Materials Science and Engineering B 137 (2007) 237–246
Structural and Polaronic transport properties of semiconducting CuO–V2O5–TeO2 glasses M.M. El-Desoky a,∗ , M.S. Al-Assiri b a
b
Physics Department, Faculty of Education, Suez Canal University, El-Arish, Egypt Physics Department, Faculty of Science, King Khalid University, P.O. Box 9003, Abha, Saudi Arabia
Received 26 September 2006; received in revised form 21 November 2006; accepted 22 November 2006
Abstract Ternary semiconducting glasses in the CuO–V2 O5 –TeO2 system have prepared by the press-quenching technique. X-ray diffraction (XRD), scanning electron microscopy (SEM), differential scanning calorimeter (DSC), infrared (IR) spectra, density (d) and oxygen molar volume (Vm ) and dc conductivity (σ) of these glasses were reported. The overall features of XRD curves confirm the amorphous nature of the present glasses. SEM exhibits a surface without any presence of microstructure which is a characteristic of the amorphous phase. Density was observed to decrease with an increase in V2 O5 content. The network structure for the glass compositions with 57.5 mol% V2 O5 is built up of the VO5 polyhedra, while the other glass compositions consist of VO4 polyhedra. The temperature dependence of the conductivity data has been analyzed in terms of different polaronic models. In high-temperature region above θ D /2 the Mott model of SPH between nearest neighbors is consistent with the conductivity data, while at intermediate temperature the Greaves VRH (variable-range hopping) model was found to be appropriate. The conduction was confirmed to obey the adiabatic SPH and was mainly due to electronic transport between V ions. The dominant factor determining conductivity was the hopping carrier mobility in these glasses. © 2006 Elsevier B.V. All rights reserved. Keywords: Vanadate glasses; IR spectra; Density; SEM; SPH; VRH; Hopping carrier mobility
1. Introduction The semiconducting properties of transition metal oxide (TMO) glasses arise from the presence of different valence states of transition metal ions [1–9]. In these glasses the electrical conduction is due to the transport of electrons. The research in consideration with the structural and physical properties of glasses in general, and glassy semiconducting in particular have increased considerably due to the potential applications apparent for semiconducting glasses. There has been continued research work in the V2 O5 -based semiconducting glasses [10–13] because of their applications such as switching and memory devices [14], transducers, superior insulators and dielectrics, from switching and memory diodes to computer memories height being cheaply produced with glass [3–8]. The conduction mechanism of these glasses was interpreted
∗
Corresponding author. Present address: Physics Department, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia. E-mail address:
[email protected] (M.M. El-Desoky). 0921-5107/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.mseb.2006.11.032
by the small polaron hopping (SPH) model [15–17]. Vanadate glasses with a large concentration of V2 O5 (≥50 mol%) [4] are highly conductive. Lately, works on vanadium tellurite glasses [18] were carried out owing to their relatively high conductivities. We have studied the dc conductivity of V2 O5 –NiO–TeO2 [4] and V2 O5 –Fe2 O3 –TeO2 [19] from room temperature to 450 K, and the conduction was attributed to adiabatic SPH for V2 O5 ≥ 50 mol%. The effect of the second TMO on the conductivity were reported [4,18,19] and the glasses containing two kinds of transition metal ions have become the center of this conductivity study. These glasses showed relatively high conductivities of ∼10−4 S cm−1 above 400 K [4,18,19]. Highly conductive tellurite glasses containing two TMO have a potential applicability as electrical devices (e.g. memory switching and gas sensor). However, there exists a controversy over the nature of hopping mechanism in different temperature and composition regions [4,19]. There are also contradictory reports on the effect of the network formers and modifiers on the hopping mechanism. Studies of the infrared (IR) properties of a number of vanadate glasses have been reported [19–22]. It has been observed that the structure of these glasses depends on the
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nature of the network formers as well as the network modifiers [19–22]. The main objective of the present work was to investigate three subjects. The first was to prepare ternary CuO–V2 O5 –TeO2 glasses. The second was to investigate the compositional dependence of the structural and transport properties of V2 O5 –TeO2 -based glasses in view of different models. The third was to clarify the mechanism of electrical conduction of CuO–V2 O5 –TeO2 glasses and to discuss the V2 O5 concentration dependence of conduction.
ished samples. The I–V characteristic between electrodes was confirmed. 3. Results The X-ray diffraction (XRD) patterns of several compositions of the prepared samples are shown in Fig. 1. From the XRD studies it is observed that homogenous glasses are formed for V2 O5 concentration between 50 and 57.5 mol%. Fig. 2(a and b) shows the scanning electron microscopy (SEM) and dot mapping micrographs of oxygen, copper,
2. Experimental Reagent grade CuO (99.9%),V2 O5 (99.9%) and TeO2 (99.999%) were used as raw materials. After mixing in air a batch 10 g with prescribed compositions, the mixed mass of each glass composition was melted in platinum crucible for 1 h at 1150 K in an electric furnace. The melt was then poured on a thick copper block and immediately quenched by pressing with another similar copper block. Following this procedure we obtained bulk glass of 2 cm × 2 cm size and about 1 mm in thickness. The amorphous nature of the glasses was ascertained from X-ray diffraction (XRD) analysis using XRD-6000 Shimadzu (with Cu K␣ radiation). Scanning electron microscopy (SEM) of the glass samples was measured using JEOL JSM–636oLA. The density of the glasses was measured by the Archimedes method using toluene as the immersion liquid. Infrared (IR) spectra of the glass samples were measured from 400 to 2000 cm−1 by a conventional KBr pellet method on a Fourier transform infrared (FT-IR) spectrometer (Perkin-Elmer 1760X). Differential scanning calorimeter (DSC) of the samples was investigated using a Shimadzu DSC-50 with heating rate 20 ◦ C/min. The dc conductivity (σ) of the as-quenched glasses was measured at temperatures between 293 K and 473 K. Silver paste electrodes deposited on both faces of the pol-
Fig. 1. Room-temperature XRD for different glass compositions.
Fig. 2. SEM (a) and dot mapping (b) micrographs for 10CuO–50V2 O5 –40TeO2 glass.
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Fig. 4. Composition dependence of density (d) and oxygen molar volume (Vm ) for CuO–V2 O5 –TeO glasses.
Fig. 3. Room-temperature IR spectra for CuO–V2 O5 –TeO2 glasses.
tellurium and vanadium for 10CuO–50V2 O5 –40TeO2 glass, respectively. The room temperature IR spectra in the region 400– 2000 cm−1 of all glass compositions are shown in Fig. 3. The IR absorption studies of all these glasses are very similar, as shown in Fig. 3, for some of these glasses. A weak band at 1110–1125 cm−1 is observed for some glasses. This band is assigned to the vibrations of isolated V O vanadyl groups in VO5 trigomal bi-pyramids [19,20]. However, in the glass compositions containing 57.5 mol% V2 O5 this band completely vanishes. Fig. 4 shows the composition dependence of density (d) and oxygen molar volume (V) of the present glass system. It may be observed that density (d) decreases gradually with the increase of the vanadium oxide content in the glass compositions. The relationship between density and composition of an oxide glass system can be expressed in terms of an apparent volume Vm occupied by 1 g atom of oxygen. Fig. 5 shows the composition dependence of glass transition temperature (Tg ) for the present glass system and DSC for10CuO–50V2 O5 –40TeO2 glass. Each curve exhibits an endothermic dip due to glass transition (Tg ) and exothermic peak corresponding to crystallization (Tc ). Also, from the figure it is clear that Tg decreased with increasing V2 O5 content
and lie between 531 K and 541 K. Moreover, Tc lies between 518 K and 585 K for the present glass system. It is known that the thermal stability of a glass depends on T = Tc − Tg of the glass [19]. This result is due to the fact that the present glasses were thermal stable in comparison with the thermal stability of V2 O5 –MnO–TeO2 glasses [23], because the T values of the present glasses (T ≈ 67 K) were higher than those of V2 O5 –MnO–TeO2 glasses (T ≈ 60 K). The electrical conductivity (σ) for several glass compositions is shown in Fig. 6 as a function of 1/T. Fig. 6 shows a linear temperature dependence up to a critical temperature θ D /2 (θ D /2: θ D Debye temperature) and then the slope changes with deviation from linearity and the activation energy (W) is temperature dependent. Such a behavior is a feature of SPH [15,16]. However, above this temperature range, the variation of activation
Fig. 5. DSC for 10CuO–50V2 O5 –40TeO2 glass and composition dependence of glass transition temperature (Tg ) for different glass compositions.
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Cu, Te and V) are mainly consistent with start elements ratio of the present glass sample. A similar feature was observed in the other samples. 4.2. IR Spectra
Fig. 6. Temperature dependence of dc conductivity (σ) for CuO–V2 O5 –TeO glasses. The dash lines are the least-square straight-line fits.
energy with temperature is negligibly small so that the behavior may be treated as activated. The experimental conductivity data in such a situation is well described with an activation energy for conduction (W) given by Mott formula [15,16]: σ = σo exp(−W/kT )
(1)
where σ o is a pre-exponential factor as discussed below. The activation energy (W) and pre-exponential factor (σ o ) were obtained from the least square straight line fits of the data above 312 K. For these glass samples r2 = 0.9900 (r = correlation coefficient) and range = 1.04 × 10−5 S m−1 were obtained, which indicate a satisfactory fit.
In the glass containing 57.5 mol% V2 O5 , VO5 groups with unaffected V O bonds are preserved along with the affected VO5 polyhedra [14,15]. With decrease of V2 O5, only affected ones are obtained in the glass samples containing 55–50 mol% V2 O5. This means that the network structure is build up of VO5 polyhedra for the glass compositions with higherV2 O5 content [14]. However, as the V2 O5 content decreases, the glass structure consists of the VO4 polyhedra [19]. Finally, Dimitiev and co-workers [20] attributed the IR spectra absorption band in the range from 645 to 675 cm−1 , to TeO3 trigonal pyramids. This band corresponds to phonon frequency (o ) of about (1.92–2.01) × 1013 Hz, which agree well with that measured from the electrical conductivity data, as discussed in Section 5. 4.3. Density and oxygen molar volume The value of Vm has been calculated from the density and composition using the formula reported earlier [19] and its composition dependence is shown in Fig. 4. It is observed that Vm increases monotonically with an increase of V2 O5 content in the composition. These indicate that the topology of the network does not considerably change with composition and the glass compositions appear to be in single phase with random network structure [21,22]. These results are also agreed well with the SEM micrographs. The density (d) and molar volume (Vm ) are given in Table 1.
4. Discussion 4.4. DSC 4.1. X-ray diffraction and scanning electron microscopy The overall features of these XRD patterns confirm the amorphous nature of the present glasses. The XRD patterns of present glasses as shown in Fig. 1 indicate glassy behavior with a broad hump at 2θ = 25–27◦ . No peak corresponding to V2 O5 is observed indicating that V2 O5 has completely entered the glass matrix. The micrograph of 10CuO–50V2 O5 –40TeO2 sample (Fig. 2a) exhibits a surface without any presence microstructure which is again a characteristic of the amorphous phase. The dot mapping micrographs (Fig. 2b) for different elements (O,
Thermal stability of glasses is a result of glass structure. Normally, thermally stable glasses have a closely backed structure [24]. Inversely, the structure of thermally unstable glasses possesses a loose packing [24]. Thus, we assumed the present glasses have a more closely packed structure. For vanadate glasses, when a layered-network structure including a VO4 polyhedra unit [19,21] increases in the concentration, the glasses from a closely backed structure [21,22], while the glasses form a loosely packed structure, when the network structure with VO5 polyhedra unit increases in concentration [21]. On the other hand, DSC studies [24] on the structure of many glasses have
Table 1 Chemical composition and physical properties of CuO–V2 O5 –TeO2 glasses Glass no.
1 2 3 4
Nominal composition (mol%) CuO
V2 O5
TeO2
10 10 10 10
50 52.5 55 57.5
40 37.5 35 32.5
d ± 0.02 (g cm−3 )
Vm ± 0.02 (cm3 /mol%)
Tg ± 1 (K)
Tc ± 1 (K)
R ± 0.01 (eV)
N ± 0.01 (×1022 cm−3 )
W ± 0.01 (eV)
3.78 3.55 3.33 2.91
43.05 45.99 49.19 56.49
541 538 536 531
618 611 601 585
0.40 0.35 0.33 0.30
1.44 1.35 1.26 1.10
0.40 0.35 0.33 0.30
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Fig. 7. Effect of V2 O5 content on dc conductivity (σ) at 400 K and activation energy for different glass compositions.
already exposed that Tg shows a obvious correlation with the change in the coordination number of the network former and the construction of non-bridging oxygen (NBO) atoms, which means destruction of the network structure [24]. The Tg usually, shows a distinct increase when the coordination number of the network former increases. Converse to this, a construction of NOB causes a decrease in the Tg . The continuous decrease in the Tg in the present system, therefore, seems to suggest continuing decrease in the coordination number of V5+ and V4+ ions and construction of NOB atoms. These results are consistent with the IR spectra and density and oxygen molar volume data. Also, the decrease in Tg suggests that the strength of the chemical bond between metal and oxygen atoms becomes weakened. This is ascribed to the increased interatomic distances between metal and oxygen ions leading to decrease in the density and increase in the oxygen molar volume in the present glass system [19,24]. The Tg and Tc data are given in Table 1. 4.5. Electrical conductivity 4.5.1. Conductivity and activation energy The compositional dependence of the conductivity at 400 K and the activation energy are shown in Fig. 7. A general trend observed in Fig. 7 is that the magnitude of the conductivity at fixed (400 K)) tends to be highest in those compositions having smallest activation energy, which is consistent with SPH mechanism. The high value of activation energy and low value of electrical conductivity are similar to those forV2 O5 –BaO–B2 O3 , V2 O5 –NiO–TeO2 and Fe2 O3 –V2 O5 –TeO2 glasses [1,4,19]. Fig. 8 presents variation in conductivity with increasing in V2 O5 content at fixed temperature (300 K and 400 K). This means a ratio of V4+ ion CV (=V4+ /Vtotal ) increases, causing the activation energy W to decrease and σ to increase (Fig. 7). In the CuO–V2 O5 –TeO2 glasses of our present investigation, the V2 O5 addition increased the conductivity (Fig. 8). Generally, it is known that addition of vanadium oxide to the glass increases the conductivity as a result of increasing of nonbridging oxygen ion [5]. This may increase the open structure,
Fig. 8. Effect of V2 O5 content on dc conductivity (σ) for different glass compositions.
through which the charge carriers can move with higher mobility. This result is consistent with IR spectra, density and DSC results. A similar increasing of conductivity was also observed in V2 O5 –Fe2 O3 –TeO2 [19] and V2 O5 –NiO–TeO2 [4] glasses. The concentration of vanadium ion, N (cm−3 ) was estimated using N = dpNA /(Aw × 100), where d is the density of the sample, p the weight percentage of atoms, NA the Avogadro constant and Aw the atomic number. The relationship between N and mean distance (R) is generally described as follows: 1/3 1 R= (2) N The calculated values of R and N are summarized in Table 1. The relation between the activation energy (W) and the mean distance (R) between V ions is illustrated in Fig. 9 and Table 1. In the range of measurements, W depends on the site-to-site distance R. These results show that there is a prominent positive correlation between W and R between transition metal ions. This agrees with the results suggested by Sayer and Mansingh [6] and El-Desoky [4,19] delineated the dependence of W on the mean distance between transition metal ions. A similar behavior was observed in V2 O5 –NiO–TeO2 [4] glasses. Mott [15] has investigated the hopping conductivity in oxide glasses containing transition metal ions. The conductivity of the nearest neighbor at high temperatures (T > θ D /2) is given by [15]: σ
νo Ne2 R2 C(1 − C) exp(−2αR) exp(−W/kT ) kT = σo exp(−W/kT ) =
(3)
The pre-exponential factor (σ o ) in Eq. (3) is given by: σo =
νo Ne2 R2 C(1 − C) exp(−2αR) kT
(4)
where o is the optical phonon frequency, α the tunneling factor (the ratio of wave function decay), N the transition metal
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Fig. 9. Effect of mean V-ion spacing (R) on activation energy (W) for different glass compositions.
density, C the fraction of reduced transition metal ion (=C and C = V4+ /Vtotal ) and W is the activation energy for hopping conduction. Assuming a strong electron–phonon interaction, Austin and Mott [16] have shown that: W = WH + WD /2 W = WD
(for T > θD /2)
(for T < θD /4)
(5a) (5b)
where WH is the hopping energy and WD the disorder energy defined as the difference of electronic energies between two hopping sites. In the adiabatic hopping regime, however, when αR in Eq. (3) becomes negligible [15,16,25,26], then the conductivity (σ) and the pre-exponential factor (σ o ) in Eq. (3) are expressed by the following equations [15,16]: σ=
νo NeN 2 R2 C(1 − C) exp(−W/kT ) kT
Fig. 10. Effect of V2 O5 content on pre-exponential factor (σ o )for different glass compositions.
the relation log σ versus W for the present glasses by the leastsquare technique, and the slope of the regression line in Fig. 10 was obtained to be −12.40 eV−1 . This value was almost the same as the theoretical slope for the adiabatic hopping (tan θ in Fig. 11), i.e. −12.40 eV−1 (=−1/2.303kT, T = 400 K). The equivalent temperature evaluated from the slope of regression line gave T = 405 K, which is nearly equal to the measured value T = 400 K. From both these results, we conclude the conduction of the present glasses to be due to adiabatic SPH of electrons [15,16]. The SPH model [15,16] predicts that an appreciable departure from linear plot of dc conductivity versus inverse temperature should occur at a critical temperature θ D /2. Fig. 6 shows linear temperature dependence up to a critical temperature θ D /2
(6)
and σo =
νo Ne2 R2 C(1 − C) kT
(7)
From Eq. (6) σ o is independent of V2 O5 concentration and hardly varies with V2 O5 content [4,19]. Therefore, the dominant factor contributing to the conductivity should be W in the adiabatic regime [4,19]. For the present glasses, we calculated the term of σ o using experimental values in Table 1. Fig. 10 presents the effect of V2 O5 concentration on σ o , indicating almost unchanged value of σ o for V2 O5 : 50–57.5 mol%. These results indicate that σ depends only on W in Eq. (6) in adiabatic regime for the present glasses as well as previous glasses [4,19]. Then, based on this result, log σ at a given temperature is proportional to W and the log σ–W relation should become log σ = log σ o − W/2.303kT from Eqs. (3) and (6). Fig. 11 shows the relationship between log σ at 400 K and W. This relationship was linear for the present glasses. We filled the data to
Fig. 11. Effect of activation energy (W) on dc conductivity (σ) at T = 400 K for different glass compositions.
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Table 2 Polaron hopping parameters of CuO–V2 O5 –TeO2 glasses Glass no.
θD ± 1 (K)
o ± 0.01 (×1013 Hz)
WH ± 0.01 (eV)
εp ± 0.02
rP ± 0.001 ˚ (A)
N (EF ) (×1021 eV−1 cm−3 )
γ p ± 0.1
J ± 0.01 (eV)
mp /m* ± 0.01 (×105 )
1 2 3 4
666 645 635 625
1.39 1.34 1.32 1.30
0.37 0.34 0.31 0.28
49.65 52.96 56.95 60.23
1.65 1.69 1.73 1.81
8.59 9.21 9.16 8.79
12.88 12.21 11.32 10.39
0.76 0.61 0.54 0.48
3.92 2.00 0.82 0.33
and then the slope changes with deviation from linearity and the activation energy is temperature dependent. Such a behavior is a feature of SPH [15,16]. The Debye temperatures of the present system were obtained to be 625–666 K. The estimated phonon frequency of all our glass samples is of the order 1013 Hz, as shown in Table 2 [19]. The characteristic phonon frequency evaluated from IR spectra (Fig. 3) are found to be (1.92–2.01) × 1013 Hz, corresponding to an IR bands (640–670) cm−1 . Then, the values of phonon frequency estimated from SPH model are close to the optical phonon frequency (o ) estimated from IR spectra studies [23]. 4.5.2. Polaron hopping parameters A polaron hopping model has been investigated by Friedman and Holeston [27] considering zero disorder energy and covering both the adiabatic and non-adiabatic hopping processes. On the basis of molecular crystal model, Emin and Holstein [28] have derived an expression for the dc conductivity: 2 π 3e NR2 J 2 (−2αR) exp(−WH /kT ) (8) σ= 2kT kTWH For the case of non-adiabatic hopping, while Emin and Holstein [28] have shown that for the case of adiabatic hopping: (WH − J) 8νo πe2 NR2 exp − , (9) σ= 3kT kT where J is a polaron band width related to electron wave function overlap on the adjacent sites. The present experimental results follow Eq. (9) much more closely, with a thermal activation WH , which varies with the V2 O5 content. This model also provides an independent way of ascertaining the nature of hopping mechanism at high temperatures. The condition for the nature of hopping can be expressed by [28]: 2kTWH 1/4 h ¯ νo 1/2 J> (adiabatic) (10) π π
can be obtained from [28]: 1/2 3 N(EF ) J ≈e (ε0 εp )3
(12)
Using the values of N(EF ) and εp from Table 2, Eq. (12) gives J ≈ 0.65 eV, and thus adiabatic hopping theory is most appropriate to describe the polaronic conduction at high temperatures in the present glasses. Holstein [29] has suggested a method for calculating the polaron hopping energy WH WH = (1/4N) [γp ]2h ¯ ωp (13) p
where [γ p ]2 is the electron–phonon coupling constant and ωq is the frequency of the optical phonons of wave number. Bogomolov et al. [30] have calculated the polaron radius rp for a non-dispersive system of frequency υo for Eq. (13): π 1/3 R (14) rp = 6 2 The values of the polaron radii calculated from Eq. (14), using R from Table 1 is shown in Table 2 for the present glasses. Although the possible effect of disorder has been neglected in the above calculation, the small values of polaron radii suggest that the polarons are highly localized. These results are very similar to the V2 O5 –NiO–TeO2 glasses [4]. The polaron hopping energy WH is given by [30]: 1 e2 1 WH = (15) − 4εP rP R where 1 1 1 = − εP ε∞ εS
(16)
(11)
εS and ε∞ are the static and high frequencies dielectric constants of the glass. An estimate of WH can be made from Eq. (15) from the known values of R and rp , while εP was estimated from cole–cole plot [31]. The values of WH and εP are given in Table 2. The density of states (N(EF )) for thermally activated electron hopping near the Fermi level is given from basic principles as [19,23]:
The limiting value of J calculated from the right-hand side of expression (10) or (11) at 400 K is of the order of 0.036–0.040 eV, depending on composition. An unambiguous decision as to whether the polaron is actually in the adiabatic or in the nonadiabatic regime requires an estimate of the value of J, which
3 (17) 4πR3 W Using R and W values from Table 1, one can calculate N(EF ) for the present glasses. It is clear that, the density of states N(EF ) is of the order 1021 (eV−1 cm−3 ) [4–8]. The values of N(EF )
and J<
2kTWH π
1/4
h ¯ νo π
1/2 (non − adiabatic)
N(EF ) =
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Table 3 Hopping carrier mobility and density of CuO–V2 O5 –TeO2 glasses Glass no.
μ ± 0.3 (×10−5 cm2 V−1 s−1 ) (400 K)
Nc ± 0.2 (×1020 cm−3 ) ± (400 K)
1 2 3 4
1.49 3.61 8.84 22.72
2.65 3.22 3.46 2.79
are listed in Table 2. The N(EF ) values are reasonable for the localized states [4–8,19,25,26]. The small polaron coupling constant (γ p ), a measure of the electron–phonon interaction is given by γ p = 2WH /hνo [15]. The estimated γ p for these glasses was γ p = 10.39–12.88 (Table 2), which was similar to those for V2 O5 –Fe2 O3 –TeO2 glasses [19] (γ p = 21–26), and CaO–BaO–Fe2 O3 –P2 O5 glasses [3] (γ p = 21–29.2) but larger than those for V2 O5 –Bi2 O3 glasses doped with BaTiO3 [9] (γ p = 7–7.6). Austin and Mott [16] suggested that a value of γ p > 4 usually indicates a strong electron–phonon interaction in glasses. From the values of γ p , an estimate of polaron effective mass, mp , in the present system is obtained using the relation [15]: h exp(γp ) = m∗ exp(γp ) (18) mp = 2EJ R2 where m* is the rigid lattice effective mass. The calculated values of γ p and mp /m* are found to be quite large (Table 2) indicating strong phonon interaction in the present system [25]. 4.5.3. Hopping carrier mobility and density The hopping carrier mobility (μ) in the adiabatic and non-adiabatic hopping regions is described by the following equations [32]: νo eR2 (19) exp(−WH /kT ) (adiabatic) μ= kT μ=
eR2 kT
1/2 1 π J 2 exp(−W/kT ) h ¯ 4WH kT
(non − adiabatic)
relation μ ∼ μo exp (V2 O5 ), similar to V2 O5 –NiO–TeO2 and V2 O5 –Fe2 O3 –TeO2 glasses [4,19]. Thus, the results indicate that the increase in the conductivity with increasing V2 O5 content is mainly due to an increase in the hopping carrier mobility of the glass. In addition, the nearly constant of Ne ∼ 1020 cm−3 indicates that the conductivity of the glasses is primarily determined by the hopping mobility [4,19]. 4.5.4. Variable-range hopping (VRH) models We then attempted to apply VRH [15,33] as reported for binary or ternary vanadate glasses [4,19]. However, the validity of such a high temperature range is not beyond question. But it has been pointed out that depending on the strength of coulomb interaction, the expression for the density of states at the Fermi level N(EF ) is modified and the VRH [15,33] may be applied even at high temperatures ∼312 K and above, though the VRH should actually be applicable in the low temperature regime (below θ D /4) which is below 100 K. For these glasses we, therefore, attempted to apply the VRH models proposed by Mott [15], Triberis and Friedman [34] and Greaves [33] which are valid for the intermediate range of temperature. The expression for the conduction by the Mott VRH model [15] is based on a single optical phonon approach. In this model σ is given by [15]: σ = B exp(−A/T 1/4 )
(22)
where A=4
2α3 9πkN(EF )
1/4 (23)
(20)
The μ values of the present glasses were calculated using the experimental data in Tables 1 and 2 and the results are given in Table 3. Also, the carrier density (Ne ) values were calculated using the well-known relation [4,19]: σ = Ne eμ
(21)
The values of μ and Ne (Eqs. (19) and (21), respectively) for various glass compositions are presented in Table 3. The carrier mobility (μ) of the present system at 400 K is very small (1.49 × 10−5 to 22.72 × 10−5 cm2 V−1 s−1 ), suggesting that electrons are highly localized at the V ion sites. Because the condition of the localized for the conductive electrons is generally for μ < 10−2 cm2 V−1 s−1 [25], the formation of small polaron in these glasses was reconfirmed. From Fig. 12 it is seen that μ increases with increasing V2 O5 content. The increase is expressed by the experimental
Fig. 12. Effect of V2 O5 content on hopping carrier mobility (μ) and density Nc for different glass compositions.
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Table 4 Mott parameters for variable-range hopping conduction of CuO–V2 O5 –TeO2 glasses Glass no.
B ± 0.2 (S cm−1 )
A ± 0.1 (K1/4 )
˚ −1 α ± 0.01 (A)
˚ RVRH ± 0.01 (A)
1 2 3 4
20.48 17.10 15.11 10.58
106.14 88.66 77.91 56.27
0.57 0.72 0.85 1.34
5.12 5.34 5.56 6.31
N(EF ) is the density of states at the Fermi level. α (Table 4) is obtained from the slopes of the log σ versus T−1/4 (Fig. 13). Next, using N(EF ) calculated from Eq. (17), the mean hopping in variable-range hopping (RVRH ) (Table 4) is estimated as [15]: RVRH =
91/4 [8πN(EF )αkT ]1/4
(24)
The values of RVRH are given in Table 4. These values of RVRH and ␣ are found to be the same compared with those of the other TMO glasses [4,19,25,26]. Recently, Triberis and Friedman [34] have applied percolation theory to SPH regime and evaluated the conductivity in disordered systems. Considering relation due to the energy of common site in percolation cluster they have obtained the following: To 1/4 σ = σo exp − (25) kT where σ o and To are constants and To is given by: Lα3 To = kNo
(26)
where No is the density of localized states assumed constant and the constant L = 17.8 and 12.5 at high and low temperatures, respectively. It might be noted that the Eq. (25) is similar to predictions of Mott (Eq. (22)) for the VRH with different value of To .
Fig. 13. Relation between log σ and T−1/4 for different glass compositions. The solid lines are the least-square straight-line fits.
The percolation model (Eq. (25)) of Triberis and Friedman [34] predicts a T−1/4 dependence of the logarithmic conductivity in the high as well as in the low-temperature region. The data present in Fig. 13 also show linearity in the log σ versus T1/4 plot above and below (312 K) in consistence with the percolation model. However it has been observed earlier in the text that the data above 312 K is consistent with VRH model of Mott [15]. When the model of Greaves [33] is fitted to the data above 312 K the values of α obtained are not close to the values obtained from Mott’s model. Thus, we conclude that the dc conductivity as predicted by Greaves [33] model has not been observed for the present glass system. The procedure suggested by Greave [33] as a modification of Mott’s model of VRH [15] could be applied at intermediate temperature and proposed the following expression for the dc conductivity. B σT 1/2 = A exp − 1/4 (27) T where A and B are constants and B is given by: 1/4 α3 B = 2.1 kN(EF )
(28)
A plot of ln(σ T1/2 ) versus T−1/4 is shown in Fig. 14. A good fit of the experimental data to Eq. (27) in the whole tempera-
Fig. 14. Relation between log σT1/2 and T−1/4 for different glass compositions. The solid lines are the least-square straight-line fits.
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Table 5 Parameters for Greaves variable–range hopping conduction of V2 O5 –Fe2 O3 – TeO2 glasses Glass no.
A ± 0.1 (S cm−1 K1/2 )
B ± 0.2 (K1/4 )
˚ −1 α ± 0.01 (A)
1 2 3 4
23.29 19.44 17.36 12.42
112.82 93.31 82.17 58.66
0.55 0.69 0.81 1.29
ture range, suggesting that Greave’s VRH may be valid in these glasses over the entire temperature range. The values of parameters A and B obtained from these curves are given in Table 5. Using the slope obtained from this linear relation and the value of N(EF ) given in Table 2 we can apply Eq. (28) to calculate the factor α. These values of α are reasonable for the localized states and close to the values obtained from Mott’s VRH model [35,36]. 5. Conclusions Semiconducting CuO–V2 O5 –TeO2 glasses were prepared by the press-quenching technique from the melts. XRD, DSC, IR, density and molar volume and the dc conduction mechanics in terms of different physical models were reported. The overall features of XRD curves confirm the amorphous nature of the present glasses. SEM exhibits a surface without any presence of microstructure which is a characteristic of the amorphous phase. Density was observed to decrease with an increase in V2 O5 content. From IR spectra the network structure for the glass compositions with 57.5 mol% V2 O5 is built up of the VO5 polyhedra, while the other glass compositions consist of VO4 polyhedra. The electrical conduction in high-temperature regime (temperature higher than half of Debye temperature θ D ) was confirmed to be due to adiabatic SPH of electrons between vanadium ions. However, both Mott VRH and Greaves intermediate range hopping models are found to be applicable. The percolation model of Triberis and Friedman applied to SPH regime is not consistent with data. The polaron bandwidth ranged from 0.48 to 0.76 eV. The hopping carrier mobility varied from 1.49 × 10−5 to 22.72 × 10−5 cm2 V−1 s−1 at 400 K. The carrier density is evaluated to be 2.65 × 1020 to 2.79 × 1020 cm−3 . The conductivity of the present glasses was primarily determined by hopping carrier mobility.
Acknowledgments The authors would like to thank A.A. Assiri and A.S.AlCahtani for their efforts. References [1] M.M. El-Desoky, Phys. Stat. Sol. (a) 195 (2) (2003) 422. [2] M.M. El-Desoky, S.M. Abo-Naf, J. Mater. Sci.: Mater. Electron. 15 (2004) 425. [3] M.M. El-desoky, I. Kashif, Phys. Stat. Sol. (a) 194 (1) (2002) 89. [4] M.M. El-Desoky, J. Mater. Sci.: Mater. Electron. 14 (2003) 215. [5] A. Al-Shahrani, A. Al-Hajry, M.M. El-Desoky, Phys. Stat. Sol. (a) 300 (2003) 378. [6] M. Sayer, A. Mansingh, J. Non-Cryst. Solids 42 (1980) 357. [7] H.H. Qiu, T. Ito, H. Sakata, Mater. Chem. Phys. 58 (1999) 243. [8] M.S. Al-Assiri, S.A. Salem, M.M. El-Desoky, J. Phy. Chem. Solids 67 (2006) 1873. [9] S. Chakraborty, M. Sadhukhan, D.K. Modak, B.K. Chaudhuri, J. Mater. Sci. 30 (1995) 5139. [10] A. Ghosh, Phys. Rev. B 42 (1990) 5665. [11] A. Ghosh, B.K. Choudhuri, J. Non-Cryst. Solids 83 (1986) 83. [12] A. Ghosh, J. Appl. Phys. 74 (1993) 3961. [13] A. Ghosh, Phys. Rev. 41 (1993) 1479. [14] A. Ghosh, J. Appl. Phys. 64 (1988) 2652. [15] N.F. Mott, Adv. Phys. 16 (1967) 49. [16] I.G. Austin, N.F. Mott, Adv. Phys. 18 (1969) 41. [17] H. Mori, H. Matsuno, H. Sakata, J. Non-Cryst. Solids 27 (2000) 78. [18] H. Moi, T. Kitami, H. Sakata, J. Non-Cryst. Solids 168 (1994) 157. [19] M.M. El-Desoky, J. Non-Cryst. Solids 35 (2005) 3139. [20] V. Pimitrov, Y. Dimitiev, M. Arnaudov, D. Topalov, J. Non-Cryst. Solids 57 (1983) 147. [21] S. Sen, A. Ghosh, J. Non-Cryst. Solids 258 (1999) 29. [22] S. Sen, A. Ghosh, J. Mater. Res. 15 (2000) 995. [23] K. Sega, Y. Kuroda, H. Sakata, J. Mater. Sci. 33 (1998) 1303. [24] S. Mandal, A. Ghosh, J. Appl. Phys. 48 (1993) 9388. [25] N.F. Mott, E.A. Davis, Electronic Processes in Non-Crystalline Materials, Clarendon, Oxford, 1979. [26] M. Sayer, A. Manshingh, Phys. Rev. B 6 (1972) 4629. [27] L. Friedman, T. Holeston, An. Phys. 21 (1963) 494. [28] D. Emin, T. Holstein, Ann. Phys. (NY) 53 (1969) 439. [29] T. Holstein, Ann. Phys. 8 (1959) 343. [30] V.N. Bogomolov, E.K. Kudinev, U.N. Firsov, Sov. Phys. Solid State 9 (1968) 2502. [31] K.S. Cole, R.H. Cole, J. Chem. Phys. 9 (1941) 341. [32] A. Ghosh, J. Appl. Phys. 66 (1989) 2425. [33] G.N. Greaves, J. Non-Cryst. Solids 11 (1973) 427. [34] G.P. Triberis, L.R. Friedman, J. Phys. C 18 (1985) 2281. [35] M.M. El-Desoky, A. Al-Shahrani, J. Mater. Sci.: Mater. Electron. 16 (2003) 221. [36] M.M. El-Desoky, A. Al-Shahrani, Phys. B 383 (2006) 163.
