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Preparation of REBa2Cu3O7−x films grown by metal trifluoroacetate precursors
Physica C 357±360 (2001) 999±1002
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Preparation of REBa2Cu3O7 x ®lms grown by metal tri¯uoroacetate precursors Tetsuji Honjo *, Hiroshi Fuji, Daxiang Huang, Yuichi Nakamura, Teruo Izumi, Yuh Shiohara Superconductivity Research Laboratory, ISTEC, 1-10-13 Shinonome, Koto-ku, Tokyo 135-0062, Japan Received 16 October 2000; accepted 20 December 2000
Abstract Metal organic deposition (MOD) process using metal tri¯uoroacetate (TFA) precursors was applied to the NdBa2 Cu3 O6y (Nd123) and the Tc dependence of experimental conditions such as oxygen partial pressure (PO2 ) and substrate temperature (Ts ) for annealing was investigated. Thin ®lms grown on single crystal SrTiO3 at Ts 800°C under PO2 3 10 4 atm showed a Tc0 of 89 K. However, from the results of TEM-EDS measurements, the substitution value of x in Nd1x Ba2 x Cu3 O6y increased from the substrate toward the surface in the ®lm. These experimental results could be explained thermodynamically by the following model. The basic idea of our model is that the Ba potential is changed by coarsening of BaF2 during the annealing for the growth. This model predicts that the small substitution value can be obtained with a higher growth rate of the Nd123 phase under low PO2 . Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 74.76.Bz; 81.20.Ka Keywords: Nd123; Metal organic deposition; Tri¯uoroacetate; Film
1. Introduction Metal organic deposition (MOD) is expected as one of attractive processes for tape conductor applications because of a non-vacuum process, a rapid deposition rate and compositional controllability. Especially, the MOD process of YBa2 Cu3 O7 d only (Y123) using metal tri¯uoroacetate (TFA) precursors has been of great interest for development of coated conductors since high
*
Corresponding author. Fax: +81-3-3536-5714. E-mail address: [email protected] (T. Honjo).
quality Y123 ®lms with high critical current density (Jc ) can be fabricated by this process [1]. Actually, this process has been started to apply for coated conductors on metal and realized high Jc [2]. From a material point of view, the RE±Ba± Cu±O system (RE Nd or Sm) is one of the most promising materials, since NdBa2 Cu3 O7 d (Nd123) and SmBa2 Cu3 O7 d (Sm123) have demonstrated higher Tc than Y123 [3] as well as stronger vortex¯ux pinning, which results in the high irreversibility ®eld of the materials and the high Jc [4]. However, these REBa2 Cu3 O7 d phases have the RE1x Ba2 x Cu3 Oy (RE123) type solid solution, in which RE substitutions for Ba sites considerably suppress
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T. Honjo et al. / Physica C 357±360 (2001) 999±1002
Tc [5]. Therefore, the control of x values in the RE123 phase is a very important factor. In this study, the TFA process was applied to the Nd-system and the dependence of experimental conditions such as oxygen partial pressure (PO2 ) and substrate temperature (Ts ) for annealing was investigated.
Table 1 Tc0 values of Nd123 ®lms on SrTiO3 deposited under dierent Ts and PO2
2. Experimental
Nd123 ®lms deposited on SrTiO3 substrates. From these results, it can be seen that the Tc increased with decreasing the PO2 . The highest transition temperature Tc0 89 K was achieved at Ts of 800°C under PO2 of 3 10 4 atm. However, this Tc0 value is lower than that of the stoichiometric single crystal (96 K) [3] and that of Nd123 ®lms deposited by pulsed laser deposition ( Tc0 93 K) [6]. One possible reason for the low Tc is diusion of cations as a contamination from the substrate. It was known that the Tc value of Y123 ®lms deposited on SrTiO3 decreased with increasing the Ts due to interdiusion of ionic species [7]. Actually, in order to con®rm the diusion of cations from the substrate in the Nd123 ®lm, secondary ion mass spectroscopy (SIMS) was carried out for the sample annealed at 800°C under PO2 of 10 3 atm. Fig. 1 shows the concentration pro®les of Sr and Ti in the Nd123 ®lm deposited on SrTiO3 substrate. It was observed by SIMS that the diusion of Sr and Ti existed in the ®lm from the substrate. However, the diusion layer was limited to be 60 nm in thickness in the Nd123 ®lm with 130 nm in total thickness as shown in Fig. 1. Therefore, the reason for the low Tc could not be only explained due to the in¯uence of the contamination. Another possibility as a reason for the low Tc is the substitution of Nd for Ba sites. It was also reported that the Tc value decreased with increasing the substitution ratio [5]. Therefore, TEMEDS measurements were carried out in order to investigate the distribution of the Nd/Ba ratio in Nd123 ®lm deposited at 800°C under PO2 of 10 3 atm. The depth pro®le for Nd/Ba ratio in the ®lm is shown in Fig. 2. From the results of TEM-EDS, the phase with small substitution (x < 0:1) could be observed near the substrate in the ®lm. However, the substitution values of x in Nd123 increased from the substrate toward the surface of
A TFA precursor solution for RE123 was prepared by dissolving the TFA salts of Nd, Ba and Cu with 1:2:3 cation ratio into sucient methyl alcohol to give a solution with total metal ions concentration of 1.5 M. The coating solution so prepared was spin-coated onto the single crystal substrate of SrTiO3 (1 0 0) with a size of 10 mm square. The sample was ®red in the following two steps. In the ®rst calcination, the coated ®lms were decomposed to amorphous precursor ®lms by slowly heating up to 400°C in a humid oxygen atmosphere. In the second annealing, the precursor ®lms were heated above 750°C at a rate of 25°C/ min and then held for 1 h at dierent annealing temperatures in a humid argon and oxygen gas mixture atmosphere with low PO2 of 10 3 ±10 4 atm. Then, the furnace atmosphere was switched from humid to a dry argon and oxygen gas mixture atmosphere, and the ®lms were cooled to the room temperature. Humid atmospheres mentioned above in the furnace were produced by bubbling the inlet gas through an attached reservoir of de-ionized water at 30°C. Also, the thickness of ®lm so prepared was 150 nm. Electrical properties were directly measured by four-point dc current±voltage measurements. Silver electrodes were deposited onto the ®red ®lms by evaporation in a vacuum chamber. The ®lms with the electrodes were annealed at 350°C for 1 h in oxygen to obtain superconducting characteristics. 3. Results and discussion Several series of Nd123 ®lms were prepared under dierent deposition conditions of Ts and PO2 . Table 1 shows the Tc dependence on Ts and PO2 for
Ts (°C)
PO2 (atm) 3 10
750 800
± 89
4
5 10 74 81
4
1 10
3
72 81
T. Honjo et al. / Physica C 357±360 (2001) 999±1002
1001
the other hand, for the Ba potential, it was also reported that the substitution values in Ba-rich composition was found to be relatively small [9]. According to Cima and coworkers [10], the overall reaction of Y123 can be represented by the following equation: 2BaF2 2CuO 12Y2 Cu2 O5 2H2 O ! YBa2 Cu3 O6:5 4HF:
1
On the basis of Eq. (1), the overall reaction of Nd123 is assumed to be: 2BaF2 2CuO 12Nd2 Cu2 O5 2H2 O ! NdBa2 Cu3 O6:5 4HF: Fig. 1. Concentration pro®les of Sr and Ti in the Nd123 ®lm deposited on SrTiO3 substrate at 800°C under PO2 of 10 3 atm.
The equilibrium phases prior to introduction of water are assumed to be BaF2 , CuO and Nd2 Cu2 O5 . From Eq. (2), we focussed the existence of BaF2 particles. Then, the experimental results obtained in Fig. 2 could be explained thermodynamically by the following model. The basic idea of our model is that the Ba potential is changed by coarsening of BaF2 during the annealing for the growth. According to the Ostwald ripening theory, a radius (r) of BaF2 will increase with increasing time (t) as the following equation: r ADL CBaF2 t1=3
Fig. 2. Distribution of the Nd/Ba ratio in Nd123 ®lm deposited on SrTiO3 substrate at 800°C under PO2 of 10 3 atm.
the ®lm and existence of the non-superconducting phase (x > 0:4) was observed near the surface. It should be noted here that lattice mismatch eect can not explain this tendency. According to previous studies on the phase diagram of this system, the substitution value of x in Nd123 was aected by both chemical potentials of O2 and Ba during the growth. For the O2 potential, the substitutional range of Nd for Ba sites in low oxygen pressure was found to be relatively small [8]. On
2
3
where CBaF2 is Gibbs±Thomson coecient (rBaF2 = zDS), r is the interface energy between the BaF2 particle and the precursor matrix, S is the volumetric entropy of fusion, DL is the diusitivity and A is the proportional constant. In addition, the total Gibbs free energy (DGr ) of a small solid particle is inversely proportional to its size as given by the following equation: DGr vm rKBaF2
4
where vm is the molar volume and K is the curvature of BaF2 particles. The concept of the substitution model is shown in Fig. 3. Here the O2 potential for Nd123 crystal growth was assumed to be constant in the reaction. From Eqs. (3) and (4), the Ba potential of the BaF2 particles in the precursor is relatively large in the initial reaction stage since the particles might be smaller in size. It
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T. Honjo et al. / Physica C 357±360 (2001) 999±1002
phase (x > 0:4) was con®rmed near the surface. Based on the idea that the change of the Ba potential caused by the curvature of the BaF2 particles in the precursor and PO2 aects the substitution value for the Nd-system, the substitution model during the growth was proposed. This model predicts that the small substitution value can be obtained with a higher growth rate of the Nd123 phase under low PO2 .
Acknowledgements Fig. 3. Schematic drawing of the concept for the substitution model.
suggests that the small x value phase of Nd1x Ba2 x Cu3 O6y crystals should be grown in the initial stage of the growth near the substrate. As the reaction proceeds, the x value gradually increases with decreasing the Ba potential by coarsening of BaF2 particles. In addition, it can be considered that the maximum substitutional range of Nd for Ba sites, which strongly aects the x value in the later stage of the growth, is limited by the PO2 . Consequently, this model predicts that the small substitution value can be obtained with the higher growth rate of Nd123 phase, which can suppress the coarsening, and low PO2 . 4. Conclusion We applied the TFA process to the Nd123 ®lms and investigated the Tc dependence of annealing parameters for the growth such as the oxygen partial pressure and the annealing temperature. As a result, the Tc0 value of 89 K was achieved at Ts of 800°C under PO2 of 3 10 4 atm. However, from the results of TEM-EDS measurements, the substitution value of x in Nd1x Ba2 x Cu3 O6y increased from the substrate toward the surface in the ®lm and the existence of non-superconducting
This work is supported by the New Energy and Industrial Technology Development Organization (NEDO) as Collaborative Research and Development of Fundamental Technologies for Superconductivity Applications.
References [1] P.C. Mclntyre, M.J. Cima, M.F. Ng, J. Appl. Phys. 68 (1990) 4183. [2] H. Fuji, T. Honjo, Y. Nakamura, T. Izumi, T. Araki, I. Hirabayashi, Y. Shiohara, I. Iijima, K. Takeda, Physica C 357±360 (2001), these Proceedings. [3] S.I. Yoo, M. Murakami, N. Sakai, T. Higuchi, S. Tanaka, Jpn. J. Appl. Phys. 33 (1994) 1000. [4] M. Murakami, S.I. Yoo, T. Higuchi, N. Sakai, Jpn. J. Appl. Phys. 33 (1994) 715. [5] K. Takita, H. Akinaga, H. Katoh, H. Asano, K. Masuda, Jpn. J. Appl. Phys. 27 (1988) 67. [6] C. Cantoni, D.P. Norton, D.K. Christen, A. Goyal, D.M. Kroeger, D.T. Verebelyi, M. Paranthaman, Physica C 324 (1999) 177. [7] N. Naito, R.H. Hammond, B. Oh, M.R. Hahn, J.W.P. Hsu, P. Rosenthal, A.F. Marshall, M.R. Beasley, T.H. Geballe, A. Kapitulnik, J. Matel. Res. 2 (1987) 713. [8] M. Yoshizumi, M. Kambara, Y. Shiohara, T. Umeda, Physica C 334 (2000) 77. [9] M. Kambara, T. Umeda, M. Tagami, X. Yao, E.A. Goodilin, Y. Shiohara, J. Am. Ceram. Soc. 81 (1998) 2116. [10] J.A. Smith, M.J. Cima, N. Sonnenberg, IEEE Trans. Appl. Supercond. 9 (1999) 1531.
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Preparation of REBa2Cu3O7 x ®lms grown by metal tri¯uoroacetate precursors Tetsuji Honjo *, Hiroshi Fuji, Daxiang Huang, Yuichi Nakamura, Teruo Izumi, Yuh Shiohara Superconductivity Research Laboratory, ISTEC, 1-10-13 Shinonome, Koto-ku, Tokyo 135-0062, Japan Received 16 October 2000; accepted 20 December 2000
Abstract Metal organic deposition (MOD) process using metal tri¯uoroacetate (TFA) precursors was applied to the NdBa2 Cu3 O6y (Nd123) and the Tc dependence of experimental conditions such as oxygen partial pressure (PO2 ) and substrate temperature (Ts ) for annealing was investigated. Thin ®lms grown on single crystal SrTiO3 at Ts 800°C under PO2 3 10 4 atm showed a Tc0 of 89 K. However, from the results of TEM-EDS measurements, the substitution value of x in Nd1x Ba2 x Cu3 O6y increased from the substrate toward the surface in the ®lm. These experimental results could be explained thermodynamically by the following model. The basic idea of our model is that the Ba potential is changed by coarsening of BaF2 during the annealing for the growth. This model predicts that the small substitution value can be obtained with a higher growth rate of the Nd123 phase under low PO2 . Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 74.76.Bz; 81.20.Ka Keywords: Nd123; Metal organic deposition; Tri¯uoroacetate; Film
1. Introduction Metal organic deposition (MOD) is expected as one of attractive processes for tape conductor applications because of a non-vacuum process, a rapid deposition rate and compositional controllability. Especially, the MOD process of YBa2 Cu3 O7 d only (Y123) using metal tri¯uoroacetate (TFA) precursors has been of great interest for development of coated conductors since high
*
Corresponding author. Fax: +81-3-3536-5714. E-mail address: [email protected] (T. Honjo).
quality Y123 ®lms with high critical current density (Jc ) can be fabricated by this process [1]. Actually, this process has been started to apply for coated conductors on metal and realized high Jc [2]. From a material point of view, the RE±Ba± Cu±O system (RE Nd or Sm) is one of the most promising materials, since NdBa2 Cu3 O7 d (Nd123) and SmBa2 Cu3 O7 d (Sm123) have demonstrated higher Tc than Y123 [3] as well as stronger vortex¯ux pinning, which results in the high irreversibility ®eld of the materials and the high Jc [4]. However, these REBa2 Cu3 O7 d phases have the RE1x Ba2 x Cu3 Oy (RE123) type solid solution, in which RE substitutions for Ba sites considerably suppress
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 4 6 9 - 5
1000
T. Honjo et al. / Physica C 357±360 (2001) 999±1002
Tc [5]. Therefore, the control of x values in the RE123 phase is a very important factor. In this study, the TFA process was applied to the Nd-system and the dependence of experimental conditions such as oxygen partial pressure (PO2 ) and substrate temperature (Ts ) for annealing was investigated.
Table 1 Tc0 values of Nd123 ®lms on SrTiO3 deposited under dierent Ts and PO2
2. Experimental
Nd123 ®lms deposited on SrTiO3 substrates. From these results, it can be seen that the Tc increased with decreasing the PO2 . The highest transition temperature Tc0 89 K was achieved at Ts of 800°C under PO2 of 3 10 4 atm. However, this Tc0 value is lower than that of the stoichiometric single crystal (96 K) [3] and that of Nd123 ®lms deposited by pulsed laser deposition ( Tc0 93 K) [6]. One possible reason for the low Tc is diusion of cations as a contamination from the substrate. It was known that the Tc value of Y123 ®lms deposited on SrTiO3 decreased with increasing the Ts due to interdiusion of ionic species [7]. Actually, in order to con®rm the diusion of cations from the substrate in the Nd123 ®lm, secondary ion mass spectroscopy (SIMS) was carried out for the sample annealed at 800°C under PO2 of 10 3 atm. Fig. 1 shows the concentration pro®les of Sr and Ti in the Nd123 ®lm deposited on SrTiO3 substrate. It was observed by SIMS that the diusion of Sr and Ti existed in the ®lm from the substrate. However, the diusion layer was limited to be 60 nm in thickness in the Nd123 ®lm with 130 nm in total thickness as shown in Fig. 1. Therefore, the reason for the low Tc could not be only explained due to the in¯uence of the contamination. Another possibility as a reason for the low Tc is the substitution of Nd for Ba sites. It was also reported that the Tc value decreased with increasing the substitution ratio [5]. Therefore, TEMEDS measurements were carried out in order to investigate the distribution of the Nd/Ba ratio in Nd123 ®lm deposited at 800°C under PO2 of 10 3 atm. The depth pro®le for Nd/Ba ratio in the ®lm is shown in Fig. 2. From the results of TEM-EDS, the phase with small substitution (x < 0:1) could be observed near the substrate in the ®lm. However, the substitution values of x in Nd123 increased from the substrate toward the surface of
A TFA precursor solution for RE123 was prepared by dissolving the TFA salts of Nd, Ba and Cu with 1:2:3 cation ratio into sucient methyl alcohol to give a solution with total metal ions concentration of 1.5 M. The coating solution so prepared was spin-coated onto the single crystal substrate of SrTiO3 (1 0 0) with a size of 10 mm square. The sample was ®red in the following two steps. In the ®rst calcination, the coated ®lms were decomposed to amorphous precursor ®lms by slowly heating up to 400°C in a humid oxygen atmosphere. In the second annealing, the precursor ®lms were heated above 750°C at a rate of 25°C/ min and then held for 1 h at dierent annealing temperatures in a humid argon and oxygen gas mixture atmosphere with low PO2 of 10 3 ±10 4 atm. Then, the furnace atmosphere was switched from humid to a dry argon and oxygen gas mixture atmosphere, and the ®lms were cooled to the room temperature. Humid atmospheres mentioned above in the furnace were produced by bubbling the inlet gas through an attached reservoir of de-ionized water at 30°C. Also, the thickness of ®lm so prepared was 150 nm. Electrical properties were directly measured by four-point dc current±voltage measurements. Silver electrodes were deposited onto the ®red ®lms by evaporation in a vacuum chamber. The ®lms with the electrodes were annealed at 350°C for 1 h in oxygen to obtain superconducting characteristics. 3. Results and discussion Several series of Nd123 ®lms were prepared under dierent deposition conditions of Ts and PO2 . Table 1 shows the Tc dependence on Ts and PO2 for
Ts (°C)
PO2 (atm) 3 10
750 800
± 89
4
5 10 74 81
4
1 10
3
72 81
T. Honjo et al. / Physica C 357±360 (2001) 999±1002
1001
the other hand, for the Ba potential, it was also reported that the substitution values in Ba-rich composition was found to be relatively small [9]. According to Cima and coworkers [10], the overall reaction of Y123 can be represented by the following equation: 2BaF2 2CuO 12Y2 Cu2 O5 2H2 O ! YBa2 Cu3 O6:5 4HF:
1
On the basis of Eq. (1), the overall reaction of Nd123 is assumed to be: 2BaF2 2CuO 12Nd2 Cu2 O5 2H2 O ! NdBa2 Cu3 O6:5 4HF: Fig. 1. Concentration pro®les of Sr and Ti in the Nd123 ®lm deposited on SrTiO3 substrate at 800°C under PO2 of 10 3 atm.
The equilibrium phases prior to introduction of water are assumed to be BaF2 , CuO and Nd2 Cu2 O5 . From Eq. (2), we focussed the existence of BaF2 particles. Then, the experimental results obtained in Fig. 2 could be explained thermodynamically by the following model. The basic idea of our model is that the Ba potential is changed by coarsening of BaF2 during the annealing for the growth. According to the Ostwald ripening theory, a radius (r) of BaF2 will increase with increasing time (t) as the following equation: r ADL CBaF2 t1=3
Fig. 2. Distribution of the Nd/Ba ratio in Nd123 ®lm deposited on SrTiO3 substrate at 800°C under PO2 of 10 3 atm.
the ®lm and existence of the non-superconducting phase (x > 0:4) was observed near the surface. It should be noted here that lattice mismatch eect can not explain this tendency. According to previous studies on the phase diagram of this system, the substitution value of x in Nd123 was aected by both chemical potentials of O2 and Ba during the growth. For the O2 potential, the substitutional range of Nd for Ba sites in low oxygen pressure was found to be relatively small [8]. On
2
3
where CBaF2 is Gibbs±Thomson coecient (rBaF2 = zDS), r is the interface energy between the BaF2 particle and the precursor matrix, S is the volumetric entropy of fusion, DL is the diusitivity and A is the proportional constant. In addition, the total Gibbs free energy (DGr ) of a small solid particle is inversely proportional to its size as given by the following equation: DGr vm rKBaF2
4
where vm is the molar volume and K is the curvature of BaF2 particles. The concept of the substitution model is shown in Fig. 3. Here the O2 potential for Nd123 crystal growth was assumed to be constant in the reaction. From Eqs. (3) and (4), the Ba potential of the BaF2 particles in the precursor is relatively large in the initial reaction stage since the particles might be smaller in size. It
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T. Honjo et al. / Physica C 357±360 (2001) 999±1002
phase (x > 0:4) was con®rmed near the surface. Based on the idea that the change of the Ba potential caused by the curvature of the BaF2 particles in the precursor and PO2 aects the substitution value for the Nd-system, the substitution model during the growth was proposed. This model predicts that the small substitution value can be obtained with a higher growth rate of the Nd123 phase under low PO2 .
Acknowledgements Fig. 3. Schematic drawing of the concept for the substitution model.
suggests that the small x value phase of Nd1x Ba2 x Cu3 O6y crystals should be grown in the initial stage of the growth near the substrate. As the reaction proceeds, the x value gradually increases with decreasing the Ba potential by coarsening of BaF2 particles. In addition, it can be considered that the maximum substitutional range of Nd for Ba sites, which strongly aects the x value in the later stage of the growth, is limited by the PO2 . Consequently, this model predicts that the small substitution value can be obtained with the higher growth rate of Nd123 phase, which can suppress the coarsening, and low PO2 . 4. Conclusion We applied the TFA process to the Nd123 ®lms and investigated the Tc dependence of annealing parameters for the growth such as the oxygen partial pressure and the annealing temperature. As a result, the Tc0 value of 89 K was achieved at Ts of 800°C under PO2 of 3 10 4 atm. However, from the results of TEM-EDS measurements, the substitution value of x in Nd1x Ba2 x Cu3 O6y increased from the substrate toward the surface in the ®lm and the existence of non-superconducting
This work is supported by the New Energy and Industrial Technology Development Organization (NEDO) as Collaborative Research and Development of Fundamental Technologies for Superconductivity Applications.
References [1] P.C. Mclntyre, M.J. Cima, M.F. Ng, J. Appl. Phys. 68 (1990) 4183. [2] H. Fuji, T. Honjo, Y. Nakamura, T. Izumi, T. Araki, I. Hirabayashi, Y. Shiohara, I. Iijima, K. Takeda, Physica C 357±360 (2001), these Proceedings. [3] S.I. Yoo, M. Murakami, N. Sakai, T. Higuchi, S. Tanaka, Jpn. J. Appl. Phys. 33 (1994) 1000. [4] M. Murakami, S.I. Yoo, T. Higuchi, N. Sakai, Jpn. J. Appl. Phys. 33 (1994) 715. [5] K. Takita, H. Akinaga, H. Katoh, H. Asano, K. Masuda, Jpn. J. Appl. Phys. 27 (1988) 67. [6] C. Cantoni, D.P. Norton, D.K. Christen, A. Goyal, D.M. Kroeger, D.T. Verebelyi, M. Paranthaman, Physica C 324 (1999) 177. [7] N. Naito, R.H. Hammond, B. Oh, M.R. Hahn, J.W.P. Hsu, P. Rosenthal, A.F. Marshall, M.R. Beasley, T.H. Geballe, A. Kapitulnik, J. Matel. Res. 2 (1987) 713. [8] M. Yoshizumi, M. Kambara, Y. Shiohara, T. Umeda, Physica C 334 (2000) 77. [9] M. Kambara, T. Umeda, M. Tagami, X. Yao, E.A. Goodilin, Y. Shiohara, J. Am. Ceram. Soc. 81 (1998) 2116. [10] J.A. Smith, M.J. Cima, N. Sonnenberg, IEEE Trans. Appl. Supercond. 9 (1999) 1531.