Superlattices and Microstructures 50 (2011) 591–600

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Superlattices and Microstructures

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o ca t e / s u p e r l a t t i c es

Review

Impedance studies of Sb doped SnO2 thin film preparedby sol gel process

B. Benrabah a,⇑, A. Bouaza a, A. Kadari b, M.A. Maaref c

a Laboratoire de Génie Physique, Université Ibn-Khaldoun, Tiaret, Algeriab Laboratoire de Microscopie Électronique et Sciences des Matériaux, U.S.T.M.B, Oran, Algeriac Unité de Recherche de Physique des Semiconducteurs et Capteurs, IPEST, La Marsa, Tunis, Tunisia

a r t i c l e i n f o a b s t r a c t

Article history:Received 30 September 2010Received in revised form 25 June 2011Accepted 19 August 2011Available online 30 August 2011

Keywords:SnO2

SbSol–gelImpedance spectroscopy

0749-6036/$ - see front matter � 2011 Elsevier Ltdoi:10.1016/j.spmi.2011.08.009

⇑ Corresponding author.E-mail address: benrabah64@yahoo.fr (B. Benra

Antimony-doped tin oxide thin films have a range of technologicalapplications as conductive coatings, and sol–gel processing seemsto offer some advantages over other coating techniques. In thisstudy antimony-doped tin oxide (ATO) thin films have been pre-pared by the sol–gel dip-coating (SGDC) process, using tin (II) chlo-ride dehydrate (SnCl2, 2H2O) and antimony (III) chloride (SbCl3) ashost and dopant precursors respectively. The structure of the (ATO)powders was analysed by X-ray diffraction (XRD) and the micro-structure of the thin films by atomic force microscopy (AFM). Theseinvestigations show that the structure is tetragonal rutile type andthat an increase in Sb-doping decreases the crystallite size of the(ATO) particles. To analyze the impedance spectroscopy data, theNyquist (Z00 vs. Z0) plots as well as the representation of imaginary(Z0 0) and real (Z0) parts of impedance vs. frequency were used. TheNyquist plots suggest that only the grain boundaries are responsi-ble in the conduction mechanism of the material. From the varia-tion of lnr vs. inverse of absolute T we have deduced theactivation energy found to be 0.87 eV.

� 2011 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5922. Experimental details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592

2.1. Powder and sol preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 592

d. All rights reserved.

bah).

592 B. Benrabah et al. / Superlattices and Microstructures 50 (2011) 591–600

2.2. Deposition of the film . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5922.3. Powder and film characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594

3. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594

3.1. X-ray diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5943.2. Atomic force microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5943.3. FT-IR transmittance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5943.4. Impedance studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 595

4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599

1. Introduction

In recent years, transparent conducting oxide (TCO) films had reached an important place in a vari-ety of optoelectronic devices such as solar cells, gas sensors, displays, varistors [1–3]. Thus, there hasbeen growing interest in the application of TCO films as electrodes in solar cell device. Among the TCOfilms, the most appropriate material for application seems to be tin oxide films, which are chemicallyinert, mechanically hard and heat-resistant. In addition, they exhibit low electrical resistivity and highoptical transmittance in the visible and near IR regions. Controlled doping with pentavalent ions suchas Sb5+ leads to modulation of both gap and resistivity while keeping a good optical transparency.

SnO2 thin films can be fabricated by different methods such as spray pyrolysis [4], chemical vapourdeposition [5,6], rf sputtering [7] and sol–gel coating [8–10]. We have chosen the sol–gel dip-coatingtechnique because of its ability to produce homogenous and transparent films with easy and low costprocess.

The present study investigated the characteristics of Sb-doped SnO2 (ATO) powders and thin filmsprepared by the sol–gel dip-coating (SGDC) process. The structural, optical and complex impedanceproperties of these materials were examined in relationship with the variation in antimony doping.

2. Experimental details

2.1. Powder and sol preparation

Powder has been prepared from tin (II) chloride dihydrate (SnCl2, 2H2O) as host precursor, mixed to100 ml of absolute ethanol as solvent. An amount of 8.37 g of SnCl2, 2H2O as dissolved in 100 ml. ofabsolute ethanol. This mixture was stirred and heated at 80 �C for 2 h in a closed vessel. After heatingand stirring again the solution with the vessel opened, we obtain a powder. This powder is dissolved in50 ml. of absolute ethanol which was stirred and heated at 50 �C for 2 h, thus we obtain the solutionnumber one. The antimony solution was prepared simultaneously using an amount of SbCl3 (anti-mony chloride) in relation with the percent Sb doping dissolved in 20 ml. of ethanol. This solutionwas equally stirred and heated at 80 �C for 1 h in a closed vessel. Using the same process as before,a powder was obtained. This powder was added to the solution number one. The mixture was finallystirred and heated at 50 �C for 2 h; we get then the solution number two which was used for filmdeposition.

2.2. Deposition of the film

Deposition of the film from the solution (sol) was performed using the dip-coating process de-scribed by Chatelon et al. [11]. The substrates were cleaned Pyrex pieces (75 � 25 � 1 mm3) that wereat first emerged in ultrasonic bath for 5 min. and finally rinsed by ethanol. The substrates were dippedin the solution and then withdrawn at a constant speed of 80 mm/min.

Fig. 1. Typical cross-sectional micrograph of 12.5% Sb-doped SnO2 thin film.

10 20 30 40 50 60 70

(301

)

(310

)

(220

)(2

11)

(200

)

(101

)

(110

)

Inte

nsity

(arb

.uni

ts)

2θ (degree)

a : no dopingb : doping 2,5% Sbc: doping 5% Sbd : doping 10% Sb

(a)

(b)

(c)

(d)

Fig. 2. XRD patterns of (ATO) powders for different Sb-doping amounts.

B. Benrabah et al. / Superlattices and Microstructures 50 (2011) 591–600 593

Dip-coating operations were performed on Pyrex plates (1 mm thick, 2.5 wide, 7.5 cm length). Therelative humidity (RH) ratio in the vicinity of the meniscus has been fixed at approximately 40%. Pyrexplates were immersed and drawn from the prepared solution to obtain one deposition.

For each sample, the film was dried at 100 �C for 15 min. and then subjected to an annealing at500 �C for 15 min. The sample was left for 10 min. at each of the following temperatures 100, 200,

594 B. Benrabah et al. / Superlattices and Microstructures 50 (2011) 591–600

300 and 400 �C. The thickness of the films, measured by scanning electron microscope (SEM) wasabout 120 nm (Fig. 1).

2.3. Powder and film characterization

The structural characterization of the powders was analysed using X-ray diffractometer (XRD)(Philips PW1830) with CuKa radiation. FT-IR spectra of the samples were recorded using a Shimadzu1800 spectrophotometer. The surface morphology of the films was examined by atomic forcemicroscopy (AFM) (Hitachi 2500C). The thickness of the films was performed by scanning electronmicroscope (SEM) (S-2500C). Impedance measurements were carried out using an Agilent 4284ALCR meter operating at oscillation amplitude of 1 V. Impedance measurements have been made inthe temperature range 80–250 �C and frequency ranging from 20 Hz to 1 MHz.

3. Results and discussion

3.1. X-ray diffraction

Fig. 2 shows the XRD patterns of the undoped and Sb-doped SnO2 powders heat treated at700 �C during 2 h for several amount of Sb-doping (0%, 2.5%, 5% and 12.5% Sb). After evaporationand calcination, the percent (%) of doping of the powders should be close to those of the solutions.For all the samples, the peak positions agree well with the reflections of tetragonal rutile structureof pure SnO2 (JCPDS card No. 88–2348) and the diffraction peaks arise at (110), (101), (200),(211), (220), (310) and (301) without any other phases detected, indicating that all antimonyions were embedded into the crystal lattice of rutile SnO2. As the amount of Sb increases the peaksbecome weaker.

The lattice parameters were determined by using the formula: d ¼ affiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

h2þk2þðacÞ2 l2

p . The values found

were: a = b = 4.74 Å, c = 3.19 Å in good agreement with those calculated by L. Zhao et al. [12].The crystallite size of the (ATO) particles was determined using the peak at (110) by the Scherrer’s

formula:

Ig ¼ 0;9k=Bcosh ð1Þ

Where Ig is the crystallite size, k = 0.154 056 nm the mean wavelength of CuKa radiation and B the fullwidth half maximum (FWHM) of Bragg peak observed at Bragg angle h (radian). From the values of Ig

obtained, it is obvious that the crystallite size of the particles deceases when Sb amount increases, it is40 nm for 2.5% Sb doping , 33 nm for 5% and 28 nm for 10% respectively. Our results correspond withthose of E. Elangovan et al. [13] who also observed that the crystallite size of the (ATO) particles ob-tained by spray pyrolysis became smaller with increasing antimony doping amount.

3.2. Atomic force microscopy

Surface morphology of the films was examined by atomic force microscopy (AFM). Root meansquare (RMS) roughness of the films was extracted from the AFM data. The AFM micrographs obtainedfor 2.5% and 12.5% Sb-doped SnO2 films are shown in Fig. 3(a, b). The RMS roughness of 45 nm ob-tained for the 2.5% doped film has been considerably reduced to 15 nm for the 12.5% doped film. Thisstudy reveals that the roughness decrease with increasing Sb-doping, which is in good agreement withthe XRD analysis confirming that the crystallite size of the particles decrease with increasing Sb-dop-ing (calculated values from the XRD patterns widths at half maximum of the peaks by Scherrer’s for-mula, from 40 nm for 2.5% to 28 nm for 12.5% Sb-doping).

3.3. FT-IR transmittance

The FT-IR transmittance spectra of the SnO2:Sb film with 12.5% Sb-doping after drying at 500 �C isshown in Fig. 4. The absorption peak located at 3430 cm�1 characterizes the hydroxyl groups of

Fig. 3. AFM micrograph of (a) 2.5% and (b) 12.5% Sb-doped SnO2 thin films.

B. Benrabah et al. / Superlattices and Microstructures 50 (2011) 591–600 595

physisorbed water molecules bound by weak hydrogen bonds with OH� groups of SnO2 surface [14].The weak adsorption at 1635 cm�1 is associated with the deformation vibration for H–O–H bonds ofphysisorbed water. The bands observed in the range of 1060 and 970 cm�1 are due to vibration ofSn@O, Sn–O and Sb–O surface cation-oxygen bonds [15]. The typical M–O–M (in this case Sn–O–Sn) vibrations appear in the range of 530–700 cm�1 [16].

3.4. Impedance studies

Impedance spectroscopy (IS) is a powerful method of characterizing many of the electrical proper-ties of materials and their interfaces with electronically conducting electrodes [17]. A great strength ofimpedance spectroscopy is that, with appropriate data analysis, it is often possible to characterize thedifferent electrically active regions in a material by demonstrating their existence and by their indi-vidual electric properties [18].

500 1000 1500 2000 2500 3000 3500 40000.90

0.92

0.94

0.96

0.98

1.00(3430)

(1635)(970-1060)

Tra

nsm

ittan

ce (

a.u)

Wave number (cm-1)

SnO2 doped 12.5% of Sb

(530-700)

Fig. 4. FT-IR spectra of 12.5% Sb-doped SnO2 dried thin film.

0 2 4 6 8 100

1

2

3

4

5

6R

C

R

C

-Z''

x105 (

Ohm

s)

Z' x105 (Ohms)

T = 80 °C T = 100 °C T = 130 °C T = 250 °C

Fig. 5. Complex impedance spectrum (Nyquist plots) of 12.5% Sb-doped SnO2 thin film.

596 B. Benrabah et al. / Superlattices and Microstructures 50 (2011) 591–600

The frequency dependent properties of a material are normally described in terms of compleximpedance formalism which consist of real as well as imaginary components [19]: compleximpedance,

Z� ¼ Z0 þ jZ00 ¼ RS � j=xCS ð2Þ

where RS, CS are the series resistance and capacitance; RP, CP are the parallel resistance andcapacitance. Here, primed and double parameters denote, respectively, the real and imaginary compo-nents; x = 2pt, t is the applied frequency; C0 is the empty capacitance and j ¼

ffiffiffiffiffiffiffi

�1p

.The sample of 1 cm � 1 cm of size is placed in a small oven that has gold tabs to prevent oxidation

upon contact with the sample. To make contact with the sample, we used the silver lacquer. The LCR-meter is controlled by a computer and for each selected temperature the values of IZI, Z0, Z00 and fre-quency are stored in a data acquisition card. Then we draw the curves of the desired function, usingOrigin program.

Table 1Bulk resistances and capacitances of SnO2:Sb (12.5%).

Temperature (�C) Rgb (KX) Cgb (pF)

80 990 8.88100 826 13.7130 795 15.2250 440 20.0

10 100 1000 100000

1

2

3

4

5

6

-Z''

x105 (

Ohm

s)

Frequency (KHz)

T = 80 °C T = 100 °C T = 130 °C T = 250 °C

Fig. 6. Variation of imaginary part of impedance (Z00) with frequency of 12.5% Sb-doped SnO2 thin film.

B. Benrabah et al. / Superlattices and Microstructures 50 (2011) 591–600 597

The electrical characteristic of a material is exhibited by the appearance of semicircular arcs in theNyquist plots. Fig. 5 shows the complex impedance plots (Nyquist plots) of 12.5% Sb-doped SnO2 filmat different temperatures (80, 100, 130 and 250 �C) taken over a wide frequency range (20 Hz–1 MHz).It can be seen from the figure the existence of a single semicircle, while in the case of pure SnO2 film, A.Chandra Bose et al. [20] have found two semicircles.

This can be explained on the basis of reduction in grain size with doping. Indeed, nanomaterialsconsist of nanometer size grains which introduce more grain boundaries within the samples. In pureSnO2 films a small semicircle is obtained in the high frequency region attributed to grain conductionwhile a large semicircle is obtained in the low frequency region due to the grain boundaries conduc-tion. As the particle size decrease with increasing Sb-doping according to the X-ray diffraction results,the number of grain boundaries increases. Hence, the grain boundaries effect becomes more dominantover grain contribution and therefore giving one semicircle in the Nyquist plot.

Each of the semicircles of Fig. 5 could be represented by a single parallel RC combination as shownin Fig. 5. The values of grain boundaries resistance (Rgb) at different temperatures have been obtainedfrom the intercept of the semicircular arcs on the real axis (Z0) and are given in Table 1.

Fig. 6 shows the variation of the imaginary part of impedance (Z00) with frequency at different tem-peratures (i.e., loss spectrum). The typical nature of variation indicates that Z00 attains a maximum va-lue at a particular frequency, which is different for each temperature. This variation shows a decreasein the magnitude of Z00 with a shift in the peak frequency towards the higher side with rise in temper-ature. This feature becomes notable at the higher temperature. The nature of variation of Z00 with ashift in peak frequency is because of electronic relaxation phenomenon in the material, and it is a clearproof of temperature dependence of relaxation. The decrease in the magnitude of Z00 with a shift in thepeak frequency towards the higher side with rise in temperature is possibly due to the presence of

10 100 100000

2

4

6

8

Z' x

105(O

hms)

T = 80 °C T = 100 °C T = 130 °C T = 250 °C

Frequency(KHz)

Fig. 7. Variation of real part of impedance (Z0) with frequency of 12.5% Sb-doped SnO2 thin film.

598 B. Benrabah et al. / Superlattices and Microstructures 50 (2011) 591–600

charge space in the material which is in good agreement with observation of complex impedance data[21].

Fig. 7 shows variation of the real part of impedance (Z0) as a function of frequency for different tem-peratures. It has been observed that a monotonous decrease in the value of Z0 with rise in temperatureoccurs with the values finally merging at higher frequencies (�100 kHz) for all temperatures. The fre-quency at which merging of Z0 values for all temperatures takes place appears to shift towards higherfrequency side of the spectrum with rise in temperature. The impedance value is higher at low tem-perature in the low frequency domain but gradually decreases with increasing temperature. A de-crease in Z0 with rise in temperature and frequency indicates a possibility of increase in the acconductivity with increase in temperature and frequencies. The merger of real part of impedance(Z0) in the higher frequency domain suggests release of space charge and a consequent lowering ofthe barrier properties in the material.

The temperature dependence of conductivity is shown in Fig. 8 in the form of Arrhenius plots for12.5% Sb-doped SnO2 film. The activation energy was obtained by least-squares fitting of the data to

1.8 2.0 2.2 2.4 2.6 2.8 3.0-20.6

-20.4

-20.2

-20.0

-19.8

-19.6

-19.4

lnσ

(S/c

m)

1000/T (K-1)

Fig. 8. Arrhenius plot for dc conductivity of 12.5% Sb-doped SnO2 thin film.

B. Benrabah et al. / Superlattices and Microstructures 50 (2011) 591–600 599

the equation r = r0 exp(�Ea/kBT) where r0 is a pre-exponential factor and Ea is the activation energy ofthe dc conductivity and kB the Boltzmann constant. The activation energy of this conductivity due tograin boundaries is 0.87 eV, very close to that found by A. Chandra et al. (0.82 eV). The activation en-ergy studies show that at higher temperatures, low-frequency relaxation is observed due to the migra-tion of charged particles of SnO2 such as O�2 , O� and O2� or bulk species such as oxygen defects acrossthe grain boundaries, i.e., with large relaxation times [20].

4. Conclusion

In this work, undoped and antimony doped tin oxide (SnO2:Sb) powders and thin films have beenprepared by the sol–gel dip-coating (SGDC) process. X-ray diffraction analysis of (ATO) powders showsthat its structure is tetragonal rutile type with a decrease of the crystallite size of the particles whenthe amount of Sb increases, which was in good agreement with the AFM measurements. Compleximpedance spectroscopy reveals that effect of grain boundaries is dominant in the conduction mech-anism. The activation energy for conduction (Ea) of the material is found to be 0.87 eV.

Acknowledgment

This work has been supported by the Algerian Ministry of Higher Education and Scientific Research,within the framework of project called (CNEPRU).

References

[1] I. Saadaddin, B. Pecquenard, J.P. Manaud, R. Decourt, C. Labrugère, Synthesis and characterization of single-and co-dopedSnO2thin films for optoelectronic applications, Appl. Surf. Sci. 253 (2007) 5240.

[2] R.S. Niranjan, Y.K. Hwang, D.K. Kim, S.H. Jhung, S.J. Chang, I.S. Mulla, Nanostructured tin oxide: synthesis and gas-sensingproperties, Mater Chem. Phys. 92 (2005) 384.

[3] F.M. Filho, A.Z. Simoes, A. Ries, E.C. Souza, L. Perazolli, M. Cilence, E. Longo, J.A. Varela, Investigation of electrical propertiesof tantalum doped SnO2 varistor system, Ceram. Int. 31 (2005) 399.

[4] B. Thangaraju, Structural and electrical studies on highly conducting spray deposited fluorine and antimony doped SnO2

thin films from SnCl2 precursor, Thin Solid Films 402 (2002) 71.[5] T.H. Fang, W.J. Chang, Nanomechanical characteristics of SnO2:F thin films deposited by chemical vapor deposition, Appl.

Surf. Sci. 220 (2003) 175.[6] H.L. Wang, J.A. Turner, X.N. Li, R. Bhattacharya, SnO2: F coated austenite stainless steels for PEM fuel cell bipolar plates, J.

Power Sources 171 (2007) 567.[7] Y. Wang, J. Ma, F. Ji, X.H. Hu, H.L. Ma, Structural and photoluminescence characters of SnO2: Sb films deposited by RF

magnetron sputtering, J. Lumin. 114 (2005) 71.[8] J. Gonga, Q. Chena, M.R. Lian, N.C. Liu, R.G. Stevenson, F. Adami, Synthesis and properties of pure and antimony-doped tin

dioxide thin films fabricated by sol–gel technique on silicon wafer, Sens. Actuators B 14 (2006) 32.[9] S.C. Lee, J.H. Lee, T.S. Oh, Y.H. Kim, Effect of ambient oxygen pressure on structural, optical and electrical properties of SnO2

thin films Sol. Energy Mater. Sol. Cells 75 (2003) 481.[10] G. Du, D.L. Zhang, L. Zhao, J.M. Xu, D.X. Zhou, Surface morphologies and properties of pure and antimony-doped tin oxide

films derived by sol-gel dip-coating processing, Key Eng. Mater. 280–283 (2005) 831.[11] J.P. Chatelon, C. Terrier, E. Bernstein, R. Berjoan, J.A. Roger, Electrical and optical properties of Sb: SnO2 thin films obtained

by the sol-gel method, Thin Solid Films 247 (1994) 162.[12] L. Zhao, D.L. Zhang, G. Du, J.M. Xu, D.X. Zhou, The properties of antimony-doped tin oxide thin films by sol-gel approach,

Key Eng. Mater, 280–283 (2005) 835–838.[13] E. Elangovan, S.A. Shivashandar, K. Ramamurthi, Studies on structural and electrical properties of sprayed SnO2: Sb films, J.

crystal growth 276 (2005) 215–221.[14] T. Bezrodna, G. Puchkovska, V. Shimanovska, I. Chashecnikova, T. Khalyavka, Baran, IR-analysis of H-bonded H2O on the

pure TiO2 surface, J. Appl. Surf. Sci. 214 (2003) 22–231.[15] S. Lenaerts, J. Roggen, G. Maes, FT-IR characterization of tin dioxide gas sensors materials under working conditions,

Spectrochim. Acta A 51 (1995) 883–894.[16] L.M. Fang, X.T. Zu, Z.J. Li, S. Zhu, C.M. Liu, et al, Synthesis and characteristics of Fe3+ doped SnO2 nanoparticles via sol-gel-

calcination or sol-gel hydrothermal route, J. Alloys Comp. 454 (2008) 261–267.[17] E. Barsoukov, J. Ross Macdonald (ed.), Impedance Spectroscopy, Theory, Experiment, and Applications. 2nd ed. John

Wiley&Sons, Inc., Publication, 2005.[18] A.R. West, D.C. Sinclair, N. Hirose, Characterization of electrical materials, especially ferroelectrics, by impedance

spectroscopy, J. Electroceram. 1 (1) (1997) 65–71.[19] J.C.C. Abrantes, J.A. Labrincha, J.R. Frade, Representation of impedance spectra of ceramics. Part I. Simulated study cases,

Mater. Res. Bull. 35 (2000) 955–964.

600 B. Benrabah et al. / Superlattices and Microstructures 50 (2011) 591–600

[20] A. Chandra Bose, P. Thangadurai, S. Ramasamy, B. Purniah, Impedance spectroscopy and DSC studies on nanotructuredSnO2, Vacuum 77 (2005) 293–300.

[21] J. Maier, The polarization of mixed conducting SOFC cathodes: effects of surface reaction coefficient, ionic conductivity andgeometry, J. Eur. Ceram. Soc. 24 (2004) 1343.