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Rs measurement of HTS films in millimeter wave region using dielectric resonator method
Physica C 392–396 (2003) 1241–1244 www.elsevier.com/locate/physc
Rs measurement of HTS films in millimeter wave region using dielectric resonator method M. Kusunoki *, M. Inadomaru, D. Kousaka, S. Ohshima, K. Aizawa, M. Mukaida Department of Electrical Engineering, Yamagata University, 4-3-16 Johnan, Yonezawa, Yamagata 992-8510, Japan Received 13 November 2002; accepted 3 March 2003
Abstract The parallel plate dielectric resonator was applied to surface resistance ðRs Þ measurement of high temperature superconducting films with small area for the purpose of material research in early stage. Using 38 GHz resonance of TE013 mode, available measurement area in the film was diameter of 9 mm. From the theoretical calculation, the measurement at higher frequency had an advantage of less error in Rs that is caused by dielectric loss tangent ðtan dÞ. The effect of dielectric loss is negligible at 38 GHz even using a sapphire with order of 107 of tan d. In lower Rs region, Rs values of YBa2 Cu3 Oy that were measured at 38 GHz agreed well with that of standard measurement method at 22 GHz. However the difference of Rs between two methods became larger with increase of Rs . It is owing to poor signal to noise ratio at higher frequency. Ó 2003 Elsevier B.V. All rights reserved. PACS: 74.25.Nf; 74.76.Bz Keywords: Surface resistance; Sapphire dielectric resonator; Millimeter wave; Loss tangent
1. Introduction Various kinds of high temperature superconductor (HTS) materials and fabrication techniques of them are developing. Many materials of them
* Corresponding author. Address: Faculty of Biology-Oriented Science and Technology, Department of Electronic System and Information Engineering, Kinki University, 930 Nishimitani, Uchida, Naga, Wakayama 649-6493, Japan. Tel.: +81-736-77-0345/238-26-3289; fax: +81-736-77-4754/238-263289/3293. E-mail addresses: [email protected], kusu@info. waka.kindai.ac.jp (M. Kusunoki).
are studied for the microwave components. Surface resistance ðRs Þ is the most noticeable parameter for the microwave application of HTS. On the other hand, the parallel plate dielectric resonator [1–4] is one of the most reliable measurement tools of Rs . Non-destructive measurement of HTS films can be performed using the parallel plate dielectric resonator. Therefore, it is placed as a standard measurements method by International Electrotechnical Commission (IEC). However this method requires the samples with relatively large area that is depended on dimension of the dielectric rod [5]. Usually films with 1–3 in. diameter are applied to the parallel plate dielectric resonator for
0921-4534/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-4534(03)01023-2
1242
M. Kusunoki et al. / Physica C 392–396 (2003) 1241–1244
Rs measurement [7–9]. In earlier stage of the most material researches, small samples are prepared for evaluation of features. In general the preparation technique of large area film requires an advanced technology [10–12] with long period from basic research. Taking into account this, experimental evaluations of Rs in earlier stage of the material researches are useful to know essential efficiencies of the objective materials. The measurement in small area is also preferable for improving of space resolution in Rs mapping system [13]. In this paper, we report an attempt to measure Rs of the HTS films with small area using the parallel plate dielectric resonator method in millimeter wave region.
2. Measurement method A sapphire dielectric resonator was designed for the measurement of 10 mm diameter film. Resonance frequency of 38 GHz was chosen to reduce the dimension of measured area in the film. High quality single crystal of sapphire produced by Kyocera Corporation was chosen as a dielectric rod in order to reduce an effect of dielectric loss tangent. Although TE011 mode is usually used for this method [5–9,14], we used TE013 mode [15] to avoid difficulty of mounting of resonator by following reason. Height of a sapphire rod for TE011 mode at 38 GHz is 1.8 mm. It makes a gap between two HTS films narrower; as a result the gap is close to diameter of semi-rigid cables for antennas. When we use TE013 mode, the gap can be taken 3 times larger than TE011 mode. Schematic view of the resonator is shown in Fig. 1. Diameter of inner wall of Cu enclosure is 9 mm, which corresponds to the measured area in the film. The height and the diameter of sapphire rod are 5.4 and 3.6 mm, respectively. The resonator is cooled by a cryocooler. Temperature is monitored on the top and the bottom side of resonator as Fig. 1. Difference of the temperature between two points is less than 1 K at whole range of measuring temperature. Surface resistance is given by 1 A Rs ¼ tan d ð1Þ B Qu
Fig. 1. Schematic view of the parallel plate dielectric resonator. It is cooled by cryocooler. Temperature is monitored on the top and bottom side of the resonator. Difference of the temperature between two points is less than 1 K at whole range of measuring temperature.
A¼
1þW er
B¼
cm 2Lf0
ð2Þ 3
1þW ; 30p2 er m
ð3Þ
where Qu , c, L, er tan d, f0 and W are unloaded quality factor, the light velocity in vacuum, length of the rod, relative permittivity, loss tangent of the sapphire, resonance frequency and the ratio of electric field energy stored outside to inside the rod, respectively. Integer m takes 3 that is given by TE01m mode. The values of er and W can be calculated using f0 , L and diameter of sapphire [4].
3. Loss tangent of sapphire rod In most papers [6–9,13,14], the values of tan d is neglected to obtain Rs with the dielectric resonator method. From a practical point of view, considerable difference of tan d is confirmed in individual samples of sapphire single crystal [16]. Since the estimation of tan d is not so easy in general [15], it is desirable to measure Rs under a condition with
M. Kusunoki et al. / Physica C 392–396 (2003) 1241–1244
1243
Surface resistance (mΩ)
100 38GHz 22GHz 38GHz scaled from 22GHz
10
1
0.1 10
20
30
40
50
60
70
80
90
Temperature (K)
Fig. 2. Calculation of the error in Rs when tan d is neglected. Each curves corresponds to the original value of tan d of the sapphire that is neglected. The calculation assumes that HTS films have 0.1 mX of Rs at 10 GHz. At 38 GHz tan d is sufficiently small, even if the sapphire has tan d of order of 107 .
less effect of tan d. Taking into account that Rs of HTS film increases with increase of frequency in accordance with f 2 law, the measurement at higher frequency is preferable. We calculated the error ðDRs Þ that is included in Rs when tan d of sapphire is neglected in the measurement. A relationship between DRs and f0 is shown in Fig. 2. Each curves corresponds to the original values of tan d that are neglected. The vertical axis represents the error in Rs due to the neglect of tan d. The calculation assumes that HTS film has 0.1 mX of Rs at 10 GHz. The graph shows that tan d is sufficiently small at 38 GHz, even if the sapphire has tan d of order of 107 .
Fig. 3. Comparison of the measurement in millimeter wave region (38 GHz) with standard measurement method (22 GHz). Difference between two methods was arisen in larger Rs region because of poor S/N ratio.
shown with open squares in the graph. Open triangles correspond to Rs values scaled from 22 to 38 GHz by using f 2 low. In lower Rs region, the results that were obtained at two frequencies agree well. However difference in Rs values between two frequencies was arisen with increase of Rs . It is caused by poor signal to noise (S/N) ratio at 38 GHz. The resonance curve becomes too broader because resonance peak close to the higher noise level as Rs goes up near critical temperature ðTc Þ. To improve S/N ratio, strong couple of antenna to resonator is necessary. However fine adjustment of coupling coefficient for input and output antenna is required when standard measurement method is applied. The problem will be able to solved by using circle fit method [9,17].
5. Conclusion 4. Experimental results and discussion Fig. 3 shows a dependence of Rs on the temperature. A pair of YBa2 Cu3 Oy (YBCO) thin films was used for the test. Open circles depict Rs values measured at 38 GHz. In order to compare this method with standard measurement method, the same pair of YBCO was measured at 22 GHz. It is
The surface resistance of YBCO films with 9 mm diameter was measured using the parallel plate dielectric resonator method in millimeter wave region. TE013 resonance mode at 38 GHz is applied for the measurement. Theoretical calculation indicated that Rs measurement in millimeter wave region is superior in reducing the error caused by
1244
M. Kusunoki et al. / Physica C 392–396 (2003) 1241–1244
the dielectric loss. To ensure the reliability of this method, the values of Rs was compared with that had been obtained by standard measurement method at 22 GHz. Unique set of YBCO films were used for the comparison. In lower Rs region, the values of Rs showed good agreement with that of standard measurement. However, difference between two methods was arisen in larger Rs region near Tc because of poor S/N ratio. The problem can be improved by using circle fit method with strong coupling of antenna to resonator.
References [1] B.W. Hakki, P.D. Coleman, IRE Trans. Microwave Theory Tech. 8 (1960) 402. [2] M.W. Pospieszalski, IEEE Trans. Microwave Theory Tech. 25 (1977) 228. [3] Y. Kobayashi, M. Katoh, IEEE Trans. Microwave Theory Tech. 33 (1985) 586. [4] J. Krupka, M. Klinger, M. Kuhn, A. Baranyak, M. Stiller, J. Hinken, J. Modelski, IEEE Trans. Appl. Supercond. 3 (1993) 3043. [5] S. Okajima, H. Yoshikawa, Y. Kobayashi, Tech. Rep. ICICE MW98-4 (1998) 23.
[6] Z. Shen, C. Wilker, P. Pang, W.L. Holstein, D. Face, D.J. Kountz, IEEE Trans. Microwave Theory Tech. 40 (1992) 2424. [7] W.L. Holstein, L.A. Parisi, Z.Y. Shen, C. Wilker, M.S. Brenner, S. Martens, J. Supercond. 6 (1993) 191. [8] G. Kastner, C. Schafer, St Senz, T. Kaiser, M.A. Hein, M. Lorenz, H. Hochmuth, D. Hesse, Supercond. Sci. Technol. 12 (1999) 366. [9] K. Leong, J. Mazierska, J. Supercond. 14 (2001) 93. [10] M. Lorenz, H. Hochmuth, H. Borner, D. Natusch, Physica C 235–240 (1994) 639. [11] B. Utz, R. Semerad, M. Bauer, W. Prusseit, P. Berberich, H. Kinder, IEEE Trans. Appl. Supercond. 7 (1997) 1272. [12] T. Kumagai, T. Manabe, I. Yamaguchi, W. Kondo, F. Imai, K. Murayama, S. Mizuta, Physica C 357–360 (2001) 1346. [13] M. Kusunoki, Y. Takano, K. Nakamura, M. Inadomaru, D. Kosaka, A. Nozaki, S. Abe, M. Yokoo, M. Lorenz, H. Hochmuth, M. Mukaida, S. Ohshima, Physica C 383 (2002) 374. [14] M. Kusunoki, Y. Takano, M. Mukaida, S. Ohshima, Physica C 321 (1999) 81. [15] H. Yoshikawa, S. Okajima, Y. Kobayashi, Proc. 1998 Asia–Pacific Microwave Conference 1083 (1998). [16] M. Kusunoki, M. Inadomaru, S. Ohshima, K. Aizawa, M. Mukaida, M. Lorenz, H. Hochmuth, Physica C 377 (2002) 313. [17] H. Obara, S. Kosaka, A. Sawa, H. Yamasaki, Y. Kobayashi, T. Hashimoto, S. Ohshima, M. Kusunoki, M. Inadomaru, Physica C 357–360 (2001) 1511.
Rs measurement of HTS films in millimeter wave region using dielectric resonator method M. Kusunoki *, M. Inadomaru, D. Kousaka, S. Ohshima, K. Aizawa, M. Mukaida Department of Electrical Engineering, Yamagata University, 4-3-16 Johnan, Yonezawa, Yamagata 992-8510, Japan Received 13 November 2002; accepted 3 March 2003
Abstract The parallel plate dielectric resonator was applied to surface resistance ðRs Þ measurement of high temperature superconducting films with small area for the purpose of material research in early stage. Using 38 GHz resonance of TE013 mode, available measurement area in the film was diameter of 9 mm. From the theoretical calculation, the measurement at higher frequency had an advantage of less error in Rs that is caused by dielectric loss tangent ðtan dÞ. The effect of dielectric loss is negligible at 38 GHz even using a sapphire with order of 107 of tan d. In lower Rs region, Rs values of YBa2 Cu3 Oy that were measured at 38 GHz agreed well with that of standard measurement method at 22 GHz. However the difference of Rs between two methods became larger with increase of Rs . It is owing to poor signal to noise ratio at higher frequency. Ó 2003 Elsevier B.V. All rights reserved. PACS: 74.25.Nf; 74.76.Bz Keywords: Surface resistance; Sapphire dielectric resonator; Millimeter wave; Loss tangent
1. Introduction Various kinds of high temperature superconductor (HTS) materials and fabrication techniques of them are developing. Many materials of them
* Corresponding author. Address: Faculty of Biology-Oriented Science and Technology, Department of Electronic System and Information Engineering, Kinki University, 930 Nishimitani, Uchida, Naga, Wakayama 649-6493, Japan. Tel.: +81-736-77-0345/238-26-3289; fax: +81-736-77-4754/238-263289/3293. E-mail addresses: [email protected], kusu@info. waka.kindai.ac.jp (M. Kusunoki).
are studied for the microwave components. Surface resistance ðRs Þ is the most noticeable parameter for the microwave application of HTS. On the other hand, the parallel plate dielectric resonator [1–4] is one of the most reliable measurement tools of Rs . Non-destructive measurement of HTS films can be performed using the parallel plate dielectric resonator. Therefore, it is placed as a standard measurements method by International Electrotechnical Commission (IEC). However this method requires the samples with relatively large area that is depended on dimension of the dielectric rod [5]. Usually films with 1–3 in. diameter are applied to the parallel plate dielectric resonator for
0921-4534/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/S0921-4534(03)01023-2
1242
M. Kusunoki et al. / Physica C 392–396 (2003) 1241–1244
Rs measurement [7–9]. In earlier stage of the most material researches, small samples are prepared for evaluation of features. In general the preparation technique of large area film requires an advanced technology [10–12] with long period from basic research. Taking into account this, experimental evaluations of Rs in earlier stage of the material researches are useful to know essential efficiencies of the objective materials. The measurement in small area is also preferable for improving of space resolution in Rs mapping system [13]. In this paper, we report an attempt to measure Rs of the HTS films with small area using the parallel plate dielectric resonator method in millimeter wave region.
2. Measurement method A sapphire dielectric resonator was designed for the measurement of 10 mm diameter film. Resonance frequency of 38 GHz was chosen to reduce the dimension of measured area in the film. High quality single crystal of sapphire produced by Kyocera Corporation was chosen as a dielectric rod in order to reduce an effect of dielectric loss tangent. Although TE011 mode is usually used for this method [5–9,14], we used TE013 mode [15] to avoid difficulty of mounting of resonator by following reason. Height of a sapphire rod for TE011 mode at 38 GHz is 1.8 mm. It makes a gap between two HTS films narrower; as a result the gap is close to diameter of semi-rigid cables for antennas. When we use TE013 mode, the gap can be taken 3 times larger than TE011 mode. Schematic view of the resonator is shown in Fig. 1. Diameter of inner wall of Cu enclosure is 9 mm, which corresponds to the measured area in the film. The height and the diameter of sapphire rod are 5.4 and 3.6 mm, respectively. The resonator is cooled by a cryocooler. Temperature is monitored on the top and the bottom side of resonator as Fig. 1. Difference of the temperature between two points is less than 1 K at whole range of measuring temperature. Surface resistance is given by 1 A Rs ¼ tan d ð1Þ B Qu
Fig. 1. Schematic view of the parallel plate dielectric resonator. It is cooled by cryocooler. Temperature is monitored on the top and bottom side of the resonator. Difference of the temperature between two points is less than 1 K at whole range of measuring temperature.
A¼
1þW er
B¼
cm 2Lf0
ð2Þ 3
1þW ; 30p2 er m
ð3Þ
where Qu , c, L, er tan d, f0 and W are unloaded quality factor, the light velocity in vacuum, length of the rod, relative permittivity, loss tangent of the sapphire, resonance frequency and the ratio of electric field energy stored outside to inside the rod, respectively. Integer m takes 3 that is given by TE01m mode. The values of er and W can be calculated using f0 , L and diameter of sapphire [4].
3. Loss tangent of sapphire rod In most papers [6–9,13,14], the values of tan d is neglected to obtain Rs with the dielectric resonator method. From a practical point of view, considerable difference of tan d is confirmed in individual samples of sapphire single crystal [16]. Since the estimation of tan d is not so easy in general [15], it is desirable to measure Rs under a condition with
M. Kusunoki et al. / Physica C 392–396 (2003) 1241–1244
1243
Surface resistance (mΩ)
100 38GHz 22GHz 38GHz scaled from 22GHz
10
1
0.1 10
20
30
40
50
60
70
80
90
Temperature (K)
Fig. 2. Calculation of the error in Rs when tan d is neglected. Each curves corresponds to the original value of tan d of the sapphire that is neglected. The calculation assumes that HTS films have 0.1 mX of Rs at 10 GHz. At 38 GHz tan d is sufficiently small, even if the sapphire has tan d of order of 107 .
less effect of tan d. Taking into account that Rs of HTS film increases with increase of frequency in accordance with f 2 law, the measurement at higher frequency is preferable. We calculated the error ðDRs Þ that is included in Rs when tan d of sapphire is neglected in the measurement. A relationship between DRs and f0 is shown in Fig. 2. Each curves corresponds to the original values of tan d that are neglected. The vertical axis represents the error in Rs due to the neglect of tan d. The calculation assumes that HTS film has 0.1 mX of Rs at 10 GHz. The graph shows that tan d is sufficiently small at 38 GHz, even if the sapphire has tan d of order of 107 .
Fig. 3. Comparison of the measurement in millimeter wave region (38 GHz) with standard measurement method (22 GHz). Difference between two methods was arisen in larger Rs region because of poor S/N ratio.
shown with open squares in the graph. Open triangles correspond to Rs values scaled from 22 to 38 GHz by using f 2 low. In lower Rs region, the results that were obtained at two frequencies agree well. However difference in Rs values between two frequencies was arisen with increase of Rs . It is caused by poor signal to noise (S/N) ratio at 38 GHz. The resonance curve becomes too broader because resonance peak close to the higher noise level as Rs goes up near critical temperature ðTc Þ. To improve S/N ratio, strong couple of antenna to resonator is necessary. However fine adjustment of coupling coefficient for input and output antenna is required when standard measurement method is applied. The problem will be able to solved by using circle fit method [9,17].
5. Conclusion 4. Experimental results and discussion Fig. 3 shows a dependence of Rs on the temperature. A pair of YBa2 Cu3 Oy (YBCO) thin films was used for the test. Open circles depict Rs values measured at 38 GHz. In order to compare this method with standard measurement method, the same pair of YBCO was measured at 22 GHz. It is
The surface resistance of YBCO films with 9 mm diameter was measured using the parallel plate dielectric resonator method in millimeter wave region. TE013 resonance mode at 38 GHz is applied for the measurement. Theoretical calculation indicated that Rs measurement in millimeter wave region is superior in reducing the error caused by
1244
M. Kusunoki et al. / Physica C 392–396 (2003) 1241–1244
the dielectric loss. To ensure the reliability of this method, the values of Rs was compared with that had been obtained by standard measurement method at 22 GHz. Unique set of YBCO films were used for the comparison. In lower Rs region, the values of Rs showed good agreement with that of standard measurement. However, difference between two methods was arisen in larger Rs region near Tc because of poor S/N ratio. The problem can be improved by using circle fit method with strong coupling of antenna to resonator.
References [1] B.W. Hakki, P.D. Coleman, IRE Trans. Microwave Theory Tech. 8 (1960) 402. [2] M.W. Pospieszalski, IEEE Trans. Microwave Theory Tech. 25 (1977) 228. [3] Y. Kobayashi, M. Katoh, IEEE Trans. Microwave Theory Tech. 33 (1985) 586. [4] J. Krupka, M. Klinger, M. Kuhn, A. Baranyak, M. Stiller, J. Hinken, J. Modelski, IEEE Trans. Appl. Supercond. 3 (1993) 3043. [5] S. Okajima, H. Yoshikawa, Y. Kobayashi, Tech. Rep. ICICE MW98-4 (1998) 23.
[6] Z. Shen, C. Wilker, P. Pang, W.L. Holstein, D. Face, D.J. Kountz, IEEE Trans. Microwave Theory Tech. 40 (1992) 2424. [7] W.L. Holstein, L.A. Parisi, Z.Y. Shen, C. Wilker, M.S. Brenner, S. Martens, J. Supercond. 6 (1993) 191. [8] G. Kastner, C. Schafer, St Senz, T. Kaiser, M.A. Hein, M. Lorenz, H. Hochmuth, D. Hesse, Supercond. Sci. Technol. 12 (1999) 366. [9] K. Leong, J. Mazierska, J. Supercond. 14 (2001) 93. [10] M. Lorenz, H. Hochmuth, H. Borner, D. Natusch, Physica C 235–240 (1994) 639. [11] B. Utz, R. Semerad, M. Bauer, W. Prusseit, P. Berberich, H. Kinder, IEEE Trans. Appl. Supercond. 7 (1997) 1272. [12] T. Kumagai, T. Manabe, I. Yamaguchi, W. Kondo, F. Imai, K. Murayama, S. Mizuta, Physica C 357–360 (2001) 1346. [13] M. Kusunoki, Y. Takano, K. Nakamura, M. Inadomaru, D. Kosaka, A. Nozaki, S. Abe, M. Yokoo, M. Lorenz, H. Hochmuth, M. Mukaida, S. Ohshima, Physica C 383 (2002) 374. [14] M. Kusunoki, Y. Takano, M. Mukaida, S. Ohshima, Physica C 321 (1999) 81. [15] H. Yoshikawa, S. Okajima, Y. Kobayashi, Proc. 1998 Asia–Pacific Microwave Conference 1083 (1998). [16] M. Kusunoki, M. Inadomaru, S. Ohshima, K. Aizawa, M. Mukaida, M. Lorenz, H. Hochmuth, Physica C 377 (2002) 313. [17] H. Obara, S. Kosaka, A. Sawa, H. Yamasaki, Y. Kobayashi, T. Hashimoto, S. Ohshima, M. Kusunoki, M. Inadomaru, Physica C 357–360 (2001) 1511.