- Email: [email protected]
Immittance response of the SnO2–Bi2O3 based thick-films
Physica B 406 (2011) 1445–1452
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Immittance response of the SnO2–Bi2O3 based thick-films Mohammad A. Alim a,n, A.K. Batra b, M.D. Aggarwal b, James R. Currie c a b c
Department of Electrical Engineering, Alabama A & M University, P.O. Box 297, Huntsville, AL 35762, USA Department of Physics, Alabama A & M University, P.O. Box 1268, Huntsville, AL 35762, USA NASA—Marshall Space Flight Center, Huntsville, AL 35812, USA
a r t i c l e i n f o
abstract
Article history: Received 29 March 2010 Received in revised form 21 December 2010 Accepted 20 January 2011 Available online 26 January 2011
The SnO2–Bi2O3 based thick-film polycrystalline material is fabricated on alumina substrate via screenprinting technique. This material system is evaluated at various temperatures (35 1Cr Tr 100 1C) using ac small-signal (immittance) measurements in the frequency range 10 Hz r fr 106 Hz. The simplistic analytical scenario for the immittance data employed the Cole–Cole empirical equation in conjunction with the estimation of the inspected input parameters. This is an alternate approach compared to the complex nonlinear least squares (CNLS) fitting procedure, and purely based on the appearance of the semicircular relaxation in the complex plane. It is found that the constituting components of the semicircular relaxation in the impedance plane are thermally activated indicating complexity in the grain boundary contributions despite the Debye and non-Debye relaxation responses. The possible degree of uniformity or non-uniformity in the grain boundary activity associated with its capacitance term observed via the Debye or non-Debye semicircular relaxation in the impedance (Z*) plane has been postulated. & 2011 Elsevier B.V. All rights reserved.
Keywords: Tin oxide Binary oxides Bismuth oxide Impedance Immittance
1. Introduction Binary compounds play important role in the nonlinear devices used as gas sensors, resistors, capacitors, thermistors, varistors, piezoelectrics, radiation detectors, etc. On many occasions thrust goes on with the oxide-based binary compound as the potential gas sensing device. Thus, the electrical properties are assessed extensively for the compounds. The oxides are selected in such a way that they exhibit surface modification in conjunction with porosity so that the detection of toxic pollutants, combustible gases, flammable organic vapors, etc. can be performed. Metal oxides such as tin oxide (SnO2), zinc oxide (ZnO), titanium dioxide (TiO2), tungsten oxide (WO3), gallium oxide (Ga2O3), copper oxide (CuO or Cu2O), and others have been examined for gas sensing applications, including control of industrial processes. Tin oxide is the most extensively studied material among the metal oxides as gas sensing material, varistor, thermistor, resistor, etc. [1]. Intrinsically it is n-type semiconductor having tetragonal structure similar to that of rutile with direct band-gap of about 4 eV and indirect band-gap of 2.6 eV [2]. Thus, it is a metal-excess non-stoichiometric compound semiconductor having oxygen vacancies and electron donor states. When polycrystalline SnO2 film is exposed to air physisorbed oxygen
n
Corresponding author. Tel.: +1 256 372 5562. E-mail address: [email protected] (M.A. Alim).
0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.01.046
molecules pick up electrons from the conduction band to yield O2(ads) or O(ads) species [1]. Consequently a positive space charge layer forms just below the surface of the SnO2 particles, which creates a potential barrier between the particles. This process increases the electrical resistance of the SnO2 film. However, when a reducing gas comes in contact with the same film it gets oxidized via reaction with O2(ads) and O(ads) species, and consequently electrons are reintroduced into the electron depletion layer leading to a decrease in potential barrier. This process decreases the resistance of the film. Thus, a semiconductor sensing material detects various gases attributing to the change in resistance (or conductance) and associated capacitance of the film. The simultaneous change in resistance and capacitance may result from a combination of several physical properties, but not limited to: (i) bulk defects (interstitials, oxygen vacancies, complex substitutions, etc.) [3], (ii) surface states (donor type oxygen vacancy [4,5] or acceptor type cation vacancy [6] or clusters capable of holding both positive and negative charges simultaneously), (iii) catalytic action (chemical breakdown or dissociation of an incoming gas by catalyst on the surface of the sensing element) [7], (iv) nature of microstructure and grain boundaries (grain size distribution and shape of the grains, number of grain boundaries and interface states, effective surface area to actual volume ratio) [8], (v) interphase regions, including tri-phase or tetra-phase intersections (change in interface conductance and capacitance due to the incoming gas striking at the tri-grain or
1446
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
tetra-grain intersections) [9–13], etc. It is important to note that the sensing behavior of the single constituent material such as SnO2 exhibits less sensitivity than the composites based on binary constituents. Alternately the sensing materials based on composites have shown significantly higher sensitivity than the individual constituent such as SnO2. As an example in a recent work, different proportions of SnO2 and ZnO exhibited higher sensitivity for certain range of organic vapor constituents [14]. ZnO has wurtzite structure and known intrinsic n-type metal-excess nonstoichiometric compound semiconductor having zinc interstitials with direct band-gap [15] of about 3.3 eV. Frequency response characteristics of the polycrystalline materials can be used to discriminate various contributions to overall conduction processes due to the contact surfaces, grain boundaries, intergranular contact regions, and the overall bulk comprising of the grains [16–18]. Quantitative information for each of these contributing regions may be extracted from the experimental situation via lumped equivalent circuit model resulting from the series-parallel network comprising of R–C (resistance–capacitance) elements attributing to the bulk grains, grain boundaries, and possible contributions from the presence of secondary phase(s), etc. Often possible contribution from the electrode contact on to the surface of the sensing materials is minimized using proper metal(s) delineating work function(s). The immittance (impedance or admittance) measurement employing spectroscopic characterization approaches is very popular for investigating novel devices and material systems. These spectroscopic approaches include lumped parameter/complex plane analysis (LP/CPA) combining with the Bode plane analysis (BPA) and become a very powerful tool/technique for investigating polycrystalline semiconductors [16–21]. In the present effort SnO2–Bi2O3 based polycrystalline binary composite system is characterized via LP/CPA technique using ac small-signal electrical data. The major emphasis in this work is directed toward the ac electrical characterization in order to understand the composite rather than presenting the gas sensing behavior. It is not sintered but heat-treated at elevated temperature, and exhibited some gas sensing behavior [22,23]. In the literature it is proposed that the increase in sensitivity attributing to the synergistic effects comprises of (i) complementary catalytic activity, [24] and (ii) formation of hetro-junctions, including microstructural changes following sintering [25]. In this investigation ac electrical measurement is conducted for the SnO2–Bi2O3 based polycrystalline films consisting of ultra-fine grains that can be used in the detection of toxic vapors [24]. Temperature dependence of the electrical measurement is also carried out to understand thermal behavior of the sensing composite materials. This study further provides ac conduction processes between the measurement terminals via an equivalent circuit model that illustrated the Cole–Cole [26] response in a simplistic analytical perspective. In the data analyses procedure, iterative method is used to extract constituents of the relaxation parameters. These parameters are identical parameters that are extracted from the traditional complex nonlinear least squares (CNLS) fitting procedure. Thus, iterative approach provides a viable procedure for the LP/CPA technique.
2. Experimental The SnO2–Bi2O3 based polycrystalline binary composite system is fabricated using thick-film technology (TFT) applying on to the alumina substrate. The flow chart of this fabrication is given in Fig. 1. Spec pure SnO2 powder (99.99% metals basis, Alpha Aesar) and Bi2O3 powder (99.99% metals basis Alpha Aesar) were used in processing of the samples. Four different samples were
Ultrasonic Cleaning of Substrates
Preparation Of Paste
Thick Film Deposition
5 min
100 °C, 15 min
Rest
Drying
Add Another Layer
yes
no 400 °C, 120 min
Calcination
800 °C, 360 min
Sintering
Electroding
Characterization Fig. 1. Flow chart of the thick-film fabrication process.
prepared using the screen-printing technique for the following proportions of the binary ingredients by weight: (i) SnO2:Bi2O3 (¼ 100:0.25), (ii) SnO2:Bi2O3 (¼ 100:0.5), (iii) SnO2:Bi2O3 (¼ 100:1.00), and (iv) SnO2:Bi2O3 ( ¼100:1.50). Each mixture was ground and/or milled with mortar and pestle for more than one hour. To prepare the ink-paste for the screen-printing a commercially available terpineol-based vehicle ESL-449 was used as active mixture to get blended together for half an hour. The paste was then applied on to the ultrasonically cleaned alumina substrate a using screen-printing machine [27,28]. The substrate is approximately 25 mm 16 mm 0.5 mm thick and the coating is 50 mm thick. The resulting samples were then heat-treated using a temperature profile shown in Fig. 2. The thick-film samples were placed in the furnace and applied to ramp up at 2 1C/min to 400 1C from room temperature. The samples were held for 2 h at this temperature. Again, the furnace was ramped up at 2 1C/min to 800 1C, and then held for 6 h. The furnace was then cooled down using 2 1C/min to the ambient room temperature. The silver print electrodes were then deposited on the surfaces of the layer as depicted in Fig. 3, where the front view of the cross-sectional geometry is evident. The composite samples prepared this way are then electrically characterized. Measurements of parallel capacitance and dielectric loss were made with a QuadTech 7600 precision LCR meter interfaced with the personal computer for recording the ac electrical data. These electrical data are referred to as the immittance data. The measurement system utilized a thermolyne hot-plate chamber controlled via a Cole–Parmer Digi-Sense Temperature Controller
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
900 800 Temperature (°C)
700 600 500 400 300 200 100 0 13 20
00
0
80
12
10
0
0
96
84
0
0
72
60
0
0
48
36
0
24
12
0
Time (min) Fig. 2. Temperature profile used in the heat treatment process of samples.
Sensing Film
Silver Paint Electrode
Alumina Substrate
interfaced to the same personal computer using an RS-232 Null Modem Cable, as presented elsewhere [27]. The same personal computer was used running the LabVIEW for Windows Version 7.1 to achieve overall instrument control and eventual ac electrical data acquisition. Each sample was fixed on to a sample holder and the temperature of the film was ascertained by a Type K (chromel–alumel) thermocouple attached to the sensing material.
3. Dielectric relaxation 3.1. Debye and non-Debye relaxations The non-ideal response termed as the non-Debye behavior was originally given by the empirical form known as single-relaxation Cole–Cole dielectric function [26,29]
e ðoÞ ¼ e1 þ
ðes e1 Þ 1 þ ðjotÞð1aÞ
angle (y) measured from the point at the left-intercept to the center of the semicircle below the x-axis. This depression angle becomes a measure of the depression parameter, a, where a ¼(2y/p). The value of a ranges between 0 and 1 depending upon the idealized Debye or extreme non-Debye response of a semicircular relaxation, thus, a Debye-like behavior can be achieved, as y-01 (a-0), and an extreme non-Debye response can be visualized with y-901 (a-1). The conversion of the data from impedance to admittance or vice versa is straightforward only for the Debye relaxation, and Eq. (1) can be used for a ¼ 0, which is essentially the Debye relation. In the case of the non-Debye relaxation Eq. (1) is referred to as the empirical Cole–Cole relation. The conversion from impedance to admittance or vice versa for the non-Debye relaxation yields complexity and does not portray the Debye or Debyelike behavior for subsequent analysis. Treatment of the nonDebye data as Debye-like invariably yields non-Debye equivalent circuit elements though converted to another form of data via another complex plane. This is evidenced in numerous previously published papers [16–21,31–34] when multiple complex plane analyses are displayed of the same data. The single-relaxation Cole–Cole dielectric function of Eq. (1) can be manipulated in the impedance (Z*) plane for a single semicircular relaxation in the analogous form represented as [30] Z ð oÞ ¼ Z 1 þ
Fig. 3. Cross section of a sensor fabricated using alumina substrate.
ð1Þ
where j¼O(–1), e is the dielectric behavior of the material referring to eN for the high-frequency limit (measurement frequency f-N), and es for the static or dc condition (measurement frequency f-0) with angular frequency o ¼ 2pf in rad/s, t ¼relaxation time in second, and a ¼depression parameter. Eq. (1) provides a semicircular loci [26,29] when real part is plotted on x-axis against the imaginary part on y-axis. The ordinate (y-axis) and abscissa (x-axis) must have the same plotting scale so that the semicircular relaxation in any of the complex planes can be clearly observed. This means that the magnitude of each unit grid (or graphical segment) in length on the ordinate and the abscissa must be equal. The quantity (es eN) refers to the diameter of the semicircle when the center of the semicircle lies on the x-axis implying ideal or Debye or Debye-like behavior. The same quantity is referred to the chord of the semicircle when the center of the semicircle lies below the x-axis implying non-ideal or non-Debye behavior [16–21]. The depression parameter a arises for the center lying below the x-axis [29–31]. A non-Debye relaxation gives rise to a depression
1447
ðZs Z1 Þ 1 þ ðjotÞð1aÞ
¼ Z1 þ
ZC 1 þðjotÞð1aÞ
ð2Þ
where ZC is the resistance obtained as chord when the center of the semicircle lies below x-axis or as diameter when the center of the semicircle lies on the x-axis; Zs is the resistance at static (f-0 Hz or dc) condition and ZN ( ¼ZHF ¼Z0 N) is the resistance and high-frequency (f-N) condition. Eqs. (1) and (2) are not the same but identical in appearance. Invariably relaxation time t, depression parameter a, and left-intercept are not the same for two complex plane semicircular relaxations. The equivalent circuit elements extracted from each semicircular relaxation [simulating Eqs. (1) and (2)] are also different in these two complex planes [16]. The contributing capacitance C in the semicircular relaxation time t for the semicircular relaxation in the impedance plane is obtained using R¼ZC ( ¼Z0 C) in conjunction with the peak-frequency (fpeak) given by t ¼RC ¼1/opeak ¼ 1/(2pfpeak). Often Zs is referred to as ZLF (or Z0 LF) attributing to the low-frequency response. Users may refer this situation to the dc condition as near zero frequency or low-frequency. 3.2. Single semicircle relaxation: impedance plane Fig. 4 shows impedance plot of the experimental data and corresponding simulation at various temperatures for the thick film based on SnO2 containing 0.25 wt% Bi2O3 deposited on the alumina substrate. The reactance on the y-axis is treated as a positive quantity, which is normally done by most investigators [16–21]. In this display each semicircular relaxation curve is fitted using a method demonstrated recently for the Davidson–Cole relaxation [30]. In this fitting procedure, chord of each semicircle is determined using strong eye estimation via high magnification of the low-frequency (right-side of the semicircle) and the highfrequency (left-side of the semicircle) ends for the impedance plane semicircular relaxation. Then iteration process using Eq. (2) is employed for the depression parameter a ¼0 for the Debye response or a ¼ some finite value for non-Debye response, based on individual assessment until the shape of the arc is matched with the loci of the experimental data. This is a fitting process that can frequently adopt eye estimation of the diameter or chord of the semicircle. For each iteration process it is made sure that the peak-frequency matches with the experimental data like rest of the data. Such a procedure ascertains the level of accuracy when iteration process is employed.
1448
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
3000000 35°C 80°C 35° Sim 80° Sim
2500000
60°C 100°C 60° Sim 100° Sim
Z"
2000000
1500000
1000000
500000
0
45
40
35
30
25
00
00
00
00
00
00
00
00
0
0
0
0
0
0
0
00
00
00
00
20
00
00 0
00
00
00
00
15
10
50
0
Z' Fig. 4. Impedance plot of the experimental and simulated data at various temperatures for the thick film based on tin oxide containing 0.25 wt% bismuth oxide deposited on an alumina substrate.
Table 1 Simulated parameters obtained from the impedance of Fig. 5 using empirical Eq. (2). Temperature (1C)
Z0 N (O)
Z0 LF (O)
Z0 C (O)
Z0 0 peak or Z0 0 max at fpeak (O)
fpeak (Hz)
C (¼ t/R) (pf)
1a
Depression y (deg)
35 60 80 100
3045 5610 10,202 14,647
4,322,397 3,167,032 2,290,911 1,481,998
4,319,352 3,161,422 2,280,709 1,467,351
2,087,589 1,560,468 1,182,029 755,724.7
47,434 72,871 105,200 143,000
1.60726 1.39962 1.2799 1.47272
0.975 1 1 1
2.25 0 0 0
The foregoing iteration process is a viable effort when compared to the complex nonlinear least squares (CNLS) fitting procedure used in the previous work [16–19,31–34] for single plane or multiple plane semicircular relaxation analysis. The iteration approach is found to be reasonable and effective concerning time-saving aspect of the data-handling criteria. Furthermore, it is a legitimate approach as long as the results are concerned besides easy route of data-handling for the users and/or the learners. The customary CNLS fitting procedure and iteration process yield identical results that are equally reliable. In this work both CNLS and eye estimation iteration processes are verified via the contributing components of the relaxation time and each measure data points. The errors are so small that it is considered to be insignificant to report. Thus, either method is perfectly appropriate as there is nothing inherently wrong with the iterative approach. Each semicircular curve in the impedance plane of Fig. 4 represents a simplified R–C (resistance–capacitance) parallel equivalent circuit. The intercept on the left-side of the semicircular relaxation on the x-axis represents a resistor in series with the same R–C parallel combination. This intercept may be termed as the left-intercept. As shown in Table 1, the semicircular response at 35 1C in Fig. 5 is determined to be slightly non-Debye in nature exhibiting a small depression angle of about 2.251. The presence of a finite (non-zero) depression angle in the semicircular relaxation indicates that this is not an ideal system for temperatures less than or equal to 35 1C. This finite depression angle indicates an inhomogeneity in the conduction path(s) of the composite microstructural system for the SnO2 containing 0.25 wt% Bi2O3, and the electrical response is referred to as the non-Debye response. The degree of inhomogeneity in the
conduction process is likely to be associated with the capacitive component represented via the depressed ordinate parameter (i.e., reactance) in the impedance plane plot. The capacitive component causing inhomogeneity is likely to be originated from the grain boundary regions from junction to junction of both SnO2 and Bi2O3 as independent phases or interfaces between them. A small variation in the depression angle for this material system is not too definitive or conclusive on inhomogeneity of the conduction process, but indicative of a fluctuation in the degree of inhomogeneity in the effective conducting paths between the two terminals [12,13]. The semicircular relaxation for other elevated temperatures (T4 35 1C) indicate Debye or Debye-like response as a ¼0. As temperature increases, the conduction level increases within the material system reflecting thermal transport of the increased carriers across the grain boundaries of the same microstructural network. Thus, the conduction process turns to homogeneity throughout the material system as reflected via the Debye-like response. For depression angle y E0o implies no distribution of activation energies and/or relaxation times involving uniform conduction path. Nevertheless, conducting paths controlled by the capacitive component eventually yields homogeneous carrier transport across the junctions resulting in Debye-like behavior as also noticed for the multi-component/phase ZnO based varistors [12,13,31]. The impedance plane relaxation response is identical for the other three samples [SnO2:Bi2O3 ( ¼100:0.5), SnO2:Bi2O3 (¼ 100:1.00), and SnO2:Bi2O3 ( ¼100:1.50)] at each temperature. Each sample exhibited non-Debye behavior via the presence of small depression angle for the semicircular relaxation at 35 1C, and Debye behavior at temperatures above 35 1C. Since each
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
1449
2500000
2000000
Z"
1500000
1000000
500000 35°C 80°C
60°C 100°C
0 0
1
2
3
4
5
(ωτ) Fig. 5. The product o t is displayed as a function of the imaginary part of the impedance for the data displayed in the inset (Fig. 4).
response of these samples is identical in nature with respect to the SnO2 containing 0.25 wt% Bi2O3 sample the semicircular relaxations are not added here. 3.3. Behavior of the impedance relaxation function The permittivity or impedance relaxation function can be ascribed either from Eq. (1) or Eq. (2) in the form [28] F ðoÞ ¼
1 1þ ðjotÞð1aÞ
¼ Fu þ jF 00
ð3Þ
The relaxation function F*(o) provides permittivity function e*(o) given in Eq. (1) or impedance function Z*(o) given in Eq. (2). In Fig. 4 the imaginary part of the impedance contains maximum magnitude at the peak-frequency (fp or fpeak or opeak ( ¼2pfpeak) or tpeak [ ¼1/(2pfpeak)]), where the semicircle gives ot ¼1 for both ideal (Debye) and non-ideal (non-Debye) relaxation cases. The imaginary part F00 of the relaxation function in Eq. (3) is treated as positive. It is expected that the same ot ¼1 would appear for the Debye or non-Debye relaxation by setting various values of the product o t. Thus, the imaginary part of the relaxation function (F00 ) or the imaginary part of the impedance function (Z00 ) when checked as a function of the product o t can verify ot ¼1 as demonstrated in Fig. 5. Additional representations of the relaxation times can be found elsewhere [35,36]. Fig. 5 represents the behavior of the imaginary part of Z*(o) plotted on the y-axis versus the product o t on the x-axis at different temperatures corresponding to the data displayed in Fig. 4. The imaginary part of the impedance Z00 is analogous to the relaxation function F00 and treated as the positive quantity on the y-axis. Fig. 5 indicates ot ¼1 for both Debye (T435 1C) and nonDebye (T¼35 1C) responses. This is an important illustration of the ot ¼1 feature of the semicircular relaxation whether the response is Debye or non-Debye. Furthermore, Fig. 5 essentially depicts no shift in the peak of Z00 and the simulated data for the Debye and nonDebye behavior. A similar response for the product o t is plotted for the imaginary part of Z*(o) for the lithium niobate crystals [37]. Since all the points in Fig. 5 correspond to the experimental data and fpeak realized from the peak of Z00 via ot ¼1 for each semicircular relaxation of Fig. 4, it is reasonable to describe the entire analysis as worthy and reliable. This alternate method via iterative way fitting approach demonstrates valid dielectric response of the material system. It employs strong eye estimation of the input
parameters for the Cole–Cole empirical equation. Invariably the present analytical approach has proven to be effective and reasonable. In an earlier work such approach is successfully demonstrated for the Davidson–Cole relaxation behavior [30]. It may not be necessary to utilize traditional CNLS fitting procedure for the semicircular relaxation if the present approach is used for distinct semicircular relaxation that is verifiable via the Cole–Cole empirical equation [27]. Indeed this is a reliable alternate method, as verified via Fig. 5, of obtaining worthy results, and the corresponding interpretation remains identical as always done in the past.
4. Results and discussion Each of the four samples exhibited Debye relaxation at temperatures above 35 1C but less than 100 1C while small amount of non-Debye behavior is observed around 35 1C. The possible degree of uniformity or non-uniformity within the conducting paths realized via Debye or non-Debye semicircular relaxation in the Z*-plane associated with the capacitance ascertained further via the presence of thermal activation. The semicircular relaxation response of Fig. 4 attributed to the lumped grain boundaries provides R–C parallel equivalent circuit. The small resistive element may be visualized from the leftintercept having very small magnitude is nearly invisible at high frequencies. Such a magnitude may have resulted from the contacts and leads of the material used in the measurement. The lumped relaxation indicates merged behavior of both grain and grain boundaries. This lumped behavior is realized from the magnitude of resistance and capacitance. The experimental data points are simulated using Eq. (2) and the curve is displayed in the same illustration. Table 1 documents these simulated parameters. Fig. 5 proves the relaxation peak occurring at ot ¼1 for both non-Debye and Debye relaxations. This is confirmed despite the role of the depression parameter, a. The simulation further affirms that Fig. 5 is a valid approach for the relaxation function of Eq. (3). Figs. 6 through 9 show SEM micrographs at 15,000 magnification of four samples described earlier. The surface of each sample is smooth polycrystalline botryoidal structure in nature. The resulting grain size of each sample is sub-micron (nanometer) in configuration. Using LP/CPA technique [12,13,16–21] in conjunction with the Cole–Cole empirical equation the temperature dependence of the components of the relaxation time t for two selected samples is
1450
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
Fig. 6. SEM image (6000 magnification) of SnO2:Bi2O3 (¼100:0.25) thick film deposited on an alumina substrate.
Fig. 8. SEM image (15,000 magnification) of SnO2:Bi2O3 (¼100:1.00) thick film deposited on an alumina substrate.
Fig. 7. SEM image (6000 magnification) of SnO2:Bi2O3 (¼ 100:0.5) thick film deposited on an alumina substrate.
Fig. 9. SEM image (6000 magnification) of SnO2:Bi2O3 (¼100:1.50) thick film deposited on an alumina substrate.
depicted in Fig. 10. The inset shows the thermal behavior of t. The thermal activation energies of 0.170 eV obtained for t25 [SnO2:Bi2O3 ( ¼100:0.25)], and 0.193 eV obtained for t50 [SnO2:Bi2O3 ( ¼100:0.5)] samples. The subscripts 25 and 50 correspond to the constituent 0.25 wt% Bi2O3 and 0.50 wt% Bi2O3, respectively. The same illustration also shows the temperature dependence of the constituting components of the relaxation time t. Indicating thermal activation of t25 (R25 and C25) according to the equation [12]
t25 ¼ R25 C25 ¼ t25,0 expðE25 =kTÞ
ð4Þ
or
t25 ¼ R25,0 expðER25,0 =kTÞ C25,0 expðEC25,0 =kTÞ
ð5Þ
or
t25 ¼ R25,0 C25,0 exp ðER25,0 þEC25,0 Þ=kT
ð6Þ
where
t25,0 ¼ R25,0 C25,0
ð7Þ
Fig. 10. Temperature dependence of the equivalent circuit parameters designated as R2–C2 corresponding to the relaxation time t (shown in the inset) for two samples: (i) SnO2:Bi2O3 (¼ 100:0.25) and (ii) SnO2:Bi2O3 (¼ 100:0.5).
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
1451
R2
R2
C2
C2
R1
Fig. 11. Equivalent circuit model of the polycrystalline binary metal oxide thick-film.
and E25 ¼ ER25,0 þ EC25,0 ¼ Et25
ð8Þ
The components of t50 (R50, C50) are also thermally activated and can be ascribed in identical manner with Eqs. (4) through (8). About 95% of the activation energy E25 is associated with R25 and about 5% is associated with C25 in the SnO2:Bi2O3 ( ¼100:0.25) thick-film sample. About 99% of the activation energy E50 is associated with R50 and 1% is from C50 in the SnO2:Bi2O3 ( ¼100:0.5) thick-film sample. The other two samples show very similar activation energies around 0.180 eV for the relaxation time and their components. The small activation energy associated with the relaxation capacitance indicates complicated type relaxation though the Debye response is observed at temperatures above 35 1C. This type of complicated relaxation capacitance was observed previously for the trapping and de-trapping behavior of the ZnO based varistors [35,36]. The trapping response or charge storage behavior should not be temperature dependent. In the present case the relaxation capacitance refers to the lumped bulk and grain boundary behavior along with the SnO2–Bi2O3 interfaces. This capacitance is not expected to be thermally activated [12,35] as the thermal activation of the relaxation resistance is usually proportional to the relaxation time. Thus, C25 and C50 should not be thermally activated. In general, the thermal activation of the relaxation time and the relaxation resistance are identical [35]. Considering these responses in conjunction with the presence of the depression angle for each sample at 35 1C implies that the nature of t25, t50, t100, and t150 (subscripts 100 and 150 correspond to the constituent 1.00 wt% Bi2O3 and 1.50 wt% Bi2O3, respectively) relaxations are more complex despite small non-Debye response. It suggests a complicated distribution of activation energies and/or relaxation times [12,38]. The origin of such complexity is not known at this time though the relaxation is identified as the lumped grain boundary contribution for each sample. The activation energies of four samples do not correspond to the differences in the microstructure or the distribution of the SnO2–Bi2O3 interfaces. The activation is associated with the origin of the lumped resistance and lumped capacitance comprising SnO2 grain, Bi2O3 grains, and SnO2–Bi2O3 interfaces. Thus, the value of the relaxation time t is changed but the process of conduction is identical for each of these samples. The thermal behavior of the peak-frequency given by [39] fpeak ¼ fpeak,0 expðEpeak =kTÞ
ð9Þ
which exhibited linear behavior yielding fpeak,0 ( ¼f0) of the order of 1010 Hz, which is nearly identical to the previously published results. The activation energy Epeak is found to be identical with the observed values for t25 and t50. The range of fpeak,0 is also the same for the other two samples [25,26]. In general, polycrystalline materials show complicated thermal behavior for the relaxation time as well as the contributing components of the same relaxation time. Often such complexity is observed with the trapping and de-trapping behaviors as demonstrated with the multi-component ZnO varistors [12,31,38]. Binary constituents provide a simple viewpoint of the material systems compared to the multi-component varistors. In the binary material
systems trapping complexity may not be recognized via semicircular relaxation in the impedance plane. Usually trapping response is a series of event prompting R–C series equivalent circuit, which is not evident in the impedance plane relaxation. The impedance plane relaxation provides R–C parallel combination as simplistic equivalent circuit. Fig. 11 shows the equivalent circuit model of the SnO2–Bi2O3 based material system regardless of exhibiting Debye relaxation at above 35 1C and non-Debye relaxation at 35 1C. The circuit on the left can be approximated as the R2–C2 parallel circuit on the right. The constituting components of the relaxation time t are designated as the equivalent R2–C2 parallel circuit elements. For all practical purposes it is convenient to apprehend only the R2–C2 parallel circuit combination rather than the existence of the leftintercept. The R2–C2 parallel combination represents SnO2 grain, Bi2O3 grains, and SnO2–Bi2O3 interfaces or grain boundary effect of the material. The parameter visualized from the left-intercept as resistor R1 having very small magnitude that is nearly invisible at high frequencies may have resulted from the contacts and leads used in the measurement.
5. Conclusions All the four SnO2–Bi2O3 based composite samples exhibited non-Debye relaxation in the impedance plane at 35 1C. The same samples exhibited Debye relaxation above room temperature. The analysis of the relaxation process is conducted using the Cole– Cole empirical equation in conjunction with strong eye estimation of the input parameters attributing to the nature of near fullsize semicircular appearance. This eye estimation procedure for the observed semicircular relaxation provides iterative approach for extracting the contributing components. The analysis conducted this way assures both confidence and level of accuracy for these parameters. The thermal behavior of the relaxation components indicated complicated nature of the lumped capacitance. The equivalent circuit developed from the Z*-plane semicircular behavior is based on very small magnitude of the left-intercept R1 in series with the parallel R2–C2 combination for the lumped grains and grain boundaries. The resistor R1 is presumed to be close to zero or non-existent while R2–C2 becomes the ultimate equivalent circuit of the SnO2–Bi2O3 based material system. Acknowledgments The authors gratefully acknowledge the support of the present work through NSF RISE grant no. 0927644. Thanks to Mr. G. Sharp for fabrication of the sample holder and heater assembly. References [1] K. Ihokura, J. Watson, The Stannic Oxide Gas Sensor: Principles and Applications, CRC Press Incorporated, Florida, USA, 1994. [2] B.S. Joo, N.J. Choi, Y.S. Lee, J.W. Lim, B.H. Kang, D.D. Lee, Sensors and Actuators B 77 (2001) 209. [3] C.R.M. Grovenor, Journal of Physics C: Solid State Physics 18 (1985) 4079. [4] Z. Hajnal, J. Miro, G. Kiss, F. Reti, P. Deak, R.C. Herndon, J.M. Kuperberg, Journal of Applied Physics 86 (7) (1999) 3792.
1452
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
[5] A. Janotti, C.G. Van de Walle, Applied Physics Letters 87 (2005) 122102. [6] C.A.J. Ammerlaan, Physica B 302–303 (2001) 425. [7] (a) J.J. McCarroll, Surface Science 53 (1) (1975) 297; (b) G. Erti, H.-J. Freund, Physics Today 52 (1999) 32. [8] H. Gleiter, Acta Materilia 48 (2000) 1. [9] P. Cheng, S. Li, M.A. Alim, Physica Status Solidi A 204 (3) (2007) 887. [10] M. Lei, S. Li, J. Li, M.A. Alim, Journal of Applied Sciences 6 (8) (2006) 1671. [11] M. Lei, S. Li, X. Jiao, J. Li, M.A. Alim, Journal of Physics D: Applied Physics 37 (2004) 804. [12] M.A. Alim, Journal of the American Ceramic Society 72 (1) (1989) 28. [13] M.A. Alim, M.A. Seitz, Journal of the American Ceramic Society 71 (1988) C246. [14] J.H. Yu, G.M. Choi, Sensors and Actuators B 52 (3) (1998) 251. [15] L. Schmidt-Mende, J.L. MacManus-Driscoll, Materials Today 10 (5) (2007) 40. [16] M.A. Alim, Active and Passive Electronic Components 19 (3) (1996) 139. [17] M.A. Alim, Immittance data-handling/analyzing criteria for heterogeneous systems, in: Proceedings of the Materials Research Society Symposium on Electrically Based Microstructural Characterization, R.A. Gerhardt, S.R. Taylor, E.J. Garboczi (Eds.), 411, (1996), 13–23. [18] M.A. Alim, Phenomena related to concurrent multiple complex plane representations of the immittance data, in: Proceedings of the Materials Research Society Symposium on Electrically-Based Microstructural Characterization, R.A. Gerhardt, S.R. Taylor, E.J. Garboczi (Eds.), 411, (1996), 113–122. [19] M.A. Seitz, International Journal of Hybrid Microelectronics (ISHM) 3 (1980) 1. [20] I.M. Hodge, M.D. Ingram, A.R. West, Journal of Electroanalytical Chemistry 74 (2) (1976) 125. [21] I.M. Hodge, M.D. Ingram, A.R. West, Journal of Electroanalytical Chemistry and Interfacial Electrochemistry 58 (2) (1975) 429. [22] M.A. Alim, B.G. Penn, J.R. Currie, Jr., A.K. BatraM.D. Aggarwal, NASA Technical Memorandum, NASA/TM2008, October 2008.
[23] J.R. Currie, Jr, Ph.D. Dissertation, Alabama A & M University, Huntsville, Alabama, May, 2008. [24] B.P.J. de Lacy Costello, R.J. Ewen, P.R.H. Jones, N.M. Ratcliffe, R.K.M. Watt, Sensors and Actuators B 61 (1–3) (1999) 199. [25] J.H. Yu, G.M. Choi, Sensors and Actuators B 61 (1–3) (1999) 61. [26] K.S. Cole, R.H. Cole, Journal of Chemical Physics 9 (1941) 341. [27] A.K. Batra, M.A. Alim, J.R. Currie, M.D. Aggarwal, Physica B 404 (2009) 1905. [28] (a) J.R. Currie, A.K. Batra, M.A. Alim, M.D. Aggarwal, R.B. Lal, Journal of Materials Science: Materials in Electronics 18 (2007) 433; (b) Erratum: J.R. Currie, A.K. Batra, M.A. Alim, M.D. Aggarwal, R.B. Lal, Journal of Materials Science: Materials in Electronics 18 (2007) 899. [29] C.P. Smith, Dielectric Behaviour and Structure,, McGram-Hill Book Company, Inc., New York, 1955. [30] M.A. Alim, S.R. Bissell, A.A. Mobasher, Physica B 403 (2008) 3040. [31] M.A. Alim, M.A. Seitz, R.W. Hirthe, Journal of Applied Physics 63 (7) (1988) 2337. [32] A.-M. Azad, L.L.W. Shyan, M.A. Alim, Journal of Materials Science 34 (1999) 1175. [33] A.-M. Azad, L.L.W. Shyan, M.A. Alim, Journal of Materials Science 34 (1999) 3375. [34] M.A. Alim, S.A. Akbar, Immittance Data Acquisition and Analytical Software Package,, Developed at The Ohio State University, Columbus, Ohio, 1992. [35] W. Cao, R. Gerhardt, Solid State Ionics 42 (3–4) (1990) 213. [36] R. Gerhardt, Journal of Physics and Chemistry of Solids 55 (12) (1994) 1491. [37] M.A. Alim, A.K. Batra, S. Bhattacharjee, M.D. Aggarwal; Complex capacitance in the representation of modulus of the lithium niobate crystals, Physica B, in press, doi:10.1016/j.physb.2010.12.047. [38] M.A. Alim, Active and Passive Electronic Components 17 (1994) 99. [39] L.M. Levinson, H.R. Philipp, Journal of Applied Physics 47 (3) (1978) 1117.
Contents lists available at ScienceDirect
Physica B journal homepage: www.elsevier.com/locate/physb
Immittance response of the SnO2–Bi2O3 based thick-films Mohammad A. Alim a,n, A.K. Batra b, M.D. Aggarwal b, James R. Currie c a b c
Department of Electrical Engineering, Alabama A & M University, P.O. Box 297, Huntsville, AL 35762, USA Department of Physics, Alabama A & M University, P.O. Box 1268, Huntsville, AL 35762, USA NASA—Marshall Space Flight Center, Huntsville, AL 35812, USA
a r t i c l e i n f o
abstract
Article history: Received 29 March 2010 Received in revised form 21 December 2010 Accepted 20 January 2011 Available online 26 January 2011
The SnO2–Bi2O3 based thick-film polycrystalline material is fabricated on alumina substrate via screenprinting technique. This material system is evaluated at various temperatures (35 1Cr Tr 100 1C) using ac small-signal (immittance) measurements in the frequency range 10 Hz r fr 106 Hz. The simplistic analytical scenario for the immittance data employed the Cole–Cole empirical equation in conjunction with the estimation of the inspected input parameters. This is an alternate approach compared to the complex nonlinear least squares (CNLS) fitting procedure, and purely based on the appearance of the semicircular relaxation in the complex plane. It is found that the constituting components of the semicircular relaxation in the impedance plane are thermally activated indicating complexity in the grain boundary contributions despite the Debye and non-Debye relaxation responses. The possible degree of uniformity or non-uniformity in the grain boundary activity associated with its capacitance term observed via the Debye or non-Debye semicircular relaxation in the impedance (Z*) plane has been postulated. & 2011 Elsevier B.V. All rights reserved.
Keywords: Tin oxide Binary oxides Bismuth oxide Impedance Immittance
1. Introduction Binary compounds play important role in the nonlinear devices used as gas sensors, resistors, capacitors, thermistors, varistors, piezoelectrics, radiation detectors, etc. On many occasions thrust goes on with the oxide-based binary compound as the potential gas sensing device. Thus, the electrical properties are assessed extensively for the compounds. The oxides are selected in such a way that they exhibit surface modification in conjunction with porosity so that the detection of toxic pollutants, combustible gases, flammable organic vapors, etc. can be performed. Metal oxides such as tin oxide (SnO2), zinc oxide (ZnO), titanium dioxide (TiO2), tungsten oxide (WO3), gallium oxide (Ga2O3), copper oxide (CuO or Cu2O), and others have been examined for gas sensing applications, including control of industrial processes. Tin oxide is the most extensively studied material among the metal oxides as gas sensing material, varistor, thermistor, resistor, etc. [1]. Intrinsically it is n-type semiconductor having tetragonal structure similar to that of rutile with direct band-gap of about 4 eV and indirect band-gap of 2.6 eV [2]. Thus, it is a metal-excess non-stoichiometric compound semiconductor having oxygen vacancies and electron donor states. When polycrystalline SnO2 film is exposed to air physisorbed oxygen
n
Corresponding author. Tel.: +1 256 372 5562. E-mail address: [email protected] (M.A. Alim).
0921-4526/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2011.01.046
molecules pick up electrons from the conduction band to yield O2(ads) or O(ads) species [1]. Consequently a positive space charge layer forms just below the surface of the SnO2 particles, which creates a potential barrier between the particles. This process increases the electrical resistance of the SnO2 film. However, when a reducing gas comes in contact with the same film it gets oxidized via reaction with O2(ads) and O(ads) species, and consequently electrons are reintroduced into the electron depletion layer leading to a decrease in potential barrier. This process decreases the resistance of the film. Thus, a semiconductor sensing material detects various gases attributing to the change in resistance (or conductance) and associated capacitance of the film. The simultaneous change in resistance and capacitance may result from a combination of several physical properties, but not limited to: (i) bulk defects (interstitials, oxygen vacancies, complex substitutions, etc.) [3], (ii) surface states (donor type oxygen vacancy [4,5] or acceptor type cation vacancy [6] or clusters capable of holding both positive and negative charges simultaneously), (iii) catalytic action (chemical breakdown or dissociation of an incoming gas by catalyst on the surface of the sensing element) [7], (iv) nature of microstructure and grain boundaries (grain size distribution and shape of the grains, number of grain boundaries and interface states, effective surface area to actual volume ratio) [8], (v) interphase regions, including tri-phase or tetra-phase intersections (change in interface conductance and capacitance due to the incoming gas striking at the tri-grain or
1446
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
tetra-grain intersections) [9–13], etc. It is important to note that the sensing behavior of the single constituent material such as SnO2 exhibits less sensitivity than the composites based on binary constituents. Alternately the sensing materials based on composites have shown significantly higher sensitivity than the individual constituent such as SnO2. As an example in a recent work, different proportions of SnO2 and ZnO exhibited higher sensitivity for certain range of organic vapor constituents [14]. ZnO has wurtzite structure and known intrinsic n-type metal-excess nonstoichiometric compound semiconductor having zinc interstitials with direct band-gap [15] of about 3.3 eV. Frequency response characteristics of the polycrystalline materials can be used to discriminate various contributions to overall conduction processes due to the contact surfaces, grain boundaries, intergranular contact regions, and the overall bulk comprising of the grains [16–18]. Quantitative information for each of these contributing regions may be extracted from the experimental situation via lumped equivalent circuit model resulting from the series-parallel network comprising of R–C (resistance–capacitance) elements attributing to the bulk grains, grain boundaries, and possible contributions from the presence of secondary phase(s), etc. Often possible contribution from the electrode contact on to the surface of the sensing materials is minimized using proper metal(s) delineating work function(s). The immittance (impedance or admittance) measurement employing spectroscopic characterization approaches is very popular for investigating novel devices and material systems. These spectroscopic approaches include lumped parameter/complex plane analysis (LP/CPA) combining with the Bode plane analysis (BPA) and become a very powerful tool/technique for investigating polycrystalline semiconductors [16–21]. In the present effort SnO2–Bi2O3 based polycrystalline binary composite system is characterized via LP/CPA technique using ac small-signal electrical data. The major emphasis in this work is directed toward the ac electrical characterization in order to understand the composite rather than presenting the gas sensing behavior. It is not sintered but heat-treated at elevated temperature, and exhibited some gas sensing behavior [22,23]. In the literature it is proposed that the increase in sensitivity attributing to the synergistic effects comprises of (i) complementary catalytic activity, [24] and (ii) formation of hetro-junctions, including microstructural changes following sintering [25]. In this investigation ac electrical measurement is conducted for the SnO2–Bi2O3 based polycrystalline films consisting of ultra-fine grains that can be used in the detection of toxic vapors [24]. Temperature dependence of the electrical measurement is also carried out to understand thermal behavior of the sensing composite materials. This study further provides ac conduction processes between the measurement terminals via an equivalent circuit model that illustrated the Cole–Cole [26] response in a simplistic analytical perspective. In the data analyses procedure, iterative method is used to extract constituents of the relaxation parameters. These parameters are identical parameters that are extracted from the traditional complex nonlinear least squares (CNLS) fitting procedure. Thus, iterative approach provides a viable procedure for the LP/CPA technique.
2. Experimental The SnO2–Bi2O3 based polycrystalline binary composite system is fabricated using thick-film technology (TFT) applying on to the alumina substrate. The flow chart of this fabrication is given in Fig. 1. Spec pure SnO2 powder (99.99% metals basis, Alpha Aesar) and Bi2O3 powder (99.99% metals basis Alpha Aesar) were used in processing of the samples. Four different samples were
Ultrasonic Cleaning of Substrates
Preparation Of Paste
Thick Film Deposition
5 min
100 °C, 15 min
Rest
Drying
Add Another Layer
yes
no 400 °C, 120 min
Calcination
800 °C, 360 min
Sintering
Electroding
Characterization Fig. 1. Flow chart of the thick-film fabrication process.
prepared using the screen-printing technique for the following proportions of the binary ingredients by weight: (i) SnO2:Bi2O3 (¼ 100:0.25), (ii) SnO2:Bi2O3 (¼ 100:0.5), (iii) SnO2:Bi2O3 (¼ 100:1.00), and (iv) SnO2:Bi2O3 ( ¼100:1.50). Each mixture was ground and/or milled with mortar and pestle for more than one hour. To prepare the ink-paste for the screen-printing a commercially available terpineol-based vehicle ESL-449 was used as active mixture to get blended together for half an hour. The paste was then applied on to the ultrasonically cleaned alumina substrate a using screen-printing machine [27,28]. The substrate is approximately 25 mm 16 mm 0.5 mm thick and the coating is 50 mm thick. The resulting samples were then heat-treated using a temperature profile shown in Fig. 2. The thick-film samples were placed in the furnace and applied to ramp up at 2 1C/min to 400 1C from room temperature. The samples were held for 2 h at this temperature. Again, the furnace was ramped up at 2 1C/min to 800 1C, and then held for 6 h. The furnace was then cooled down using 2 1C/min to the ambient room temperature. The silver print electrodes were then deposited on the surfaces of the layer as depicted in Fig. 3, where the front view of the cross-sectional geometry is evident. The composite samples prepared this way are then electrically characterized. Measurements of parallel capacitance and dielectric loss were made with a QuadTech 7600 precision LCR meter interfaced with the personal computer for recording the ac electrical data. These electrical data are referred to as the immittance data. The measurement system utilized a thermolyne hot-plate chamber controlled via a Cole–Parmer Digi-Sense Temperature Controller
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
900 800 Temperature (°C)
700 600 500 400 300 200 100 0 13 20
00
0
80
12
10
0
0
96
84
0
0
72
60
0
0
48
36
0
24
12
0
Time (min) Fig. 2. Temperature profile used in the heat treatment process of samples.
Sensing Film
Silver Paint Electrode
Alumina Substrate
interfaced to the same personal computer using an RS-232 Null Modem Cable, as presented elsewhere [27]. The same personal computer was used running the LabVIEW for Windows Version 7.1 to achieve overall instrument control and eventual ac electrical data acquisition. Each sample was fixed on to a sample holder and the temperature of the film was ascertained by a Type K (chromel–alumel) thermocouple attached to the sensing material.
3. Dielectric relaxation 3.1. Debye and non-Debye relaxations The non-ideal response termed as the non-Debye behavior was originally given by the empirical form known as single-relaxation Cole–Cole dielectric function [26,29]
e ðoÞ ¼ e1 þ
ðes e1 Þ 1 þ ðjotÞð1aÞ
angle (y) measured from the point at the left-intercept to the center of the semicircle below the x-axis. This depression angle becomes a measure of the depression parameter, a, where a ¼(2y/p). The value of a ranges between 0 and 1 depending upon the idealized Debye or extreme non-Debye response of a semicircular relaxation, thus, a Debye-like behavior can be achieved, as y-01 (a-0), and an extreme non-Debye response can be visualized with y-901 (a-1). The conversion of the data from impedance to admittance or vice versa is straightforward only for the Debye relaxation, and Eq. (1) can be used for a ¼ 0, which is essentially the Debye relation. In the case of the non-Debye relaxation Eq. (1) is referred to as the empirical Cole–Cole relation. The conversion from impedance to admittance or vice versa for the non-Debye relaxation yields complexity and does not portray the Debye or Debyelike behavior for subsequent analysis. Treatment of the nonDebye data as Debye-like invariably yields non-Debye equivalent circuit elements though converted to another form of data via another complex plane. This is evidenced in numerous previously published papers [16–21,31–34] when multiple complex plane analyses are displayed of the same data. The single-relaxation Cole–Cole dielectric function of Eq. (1) can be manipulated in the impedance (Z*) plane for a single semicircular relaxation in the analogous form represented as [30] Z ð oÞ ¼ Z 1 þ
Fig. 3. Cross section of a sensor fabricated using alumina substrate.
ð1Þ
where j¼O(–1), e is the dielectric behavior of the material referring to eN for the high-frequency limit (measurement frequency f-N), and es for the static or dc condition (measurement frequency f-0) with angular frequency o ¼ 2pf in rad/s, t ¼relaxation time in second, and a ¼depression parameter. Eq. (1) provides a semicircular loci [26,29] when real part is plotted on x-axis against the imaginary part on y-axis. The ordinate (y-axis) and abscissa (x-axis) must have the same plotting scale so that the semicircular relaxation in any of the complex planes can be clearly observed. This means that the magnitude of each unit grid (or graphical segment) in length on the ordinate and the abscissa must be equal. The quantity (es eN) refers to the diameter of the semicircle when the center of the semicircle lies on the x-axis implying ideal or Debye or Debye-like behavior. The same quantity is referred to the chord of the semicircle when the center of the semicircle lies below the x-axis implying non-ideal or non-Debye behavior [16–21]. The depression parameter a arises for the center lying below the x-axis [29–31]. A non-Debye relaxation gives rise to a depression
1447
ðZs Z1 Þ 1 þ ðjotÞð1aÞ
¼ Z1 þ
ZC 1 þðjotÞð1aÞ
ð2Þ
where ZC is the resistance obtained as chord when the center of the semicircle lies below x-axis or as diameter when the center of the semicircle lies on the x-axis; Zs is the resistance at static (f-0 Hz or dc) condition and ZN ( ¼ZHF ¼Z0 N) is the resistance and high-frequency (f-N) condition. Eqs. (1) and (2) are not the same but identical in appearance. Invariably relaxation time t, depression parameter a, and left-intercept are not the same for two complex plane semicircular relaxations. The equivalent circuit elements extracted from each semicircular relaxation [simulating Eqs. (1) and (2)] are also different in these two complex planes [16]. The contributing capacitance C in the semicircular relaxation time t for the semicircular relaxation in the impedance plane is obtained using R¼ZC ( ¼Z0 C) in conjunction with the peak-frequency (fpeak) given by t ¼RC ¼1/opeak ¼ 1/(2pfpeak). Often Zs is referred to as ZLF (or Z0 LF) attributing to the low-frequency response. Users may refer this situation to the dc condition as near zero frequency or low-frequency. 3.2. Single semicircle relaxation: impedance plane Fig. 4 shows impedance plot of the experimental data and corresponding simulation at various temperatures for the thick film based on SnO2 containing 0.25 wt% Bi2O3 deposited on the alumina substrate. The reactance on the y-axis is treated as a positive quantity, which is normally done by most investigators [16–21]. In this display each semicircular relaxation curve is fitted using a method demonstrated recently for the Davidson–Cole relaxation [30]. In this fitting procedure, chord of each semicircle is determined using strong eye estimation via high magnification of the low-frequency (right-side of the semicircle) and the highfrequency (left-side of the semicircle) ends for the impedance plane semicircular relaxation. Then iteration process using Eq. (2) is employed for the depression parameter a ¼0 for the Debye response or a ¼ some finite value for non-Debye response, based on individual assessment until the shape of the arc is matched with the loci of the experimental data. This is a fitting process that can frequently adopt eye estimation of the diameter or chord of the semicircle. For each iteration process it is made sure that the peak-frequency matches with the experimental data like rest of the data. Such a procedure ascertains the level of accuracy when iteration process is employed.
1448
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
3000000 35°C 80°C 35° Sim 80° Sim
2500000
60°C 100°C 60° Sim 100° Sim
Z"
2000000
1500000
1000000
500000
0
45
40
35
30
25
00
00
00
00
00
00
00
00
0
0
0
0
0
0
0
00
00
00
00
20
00
00 0
00
00
00
00
15
10
50
0
Z' Fig. 4. Impedance plot of the experimental and simulated data at various temperatures for the thick film based on tin oxide containing 0.25 wt% bismuth oxide deposited on an alumina substrate.
Table 1 Simulated parameters obtained from the impedance of Fig. 5 using empirical Eq. (2). Temperature (1C)
Z0 N (O)
Z0 LF (O)
Z0 C (O)
Z0 0 peak or Z0 0 max at fpeak (O)
fpeak (Hz)
C (¼ t/R) (pf)
1a
Depression y (deg)
35 60 80 100
3045 5610 10,202 14,647
4,322,397 3,167,032 2,290,911 1,481,998
4,319,352 3,161,422 2,280,709 1,467,351
2,087,589 1,560,468 1,182,029 755,724.7
47,434 72,871 105,200 143,000
1.60726 1.39962 1.2799 1.47272
0.975 1 1 1
2.25 0 0 0
The foregoing iteration process is a viable effort when compared to the complex nonlinear least squares (CNLS) fitting procedure used in the previous work [16–19,31–34] for single plane or multiple plane semicircular relaxation analysis. The iteration approach is found to be reasonable and effective concerning time-saving aspect of the data-handling criteria. Furthermore, it is a legitimate approach as long as the results are concerned besides easy route of data-handling for the users and/or the learners. The customary CNLS fitting procedure and iteration process yield identical results that are equally reliable. In this work both CNLS and eye estimation iteration processes are verified via the contributing components of the relaxation time and each measure data points. The errors are so small that it is considered to be insignificant to report. Thus, either method is perfectly appropriate as there is nothing inherently wrong with the iterative approach. Each semicircular curve in the impedance plane of Fig. 4 represents a simplified R–C (resistance–capacitance) parallel equivalent circuit. The intercept on the left-side of the semicircular relaxation on the x-axis represents a resistor in series with the same R–C parallel combination. This intercept may be termed as the left-intercept. As shown in Table 1, the semicircular response at 35 1C in Fig. 5 is determined to be slightly non-Debye in nature exhibiting a small depression angle of about 2.251. The presence of a finite (non-zero) depression angle in the semicircular relaxation indicates that this is not an ideal system for temperatures less than or equal to 35 1C. This finite depression angle indicates an inhomogeneity in the conduction path(s) of the composite microstructural system for the SnO2 containing 0.25 wt% Bi2O3, and the electrical response is referred to as the non-Debye response. The degree of inhomogeneity in the
conduction process is likely to be associated with the capacitive component represented via the depressed ordinate parameter (i.e., reactance) in the impedance plane plot. The capacitive component causing inhomogeneity is likely to be originated from the grain boundary regions from junction to junction of both SnO2 and Bi2O3 as independent phases or interfaces between them. A small variation in the depression angle for this material system is not too definitive or conclusive on inhomogeneity of the conduction process, but indicative of a fluctuation in the degree of inhomogeneity in the effective conducting paths between the two terminals [12,13]. The semicircular relaxation for other elevated temperatures (T4 35 1C) indicate Debye or Debye-like response as a ¼0. As temperature increases, the conduction level increases within the material system reflecting thermal transport of the increased carriers across the grain boundaries of the same microstructural network. Thus, the conduction process turns to homogeneity throughout the material system as reflected via the Debye-like response. For depression angle y E0o implies no distribution of activation energies and/or relaxation times involving uniform conduction path. Nevertheless, conducting paths controlled by the capacitive component eventually yields homogeneous carrier transport across the junctions resulting in Debye-like behavior as also noticed for the multi-component/phase ZnO based varistors [12,13,31]. The impedance plane relaxation response is identical for the other three samples [SnO2:Bi2O3 ( ¼100:0.5), SnO2:Bi2O3 (¼ 100:1.00), and SnO2:Bi2O3 ( ¼100:1.50)] at each temperature. Each sample exhibited non-Debye behavior via the presence of small depression angle for the semicircular relaxation at 35 1C, and Debye behavior at temperatures above 35 1C. Since each
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
1449
2500000
2000000
Z"
1500000
1000000
500000 35°C 80°C
60°C 100°C
0 0
1
2
3
4
5
(ωτ) Fig. 5. The product o t is displayed as a function of the imaginary part of the impedance for the data displayed in the inset (Fig. 4).
response of these samples is identical in nature with respect to the SnO2 containing 0.25 wt% Bi2O3 sample the semicircular relaxations are not added here. 3.3. Behavior of the impedance relaxation function The permittivity or impedance relaxation function can be ascribed either from Eq. (1) or Eq. (2) in the form [28] F ðoÞ ¼
1 1þ ðjotÞð1aÞ
¼ Fu þ jF 00
ð3Þ
The relaxation function F*(o) provides permittivity function e*(o) given in Eq. (1) or impedance function Z*(o) given in Eq. (2). In Fig. 4 the imaginary part of the impedance contains maximum magnitude at the peak-frequency (fp or fpeak or opeak ( ¼2pfpeak) or tpeak [ ¼1/(2pfpeak)]), where the semicircle gives ot ¼1 for both ideal (Debye) and non-ideal (non-Debye) relaxation cases. The imaginary part F00 of the relaxation function in Eq. (3) is treated as positive. It is expected that the same ot ¼1 would appear for the Debye or non-Debye relaxation by setting various values of the product o t. Thus, the imaginary part of the relaxation function (F00 ) or the imaginary part of the impedance function (Z00 ) when checked as a function of the product o t can verify ot ¼1 as demonstrated in Fig. 5. Additional representations of the relaxation times can be found elsewhere [35,36]. Fig. 5 represents the behavior of the imaginary part of Z*(o) plotted on the y-axis versus the product o t on the x-axis at different temperatures corresponding to the data displayed in Fig. 4. The imaginary part of the impedance Z00 is analogous to the relaxation function F00 and treated as the positive quantity on the y-axis. Fig. 5 indicates ot ¼1 for both Debye (T435 1C) and nonDebye (T¼35 1C) responses. This is an important illustration of the ot ¼1 feature of the semicircular relaxation whether the response is Debye or non-Debye. Furthermore, Fig. 5 essentially depicts no shift in the peak of Z00 and the simulated data for the Debye and nonDebye behavior. A similar response for the product o t is plotted for the imaginary part of Z*(o) for the lithium niobate crystals [37]. Since all the points in Fig. 5 correspond to the experimental data and fpeak realized from the peak of Z00 via ot ¼1 for each semicircular relaxation of Fig. 4, it is reasonable to describe the entire analysis as worthy and reliable. This alternate method via iterative way fitting approach demonstrates valid dielectric response of the material system. It employs strong eye estimation of the input
parameters for the Cole–Cole empirical equation. Invariably the present analytical approach has proven to be effective and reasonable. In an earlier work such approach is successfully demonstrated for the Davidson–Cole relaxation behavior [30]. It may not be necessary to utilize traditional CNLS fitting procedure for the semicircular relaxation if the present approach is used for distinct semicircular relaxation that is verifiable via the Cole–Cole empirical equation [27]. Indeed this is a reliable alternate method, as verified via Fig. 5, of obtaining worthy results, and the corresponding interpretation remains identical as always done in the past.
4. Results and discussion Each of the four samples exhibited Debye relaxation at temperatures above 35 1C but less than 100 1C while small amount of non-Debye behavior is observed around 35 1C. The possible degree of uniformity or non-uniformity within the conducting paths realized via Debye or non-Debye semicircular relaxation in the Z*-plane associated with the capacitance ascertained further via the presence of thermal activation. The semicircular relaxation response of Fig. 4 attributed to the lumped grain boundaries provides R–C parallel equivalent circuit. The small resistive element may be visualized from the leftintercept having very small magnitude is nearly invisible at high frequencies. Such a magnitude may have resulted from the contacts and leads of the material used in the measurement. The lumped relaxation indicates merged behavior of both grain and grain boundaries. This lumped behavior is realized from the magnitude of resistance and capacitance. The experimental data points are simulated using Eq. (2) and the curve is displayed in the same illustration. Table 1 documents these simulated parameters. Fig. 5 proves the relaxation peak occurring at ot ¼1 for both non-Debye and Debye relaxations. This is confirmed despite the role of the depression parameter, a. The simulation further affirms that Fig. 5 is a valid approach for the relaxation function of Eq. (3). Figs. 6 through 9 show SEM micrographs at 15,000 magnification of four samples described earlier. The surface of each sample is smooth polycrystalline botryoidal structure in nature. The resulting grain size of each sample is sub-micron (nanometer) in configuration. Using LP/CPA technique [12,13,16–21] in conjunction with the Cole–Cole empirical equation the temperature dependence of the components of the relaxation time t for two selected samples is
1450
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
Fig. 6. SEM image (6000 magnification) of SnO2:Bi2O3 (¼100:0.25) thick film deposited on an alumina substrate.
Fig. 8. SEM image (15,000 magnification) of SnO2:Bi2O3 (¼100:1.00) thick film deposited on an alumina substrate.
Fig. 7. SEM image (6000 magnification) of SnO2:Bi2O3 (¼ 100:0.5) thick film deposited on an alumina substrate.
Fig. 9. SEM image (6000 magnification) of SnO2:Bi2O3 (¼100:1.50) thick film deposited on an alumina substrate.
depicted in Fig. 10. The inset shows the thermal behavior of t. The thermal activation energies of 0.170 eV obtained for t25 [SnO2:Bi2O3 ( ¼100:0.25)], and 0.193 eV obtained for t50 [SnO2:Bi2O3 ( ¼100:0.5)] samples. The subscripts 25 and 50 correspond to the constituent 0.25 wt% Bi2O3 and 0.50 wt% Bi2O3, respectively. The same illustration also shows the temperature dependence of the constituting components of the relaxation time t. Indicating thermal activation of t25 (R25 and C25) according to the equation [12]
t25 ¼ R25 C25 ¼ t25,0 expðE25 =kTÞ
ð4Þ
or
t25 ¼ R25,0 expðER25,0 =kTÞ C25,0 expðEC25,0 =kTÞ
ð5Þ
or
t25 ¼ R25,0 C25,0 exp ðER25,0 þEC25,0 Þ=kT
ð6Þ
where
t25,0 ¼ R25,0 C25,0
ð7Þ
Fig. 10. Temperature dependence of the equivalent circuit parameters designated as R2–C2 corresponding to the relaxation time t (shown in the inset) for two samples: (i) SnO2:Bi2O3 (¼ 100:0.25) and (ii) SnO2:Bi2O3 (¼ 100:0.5).
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
1451
R2
R2
C2
C2
R1
Fig. 11. Equivalent circuit model of the polycrystalline binary metal oxide thick-film.
and E25 ¼ ER25,0 þ EC25,0 ¼ Et25
ð8Þ
The components of t50 (R50, C50) are also thermally activated and can be ascribed in identical manner with Eqs. (4) through (8). About 95% of the activation energy E25 is associated with R25 and about 5% is associated with C25 in the SnO2:Bi2O3 ( ¼100:0.25) thick-film sample. About 99% of the activation energy E50 is associated with R50 and 1% is from C50 in the SnO2:Bi2O3 ( ¼100:0.5) thick-film sample. The other two samples show very similar activation energies around 0.180 eV for the relaxation time and their components. The small activation energy associated with the relaxation capacitance indicates complicated type relaxation though the Debye response is observed at temperatures above 35 1C. This type of complicated relaxation capacitance was observed previously for the trapping and de-trapping behavior of the ZnO based varistors [35,36]. The trapping response or charge storage behavior should not be temperature dependent. In the present case the relaxation capacitance refers to the lumped bulk and grain boundary behavior along with the SnO2–Bi2O3 interfaces. This capacitance is not expected to be thermally activated [12,35] as the thermal activation of the relaxation resistance is usually proportional to the relaxation time. Thus, C25 and C50 should not be thermally activated. In general, the thermal activation of the relaxation time and the relaxation resistance are identical [35]. Considering these responses in conjunction with the presence of the depression angle for each sample at 35 1C implies that the nature of t25, t50, t100, and t150 (subscripts 100 and 150 correspond to the constituent 1.00 wt% Bi2O3 and 1.50 wt% Bi2O3, respectively) relaxations are more complex despite small non-Debye response. It suggests a complicated distribution of activation energies and/or relaxation times [12,38]. The origin of such complexity is not known at this time though the relaxation is identified as the lumped grain boundary contribution for each sample. The activation energies of four samples do not correspond to the differences in the microstructure or the distribution of the SnO2–Bi2O3 interfaces. The activation is associated with the origin of the lumped resistance and lumped capacitance comprising SnO2 grain, Bi2O3 grains, and SnO2–Bi2O3 interfaces. Thus, the value of the relaxation time t is changed but the process of conduction is identical for each of these samples. The thermal behavior of the peak-frequency given by [39] fpeak ¼ fpeak,0 expðEpeak =kTÞ
ð9Þ
which exhibited linear behavior yielding fpeak,0 ( ¼f0) of the order of 1010 Hz, which is nearly identical to the previously published results. The activation energy Epeak is found to be identical with the observed values for t25 and t50. The range of fpeak,0 is also the same for the other two samples [25,26]. In general, polycrystalline materials show complicated thermal behavior for the relaxation time as well as the contributing components of the same relaxation time. Often such complexity is observed with the trapping and de-trapping behaviors as demonstrated with the multi-component ZnO varistors [12,31,38]. Binary constituents provide a simple viewpoint of the material systems compared to the multi-component varistors. In the binary material
systems trapping complexity may not be recognized via semicircular relaxation in the impedance plane. Usually trapping response is a series of event prompting R–C series equivalent circuit, which is not evident in the impedance plane relaxation. The impedance plane relaxation provides R–C parallel combination as simplistic equivalent circuit. Fig. 11 shows the equivalent circuit model of the SnO2–Bi2O3 based material system regardless of exhibiting Debye relaxation at above 35 1C and non-Debye relaxation at 35 1C. The circuit on the left can be approximated as the R2–C2 parallel circuit on the right. The constituting components of the relaxation time t are designated as the equivalent R2–C2 parallel circuit elements. For all practical purposes it is convenient to apprehend only the R2–C2 parallel circuit combination rather than the existence of the leftintercept. The R2–C2 parallel combination represents SnO2 grain, Bi2O3 grains, and SnO2–Bi2O3 interfaces or grain boundary effect of the material. The parameter visualized from the left-intercept as resistor R1 having very small magnitude that is nearly invisible at high frequencies may have resulted from the contacts and leads used in the measurement.
5. Conclusions All the four SnO2–Bi2O3 based composite samples exhibited non-Debye relaxation in the impedance plane at 35 1C. The same samples exhibited Debye relaxation above room temperature. The analysis of the relaxation process is conducted using the Cole– Cole empirical equation in conjunction with strong eye estimation of the input parameters attributing to the nature of near fullsize semicircular appearance. This eye estimation procedure for the observed semicircular relaxation provides iterative approach for extracting the contributing components. The analysis conducted this way assures both confidence and level of accuracy for these parameters. The thermal behavior of the relaxation components indicated complicated nature of the lumped capacitance. The equivalent circuit developed from the Z*-plane semicircular behavior is based on very small magnitude of the left-intercept R1 in series with the parallel R2–C2 combination for the lumped grains and grain boundaries. The resistor R1 is presumed to be close to zero or non-existent while R2–C2 becomes the ultimate equivalent circuit of the SnO2–Bi2O3 based material system. Acknowledgments The authors gratefully acknowledge the support of the present work through NSF RISE grant no. 0927644. Thanks to Mr. G. Sharp for fabrication of the sample holder and heater assembly. References [1] K. Ihokura, J. Watson, The Stannic Oxide Gas Sensor: Principles and Applications, CRC Press Incorporated, Florida, USA, 1994. [2] B.S. Joo, N.J. Choi, Y.S. Lee, J.W. Lim, B.H. Kang, D.D. Lee, Sensors and Actuators B 77 (2001) 209. [3] C.R.M. Grovenor, Journal of Physics C: Solid State Physics 18 (1985) 4079. [4] Z. Hajnal, J. Miro, G. Kiss, F. Reti, P. Deak, R.C. Herndon, J.M. Kuperberg, Journal of Applied Physics 86 (7) (1999) 3792.
1452
M.A. Alim et al. / Physica B 406 (2011) 1445–1452
[5] A. Janotti, C.G. Van de Walle, Applied Physics Letters 87 (2005) 122102. [6] C.A.J. Ammerlaan, Physica B 302–303 (2001) 425. [7] (a) J.J. McCarroll, Surface Science 53 (1) (1975) 297; (b) G. Erti, H.-J. Freund, Physics Today 52 (1999) 32. [8] H. Gleiter, Acta Materilia 48 (2000) 1. [9] P. Cheng, S. Li, M.A. Alim, Physica Status Solidi A 204 (3) (2007) 887. [10] M. Lei, S. Li, J. Li, M.A. Alim, Journal of Applied Sciences 6 (8) (2006) 1671. [11] M. Lei, S. Li, X. Jiao, J. Li, M.A. Alim, Journal of Physics D: Applied Physics 37 (2004) 804. [12] M.A. Alim, Journal of the American Ceramic Society 72 (1) (1989) 28. [13] M.A. Alim, M.A. Seitz, Journal of the American Ceramic Society 71 (1988) C246. [14] J.H. Yu, G.M. Choi, Sensors and Actuators B 52 (3) (1998) 251. [15] L. Schmidt-Mende, J.L. MacManus-Driscoll, Materials Today 10 (5) (2007) 40. [16] M.A. Alim, Active and Passive Electronic Components 19 (3) (1996) 139. [17] M.A. Alim, Immittance data-handling/analyzing criteria for heterogeneous systems, in: Proceedings of the Materials Research Society Symposium on Electrically Based Microstructural Characterization, R.A. Gerhardt, S.R. Taylor, E.J. Garboczi (Eds.), 411, (1996), 13–23. [18] M.A. Alim, Phenomena related to concurrent multiple complex plane representations of the immittance data, in: Proceedings of the Materials Research Society Symposium on Electrically-Based Microstructural Characterization, R.A. Gerhardt, S.R. Taylor, E.J. Garboczi (Eds.), 411, (1996), 113–122. [19] M.A. Seitz, International Journal of Hybrid Microelectronics (ISHM) 3 (1980) 1. [20] I.M. Hodge, M.D. Ingram, A.R. West, Journal of Electroanalytical Chemistry 74 (2) (1976) 125. [21] I.M. Hodge, M.D. Ingram, A.R. West, Journal of Electroanalytical Chemistry and Interfacial Electrochemistry 58 (2) (1975) 429. [22] M.A. Alim, B.G. Penn, J.R. Currie, Jr., A.K. BatraM.D. Aggarwal, NASA Technical Memorandum, NASA/TM2008, October 2008.
[23] J.R. Currie, Jr, Ph.D. Dissertation, Alabama A & M University, Huntsville, Alabama, May, 2008. [24] B.P.J. de Lacy Costello, R.J. Ewen, P.R.H. Jones, N.M. Ratcliffe, R.K.M. Watt, Sensors and Actuators B 61 (1–3) (1999) 199. [25] J.H. Yu, G.M. Choi, Sensors and Actuators B 61 (1–3) (1999) 61. [26] K.S. Cole, R.H. Cole, Journal of Chemical Physics 9 (1941) 341. [27] A.K. Batra, M.A. Alim, J.R. Currie, M.D. Aggarwal, Physica B 404 (2009) 1905. [28] (a) J.R. Currie, A.K. Batra, M.A. Alim, M.D. Aggarwal, R.B. Lal, Journal of Materials Science: Materials in Electronics 18 (2007) 433; (b) Erratum: J.R. Currie, A.K. Batra, M.A. Alim, M.D. Aggarwal, R.B. Lal, Journal of Materials Science: Materials in Electronics 18 (2007) 899. [29] C.P. Smith, Dielectric Behaviour and Structure,, McGram-Hill Book Company, Inc., New York, 1955. [30] M.A. Alim, S.R. Bissell, A.A. Mobasher, Physica B 403 (2008) 3040. [31] M.A. Alim, M.A. Seitz, R.W. Hirthe, Journal of Applied Physics 63 (7) (1988) 2337. [32] A.-M. Azad, L.L.W. Shyan, M.A. Alim, Journal of Materials Science 34 (1999) 1175. [33] A.-M. Azad, L.L.W. Shyan, M.A. Alim, Journal of Materials Science 34 (1999) 3375. [34] M.A. Alim, S.A. Akbar, Immittance Data Acquisition and Analytical Software Package,, Developed at The Ohio State University, Columbus, Ohio, 1992. [35] W. Cao, R. Gerhardt, Solid State Ionics 42 (3–4) (1990) 213. [36] R. Gerhardt, Journal of Physics and Chemistry of Solids 55 (12) (1994) 1491. [37] M.A. Alim, A.K. Batra, S. Bhattacharjee, M.D. Aggarwal; Complex capacitance in the representation of modulus of the lithium niobate crystals, Physica B, in press, doi:10.1016/j.physb.2010.12.047. [38] M.A. Alim, Active and Passive Electronic Components 17 (1994) 99. [39] L.M. Levinson, H.R. Philipp, Journal of Applied Physics 47 (3) (1978) 1117.