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Spatial distribution of the local resistive transition and the critical current density in YBCO coated conductors using Low-temperature Scanning Laser Microscopy
Cryogenics 51 (2011) 241–246
Contents lists available at ScienceDirect
Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Spatial distribution of the local resistive transition and the critical current density in YBCO coated conductors using Low-temperature Scanning Laser Microscopy S.K. Park, J.M. Kim, S.B. Lee, S.H. Kim, G.Y. Kim, H.-C. Ri * Dept. of Physics, Kyungpook National University, 1370 Sangyeok-Dong, Buk-Gu, Daegu 702-701, Republic of Korea
a r t i c l e
i n f o
Article history: Available online 11 June 2010 Keywords: D. LTSLM A. YBCO A. Coated conductor C. Critical temperature C. Critical current density
a b s t r a c t Low-temperature Scanning Laser Microscopy (LTSLM) was carried out to reveal the spatial distribution of the local resistive transition temperature and the local current density in commercial YBCO coated conductors near the superconducting transition. The result of the sample with an array of holes of various sizes shows that the signal dV is proportional to the current density. The distribution of the critical temperature of the sample with two parallel bridges is quite homogeneous and the transport current flows mainly along the outer edge of the sample. Using LTSLM we directly image the current path in YBCO coated conductors of different patterns. Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved.
1. Introduction High critical current density and high critical temperature are required for large scale applications of superconductors. Many experiments have shown that the critical current density of high temperature superconductors is influenced by the microstructure of the materials [1,2]. In many studies of superconducting thin films and coated conductors, the properties of samples such as critical temperature and critical current density represented average value of the whole sample. They did not offer the information of local properties. Therefore, it is important to develop methods or equipments for analyzing the spatial distribution of local critical temperature and critical current density [3–12]. For electrical power applications of superconductors, AC losses are of crucial importance. The width of YBCO coated conductors 2w is typically 0.4–1 cm. Since hysteresis losses per unit length are proportional to w2, AC losses of planar superconducting film in perpendicular magnetic field are quite high. To reduce hysteresis losses, considerable efforts are being made to develop periodically arranged multi-strip type as the geometry of superconducting thin film [13–16]. Recently, direct visualization of the local transport properties in the YBCO coated conductors has been performed by LTSLM [17], low-temperature scanning SQUID microscopy [18], low-temperature scanning electron microscopy [19]. Especially, LTSLM is a powerful tool for measuring the local superconducting properties using focused laser beam in transport measurement. * Corresponding author. Fax: +82 53 952 1739. E-mail address: [email protected] (H.-C. Ri).
In this study, we used LTSLM to investigate local superconducting properties in YBCO coated conductors with different geometry. The spatial distribution of the local resistive transition and the local current density of YBCO layers are analyzed. 2. Experimental 2.1. Specifications of the LTSLM Fig. 1 shows schematic diagram of LTSLM. The principle of LTSLM measurement is to detect the local bolometric response induced by the laser beam. For precise measurements of local properties in superconducting samples using LTSLM, the temperature stability is of importance. To improve the temperature stability, we modified our cooling system into a double-shielding type and achieved the stability of ±2 mK. A laser beam (wavelength 660 nm) is coupled into an optical fiber and modulated at 3 kHz using a standard mechanical chopper. The modulated laser beam is focused on the sample surface by an objective lens having 30.5 mm of working distance and 0.28 of numerical aperture. The minimum spot size of the focused laser beam is 3 lm. The spatial resolution of LTSLM is determined, however, mainly by the thermal healing length K of the laser beam induced temperature field. Since the characteristic length K is proportional to the output power of the laser beam [19], we minimized the power of laser beam to get better resolution. The optical fiber and lens are fixed to a three-axis motorized stage which focuses the laser beam and scans on the sample surface in horizontal and vertical direction. The voltage response is measured by a lock-in with a pre-amplifier.
0011-2275/$ - see front matter Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2010.06.004
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S.K. Park et al. / Cryogenics 51 (2011) 241–246
Cryostat
3. Results and discussion
Laser beam GPIB or serial
Heater & Temp. sensor Sample holder Sample
Electrical signal
Current source Temp. controller Lock-in Amplifier
Focusing devices
The temperature dependence of the resistivity is shown in Fig. 3a. In the inset is shown the enlargement of the superconducting transition region. The sample has the critical temperature Tc0 (R = 0 X) of 89.5 K with the transition width of 1.4 K. Fig. 3b shows the temperature dependence of @ q/@T at different bias currents. While the laser beam was fixed at a certain position, the temperature was slowly increased and the voltage response was acquired. The voltage signal dV which is measured using LTSLM can be expressed as [19]
dVðx; yÞ J B ðx; yÞ
Motorized XYZ stage
PC
Laser & Lens Optical fiber Fig. 1. Schematic diagram of the LTSLM.
2.2. Specifications of the samples The samples analyzed by LTSLM are commercial YBCO coated conductors which were produced by Superpower, Inc. SCS4050 model (surround copper stabilizer) was used for the sample A and SF12100 model (stabilizer free) was used for the sample B. We could improve the contrast and spatial resolution by removing the copper stabilizer and Ag overlayer, which covered YBCO film. After removal of cover layers, YBCO layer was patterned by wetetching process. Fig. 2 shows the geometry of YBCO layer of the sample. The bridge width of the sample A is 260 lm. In order to regulate the effective width of the bridge, square and circular holes with different sizes from 50 lm to 130 lm are arrayed in the bridge. We patterned the sample B into two parallel 260 lm wide bridges. The interval between two bridges is 140 lm. The thickness of the YBCO layer of two samples is about 1 lm.
(a) Sample A
3.1. Sample A
(b) Sample B
Fig. 2. YBCO layer geometry of the samples A and B.
@ qðx; yÞ KdT 0 @T
ð1Þ
where JB(x, y) is the local current density, @ q(x, y)/@T is the derivative of resistivity with respect to temperature, K is the characteristic length of the laser beam induced temperature field and dT0 is the laser beam induced temperature increment, respectively. Based on the assumption that KdT0 is about constant for all sample positions, the measured signal dV normalized by the bias current can be expressed as @ q/@T. The non-zero @ q/@T at bias current of 10 mA was detected first at 89.45 K. Though the temperature was kept below Tc0, the sample was heated up by the irradiated laser beam and became locally resistive. Because the critical temperature Tc0 is 89.5 K, we can estimate that the temperature increment due to the laser beam irradiation is approximately 50 mK. With increasing temperature from below critical temperature, dV reaches its maximum value at a certain temperature. We define dVmax as the maximum of dV and T max as the temperature where dV is a maximum, c respectively. Fig. 4 shows 2D images from LTSLM measurements at various temperatures. 2D images of dV were gathered at the center part of the sample and the scan area was 750 lm 420 lm. The legend indicates the magnitude of voltage response dV measured by lockin. For all images of Fig. 4 are used the same legend. Arrows indicate the region of the superconducting layer and squares and circles of Fig. 4a indicate holes. Fig. 4a is 2D image taken at 89.5 K. The sample is just at the global critical temperature Tc0 and remarkable signals can be measured only in the area near to L2. The local current density at L2 is the highest because the hole across the line L2 is the biggest. The resistive transition shown in Fig. 4a is associated mainly with the higher local current density. As shown in Fig. 4c, the largest signal dV occurs in the vicinity of line L2 where the local current density is largest. To investigate in detail, we executed line scans at various temperatures from 89.4 K to 90.5 K (DT = 0.05 K) and compiled the results. Fig. 5 shows distribution of dVmax and T max . From a series of c line scans, dVmax and T max for different horizontal positions are c evaluated. The squares represent dVmax and the triangles indicate T max at given horizontal positions. T max of L1 distribute from c c 90.1 K to 90.25 K in the range of 0.15 K except one point. And T max of L2 distribute from 89.9 K to 90.2 K in the range of 0.3 K. This c reveals that superconducting transition properties of L2 are more inhomogeneous than L1. In addition, the average temperature of T max of L1 and L2 are 90.15 K and 90.05 K, respectively. This indic cates that L1 has higher superconducting transition temperature than L2. In this way, we have analyzed the spatial distribution of local resistive transition with 2D images and line scans. 2D images obtained at various bias currents are presented in Fig. 6. The temperature of the sample is 89.6 K which is near the critical temperature at bias current of 10 mA. As can be seen in Fig. 6, the signal level of dV is the highest at bias current of 40 mA. This result indicates that dV is proportional to the bias current.
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Fig. 3. (a) The temperature dependence of resistivity of sample A. The critical temperature is 89.5 K at bias current 10 mA. (b) The temperature dependence of @ q/@T at various bias currents. With increasing bias current, the maximum of @ q/@T shifts to the lower temperature.
(a) 89.5 K
(b) 89.7 K
(c) 90.0 K
(d) 90.3 K
(e) 90.6 K
Fig. 4. 2D images at various temperatures. The bias current is 10 mA. The size of image is 750 lm 420 lm. Arrows indicate the region of the superconducting layer and squares and circles of (a) indicate holes.
Fig. 5. The distribution of dVmax and T max of (a) L1 and (b) L2. The bias current is 10 mA. c
Fig. 7 shows 2D image of the part taken at the temperature of 90.0 K and at bias current of 10 mA. As we pointed out in the previous section, the effective width changes along the bridge because of holes with different sizes. All 2D images are taken in constant current mode so that the local current density is modulated. As shown in Fig. 7, the voltage response is large in the region where large holes are located. In other words, dV is proportional to the current density. This result corresponds to Eq. (1). According to
above experimental results, the voltage signal dV measured in homogeneous sample near the superconducting transition is proportional to the local current density. 3.2. Sample B Fig. 8a shows the temperature dependence of the resistivity of the sample B. The inset indicates that the critical temperature is
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(a) 5 mA
(b) 10 mA
(c) 20 mA
(d) 30 mA
(e) 40 mA
Fig. 6. 2D images at various bias currents. The temperature is 89.6 K. Arrows indicate the region of the superconducting layer and squares and circles of (a) indicate holes.
Fig. 7. 2D image of the part of the sample A. The temperature is 90.0 K and the bias current is 10 mA. Arrows indicate the region of the superconducting layer and squares indicate holes with different sizes.
92.1 K with the transition width of 1.0 K. The sample B has higher critical temperature and smaller transition width than the sample A. This result implies the sample B is more homogeneous than the sample A. R vs. T of the sample B at various bias currents is shown in Fig. 8b. Fig. 9 represents the result of 2D images taken at various temperatures. The scan area of all 2D images is 1000 lm 850 lm. In general, the signal dV of outer edges are larger than any other region of the sample. From results of the sample A, this indicates that the current density of the outer edge is higher than any other region of the sample. For analyzing the spatial distribution of the superconducting transition, we executed line scans at two positions (L3 and L4 of
Fig. 9b) at various temperatures from 92.1 K to 93.2 K (DT = 0.05 K). Fig. 10 shows the compiled result of line scans at bias current of 10 mA. T max of L3 and L4 distribute from 92.4 K to 92.6 K in the c range of 0.2 K. This reveals that the inhomogeneity of the critical temperature of L3 and L4 is almost same. In addition, the average of T max of L3 and L4 is 92.55 K and 92.5 K, respectively. c The result of line scans at bias current of 40 mA is shown in Fig. 11. From a series of experiments on the temperature dependence of resistivity at various bias currents (see Fig. 8b), we ascertain the fact that the bias current has an effect on the width of transition region. Because the magnitude of the bias current is 4 times larger, dV is also increased in almost same rate. T max of L3 c and L4 distribute from 92.15 K to 92.2 K in the range of 0.05 K. This result corresponds to R vs. T measurement at various bias currents. Fig. 12 shows the distribution of dV/dVmax of L4 at bias current of 10 mA, 20 mA and 40 mA. For investigating the bias current dependence of dV, we divided dV signals by dVmax. Whereas the ratio (dV/ dVmax) of outer edges is almost unchanged with variation of bias currents, the ratio in other region of the bridge is increased. With increasing the bias current, the width of the transport current channel becomes larger and the current penetrates from outer edge into the inside of the bridge. 4. Conclusion We analyzed the spatial distribution of the local resistive transition and current density of YBCO coated conductors. From a series of LTSLM images, we investigated the relationship between the
Fig. 8. (a) The temperature dependence of resistivity of the sample B. The critical temperature is 92.1 K at bias current 10 mA. (b) R vs. T at various bias currents.
S.K. Park et al. / Cryogenics 51 (2011) 241–246
(a) 92.3 K
(b) 92.5 K
245
(c) 93.0 K
Fig. 9. 2D images of center part at (a) 92.3 K, (b) 92.5 K, and (c) 93.0 K. The bias current is 10 mA. The size of image is 1000 lm 850 lm. Arrows indicate the region of the superconducting layer.
Fig. 10. The distribution of dVmax and T max of L3 and L4 of Fig. 9b. The bias current is 10 mA. c
Fig. 11. The distribution of dVmax and T max of L3 and L4. The bias current is 40 mA. c
critical temperature and T max . We showed also that high voltage rec sponse dV related to the high current density. These results indicate that the LTSLM is one of the most useful equipment for investigating about the spatial distribution of the superconducting properties such as the local critical temperature and local current density.
Acknowledgments This work was supported by the Nuclear Research and Development Program of the National Research Foundation of Korea (NRF) grant and the R&D Program through the National Fusion Research Institute of Korea (NFRI) funded by the Korean government MEST.
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[6]
[7]
[8]
[9]
[10]
[11]
[12] Fig. 12. The distribution of dV/dVmax at various bias current of L4. Sample is at temperature of 92.2 K.
[13] [14]
References [1] Swartzendruber LJ, Roitburd A, Kaiser DL, Gayle FW, Bennett LH. Direct evidence for an effect of twin boundaries on flux pinning in single-crystal YBa2Cu3O6+x. Phys Rev Lett 1990;64(4):483–6. [2] Crabtree GW, Liu JZ, Umezawa A, Kwon WK, Sowers CH, Malik SK, et al. Large anisotropic critical magnetization currents in single-crystal YBa2Cu3O7d. Phys Rev B 1987;36(7):4021–4. [3] Gross R, Hartmann M, Hipler K, Huebener RP, Kober F, Koelle D. Spatial resolution limit for the investigation of high-Tc films by low temperature scanning electron microscopy. IEEE Trans Magn 1989;25(2):2250–3. [4] Dieckmann N, Bock A, Merkt U. Spatially resolved analyses of epitaxial and electrical properties of YBa2Cu3O7 devices. Appl Phys Lett 1996;68(25):3626–8. [5] Abraimov D, Sivakov AG, Lukashenko AV, Fistul MV, Muller P, Ustinov AV. Spatially resolved measurements of critical parameters in superconducting
[15] [16]
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[18]
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filaments by laser scanning technique. IEEE Trans Appl Supercond 2001;11(1):3170–3. Kiss T, Inoue M, Yasunaga M, Tokutomi H, Iijima Y, Kakimoto K, et al. Low temperature scanning laser microscopy of YBCO coated IBAD tapes. IEEE Trans Appl Supercond 2005;15(2):3656–9. Wang LB, Price MB, Kwon C, Jia QX. Variable temperature scanning laser microscopy of wider width high temperature superconducting films. IEEE Trans Appl Supercond 2003;13(2):2611–3. Kwon C, Wang LB, Seo S, Park BH, Jia QX. Spatial distribution analysis of critical temperature in epitaxial Y–Ba–Cu–O film using variable temperature scanning laser microscopy. IEEE Trans Appl Supercond 2003;13(2):2894–6. Wang LB, Price MB, Young JL, Kwon C, Haugen TJ, Barnes PN. Observation of nonuniform current transport in epitaxial YBa2Cu3O7x film near the superconducting transition temperature. Physica C 2004;405:240–4. Wang LB, Selby P, Khanal C, Levin G, Haugen TJ, Barnes PN, et al. The distribution of transport current in YBCO coated conductor with zipper striations. IEEE Trans Appl Supercond 2005;15(2):2950–3. Wang LB, Price MB, Young JL, Kwon C, Levin GA, Haugen TJ, et al. Mapping the current distribution in YBa2Cu3O7x thin films with striations. Physica C 2005;419:79–84. Clem JR, Huebener RP. Application of low-temperature scanning electron microscopy to superconductors. J Appl Phys 1980;51(5):2764–73. Brandt EH. Thin superconductors in a perpendicular magnetic ac field: general formulation and strip geometry. Phys Rev B 1994;49(13):9024–40. Schuster T, Indenbom MV, Koblishka MR, Kuhn H, Kronmuller H. Observation of current-discontinuity lines in type-II superconductors. Phys Rev B 1994;49(5):3443–52. Mawatari Y. Critical state of periodically arranged superconducting-strip lines in perpendicular fields. Phys Rev B 1996;54(18):13215–21. Johansen TH, Baziljevich M, Bratsberg H, Galperin Y, Lindelof PE, Shen Y, et al. Direct observation of the current distribution in thin superconducting strips using magneto-optic imaging. Phys Rev B 1996;54(22):16264–9. Inoue M, Kiss T, Tokutomi H, Imamura K, Takeo M, Iijima Y, et al. Study on local inhomogeneity in TFA-MOD YBCO coated conductor by use of low temperature scanning laser microscopy. Physica C 2005;426–31:1073–7. Kiss T, Inoue M, Shoyama T, Koyanagi S, Mitsui D, Nakamura T, et al. Visualizing transport properties in IBAD based YBCO coated conductors by multiple analysis techniques. IEEE Trans Appl Supercond 2007;17(2):3211–4. Gross R, Koelle D. Low temperature scanning electron microscopy of superconducting thin films and Josephson junctions. Rep Prog Phys 1994;57:651–741.
Contents lists available at ScienceDirect
Cryogenics journal homepage: www.elsevier.com/locate/cryogenics
Spatial distribution of the local resistive transition and the critical current density in YBCO coated conductors using Low-temperature Scanning Laser Microscopy S.K. Park, J.M. Kim, S.B. Lee, S.H. Kim, G.Y. Kim, H.-C. Ri * Dept. of Physics, Kyungpook National University, 1370 Sangyeok-Dong, Buk-Gu, Daegu 702-701, Republic of Korea
a r t i c l e
i n f o
Article history: Available online 11 June 2010 Keywords: D. LTSLM A. YBCO A. Coated conductor C. Critical temperature C. Critical current density
a b s t r a c t Low-temperature Scanning Laser Microscopy (LTSLM) was carried out to reveal the spatial distribution of the local resistive transition temperature and the local current density in commercial YBCO coated conductors near the superconducting transition. The result of the sample with an array of holes of various sizes shows that the signal dV is proportional to the current density. The distribution of the critical temperature of the sample with two parallel bridges is quite homogeneous and the transport current flows mainly along the outer edge of the sample. Using LTSLM we directly image the current path in YBCO coated conductors of different patterns. Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved.
1. Introduction High critical current density and high critical temperature are required for large scale applications of superconductors. Many experiments have shown that the critical current density of high temperature superconductors is influenced by the microstructure of the materials [1,2]. In many studies of superconducting thin films and coated conductors, the properties of samples such as critical temperature and critical current density represented average value of the whole sample. They did not offer the information of local properties. Therefore, it is important to develop methods or equipments for analyzing the spatial distribution of local critical temperature and critical current density [3–12]. For electrical power applications of superconductors, AC losses are of crucial importance. The width of YBCO coated conductors 2w is typically 0.4–1 cm. Since hysteresis losses per unit length are proportional to w2, AC losses of planar superconducting film in perpendicular magnetic field are quite high. To reduce hysteresis losses, considerable efforts are being made to develop periodically arranged multi-strip type as the geometry of superconducting thin film [13–16]. Recently, direct visualization of the local transport properties in the YBCO coated conductors has been performed by LTSLM [17], low-temperature scanning SQUID microscopy [18], low-temperature scanning electron microscopy [19]. Especially, LTSLM is a powerful tool for measuring the local superconducting properties using focused laser beam in transport measurement. * Corresponding author. Fax: +82 53 952 1739. E-mail address: [email protected] (H.-C. Ri).
In this study, we used LTSLM to investigate local superconducting properties in YBCO coated conductors with different geometry. The spatial distribution of the local resistive transition and the local current density of YBCO layers are analyzed. 2. Experimental 2.1. Specifications of the LTSLM Fig. 1 shows schematic diagram of LTSLM. The principle of LTSLM measurement is to detect the local bolometric response induced by the laser beam. For precise measurements of local properties in superconducting samples using LTSLM, the temperature stability is of importance. To improve the temperature stability, we modified our cooling system into a double-shielding type and achieved the stability of ±2 mK. A laser beam (wavelength 660 nm) is coupled into an optical fiber and modulated at 3 kHz using a standard mechanical chopper. The modulated laser beam is focused on the sample surface by an objective lens having 30.5 mm of working distance and 0.28 of numerical aperture. The minimum spot size of the focused laser beam is 3 lm. The spatial resolution of LTSLM is determined, however, mainly by the thermal healing length K of the laser beam induced temperature field. Since the characteristic length K is proportional to the output power of the laser beam [19], we minimized the power of laser beam to get better resolution. The optical fiber and lens are fixed to a three-axis motorized stage which focuses the laser beam and scans on the sample surface in horizontal and vertical direction. The voltage response is measured by a lock-in with a pre-amplifier.
0011-2275/$ - see front matter Crown Copyright Ó 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.cryogenics.2010.06.004
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S.K. Park et al. / Cryogenics 51 (2011) 241–246
Cryostat
3. Results and discussion
Laser beam GPIB or serial
Heater & Temp. sensor Sample holder Sample
Electrical signal
Current source Temp. controller Lock-in Amplifier
Focusing devices
The temperature dependence of the resistivity is shown in Fig. 3a. In the inset is shown the enlargement of the superconducting transition region. The sample has the critical temperature Tc0 (R = 0 X) of 89.5 K with the transition width of 1.4 K. Fig. 3b shows the temperature dependence of @ q/@T at different bias currents. While the laser beam was fixed at a certain position, the temperature was slowly increased and the voltage response was acquired. The voltage signal dV which is measured using LTSLM can be expressed as [19]
dVðx; yÞ J B ðx; yÞ
Motorized XYZ stage
PC
Laser & Lens Optical fiber Fig. 1. Schematic diagram of the LTSLM.
2.2. Specifications of the samples The samples analyzed by LTSLM are commercial YBCO coated conductors which were produced by Superpower, Inc. SCS4050 model (surround copper stabilizer) was used for the sample A and SF12100 model (stabilizer free) was used for the sample B. We could improve the contrast and spatial resolution by removing the copper stabilizer and Ag overlayer, which covered YBCO film. After removal of cover layers, YBCO layer was patterned by wetetching process. Fig. 2 shows the geometry of YBCO layer of the sample. The bridge width of the sample A is 260 lm. In order to regulate the effective width of the bridge, square and circular holes with different sizes from 50 lm to 130 lm are arrayed in the bridge. We patterned the sample B into two parallel 260 lm wide bridges. The interval between two bridges is 140 lm. The thickness of the YBCO layer of two samples is about 1 lm.
(a) Sample A
3.1. Sample A
(b) Sample B
Fig. 2. YBCO layer geometry of the samples A and B.
@ qðx; yÞ KdT 0 @T
ð1Þ
where JB(x, y) is the local current density, @ q(x, y)/@T is the derivative of resistivity with respect to temperature, K is the characteristic length of the laser beam induced temperature field and dT0 is the laser beam induced temperature increment, respectively. Based on the assumption that KdT0 is about constant for all sample positions, the measured signal dV normalized by the bias current can be expressed as @ q/@T. The non-zero @ q/@T at bias current of 10 mA was detected first at 89.45 K. Though the temperature was kept below Tc0, the sample was heated up by the irradiated laser beam and became locally resistive. Because the critical temperature Tc0 is 89.5 K, we can estimate that the temperature increment due to the laser beam irradiation is approximately 50 mK. With increasing temperature from below critical temperature, dV reaches its maximum value at a certain temperature. We define dVmax as the maximum of dV and T max as the temperature where dV is a maximum, c respectively. Fig. 4 shows 2D images from LTSLM measurements at various temperatures. 2D images of dV were gathered at the center part of the sample and the scan area was 750 lm 420 lm. The legend indicates the magnitude of voltage response dV measured by lockin. For all images of Fig. 4 are used the same legend. Arrows indicate the region of the superconducting layer and squares and circles of Fig. 4a indicate holes. Fig. 4a is 2D image taken at 89.5 K. The sample is just at the global critical temperature Tc0 and remarkable signals can be measured only in the area near to L2. The local current density at L2 is the highest because the hole across the line L2 is the biggest. The resistive transition shown in Fig. 4a is associated mainly with the higher local current density. As shown in Fig. 4c, the largest signal dV occurs in the vicinity of line L2 where the local current density is largest. To investigate in detail, we executed line scans at various temperatures from 89.4 K to 90.5 K (DT = 0.05 K) and compiled the results. Fig. 5 shows distribution of dVmax and T max . From a series of c line scans, dVmax and T max for different horizontal positions are c evaluated. The squares represent dVmax and the triangles indicate T max at given horizontal positions. T max of L1 distribute from c c 90.1 K to 90.25 K in the range of 0.15 K except one point. And T max of L2 distribute from 89.9 K to 90.2 K in the range of 0.3 K. This c reveals that superconducting transition properties of L2 are more inhomogeneous than L1. In addition, the average temperature of T max of L1 and L2 are 90.15 K and 90.05 K, respectively. This indic cates that L1 has higher superconducting transition temperature than L2. In this way, we have analyzed the spatial distribution of local resistive transition with 2D images and line scans. 2D images obtained at various bias currents are presented in Fig. 6. The temperature of the sample is 89.6 K which is near the critical temperature at bias current of 10 mA. As can be seen in Fig. 6, the signal level of dV is the highest at bias current of 40 mA. This result indicates that dV is proportional to the bias current.
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Fig. 3. (a) The temperature dependence of resistivity of sample A. The critical temperature is 89.5 K at bias current 10 mA. (b) The temperature dependence of @ q/@T at various bias currents. With increasing bias current, the maximum of @ q/@T shifts to the lower temperature.
(a) 89.5 K
(b) 89.7 K
(c) 90.0 K
(d) 90.3 K
(e) 90.6 K
Fig. 4. 2D images at various temperatures. The bias current is 10 mA. The size of image is 750 lm 420 lm. Arrows indicate the region of the superconducting layer and squares and circles of (a) indicate holes.
Fig. 5. The distribution of dVmax and T max of (a) L1 and (b) L2. The bias current is 10 mA. c
Fig. 7 shows 2D image of the part taken at the temperature of 90.0 K and at bias current of 10 mA. As we pointed out in the previous section, the effective width changes along the bridge because of holes with different sizes. All 2D images are taken in constant current mode so that the local current density is modulated. As shown in Fig. 7, the voltage response is large in the region where large holes are located. In other words, dV is proportional to the current density. This result corresponds to Eq. (1). According to
above experimental results, the voltage signal dV measured in homogeneous sample near the superconducting transition is proportional to the local current density. 3.2. Sample B Fig. 8a shows the temperature dependence of the resistivity of the sample B. The inset indicates that the critical temperature is
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(a) 5 mA
(b) 10 mA
(c) 20 mA
(d) 30 mA
(e) 40 mA
Fig. 6. 2D images at various bias currents. The temperature is 89.6 K. Arrows indicate the region of the superconducting layer and squares and circles of (a) indicate holes.
Fig. 7. 2D image of the part of the sample A. The temperature is 90.0 K and the bias current is 10 mA. Arrows indicate the region of the superconducting layer and squares indicate holes with different sizes.
92.1 K with the transition width of 1.0 K. The sample B has higher critical temperature and smaller transition width than the sample A. This result implies the sample B is more homogeneous than the sample A. R vs. T of the sample B at various bias currents is shown in Fig. 8b. Fig. 9 represents the result of 2D images taken at various temperatures. The scan area of all 2D images is 1000 lm 850 lm. In general, the signal dV of outer edges are larger than any other region of the sample. From results of the sample A, this indicates that the current density of the outer edge is higher than any other region of the sample. For analyzing the spatial distribution of the superconducting transition, we executed line scans at two positions (L3 and L4 of
Fig. 9b) at various temperatures from 92.1 K to 93.2 K (DT = 0.05 K). Fig. 10 shows the compiled result of line scans at bias current of 10 mA. T max of L3 and L4 distribute from 92.4 K to 92.6 K in the c range of 0.2 K. This reveals that the inhomogeneity of the critical temperature of L3 and L4 is almost same. In addition, the average of T max of L3 and L4 is 92.55 K and 92.5 K, respectively. c The result of line scans at bias current of 40 mA is shown in Fig. 11. From a series of experiments on the temperature dependence of resistivity at various bias currents (see Fig. 8b), we ascertain the fact that the bias current has an effect on the width of transition region. Because the magnitude of the bias current is 4 times larger, dV is also increased in almost same rate. T max of L3 c and L4 distribute from 92.15 K to 92.2 K in the range of 0.05 K. This result corresponds to R vs. T measurement at various bias currents. Fig. 12 shows the distribution of dV/dVmax of L4 at bias current of 10 mA, 20 mA and 40 mA. For investigating the bias current dependence of dV, we divided dV signals by dVmax. Whereas the ratio (dV/ dVmax) of outer edges is almost unchanged with variation of bias currents, the ratio in other region of the bridge is increased. With increasing the bias current, the width of the transport current channel becomes larger and the current penetrates from outer edge into the inside of the bridge. 4. Conclusion We analyzed the spatial distribution of the local resistive transition and current density of YBCO coated conductors. From a series of LTSLM images, we investigated the relationship between the
Fig. 8. (a) The temperature dependence of resistivity of the sample B. The critical temperature is 92.1 K at bias current 10 mA. (b) R vs. T at various bias currents.
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(a) 92.3 K
(b) 92.5 K
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(c) 93.0 K
Fig. 9. 2D images of center part at (a) 92.3 K, (b) 92.5 K, and (c) 93.0 K. The bias current is 10 mA. The size of image is 1000 lm 850 lm. Arrows indicate the region of the superconducting layer.
Fig. 10. The distribution of dVmax and T max of L3 and L4 of Fig. 9b. The bias current is 10 mA. c
Fig. 11. The distribution of dVmax and T max of L3 and L4. The bias current is 40 mA. c
critical temperature and T max . We showed also that high voltage rec sponse dV related to the high current density. These results indicate that the LTSLM is one of the most useful equipment for investigating about the spatial distribution of the superconducting properties such as the local critical temperature and local current density.
Acknowledgments This work was supported by the Nuclear Research and Development Program of the National Research Foundation of Korea (NRF) grant and the R&D Program through the National Fusion Research Institute of Korea (NFRI) funded by the Korean government MEST.
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[12] Fig. 12. The distribution of dV/dVmax at various bias current of L4. Sample is at temperature of 92.2 K.
[13] [14]
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