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Voltage–current characteristics of c-axis oriented YBa2Cu3O7−δ films deposited by dc sputtering
Physica C 340 (2000) 225±229
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Voltage±current characteristics of c-axis oriented YBa2Cu3O7ÿd ®lms deposited by dc sputtering q A. De Santis a, G. Grimaldi a, U. Gambardella a,*,1, S. Pace a, A.M. Cucolo a, M.C. Cucolo a, V. Boa b, G. Celentano b, F. Fabbri b a
INFM Research Unit, Department of Physics, University of Salerno, VS Allende, 84081 SA Baronissi, Italy b ENEA Frascati, v. E. Fermi 65, 00044 Frascati, Italy Received 5 April 2000; received in revised form 31 May 2000; accepted 8 June 2000
Abstract We analyze the voltage±current characteristics of high quality c-axis oriented YBa2 Cu3 O7ÿd ®lms with Tc0 91 K. The ®lms were dc sputtered in a pure oxygen atmosphere on SrTiO3 (1 0 0) substrates and then patterned in a shape of a long strip. The voltage±current characteristics are modeled with single or multiple Gaussian distributions of depinning currents. We derive the distribution features as a function of the applied magnetic ®eld at dierent temperatures. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 74.76.Bz; 74.60.Ge; 74.60.Jg Keywords: HTc ®lm; Critical current; Pinning
1. Introduction The experimental behavior of the voltage±current (V±I ) curves recorded across a superconducting strip is usually analyzed to investigate the ¯ux motion which gives rise to the bending of the V±I curve near the critical current value. Beside the thermal activation, this bending has also been ascribed to statistical ¯uctuations of some parameter which modify the critical current value: q Work partially supported by MURST/CONFIN98 program. * Corresponding author. Tel.: +39-089-96-5308; fax: +39-09953804. E-mail address: [email protected] (U. Gambardella). 1 Permanent address: INFN Frascati National Laboratory, v. E. Fermi 40, 00044 Frascati, Italy.
variation of the vortex±vortex interaction [1], grain-to-grain dispersion of the grain boundary angles [2], local critical current distribution expressed by an integrated Weibull function [3]. Moreover, the low voltage portion of the V±I curve is usually analyzed to investigate the socalled vortex glass±liquid transition. This transition features a crossover from downturning to upturning in the log±log plot of the V±I characteristics, and a critical exponent which collapse the curves to an universal curve [4]. Recently, Brown showed that these features also occurs in V±I characteristics computed by assuming a simple Gaussian distribution in the depinning currents of the superconducting YBa2 Cu3 O7ÿd (YBCO) [5]. In this work, following Warnes and Larbalestier [6], Edelman and Larbalestier [7], we derive the Gaussian distributions for the depinning currents
0921-4534/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 0 ) 0 1 3 3 6 - 8
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A. De Santis et al. / Physica C 340 (2000) 225±229
from the experimental V±I characteristics. In this approach, the bending of the V±I characteristics, occurring from the zero voltage state to the linear voltage±current behavior comes from the superimposition of ideal V±I superconducting characteristics, i.e., zero voltage up to the critical current Ic , and a linear increasing voltage above Ic , V R I ÿ Ic . Our analysis concerns measurements of the V±I curves performed on high quality sputter deposited c-axis oriented YBCO ®lms, as a function of the applied magnetic ®eld up to 12 T, and at dierent temperatures, in the 90±65 K range. The zero resistance critical temperature Tc0 and the critical current density Jc (77 K, 0 T) of the ®lms we measured are Tc0 91 K and Jc 5 106 A/cm2 , respectively. In Section 2, we brie¯y describe the fabrication of the ®lms, outline the measurement conditions showing the measured superconducting features. In Section 3, we analyze the V±I curves by using a Gaussian distribution for the depinning currents to interpolate data and extract the behavior of the distribution parameters as a function of the temperature and applied ®eld. Conclusions are summarized in Section 4.
loaded into an He gas ¯ow cryostat provided with a superconducting magnet. In this condition, the applied magnetic ®eld H was parallel to the c-axis of the ®lms, and perpendicular to the bias current. The resistive transition of the ®lms was checked during the sample cool down. The measured resistivity is q 0:28 mX cm at room temperature and q 0:09 mX cm at 100 K. The V±I curves have been recorded for dierent values of the applied magnetic ®eld at ®xed temperatures. The voltages were always computed as the V and Vÿ average, being V and Vÿ the voltages recorded with direct and inverse bias current, respectively. In this way, the voltage stability during the measurements is 100 nV. Though this sensitivity is not very high, it is enough to detect the electric ®eld E 1 lV/cm used to determine the critical current density value. The maximum bias current available in these measurements was limited to 0.1 A, thus at temperatures below 83 K, a magnetic
2. Film processing and measurements The ®lms were grown on SrTiO3 (1 0 0) substrates by means of planar dc sputtering in a pure O2 atmosphere [8]. The substrate temperature was 910°C and the oxygen pressure 300 Pa. The oxygenation process takes place at 560°C in 100 kPa of oxygen for 15 min. The epitaxial orientation of the ®lms has been checked by XRD; the x scan around the 0 0 5 peak had a full width half maximum (FWHM) 0.3, and the in-plane alignment was veri®ed from the polar ®gure around the (1 1 3) direction. The samples have then been processed with usual UV photolithography and ion beam etching [9] to obtain a 2 mm long strips, 30 or 50 lm wide. The ®lm thickness d, measured by a stylus pro®lometer, is d 160 nm. The contact pads were ®rst cleaned by argon etching, and then covered by a 0.5 lm thick silver layer deposited through a metallic mask. The samples were then put on the top loading sample holder and
Fig. 1. (a) Resistive transition of the 50 lm width YBCO strip. In the inset the transition region is magni®ed. (b) The critical current density as a function of the applied magnetic ®eld for the same sample at dierent temperatures.
A. De Santis et al. / Physica C 340 (2000) 225±229
®eld had to be applied to reduce the critical current of the samples. Low bias currents are necessary when measuring in a gas ¯ow environment, to minimize heating eects. In addition, we limited the highest voltage below 100 lV. The zero ®eld value of Jc at 77 K was recorded in a LN2 bath. Fig. 1a and b show, respectively, the resistive transition q T of the YBCO sample, and the corresponding Jc H behavior at dierent temperatures. The zero resistance critical temperature is Tc0 90:5 K, with a DTc 0:7 K. From the Jc H curves, we extrapolated the critical ®elds H~ , corresponding to Jc H~ 0. In Fig. 2, a set of the E±J characteristics recorded at T 77 K for dierent applied magnetic ®elds is shown. In Fig. 3, the temperature scaling of the pinning force Fp Jc H as measured in two samples having dierent widths is shown. The curves are normalized to the
227
maximum pinning force, and to the critical ®eld H~ T on the y and x axes, respectively. The maximum pinning force occurs at a reduced ®eld 0.2. The normalized data are very similar to the one recorded in high-j low Tc material, such as NbN [10], or NbZr [11]. The high ®eld behavior of the reduced Fp has a typical 1 ÿ H =H~ 2 shape. In the framework of the Kramer model, this suggests the presence of a large number of strong pinning centers [12]. 3. Analysis It has been reported that the voltage across a superconducting wire can be written as [7] Z I I ÿ I 0 f I 0 dI 0 ; 1 V G 0
where G accounts for the normalizing factor, and f I is the distribution of the depinning currents, which is normalized to unity. Brown simulated the V±I characteristics at dierent temperatures by using Eq. (1) with suitable Gaussian distribution parameters, J0 T and the standard deviation r T in the general distribution function: ! 2 J ÿ J0 : 2 f / exp ÿ 2r2 Fig. 2. V±I curves recorded at 77 K for dierent magnetic ®eld values in a 50 lm wide YBCO strip.
Brown showed how these curves have the typical behavior of the vortex glass±liquid transition, despite to the fact that there is not any reference to the vortex glass model [5]. From the experimental point of view, the depinning current distribution can be extracted from the data by using [6] d2 V Gf I: dI 2
Fig. 3. Reduced pinning force vs. reduced critical ®eld for two dierent samples at two dierent temperatures: (d, m) 85 K and (s, 4) 77 K (circles and triangles refer to 50 and 30 lm wide strip, respectively).
3
The function f(I) is usually computed performing a dierential smoothing of the experimental data. Fig. 4a and b show the V±I characteristics recorded at 85 K and H 0:2 and 1 T, respectively. The dashed lines are the corresponding second derivatives. The two ®eld values correspond to reduced ®elds H =H~ 0:1 and 0.4. For the same reduced ®elds, we observed similar curve shapes at 77 and 65 K. Therefore, the shape
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A. De Santis et al. / Physica C 340 (2000) 225±229
Fig. 5. V±I characteristic of YBCO at 85 K and 1 T ( ). Solid line is the ®t of the V±I by using Eq. (5) and six Gaussian distributions, while the dashed line is the same ®t by using Eq. (1) with only one Gaussian distribution.
Fig. 4. V±I characteristics of YBCO at 85 K: (a) 0.2 and (b) 1 T. The dashed lines are the corresponding second derivatives.
of the V±I characteristics are dierent for the same Fp value in the low ®eld and high ®eld region. In fact, in the ®rst case, the f I computed by Eq. (3) had one marked peak, and the data can be ®tted by a simple Gaussian distribution, from which a J0 and r is derived. In the second case, the curves showed many peaks. Previously reported f I also, concerning Nb±Ti multi®lamentary wires, are far from a simple Gaussian distribution, showing a principal peak with satellite peaks distributed over a range of currents [6]. We noted the occurrence of more complex shape in the d2 V =dI 2 vs. I as the reduced ®eld increases. In order to take into account, this eect to ®t the experimental data we assumed a sum of dierent Gaussian distributions for the depinning currents. In Fig. 5, the ®t of the V±I curve shown in Fig. 4b is reported. The dashed line represents the ®t computed by Eq. (1), where r is just the one computed from the Gaussian distribution f I which ®ts the main peak of the experimental d2 V =dI 2 vs. I. The solid line instead is the ®t computed from six contributions to the voltage: V V1 V6
4
being each Vi the voltage computed as Z I I ÿ I 0 fi I 0 dI 0 ; Vi Gi 0
5
and the coecients G1;...;6 weight the Gaussian areas. The fi I are the Gaussian distributions which ®t the six peaks in the experimental d2 V =dI 2 vs. I curve. This latter method gives a better ®t for all the three temperatures we investigated, 85, 77, and 65 K. Besides the meaning of the multiple Gaussian ®t, which is just a ®tting process, the presence of a complex structure in the d2 V =dI 2 vs. I curve should have a physical meaning. The fact that at high magnetic ®elds multiple mechanisms in the depinning of the ¯uxons becomes apparent may be, in a ®rst approximation, ascribed to (1) the enhanced number of moving ¯uxons, inducing higher voltages makes the dynamics visible with the actual sensitivity and (2) the variation in the ¯uxon±¯uxon interactions give rise to dierent kinds of ¯uxon dynamics. We emphasize that our analysis focuses on the V±I characteristic shape as a function of the applied magnetic ®eld under two well separate conditions, but actually we consider these as two limiting behaviors. The role of the magnetic ®eld may be of amplifying the observed phenomena or inducing it, or both, as discussed above. In the low ®eld region, below the maximum Fp , we have analyzed the behavior of the r increasing
A. De Santis et al. / Physica C 340 (2000) 225±229
229
the depinning current distribution features, in the low ®eld region. We found that the distribution narrows while increasing the ®eld. The presence of multiple depinning mechanisms even at low ®elds, as well as the role of the magnetic ®eld in generating this eect, is still an open question. Acknowledgements
Fig. 6. Behavior of r at three dierent temperatures in the low ®eld region.
the ®eld. In Fig. 6, the value of the single Gaussian amplitude r, as a function of the reduced applied ®eld, at three temperatures is shown. We found a reduction of the current distribution amplitude as the ®eld increases. In connection to the above discussion, within the limit of the experimental data, we may argue that a splitting in the random depinning mechanisms occurs as the ®eld increases. 4. Conclusions We have analyzed the V±I curves of YBCO ®lms having critical current densities in excess of 5 106 A/cm2 at 77 K. A temperature scaling of the pinning force is observed. The V±I curves are ®tted using a Gaussian distribution of the depinning currents, which is derived from the dierential smoothing of the experimental data. Two dierent behaviors have been found depending on the applied magnetic ®eld value. When the pinning force increases with increasing ®eld, a single Gaussian distribution can be used to ®t data. When the pinning force decreases when increasing the ®eld multiple Gaussian distributions have to be considered to get a better data ®t. Finally, we analyzed
We are grateful to A. Ferrentino for his invaluable technical support. We also wish to thank M. Boa, C. Beneduce for their support in the ®lms fabrication, and Prof. M. Cirillo (University of Rome Tor Vergata) for making the photolithographic masks. References [1] R. W ordenweber, Phys. Rev. B 46 (1992) 3076. [2] J.E. Evetts, M.J. Hogg, B.A. Glowacki, N.A. Rutter, V.N. Tsaneva, Supercond. Sci. Technol. 12 (1999) 1050. [3] F. Irie, Y. Tsujioka, T. Chiba, Supercond. Sci. Technol. 5 (1992) S379. [4] R. Koch, V. Foglietti, W.J. Gallagher, G. Koren, A. Gupta, M.P.A. Fisher, Phys. Rev. Lett. 63 (1989) 1511. [5] B. Brown, Phys. Rev. B 61 (2000) 3267. [6] W.H. Warnes, D.C. Larbalestier, Appl. Phys. Lett. 48 (1986) 1403. [7] H.S. Edelman, D.C. Larbalestier, J. Appl. Phys. 74 (1993) 3312. [8] C. Beneduce, F. Bobba, A.M. Cucolo, M.C. Cucolo, W. Evers, Int. J. Mod. Phys. B 13 (1999) 1005. [9] C. Beneduce, F. Bobba, M. Boa, A.M. Cucolo, M.C. Cucolo, U. Gambardella, R. Monaco, Presented at the 4th European Conference on Applied Superconductivity (EUCAS Õ99), September 14±27, 1999, Sitges, Spain Proc. EUCAS 1999 Conf., in press. [10] V. Boa, U. Gambardella, V. Marotta, A. Morone, F. Murtas, S. Orlando, G.P. Parisi, Appl. Surf. Sci. 106 (1996) 361. [11] U. Gambardella, D. Di Gioacchino, V. Boa, G. Paterno', S. Barbanera, F. Murtas, IEEE Appl. Supercond. 3 (1993) 1253. [12] E.J. Kramer, J. Appl. Phys. 44 (1973) 1360.
www.elsevier.nl/locate/physc
Voltage±current characteristics of c-axis oriented YBa2Cu3O7ÿd ®lms deposited by dc sputtering q A. De Santis a, G. Grimaldi a, U. Gambardella a,*,1, S. Pace a, A.M. Cucolo a, M.C. Cucolo a, V. Boa b, G. Celentano b, F. Fabbri b a
INFM Research Unit, Department of Physics, University of Salerno, VS Allende, 84081 SA Baronissi, Italy b ENEA Frascati, v. E. Fermi 65, 00044 Frascati, Italy Received 5 April 2000; received in revised form 31 May 2000; accepted 8 June 2000
Abstract We analyze the voltage±current characteristics of high quality c-axis oriented YBa2 Cu3 O7ÿd ®lms with Tc0 91 K. The ®lms were dc sputtered in a pure oxygen atmosphere on SrTiO3 (1 0 0) substrates and then patterned in a shape of a long strip. The voltage±current characteristics are modeled with single or multiple Gaussian distributions of depinning currents. We derive the distribution features as a function of the applied magnetic ®eld at dierent temperatures. Ó 2000 Elsevier Science B.V. All rights reserved. PACS: 74.76.Bz; 74.60.Ge; 74.60.Jg Keywords: HTc ®lm; Critical current; Pinning
1. Introduction The experimental behavior of the voltage±current (V±I ) curves recorded across a superconducting strip is usually analyzed to investigate the ¯ux motion which gives rise to the bending of the V±I curve near the critical current value. Beside the thermal activation, this bending has also been ascribed to statistical ¯uctuations of some parameter which modify the critical current value: q Work partially supported by MURST/CONFIN98 program. * Corresponding author. Tel.: +39-089-96-5308; fax: +39-09953804. E-mail address: [email protected] (U. Gambardella). 1 Permanent address: INFN Frascati National Laboratory, v. E. Fermi 40, 00044 Frascati, Italy.
variation of the vortex±vortex interaction [1], grain-to-grain dispersion of the grain boundary angles [2], local critical current distribution expressed by an integrated Weibull function [3]. Moreover, the low voltage portion of the V±I curve is usually analyzed to investigate the socalled vortex glass±liquid transition. This transition features a crossover from downturning to upturning in the log±log plot of the V±I characteristics, and a critical exponent which collapse the curves to an universal curve [4]. Recently, Brown showed that these features also occurs in V±I characteristics computed by assuming a simple Gaussian distribution in the depinning currents of the superconducting YBa2 Cu3 O7ÿd (YBCO) [5]. In this work, following Warnes and Larbalestier [6], Edelman and Larbalestier [7], we derive the Gaussian distributions for the depinning currents
0921-4534/00/$ - see front matter Ó 2000 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 0 ) 0 1 3 3 6 - 8
226
A. De Santis et al. / Physica C 340 (2000) 225±229
from the experimental V±I characteristics. In this approach, the bending of the V±I characteristics, occurring from the zero voltage state to the linear voltage±current behavior comes from the superimposition of ideal V±I superconducting characteristics, i.e., zero voltage up to the critical current Ic , and a linear increasing voltage above Ic , V R I ÿ Ic . Our analysis concerns measurements of the V±I curves performed on high quality sputter deposited c-axis oriented YBCO ®lms, as a function of the applied magnetic ®eld up to 12 T, and at dierent temperatures, in the 90±65 K range. The zero resistance critical temperature Tc0 and the critical current density Jc (77 K, 0 T) of the ®lms we measured are Tc0 91 K and Jc 5 106 A/cm2 , respectively. In Section 2, we brie¯y describe the fabrication of the ®lms, outline the measurement conditions showing the measured superconducting features. In Section 3, we analyze the V±I curves by using a Gaussian distribution for the depinning currents to interpolate data and extract the behavior of the distribution parameters as a function of the temperature and applied ®eld. Conclusions are summarized in Section 4.
loaded into an He gas ¯ow cryostat provided with a superconducting magnet. In this condition, the applied magnetic ®eld H was parallel to the c-axis of the ®lms, and perpendicular to the bias current. The resistive transition of the ®lms was checked during the sample cool down. The measured resistivity is q 0:28 mX cm at room temperature and q 0:09 mX cm at 100 K. The V±I curves have been recorded for dierent values of the applied magnetic ®eld at ®xed temperatures. The voltages were always computed as the V and Vÿ average, being V and Vÿ the voltages recorded with direct and inverse bias current, respectively. In this way, the voltage stability during the measurements is 100 nV. Though this sensitivity is not very high, it is enough to detect the electric ®eld E 1 lV/cm used to determine the critical current density value. The maximum bias current available in these measurements was limited to 0.1 A, thus at temperatures below 83 K, a magnetic
2. Film processing and measurements The ®lms were grown on SrTiO3 (1 0 0) substrates by means of planar dc sputtering in a pure O2 atmosphere [8]. The substrate temperature was 910°C and the oxygen pressure 300 Pa. The oxygenation process takes place at 560°C in 100 kPa of oxygen for 15 min. The epitaxial orientation of the ®lms has been checked by XRD; the x scan around the 0 0 5 peak had a full width half maximum (FWHM) 0.3, and the in-plane alignment was veri®ed from the polar ®gure around the (1 1 3) direction. The samples have then been processed with usual UV photolithography and ion beam etching [9] to obtain a 2 mm long strips, 30 or 50 lm wide. The ®lm thickness d, measured by a stylus pro®lometer, is d 160 nm. The contact pads were ®rst cleaned by argon etching, and then covered by a 0.5 lm thick silver layer deposited through a metallic mask. The samples were then put on the top loading sample holder and
Fig. 1. (a) Resistive transition of the 50 lm width YBCO strip. In the inset the transition region is magni®ed. (b) The critical current density as a function of the applied magnetic ®eld for the same sample at dierent temperatures.
A. De Santis et al. / Physica C 340 (2000) 225±229
®eld had to be applied to reduce the critical current of the samples. Low bias currents are necessary when measuring in a gas ¯ow environment, to minimize heating eects. In addition, we limited the highest voltage below 100 lV. The zero ®eld value of Jc at 77 K was recorded in a LN2 bath. Fig. 1a and b show, respectively, the resistive transition q T of the YBCO sample, and the corresponding Jc H behavior at dierent temperatures. The zero resistance critical temperature is Tc0 90:5 K, with a DTc 0:7 K. From the Jc H curves, we extrapolated the critical ®elds H~ , corresponding to Jc H~ 0. In Fig. 2, a set of the E±J characteristics recorded at T 77 K for dierent applied magnetic ®elds is shown. In Fig. 3, the temperature scaling of the pinning force Fp Jc H as measured in two samples having dierent widths is shown. The curves are normalized to the
227
maximum pinning force, and to the critical ®eld H~ T on the y and x axes, respectively. The maximum pinning force occurs at a reduced ®eld 0.2. The normalized data are very similar to the one recorded in high-j low Tc material, such as NbN [10], or NbZr [11]. The high ®eld behavior of the reduced Fp has a typical 1 ÿ H =H~ 2 shape. In the framework of the Kramer model, this suggests the presence of a large number of strong pinning centers [12]. 3. Analysis It has been reported that the voltage across a superconducting wire can be written as [7] Z I I ÿ I 0 f I 0 dI 0 ; 1 V G 0
where G accounts for the normalizing factor, and f I is the distribution of the depinning currents, which is normalized to unity. Brown simulated the V±I characteristics at dierent temperatures by using Eq. (1) with suitable Gaussian distribution parameters, J0 T and the standard deviation r T in the general distribution function: ! 2 J ÿ J0 : 2 f / exp ÿ 2r2 Fig. 2. V±I curves recorded at 77 K for dierent magnetic ®eld values in a 50 lm wide YBCO strip.
Brown showed how these curves have the typical behavior of the vortex glass±liquid transition, despite to the fact that there is not any reference to the vortex glass model [5]. From the experimental point of view, the depinning current distribution can be extracted from the data by using [6] d2 V Gf I: dI 2
Fig. 3. Reduced pinning force vs. reduced critical ®eld for two dierent samples at two dierent temperatures: (d, m) 85 K and (s, 4) 77 K (circles and triangles refer to 50 and 30 lm wide strip, respectively).
3
The function f(I) is usually computed performing a dierential smoothing of the experimental data. Fig. 4a and b show the V±I characteristics recorded at 85 K and H 0:2 and 1 T, respectively. The dashed lines are the corresponding second derivatives. The two ®eld values correspond to reduced ®elds H =H~ 0:1 and 0.4. For the same reduced ®elds, we observed similar curve shapes at 77 and 65 K. Therefore, the shape
228
A. De Santis et al. / Physica C 340 (2000) 225±229
Fig. 5. V±I characteristic of YBCO at 85 K and 1 T ( ). Solid line is the ®t of the V±I by using Eq. (5) and six Gaussian distributions, while the dashed line is the same ®t by using Eq. (1) with only one Gaussian distribution.
Fig. 4. V±I characteristics of YBCO at 85 K: (a) 0.2 and (b) 1 T. The dashed lines are the corresponding second derivatives.
of the V±I characteristics are dierent for the same Fp value in the low ®eld and high ®eld region. In fact, in the ®rst case, the f I computed by Eq. (3) had one marked peak, and the data can be ®tted by a simple Gaussian distribution, from which a J0 and r is derived. In the second case, the curves showed many peaks. Previously reported f I also, concerning Nb±Ti multi®lamentary wires, are far from a simple Gaussian distribution, showing a principal peak with satellite peaks distributed over a range of currents [6]. We noted the occurrence of more complex shape in the d2 V =dI 2 vs. I as the reduced ®eld increases. In order to take into account, this eect to ®t the experimental data we assumed a sum of dierent Gaussian distributions for the depinning currents. In Fig. 5, the ®t of the V±I curve shown in Fig. 4b is reported. The dashed line represents the ®t computed by Eq. (1), where r is just the one computed from the Gaussian distribution f I which ®ts the main peak of the experimental d2 V =dI 2 vs. I. The solid line instead is the ®t computed from six contributions to the voltage: V V1 V6
4
being each Vi the voltage computed as Z I I ÿ I 0 fi I 0 dI 0 ; Vi Gi 0
5
and the coecients G1;...;6 weight the Gaussian areas. The fi I are the Gaussian distributions which ®t the six peaks in the experimental d2 V =dI 2 vs. I curve. This latter method gives a better ®t for all the three temperatures we investigated, 85, 77, and 65 K. Besides the meaning of the multiple Gaussian ®t, which is just a ®tting process, the presence of a complex structure in the d2 V =dI 2 vs. I curve should have a physical meaning. The fact that at high magnetic ®elds multiple mechanisms in the depinning of the ¯uxons becomes apparent may be, in a ®rst approximation, ascribed to (1) the enhanced number of moving ¯uxons, inducing higher voltages makes the dynamics visible with the actual sensitivity and (2) the variation in the ¯uxon±¯uxon interactions give rise to dierent kinds of ¯uxon dynamics. We emphasize that our analysis focuses on the V±I characteristic shape as a function of the applied magnetic ®eld under two well separate conditions, but actually we consider these as two limiting behaviors. The role of the magnetic ®eld may be of amplifying the observed phenomena or inducing it, or both, as discussed above. In the low ®eld region, below the maximum Fp , we have analyzed the behavior of the r increasing
A. De Santis et al. / Physica C 340 (2000) 225±229
229
the depinning current distribution features, in the low ®eld region. We found that the distribution narrows while increasing the ®eld. The presence of multiple depinning mechanisms even at low ®elds, as well as the role of the magnetic ®eld in generating this eect, is still an open question. Acknowledgements
Fig. 6. Behavior of r at three dierent temperatures in the low ®eld region.
the ®eld. In Fig. 6, the value of the single Gaussian amplitude r, as a function of the reduced applied ®eld, at three temperatures is shown. We found a reduction of the current distribution amplitude as the ®eld increases. In connection to the above discussion, within the limit of the experimental data, we may argue that a splitting in the random depinning mechanisms occurs as the ®eld increases. 4. Conclusions We have analyzed the V±I curves of YBCO ®lms having critical current densities in excess of 5 106 A/cm2 at 77 K. A temperature scaling of the pinning force is observed. The V±I curves are ®tted using a Gaussian distribution of the depinning currents, which is derived from the dierential smoothing of the experimental data. Two dierent behaviors have been found depending on the applied magnetic ®eld value. When the pinning force increases with increasing ®eld, a single Gaussian distribution can be used to ®t data. When the pinning force decreases when increasing the ®eld multiple Gaussian distributions have to be considered to get a better data ®t. Finally, we analyzed
We are grateful to A. Ferrentino for his invaluable technical support. We also wish to thank M. Boa, C. Beneduce for their support in the ®lms fabrication, and Prof. M. Cirillo (University of Rome Tor Vergata) for making the photolithographic masks. References [1] R. W ordenweber, Phys. Rev. B 46 (1992) 3076. [2] J.E. Evetts, M.J. Hogg, B.A. Glowacki, N.A. Rutter, V.N. Tsaneva, Supercond. Sci. Technol. 12 (1999) 1050. [3] F. Irie, Y. Tsujioka, T. Chiba, Supercond. Sci. Technol. 5 (1992) S379. [4] R. Koch, V. Foglietti, W.J. Gallagher, G. Koren, A. Gupta, M.P.A. Fisher, Phys. Rev. Lett. 63 (1989) 1511. [5] B. Brown, Phys. Rev. B 61 (2000) 3267. [6] W.H. Warnes, D.C. Larbalestier, Appl. Phys. Lett. 48 (1986) 1403. [7] H.S. Edelman, D.C. Larbalestier, J. Appl. Phys. 74 (1993) 3312. [8] C. Beneduce, F. Bobba, A.M. Cucolo, M.C. Cucolo, W. Evers, Int. J. Mod. Phys. B 13 (1999) 1005. [9] C. Beneduce, F. Bobba, M. Boa, A.M. Cucolo, M.C. Cucolo, U. Gambardella, R. Monaco, Presented at the 4th European Conference on Applied Superconductivity (EUCAS Õ99), September 14±27, 1999, Sitges, Spain Proc. EUCAS 1999 Conf., in press. [10] V. Boa, U. Gambardella, V. Marotta, A. Morone, F. Murtas, S. Orlando, G.P. Parisi, Appl. Surf. Sci. 106 (1996) 361. [11] U. Gambardella, D. Di Gioacchino, V. Boa, G. Paterno', S. Barbanera, F. Murtas, IEEE Appl. Supercond. 3 (1993) 1253. [12] E.J. Kramer, J. Appl. Phys. 44 (1973) 1360.