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Magnetic flux guide for HTS SQUID microscope
Physica C 392–396 (2003) 1401–1405 www.elsevier.com/locate/physc
Magnetic flux guide for HTS SQUID microscope T. Kondo *, H. Itozaki Superconducting Materials Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan Received 13 November 2002; accepted 31 January 2003
Abstract A permalloy needle as a flux guide for a high-TC SQUID microscope has been analyzed numerically by a finite element method (FEM). Magnetic field of a meander line and the flux guide has calculated using a two-dimensional analysis model. It was shown that magnetic fluxes concentrate to the tip of the flux guide. Dependence of flux guide radius has been analyzed numerically to investigate optimum flux guide design. We have also examined the line scan with both a sharp flux guide and a blunt one experimentally to confirm our FEM analysis. Ó 2003 Elsevier B.V. All rights reserved. PACS: 85.25.)j; 85.25.Cp; 85.25.Dq Keywords: High-TC SQUID; Scanning SQUID microscope; Flux guide
1. Introduction A scanning SQUID microscope (SSM) is the most sensitive instrument which can measure very weak magnetic field distribution [1–9]. The SSM has become a powerful tool for the non-destructive evaluation in the fields of microelectronics, flux dynamics and other studies of physics [3–6]. Improvement of spatial resolution is one of the most important researches for the SSM to be feasible instrument. To achieve high spatial resolution of the SSM, the SQUID should be approached to a sample closely and it should get magnetic field from a localized area. A low-TC SSM with a small
*
Corresponding author. Tel.: +81-298-59-2357; fax: +81298-59-2301. E-mail address: [email protected] (T. Kondo).
transfer coil has been developed [2,3]. Its spatial resolution was order of 10 lm, because the transfer coil can be approached to the sample to a few microns. However, it should be used in vacuum. While, the high-TC SSM with a thin sapphire window has been developed [7–9]. It makes possible to measure the sample in the air. Although the SQUID can close to the sample to thickness of the sapphire window, the spatial resolution was worse than that of the low-TC SSM. Recently, some groups interested in using a flux guide placed between the sample and the SQUID to improve the spatial resolution [10–13]. This method makes possible to measure the sample in the air and to approach the tip of flux guide to the sample as close as possible. Pitzius et al. have greatly improved the spatial resolution to sub-100 nm using a soft magnetic flux guide, though they measured in the liquid nitrogen or cooled gas [10]. Although some groups began to utilize the flux
0921-4534/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-4534(03)01042-6
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T. Kondo, H. Itozaki / Physica C 392–396 (2003) 1401–1405
guide, the performance of the flux guide has not yet analyzed theoretically in detail. It should be clear that the SQUID can catch the actual magnetic field or not. The performances of the flux guide such as the dependence of design should be investigated. We have analyzed the performance of the flux guide numerically by a finite element method (FEM). We have compared numerical results to the experimental ones by using the high-TC SSM.
2. Analysis of the magnetic field distribution around the flux guide We have investigated the spatial resolution of the SSM by using a meander line. It produces magnetic field distribution with a period of twice width of line plus space. In the FEM analysis, a two-dimensional model was used to consider the case of line plus space. Fig. 1 shows the magnetic field distributions produced by a meander line which has 6 lines. Magnitude of magnetic field is displayed by color scale ranging from 0 to 240 lT. A meander line with 200 lm line plus space is indicated by rectangle and applied current was set to 5 mA. The current in the nearest neighboring lines flows in opposite direction. Fig. 1(a) shows the magnetic field distribution without the flux guide, Fig. 1(b)– (d) shows those with the flux guide for various scanning positions. Solid lines represent the flux guide. Diameter, length, tip angle and permeability of the flux guide were 2 mm, 5 mm, 30° and 100 000, respectively. The magnetic field distribution was changed by the flux guide. The fluxes concentrate to the tip of the flux guide. Fig. 1(b) shows that the flux guide absorbs the magnetic fluxes from summit of the tip to about 50 lm height. We used the flux guide with sharp edge in the case of Fig. 1. While, Fig. 2 shows the case of a realistic flux guide. The tip radiuses for Fig. 2(a) and (b) are 20 and 100 lm, respectively. The blunt flux guide does not absorb the magnetic flux in localized area but does wide area. This makes spatial resolution to become lower.
Fig. 1. The magnetic field distribution above a meander line made of 6 lines: (a) without flux guide and (b)–(d) with flux guide. Solid lines represent flux guide. Meander line is indicated by rectangle.
T. Kondo, H. Itozaki / Physica C 392–396 (2003) 1401–1405
1403
Magnetic filed [µT]
(a) 20 10 0 -10 200 µm -20
Magnetic filed [nT]
(b) 180 150
120
90 200 µm 60
Fig. 2. The magnetic field distribution above a meander line with flux guide for various tip radius. Tip of flux guides has the radius of (a) 20 lm and (b) 100 lm.
Magnetic filed
(c)
1 nT
3. Numerical analysis and experiment of line scan 200 µm
A line scan of the magnetic field distribution 20 lm above a meander line has been studied both numerically and experimentally. The applied current of the meander line was 5 mA. Fig. 3(a) shows the numerical result of magnetic field distribution 20 lm above the meander line. The current in the nearest neighboring lines flows in opposite direction. The magnetic fields produced by this current have same vertical direction at the space of the meander line, so that the peaks of magnetic field in the vertical direction locate at the space. Polarity of the peak changes every space. The number of these peaks is equal to number of line minus one. If the meander line has 6 lines, it becomes 5. The outermost lines produce small peak at outer of meander line. Fig. 3(b)
Fig. 3. Line scan data of the magnetic field distribution 20 lm above a meander line: (a) simulation result for 20 lm above a meander line without the flux guide, (b) simulation result of the line scan with the flux guide and (c) experimental result of the line scan with the flux guide.
shows magnetic field which was obtained by the flux guide with tip radius of 20 lm. Length and tip angle of the flux guide were 5 mm and 30°, receptively. Magnetic field is given by the summation of vertical component of the magnetic field at opposite side of tip faced to SQUID. The line scan data is extremely different from the real magnetic field. Fine structure of real magnetic field distribution is
T. Kondo, H. Itozaki / Physica C 392–396 (2003) 1401–1405
radius 0 µm 20 µm 100 µm 200 µm
Magnetic filed
20 nT
200 µm Fig. 4. Line scan of magnetic field distribution 20 lm above a meander line for various tip radius of the flux guide.
50
1.0
40
0.8
30
0.6
20
0.4
10
0.2
Amplitude of Line Scan (Experiment) [nT]
not obtained. The magnetic field as a whole of the meander line does not become zeros when the meander line has U-shape. Therefore the line scan data has bias field if the flux guide can not catch the flux locally. The flux guide decreased the amplitude of the line scan in 3 orders of magnitude from the real magnetic field distribution. To confirm our FEM analysis, we investigated the line scan experimentally. Detail of the high-TC SQUID microscope head with permalloy flux guide is explained in Ref. [14]. Length of flux guide was 6 mm and the distance between the SQUID and the flux guide was about 0.1 mm. Fig. 3(c) shows the experimental result of line scan. It resembles the numerical result in shape. The influence of bias field is observed like as the numerical result. While, the structure around peak is slightly broad compared with numerical one. Experimental amplitude is much less than the simulated one, because of the following effects. The amplitude of the line scan is emphasized compared with the case of needle, since two-dimensional analysis uses the wedge-shaped flux guide putting on the cross-section of the meander line. In addition, a coupling factor of the flux between the flux guide and SQUID is one for the simulation, but actual coupling is not so effective. We showed the magnetic field distribution around the flux guide with sharp and blunt tips in Fig. 2. We have also investigated the tip radius dependence of line scan. Fig. 4 shows the numerical results of line scan for various radius of the flux guide. The applied current of the meander line was 5 mA. The magnetic field distribution could be analyzed with the sharper tip more clearly. The performance of blunt flux guide becomes poor because the fluxes are absorbed in wide range of the surface of its tip. Fig. 5 shows the tip radius dependence of the amplitude of line scan with the flux guide which has tip angle of 30°. Five milliampere was applied to the meander line. Experimental data are plotted by filled circles. Solid line represents the simulation using the tip radius of from 0 to 200 lm. Other parameters were same as Fig. 2. For more than 50 lm, the amplitude of the line scan decreases as increasing the tip radius, because the flux guide catches the flux from more than the nearest line.
Amplitude of Line Scan (Simulation) [nT]
1404
0
0 0
50
100
150
200
Tip Radius [µm] Fig. 5. The tip radius dependence of the amplitude of the line scan with the flux guide. Solid line represents the numerical result and filled circles plot the experimental results.
The ratio of the amplitude for sharp to blunt tips in the experiment is similar to the numerical one. The amplitude of the line scan is almost constant for the tip radius of less than 50 lm. This suggests that the tip diameter should be less than the line width.
4. Conclusion The performances of the flux guide were analyzed both by experiment and by numerical analysis. The magnetic field distribution above a meander line with and without the flux guide was displayed
T. Kondo, H. Itozaki / Physica C 392–396 (2003) 1401–1405
by the vector traces. It was found that the fluxes of the sample concentrate to the tip of the flux guide. We have also analyzed the line scan of the magnetic field distribution above a meander line. The line scan data obtained by the flux guide differ from the real one, because the flux guide absorbs not only magnetic fields at the tip end but also around it. We further investigated the tip radius dependence of line scan. The result suggested that the tip diameter should be less than the line width. References [1] J.R. Kirley, J.P. Wikswo, Ann. Rev. Mater. Sci. 29 (1999) 117. [2] J.R. Kirtley, M.B. Ketchen, K.G. Stawiasz, J.Z. Sun, W.J. Gallagher, S.H. Blanton, S.J. Wind, Appl. Phys. Lett. 66 (1995) 1138. [3] T. Morooka, S. Nakayama, A. Odawara, M. Ikeda, S. Tanaka, K. Chinome, IEEE Trans. Appl. Supercond. 9 (1999) 3491.
1405
[4] M. Jeffery, T.V. Duzer, J.R. Kirtley, M.B. Ketchen, Appl. Phys. Lett. 67 (2000) 1769. [5] K. Suzuki, S. Adachi, Y. Li, T. Utagawa, K. Tanabe, IEEE Trans. Appl. Supercond. 11 (2001) 238. [6] S. Chatraphorn, E.F. Fleet, F.C. Wellstood, L.A. Knauss, T.M. Elies, Appl. Phys. Lett. 76 (2000) 2304. [7] R.C. Black, A. Mathai, F.C. Wellstood, Appl. Phys. Lett. 62 (1993) 2128. [8] T.S. Lee, Y.R. Chemla, E. Dantsker, J. Clarke, IEEE Trans. Appl. Supercond. 7 (1997) 3147. [9] T. Nagaishi, H. Itozaki, Supercond. Sci. Technol. 12 (1999) 1039. [10] P. Pitzius, V. Dworak, U. Hartmann, Ext. Abstr. 6th Int. Supercond. Electron. Conf. (ISECÕ97) (1997) 3395. [11] S.A. Gudoshnikov, Y.V. Deryuzhkina, P.E. Rudenchik, Y.S. Sitnov, S.I. Bondarenko, A.A. Shablo, P.P. Pavlov, A.S. Kalabukhov, P. Seidel, IEEE Trans. Appl. Supercond. 11 (2001) 229. [12] S. Tanaka, K. Matsuda, O. Yamazaki, M. Natsume, H. Ota, T. Mizoguchi, Jpn. J. Appl. Phys. 40 (2001) L431. [13] T. Nagaishi, K. Minamimura, H. Itozaki, IEEE Trans. Appl. Supercond. 11 (2001) 226. [14] H. Itozaki, T. Kondo, T. Nagaishi, Physica C (2003), these Proceedings.
Magnetic flux guide for HTS SQUID microscope T. Kondo *, H. Itozaki Superconducting Materials Center, National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan Received 13 November 2002; accepted 31 January 2003
Abstract A permalloy needle as a flux guide for a high-TC SQUID microscope has been analyzed numerically by a finite element method (FEM). Magnetic field of a meander line and the flux guide has calculated using a two-dimensional analysis model. It was shown that magnetic fluxes concentrate to the tip of the flux guide. Dependence of flux guide radius has been analyzed numerically to investigate optimum flux guide design. We have also examined the line scan with both a sharp flux guide and a blunt one experimentally to confirm our FEM analysis. Ó 2003 Elsevier B.V. All rights reserved. PACS: 85.25.)j; 85.25.Cp; 85.25.Dq Keywords: High-TC SQUID; Scanning SQUID microscope; Flux guide
1. Introduction A scanning SQUID microscope (SSM) is the most sensitive instrument which can measure very weak magnetic field distribution [1–9]. The SSM has become a powerful tool for the non-destructive evaluation in the fields of microelectronics, flux dynamics and other studies of physics [3–6]. Improvement of spatial resolution is one of the most important researches for the SSM to be feasible instrument. To achieve high spatial resolution of the SSM, the SQUID should be approached to a sample closely and it should get magnetic field from a localized area. A low-TC SSM with a small
*
Corresponding author. Tel.: +81-298-59-2357; fax: +81298-59-2301. E-mail address: [email protected] (T. Kondo).
transfer coil has been developed [2,3]. Its spatial resolution was order of 10 lm, because the transfer coil can be approached to the sample to a few microns. However, it should be used in vacuum. While, the high-TC SSM with a thin sapphire window has been developed [7–9]. It makes possible to measure the sample in the air. Although the SQUID can close to the sample to thickness of the sapphire window, the spatial resolution was worse than that of the low-TC SSM. Recently, some groups interested in using a flux guide placed between the sample and the SQUID to improve the spatial resolution [10–13]. This method makes possible to measure the sample in the air and to approach the tip of flux guide to the sample as close as possible. Pitzius et al. have greatly improved the spatial resolution to sub-100 nm using a soft magnetic flux guide, though they measured in the liquid nitrogen or cooled gas [10]. Although some groups began to utilize the flux
0921-4534/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-4534(03)01042-6
1402
T. Kondo, H. Itozaki / Physica C 392–396 (2003) 1401–1405
guide, the performance of the flux guide has not yet analyzed theoretically in detail. It should be clear that the SQUID can catch the actual magnetic field or not. The performances of the flux guide such as the dependence of design should be investigated. We have analyzed the performance of the flux guide numerically by a finite element method (FEM). We have compared numerical results to the experimental ones by using the high-TC SSM.
2. Analysis of the magnetic field distribution around the flux guide We have investigated the spatial resolution of the SSM by using a meander line. It produces magnetic field distribution with a period of twice width of line plus space. In the FEM analysis, a two-dimensional model was used to consider the case of line plus space. Fig. 1 shows the magnetic field distributions produced by a meander line which has 6 lines. Magnitude of magnetic field is displayed by color scale ranging from 0 to 240 lT. A meander line with 200 lm line plus space is indicated by rectangle and applied current was set to 5 mA. The current in the nearest neighboring lines flows in opposite direction. Fig. 1(a) shows the magnetic field distribution without the flux guide, Fig. 1(b)– (d) shows those with the flux guide for various scanning positions. Solid lines represent the flux guide. Diameter, length, tip angle and permeability of the flux guide were 2 mm, 5 mm, 30° and 100 000, respectively. The magnetic field distribution was changed by the flux guide. The fluxes concentrate to the tip of the flux guide. Fig. 1(b) shows that the flux guide absorbs the magnetic fluxes from summit of the tip to about 50 lm height. We used the flux guide with sharp edge in the case of Fig. 1. While, Fig. 2 shows the case of a realistic flux guide. The tip radiuses for Fig. 2(a) and (b) are 20 and 100 lm, respectively. The blunt flux guide does not absorb the magnetic flux in localized area but does wide area. This makes spatial resolution to become lower.
Fig. 1. The magnetic field distribution above a meander line made of 6 lines: (a) without flux guide and (b)–(d) with flux guide. Solid lines represent flux guide. Meander line is indicated by rectangle.
T. Kondo, H. Itozaki / Physica C 392–396 (2003) 1401–1405
1403
Magnetic filed [µT]
(a) 20 10 0 -10 200 µm -20
Magnetic filed [nT]
(b) 180 150
120
90 200 µm 60
Fig. 2. The magnetic field distribution above a meander line with flux guide for various tip radius. Tip of flux guides has the radius of (a) 20 lm and (b) 100 lm.
Magnetic filed
(c)
1 nT
3. Numerical analysis and experiment of line scan 200 µm
A line scan of the magnetic field distribution 20 lm above a meander line has been studied both numerically and experimentally. The applied current of the meander line was 5 mA. Fig. 3(a) shows the numerical result of magnetic field distribution 20 lm above the meander line. The current in the nearest neighboring lines flows in opposite direction. The magnetic fields produced by this current have same vertical direction at the space of the meander line, so that the peaks of magnetic field in the vertical direction locate at the space. Polarity of the peak changes every space. The number of these peaks is equal to number of line minus one. If the meander line has 6 lines, it becomes 5. The outermost lines produce small peak at outer of meander line. Fig. 3(b)
Fig. 3. Line scan data of the magnetic field distribution 20 lm above a meander line: (a) simulation result for 20 lm above a meander line without the flux guide, (b) simulation result of the line scan with the flux guide and (c) experimental result of the line scan with the flux guide.
shows magnetic field which was obtained by the flux guide with tip radius of 20 lm. Length and tip angle of the flux guide were 5 mm and 30°, receptively. Magnetic field is given by the summation of vertical component of the magnetic field at opposite side of tip faced to SQUID. The line scan data is extremely different from the real magnetic field. Fine structure of real magnetic field distribution is
T. Kondo, H. Itozaki / Physica C 392–396 (2003) 1401–1405
radius 0 µm 20 µm 100 µm 200 µm
Magnetic filed
20 nT
200 µm Fig. 4. Line scan of magnetic field distribution 20 lm above a meander line for various tip radius of the flux guide.
50
1.0
40
0.8
30
0.6
20
0.4
10
0.2
Amplitude of Line Scan (Experiment) [nT]
not obtained. The magnetic field as a whole of the meander line does not become zeros when the meander line has U-shape. Therefore the line scan data has bias field if the flux guide can not catch the flux locally. The flux guide decreased the amplitude of the line scan in 3 orders of magnitude from the real magnetic field distribution. To confirm our FEM analysis, we investigated the line scan experimentally. Detail of the high-TC SQUID microscope head with permalloy flux guide is explained in Ref. [14]. Length of flux guide was 6 mm and the distance between the SQUID and the flux guide was about 0.1 mm. Fig. 3(c) shows the experimental result of line scan. It resembles the numerical result in shape. The influence of bias field is observed like as the numerical result. While, the structure around peak is slightly broad compared with numerical one. Experimental amplitude is much less than the simulated one, because of the following effects. The amplitude of the line scan is emphasized compared with the case of needle, since two-dimensional analysis uses the wedge-shaped flux guide putting on the cross-section of the meander line. In addition, a coupling factor of the flux between the flux guide and SQUID is one for the simulation, but actual coupling is not so effective. We showed the magnetic field distribution around the flux guide with sharp and blunt tips in Fig. 2. We have also investigated the tip radius dependence of line scan. Fig. 4 shows the numerical results of line scan for various radius of the flux guide. The applied current of the meander line was 5 mA. The magnetic field distribution could be analyzed with the sharper tip more clearly. The performance of blunt flux guide becomes poor because the fluxes are absorbed in wide range of the surface of its tip. Fig. 5 shows the tip radius dependence of the amplitude of line scan with the flux guide which has tip angle of 30°. Five milliampere was applied to the meander line. Experimental data are plotted by filled circles. Solid line represents the simulation using the tip radius of from 0 to 200 lm. Other parameters were same as Fig. 2. For more than 50 lm, the amplitude of the line scan decreases as increasing the tip radius, because the flux guide catches the flux from more than the nearest line.
Amplitude of Line Scan (Simulation) [nT]
1404
0
0 0
50
100
150
200
Tip Radius [µm] Fig. 5. The tip radius dependence of the amplitude of the line scan with the flux guide. Solid line represents the numerical result and filled circles plot the experimental results.
The ratio of the amplitude for sharp to blunt tips in the experiment is similar to the numerical one. The amplitude of the line scan is almost constant for the tip radius of less than 50 lm. This suggests that the tip diameter should be less than the line width.
4. Conclusion The performances of the flux guide were analyzed both by experiment and by numerical analysis. The magnetic field distribution above a meander line with and without the flux guide was displayed
T. Kondo, H. Itozaki / Physica C 392–396 (2003) 1401–1405
by the vector traces. It was found that the fluxes of the sample concentrate to the tip of the flux guide. We have also analyzed the line scan of the magnetic field distribution above a meander line. The line scan data obtained by the flux guide differ from the real one, because the flux guide absorbs not only magnetic fields at the tip end but also around it. We further investigated the tip radius dependence of line scan. The result suggested that the tip diameter should be less than the line width. References [1] J.R. Kirley, J.P. Wikswo, Ann. Rev. Mater. Sci. 29 (1999) 117. [2] J.R. Kirtley, M.B. Ketchen, K.G. Stawiasz, J.Z. Sun, W.J. Gallagher, S.H. Blanton, S.J. Wind, Appl. Phys. Lett. 66 (1995) 1138. [3] T. Morooka, S. Nakayama, A. Odawara, M. Ikeda, S. Tanaka, K. Chinome, IEEE Trans. Appl. Supercond. 9 (1999) 3491.
1405
[4] M. Jeffery, T.V. Duzer, J.R. Kirtley, M.B. Ketchen, Appl. Phys. Lett. 67 (2000) 1769. [5] K. Suzuki, S. Adachi, Y. Li, T. Utagawa, K. Tanabe, IEEE Trans. Appl. Supercond. 11 (2001) 238. [6] S. Chatraphorn, E.F. Fleet, F.C. Wellstood, L.A. Knauss, T.M. Elies, Appl. Phys. Lett. 76 (2000) 2304. [7] R.C. Black, A. Mathai, F.C. Wellstood, Appl. Phys. Lett. 62 (1993) 2128. [8] T.S. Lee, Y.R. Chemla, E. Dantsker, J. Clarke, IEEE Trans. Appl. Supercond. 7 (1997) 3147. [9] T. Nagaishi, H. Itozaki, Supercond. Sci. Technol. 12 (1999) 1039. [10] P. Pitzius, V. Dworak, U. Hartmann, Ext. Abstr. 6th Int. Supercond. Electron. Conf. (ISECÕ97) (1997) 3395. [11] S.A. Gudoshnikov, Y.V. Deryuzhkina, P.E. Rudenchik, Y.S. Sitnov, S.I. Bondarenko, A.A. Shablo, P.P. Pavlov, A.S. Kalabukhov, P. Seidel, IEEE Trans. Appl. Supercond. 11 (2001) 229. [12] S. Tanaka, K. Matsuda, O. Yamazaki, M. Natsume, H. Ota, T. Mizoguchi, Jpn. J. Appl. Phys. 40 (2001) L431. [13] T. Nagaishi, K. Minamimura, H. Itozaki, IEEE Trans. Appl. Supercond. 11 (2001) 226. [14] H. Itozaki, T. Kondo, T. Nagaishi, Physica C (2003), these Proceedings.