as-prepared samples has been performed. In this regard, SEM study has been done for x = 0.35, 0.55, 0.75 and 0.95. Fig. 1(b) exhibits SEM micrograph for a particular sample, x = 0.35, which shows surface morphology with various numbers of small irregular grains of sizes 60 - 80 nm. The histogram of particle-distribution within the glassy matrix for x = 0.35 is shown in the inset of Fig. 1(b). It is clearly observed from Fig. 1(b) that the smaller grains tend to form agglomerates, which should be treated as close pairs of impurity states. The above-mentioned “second effect” can be realised here at high temperature due to formation of such agglomerated defect states. In addition to this, polaron conduction may be trapped in the small grains in the high frequency and high temperature region. As a consequence, frequency-dependent portion of the conductivity above the frequency-independent portion of the conductivity decreases with increasing temperature. Fig. 2(a) presents the frequency dependent conductivity spectra of all compositions at a constant temperature (473 K). It has been identified from Fig. 2 (a) that with a rise in the concentration of V2 O5 , AC conductivity increases. The estimated total conductivity (σ total ) at five different frequencies is depicted in Fig. 2 (b) with temperature for x = 0.95. The DC conductivity (σ dc ) is also included here for comparison. At lower temperature, temperature dependence of σ total is less in comparison of frequency dependency and is just activated by thermal energy. At higher temperature, temperature dependence of σ total , however, strong, and their dependence on frequency become small and they are almost identical with a certain deviation in the values of σ dc . To explore frequency dependence conductivity (σ (ω )), Jonscher’s universal power law can be exploited for the present system like other amorphous semiconductors [10]. It can be expressed as
σ (ω) = σdc + AωHs
(2)
Here, σ dc is DC conductivity, A is a temperature dependent constant, which is expressed as: A = σ dc x ωH -s . It is reported [15] that the values of -log10 A/s is independent of the composition [15], which is indicative of non-hopping process [15] where A is a pre-exponential factor and s is the power law exponent.
3
Fig. 2. (a) AC conductivity at a constant temperature (493 K) for all x, (b) total conductivity (σ total ) as a function of reciprocal of temperature at five frequencies for x = 0.95.
Fig. 3. (a) The variation of ratio of -log10 A/s as functions of temperature of all asprepared samples; (b) reciprocal temperature dependence of mobile charge carrier concentration (N0 ).
However, study on Ag-ion conducting glasses [16] reveals contradictory results. Here [16], the values of -log10 A/n is dependent on the composition. Fig. 3(a) shows the plot of -log10 A/n with temperature, which is not constant for the entire temperature window. The feature of the -log10 A/s ratio (as seen in Fig. 3(a)) specifies that the temperature advancement of log10 A is not comparative to the temperature advancement of s, which may reveal hopping type
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S. Bhattacharya / Physics Letters A ••• (••••) ••••••
4
of conduction process in the present system. The ratio between log10 A and s may be considered to be dependent on the microstructural network, as the power law exponent (s) represents the strength of cooperation between polarons and their surrounding environments. At higher frequency, σ (ω ) increases proportionally with frequency as the intra-well hopping [10] becomes dominant in the higher frequency regime. The power-law exponent (s) has been frequently applied to comprehend the mechanism of electrical conduction in amorphous semiconductors, disorder and ionic glasses [17] and also describes how the transportation of polaron hopping proceeds concerning localized sites. The values of the power law exponent (s) are estimated from the best least-square straight-line fits of the high frequency conductivity data, which may be an outcome of the collective motion of polarons in the short-range order. “Mobile charge carrier concentration” is one of the key parameters of “electrical transport properties of a disordered solid”. Nernst-Einstein relation [8] has been employed here to evaluate the value of the mobile charge carrier concentration, which is expressed as
σdc =
q2 λ2 Nc ωH 12π KT
(3)
where Nc is the free charge carrier or polaron concentration, q is the charge, λ is the average jump distance and ωH is the hopping frequency of charge carriers or polaron. Here, polaron hopping frequency is assumed to be same as ωH as the conductivity is realised due to polaron hopping [10]. The shortest distance in relation to the neighbouring charge carriers is considered as a mean jump distance (λ) [8]. Estimated values of Nc of all as-prepared samples with temperature are presented in Fig. 3(b), which signifies that Nc is not dependent on temperature. Almost steady values of Nc may directly indicate that the concentration of charge carriers, therefore, do not undertake a considerable part in electrical conduction, as the mobility of the charge carrier [8] plays a most significant role in the conduction process. The total concentration (N) of charge carrier is evaluated from the composition and density of the as-prepared glassy samples. The ratio Nc /N indicates that only 15-20% of the total charge carriers or polarons are responsible for the electrical conduction. As the concentration of V2 O5 in the glassy system increases, the network structure are expected to vary from two to three dimensions, which may cause to diverge
the configuration of V2 O5 from VO4 tetrahedral to VO5 trigonal bi-pyramid. The present result may predict the structural modifications, which is manifested by change in mobility of the charge carrier [8]. 4. Conclusion The high frequency dispersion in the conductivity of a semiconducting vanadate glassy system shows important feature, which follows the Jonscher’s universal power law. The fits of AlmondWest formalism of experimental data are in good agreement for as-prepared samples. The ratio between conductivity pre-factor and frequency power may be considered to be dependent on the micro-structural network. It is also perceived that only 15-20% of the total charge-carriers take part in the electrical conduction process. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] H. Masai, S. Matsumoto, Y. Ueda, A. Koreeda, J. Appl. Phys. 119 (2016) 185104. [2] A. Ghosh, J. Appl. Phys. 64 (1988) 2652–2655. [3] B. Peng, Z. Fan, X. Qui, L. Jaing, H.D. Ford, W. Huang, Adv. Mater. 17 (2005) 857–859. [4] N.F. Mott, J. Non-Cryst. Solids 1 (1968) 1–17. [5] I.G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41–102. [6] P. Petkova, K. Boubaker, P. Vasilev, M. Mustafa, A. Yumak, H. Touihri, M.T. Soltani, AIP Conf. Proc. 1727 (2016) 020017. [7] D.C. Look, Mater. Sci. Eng. B 80 (2001) 383–387. [8] Glass Nanocomposites: Synthesis, Properties and Applications, Elsevier, 2016. [9] D.P. Almond, A.R. West, Nature 306 (1983) 456–457. [10] A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics, London, 1983. [11] A.N. Papathanassiou, I. Sakellis, J. Grammatikakis, Appl. Phys. Lett. 91 (2007) 122911. [12] A. Palui, A. Ghosh, J. Appl. Phys. 121 (2017) 125104. [13] D. Emin, Adv. Phys. 24 (1975) 305. [14] M. Pollak, T.H. Geballe, Phys. Rev. 122 (1961) 1742. [15] A.N. Papathanassiou, J. Non-Cryst. Solids 352 (2006) 5444–5445. [16] J.L. Ndeugueu, M. Aniya, J. Mater. Sci. 44 (2009) 2483–2488. [17] M.D. Ingram, Phys. Chem. Glasses 28 (1987) 215–234.
[m5G; v1.282; Prn:17/02/2020; 13:13] P.1 (1-4)
Physics Letters A ••• (••••) ••••••
Contents lists available at ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
AC conductivity behaviour and charge carrier concentrations of some vanadate glassy system Sanjib Bhattacharya Department of Engineering Sciences and Humanities, Siliguri Institute of Technology, Darjeeeling-734009, West Bengal, India
a r t i c l e
i n f o
Article history: Received 4 November 2019 Received in revised form 5 January 2020 Accepted 8 February 2020 Available online xxxx Communicated by M. Wu
a b s t r a c t The investigation of wide range of temperature and frequency dependent conductivity of some semiconducting glassy system reveals DC conductivity, crossover frequency and frequency exponent. The composition dependence of AC conduction activation energy and the permissible energy of polaron migration have also been computed. The Nernst-Einstein relation proves that the concentration of mobile charge carriers does not undertake a substantial part in electrical conduction. © 2020 Published by Elsevier B.V.
Keywords: Amorphous materials Electrical properties Vanadate semiconducting glassy system AC conductivity and frequency exponent (n) Power law exponent (s) Mobile charge carrier concentrations
1. Introduction Transition metal oxide (TMO) such as V2 O5 doped glassy materials usually exhibit semiconducting behaviour [1], which make them important for various applications such as electrochromic devices, optical devices, switching, and memory switching devices, etc. [2,3]. In glassy system containing vanadium pentoxide (V2 O5 ) as a glass network former, the electrical conduction may arise for hopping conduction of unpaired 3d1 electron between V4+ and V5+ valence states [4,5]. These unpaired electrons are supposed to start polarization about vanadium ions to form a quasi-particle, known as polaron [4,5]. The transparent conducting oxide (TCO) ZnO has been broadly used as touch panels, window electrodes for flat panel displays, and in solar cells as they reveal excellent electrical and optical properties [6]. Moreover, it has also been typically used in varistors, piezoelectric transducers, optical waveguides, and gas sensor [7]. “AC conductivity” can be considered as a significant feature to retrieve confirmation of the occurrence of defect states in the glassy system and can be utilized to discriminate the conduction process [8]. Certain models, for instance, quantum-mechanical tunnelling model (QMT) [8], non-overlapping small polaron tunnelling model (NSPT) [8] etc have been predicted by many researchers to exhibit AC conduction mechanism owing to hopping or tunnelling of electrons or polarons. But till date, no concrete explanation on this conduction process has been revealed.
E-mail address: [email protected]. https://doi.org/10.1016/j.physleta.2020.126324 0375-9601/© 2020 Published by Elsevier B.V.
So, the study of AC conductivity of semiconducting glassy system is essential for material researchers not only for practical applications but also for academic interest. In the present communication, the AC conductivity of a semiconducting glassy system has been investigated in a wide frequency and temperature range. The electrical measurements data have been analyzed using some theoretical models to elucidate conduction mechanism, power law exponent and charge carrier concentration. 2. Experimental TMO-doped semiconducting glassy system, xV2 O5 –(1-x) (0.05 SeO2 –0.95 ZnO) with x = 0.35, 0.55, 0.75 and 0.95 have been prepared using melt quenching route from reagent grade chemicals. To conduct electrical measurements, both sides of the as-prepared glassy samples are coated with conducting silver paste to serve as the electrode. Electrical measurements of the as-prepared samples have been measured using HIOKI (model no. 3532-50) made programmable high precision LCR meter at various temperatures and in the frequency window 42 Hz to 5 MHz. The microstructures of as-prepared samples have been performed using a JEOL made Scanning Electron Microscopic (SEM) studies. 3. Results and discussions AC conductivity spectra for x = 0.35 is presented in Fig. 1(a) at various temperatures, which reveal two distinct regions: (i) almost
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[m5G; v1.282; Prn:17/02/2020; 13:13] P.2 (1-4)
S. Bhattacharya / Physics Letters A ••• (••••) ••••••
2
Fig. 1. (a): Real part of conductivity spectra at different temperature for x = 0.35; (b) Imaginary part of conductivity spectra at different temperature for x = 0.35; (c) SEM micrograph for a particular sample, x = 0.35; (d) The histogram of particle-distribution within the glassy matrix for x = 0.35.
flat or plateau region and (ii) dispersion region. At lower frequency, the flat region is recognized where conductivity (σ (ω )) is almost frequency independent, and the width of the plateau region rises with a rise in temperature. However, dispersion commences at higher frequency region, which reveals frequency dependent conductivity in terms of introduction to power-law [8,9]. The width of dispersion region (high frequency range) is found to reduce with temperature. The real part of AC conductivity of amorphous materials exhibits the power-law dependency, suggested by AlmondWest [9]
σ (ω) = σdc 1 +
ω ωH
Table 1 The values of hopping frequency (ωH ) at 493 K, activation energy for hopping frequency (EH ), DC conductivity (σ dc ) at 493 K, average frequency exponent (n) from Almond West Power Law. x
Log ωH (rad s−1 ) at 493 K
EH (±0.002 eV)
Log σ dc (−1 cm−1 ) at 493 K
Average value of n
0.35 0.55 0.75 0.95
6.134 6.448 7.535 8.549
0.148 0.324 0.267 0.264
-7.271 -6.264 -5.201 -4.421
0.872 0.756 0.536 1.146
n (1)
where, σ dc is DC conductivity, ωH is hopping or crossover frequency from DC region (plateau region) to the dispersion region and n is the frequency exponent. The values of σ dc , ωH and n are obtained from the non-linear best fitted curve fitting of conductivity spectra using Eq. (1) as presented in Fig. 1(a) by solid lines. The values of σ dc and ωH at temperature 493 K and the average values of n are estimated and included in Table 1. Here, ωH shows thermally activated nature, which follows similar nature of DC conductivity. Hopping of polaron can be the best-suited process for AC conduction in all as-prepared samples [10]. In Almond-West formalism, n is associated with diffusion of charge carriers in random charge conducting paths in term of dimensionality of conduction pathways [8]. It may be put forward that the dispersion in the AC conductivity is influenced by the dimensionality of the charge carrier, which is evidenced by the numerical values of frequency exponent (n) [8]. The frequency dependent conductivity may re-
late to hopping of polaron in a bit of short distances concerning adjacent sites, separated by energy barriers of varying heights. If polaron hopping in the present glassy system appears suddenly between randomly distributed localized charge states, n value lies between 0.7 and 1 (Table 1). The lower value of n usually arises in multiple hops, while the higher value of n ensues for single hop and it indicates a strong drift of polarons [8]. It is pointed out from Table 1 that the value of n is highest of the sample for x = 0.95 that denotes strong polaron drift, thus, exhibiting highest conductivity. It can be concluded that in consequence of the morphological dispersion, the inter-site potential energy barrier should be significantly altered, which contribute to an excessive growth in the degree of polaron hopping. Papathanassiou et al. [11] successfully developed a model based on the aspect of the distribution of the length of conduction paths regarding the universal powerlaw dispersive AC conductivity, observed in polymer networks and, generally, in disordered matter. Larger values of power law ex-
JID:PLA AID:126324 /SCO Doctopic: Condensed matter
[m5G; v1.282; Prn:17/02/2020; 13:13] P.3 (1-4)
S. Bhattacharya / Physics Letters A ••• (••••) ••••••
ponent (>1) are physically acceptable within this model, which should be restricted by an upper frequency limit. For complete understanding of the conductivity, imaginary part of conductivity [12] is also studied. Fig. 1(b) presents the imaginary part of conductivity spectra for a particular sample, x = 0.35. At higher frequencies, a gradual increase of conductivity is observed in Fig. 1(b). As the frequency is decreased, conductivity is found to decrease up to certain frequency, below which it shows an increasing nature. It is also noted that electrode polarization becomes significant at lower frequencies. To shed more light on the nature of conductivity spectra as shown in Fig. 1(a), Emin-model [13] has been considered, which indicates that there are two sources of the frequency-dependence for polaron-hopping conductivity’s. Firstly, the jump rate for a polaron hop increases with applied frequency (except at exceptionally high temperatures) as per Eq. (94) and curve b of Fig. 7 in Ref. [13]. Secondly, the conductivity of carriers confined within spatial regions by disorder rises as the applied frequency is increased [13]. The second effect [13] generates the very lowtemperature (< 10 K) AC conductivity of charge carriers that hop between especially close pairs of impurity states of very lightly doped compensated covalent semiconductors [14]. However, the major issue is to explain of such an effect, which should dominate the high-temperature hopping of high densities of polarons in the present glassy system. To shed some light on this issue, microstructural investigation of the as-prepared samples has been performed. In this regard, SEM study has been done for x = 0.35, 0.55, 0.75 and 0.95. Fig. 1(b) exhibits SEM micrograph for a particular sample, x = 0.35, which shows surface morphology with various numbers of small irregular grains of sizes 60 - 80 nm. The histogram of particle-distribution within the glassy matrix for x = 0.35 is shown in the inset of Fig. 1(b). It is clearly observed from Fig. 1(b) that the smaller grains tend to form agglomerates, which should be treated as close pairs of impurity states. The above-mentioned “second effect” can be realised here at high temperature due to formation of such agglomerated defect states. In addition to this, polaron conduction may be trapped in the small grains in the high frequency and high temperature region. As a consequence, frequency-dependent portion of the conductivity above the frequency-independent portion of the conductivity decreases with increasing temperature. Fig. 2(a) presents the frequency dependent conductivity spectra of all compositions at a constant temperature (473 K). It has been identified from Fig. 2 (a) that with a rise in the concentration of V2 O5 , AC conductivity increases. The estimated total conductivity (σ total ) at five different frequencies is depicted in Fig. 2 (b) with temperature for x = 0.95. The DC conductivity (σ dc ) is also included here for comparison. At lower temperature, temperature dependence of σ total is less in comparison of frequency dependency and is just activated by thermal energy. At higher temperature, temperature dependence of σ total , however, strong, and their dependence on frequency become small and they are almost identical with a certain deviation in the values of σ dc . To explore frequency dependence conductivity (σ (ω )), Jonscher’s universal power law can be exploited for the present system like other amorphous semiconductors [10]. It can be expressed as
σ (ω) = σdc + AωHs
(2)
Here, σ dc is DC conductivity, A is a temperature dependent constant, which is expressed as: A = σ dc x ωH -s . It is reported [15] that the values of -log10 A/s is independent of the composition [15], which is indicative of non-hopping process [15] where A is a pre-exponential factor and s is the power law exponent.
3
Fig. 2. (a) AC conductivity at a constant temperature (493 K) for all x, (b) total conductivity (σ total ) as a function of reciprocal of temperature at five frequencies for x = 0.95.
Fig. 3. (a) The variation of ratio of -log10 A/s as functions of temperature of all asprepared samples; (b) reciprocal temperature dependence of mobile charge carrier concentration (N0 ).
However, study on Ag-ion conducting glasses [16] reveals contradictory results. Here [16], the values of -log10 A/n is dependent on the composition. Fig. 3(a) shows the plot of -log10 A/n with temperature, which is not constant for the entire temperature window. The feature of the -log10 A/s ratio (as seen in Fig. 3(a)) specifies that the temperature advancement of log10 A is not comparative to the temperature advancement of s, which may reveal hopping type
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AID:126324 /SCO Doctopic: Condensed matter
[m5G; v1.282; Prn:17/02/2020; 13:13] P.4 (1-4)
S. Bhattacharya / Physics Letters A ••• (••••) ••••••
4
of conduction process in the present system. The ratio between log10 A and s may be considered to be dependent on the microstructural network, as the power law exponent (s) represents the strength of cooperation between polarons and their surrounding environments. At higher frequency, σ (ω ) increases proportionally with frequency as the intra-well hopping [10] becomes dominant in the higher frequency regime. The power-law exponent (s) has been frequently applied to comprehend the mechanism of electrical conduction in amorphous semiconductors, disorder and ionic glasses [17] and also describes how the transportation of polaron hopping proceeds concerning localized sites. The values of the power law exponent (s) are estimated from the best least-square straight-line fits of the high frequency conductivity data, which may be an outcome of the collective motion of polarons in the short-range order. “Mobile charge carrier concentration” is one of the key parameters of “electrical transport properties of a disordered solid”. Nernst-Einstein relation [8] has been employed here to evaluate the value of the mobile charge carrier concentration, which is expressed as
σdc =
q2 λ2 Nc ωH 12π KT
(3)
where Nc is the free charge carrier or polaron concentration, q is the charge, λ is the average jump distance and ωH is the hopping frequency of charge carriers or polaron. Here, polaron hopping frequency is assumed to be same as ωH as the conductivity is realised due to polaron hopping [10]. The shortest distance in relation to the neighbouring charge carriers is considered as a mean jump distance (λ) [8]. Estimated values of Nc of all as-prepared samples with temperature are presented in Fig. 3(b), which signifies that Nc is not dependent on temperature. Almost steady values of Nc may directly indicate that the concentration of charge carriers, therefore, do not undertake a considerable part in electrical conduction, as the mobility of the charge carrier [8] plays a most significant role in the conduction process. The total concentration (N) of charge carrier is evaluated from the composition and density of the as-prepared glassy samples. The ratio Nc /N indicates that only 15-20% of the total charge carriers or polarons are responsible for the electrical conduction. As the concentration of V2 O5 in the glassy system increases, the network structure are expected to vary from two to three dimensions, which may cause to diverge
the configuration of V2 O5 from VO4 tetrahedral to VO5 trigonal bi-pyramid. The present result may predict the structural modifications, which is manifested by change in mobility of the charge carrier [8]. 4. Conclusion The high frequency dispersion in the conductivity of a semiconducting vanadate glassy system shows important feature, which follows the Jonscher’s universal power law. The fits of AlmondWest formalism of experimental data are in good agreement for as-prepared samples. The ratio between conductivity pre-factor and frequency power may be considered to be dependent on the micro-structural network. It is also perceived that only 15-20% of the total charge-carriers take part in the electrical conduction process. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1] H. Masai, S. Matsumoto, Y. Ueda, A. Koreeda, J. Appl. Phys. 119 (2016) 185104. [2] A. Ghosh, J. Appl. Phys. 64 (1988) 2652–2655. [3] B. Peng, Z. Fan, X. Qui, L. Jaing, H.D. Ford, W. Huang, Adv. Mater. 17 (2005) 857–859. [4] N.F. Mott, J. Non-Cryst. Solids 1 (1968) 1–17. [5] I.G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41–102. [6] P. Petkova, K. Boubaker, P. Vasilev, M. Mustafa, A. Yumak, H. Touihri, M.T. Soltani, AIP Conf. Proc. 1727 (2016) 020017. [7] D.C. Look, Mater. Sci. Eng. B 80 (2001) 383–387. [8] Glass Nanocomposites: Synthesis, Properties and Applications, Elsevier, 2016. [9] D.P. Almond, A.R. West, Nature 306 (1983) 456–457. [10] A.K. Jonscher, Dielectric Relaxation in Solids, Chelsea Dielectrics, London, 1983. [11] A.N. Papathanassiou, I. Sakellis, J. Grammatikakis, Appl. Phys. Lett. 91 (2007) 122911. [12] A. Palui, A. Ghosh, J. Appl. Phys. 121 (2017) 125104. [13] D. Emin, Adv. Phys. 24 (1975) 305. [14] M. Pollak, T.H. Geballe, Phys. Rev. 122 (1961) 1742. [15] A.N. Papathanassiou, J. Non-Cryst. Solids 352 (2006) 5444–5445. [16] J.L. Ndeugueu, M. Aniya, J. Mater. Sci. 44 (2009) 2483–2488. [17] M.D. Ingram, Phys. Chem. Glasses 28 (1987) 215–234.