Investigation of structural and electrical properties of CuO modified SnO2 nanoparticles

Materials Science in Semiconductor Processing 19 (2014) 114–123

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Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp

Investigation of structural and electrical properties of CuO modified SnO2 nanoparticles Navnita Kumari a, Arindam Ghosh a,b, Ayon Bhattacharjee a,n a b

National Institute of Technology Silchar, Silchar 788010, Assam, India Don Bosco College, Tura 794002, Meghalaya, India

a r t i c l e in f o

abstract

Available online 30 December 2013

Nanocrystalline SnO2 was prepared by the co-precipitation method and doped with CuO. Crystallite sizes were estimated by Scherrer formula to be of the order of 90 nm and lesser. A.C. conduction behaviour of the samples has been described by the different hopping processes. From impedance analysis multi-relaxation processes in the samples are evident. Shrinkage of Cole–Cole plots with increase in temperature is also observed in our case which shows role of grain and grain boundary effects in the conduction mechanism with rise in temperature. Dielectric constant decreases with frequency but increases with rise in temperature which is governed by different components of polarizability (deformational and relaxational polarization). Dielectric constant increases with rise in temperature but at higher frequency range it takes constant value. Impedance analysis is used to explain the effects of grain and grain boundary on transport mechanism of undoped and CuO modified SnO2 nanoparticles. & 2013 Elsevier Ltd. All rights reserved.

Keywords: Hopping Polarizability Dielectric Impedance A.C. conductivity

1. Introduction Most of the well-known and widely used transparent conducting oxides such as ZnO, SnO2 and ITO are n-type materials [1]. Tin dioxide (Tin(IV)), SnO2 is well known n-type wide bandgap semiconductor with a direct band gap of about 3.65 eV (at 300k). Kim et al. have also reported an indirect band gap of about 2.7 eV in SnO2 [2]. The structural and morphological properties of semiconductor oxides have a substantial effect on their optical, electrical and gas sensing properties [3]. SnO2 is an industrially important material which is used in numerous purposes where application specific electrical, optical and mechanical properties are desired. Performance of SnO2 is directly related to the particle size and compositional characteristics. Consequently performance of SnO2 is a

n

Corresponding author. Tel.: þ 91 94 355 22284; fax: þ 91 381 224797. E-mail addresses: [email protected], [email protected] (A. Bhattacharjee). 1369-8001/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.mssp.2013.12.003

strong function of the synthesis process used to generate the material. The efficiency of SnO2 based devices have been improved by reducing the size of SnO2 particles and/ or by adding dopants (typically noble metals or other metal oxides). Traditionally thickly deposited SnO2 ceramics are used which is prepared by the compaction of fine SnO2 powder under high pressure [4] or by use of isostatic pressing [5]. One of the primary methods for using SnO2 in device application is the use of sintering additives. Various oxides have been used as sintering aids to densify SnO2 like ZnO, Nb2O5, MnO, Li2O or CuO. CuO has been found to be particularly effective because low concentrations ( E1 wt%) of CuO are enough to yield good densification of SnO2 [6,7]. CuO is a p-type semiconductor having a bandgap of 1.2 eV. The gas sensing capability of SnO2 has been reported to increases by CuO doping, especially for H2S sensing in thin films and pellets [8]. The ionic radii value of Sn4 þ E0.069 nm and that for Cu2 þ E0.073 nm, as the radii of these two compounds are very close to each other they are compatible for doping without any serious changes in the crystallite structure. SnO2 is known to have

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a tetragonal rutile structure whereas CuO has a monoclinic structure. In SnO2 it has been reported that conduction band is mainly from Sn 5s electrons and the valence band is from O 2p electrons [9,10]. The correlated barrierhopping (CBH) model [11] has been extensively applied to understand the behaviour of the chalcogenide semiconductors. Later on this model was applied for all types of compound semiconductors. According to this model, the conduction occurs via a bipolaron hopping process wherein two electrons simultaneously hop over the potential barrier between two charged defect states (D þ and D  ) and the barrier height is correlated with the intersite separation via a coulombic interaction. Shimakawa [12] suggested further that, at higher temperatures, Do states are produced by thermal excitation of D þ and D  states and single polaron hopping (i.e. one electron hopping between Do and D þ and a hole between Do and D  ) becomes a dominant process. This work presents a study of structural and electrical properties of sintered CuO doped SnO2 nanoparticles. The A.C. conductivity behaviour of samples can be successfully explained by correlated barrier hopping (CBH) model. Even though much research work has been under taken study on the SnO2–CuO sensing mechanism and properties [8,13–17], a clear understanding of the A.C. transport mechanism behaviour is yet to be realized. In this paper structural and electrical property of undoped SnO2 and CuO-modified SnO2 nanoparticles are reported. The structure, morphology and composition of these nanoparticles were determined by the X-ray diffractometer (XRD), field emission scanning electron microscopy (FESEM) along with energy dispersive spectroscopy (EDS). The effects of temperature on the A.C. conductivity (sa.c.), dielectric constant (εr) and impedance (Z)—as a function of frequency (f) for undoped, 1 wt% CuO and 3 wt% CuO-doped SnO2 nanoparticles.

heated at 600 1C for 4 h. The resulting mass was then crushed again into fine powder form. The obtained powders were then pelletized at a pressure of approximately 13 MPa to form cylindrical pellets by means of dye and punch (13 mm in diameter and 2 mm in thickness). These pellets were sintered at around 850 1C for 12 h in air. Sintered pellets were then polished into discs of 13 mm in diameter and 2 mm in thickness. Characterizations of the phases in these samples were carried out by X-ray diffraction using PANalytical X'Pert Pro X-ray Diffractometer system with Cu-Kα radiation (λ ¼0.15418 nm) as X-ray source at 40 kV and 30 mA. The diffractograms were obtained in the scanning angle (2θ) from 201 to 801. For the microstructural observations, the samples were also studied by field emission scanning electron microscopy along with energy dispersive spectroscopy (FESEM-EDS with HITACHI model no. S 4800) to verify the particle size and composition. For A.C. measurements, the flat faces of the pellets were coated with a thin layer of highly conducting silver paste for making the good electrical contacts. The pellets were then mounted on a homemade two probe assembly inserted coaxially inside a resistance heated furnace. The temperature of the pellets was monitored using a chromel–alumel thermocouple with the help of an Omega digital multimeter and further verified by inserting a thermometer in the furnace. The A.C. measurement of conductance (Cp), impedance (Z), phase angle (θ) and tangent loss (tanδ) are carried out using a HIOKI LCR meter Hitester (model:3522-50 HIOKI Japan) by an A.C. bias of 0.1 mV. Throughout the measurements, the pellets were allowed to equilibrate at each temperature for more than 30 min for thermal stability.

2. Experimental details

The XRD pattern of the samples prepared is shown in Fig. 1(a). The observed XRD pattern was analyzed using X-pert Highscore software using the search-match tool. It was found to match with the ICDD-Powder diffraction pattern (JCPDS file no. 71-0652). The crystallite size was calculated by using the Scherrer formula [18]

SnO2 powder was prepared by the co-precipitation method in which ammonia (NH4OH) solution was added to stannic tetrachloride pentahydrate (SnCl4  5H2O) solution. In this process, 2 g of stannic tetrachloride pentahydrate is dissolved in 100 ml of water. After complete dissolution, 4 ml of ammonia solution is added to the above aqueous solution with continuous stirring for 20 min so that pH is maintained a value of 8. White slurry like precipitate is formed. This slurry is allowed to settle for 12 h and then filtered and purified. For dopant source 99.5% pure copper(II) sulphate pentahydrate (CuSO4  5H2O) (Merck India Ltd.) precursor has been used. Copper(II) hydroxide precipitates by addition of sodium hydroxide and then unstable Cu(OH)2 dehydrates into insoluble CuO. The SnO2-based nanoparticles were doped with various quantities of CuO: 1.0 and 3.0 wt%. Suitable quantities of SnO2 and CuSO4  5H2O were mixed in a beaker with a minimum amount of water. After precipitation of samples, there was a succession of stirring and washing stages with deionised water to eliminate the soluble impurities. The obtained mixture was dried for 24 h at 70 1C. The dried powder is then crushed and

3. Results and discussion 3.1. Structural characterization

D¼

0:89λ β cos θ

ð1Þ

where λ is the wavelength of incident X-ray (λ¼0.1541 nm), β is the half of maximum line width, θ is the angle at which maximum peak occurs. From the diffraction pattern we observed the formation of polycrystalline undoped SnO2, 1 wt% CuO doped and 3 wt% CuO-doped SnO2 nanoparticles having an estimated crystallite size of the order of 90 nm, 69 nm and 59 nm, respectively. The radii of Sn4 þ and Cu2 þ are comparable (0.069 nm and 0.073 nm, respectively, according to Shannon and Perwitt tables), which means a small solubility of CuO in SnO2 is not expected to change the cell parameters of the solid solution very much. In fact, the sensitivity of XRD is insufficient to allow the detection of low concentration of any CuO-rich secondary phase or of a solid-solution. In materials with low CuO contents, XRD cannot be used

N. Kumari et al. / Materials Science in Semiconductor Processing 19 (2014) 114–123

JCPDS card no. 71-0652 3 wt% CuO-doped SnO2

(202)

(112) (301)

(202)

(301)

(112)

(310)

(002)

(200)

20

(220)

(211)

(101)

40

1 wt% CuO-doped SnO2

(110)

Intensity (a. u.)

60

(310)

20

(220)

(200)

(211)

(101)

40

(110)

60

(002)

116

Undoped SnO2

(211)

(101)

(110)

60

0

30

(202)

(301)

(310)

(112)

20

(002)

(220)

(200)

40

60

90

2θ (Degree)

0.022

0.024

0.024 0.020

0.018

0.022 βcosθ/λ

0.020

βcosθ/λ

βcosθ/λ

0.022

0.018 0.016

0.016 0.014

0.026

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2

0.018 0.016 0.014 0.012

0.014 1.8 2.0 2.2 2.4 2.6 2.8 3.0

sinθ/λ

0.020

1.8

2.0

sinθ/λ

2.2

2.4

2.6

2.8

sinθ/λ

Fig. 1. (a) XRD pattern of undoped and CuO-doped SnO2 nanoparticles and (b) WH plot of undoped and CuO-doped SnO2 nanoparticles.

to discriminate between the two possible cases of (i) copper segregated in Cu-containing secondary phases or (ii) copper dissolved in a SnO2-based solid solution. However we observed some minor changes in lattice parameters due to doping which was calculated and was found to be very close to those of pure SnO2 given in Table 1. The porosity is also calculated for all the samples and increase in porosity is observed which also presented in Table 1. The lattice constants ‘a' and ‘c’ for tetragonal rutile phase structure have been calculated by using the

following expression [19]. 1 d

2

2

¼

2

h þk a2

!

2

l þ 2 c

! ð2Þ

where ‘d’ is interplanar spacing and (h k l) are Miller indices, respectively. The X-ray density (ρx), experimental density (ρa) and porosity (P) of the synthesized SnO2 nanoparticles were

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Table 1 Crystallite size (nm), lattice constant (Å) and porosity for samples. Sample

Crystallite size (Scherrer) D (nm)

(a) Undoped SnO2

90

(b) 1 wt% CuO doped SnO2 (c) 3 wt% CuO doped SnO2

69 59

Lattice constant (Å)

a¼ b ¼4.68, c ¼3.16 a¼ b ¼4.77, c ¼3.21 a¼ b ¼4.74, c ¼3.21

also calculated using the following relations [19] ρx ¼

nM Na2 c

m v   ρ P ¼ 1  a  100% ρx ρa ¼

ð3Þ ð4Þ ð5Þ

In these equations n is the number of molecules per unit cell, M is the molecular weight, a and c are the lattice constant parameters, N is the Avogadro’s number while m, v are the mass and volume respectively of the prepared pellets. The porosity thus calculated has been found to be 54.14%, 66.72% and 68.57% for undoped SnO2, 1 wt% CuOdoped SnO2 and 3 wt% CuO-doped SnO2 respectively. Porosity reported to depend on crystallite size, porosity or void fraction is a measure of the void or pore (i.e., “empty”) spaces in a material [20]. With decrease in crystallite size there is an increase in surface to volume ratio which causes increase in porosity [21,22]. Much attention has been paid to detect H2S gas and develop H2S gas sensing materials using CuO doped SnO2 nanoparticles [8,23–25]. Based on our porosity calculations we expect that the present sample can be an extremely efficient material for H2S gas sensing. 3.2. Williamson’s Hall plot A mathematical expression relating the crystallite size and strain-induced broadening was proposed by Williamson and Hall (WH). According to this expression, the peak width is considered as a function of diffraction angle 2θ analyzing X-ray peak broadening [26,27]. The expression is defined as β cos θ 1 ε sin θ ¼ þ λ D λ

ð6Þ

where β is FWHM in radians, D is crystallite size in nm, λ is X-ray wavelength taken in nm and ε is strain induced on the particles. The plot shown in Fig. 1(b) is drawn with sinθ/λ along x-axis and βcosθ/λ along y-axis and the crystallite size of the samples are obtained from the inverse of the intercept at the y-axis. The strain is directly obtained from slope of the plot. The average crystallite size and strain estimated through the Scherrer relation and WH plot are compared

W–H plot

U¼ c/a Cell volume (Å)

Porosity (%)

Crystallite size (nm)

Strain

103.95

0.0039

0.6757 69.29

54.14

89.52

0.0032

0.6729 73.08

66.72

96.61

0.0063

0.6769 72.27

68.57

in Table 1. From the table it is evident that the average crystallite size estimated from the two methods are dissimilar. The difference in crystallite size is due to the inclusion of strain in the WH calculations of the synthesized sample materials. Considering the strain estimated from the WH plot these values appear reasonable. Due to the changes in crystallite size and inclusion of strain associated with the tetragonal rutile crystal, there is a non-linear behaviour of the WH plot. The WH plot thus serves as an additional method to evaluate and deconvolute crystallite size and strain-induced broadening. The variation of crystallite size is more in case of 3 wt% CuOdoped SnO2 compared to 1 wt% CuO-doped and undoped nanoparticles. Fig. 2(a) represents the FESEM micrographs. Particles having a size of 90 nm or lesser are visible. FESEM images also show that the particles tend to agglomerate and exhibit a varied distribution in terms of particle shape and size even though the texture remains more or less uniform. Along with FESEM, EDS was also performed on these samples which confirmed that the samples were composed of Sn, Cu and O only. No other impurities were reported in EDS as shown in Fig. 2(b). 3.3. Frequency and temperature dependence of a.c. conductivity Frequency dependence of A.C. conductivity occurs in accordance with hopping type of conduction. The a.c. conductivity of the samples is calculated with the data available from dielectric measurement using the relation sa:c: ¼ 2πf ð tan δÞε0 εr

ð7Þ

where f is frequency of applied field, tanδ is dielectric loss, εr is relative permittivity of the nanoparticles and ε0 is relative permittivity of vacuum (8:854  10  12 F=m). The hopping of charge carries among the trap levels situated in the band gap of the material gives rise to frequency dependent a.c. conductivity that can be understood according to following relation sa:c: ¼ Aωs ; 0 os o 1

ð8Þ

where A is a constant of proportionality and s is an exponent. The value of s depends on both the temperature and frequency and it is calculated from the slope of lnsac versus lnf curves from Fig. 3(a)–(c). For undoped SnO2 s ranges from 0.745 to 0.303 which is clearly shown in Fig. 3(a), for

118

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Undoped SnO2

3 wt % CuO- doped SnO2

1 wt% CuO- doped SnO2

Undoped SnO2

3 wt % CuO doped SnO2

1 wt % CuO doped SnO2

Fig. 2. (a) Field emission scanning electron microscopy micrograph of undoped and CuOdoped SnO2 nanoparticles and (b) EDS images of samples.

1 wt% CuO doped SnO2 s ranges from 0.974 to 0.378 as shown in Fig. 3(b) and for 3 wt% CuO doped SnO2 it varies from 0.791 to 0.347 as observed in Fig. 3(c). This is in accordance with the CBH model of A.C. transport mechanism of conduction models.

In describing about the A.C. conductivity we have adopted a hypothesis proposed by Mott et al. [28]. The model is based on the variation of parameters with temperature which ultimately governs the conductivity behaviour of the material. According to this model, when a sample is placed in an

N. Kumari et al. / Materials Science in Semiconductor Processing 19 (2014) 114–123

1.0

100 Hz - 50 kHz 50 kHz - 100 kHz

0.80 0.75

0.9

0.70

0.8

0.60

Exponent (s)

Exponent (s)

0.65 0.55 0.50 0.45

0.8

0.7 0.6 0.5

100 Hz - 50 kHz 50 kHz - 100 kHz

1.0

Exponent (s)

0.85

119

100 Hz - 50 kHz 50 kHz-100 kHz

0.6

0.4

0.4

0.40 0.35

0.2

0.3

0.30

0.2

0.25 40

60

80

100

120

140

160

0.0 40

60

Temperature (°C)

80

100

120

140

Temperature (°C)

160

40

60

80

100

120

140

160

Temperature (°C)

Fig. 3. (a) Variation of A.C. conductivity with frequency at different temperature for undoped SnO2. (b) Variation of A.C. conductivity with frequency with rise in temperature for 1 wt% CuO doped SnO2. (c) Variation of A.C. conductivity with frequency with rise in temperature for 3 wt% CuO doped SnO2. (d) Variation of exponent (s) with temperature in different frequency range for undoped and CuO doped SnO2.

electrical field, electrons hop between localized sites. The charge carriers, moving between these sites hop from a donor to an acceptor state. In that respect, each pair of sites forms a dipole. By considering these sets of dipoles, the dielectric properties of metal oxides can be interpreted, provided that the temperature is high enough. In case of metal oxide semiconductors, it is known that below a certain temperature the dielectric permittivity does not depend on temperature [29]. Fig. 3(d) shows the variation of A.C. conductivity with temperature where we find that A.C. conductivity increases with rise in temperature. This rise of A.C. conductivity with temperature is attributed to thermal activation which allows the hopping of charged carriers between different localized states. This provides further evidence in support of the thermally activated conduction process in SnO2 [30]. If one considers the quantum mechanical tunnelling (QMT) model [31], the exponent s should be almost equal to 0.8 and either exhibits a slight increase with increasing temperature or is independent of temperature. As such, QMT model is definitely not applicable to the obtained results. On the other hand in the overlapping large polaron tunnelling (OLPT) model [32–34], the exponent s is both temperature and frequency dependent. The value of s starts decreasing from a value of unity at room temperature. As the temperature raises s attains a minimum value and after that s rises with increase in temperature. Thus it is obvious that OLPT model is also not applicable to the obtained results. According to correlated barrier hopping (CBH) model, values of the frequency exponent s ranges from 0.7 to 1 at room temperature and is found to decrease with increasing temperature. The temperature dependent behaviour of exponent s at different frequency range (100 Hz– 10 kHz) has been explained in terms of CBH model [35,36]

as shown Fig. 3(a)–(c) for undoped and CuO-doped SnO2 nanoparticles. In our case it is observed that the value of s lies between 0.7 and 1 at room temperature in case of both doped and undoped samples. With increase of temperature this value is found to decrease upto 0.3. This clearly shows that CBH model can explain the conduction process for both doped and undoped samples. s ¼ 1

6kT Eg

ð9Þ

where k is Boltzmann constant, T is temperature in kelvin and Eg is optical band gap of material. The variation of exponent with temperature at different frequency ranges graph is shown in Fig. 3(d) for undoped, 1 wt% CuO and 3 wt % CuO-doped SnO2. As the doping concentration increases, the bipolaron hopping contribution decreases due to the decrease in the density of D þ defect states. But single polaron hopping contribution increases because of the shift of the Fermi (EF) level towards the conduction band. Due to the shift of EF towards conduction band, single polaron hopping starts to dominate over bipolaron hopping as the concentration of metal dopant increases. This is observed in the case of 3 wt % CuO-doped SnO2 nanoparticles.

3.4. Frequency and temperature dependence of the dielectric constant (εr) Dielectric constant (εr) is calculated by using the formula εr ¼

Cd ε0 A

ð10Þ

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Fig. 4. (a) Variation of dielectric constant with frequency at different fixed temperature for undoped SnO2. (b) Variation of dielectric constant with frequency at different fixed temperature for 1 wt% CuO doped SnO2. (c) Variation of dielectric constant with frequency at different temperature for 3 wt% CuO doped SnO2.

where εr is dielectric constant, ε0 is relative permittivity, A is area of pellets, C is capacitance and d is thickness of pellets. Fig. 4(a)–(c) shows the frequency dependence of dielectric constant at different temperatures for undoped, 1 wt% CuO-doped and 3 wt% CuO-doped SnO2 nanoparticles respectively. It is clear from Fig. 4(a) that εr decreases with frequency and increases with temperature for undoped SnO2. For a polar material like SnO2 the decrease of εr with frequency is explained by the fact that there are contributions from the different components of polarizability, i.e., deformational (electronic, ionic) and relaxation (orientational and interfacial) polarization. At higher frequencies orientational polarization is found to decrease since it takes longer time compared to deformational polarization. This results in decrease of the value of dielectric constant with frequency and it reaches a constant value at higher frequencies that correspond to interfacial polarization. On the other hand εr increases with temperature. This is attributed to the fact that the orientation polarization is connected with the thermal motion of molecules. The high temperature imparts enough freedom so that dipoles can orient themselves [37–39]. This increases the value of orientational polarization. Normally nanostructured materials have about 1019 interfaces/cm3, much more than

those of bulk solids [40]. In the typical n-type semiconductor, there are a large amount of oxygen vacancies acting as shallow donors in SnO2. As a result of this number of oxygen vacancies exist in the interfaces of SnO2 nanoparticles [41,42]. Two hypothesis can describe such behaviour of dielectric properties (i) Space charge polarization (SCP) and (ii) Rotation direction polarization (RDP). In RDP these dipole moments will rotate in an external electric field, which leads to the rotation direction polarization (RDP) occurring in the interfaces of n-type SnO2 nanoparticles. On the other hand in the SCP process negative and positive space in interfaces move towards each other. These are trapped by defects resulting in formation of dipole moments. Because the volume fraction of the interfaces of nano-size sample is larger than that of bulk materials so SCP is stronger than that in the bulk materials. Thus, εr of the SnO2 nanoparticles is found to be higher than that of bulk. Nevertheless, in the high frequency range, dielectric response of RDP and SCP cannot keep up with the electrical field frequency variation, resulting in the rapid decrease of εr in undoped and CuO-doped SnO2 nanoparticles. From Fig. 4(a)–(c) shows the temperature frequency dependent of εr for undoped and CuO-doped SnO2

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Fig. 5. (a) Variation of impedance with frequency at different fixed temperatures. (b) Equivalent circuit model diagram. (c) Variation of impedance (Z) with frequency at different fixed temperatures for 1 wt% CuO doped SnO2. (d) Variation of impedance (Z) with frequency at different fixed temperatures for 3 wt % CuO doped SnO2. (e) Cole–Cole plot for undoped SnO2 at different fixed temperature. (f) Cole–Cole plot for 1 wt% CuO doped SnO2. (g) Cole–Cole plot for 3 wt% CuO doped SnO2.

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nanoparticles. It is observed that εr remains almost constant for undoped SnO2 up to temperature 100 1C and shows a rise with temperature in the range of 120–160 1C. In case of 1 wt% CuO-doped SnO2 and 3 wt% CuO-doped SnO2 some hopping behaviour is observed at the higher frequency range. Hopping increases with rise in temperature as a result of the increase in amount of defects due to doping. These defects can cause a change of positive and negative space charge distributions in interfaces [43,44]. The dielectric constant (εr ) increases with temperature but decreases with frequency for undoped as well as CuOdoped SnO2 nanoparticles. With rise in temperature the dipoles become comparatively free and they respond to the applied electric field. Thus polarization is increased and hence dielectric constant is also increases with increase in temperature [45]. 3.5. Frequency and temperature dependence of the impedance (Z) The variation of impedance (Z) of the SnO2 pellets with frequency is shown in Fig. 5(a) for undoped SnO2 nanoparticles. Here a rapid decrease in impedance with increase in temperature is observed. The change is more prominent in the temperature range 60–100 1C as compared to lower temperatures. It is also observed that beyond a frequency of 40 kHz, impedance becomes almost constant from temperature range 40–160 1C. From the trends shown in Fig. 5(a) one can safely assume that Z varies inversely with frequency. This type of behaviour is an indication of thermally activated and frequency dependent conduction and the features of the plots are similar to those observed for RC circuit in parallel (equivalent circuit model) as shown in Fig. 5(b). The variation of impedance with frequency at various temperatures shown in Fig. 5(a), (c) and (d) for undoped 1 wt% CuO-doped and 3 wt% CuOdoped SnO2 pellets respectively. The impedance takes the phase difference into consideration and in A.C. measurements the resistance R is replaced by Z which takes into account both resistance and reactance. Therefore, the impedance (Z) is given by, Z ¼ Z 0 þ Z″

ð11Þ

are typical for material with multi relaxation processes [47,48]. The curves have non-zero intersection with real axis in the high frequency region and also, there is a decrease in the size of the plots with rise of temperature. The observed behaviour can be explained in accordance with an equivalent circuit model shown in Fig. 5(b) proposed elsewhere [49]. A single arc is an indicative of single RC element, here the small resistance of value RS is attributed to the core of grains while RP and CP are attributed to the grain boundary effect. The measured capacitance of such circuit is given by C ¼ Cp þ

1 ω2 C p R2p

ð12Þ

In this model the resistive element is assumed to vary with temperature according to the relation   E ð13Þ Rp ¼ R0 exp kT where R0 is pre-exponential factor (constant), E is activation energy, k is Boltzmann constant and T is temperature. In accordance with the RC Circuit model the value of Z 0 and Z″ can be calculated as Z 0 ¼ Rs þ

Z″ ¼

Rp 1 þ ω2 R2p C 2p

ωC p R2p 1 þ ω2 C 2p R2p

ð14Þ

ð15Þ

These equations predict that the values of Z 0 and Z″ should decrease with increase in temperature which causes shrinkage of the Cole–Cole plots. We observed such shrinking of the Cole–Cole plots in our experiments for undoped as well as doped SnO2 nanoparticles. Similar type of behaviour is also reported for pure SnO2 pellets by the authors [50]. The results confirm the effect of grain and grain boundary with increase in doping concentration and temperature plays major role on A.C. transport mechanism.

0

where Z is the real part of Z and is expressed as ReðZÞ ¼ Z 0 ¼ jZ j cos θ and Z is imaginary part of Z expressed as ImðZÞ ¼ Z″ ¼ jZ j sin θ, where θ is the phase angle. By these imaginary and real impedance spectra information on negative impedance can be gathered which in turn provides information on the applicability of the samples in components such as Gunn diode or tunnel diode. The Cole–Cole plots of the real and imaginary parts of Impedance Z 0 and Z″ are shown in Fig. 5(e)–(g) over the studied frequency range 100 Hz to 100 kHz for the temperature ranges from 40 to 160 1C, respectively. Using the Fricke model [46] it has been reported that in the impedance spectrum of two phase dispersions the grain and grain boundary arcs are still not resolved [46]. The plots are found to be a semi-circular arc with their centres lying below the real axis at an angle θ. Only the first single semicircular arcs are considered in our discussion. The finite value of the distribution parameter θ and a depressed arc

4. Conclusions On the basis of the experimental studies we conclude that the concentration of doping amount governs the crystallite size which results to increase in porosity which is useful for fabrication of environmental gas sensor. Transport mechanism in A.C. conductivity is explained due to the CBH model for undoped and CuO-doped SnO2 nanoparticles. Dielectric constant increases with rise in temperature but at higher frequency range it shows temperature independent behaviour which is explained on the basis of different types of polarization. From impedance analysis effects of grain and grain boundary is clearly observed and it is discussed on the basis of Cole– Cole plots which is also play a major role in the A.C. transport mechanism.

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