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Shorted two-dimensional high-Tc Josephson arrays for oscillator applications
PII:
Applied Superconductivity Vol. 6, Nos 10±12, pp. 675±680, 1998 # 1999 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0964-1807(99)00028-9 0964-1807/99 $ - see front matter
SHORTED TWO-DIMENSIONAL HIGH-TC JOSEPHSON ARRAYS FOR OSCILLATOR APPLICATIONS S. BEUVEN*, O. HARNACK and M. DARULA Institut fuÈr Schicht- und Ionentechnik, Forschungszentrum JuÈlich GmbH, 52425 JuÈlich, Germany AbstractÐWe present results of our experimental investigations of the dynamic properties of two types of shorted two-dimensional (2D) arrays. The ®rst type consisted of 4 4 YBCO step edge junctions integrated into a circuit, which allowed the simultaneous detection of all single row voltages. Thus, using only dc-measurements, the interaction and synchronization between the rows could be observed. In the second investigated array type the edge junctions of the rows were closed into superconducting loops in the form of coplanar resonators. Resonant steps were observed on the current±voltage characteristic due to interaction of the junctions with the resonators. The circuits were integrated into a stripline geometry and coupled to another (detector) Josephson junction. A clear detector response, i.e. Shapiro steps, was measured up to 460 GHz. Steps up to 4th harmonic were observed in the frequency range 150±200 GHz. # 1999 Elsevier Science Ltd. All rights reserved
INTRODUCTION
Josephson junctions are natural high frequency oscillators. The oscillation frequency f of a Josephson junction depends on the junction dc voltage V and obeys the second Josephson relation f V=F0 , where F0 is the ¯ux quantum. The realization of a (sub) mm microwave source based on Josephson junction is very attractive, especially if using high-Tc superconductors, because their operation up to THz frequencies is expected due to the higher superconducting gap. However, the power and the linewidth of radiation generated by a single Josephson junction does not ful®l the requirements of typical applications. To overcome this drawback, the collective synchronous operation (phase-locking) of several junctions arranged in array is necessary. If all junctions in an array are oscillating in phase, the generated radiation power is proportional to the number of junctions and at the same time the linewidth of the emitted radiation decreases. To reach the phase locked state a proper mutual coupling between the junctions of an array is required. For this purpose several types of arrays were developed, e.g. dierent types of series arrays [1], series arrays coupled via superconducting loops [2] and two-dimensional (2D) arrays [3]. Among these dierent types of discrete Josephson arrays, the 2D arrays are believed to be most tolerant against spreads in junction parameters [4], because the bias current can distribute over the whole circuit such a way, that the bias condition for each junction is nearly the same. A suitable external or internal electromagnetic coupling then leads to the desired mutual phase locking. The goal of this work is to demonstrate the suitability of discrete 2D arrays consisting of high-Tc junctions for their application as oscillators. We investigated two types of 2D Josephson arrays: the `shorted' 2D array and a parallel biased 2D array. Detailed circuit descriptions follow below. Both array types were investigated fundamentally using dc measurements. The parallel biased arrays were characterized additionally by detecting the radiation from the circuits. This detection was performed o-chip by an external receiver as well as using an on-chip integrated Josephson detector junction. TECHNOLOGY
All array circuits were fabricated using a standard single layer high-Tc technology for YBa2Cu3O7 (YBCO). We used the so called step-edge junctions, i.e. the junctions are grain boundaries in the YBCO thin ®lm nucleating across steep steps in LaAlO3 (LAO) substrates. *Corresponding author. 675
676
S. BEUVEN et al.
The approximately 200-nm thick YBCO ®lms were deposited using pulsed laser deposition. The patterning of the ®lms was done using a standard photolithographical process and Ar+-ion beam milling. The typical width of the junctions was 5 mm. After fabrication some circuits were integrated into an ex-situ coupling structure consisting of an insulating SiO layer and a gold metallization on top acting as a ground plane. The SiO layers were fabricated by e-beam evaporation and lift-o. The typical thickness was about 400 nm. The top metallization, fabricated by a lift-o process, was about 30% thicker than the insulation in order to obtain contact to the underlying YBCO layer. THE `SHORTED' 2D ARRAY
Circuit description The 2D array type investigated in this work is the so-called shorted 2D array. The circuit scheme is shown in Fig. 1. We investigated the 4 4 array, which is the smallest possible n n circuit with real two-dimensional topology, i.e. the smallest circuit, where not only edge cells exist. The junctions in one row are coupled through ¯ux quantization in the single cells of the array. The junctions dc voltages and hence their intermediate oscillation frequencies are always the same. The coupling between the single rows has to be induced by a suitable external coupling mechanism, e.g. via an external load. Due to the topology of the circuit the detection of the dc-voltages of all edge junctions was possible. This voltages are in fact identical with the dc voltages of all junctions in this row. Therefore a layout was designed where the simultaneous detection of all row voltages was possible. This way the interaction between the dierent rows of an array could be observed and analyzed. At the same time the layout allowed the feeding of single rows with additional currents and thus to in¯uence actively the interaction between the rows. The circuits were embedded in a simple bow-tie antenna which served as an external coupling circuit. Circuit characterization The circuits were characterized by simultaneous measuring of the IV curves of all rows as a function of the total bias current of the array. From this measurements the Ic spread was estimated to be around 230% (min±max). With zero external magnetic ®eld no voltage locking and hence no phase locking between rows was observed, because the Ic spread in the fabricated arrays was too high for synchronization. Nevertheless, by applying an external magnetic ®eld and biasing single rows in a suitable way, the interaction between single rows could be observed. As shown in Fig. 2(a), the synchronization of two adjacent rows in a relatively large frequency interval (synchronization interval) from a few GHz up to 200 GHz was observed. In a similar manner the synchronization of three adjacent rows and of all four rows [see Fig. 2(b)] could be obtained. The stability of synchronization, however, expressed as the size of the synchronization interval, decreased strongly with increasing number of synchronized rows. Further, the stability of the synchronization was extremely sensitive to the applied magnetic ®eld.
Fig. 1. Scheme of the investigated `shorted' 2D array.
Shorted 2-dimensional high-TC Josephson arrays for oscillator applications
677
Fig. 2. IV curves of all four single rows of a `shorted' 2D array with respect to the common bias current: (a) synchronization of two rows. (b) synchronization of all four rows. In both cases the locking interval is indicated by arrows.
THE PARALLEL BIASED 2D-ARRAY
Circuit description The second 2D array type under investigation is a more sophisticated design of a shorted 2D array with a special coupling between the rows. To force the single rows of a `shorted' 2D array to oscillate at least with the same average frequency we added one row (4 5-array) and closed the edge junctions of the array in pairs into superconducting loops (see Fig. 3). This way all junctions of the array are connected in parallel for dc currents. We call this a parallel biased 2D array. The edge loops were designed as coplanar resonators. At the resonance frequency the edge junctions should be strongly electromagnetically coupled. A similar resonant coupling was proposed by Kunkel et al. [5] for series arrays. In analogy to Kunkel et al., we expected resonant eects and a possible reduction of the oscillation linewidth in the vicinity of a resonance. Some of the fabricated circuits were integrated into a stripline geometry as shown schematically in Fig. 3. The array was coupled to another Josephson junction, which served as a frequency and power sensitive radiation detector. The stripline was terminated by a capacitor on one end and by a short in close vicinity of the detector junction on the other end. Figure 4 shows a photograph of the structure in the stage before fabrication of the coupling loop. The fabrication of the ex-situ multilayer structure is described in Section 2. Circuit characterization In Fig. 5(a) the IV curve of one of our parallel biased 2D arrays, measured at 4 K, is shown. This measurements were performed without the coupling structure. Since all 20 junctions are
Fig. 3. Scheme of the investigated parallel biased 2D array with coplanar resonators.
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S. BEUVEN et al.
Fig. 4. Scheme of the investigated parallel biased 2D array with coplanar resonators embedded in a stripline coupling circuit.
connected in parallel for dc currents, one can calculate the critical current per junction to be around 35 mA if self-®eld eects are neglected. The IV curve exhibits a signi®cant structure which indicates resonant eects. The self-induced and equidistant steps on the IV curve are related to the geometric resonances of the coplanar lines. The fundamental resonance frequency was approximately 60 GHz. Steps appeared up to the 10th harmonic (1600 GHz). The position and shape of the second very broad structure seen in the IV depended strongly on the applied magnetic ®eld. This is typical for the so called Fiske resonances in long junctions and Josephson transmission lines. Therefore we attribute this structure to `Fiske'-like resonances inside the rows. Under certain condition this resonance can positively in¯uence the phase locking of junctions as it was shown by Kunkel [6] in a circuit consisting of two coupled junctions.
Fig. 5. (a) Measured IV curve of a parallel biased 2D array at 4 K. Some self induced resonant steps and the `Fiske'-like resonance are marked by arrows. (b) Detected power at 140 GHz (right axis) and correlated IV curve of a parallel biased 2D array. The emission peaks at approximately 290 mV correspond to the receiving frequency.
Shorted 2-dimensional high-TC Josephson arrays for oscillator applications
679
To obtain information about the radiation properties of our arrays we performed a direct radiation detection. For this purpose we coupled the array o-chip via an impedance transformer to a waveguide. The radiation was detected by a sensitive, heterodyne ®xed frequency receiver at 141 GHz. In Fig. 5(b) the detected power is shown together with the corresponding IV curve. Due to the large impedance mismatch between array structure and waveguide system the detected power at 141 GHz was rather low. The detected linewidth diers signi®cantly between the negative and positive branches of the IV curve. This re¯ects the fact that the dierential resistances at the positive and negative branch of the IV curve are dierent (mostly due to the applied magnetic ®eld). In the circuits, where the array was coupled to a detector junction, the dynamical behaviour of the circuits was dominated by another resonant feature. This resonant eect came due to the stripline geometry of the coupling structure. We conclude this from slight resonant steps appearing in the IV curves of both the array and the detector. Operating the array at dierent bias points we measured independently the IV curve of the detector junction. The result is shown in Fig. 6. Clear and sharp Shapiro steps up to the 4th order can be seen in the frequency range from 150 to 200 GHz. This indicates that substantial microwave power ¯ows from the array to
Fig. 6. Detector IV curves for dierent array operating frequencies up to 460 GHz. Shapiro steps are marked by arrows. The single IV curves are shifted along current and voltage axis.
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the detector junction. Above 200 GHz the number and height of the steps is decreasing, indicating a decrease of power coupled to the detector. Above 500 GHz no signi®cant steps were observed. In the optimum operating range the power was sucient to depress the Ic of the detector junction by approximately 50%. This is the optimum condition to operate the detector junction as a Josephson mixer. It was dicult to estimate the power generated by the array, because coupling coecients are not known and a signi®cant part of the coupled power is dissipated in the terminating short contact. CONCLUSION
We have fabricated and tested two types of two-dimensional arrays with 4 4 and 4 5 highTc step-edge junctions, respectively. With the simple shorted 2D arrays the synchronization between all single rows was demonstrated using a special dc measurement scheme. Due to relatively high Ic spread and strong sensitivity to magnetic ®eld it was very dicult to achieve stable and synchronized operation. Nevertheless, the relatively large locking intervals experimentally observed in certain magnetic ®elds, suggest a strong interaction between the rows. The parallel biased shorted 2D array in connection with resonant eects is a promising candidate for an application where a complete and stable synchronization is required. The evaluation of the IV curves showed, that the electromagnetic interaction via resonances has a signi®cant eect on the dynamic behaviour of the circuit. The mm-wave radiation from this type of array was detected successfully o-chip as well as on-chip. Using the on-chip coupling structure radiation was measured up to 460 GHz and Shapiro steps up to the 4th harmonic were induced in the detector IV curve. In conclusion, we demonstrated successfully a suitable method to synchronize two-dimensional high-Tc arrays and to operate them as mm-wave oscillators. REFERENCES 1. 2. 3. 4.
A.K. Jain, K.K. Likharev, J.E. Lukens and J.E. Sauvageau, Phys. Rep. 109, 309 (1984). M. Darula, S. Beuven, M. Siegel, P. Seidel and A. Darulova, Appl. Phys. Lett. 67, 1618 (1995). S.P. Benz and C.J. Burroughs, Supercond. Sci. Technol. 4, 561 (1991). M. Darula, P. Seidel, J. von Zameck Glyscinski, A. Darulova, F. Busse and S. Benacka, In Applied Superconductivity (Edited by H. C. Freyhardt). DGM Informationsgesellschaft, Oberursel (1993). 5. G. Kunkel, R.H. Ono and A.M. Klushin, Supercond. Sci. Technol. 9, A1 (1996). 6. G. Kunkel, Dynamische Eigenschaften und Wechselwirkungen von Hochtemperatur josephson-kontakten. Ph.D. thesis, BUGH, Wuppertal (1996).
Applied Superconductivity Vol. 6, Nos 10±12, pp. 675±680, 1998 # 1999 Elsevier Science Ltd. All rights reserved Printed in Great Britain S0964-1807(99)00028-9 0964-1807/99 $ - see front matter
SHORTED TWO-DIMENSIONAL HIGH-TC JOSEPHSON ARRAYS FOR OSCILLATOR APPLICATIONS S. BEUVEN*, O. HARNACK and M. DARULA Institut fuÈr Schicht- und Ionentechnik, Forschungszentrum JuÈlich GmbH, 52425 JuÈlich, Germany AbstractÐWe present results of our experimental investigations of the dynamic properties of two types of shorted two-dimensional (2D) arrays. The ®rst type consisted of 4 4 YBCO step edge junctions integrated into a circuit, which allowed the simultaneous detection of all single row voltages. Thus, using only dc-measurements, the interaction and synchronization between the rows could be observed. In the second investigated array type the edge junctions of the rows were closed into superconducting loops in the form of coplanar resonators. Resonant steps were observed on the current±voltage characteristic due to interaction of the junctions with the resonators. The circuits were integrated into a stripline geometry and coupled to another (detector) Josephson junction. A clear detector response, i.e. Shapiro steps, was measured up to 460 GHz. Steps up to 4th harmonic were observed in the frequency range 150±200 GHz. # 1999 Elsevier Science Ltd. All rights reserved
INTRODUCTION
Josephson junctions are natural high frequency oscillators. The oscillation frequency f of a Josephson junction depends on the junction dc voltage V and obeys the second Josephson relation f V=F0 , where F0 is the ¯ux quantum. The realization of a (sub) mm microwave source based on Josephson junction is very attractive, especially if using high-Tc superconductors, because their operation up to THz frequencies is expected due to the higher superconducting gap. However, the power and the linewidth of radiation generated by a single Josephson junction does not ful®l the requirements of typical applications. To overcome this drawback, the collective synchronous operation (phase-locking) of several junctions arranged in array is necessary. If all junctions in an array are oscillating in phase, the generated radiation power is proportional to the number of junctions and at the same time the linewidth of the emitted radiation decreases. To reach the phase locked state a proper mutual coupling between the junctions of an array is required. For this purpose several types of arrays were developed, e.g. dierent types of series arrays [1], series arrays coupled via superconducting loops [2] and two-dimensional (2D) arrays [3]. Among these dierent types of discrete Josephson arrays, the 2D arrays are believed to be most tolerant against spreads in junction parameters [4], because the bias current can distribute over the whole circuit such a way, that the bias condition for each junction is nearly the same. A suitable external or internal electromagnetic coupling then leads to the desired mutual phase locking. The goal of this work is to demonstrate the suitability of discrete 2D arrays consisting of high-Tc junctions for their application as oscillators. We investigated two types of 2D Josephson arrays: the `shorted' 2D array and a parallel biased 2D array. Detailed circuit descriptions follow below. Both array types were investigated fundamentally using dc measurements. The parallel biased arrays were characterized additionally by detecting the radiation from the circuits. This detection was performed o-chip by an external receiver as well as using an on-chip integrated Josephson detector junction. TECHNOLOGY
All array circuits were fabricated using a standard single layer high-Tc technology for YBa2Cu3O7 (YBCO). We used the so called step-edge junctions, i.e. the junctions are grain boundaries in the YBCO thin ®lm nucleating across steep steps in LaAlO3 (LAO) substrates. *Corresponding author. 675
676
S. BEUVEN et al.
The approximately 200-nm thick YBCO ®lms were deposited using pulsed laser deposition. The patterning of the ®lms was done using a standard photolithographical process and Ar+-ion beam milling. The typical width of the junctions was 5 mm. After fabrication some circuits were integrated into an ex-situ coupling structure consisting of an insulating SiO layer and a gold metallization on top acting as a ground plane. The SiO layers were fabricated by e-beam evaporation and lift-o. The typical thickness was about 400 nm. The top metallization, fabricated by a lift-o process, was about 30% thicker than the insulation in order to obtain contact to the underlying YBCO layer. THE `SHORTED' 2D ARRAY
Circuit description The 2D array type investigated in this work is the so-called shorted 2D array. The circuit scheme is shown in Fig. 1. We investigated the 4 4 array, which is the smallest possible n n circuit with real two-dimensional topology, i.e. the smallest circuit, where not only edge cells exist. The junctions in one row are coupled through ¯ux quantization in the single cells of the array. The junctions dc voltages and hence their intermediate oscillation frequencies are always the same. The coupling between the single rows has to be induced by a suitable external coupling mechanism, e.g. via an external load. Due to the topology of the circuit the detection of the dc-voltages of all edge junctions was possible. This voltages are in fact identical with the dc voltages of all junctions in this row. Therefore a layout was designed where the simultaneous detection of all row voltages was possible. This way the interaction between the dierent rows of an array could be observed and analyzed. At the same time the layout allowed the feeding of single rows with additional currents and thus to in¯uence actively the interaction between the rows. The circuits were embedded in a simple bow-tie antenna which served as an external coupling circuit. Circuit characterization The circuits were characterized by simultaneous measuring of the IV curves of all rows as a function of the total bias current of the array. From this measurements the Ic spread was estimated to be around 230% (min±max). With zero external magnetic ®eld no voltage locking and hence no phase locking between rows was observed, because the Ic spread in the fabricated arrays was too high for synchronization. Nevertheless, by applying an external magnetic ®eld and biasing single rows in a suitable way, the interaction between single rows could be observed. As shown in Fig. 2(a), the synchronization of two adjacent rows in a relatively large frequency interval (synchronization interval) from a few GHz up to 200 GHz was observed. In a similar manner the synchronization of three adjacent rows and of all four rows [see Fig. 2(b)] could be obtained. The stability of synchronization, however, expressed as the size of the synchronization interval, decreased strongly with increasing number of synchronized rows. Further, the stability of the synchronization was extremely sensitive to the applied magnetic ®eld.
Fig. 1. Scheme of the investigated `shorted' 2D array.
Shorted 2-dimensional high-TC Josephson arrays for oscillator applications
677
Fig. 2. IV curves of all four single rows of a `shorted' 2D array with respect to the common bias current: (a) synchronization of two rows. (b) synchronization of all four rows. In both cases the locking interval is indicated by arrows.
THE PARALLEL BIASED 2D-ARRAY
Circuit description The second 2D array type under investigation is a more sophisticated design of a shorted 2D array with a special coupling between the rows. To force the single rows of a `shorted' 2D array to oscillate at least with the same average frequency we added one row (4 5-array) and closed the edge junctions of the array in pairs into superconducting loops (see Fig. 3). This way all junctions of the array are connected in parallel for dc currents. We call this a parallel biased 2D array. The edge loops were designed as coplanar resonators. At the resonance frequency the edge junctions should be strongly electromagnetically coupled. A similar resonant coupling was proposed by Kunkel et al. [5] for series arrays. In analogy to Kunkel et al., we expected resonant eects and a possible reduction of the oscillation linewidth in the vicinity of a resonance. Some of the fabricated circuits were integrated into a stripline geometry as shown schematically in Fig. 3. The array was coupled to another Josephson junction, which served as a frequency and power sensitive radiation detector. The stripline was terminated by a capacitor on one end and by a short in close vicinity of the detector junction on the other end. Figure 4 shows a photograph of the structure in the stage before fabrication of the coupling loop. The fabrication of the ex-situ multilayer structure is described in Section 2. Circuit characterization In Fig. 5(a) the IV curve of one of our parallel biased 2D arrays, measured at 4 K, is shown. This measurements were performed without the coupling structure. Since all 20 junctions are
Fig. 3. Scheme of the investigated parallel biased 2D array with coplanar resonators.
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S. BEUVEN et al.
Fig. 4. Scheme of the investigated parallel biased 2D array with coplanar resonators embedded in a stripline coupling circuit.
connected in parallel for dc currents, one can calculate the critical current per junction to be around 35 mA if self-®eld eects are neglected. The IV curve exhibits a signi®cant structure which indicates resonant eects. The self-induced and equidistant steps on the IV curve are related to the geometric resonances of the coplanar lines. The fundamental resonance frequency was approximately 60 GHz. Steps appeared up to the 10th harmonic (1600 GHz). The position and shape of the second very broad structure seen in the IV depended strongly on the applied magnetic ®eld. This is typical for the so called Fiske resonances in long junctions and Josephson transmission lines. Therefore we attribute this structure to `Fiske'-like resonances inside the rows. Under certain condition this resonance can positively in¯uence the phase locking of junctions as it was shown by Kunkel [6] in a circuit consisting of two coupled junctions.
Fig. 5. (a) Measured IV curve of a parallel biased 2D array at 4 K. Some self induced resonant steps and the `Fiske'-like resonance are marked by arrows. (b) Detected power at 140 GHz (right axis) and correlated IV curve of a parallel biased 2D array. The emission peaks at approximately 290 mV correspond to the receiving frequency.
Shorted 2-dimensional high-TC Josephson arrays for oscillator applications
679
To obtain information about the radiation properties of our arrays we performed a direct radiation detection. For this purpose we coupled the array o-chip via an impedance transformer to a waveguide. The radiation was detected by a sensitive, heterodyne ®xed frequency receiver at 141 GHz. In Fig. 5(b) the detected power is shown together with the corresponding IV curve. Due to the large impedance mismatch between array structure and waveguide system the detected power at 141 GHz was rather low. The detected linewidth diers signi®cantly between the negative and positive branches of the IV curve. This re¯ects the fact that the dierential resistances at the positive and negative branch of the IV curve are dierent (mostly due to the applied magnetic ®eld). In the circuits, where the array was coupled to a detector junction, the dynamical behaviour of the circuits was dominated by another resonant feature. This resonant eect came due to the stripline geometry of the coupling structure. We conclude this from slight resonant steps appearing in the IV curves of both the array and the detector. Operating the array at dierent bias points we measured independently the IV curve of the detector junction. The result is shown in Fig. 6. Clear and sharp Shapiro steps up to the 4th order can be seen in the frequency range from 150 to 200 GHz. This indicates that substantial microwave power ¯ows from the array to
Fig. 6. Detector IV curves for dierent array operating frequencies up to 460 GHz. Shapiro steps are marked by arrows. The single IV curves are shifted along current and voltage axis.
680
S. BEUVEN et al.
the detector junction. Above 200 GHz the number and height of the steps is decreasing, indicating a decrease of power coupled to the detector. Above 500 GHz no signi®cant steps were observed. In the optimum operating range the power was sucient to depress the Ic of the detector junction by approximately 50%. This is the optimum condition to operate the detector junction as a Josephson mixer. It was dicult to estimate the power generated by the array, because coupling coecients are not known and a signi®cant part of the coupled power is dissipated in the terminating short contact. CONCLUSION
We have fabricated and tested two types of two-dimensional arrays with 4 4 and 4 5 highTc step-edge junctions, respectively. With the simple shorted 2D arrays the synchronization between all single rows was demonstrated using a special dc measurement scheme. Due to relatively high Ic spread and strong sensitivity to magnetic ®eld it was very dicult to achieve stable and synchronized operation. Nevertheless, the relatively large locking intervals experimentally observed in certain magnetic ®elds, suggest a strong interaction between the rows. The parallel biased shorted 2D array in connection with resonant eects is a promising candidate for an application where a complete and stable synchronization is required. The evaluation of the IV curves showed, that the electromagnetic interaction via resonances has a signi®cant eect on the dynamic behaviour of the circuit. The mm-wave radiation from this type of array was detected successfully o-chip as well as on-chip. Using the on-chip coupling structure radiation was measured up to 460 GHz and Shapiro steps up to the 4th harmonic were induced in the detector IV curve. In conclusion, we demonstrated successfully a suitable method to synchronize two-dimensional high-Tc arrays and to operate them as mm-wave oscillators. REFERENCES 1. 2. 3. 4.
A.K. Jain, K.K. Likharev, J.E. Lukens and J.E. Sauvageau, Phys. Rep. 109, 309 (1984). M. Darula, S. Beuven, M. Siegel, P. Seidel and A. Darulova, Appl. Phys. Lett. 67, 1618 (1995). S.P. Benz and C.J. Burroughs, Supercond. Sci. Technol. 4, 561 (1991). M. Darula, P. Seidel, J. von Zameck Glyscinski, A. Darulova, F. Busse and S. Benacka, In Applied Superconductivity (Edited by H. C. Freyhardt). DGM Informationsgesellschaft, Oberursel (1993). 5. G. Kunkel, R.H. Ono and A.M. Klushin, Supercond. Sci. Technol. 9, A1 (1996). 6. G. Kunkel, Dynamische Eigenschaften und Wechselwirkungen von Hochtemperatur josephson-kontakten. Ph.D. thesis, BUGH, Wuppertal (1996).