- Email: [email protected]
Permalloy electroplating through photoresist molds
Sensors and Actuators 74 Ž1999. 1–4
Permalloy electroplating through photoresist molds Jean-Marie Quemper ) , S. Nicolas, J.P. Gilles, J.P. Grandchamp, A. Bosseboeuf, T. Bourouina, E. Dufour-Gergam Institut d’Electronique Fondamentale, URA CNRS 022, UniÕersite´ Paris Sud, Bat. ˆ 220, 91405 Orsay Cedex, France
Abstract Electrodeposited Ni 80 Fe 20 magnetic films are used in storage devices and are usually used for MEMS. In this paper, we present some fundamental results concerning the influence of electrodeposition conditions on the films characteristics. In the first step, permalloy electrodeposition has been studied on copper evaporated films without resist patterns. The growth rate varies linearly as function of the current density Žtypically 120 nm miny1 for 10 mA cmy2 .. The variation of the alloy composition with deposition parameters is consistent with the so-called anomalous deposition effect, i.e., a preferential deposition of iron. The composition is the same for films with thickness in the range 0.6–20 mm and the Fe concentration decreases with current density. An alloy Ni 80 Fe 20 with a density close to the bulk value is obtained for a current density of 14.5 mA cmy2 . Characterization of magnetic properties with a vibrating magnetometer shows that good properties can be obtained Žcoercivitys 0.35 Oe for a thickness of 600 nm.. These results are applied to the patterning of permalloy by electrodeposition through photoresist molds. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Permalloy; Electrodeposition; Micromolding; UV lithography
1. Introduction The Permalloy Ž80% Ni, 20% Fe. is used in several magnetic device applications like cording heads w1x, magnetic yokes in printed heads w2x, microsolenoıds ¨ w3x and w x microvalves 4 . The magnetic film can be elaborated on different conductive seed-layer w5–7x by electrodeposition. Recently, several authors presented some papers about the electrodeposition of permalloy through molds w8–10x using conventional UV lithography. This technique allows for the realization of high-aspect-ratio magnetic components without etching step. In this paper, we present results obtained on a small surface concerning the effect of current density on deposition rate, density, composition and stress, and some preliminary results of film growth through photoresist molds.
2. Experimental An evaporated copper seed-layer Ž200 nm thick. was first deposited on cleaned high resistivity silicon ²100: wafers with an n-doping density around 10 14 cmy3 and a
) Corresponding author. Tel.: q33-1-69-15-62-98; Fax: q33-1-69-1540-80; E-mail: [email protected]
thickness of 280 mm. The copper permits a good electrical connection and a good adhesion of permalloy. Moreover, it can be used as a sacrificial metallic layer because of the high etching selectivity between NiFe and Cu. Before electrodeposition, the sample was cleaved in 11 = 11 mm2 parts. In the case of electrodeposition through molds, we used a high transparency and high viscosity UV positive photoresist AZ4562 ŽHoechst.. After a classical spin-coating of the resist, a prebake was performed on a ramped hotplate to allow solvent evaporation Žtemperature ramp: from 20 to 908C for 15 min, plateau: 908C for 45 min.. The photoresist layers were exposed in a Karl Suss ¨ contact masker with a dose of 1200 mJ cmy2 . Then, the patterns were developed in a diluted alkaline solution ŽAZ400K. for 4 min. The final resist thickness is about 18 mm. This process leads to resist molds with a high aspect ratio close to 8. The electrochemical cell used for Ni x Fe y deposition is a two-electrodes system with a nickel anode in a 1-l glass beaker. The volume of the plating bath is approximately 450 ml with an interelectrode distance of 10 cm. DC current densities from 2 to 16 mA cmy2 were applied at room temperature without stirring. The samples were removed from the solution for a short time every minute to allow hydrogen desorption from the surface w11x. A solution containing NiSO4 Ž0.7 mol ly1 ., FeSO4 Ž0.03 mol ly1 ., NiCl 2 Ž0.02 mol ly1 . and saccharine
0924-4247r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 8 . 0 0 3 2 3 - 9
J.-M. Quemper et al.r Sensors and Actuators 74 (1999) 1–4
2
Fig. 1. Deposition rate as a function of DC current density.
Fig. 3. Partial cationic currents as a function of total current.
Ž0.016 mol ly1 . as a leveller was used as the electroplating bath. Boric acid was added in the aim to obtain a good appearance of the deposit Ž0.4 mol ly1 . w12x.
The copper seed-layer presents a resistivity of 2.2 mV cm. A rest surface potential of y0.37 V ŽENH. without applied voltage was measured with a three-electrodes system ŽEGG PotentiostatrGalvanostat model 263A.. This value is approximately the same for bulk massic copper Žy0.33 V, ENH. in the same experimental conditions. So, the influence of the silicon substrate in the surface potential is not significative. Fig. 1 shows that the deposition rate varies linearly with the current density in agreement with the Faraday’s law. ˚ miny1 mAy1 cmy2 . No The resulting slope is 1300 A deposition occurs below a threshold of 1.5 mA cmy2 corresponding to the discharge limit potential of metallic cations. The deposition rate was calculated from the average thickness of the sample. Thickness inhomogeneity can reach 150% in the corners of the sample due to an edge effect w13,14x. This average thickness was calculated by averaging the thickness values obtained in the four corners and in the center of the samples.
The film density was found constant whatever the current density Ž6–16 mA cmy2 . with a value Ž8.9 g cmy3 for a 1-mm thick film. close to bulk value. No significative variation of the square resistance of the metallic structure is observed in this range of current densities for a 1-mm thick NiFe alloy. We observed an inhomogeneous surface film composition determined by EDS ŽEnergy Dispersive Spectrometry. because the growth mechanisms induce a composition variation with the deposition rate. The edge effect introduces a large variation of the composition close to 8%. The variation of the mean film composition with current density ŽFig. 2. shows the well-known anomalous codeposition effect of permalloy w15x: despite a standard reduction potential of nickel higher than that of iron Žy0.25 and y0.44 V, respectively. and a large excess of nickel species in the electrolyte Žfactor 25., a preferential deposition of iron occurs. Several models have been proposed to explain this process w10,16–19x. For a current density variation in the range of 2–16 mA cmy2 , the average iron composition decreases from 43% to 16.5%. The permalloy stoichiometry Ni 80 Fe 20 is reached for a current density of 14.5 mA cmy2 . The average composition is quite constant in the film thickness, for film thicknesses varying from 0.6 to 20 mm. Fig. 3 shows the variation of the cationic current with the total current density j. In our experimental conditions,
Fig. 2. Evolution of iron concentration with current density.
Fig. 4. Variation of current efficiency with current density.
3. Results and discussion
J.-M. Quemper et al.r Sensors and Actuators 74 (1999) 1–4
3
Žscanned surface s 20 mm = 20 m.. No correlation between roughness and current density for a thickness larger than 600 nm can be clearly established. An rms roughness of 6 nm is found for a composition of 80% Ni 20% Fe ŽFig. 5..
Fig. 5. AFM picture of a 1-mm thick NiFe film elaborated with a current density of 14.5 mA cmy2 .
the limit current is reached for iron, but the nickel current is not yet limited by the mass transport. This explains the iron concentration decreases with j. We calculated the current efficiency from the average thickness and average composition ŽFig. 4.. A maximum value Ž60%. is obtained for a current density of 16 mA cmy2 . For the Ni 80 Fe 20 stoichiometry, the current efficiency is 56%. This quite low value is due to the hydrogen reduction which leads to H 2 bubbles desorption on the sample surface during growth. This is why it is so important to remove the sample from the electroplating bath, in order to allow desorption of the H 2 bubbles. Currently, this is the main condition to obtain electrodeposits displaying a smooth and bright surface for all current densities. Analysis of Atomic Force Microscopy ŽAFM. images leads to an rms roughness in the range of 5–10 nm
Fig. 6. Magnetic properties for a 600-nm thick film Ž Hc s 28 A my1 , Bsat s 0.8 T..
Fig. 7. Ža. Photoresist mold ŽAZ4562. 18 mm thick, Žb. Ni 80 Fe 20 electrodeposit through mold after mask removing in acetone, Žc. detail of micromotor structure air-gap of 2 mm wide with a thickness of 8 mm.
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J.-M. Quemper et al.r Sensors and Actuators 74 (1999) 1–4
Films residual stress was calculated from the induced change of the substrate curvature measured with a stylustype surface profilometer before and after electrodeposition. A low tensile stress value in the range of 0.15–0.4 GPa was found for all deposition condition. These values are similar to those obtained by other authors using different experimental conditions w7,9x. The magnetic properties of the Ni 80 Fe 20 films were characterized by using an alternative field gradient magnetometer. The coercitive field Hc is 640 A my1 for a 150-nm thick film and 28 A my1 for a 600-nm thick film. These values were determined from the curves of flux density B as a function of applied magnetic film H ŽFig. 6.. These values which demonstrate the high films quality are close to those mentioned by several authors for electrodeposited Ni 80 Fe 20 films w7,9x. Results described above have been applied to the realization of patterns in Ni 80 Fe 20 films by electrodeposition through photoresist molds. For these experiments, no hard baking of the photoresist was performed after development to avoid pattern distortion by swelling. Fig. 7 shows SEM pictures of a lithographic mold and an electrodeposit after mold removing. No degradation of the resist can be underlined during film growth. The alloy surface is very smooth and the thickness is quite constant at this observation scale. However, the observation of the whole sample surface Ž1.21 cm2 . reveals a thickness inhomogeneity induced by the edge effect mentioned above.
4. Conclusion The permalloy stoichiometry Ni 80 Fe 20 is reached for a current density of 14.5 mA cmy2 in our experimental conditions. Films with a good quality can be obtained without using pulsed current if hydrogen desorption is facilitated Žlow roughness and bright appearance, density
close to the bulk value, low residual stress and good magnetic properties.. Successful electrodeposition through resist molds without hard baking is demonstrated. A large thickness inhomogeneity induced by edge effects has been observed. This phenomenon, which is emphasized by the small size of the sample, can be reduced by using larger substrates. References w1x K. Ohashi, M. Ito, M. Watanabe, Electrochemical technology in electronics, in: L.T. Romankiw, T. Osaka ŽEds.., The Electrochemical Society Proceeding Series, Pennington, NJ, PV 88-23, 1988, p. 285. w2x J. Gobet, F. Cardot, J. Bergqvist, F. Rudolf, J. Micromech. Microeng. 3 Ž1993. 123. w3x B. Loechel, M. Maciossek, M. Rothe, W. Windbracke, Sensors and Actuators 1–3 Ž1996. 663, SNA.054. w4x B. Loechel, M. Maciossek, J. Electrochem. Soc. 143 Ž1996. 3343– 3348. w5x M.M. Yang, J.A. Aboaf, J. Appl. Phys. 66 Ž1989. 3734. w6x L.J. Gao, P. Ma, K.M. Novogradecz, P.R. Norton, J. Appl. Phys. 81 Ž11. Ž1997. 7595–7599. w7x F. Czerninski, J. Electrochem. Soc. 143 Ž1996. 3327–3332. w8x A.B. Frazier, M.G. Allen, J. Microelectrochem. Syst. 2 Ž1993. . w9x J.T. Christensen, O. Hansen, P.T. Tang, The 9th Micromechanics Europe Workshop, MME’98, June 3–5, 1998, Ulvik in Hardanger, Norway, pp. 86–89. w10x H. Dahms, I.M. Croll, J. Electrochem. Soc. 112 Ž8. Ž1965. 771–775. w11x D.R. Gabe, J. Appl. Electrochem. 27 Ž1997. 908–915. w12x J. Horkans, J. Electrochem. Soc. 128 Ž1. Ž1981. 45–49. w13x R.V. Shenoy, M. Datta, J. Electrochem. Soc. 143 Ž2. Ž1996. 544– 549. w14x K. Kondo, K. Fukui, J. Electrochem Soc. 145 Ž3. Ž1998. 840–844. w15x A. Brenner, Electrodeposition of Alloys, Vol. 1, Academic Press, New York, 1963, p. 77. w16x T.M. Harris, J. St. Clair, J. Electrochem. Soc. 143 Ž12. Ž1996. 3918–3922. w17x M. Matlosz, J. Electrochem. Soc. 140 Ž8. Ž1993. 2272–2279. w18x D. Gangasingh, J.B. Talbot, J. Electrochem. Soc. 138 Ž2. Ž1991. 3605–3611. w19x K.Y. Sasaki, J.B. Talbot, J. Electrochem. Soc. 145 Ž3. Ž1998. 981–990.
Permalloy electroplating through photoresist molds Jean-Marie Quemper ) , S. Nicolas, J.P. Gilles, J.P. Grandchamp, A. Bosseboeuf, T. Bourouina, E. Dufour-Gergam Institut d’Electronique Fondamentale, URA CNRS 022, UniÕersite´ Paris Sud, Bat. ˆ 220, 91405 Orsay Cedex, France
Abstract Electrodeposited Ni 80 Fe 20 magnetic films are used in storage devices and are usually used for MEMS. In this paper, we present some fundamental results concerning the influence of electrodeposition conditions on the films characteristics. In the first step, permalloy electrodeposition has been studied on copper evaporated films without resist patterns. The growth rate varies linearly as function of the current density Žtypically 120 nm miny1 for 10 mA cmy2 .. The variation of the alloy composition with deposition parameters is consistent with the so-called anomalous deposition effect, i.e., a preferential deposition of iron. The composition is the same for films with thickness in the range 0.6–20 mm and the Fe concentration decreases with current density. An alloy Ni 80 Fe 20 with a density close to the bulk value is obtained for a current density of 14.5 mA cmy2 . Characterization of magnetic properties with a vibrating magnetometer shows that good properties can be obtained Žcoercivitys 0.35 Oe for a thickness of 600 nm.. These results are applied to the patterning of permalloy by electrodeposition through photoresist molds. q 1999 Elsevier Science S.A. All rights reserved. Keywords: Permalloy; Electrodeposition; Micromolding; UV lithography
1. Introduction The Permalloy Ž80% Ni, 20% Fe. is used in several magnetic device applications like cording heads w1x, magnetic yokes in printed heads w2x, microsolenoıds ¨ w3x and w x microvalves 4 . The magnetic film can be elaborated on different conductive seed-layer w5–7x by electrodeposition. Recently, several authors presented some papers about the electrodeposition of permalloy through molds w8–10x using conventional UV lithography. This technique allows for the realization of high-aspect-ratio magnetic components without etching step. In this paper, we present results obtained on a small surface concerning the effect of current density on deposition rate, density, composition and stress, and some preliminary results of film growth through photoresist molds.
2. Experimental An evaporated copper seed-layer Ž200 nm thick. was first deposited on cleaned high resistivity silicon ²100: wafers with an n-doping density around 10 14 cmy3 and a
) Corresponding author. Tel.: q33-1-69-15-62-98; Fax: q33-1-69-1540-80; E-mail: [email protected]
thickness of 280 mm. The copper permits a good electrical connection and a good adhesion of permalloy. Moreover, it can be used as a sacrificial metallic layer because of the high etching selectivity between NiFe and Cu. Before electrodeposition, the sample was cleaved in 11 = 11 mm2 parts. In the case of electrodeposition through molds, we used a high transparency and high viscosity UV positive photoresist AZ4562 ŽHoechst.. After a classical spin-coating of the resist, a prebake was performed on a ramped hotplate to allow solvent evaporation Žtemperature ramp: from 20 to 908C for 15 min, plateau: 908C for 45 min.. The photoresist layers were exposed in a Karl Suss ¨ contact masker with a dose of 1200 mJ cmy2 . Then, the patterns were developed in a diluted alkaline solution ŽAZ400K. for 4 min. The final resist thickness is about 18 mm. This process leads to resist molds with a high aspect ratio close to 8. The electrochemical cell used for Ni x Fe y deposition is a two-electrodes system with a nickel anode in a 1-l glass beaker. The volume of the plating bath is approximately 450 ml with an interelectrode distance of 10 cm. DC current densities from 2 to 16 mA cmy2 were applied at room temperature without stirring. The samples were removed from the solution for a short time every minute to allow hydrogen desorption from the surface w11x. A solution containing NiSO4 Ž0.7 mol ly1 ., FeSO4 Ž0.03 mol ly1 ., NiCl 2 Ž0.02 mol ly1 . and saccharine
0924-4247r99r$ - see front matter q 1999 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 4 - 4 2 4 7 Ž 9 8 . 0 0 3 2 3 - 9
J.-M. Quemper et al.r Sensors and Actuators 74 (1999) 1–4
2
Fig. 1. Deposition rate as a function of DC current density.
Fig. 3. Partial cationic currents as a function of total current.
Ž0.016 mol ly1 . as a leveller was used as the electroplating bath. Boric acid was added in the aim to obtain a good appearance of the deposit Ž0.4 mol ly1 . w12x.
The copper seed-layer presents a resistivity of 2.2 mV cm. A rest surface potential of y0.37 V ŽENH. without applied voltage was measured with a three-electrodes system ŽEGG PotentiostatrGalvanostat model 263A.. This value is approximately the same for bulk massic copper Žy0.33 V, ENH. in the same experimental conditions. So, the influence of the silicon substrate in the surface potential is not significative. Fig. 1 shows that the deposition rate varies linearly with the current density in agreement with the Faraday’s law. ˚ miny1 mAy1 cmy2 . No The resulting slope is 1300 A deposition occurs below a threshold of 1.5 mA cmy2 corresponding to the discharge limit potential of metallic cations. The deposition rate was calculated from the average thickness of the sample. Thickness inhomogeneity can reach 150% in the corners of the sample due to an edge effect w13,14x. This average thickness was calculated by averaging the thickness values obtained in the four corners and in the center of the samples.
The film density was found constant whatever the current density Ž6–16 mA cmy2 . with a value Ž8.9 g cmy3 for a 1-mm thick film. close to bulk value. No significative variation of the square resistance of the metallic structure is observed in this range of current densities for a 1-mm thick NiFe alloy. We observed an inhomogeneous surface film composition determined by EDS ŽEnergy Dispersive Spectrometry. because the growth mechanisms induce a composition variation with the deposition rate. The edge effect introduces a large variation of the composition close to 8%. The variation of the mean film composition with current density ŽFig. 2. shows the well-known anomalous codeposition effect of permalloy w15x: despite a standard reduction potential of nickel higher than that of iron Žy0.25 and y0.44 V, respectively. and a large excess of nickel species in the electrolyte Žfactor 25., a preferential deposition of iron occurs. Several models have been proposed to explain this process w10,16–19x. For a current density variation in the range of 2–16 mA cmy2 , the average iron composition decreases from 43% to 16.5%. The permalloy stoichiometry Ni 80 Fe 20 is reached for a current density of 14.5 mA cmy2 . The average composition is quite constant in the film thickness, for film thicknesses varying from 0.6 to 20 mm. Fig. 3 shows the variation of the cationic current with the total current density j. In our experimental conditions,
Fig. 2. Evolution of iron concentration with current density.
Fig. 4. Variation of current efficiency with current density.
3. Results and discussion
J.-M. Quemper et al.r Sensors and Actuators 74 (1999) 1–4
3
Žscanned surface s 20 mm = 20 m.. No correlation between roughness and current density for a thickness larger than 600 nm can be clearly established. An rms roughness of 6 nm is found for a composition of 80% Ni 20% Fe ŽFig. 5..
Fig. 5. AFM picture of a 1-mm thick NiFe film elaborated with a current density of 14.5 mA cmy2 .
the limit current is reached for iron, but the nickel current is not yet limited by the mass transport. This explains the iron concentration decreases with j. We calculated the current efficiency from the average thickness and average composition ŽFig. 4.. A maximum value Ž60%. is obtained for a current density of 16 mA cmy2 . For the Ni 80 Fe 20 stoichiometry, the current efficiency is 56%. This quite low value is due to the hydrogen reduction which leads to H 2 bubbles desorption on the sample surface during growth. This is why it is so important to remove the sample from the electroplating bath, in order to allow desorption of the H 2 bubbles. Currently, this is the main condition to obtain electrodeposits displaying a smooth and bright surface for all current densities. Analysis of Atomic Force Microscopy ŽAFM. images leads to an rms roughness in the range of 5–10 nm
Fig. 6. Magnetic properties for a 600-nm thick film Ž Hc s 28 A my1 , Bsat s 0.8 T..
Fig. 7. Ža. Photoresist mold ŽAZ4562. 18 mm thick, Žb. Ni 80 Fe 20 electrodeposit through mold after mask removing in acetone, Žc. detail of micromotor structure air-gap of 2 mm wide with a thickness of 8 mm.
4
J.-M. Quemper et al.r Sensors and Actuators 74 (1999) 1–4
Films residual stress was calculated from the induced change of the substrate curvature measured with a stylustype surface profilometer before and after electrodeposition. A low tensile stress value in the range of 0.15–0.4 GPa was found for all deposition condition. These values are similar to those obtained by other authors using different experimental conditions w7,9x. The magnetic properties of the Ni 80 Fe 20 films were characterized by using an alternative field gradient magnetometer. The coercitive field Hc is 640 A my1 for a 150-nm thick film and 28 A my1 for a 600-nm thick film. These values were determined from the curves of flux density B as a function of applied magnetic film H ŽFig. 6.. These values which demonstrate the high films quality are close to those mentioned by several authors for electrodeposited Ni 80 Fe 20 films w7,9x. Results described above have been applied to the realization of patterns in Ni 80 Fe 20 films by electrodeposition through photoresist molds. For these experiments, no hard baking of the photoresist was performed after development to avoid pattern distortion by swelling. Fig. 7 shows SEM pictures of a lithographic mold and an electrodeposit after mold removing. No degradation of the resist can be underlined during film growth. The alloy surface is very smooth and the thickness is quite constant at this observation scale. However, the observation of the whole sample surface Ž1.21 cm2 . reveals a thickness inhomogeneity induced by the edge effect mentioned above.
4. Conclusion The permalloy stoichiometry Ni 80 Fe 20 is reached for a current density of 14.5 mA cmy2 in our experimental conditions. Films with a good quality can be obtained without using pulsed current if hydrogen desorption is facilitated Žlow roughness and bright appearance, density
close to the bulk value, low residual stress and good magnetic properties.. Successful electrodeposition through resist molds without hard baking is demonstrated. A large thickness inhomogeneity induced by edge effects has been observed. This phenomenon, which is emphasized by the small size of the sample, can be reduced by using larger substrates. References w1x K. Ohashi, M. Ito, M. Watanabe, Electrochemical technology in electronics, in: L.T. Romankiw, T. Osaka ŽEds.., The Electrochemical Society Proceeding Series, Pennington, NJ, PV 88-23, 1988, p. 285. w2x J. Gobet, F. Cardot, J. Bergqvist, F. Rudolf, J. Micromech. Microeng. 3 Ž1993. 123. w3x B. Loechel, M. Maciossek, M. Rothe, W. Windbracke, Sensors and Actuators 1–3 Ž1996. 663, SNA.054. w4x B. Loechel, M. Maciossek, J. Electrochem. Soc. 143 Ž1996. 3343– 3348. w5x M.M. Yang, J.A. Aboaf, J. Appl. Phys. 66 Ž1989. 3734. w6x L.J. Gao, P. Ma, K.M. Novogradecz, P.R. Norton, J. Appl. Phys. 81 Ž11. Ž1997. 7595–7599. w7x F. Czerninski, J. Electrochem. Soc. 143 Ž1996. 3327–3332. w8x A.B. Frazier, M.G. Allen, J. Microelectrochem. Syst. 2 Ž1993. . w9x J.T. Christensen, O. Hansen, P.T. Tang, The 9th Micromechanics Europe Workshop, MME’98, June 3–5, 1998, Ulvik in Hardanger, Norway, pp. 86–89. w10x H. Dahms, I.M. Croll, J. Electrochem. Soc. 112 Ž8. Ž1965. 771–775. w11x D.R. Gabe, J. Appl. Electrochem. 27 Ž1997. 908–915. w12x J. Horkans, J. Electrochem. Soc. 128 Ž1. Ž1981. 45–49. w13x R.V. Shenoy, M. Datta, J. Electrochem. Soc. 143 Ž2. Ž1996. 544– 549. w14x K. Kondo, K. Fukui, J. Electrochem Soc. 145 Ž3. Ž1998. 840–844. w15x A. Brenner, Electrodeposition of Alloys, Vol. 1, Academic Press, New York, 1963, p. 77. w16x T.M. Harris, J. St. Clair, J. Electrochem. Soc. 143 Ž12. Ž1996. 3918–3922. w17x M. Matlosz, J. Electrochem. Soc. 140 Ž8. Ž1993. 2272–2279. w18x D. Gangasingh, J.B. Talbot, J. Electrochem. Soc. 138 Ž2. Ž1991. 3605–3611. w19x K.Y. Sasaki, J.B. Talbot, J. Electrochem. Soc. 145 Ž3. Ž1998. 981–990.