Morphology, Electrical Conductivity, and Reactivity of Mixed

In the case of solid state sensors, the basic idea is to use specific interactions between the molecule to be detected and a species with high mobilit...
0 downloads 6 Views 547KB Size
J. Phys. Chem. B 2001, 105, 8327-8333

8327

Morphology, Electrical Conductivity, and Reactivity of Mixed Conductor CuBr Films: Development of a New Ammonia Gas Detector M. Bendahan,† C. Jacolin,† P. Lauque,† J.-L. Seguin,† and P. Knauth*,‡ Laboratoire Mate´ riaux et Microe´ lectronique de ProVence (L2MP, UMR 6137 CNRS), Faculte´ des Sciences de St Je´ roˆ me, Case 152, 13397 Marseille Cedex 20, France, and Laboratoire des Mate´ riaux DiVise´ s, ReVeˆ tements, Electroce´ ramiques (MADIREL, UMR 6121 UniVersite´ de ProVence-CNRS), Centre St Charles, Case 26, 13331 Marseille Cedex 3, France ReceiVed: February 7, 2001; In Final Form: June 15, 2001

The microstructure, electrical properties, aging, and electrolytic decomposition of sputtered CuBr films are described and discussed with respect to the defect chemistry of this mixed Cu+ ion-electron hole conductor. Ammonia gas adsorption increases the electrical resistance of the films. This effect can be used to design a new selective, sensitive, fast, and reversible ammonia gas sensor.

I. Introduction The electrical properties of semiconductor compounds depend on the composition of the surrounding gas atmosphere. On the basis of this effect, the development of conductometric gas sensors using thin films or porous ceramics of n-type semiconductor oxides, such as ZnO1 and SnO2,2 started in 1962. However, the gas detection mechanism is rather unspecific: the electric resistance of a n-type semiconductor under high oxygen partial pressure is high, because the electron transfer from the semiconductor to adsorbed oxygen leads to an electron-depleted space charge region near the semiconductor surface. The injection of electrons into the semiconductor after surface reaction with a reducing gas reduces the width of the depleted regions and leads to a resistance decrease. This type of conductometric gas sensor presents an inherent lack of selectivity, because more or less any type of reducing gas is detected by this mechanism. The most promising approach for the development of selective microsensors is based on “molecular recognition”. In the case of solid state sensors, the basic idea is to use specific interactions between the molecule to be detected and a species with high mobility in the solid, particularly a mobile ion in an ionic or mixed conductor. Maier and co-workers showed that a variation of NH3 partial pressure changes significantly the electrical conductivity of ionic conducting AgCl thin-films.3 This variation can be used for gas sensor development; it can be interpreted by ionic space charge effects,4 due to Ag+ ion/NH3 interactions, analogous to the electronic space charge effect used in the Taguchi sensor.5 The existence of strong interactions between copper ions and ammonia molecules is well established in aqueous solution chemistry, where they lead to the formation of stable ammine complexes, such as [Cu(NH3)2]+.6 One can assume that similar interactions exist at the interface between a gas phase containing ammonia molecules and a solid ionic or mixed conductor with mobile Cu+ ions, such as CuBr, leading to ammonia adsorption. The specificity of this process could be implemented to develop an ammonia gas sensor with a much improved selectivity in comparison to usual, especially oxide-based devices,7 given that only a few other molecules are known to interact with copper ions. * Author to whom correspondence should be addressed. † Laboratoire Mate ´ riaux et Microe´lectronique de Provence. ‡ Laboratoire des Mate ´ riaux Divise´s, Reveˆtements, Electroce´ramiques.

Besides the high selectivity, a CuBr ammonia sensor might present a certain number of further advantages. (1) The ionic conductivity is an essential factor to improve the response time of a sensor, when the composition of the gas phase changes. (2) The electron hole conductivity of CuBr8-10 enables ready integration into microelectronic devices. It may be due to a copper deficiency (composition: Cu1-xBr) or to acceptor doping. e.g.. by oxygen. (3) The higher volatility of metal halides in comparison with oxides allows an easier preparation of thinfilms by vapor deposition techniques. The application of thinfilms can help to reduce the sensor size. Furthermore, fast deposition from the gas phase might reduce the mean grain size and create a large open porosity in the material, which can improve the sensitivity of the detector by increasing its specific surface area. Compared with wet chemical deposition techniques, chemical vapor deposition (CVD) and physical vapor deposition (PVD) give the highest quality films in terms of purity and homogeneity. Radio frequency sputtering, a welladapted technique for compounds with low electrical conductivity, was employed to prepare CuBr films, applied in a selective, sensitive, fast, and reversible ammonia gas microsensor. II. Experimental Section A. Radio Frequency Sputtering. The studied films were deposited by rf sputtering in a laboratory-built equipment,11 using a CuBr target made by compression under 750 MPa of high purity CuBr powder (Aldrich 99.999%). Fixed sputtering conditions were applied throughout this work: the base pressure before deposition was 10-4 Pa and the argon pressure during deposition was 3 Pa with a flow rate of 10 mL/min. A rf power of 40 W was applied and a presputtering of 15 min was made before each deposition to clean the target and to obtain stable discharge conditions. The deposition rate was less than 0.1 nm/s and the deposited films were around 1 µm thick. B. Substrates. Different substrates were used for deposition, including silica glass and copper metal, but in the objective of an easier integration into microelectronics circuitry, plastic epoxy substrates for printed circuit boards and oxidized silicon wafers with a 500 nm SiO2 coating were preferred. On oxidized silicon substrates, copper or gold films were deposited by vacuum evaporation or sputtering. Interdigitated electrodes were then revealed by a photolithographic technique. The distance between electrodes was 0.5 mm and their total length was 96 mm. The

10.1021/jp010466j CCC: $20.00 © 2001 American Chemical Society Published on Web 08/14/2001

8328 J. Phys. Chem. B, Vol. 105, No. 35, 2001

Figure 1. Grazing-angle X-ray diffraction pattern of a CuBr film deposited on a glass substrate with copper electrodes ([ CuBr JCPDS n°06-0292, [ Cu JCPDS n°04-0836).

substrates were degreased prior to film deposition, except copper metal that was chemically etched and electropolished. The substrate holder was at room temperature. C. Characterization Techniques. Classical and grazing incidence X-ray diffraction (XRD) was applied to check the crystallinity and structure of the films. The microstructure was observed by optical microscopy, atomic force microscopy (AFM) and scanning electron microscopy (SEM). Semiquantitative chemical analysis by EDX and Auger electron spectroscopy (AES) depth profiles were used to check the presence of impurities in the films. Electrical current-voltage characteristics were measured using gold and copper contacts in various configurations: Cu substrate and sputtered Au point electrode, interdigitated Cu and Au electrodes, etc. The measurements were made with a high input impedance electrometer (Keithley 617) and a high precision constant current source (Keithley 220). For the sensor characteristics, the tested gases were diluted with nitrogen using mass flow controllers. The total gas flow was kept constant at 6 or 24 L/h. Impedance spectra were recorded with a frequency response analyzer (Solartron 1250) and a high impedance preamplifier (1014 Ω) in a frequency range between 10 mHz and 60 kHz with a signal amplitude of 20 mV. III. Results and Discussion A. Chemical Composition, Structure, and Morphology. Grazing-angle X-ray diffraction patterns showed that the films were polycrystalline with the stable low-temperature γ-CuBr structure, whatever the substrate used for deposition. Figure 1 shows a typical example on glass. The line intensities were in agreement with standard data, suggesting a random crystallite orientation, without major texture effects or secondary phases. A slight shift of peak positions to smaller angles might indicate the presence of mechanical strain or impurities. However, neither energy-dispersive X-ray spectrometry (EDX) nor Auger spectroscopy depth profiles (on a molybdenum substrate) revealed any major impurity, except trace amounts of carbon and oxygen detected in a very thin surface layer, probably in the form of copper hydroxy-carbonates of the malachite type. The EDX and Auger analysis also confirmed the global stoichiometry CuBr. However, only electrical measurements are capable to detect very small deviations from the exact stoichiometry (see below). The film morphology depended on the substrate used for deposition. Relatively smooth films were obtained on copper

Bendahan et al. substrates. On all other substrates, such as epoxy, glass, or oxidized silicon, the films presented many pores of several micrometer thickness and a rougher surface (Figure 2). In higher magnification, it appeared that the films were formed by many agglomerated grains with an average size of 0.2-0.3 µm.12 AFM observations confirmed the mean grain size (d ) (0.2 ( 0.1) µm) with an average roughness of about 10 nm (Figure 3). The difference in morphology can be related to the different thermal and electrical conductivity of the substrates, high for metallic copper and low for the other substrates so that temperature changes can be observed during deposition, but the presence of metallic copper can also lead to compositional changes, as shown below. An annealing of the films at a temperature of only 60 °C changed their properties irreversibly, because it led to significant grain growth and elimination of pores. CuBr films heated above 60 °C showed no measurable electrical response when ammonia gas was present in the gas phase and were useless as sensor material. These experiments show that pores are important for the sensor application, because they enhance significantly the surface area of the films and the number of accessible sites for gas molecules. The easy recrystallization of CuBr films is related to the mobility of copper ions. Microstructural relaxation and annealing of structural defects is generally easy in solid ionic conductors. Similar results were for instance obtained for AgBr films.13 B. Electrical Properties; Influence of the Electrode Metal. The dc Current-Voltage Characteristics. The nature of the electrode can have a significant influence on the dc characteristics of a mixed conducting material.14 In the case of CuBr films, we used copper or gold electrodes. The essential difference is that copper ions can be exchanged with copper, but not with gold; in other words, gold contacts are blocking for ionic conduction. Concerning electron exchange, the contact between a metal and a mixed conductor with p-type character, such as CuBr, behaves as a Schottky barrier if the work function of the metal is smaller than the work function of the p-type semiconductor.15 We have determined by Mott-Schottky analysis that the Fermi energy of CuBr lies approximately 6 eV below the vacuum level.9 The work functions at 20 °C of gold (≈5.3 eV16) and copper (≈4.6 eV16) are smaller and formation of Schottky barriers is expected for both gold and copper contacts. Inside the range of applied voltages (U < 0.3 V), the experimental U-I characteristics were, however, in all cases ohmic indicating that interfacial resistances were relatively small. The dc conductivity of the films was in agreement with the impedance data. The total dc conductivity σ of CuBr films, with contributions by Cu+ ions and electron holes, was obtained with two copper electrodes using the relation

σ ) [w/(Lt)](I/U)

(1)

In this equation, w is the distance between the interdigitated copper electrodes and L their total length, respectively; t is the thickness of the CuBr film. An average conductivity σ ≈ 10-6 S/cm was measured for about 50 samples with a mean grain size d ≈ 0.2 µm, about thirty times larger than for polycrystalline CuBr with a mean grain size d ) 5 µm (σ ) 3 × 10-8 S/cm 20). One can notice a correlation between σ (expressed in S/cm) and the mean grain size d (expressed in cm):

σ ≈ 2 × 10-11/d

(2)

This grain size dependence indicates that grain boundary effects are responsible for the conductivity enhancement, probably due

Properties of Mixed Conductor CuBr Films

J. Phys. Chem. B, Vol. 105, No. 35, 2001 8329

Figure 2. SEM micrograph of a CuBr film deposited on an epoxy substrate.

Figure 3. AFM picture of a CuBr film on a glass substrate.

to space charge regions.17 In an elementary brick-layer model, it can be shown easily that the conductivity σ is the sum of bulk σb and grain boundary contributions 4σgbλ/d, where λ is

the space charge layer thickness. The factor 4 takes the number of grain boundaries “parallel” to the current direction into account. It follows:

8330 J. Phys. Chem. B, Vol. 105, No. 35, 2001

Bendahan et al.

Figure 4. The dc polarization of a cell (-) Cu/CuBr/Au (+) with a current I ) ( 0.15 nA.

σ ) σb + 4σgbλ/d

(3)

For large interfacial effects, σb can be neglected against the interface term and a relation compatible with the experimental result is obtained. The thickness of the space charge region λ can be estimated from the Debye length. For a realistic value λ ) 10 nm, a conductivity σgb ) 5 × 10-6 S/cm can be calculated. This is a factor 160 larger than the conductivity of bulk CuBr, in the same order of magnitude than a value previously used in a model of CuBr-based composite materials.18 The dc characteristics with gold electrodes gave a different picture. With two gold contacts, the dc characteristics were less reproducible. The conductivity values were systematically larger and very high values, up to 10-3 S/cm, were sometimes observed. One can notice that the stoichiometry of the samples is not fixed in absence of copper metal. Considerable deviations from stoichiometry and even the formation of CuBr2 are therefore possible. The latter compound is hygroscopic, leading to apparent sample degradation in certain cases (see below). The dc measurements with two gold electrodes were thus abandoned. Figure 4 shows a typical dc polarization experiment using only one gold contact, in a structure (-) Cu/CuBr/Au (+). Two important points can be noticed. (1) In the absence of current flow, an open-circuit voltage, ∆U ≈ 0.3 V, is observed. This cell voltage fulfills the reversibility criteria and can be attributed to a cell with two different electrodes. If we apply Nernst’s equation,

∆U ) -(RT/F) ln aCu

(4)

the measured open circuit voltage corresponds to a copper activity in the gold electrode aCu ≈ 10-5. This is not unrealistic, because a small copper solubility in gold can be expected. (2) Asymmetrical polarization behavior. The polarization curves using positive currents are more noisy. They correspond to ionic blocking (“Hebb-Wagner polarization”14), because copper ions cannot be provided by the gold anode. The dc current of +0.15 nA is transported only by electron holes and the dc voltage is about 0.25 V. With a negative current, the voltage is lower, about -0.15 V, because the current can be transported by Cu+ ions and electron holes. This type of characteristic shows that the CuBr films are mixed conductors with comparable partial conductivity of Cu+ ions and electron holes. The application of large dc voltages leads to an electrolysis of the films with formation of fractal copper trees, as discussed in paragraph C. Impedance Spectroscopy. Impedance measurements are a powerful tool to separate bulk and interfacial phenomena.19 Impedance spectra with copper electrodes of CuBr films under nitrogen (Figure 5) showed two arcs. The large high frequency semicircle was nearly ideal and represented the “bulk” response. The conductivity calculated from the bulk arc was in agreement

Figure 5. Typical impedance diagram of CuBr films with copper electrodes. (a) 4: exposed to N2 (gas flow: 6 L/h), (b) exposed to step-varying concentrations of NH3 (gas flow: 6 L/h; each concentration applied during 5 min, b: 100 ppm NH3, O: 230 ppm NH3).

Figure 6. Temperature dependence of the conductance of CuBr films.

with dc experiments (see below). The low frequency semicircle is certainly related to the electrode response and will not be discussed further at this point. An intermediate response due to blocking grain boundaries was not clearly detected, in agreement with previous experiments on polycrystalline CuBr.20 Grain boundary blocking can be due to (1) crystallographic defects (“dangling bonds”) or (2) segregated electrically active impurities. The absence of a grain boundary arc suggests the absence of a significant amount of segregated impurities with electrical activity at the grain boundaries. Furthermore, the number of dangling bonds at the interfaces is certainly considerably reduced, because the large ionic mobility facilitates reconstruction and relaxation phenomena near interfaces, as we have seen previously. This conclusion is valid for the grain boundaries as well as for the electrode interface. The temperature dependence of the bulk conductivity (Figure 6), obtained from heating and cooling cycles without hysteresis, is consistent with experiments on polycrystalline CuBr. 20,21 The activation energy between 260 and 350 K, EA ) (0.5 ( 0.1) eV, is in agreement with previous work and can be attributed to the migration energy of copper vacancies (determined by NMR spectroscopy: 0.54 eV22). One notices a remarkable change of slope below 250 K, that was also observed in polycrystalline samples.21 Below that temperature, the thermal activation is insufficient for ionic motion so that predominant electron hole conduction is observed. The low-temperature activation energy EA ) (0.10 ( 0.05) eV is equal to the ionization energy EI of acceptors in CuBr that can be estimated assuming hydrogen-like ionization.21 Acceptors can be copper ion vacancies (corresponding to a nonstoichiometric compound with composition Cu1-xBr) or acceptor impurities, such as oxygen.

Properties of Mixed Conductor CuBr Films

J. Phys. Chem. B, Vol. 105, No. 35, 2001 8331

Figure 7. Representative cathodic decomposition pattern of CuBr films.

Figure 8. Leaf-like structures observed in as-deposited CuBr films.

C. Decomposition and Degradation Phenomena. Electrolytic decomposition can be observed if a dc voltage above the decomposition threshold is applied to a CuBr film, for example in a configuration: (-) Cu/CuBr/Au (+). The threshold voltage is a kinetic value and depends on the experimental conditions. It contains the thermodynamic decomposition voltage, that can be calculated from the Gibbs free energy of formation of CuBr (about 0.7 V under atmospheric pressure16), and overvoltages for different processes, including the ohmic drop, the charge transfer at the electrodes (given by the Butler-Volmer equation23), and the nucleation of the electrodeposit. According to the phase diagram of the Cu-Br system, thermodynamics predict that CuBr2 is formed by electrolysis at the gold anode and Cu at the copper cathode with the overall decomposition reaction:

2CuBr f Cu + CuBr2

(5)

However, some bromine can also be formed due to kinetic reasons. The typical cathodic decomposition pattern shown in Figure 7 was obtained after applying a voltage of 20 V during 1 h. The corresponding EDX analysis confirmed that the fractal growth structures were metallic copper. The copper trees were numerically simulated using the diffusion-limited aggregation approach.24 Star- and leaf-like structures noticed in “asdeposited” CuBr films (Figure 8) can be related to similar electrolytic decomposition, due to the existence of a strong electric field between plasma and film during the sputter deposition process. Grazing-angle X-ray diffraction patterns (Figure 9) demonstrated the presence of small amounts of CuBr2

8332 J. Phys. Chem. B, Vol. 105, No. 35, 2001

Bendahan et al.

Figure 11. Dependence of the electrical resistance of a CuBr film on ammonia partial pressure (gas flow: 6 L/h, applied dc voltage: 20 mV). Figure 9. Grazing-angle X-ray diffraction pattern of the anodic region after solid-state electrolysis. Small peaks corresponding to CuBr2 are observed ([ JCPDS n° 45-1063) together with strong lines corresponding to the gold electrode (9 JCPDS n°04-0784). No CuBr is remaining.

chemical diffusion coefficient extrapolated to room temperature in cadmium-doped CuI is in the same order of magnitude (≈ 5 10-10 cm2/s27). In contrary, the resistance of CuBr films deposited on gold electrodes remained constant over time. On the basis of these experimental facts, we assume that the origin of the aging is copper diffusion from the electrodes into an originally substoichiometric Cu1-xBr film. This is consistent with our previous discussion of conductivity data. The reaction with metallic copper leads to a reduction of the copper vacancy and electron hole concentration, written in Kro¨ger-Vink nomenclature:28

Cu + VCu’ + h• f CuCu

Figure 10. Aging of CuBr films, observed by measuring the time dependence of the electrical resistance using copper electrodes.

near the gold anode without any CuBr remaining after electrolysis. Visible brownish colorations near the anode were the trace of the hygroscopic compound CuBr2. Aging of the CuBr films was studied by impedance measurements with copper electrodes over several months. A typical time dependence of the bulk resistance in air (Figure 10) shows a relatively fast degradation during the first few days. In this period, the data are well described by a square-root time dependence,25 indicating a diffusion process as origin of the resistance increase of CuBr films. Following this initial stage, the aging slows down and the data converge asymptotically. The complete time dependence can be fitted with the numerical solution of Fick’s second law for diffusion in a thin film,26 which gives the concentration c at a distance x: ∞

(c - c0)/(c1 - c0) ) 1 - (4/π)

(-1)n/(2n + 1) ∑ n)0

exp[-D(2n + 1)2π2t /4l2] cos[(2n + 1)πx/2l] (6) Here, c0 and c1 are the initial concentrations inside and outside the film, respectively; l is the half thickness of the layer and n is a numerical parameter (0 < n < ∞). Fitting the time dependence using this numerical solution gives a chemical diffusion coefficient D ≈ 10-10 cm2/s. To the best of our knowledge, there are no chemical diffusion data on CuBr in the literature, but if we compare with related systems, the

(7)

The depletion of the two majority charge carriers of CuBr is a convincing explanation for the increase of electrical resistance during aging. D. Ammonia Adsorption and Sensor Properties. The following experiments were made after a preliminary treatment of the CuBr films under 104 Pa NH3 for 1 h. After this treatment, the sensor response was stable and reproducible. A typical dependence of the electrical resistance of CuBr films on the ammonia partial pressure in the gas phase is shown in Figure 11. One notices a fast electrical response: the time necessary to reach 50% of full signal was about 100 s. The signal was reversible and proportional to the ammonia concentration. The fast response is consistent with the hypothesis of a surface effect, especially related to ammonia adsorption at the CuBr surface. The detailed mechanism leading to the observed conductivity changes is the object of current investigations. In the Langmuir adsorption model, one assumes a constant adsorption enthalpy resulting from an absence of interactions between adsorbed molecules. Our experimental data can be used to check the existence of a Langmuir-type adsorption isotherm. To derive this relation, we assume that the observed resistance change ∆R is due to the interaction layer near the interface gassolid, i.e., that the coverage by gas molecules can be expressed by the ratio ∆R/∆R∞, where ∆R∞ is the maximum resistance change corresponding to saturation with ammonia. The Langmuir adsorption isotherm can then be written with the NH3 partial pressure P, according to a relation derived by Maier and co-workers:17

∆R/∆R∞ ) KP/(1 + KP)

(8)

where K is the adsorption constant. If a Langmuir-type adsorption isotherm is obeyed, a plot of the ratio (P/∆R) versus P should give a straight line with a slope of 1/∆R∞ and an intercept

Properties of Mixed Conductor CuBr Films

J. Phys. Chem. B, Vol. 105, No. 35, 2001 8333 that the presence of a free electron pair in the molecule, such as that of the nitrogen atom in NH3, is crucial. Hydrogen sulfide gas, that reacts with copper ions in solution to form very stable copper sulfide precipitates, also reacted with the CuBr films and degraded them irreversibly. All these results are consistent with our “molecular recognition model”. IV. Conclusion

Figure 12. Langmuir plot of (P/∆R) versus P, where P is the ammonia partial pressure and ∆R is the electrical resistance change.

CuBr thin films, deposited on different substrates using rf sputtering, are formed by agglomerates of grains with the stable low-temperature γ-CuBr structure and many pores. Electrical measurements show mixed conduction with comparable partial conductivity of Cu+ ions and electron holes. The application of large dc voltages leads to an electrolysis of the films with formation of fractal copper trees. Aging effects are related to copper diffusion from the electrodes into an originally substoichiometric Cu1-xBr film. A selective ammonia gas sensor, based on “molecular recognition”, can be designed using sputtered CuBr films. The increase of electrical resistance is the result of ammonia adsorption. The fast and reversible response and the high sensitivity of the developed ammonia gas sensor make it clearly competitive with usual commercial sensors. Acknowledgment. The authors gratefully acknowledge the fruitful collaboration with many colleagues throughout this work. We want to mention particularly the contributions by O. Scha¨f, A. Garnier, and M. Eyraud (MADIREL, Marseille), C. Lambert, J.-M. Debierre, Ch. Girardeaux, and A. Combes (L2MP, Marseille). References and Notes

Figure 13. Resistance variation versus time for CuBr films exposed to small step-varying concentrations of NH3 at room temperature (gas flow: 24 L/h, applied dc voltage: 100 mV).

of 1/(K∆R∞) that can be used to calculate the adsorption constant K. The experimental data (Figure 12) are consistent with a Langmuir-type adsorption isotherm with K ) 12000. The calculated resistance at NH3 saturation is R∞ ) 970 kΩ. Impedance spectra with copper electrodes in the presence of ammonia (Figure 5) showed an enhancement of bulk resistance compared to spectra of the same films made under pure nitrogen (e.g., Rbulk ≈ 0.6 MΩ (in N2), ≈ 1 MΩ (5 min under 230 ppm NH3)). The original spectrum was recovered after ammonia was removed. The high sensitivity of CuBr films to the presence of NH3 gas is exemplified in Figure 13, where the response to ammonia concentrations in the gas phase around and below 25 ppm is shown. This is a crucial value, because it corresponds to the maximum level authorized at the working place and a valuable ammonia sensor must obviously detect partial pressures significantly below that point. A preliminary study of selectivity of CuBr sensors confirmed the general predictions made in the Introduction. Under the investigated gases, only those known to interact strongly with copper ions gave a measurable signal. Nitrogen, oxygen, and CO2 were not detected. Acetylene, although known to form precipitates in alkaline solutions with Cu+ ions, did not give a significant signal. In alkaline solutions, acetylide ions C22- are created by proton removal. However, in the gas phase such a mechanism is impossible at the CuBr surface. This confirms

(1) Seiyama, T.; Kato, A.; Fujishi, K.; Nagatani, N. Anal. Chem. 1962, 34, 1502. (2) Taguchi, N. Japanese Patent Application No. 45-38200, 1962. (3) Maier, J.; Lauer, U. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 973. (4) Maier, J. Solid State Ionics 1993, 62, 105. (5) Maier, J. Sensors Actuators B 2000, 65, 199. (6) Cotton, F. A.; Wilkinson, G. AdVanced Inorganic Chemistry; J. Wiley: New York, 1962; p 750. (7) Shimizu Y.; Egashira M. MRS Bull. 1999, 24 (6), 18. (8) Wagner J. B.; Wagner, C. J. Chem. Phys. 1957, 26, 1597. (9) Knauth, P.; Massiani, Y. J. Electroanal. Chem. 1998, 442, 229. (10) Knauth, P.; Massiani, Y.; Pasquinelli, M. Phys. Status Solidi A 1998, 165, 461. (11) Seguin, J.-L.; Bendahan, M.; Lollmun, G.; Pasquinelli, M.; Knauth, P. Thin Solid Films 1998, 323, 31. (12) Scha¨f, O.; Lauque, P.; Seguin, J.-L.; Eyraud, M.; Knauth, P. Thin Solid Films 2001, 389, 5. (13) Kennedy, J. H.; Chen, F. J. Electrochem. Soc. 1971, 118, 1043. (14) Wagner, C. Z. Elektrochem. 1956, 60, 4. (15) Sze, S. M. Physics of Semiconductor DeVices; Wiley: New York, 1969. (16) Handbook of Physics and Chemistry, 61st ed.; Weast, R. C., Ed.; CRC Press: Boca Raton, FL, 1981; p E-83. (17) Maier, J. Prog. Solid State Chem. 1995, 23, 171. (18) Debierre, J.-M.; Knauth, P.; Albinet, G. Appl. Phys. Lett. 1997, 71, 1335. (19) Macdonald, J. R. Impedance SpectroscopysEmphasizing Solid Materials and Systems; J. Wiley: New York, 1987. (20) Villain, S.; Desvals, M.-A.; Clugnet, G.; Knauth, P. Solid State Ionics 1996, 83, 191. (21) Tortet, L.; Knauth, P.; Tuller, H. L. Solid State Ionics, submitted. (22) Boyce, J. B.; Huberman, B. A. Phys. Rep. 1979, 51, 189. (23) Bard, A. J.; Faulkner, L. R. Electrochemical MethodssFundamentals and Applications; J. Wiley: New York, 1980. (24) Lambert, C.; Memoli, L.; Debierre, J.-M.; Knauth, P.; Albinet, G. Ionics 1999, 5, 200. (25) Lauque, P.; Bendahan, M.; Seguin, J.-L.; Pasquinelli, M.; Knauth, P. Solid State Ionics 2000, 136-137, 603. (26) Kudo, T.; Fueki, K. Solid State Ionics; VCH-Kodansha: 1990; p 33. (27) Montani, R. A.; Bazan, J. C. Solid State Ionics 1991, 46, 211. (28) Kro¨ger, F. The Chemistry of Imperfect Crystals, 2nd ed.; NorthHolland: Amsterdam, 1974.