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Impedance response of polycrystalline tungsten oxide
ARTICLE IN PRESS Journal of Physics and Chemistry of Solids 70 (2009) 1142–1145
Contents lists available at ScienceDirect
Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
Impedance response of polycrystalline tungsten oxide A.K. Batra a, J.R. Currie b, Mohammad A. Alim c,, M.D. Aggarwal a a b c
Department of Physics, Alabama A & M University, P.O. Box 1268, Huntsville, AL 35762, USA Avionics Department, NASA George C. Marshall Space Flight Center, Huntsville, AL 35812, USA Department of Electrical Engineering, Alabama A & M University, P.O. Box 297, Huntsville, AL 35762, USA
a r t i c l e in f o
a b s t r a c t
Article history: Received 18 June 2007 Received in revised form 23 April 2008 Accepted 23 June 2009
Polycrystalline tungsten oxide (WO3) pellets were prepared by conventional ceramic processing technology. The ac small-signal electrical data acquired in the frequency (f) range 100 Hzrfr1 MHz at temperature (T) ranging the 31–100 1C revealed distinct semicircular relaxation in the impedance plane. This relaxation indicates device behavior originating from the grain boundaries. The lumped grain impedance associated with the device action remained too small to detect when the large resistance scale is realized. The semicircular relaxation is thermally activated indicating 0.58 eV as the activation energy for the relaxation time. & 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Ceramics A. Oxides A. Semiconductors D. Electrical Properties D. Dielectric Properties
1. Introduction The surface electronic structure of metal oxides play an important role for their use in many technological applications such as catalysis, chemical sensing, and high-efficiency solar cells [1–5]. The bulk electronic properties of tungsten oxide have been widely studied [6]. However, the surface electronic properties are little understood especially since the electronic properties of the surface can vary drastically from the bulk. Tungsten oxide is intrinsically non-stoichiometric n-type semiconductor [6,7]. The defect states contribute to the formation of the device during the ceramic processing steps. These defect states need characterization via electrical measurements. The impedance measurement employing spectroscopic characterization approaches is popular for investigating novel devices and material systems [8]. These spectroscopic approaches include lumped parameter/complex plane analysis (LP/CPA) combining with the Bode plane analysis (BPA) becomes a powerful tool/ technique for investigating polycrystalline semiconductors. This technique is especially valuable since it allows the deconvolution of the total impedance response of polycrystalline materials into their constituent components, such as bulk impedance (Zbulk), grain and grain-boundary impedance (Zg and Zgb, respectively),
Corresponding author at: Integrated Systems Health Management and Sensors Branch, EV-43, NASA George C. Marshall Space Flight Center, Huntsville, AL 35812, USA. E-mail addresses: [email protected] (A.K. Batra), mohammad.alim@aamu. edu (M.A. Alim).
0022-3697/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2009.06.024
and electrode (or contact) impedance (Zel) according to their characteristic time constants. The parallel-plate configuration is commonly used for bulk systems utilizing sinusoidal voltage as a function of measurement frequency. However, for many applications and situations it is the in-plane (surface) electrical properties rather than through-plane (bulk) properties of the sample that need to be characterized. The in-plane electrodes are of use in sensor applications, where interest is relative rather than absolute resistance values. The purpose of this work is to investigate regular surface behavior of the polycrystalline tungsten oxide via impedance measurements, and subsequent representation of data in the impedance plane to shed light on the surface electronic characteristics.
2. Experimental The commercial grade WO3 (Alfa, 99.9% purity) powder was used as the starting material to make pellets (samples). In making cylindrical pellets of 14 mm diameter and thickness of about 2 mm 10 ton pressure was used. The pellets were sintered using a stepwise profile. First the heating rate was 2 1C/min, to a temperature of 400 1C from room temperature and held for 2 h, and then the heating rate was set 1 1C/min to reach a temperature of 800 1C for 2 h in ambient air. Then the pellets were cooled down to room temperature at the rate of 1 1C/min. The summary of the ceramic processing steps is identical to those in [9]. Silver paste was used as contacts/electrodes on the same surface with a finite
ARTICLE IN PRESS A.K. Batra et al. / Journal of Physics and Chemistry of Solids 70 (2009) 1142–1145
Z ¼ Z 0 jZ 00 ¼ Rs j½1=ðoCs Þ;
electrodes
Fig. 1. The WO3 pellet shows electroded regions with shade on the top surface having a finite gap between these two physical regions.
400 32°C 41°C 56°C 78°C 95°C
350
Current (A)
300 250
1143
200 150 100 50
ð1Þ
where the impedance plot refers to the real part displayed on the x-axis and imaginary part displayed on the y-axis. The temperature dependence of the dc resistance is shown in Fig. 3. The displayed response suggests that there is an inflection in the thermal behavior indicating eruption of more than one kind of behavior for the initial mechanism. However, on the basis of the fitted curve some sort of singular activation energy of 0.336 eV may be obtained. The presence of an inflection in the Arrhenius plot is a plausible aspect for the polycrystalline sample when each contributing equivalent circuit element represented by the resistance–capacitance (R–C) relaxation does not reflect consistent or systematic dominance with increase or decrease in temperature. Thus, either R or C can increase or decrease with increase or decrease in temperature in a pattern shown in Fig. 3. This type of thermal sensitivity on constituting equivalent circuit elements may cause inflection in the origin of the dc resistance. The dual nature of the thermal behavior of the dc resistance via inflection or non-linear behavior in the Arrhenius plot indicates emergence of potential trapping contribution from the grainboundary regions where a large portion of the applied voltage is experienced. This is considered for the polycrystalline material apart from the thermal carrier contribution for the charge transport attributed to the dc resistance [14].
0 0
1
2
3
4
5
6
7
8
9
10
11 800
Voltage (V)
700
Fig. 2. Current–voltage (I–V) behavior of the tungsten oxide pellet surface.
3. Results and discussion Fig. 2 shows low sub-ohmic to minor non-ohmic behavior of tungsten oxide at various temperatures. Each curve coincides with the origin implying no current flow at 0 V. Direct extrapolation of the curve may not get through the origin because of the slight non-linear response. This type of response is identical to the previous studies [3,6]. The ac small-signal electrical data are converted to the terminal impedance in the form
Resistance (kΩ)
600 500 400 300 200 100 0 2.8
2.7
2.9
3.0
3.1
3.2
3.3
1000/T (K-1) Fig. 3. Temperature dependence of the dc resistance obtained from the current–voltage behavior.
5 Imaginary Impedance Z" (Ω x 106)
gap of about 3 mm as depicted in Fig. 1. The surface current–voltage (I–V) behavior of the tungsten oxide sample depicted in Fig. 2 was obtained using the usual measurement setup via power supply and electrometer at various temperatures. The impedance measurement set-up consists of a kiln (hotplate oven) and a QuadTech 7600 precision LCR meter interfaced with a computer via GPIB to USB2 using LabView software. The temperature was monitored using a Type K thermocouple attached to a Cole–Parmer temperature controller (Digi-Sense). The ambient temperature of the sample was varied from room temperature (E31 1C) to 100 1C. A schematic display of the impedance measurement set-up of the device under test (DUT) was displayed recently [9]. The ac small-signal voltage was 1 V peak to peak, and the acquired ac data were reproducible within small variation of the signal voltage. The automated data were recorded continuously from 100 Hz to 1 MHz at a given temperature. The ac small-signal voltage is experienced in the resistive domain within the material system. Thus, high-resistance region will experience high electric field while low-resistance region will experience low electric field. Thus, the electric field falling region can be referred to as the basis of the magnitude of resistance of the physical regions within the microstructure of polycrystalline materials [9–13].
4 3 2
33°C 41°C 63°C 82°C 99°C
1 0 0
1
2
3
4
5
6
7
Real Impedance Z' (Ω x 106) Fig. 4. Impedance plot of tungsten oxide sample at various temperatures.
8
ARTICLE IN PRESS A.K. Batra et al. / Journal of Physics and Chemistry of Solids 70 (2009) 1142–1145
a ¼ y=ðp=2Þ ¼ 2y=p:
7 6 5 Ln [fp (Hz)]
The impedance plot of these data at various temperatures for the sample shown in Fig. 1 is shown in Fig. 4. The presence of the chord in the semicircular relaxation provides non-Debye conduction processes while the presence of the diameter provides Debye conduction processes within the material system [14–16]. The semicircular response of Fig. 4 indicates non-Debye relaxation behavior via the presence of the small depression angle for the semicircle. The presence of depression angle is accounted for when the center of the semicircular response lies below the x-axis. The non-Debye relaxation behavior simply implies that the y-axis parameter (i.e., reactance) associated with capacitance is a distributed parameter causing the time constant or the relaxation time (t) the average value. The resistance determined via the chord of the semicircle on the x-axis decreases as the temperature increases, which is a response of the usual semiconductor behavior. The ordinate (y-axis) and the abscissa (x-axis) must have the same plotting scale so that the semicircular relaxation in any of the complex planes can be clearly visualized. This means that the magnitude of each unit (in length) grid or graphical segment on the ordinate and the abscissa must be equal. For a non-Debye relaxation, the center of the semicircle lies below the x-axis. In this case a chord is obtained from the magnitude on the x-axis. Thus, the chord of the semicircular relaxation refers to the behavior where the center of the semicircle lies below the x-axis. When the center of the semicircle lies on the x-axis the chord becomes the diameter of the semicircle. In this case the nonDebye response turns to the ideal Debye or Debye-like relaxation. An empirical response known as the Cole–Cole equation is used for the depressed semicircular relaxation [17]. A non-Debye relaxation gives rise to a depression angle (y) measured from the point at the left intercept of the semicircular shape to the center of the semicircle lying below the x-axis. This depression angle becomes a measure of the depression parameter a where
4 3 2 1 0 2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
1000 / T (°K-1) Fig. 5. Arrhenius plot of the peak frequency obtained from the impedance plot shown in Fig. 4.
9 31°C 41°C 60°C 80°C 100°C
8 Impedance |Z| (MΩ)
1144
7 6 5 4 3 2 1 0 1
2
ð2Þ
3
4 Log (f ) (Hz)
5
6
7
Fig. 6. Bode plot of the same data displayed in the impedance plot shown in Fig. 3.
The value of a ranges between 0 and 1 depending on the idealized Debye (Debye-like) or extreme non-Debye response obtained from a semicircular relaxation. Thus, the idealized Debye or Debye-like behavior can be achieved for y-01 or a-0. An extreme non-Debye response can be visualized with y-901 or a-1. The semicircular response provides peak frequency corresponding to the maximum value of the reactance that is realized as
ot ¼ 2pf t ¼ 1;
ð4Þ
where fpo is the equilibrium pre-exponential frequency representing typical atomic approach range having a value of about 6.2 1010 Hz and the activation energy E is found to be about 0.58 eV. The Arrhenius plot via temperature dependence of fp is shown in Fig. 5. The peak frequency essentially yields the equivalent circuit from Eq. (3) as 2pfp tp ¼ 2pfp RC ¼ 1;
fp ¼ 1=ð2ptp Þ ¼ 1=ð2pRCÞ;
ð6Þ
and fp ¼ fpo exp½E=ðkTÞ ¼ 1=ð2ptpo exp½E=ðkTÞ:
ð7Þ
ð3Þ
where o is the angular frequency, f the measurement frequency, and t [ ¼ 1/o ¼ 1/(2pf)] the relaxation time. At the maximum value of the reactance, the frequency can be termed as the peak frequency (f ¼ fp). The peak frequency has exponential temperature dependence [9,18] with fp ¼ fpo exp½E=ðkTÞ;
Figs. 4 and 6. From the thermal activation of the peak frequency it is obtained from Eq. (5) yeilds
ð5Þ
where t ¼ RC for relaxation. This R–C relaxation is obtained as the equivalent circuit for the underlying operative mechanism as evidenced via the impedance plot of Fig. 4. Nevertheless, R–C relaxation combination is parallel in nature as evidenced via both
For both fpo and tpo Eq. (7) leaves essentially with the same activation energy . In case of ideal Debye response the activation energy associated with fpo or tpo is the same as the activation energy of the resistive part of the R–C parallel combination that constitutes tpo. Furthermore, for same Debye response the associated capacitance is not thermally active [19]. Fig. 6 represents the Bode plot of the data displayed in Fig. 4. The Bode plot confirms the nature of the equivalent circuit model. The semicircular relaxation of Fig. 4 indicates R–C parallel equivalent combination. The Bode plot indicates that the resistance and the capacitance decrease simultaneously as the temperature increases. The diminishing nature of the semicircular behavior is obvious in the Bode plot as the magnitude of impedance (|Z*|) sharply decreases. The R2–C2 parallel combination represents grain-boundary effect of the material. The lumped grain contribution may be visualized from the Bode plot having very small magnitude of the resistance R1. For all practical purposes it is convenient to apprehend only R2–C2 parallel combination. This is depicted in Fig. 7. The overall resistance of the polycrystalline tungsten oxide
ARTICLE IN PRESS A.K. Batra et al. / Journal of Physics and Chemistry of Solids 70 (2009) 1142–1145
R2
1145
References
R2
R1
C2
C2
Fig. 7. Equivalent circuit model of polycrystalline tungsten oxide pellet surface showing total resistance Rtotal ¼ R1+R2ER2 since R1 is detected as too small via the left intercept (intercept on the left side of the semicircular response) in the impedance plot.
is greater than the single crystal representation of similar dimension or geometry. This is a legitimate observation as extracted from Figs. 4 and 6. Graphically the presence of R1 is too small compared to R2 indicating total resistance (Rtotal) of the material Rtotal ¼ R1 þ R2 R2 :
ð8Þ
Essentially the R1–C2 parallel combination represents the grain-boundary effect of the material. This is an indication of the potential device application of tungsten oxide. Furthermore, poor non-ohmic behavior depicted in the I–V display is identical to the primitive gapped SiC-based [20] and gapless ZnO-based [21] varistor materials systems. The grain contribution may be visualized from the Bode plot having very small magnitude of resistance.
4. Conclusions A lumped R–C parallel combination response was evident in the polycrystalline tungsten oxide having sub-ohmic to nonohmic current–voltage behavior. In the single semicircular relaxation, the intercept on the left side of the semicircle is not ignored but logically neglected for the lumped grains presuming much larger magnitude of the lumped resistance behavior of the grain boundaries. Furthermore, a correlation is found for the equivalent circuit representation obtained in the impedance plane with the Bode plane display.
Acknowledgments The authors gratefully acknowledge the support of the present work through SMDC Grant no. W9113M-05-1-0011 and NSF RISE Grant no. HRD-0531183. MAA and MDA would like to acknowledge the support of NASA Administrator’s Fellowship Program (NAFP) through the United Negro College Fund Special Program (UNCFSP) Corporation under the contract MSFC-NNG06GC58A. The authors are indebted to Dr. R.B. Lal for his support to this work.
[1] Y.D. Wang, Z.X. Chen, Y.F. Li, Z.I. Zhou, X.H Wu, Electrical and gas-sensing properties of WO3 semiconductor material, Solid State Electronics (2001) 639–644. [2] B.T. Marquis, J.F. Vetelino, A semiconducting metal oxide sensor array for the detection of NOX and NH3, Sensors and Actuators B 77 (2001) 100–110. [3] S. Pitcher, J.A. Thiele, H. Ren, J.F. Vetelino, Current/voltage characteristics of a semiconductor metal oxide gas sensor, Sensors and Actuators B 93 (2003) 454–462. [4] I. Porqueras, E. Bertraan, Efficiency of Li doping on electrochromic WO3 thin films, Thin Solid Films 377–378 (2000) 129–133. [5] A. Elshafie, H.H. Afify, A.A. Ali, Dielectric properties of tungsten oxide thin film prepared by spray pyrolysis, Physica Status Solidi (A) 174 (1999) 301–310. [6] C.M. Ghimbeu, R.C. Van Landschoot, J. Schoonman, M. Lumbreras, Tungsten trioxide thin films prepared by electrostatic spray deposition technique, Thin Solid Films 515 (2007) 5498–5504. [7] M. Ramzan, R. Brydson, Characterization of sub-stoichiometric tungsten trioxide (WO3X) using impedance spectroscopy, Sensors and Actuators A 118 (2005) 322–331. [8] M.A. Seitz, Study of heterogeneous composite materials via lumped parameter/complex plane analysis, International Journal of Hybrid Microelectronics 3 (1980) 1–7. [9] [a] J.R. Currie, A.K. Batra, M.A. Alim, M.D. Aggarwal, R.B. Lal, Impedance studies of polycrystalline tin oxide, Journal of Materials Science: Materials in Electronics 18 (2007) 433–439; [b] J.R. Currie, A.K. Batra, M.A. Alim, M.D. Aggarwal, R.B. Lal, Erratum: impedance studies of polycrystalline tin oxide, Journal of Materials Science: Materials in Electronics 18 (2007) 899. [10] M.A. Alim, Electrical characterization of engineering materials, Active and Passive Electronic Components 19 (1996) 139–169. [11] M.A. Alim, Immittance data-handling/analyzing criteria for heterogeneous systems, in: R.A. Gerhardt, S.R. Taylor, E.J. Garboczi (Eds.), Materials Research Society Symposium Proceedings: Electrically Based Microstructural Characterization, vol. 411, 1996, pp. 13–23. [12] A.M. Azad, L.L.W. Shyan, M.A. Alim, Immittance response of CaSnO3 prepared by self-heat-sustained reaction, Journal of Materials Science 34 (1999) 1175–1187. [13] A.M. Azad, L.L.W. Shyan, M.A. Alim, The AC electrical characterization of the solid-state reaction derived CaSnO3, Journal of Materials Science 34 (1999) 3375–3396. [14] M.A. Alim, M.A. Seitz, R.W. Hirthe, Complex plane analysis of trapping phenomena in zinc oxide based varistor grain boundaries, Journal of Applied Physics 63 (7) (1988) 2337–2345. [15] M.A. Alim, M.A. Seitz, Singular nature of preferential conducting paths at high electric fields in ZnO-based varistors, Journal of the American Ceramic Society 71 (5) (1988) C246–C249. [16] M.A. Alim, M.A. Seitz, R.W. Hirthe, High-temperature/field alternating current behavior of ZnO-based varistors, Journal of the American Ceramic Society 71 (5) (1988) C52–C55. [17] K.S. Cole, R.H. Cole, Dispersion and absorption in dielectrics I. Alternating current characteristics, Journal of Chemical Physics 9 (1941) 341–351. [18] L.M. Levinson, H.R. Philipp, AC properties of metal-oxide varistors, Journal of Applied Physics 47 (3) (1978) 1117–1122. [19] M.A. Alim, Admittance-frequency response in zinc oxide varistor ceramics, Journal of the American Ceramic Society 72 (1) (1989) 28–32. [20] [a] F.R. Stansel, The characteristics and some applications of varistors, Proceedings of the I.R.E. 39 (1951) 342–358; [b] C.J. Frosch, Manufacture of Silicon Carbide Varistors, US Patent 2,807,856, October 01, 1957.; [c] T. Masuyama, Sintered Silicon Carbide Varistors, US Patent 3,489,532, January 13, 1970. [21] [a] K. Nakamura, Y. Kamoshida, Voltage Nonlinear Resistor, Method for Fabricating the Same and Varistor, US Patent 6,507,077 B2, January 14, 2003.; [b] K. Nakamura, Y. Kamoshida, Voltage Nonlinear Resistor, Method for Fabricating the Same and Varistor, US Patent 6,620,696 B2, September 16, 2003.
Contents lists available at ScienceDirect
Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs
Impedance response of polycrystalline tungsten oxide A.K. Batra a, J.R. Currie b, Mohammad A. Alim c,, M.D. Aggarwal a a b c
Department of Physics, Alabama A & M University, P.O. Box 1268, Huntsville, AL 35762, USA Avionics Department, NASA George C. Marshall Space Flight Center, Huntsville, AL 35812, USA Department of Electrical Engineering, Alabama A & M University, P.O. Box 297, Huntsville, AL 35762, USA
a r t i c l e in f o
a b s t r a c t
Article history: Received 18 June 2007 Received in revised form 23 April 2008 Accepted 23 June 2009
Polycrystalline tungsten oxide (WO3) pellets were prepared by conventional ceramic processing technology. The ac small-signal electrical data acquired in the frequency (f) range 100 Hzrfr1 MHz at temperature (T) ranging the 31–100 1C revealed distinct semicircular relaxation in the impedance plane. This relaxation indicates device behavior originating from the grain boundaries. The lumped grain impedance associated with the device action remained too small to detect when the large resistance scale is realized. The semicircular relaxation is thermally activated indicating 0.58 eV as the activation energy for the relaxation time. & 2009 Elsevier Ltd. All rights reserved.
Keywords: A. Ceramics A. Oxides A. Semiconductors D. Electrical Properties D. Dielectric Properties
1. Introduction The surface electronic structure of metal oxides play an important role for their use in many technological applications such as catalysis, chemical sensing, and high-efficiency solar cells [1–5]. The bulk electronic properties of tungsten oxide have been widely studied [6]. However, the surface electronic properties are little understood especially since the electronic properties of the surface can vary drastically from the bulk. Tungsten oxide is intrinsically non-stoichiometric n-type semiconductor [6,7]. The defect states contribute to the formation of the device during the ceramic processing steps. These defect states need characterization via electrical measurements. The impedance measurement employing spectroscopic characterization approaches is popular for investigating novel devices and material systems [8]. These spectroscopic approaches include lumped parameter/complex plane analysis (LP/CPA) combining with the Bode plane analysis (BPA) becomes a powerful tool/ technique for investigating polycrystalline semiconductors. This technique is especially valuable since it allows the deconvolution of the total impedance response of polycrystalline materials into their constituent components, such as bulk impedance (Zbulk), grain and grain-boundary impedance (Zg and Zgb, respectively),
Corresponding author at: Integrated Systems Health Management and Sensors Branch, EV-43, NASA George C. Marshall Space Flight Center, Huntsville, AL 35812, USA. E-mail addresses: [email protected] (A.K. Batra), mohammad.alim@aamu. edu (M.A. Alim).
0022-3697/$ - see front matter & 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2009.06.024
and electrode (or contact) impedance (Zel) according to their characteristic time constants. The parallel-plate configuration is commonly used for bulk systems utilizing sinusoidal voltage as a function of measurement frequency. However, for many applications and situations it is the in-plane (surface) electrical properties rather than through-plane (bulk) properties of the sample that need to be characterized. The in-plane electrodes are of use in sensor applications, where interest is relative rather than absolute resistance values. The purpose of this work is to investigate regular surface behavior of the polycrystalline tungsten oxide via impedance measurements, and subsequent representation of data in the impedance plane to shed light on the surface electronic characteristics.
2. Experimental The commercial grade WO3 (Alfa, 99.9% purity) powder was used as the starting material to make pellets (samples). In making cylindrical pellets of 14 mm diameter and thickness of about 2 mm 10 ton pressure was used. The pellets were sintered using a stepwise profile. First the heating rate was 2 1C/min, to a temperature of 400 1C from room temperature and held for 2 h, and then the heating rate was set 1 1C/min to reach a temperature of 800 1C for 2 h in ambient air. Then the pellets were cooled down to room temperature at the rate of 1 1C/min. The summary of the ceramic processing steps is identical to those in [9]. Silver paste was used as contacts/electrodes on the same surface with a finite
ARTICLE IN PRESS A.K. Batra et al. / Journal of Physics and Chemistry of Solids 70 (2009) 1142–1145
Z ¼ Z 0 jZ 00 ¼ Rs j½1=ðoCs Þ;
electrodes
Fig. 1. The WO3 pellet shows electroded regions with shade on the top surface having a finite gap between these two physical regions.
400 32°C 41°C 56°C 78°C 95°C
350
Current (A)
300 250
1143
200 150 100 50
ð1Þ
where the impedance plot refers to the real part displayed on the x-axis and imaginary part displayed on the y-axis. The temperature dependence of the dc resistance is shown in Fig. 3. The displayed response suggests that there is an inflection in the thermal behavior indicating eruption of more than one kind of behavior for the initial mechanism. However, on the basis of the fitted curve some sort of singular activation energy of 0.336 eV may be obtained. The presence of an inflection in the Arrhenius plot is a plausible aspect for the polycrystalline sample when each contributing equivalent circuit element represented by the resistance–capacitance (R–C) relaxation does not reflect consistent or systematic dominance with increase or decrease in temperature. Thus, either R or C can increase or decrease with increase or decrease in temperature in a pattern shown in Fig. 3. This type of thermal sensitivity on constituting equivalent circuit elements may cause inflection in the origin of the dc resistance. The dual nature of the thermal behavior of the dc resistance via inflection or non-linear behavior in the Arrhenius plot indicates emergence of potential trapping contribution from the grainboundary regions where a large portion of the applied voltage is experienced. This is considered for the polycrystalline material apart from the thermal carrier contribution for the charge transport attributed to the dc resistance [14].
0 0
1
2
3
4
5
6
7
8
9
10
11 800
Voltage (V)
700
Fig. 2. Current–voltage (I–V) behavior of the tungsten oxide pellet surface.
3. Results and discussion Fig. 2 shows low sub-ohmic to minor non-ohmic behavior of tungsten oxide at various temperatures. Each curve coincides with the origin implying no current flow at 0 V. Direct extrapolation of the curve may not get through the origin because of the slight non-linear response. This type of response is identical to the previous studies [3,6]. The ac small-signal electrical data are converted to the terminal impedance in the form
Resistance (kΩ)
600 500 400 300 200 100 0 2.8
2.7
2.9
3.0
3.1
3.2
3.3
1000/T (K-1) Fig. 3. Temperature dependence of the dc resistance obtained from the current–voltage behavior.
5 Imaginary Impedance Z" (Ω x 106)
gap of about 3 mm as depicted in Fig. 1. The surface current–voltage (I–V) behavior of the tungsten oxide sample depicted in Fig. 2 was obtained using the usual measurement setup via power supply and electrometer at various temperatures. The impedance measurement set-up consists of a kiln (hotplate oven) and a QuadTech 7600 precision LCR meter interfaced with a computer via GPIB to USB2 using LabView software. The temperature was monitored using a Type K thermocouple attached to a Cole–Parmer temperature controller (Digi-Sense). The ambient temperature of the sample was varied from room temperature (E31 1C) to 100 1C. A schematic display of the impedance measurement set-up of the device under test (DUT) was displayed recently [9]. The ac small-signal voltage was 1 V peak to peak, and the acquired ac data were reproducible within small variation of the signal voltage. The automated data were recorded continuously from 100 Hz to 1 MHz at a given temperature. The ac small-signal voltage is experienced in the resistive domain within the material system. Thus, high-resistance region will experience high electric field while low-resistance region will experience low electric field. Thus, the electric field falling region can be referred to as the basis of the magnitude of resistance of the physical regions within the microstructure of polycrystalline materials [9–13].
4 3 2
33°C 41°C 63°C 82°C 99°C
1 0 0
1
2
3
4
5
6
7
Real Impedance Z' (Ω x 106) Fig. 4. Impedance plot of tungsten oxide sample at various temperatures.
8
ARTICLE IN PRESS A.K. Batra et al. / Journal of Physics and Chemistry of Solids 70 (2009) 1142–1145
a ¼ y=ðp=2Þ ¼ 2y=p:
7 6 5 Ln [fp (Hz)]
The impedance plot of these data at various temperatures for the sample shown in Fig. 1 is shown in Fig. 4. The presence of the chord in the semicircular relaxation provides non-Debye conduction processes while the presence of the diameter provides Debye conduction processes within the material system [14–16]. The semicircular response of Fig. 4 indicates non-Debye relaxation behavior via the presence of the small depression angle for the semicircle. The presence of depression angle is accounted for when the center of the semicircular response lies below the x-axis. The non-Debye relaxation behavior simply implies that the y-axis parameter (i.e., reactance) associated with capacitance is a distributed parameter causing the time constant or the relaxation time (t) the average value. The resistance determined via the chord of the semicircle on the x-axis decreases as the temperature increases, which is a response of the usual semiconductor behavior. The ordinate (y-axis) and the abscissa (x-axis) must have the same plotting scale so that the semicircular relaxation in any of the complex planes can be clearly visualized. This means that the magnitude of each unit (in length) grid or graphical segment on the ordinate and the abscissa must be equal. For a non-Debye relaxation, the center of the semicircle lies below the x-axis. In this case a chord is obtained from the magnitude on the x-axis. Thus, the chord of the semicircular relaxation refers to the behavior where the center of the semicircle lies below the x-axis. When the center of the semicircle lies on the x-axis the chord becomes the diameter of the semicircle. In this case the nonDebye response turns to the ideal Debye or Debye-like relaxation. An empirical response known as the Cole–Cole equation is used for the depressed semicircular relaxation [17]. A non-Debye relaxation gives rise to a depression angle (y) measured from the point at the left intercept of the semicircular shape to the center of the semicircle lying below the x-axis. This depression angle becomes a measure of the depression parameter a where
4 3 2 1 0 2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
1000 / T (°K-1) Fig. 5. Arrhenius plot of the peak frequency obtained from the impedance plot shown in Fig. 4.
9 31°C 41°C 60°C 80°C 100°C
8 Impedance |Z| (MΩ)
1144
7 6 5 4 3 2 1 0 1
2
ð2Þ
3
4 Log (f ) (Hz)
5
6
7
Fig. 6. Bode plot of the same data displayed in the impedance plot shown in Fig. 3.
The value of a ranges between 0 and 1 depending on the idealized Debye (Debye-like) or extreme non-Debye response obtained from a semicircular relaxation. Thus, the idealized Debye or Debye-like behavior can be achieved for y-01 or a-0. An extreme non-Debye response can be visualized with y-901 or a-1. The semicircular response provides peak frequency corresponding to the maximum value of the reactance that is realized as
ot ¼ 2pf t ¼ 1;
ð4Þ
where fpo is the equilibrium pre-exponential frequency representing typical atomic approach range having a value of about 6.2 1010 Hz and the activation energy E is found to be about 0.58 eV. The Arrhenius plot via temperature dependence of fp is shown in Fig. 5. The peak frequency essentially yields the equivalent circuit from Eq. (3) as 2pfp tp ¼ 2pfp RC ¼ 1;
fp ¼ 1=ð2ptp Þ ¼ 1=ð2pRCÞ;
ð6Þ
and fp ¼ fpo exp½E=ðkTÞ ¼ 1=ð2ptpo exp½E=ðkTÞ:
ð7Þ
ð3Þ
where o is the angular frequency, f the measurement frequency, and t [ ¼ 1/o ¼ 1/(2pf)] the relaxation time. At the maximum value of the reactance, the frequency can be termed as the peak frequency (f ¼ fp). The peak frequency has exponential temperature dependence [9,18] with fp ¼ fpo exp½E=ðkTÞ;
Figs. 4 and 6. From the thermal activation of the peak frequency it is obtained from Eq. (5) yeilds
ð5Þ
where t ¼ RC for relaxation. This R–C relaxation is obtained as the equivalent circuit for the underlying operative mechanism as evidenced via the impedance plot of Fig. 4. Nevertheless, R–C relaxation combination is parallel in nature as evidenced via both
For both fpo and tpo Eq. (7) leaves essentially with the same activation energy . In case of ideal Debye response the activation energy associated with fpo or tpo is the same as the activation energy of the resistive part of the R–C parallel combination that constitutes tpo. Furthermore, for same Debye response the associated capacitance is not thermally active [19]. Fig. 6 represents the Bode plot of the data displayed in Fig. 4. The Bode plot confirms the nature of the equivalent circuit model. The semicircular relaxation of Fig. 4 indicates R–C parallel equivalent combination. The Bode plot indicates that the resistance and the capacitance decrease simultaneously as the temperature increases. The diminishing nature of the semicircular behavior is obvious in the Bode plot as the magnitude of impedance (|Z*|) sharply decreases. The R2–C2 parallel combination represents grain-boundary effect of the material. The lumped grain contribution may be visualized from the Bode plot having very small magnitude of the resistance R1. For all practical purposes it is convenient to apprehend only R2–C2 parallel combination. This is depicted in Fig. 7. The overall resistance of the polycrystalline tungsten oxide
ARTICLE IN PRESS A.K. Batra et al. / Journal of Physics and Chemistry of Solids 70 (2009) 1142–1145
R2
1145
References
R2
R1
C2
C2
Fig. 7. Equivalent circuit model of polycrystalline tungsten oxide pellet surface showing total resistance Rtotal ¼ R1+R2ER2 since R1 is detected as too small via the left intercept (intercept on the left side of the semicircular response) in the impedance plot.
is greater than the single crystal representation of similar dimension or geometry. This is a legitimate observation as extracted from Figs. 4 and 6. Graphically the presence of R1 is too small compared to R2 indicating total resistance (Rtotal) of the material Rtotal ¼ R1 þ R2 R2 :
ð8Þ
Essentially the R1–C2 parallel combination represents the grain-boundary effect of the material. This is an indication of the potential device application of tungsten oxide. Furthermore, poor non-ohmic behavior depicted in the I–V display is identical to the primitive gapped SiC-based [20] and gapless ZnO-based [21] varistor materials systems. The grain contribution may be visualized from the Bode plot having very small magnitude of resistance.
4. Conclusions A lumped R–C parallel combination response was evident in the polycrystalline tungsten oxide having sub-ohmic to nonohmic current–voltage behavior. In the single semicircular relaxation, the intercept on the left side of the semicircle is not ignored but logically neglected for the lumped grains presuming much larger magnitude of the lumped resistance behavior of the grain boundaries. Furthermore, a correlation is found for the equivalent circuit representation obtained in the impedance plane with the Bode plane display.
Acknowledgments The authors gratefully acknowledge the support of the present work through SMDC Grant no. W9113M-05-1-0011 and NSF RISE Grant no. HRD-0531183. MAA and MDA would like to acknowledge the support of NASA Administrator’s Fellowship Program (NAFP) through the United Negro College Fund Special Program (UNCFSP) Corporation under the contract MSFC-NNG06GC58A. The authors are indebted to Dr. R.B. Lal for his support to this work.
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