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Physica C 445–448 (2006) 141–145

Film thickness dependence of critical current characteristicsof YBCO-coated conductors

K. Kimura a, M. Kiuchi a, E.S. Otabe a, T. Matsushita a,*, S. Miyata b, A. Ibi b,T. Muroga b, Y. Yamada b, Y. Shiohara c

a Faculty of Computer Science and Systems Engineering, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka 820-8502, Japanb Superconductivity Research Laboratory, 2-4-1 Mutsuno, Atsuta-ku, Nagoya 456-8587, Japan

c Superconductivity Research Laboratory, 1-10-13 Shinonome, Koto-ku, Tokyo 135-0062, Japan

Available online 15 May 2006

Abstract

The dependence of superconducting layer thickness on the critical current characteristics was investigated in the range of 0.5–1.5 lmfor YBCO-coated conductors made by the PLD process. Since the dimension of the pinning is considered to be three as indicated by thepinning correlation length, it is concluded that the observed thickness dependence of the critical current density at low fields come simplyfrom a degradation in the superconducting layer structure with increasing thickness. The irreversibility field and the n-value increase withthe thickness. These dependencies are well described by the theoretical model of the flux creep and flow.� 2006 Elsevier B.V. All rights reserved.

PACS: 74.72.Bk; 74.25.Qt; 74.25.Sv

Keywords: Critical current density; YBCO-coated conductor; Superconducting layer thickness; n-value; Irreversibility field; Flux creep–flow model

1. Introduction

It has been clarified that the critical current density Jc atlow magnetic fields decreases with increasing superconduc-ting layer thickness d for YBCO-coated tapes fabricated bythe PLD process. This is similar to the results on thin filmsdeposited on single crystal substrates [1]. This behaviorseems to be explained by the two-dimensional collectivepinning mechanism for random point pins [2] which pre-dicts as

J c / d�1=2. ð1ÞThe two-dimensional pinning occurs for superconductingthin films of thickness below the pinning correlation lengthl44 approximately given by

0921-4534/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.physc.2006.03.102

* Corresponding author. Tel.: +81 948 29 7663; fax: +81 948 29 7661.E-mail address: matusita@cse.kyutech.ac.jp (T. Matsushita).

l44 ’Baf

2pl0J c

� �1=2

; ð2Þ

where af is the flux line spacing.On the other hand, it has recently been found that the

structure of superconducting layer is deteriorated withappearance of voids and a-axis aligned grains for thickcoated tapes fabricated by the PLD process [3], indicatingthat these defects are the reason for the decrease in the crit-ical current density. In addition, Jc dose not depend on d

appreciably for YBCO-coated tapes fabricated by TFA-MOD method [4]. This suggests that the three-dimensionalpinning mechanism works and seems to be consistent withthe above speculation.

At hight fields, the critical current density shows theopposite thickness dependence: it is higher for a thickersuperconducting tape [5]. This decrease of Jc in thin speci-mens at high temperatures and/or high magnetic fields iscaused by the flux creep. That is, the pinning potentialU0 is small for a thin tape, since the flux bundle volume

10–2 10–1 100 101

108

1010

1012

#3

#2

77.3 K

B (T)

J c (

A/m

2 )

#1

5 K

Fig. 1. Critical current density of the three specimens at 5 K and 77.3 K.

1010

1011

1012

0.1 T

J c (A

/m2 )

5 K20 K50 K60 K

142 K. Kimura et al. / Physica C 445–448 (2006) 141–145

is limited by the thickness d. This indicates that the dimen-sionality of flux pinning becomes two-dimensional at hightemperatures and/or at high magnetic fields. Such a changeoccurs because l44 becomes large due to decreasing Jc atthis region of temperature and magnetic field.

For these reasons the thickness dependence of the criti-cal current density of YBCO-coated tapes is complicatedand the optimum thickness of the superconducting layerwill be different for different conditions of temperature,magnetic field and electric field depending on the kind ofapplication. Hence, it is necessary to clarify all the mecha-nisms which influence the critical current properties and tofind out the method of estimation of Jc for the optimumdesign of superconducting layer thickness for eachapplication.

In this paper, the thickness dependence of YBCO tapesfabricated by the PLD method is investigated in the rangeof 0.5–1.5 lm. In order to clarify the dimensionality ofpinning, the thickness dependence is measured over a widetemperature range to change l44 which determines thedimensionality. The reason for the decrease of Jc withincreasing thickness in PLD processed tapes is discussed.The irreversibility field at high temperatures and the n-valueare compared with the theoretical prediction of the fluxcreep–flow model.

2. Experimental

The specimens were PLD-processed YBCO-coated con-ductors deposited on IBAD substrates with GZO innerlayer and CeO2 cap layer. The thickness of YBCO layerwas 0.5, 1.0 and 1.5 lm. The critical temperature of thesespecimens is listed in Table 1.

The DC magnetization and its relaxation were measuredby a SQUID magnetometer in a magnetic field parallel tothe c-axis of the specimens. Measurements were done upto 7 T over the temperature range of 5–85 K. E–J character-istics were estimated from the relaxation measurements andJc was determined using the electric field criterion ofEc = 1.0 · 10�8 V/m. The irreversibility field was definedby the magnetic field at which Jc reduces to 1.0 · 108

A/m2. The n value was defined in the electric field rangeof E = 10�9–10�8 V/m.

3. Results and discussion

Fig. 1 shows the Jc–B curves of the specimens measuredat 5 and 77.3 K. It is clearly seen that Jc decreases withincreasing d at 5 K and this dependence does not change

Table 1Specification of specimens

Specimen Thickness d (lm) Tc (K)

#1 0.5 88.4#2 1.0 88.2#3 1.5 88.4

with the magnetic field. At 77.3 K, however, the thicknessdependence is much weaker and Jc of the thinnest specimendecreases most rapidly with increasing magnetic field. Thisdecrement of Jc of thin specimens at high temperatures andmagnetic fields is caused by the flux creep.

Fig. 2 shows the thickness dependence of Jc at 0.1 T atvarious temperatures. It is found that Jc obeys Eq. (1) asshown by the straight lines over a wide temperature range.Hence, the two-dimensional collective flux pinning seemsto be realized. However, a simple estimation using Eq.(2) with the Jc-value of specimen #3 reveals that l44 is about0.085 lm at 5 K and is thinner than d over a wide range of

10–1 100 101109

d ( m)

70 K77.3 K80 K

Fig. 2. Thickness dependence of critical current density at 0.1 T at varioustemperatures. Straight lines show the dependence given by Eq. (1).

0 20 40 60 80

10–1

100

T (K)

l 44(

m)

#3

0.1 T

1.5

Fig. 3. Temperature dependence of l44 estimated at 0.1 T with Jc-values ofspecimen 3.

K. Kimura et al. / Physica C 445–448 (2006) 141–145 143

temperature as show in Fig. 3. This shows that the pinningis three-dimensional for which Jc should be independent ofthe thickness. The observed thickness dependence is con-sidered to come from a degradation in the superconductinglayer structure with increasing thickness. This speculationis consistent with the fact that the thickness dependencedoes not change with temperature over a wide range below70 K.

Fig. 4 shows the temperature dependence of the irrevers-ibility field. It is found that the irreversibility field is the

0.7 0.8 0.9 110–1

100

101

T/Tc

Bi (

T)

#2

#3

#1

Jc = 1 x 108 A/m2

Fig. 4. Temperature dependence of irreversibility field.

highest for the thickest specimen #3, and this trend isclearer at a higher temperature. Fig. 5 shows the thicknessdependence of the irreversibility field at 77.3 K. This clearlydemonstrates the advantage of thicker tapes for applica-tions at high magnetic fields.

The critical current properties were analyzed using theflux creep–flow model [6]. The important quantity whichdetermines the pinning property is the pinning potentialU0, and is given by

U 0 ¼0:835g2kBJ 1=2

c0

ð2pÞ3=2B1=4; d > L;

¼ 4:23g2kBJ c0d

2pB1=2; d < L;

ð3Þ

where g2 is the number of flux lines in the flux bundle andJc0 is the virtual critical current density in a creep-free case,and L is the longitudinal flux bundle size given by the pin-ning correlation length in the creep-free case. Thus, underthe influence of the flux creep, L increases to l44. The scal-ing law of Jc0 is assumed as

J c0 ¼ A 1� TT c

� �m

Bc�1 1� BBc2

� �2

; ð4Þ

where A, m, c are the pinning parameters. The pinningparameter A which represents the pinning strength is as-sumed to be statistically distributed as

f ðAÞ ¼ K exp �ðlog A� log AmÞ2

2r2

" #; ð5Þ

10–7 10–6 10–51

2

3

4

5

Bi (

T)

d (m)

77.3 K

Jc = 1x108 A/m2

exp. theo.

Fig. 5. Thickness dependence of irreversibility field at 77.3 K. Solidand open symbols represent the experiment and theoretical results,respectively.

108 109 1010 101110–10

10–9

10–8

10–7

E(V

/m)

J(A/m2)

1 T

3 T

5 T

5 K 20 K

theo.

#2

0.1 T

0.3 T

0.5 T

theo.

70 K 77.3 K

Fig. 6. E–J curves of specimen #2 at low temperatures and hightemperatures. Solid lines are theoretical results.

0 1 20

20

40

d( m)

exp. the.5 K, 5 T

20 K, 5 T

70 K, 0.1 T

144 K. Kimura et al. / Physica C 445–448 (2006) 141–145

where Am is the most probable value of A and r2 is aparameter representing a distribution width and K is a nor-malization constant.

The parameter g2 is determined so as to maximize thecritical current density under the flux creep [7], and is givenby

g2 ¼ g2e

5kBT2U e

logBafm0

Ec

� �� �4=3

; ð6Þ

where g2e is the value of g2 for three-dimensional perfect tri-

angular flux line lattice, Ue is the pinning potential wheng = ge, Ec is the criterion of electric field to determine Jc,and m0 is the attempt frequency of the flux bundle. SinceUe depends on the thickness, g2 depends on the thickness.Recently, it was found that g2 takes a larger value in aBi-2212 superconducting film thinner than the pinning cor-relation length [8]. This means that the transverse flux bun-dle size tends to become large so as to reduce the significanteffect of flux creep in thin films, although Jc0 decreases. Thepinning parameters Am, r, m, c and g2 are adjusted so thatthe calculated E–J curves agree with the experiments. Theobtained parameters are listed in Table 2. g2 of the thinnestspecimen #1 takes a slightly larger value than other two.This behavior is similar to the case of Bi-2212 [8], althoughthe value of g2 is much smaller. This seems to be caused bythe larger value of Ue in Eq. (6) for Y-123.

In Fig. 6 the observed and calculated E–J curves arecompared for specimen #2 at low and high temperatures.It is found that the agreement is good between experimen-tal and theoretical results. The experimental and theoreticalresults of the n value are compared in Fig. 7. Although then value is high and does not appreciably depend on thethickness at 5 K, it becomes smaller and the thicknessdependence becomes stronger at high temperatures. Sucha behavior is exactly explained by the theoretical modelof the flux creep and flow. In Fig. 5 the theoreticallyestimated irreversibility field is compared with the experi-mental results. Although the thickness dependence isappreciable, it is fairly weaker than the simple theoreticalresult in which the variation in g2 is not considered.

Thus, thicker tapes have better performance at highmagnetic fields and/or at high temperatures and are suit-able for applications to superconducting coils such as

Table 2Pinning parameters of specimens in the low and high temperature regions

Specimen Am m r2 (5 K/20 K) c g2

Low temperature regions

#1 6.0 · 1011 2.5 0.0042/0.0048 0.63 3.0#2 4.8 · 1011 2.7 0.0046/0.0049 0.63 2.0#3 4.3 · 1011 2.7 0.0044/0.0045 0.63 2.0

r2 (70 K/77.3 K)High temperature regions

#1 6.6 · 1011 1.4 0.047/0.060 0.53 3.4#2 4.0 · 1011 1.6 0.019/0.023 0.64 2.0#3 2.9 · 1011 1.7 0.013/0.015 0.60 2.0

Fig. 7. Thickness dependence of n value. Solid and open symbolsrepresent the experiment and theoretical results, respectively.

NMR magnets operated in a persistent current mode inhigh magnetic fields.

4. Summary

The dependencies of the critical current density, irrevers-ibility field and n-value on the thickness of superconductinglayer were investigated for YBCO-coated tapes fabricatedby the PLD method. It was found that the estimated pin-

K. Kimura et al. / Physica C 445–448 (2006) 141–145 145

ning correlation length was much thinner than the thicknessover a wide range of temperature. Hence, it can be con-cluded that the observed pinning is the three-dimensionalone. Hence, the observed thickness dependence of thecritical current density at low fields is attributed to a degra-dation in the superconducting layer structure in PLD-pro-cessed tapes with increasing thickness. This is consistentwith the fact that the observed thickness dependence doesnot change over a wide range of temperature below 70 K.At high temperatures, the irreversibility field and the n-value increased with increasing thickness. These behaviorscan be explained by the flux creep–flow model. Thus, forthe better performance at high temperatures and/or at highmagnetic fields the thicker tapes are more suitable.

Acknowledgements

This work is partly supported by the New Energy andTechnology Development Organization (NEDO) as Col-

laborative Research and Development of FundamentalTechnologies for Superconductivity Applications.

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