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Precise surface resistance measurements of YBa2Cu3Oy films with the dielectric resonator method
Physica C 357±360 (2001) 1511±1515
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Precise surface resistance measurements of YBa2Cu3Oy ®lms with the dielectric resonator method H. Obara a,*, S. Kosaka a, A. Sawa a, H. Yamasaki a, Y. Kobayashi b, T. Hashimoto b, S. Ohshima c, M. Kusunoki c, M. Inadomaru c a
b
Electrotechnical Laboratory, 1-1-4 Umezono, Tsukuba 305-8568, Japan Department of Electrical and Electronic Engineering, Saitama University, Urawa 338-8570, Japan c Faculty of Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa 992-8510, Japan Received 16 October 2000; accepted 5 January 2001
Abstract The surface resistance of high-Tc superconducting ®lms at microwave frequencies was carefully measured by the dielectric resonator method using two sapphire rods. The dielectric resonator method is appropriate for the standard measurement of surface resistance at microwave frequencies. In the present work, we focused on asymmetry in coupling and the parasitic coupling eect which cause error in this method and discussed the precision and accuracy of the measurements. Finally, we report on a round robin test in which the observed surface resistances in three institutes gave good agreement. These results were re¯ected in the working draft of the International Electrotechnical Commission Technical Committee 90 (IEC/TC90). Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 74.25.Nf; 74.72.Bk; 74.76.Bz Keywords: Microwave surface resistance; High-Tc ®lm; Standardization
1. Introduction High-Tc superconductor materials used for microwave resonators, ®lters, antennas and delay lines have a great advantage because of their very low loss characteristics. Recently, high-Tc superconductor ®lms of several inches diameter with very low surface resistances Rs (0.1 mX at 20 K, 12 GHz) become available because of the development of improved thin-®lm deposition techniques. Reliable methods for the Rs measurements,
*
Corresponding author. Fax: +81-298-61-5726. E-mail address: [email protected] (H. Obara).
however, have not been established yet. For the design of microwave components, data on the temperature-dependent Rs are needed. Moreover, very precise measurements of low Rs are essential for the further development of thin-®lm fabrication techniques. In the present work, we adopted the dielectric resonator method using two sapphire rods for the Rs measurements of ®lms. The dielectric resonator method is considered to be the most practical and appropriate for the standardization at present. However, several sources of error are expected in this method. We focused on asymmetry in coupling and the parasitic coupling eect and then discussed the precision and accuracy of the
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 5 3 3 - 0
1512
H. Obara et al. / Physica C 357±360 (2001) 1511±1515
measurements. We also performed a round robin test which is essential to standardization of measurements. The observed Rs in three institutes gave good agreement. Some of the experimental results are re¯ected in the working draft of the International Electrotechnical Commission Technical Committee 90 (IEC/TC90).
2. Experimental The Rs of high-Tc ®lms was measured with a dielectric resonator using two sapphire rods [1,2]. Fig. 1 shows the apparatus for the measurement of Rs . A high-quality sapphire rod was sandwiched between two superconducting ®lms (2-in. diameter), which were pressed together with a spring. The diameter of the sapphire rod for the 12-GHz resonator was about 12 mm. Magnetic dipole coupling was achieved by a pair of coaxial cables with a loop at the end. To eliminate the ambiguity of the loss tangent, tan d of sapphire rods, we used two sapphire rods which have the same diameter and dierent height: one is for a TE0 1 1 mode resonator and the other is for a TE0 1 3 mode resonator. The tan d value of the sapphire rods and the Rs value of the superconducting ®lms can be determined separately from the resonance frequencies and unloaded Q value, Qu . The measured samples were coevaporated YBa2 Cu3 Oy (YBCO) ®lms deposited on MgO-(1 0 0) substrates, fabricated by THEVA. The YBCO ®lms were c-axis-oriented with a 2-in. diameter and the typical thickness of the ®lms was 500 nm. The dielectric rods were c-axis-oriented high-purity single-crystal sapphire obtained from Union
Carbide and cut and polished to appropriate sizes. Two sapphire rods were used, with dimensions of 11:8 mm diameter 5:49 mm (length), and 11:8 mm diameter 16:47 mm (length). For measurements of superconductor ®lms, the resonator must be cooled below the critical temperature of the ®lms. We designed a cryostat system which enables us to introduce the He exchange gas for uniform temperature distribution in sample space and is almost free from the vibration of the refrigerator.
3. Results and discussion Qu of the resonator was calculated using loaded Q, QL and insertion attenuation. This technique assumes that the coupling on both loop antennas of the resonator is symmetric. Asymmetry of the coupling occurs frequently because of the dierent characteristics of the loop antennas, movement of the sapphire rod during measurement and other assembly-dependent eects. To measure the asymmetry of the resonator, the re¯ection coecient method is known to be useful [3]. Qu calculated using a conventional insertion attenuation method is QL ; 1 At At 10 IAdB=20 ;
Qu
1
where IA is insertion attenuation. An alternative method, a re¯ection coecient method for extracting unloaded Qu is calculated by
Fig. 1. Dielectric resonator for surface resistance measurement of superconductor ®lms.
H. Obara et al. / Physica C 357±360 (2001) 1511±1515
Qu QL 1 b1 b2 ; 1 S11 ; S11 S22 1 S22 b2 ; S11 S22 b1
2
where S11 and S22 are S-parameters of re¯ection on each port. Fig. 2 shows determination of S-parameter from multifrequency measurements around the resonance. A simple method to determine S-parameter is measuring magnitude of re¯ection coecient at the resonance frequency. Another method is ®tting the S-parameter data to a circle in complex plane [4]. This procedure is more precise when the background signal of S11 and S22 is not ¯at. The calculated Qu values at
Fig. 2. Determination of re¯ection S-parameters. The inset shows circle ®tting in complex plane.
1513
several temperatures in TE0 1 3 mode measurement using the insertion attenuation method and the re¯ection coecient method with circle ®tting are summarized in Table 1. The dierence between Qu values from both measurements was less than 3% even though asymmetry of coupling was observed in our resonator. The re¯ection coecient method with circle ®tting is the best technique to determine Qu and does not require the additional step of through calibration. However, this method takes time to ®t and calculate data, and needs to maintain a resonator at constant temperature. The asymmetry eect is considered to cause large errors in strong coupling. In our case, the coupling was about 20 dB at low temperatures and the error due to the asymmetry eect is considered to be small. Expected error of the simple insertion attenuation method was less than 3% in our experimental setup. A round robin testing was done using the insertion attenuation method with increasing temperature. The obtained data was checked using the re¯ection coecient method at several temperatures. Parasitic coupling to an unwanted mode existing outside the resonator is known to aect the Qu value of the open-type resonator. In the present study, the sizes of the resonator and sapphire rod were carefully designed. However, we observed a variation of Qu value which is considered to be due to the parasitic coupling to the case mode. RF shield ®lms attached to the case of the sample space were eective for the reduction of parasitic coupling to the case mode. Additional coupling to the other mode, for example, the mode excited in the copper base of the resonator and the coaxis cable, was not eliminated by this RF shield. Fig. 3 shows temperature dependencies of Qu in dierent types of resonator. Higher Qu was observed in closed-type resonator which indicates
Table 1 Calculated re¯ection S-parameters and Q values of TE0 1 3 mode measurements at several temperatures T (K)
S11
S22
QL (106 )
Qu (106 ) (insertion attenuation method)
Qu (106 ) (re¯ection method)
22.6 39.4 64.9
0.85142 0.89488 0.92827
0.8519 0.92947 0.94912
4.0851 2.9623 2.0609
4.7513 3.3099 2.2270
4.6610 3.2476 2.1955
1514
H. Obara et al. / Physica C 357±360 (2001) 1511±1515
Fig. 3. Temperature dependences of Qu in dierent type of resonators.
that the additional loss occurred in open-type resonator. The disadvantage of a closed-type resonator is the possible damage to the superconducting ®lms due to the direct contact of the conductor plate to the superconducting ®lms. A round robin test was performed using the identical ®lms and sapphire rods. Each sapphire rod was selected from two rods which have the same physical dimensions. Choice of sapphire rod is quite important in the dielectric resonator method using two sapphire rods because we assume that tan d values of two sapphire rods are the same. Measurements were done in three institutes. The range of observed Qu values of the TE0 1 3 mode was from 4:2 106 to 6:4 106 at 20 K. The Qu values of the TE0 1 1 mode were also variant in three institutes, from 2:1 106 to 3:7 106 at 20 K. Two Institutes used open-type resonators and another institute used a close-type resonator. The Qu of the close-type resonator was higher than that of the open-type resonator. The Rs of ®lms is calculated using the following equation, Rs A
1 Qu
B tan d ;
3
Fig. 4. Results of the round robin test in three institutes. Temperature dependences of Rs .
where A and B are geometrical factors. tan d of sapphire rod was estimated from the measured values of Qu in TE0 1 1 and TE0 1 3 mode measurements. 1 3 1 tan d ; 4 2B Qu3 Qu1 where Qu3 and Qu1 are Qu values in TE0 1 1 and TE0 1 3 mode measurements, respectively. Calculated Rs values of the round robin test are shown in Fig. 4. The Rs values coincided well even though Qu values diered. In the open-type resonator, lower Qu was observed in TE0 1 1 and TE0 1 3 indicating that the additional loss occurs, i.e. 1 Rs 1 B tan d ; Qu Qopen A
5
where Qopen is quality factors due to the additional loss in open-type resonator. Possible mechanism of the loss is parasitic coupling eect. If Qopen values of TE0 1 1 and TE0 1 3 mode resonator are the same, this factor is canceled in Eqs. (3) and (4). The results of the round robin test suggest that the additional loss in the open-type resonators is
H. Obara et al. / Physica C 357±360 (2001) 1511±1515
canceled using TE0 1 1 and TE0 1 3 mode measurements. However, the loss in dierent mode measurements is not necessarily the same. Moreover, tan d of sapphire rods for TE0 1 1 and TE0 1 3 mode measurements may be dierent. The ambiguity still exists in the dielectric resonator measurements and further study is needed for standardization of the measurements. 4. Conclusion In the present work, we have discussed several sources of error which aect the precision and accuracy of dielectric resonator measurements. The re¯ection coecient measurement is useful to check the Qu values obtained from the conventional insertion attenuation method. The results of the round robin test in three institutes showed a good agreement in Rs values. However, a variety of Qu values was observed in the dierent-type resonators.
1515
Acknowledgements We are grateful to R. Ono of NIST and C. Wilker of DuPont for their helpful comments on the re¯ection measurements. This work was performed as an activity of Japanese National Committee of IEC/TC90 and supported by the VAMAS (Versailles Project on Advanced Materials and Standards) pre-standardization work on the thin ®lm properties of superconductors. References [1] Y. Kobayashi, T. Imai, H. Kayano, IEEE Trans. Microwave Theory Tech. 39 (1991) 1530. [2] Z. Shen, C. Wilker, P. Pang, W.L. Holstein, D. Face, D.J. Kountz, IEEE Trans. Microwave Theory Tech. 40 (1992) 2424. [3] C. Wilker, Z.-Y. Shen, V.X. Nguyen, M.S. Brenner, IEEE Trans. Appl. Supercond. 3 (1993) 1457. [4] J. Mazierska, C. Wilker, IEEE Trans. Appl. Supercond., submitted for publication.
www.elsevier.com/locate/physc
Precise surface resistance measurements of YBa2Cu3Oy ®lms with the dielectric resonator method H. Obara a,*, S. Kosaka a, A. Sawa a, H. Yamasaki a, Y. Kobayashi b, T. Hashimoto b, S. Ohshima c, M. Kusunoki c, M. Inadomaru c a
b
Electrotechnical Laboratory, 1-1-4 Umezono, Tsukuba 305-8568, Japan Department of Electrical and Electronic Engineering, Saitama University, Urawa 338-8570, Japan c Faculty of Engineering, Yamagata University, 4-3-16 Jonan, Yonezawa 992-8510, Japan Received 16 October 2000; accepted 5 January 2001
Abstract The surface resistance of high-Tc superconducting ®lms at microwave frequencies was carefully measured by the dielectric resonator method using two sapphire rods. The dielectric resonator method is appropriate for the standard measurement of surface resistance at microwave frequencies. In the present work, we focused on asymmetry in coupling and the parasitic coupling eect which cause error in this method and discussed the precision and accuracy of the measurements. Finally, we report on a round robin test in which the observed surface resistances in three institutes gave good agreement. These results were re¯ected in the working draft of the International Electrotechnical Commission Technical Committee 90 (IEC/TC90). Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 74.25.Nf; 74.72.Bk; 74.76.Bz Keywords: Microwave surface resistance; High-Tc ®lm; Standardization
1. Introduction High-Tc superconductor materials used for microwave resonators, ®lters, antennas and delay lines have a great advantage because of their very low loss characteristics. Recently, high-Tc superconductor ®lms of several inches diameter with very low surface resistances Rs (0.1 mX at 20 K, 12 GHz) become available because of the development of improved thin-®lm deposition techniques. Reliable methods for the Rs measurements,
*
Corresponding author. Fax: +81-298-61-5726. E-mail address: [email protected] (H. Obara).
however, have not been established yet. For the design of microwave components, data on the temperature-dependent Rs are needed. Moreover, very precise measurements of low Rs are essential for the further development of thin-®lm fabrication techniques. In the present work, we adopted the dielectric resonator method using two sapphire rods for the Rs measurements of ®lms. The dielectric resonator method is considered to be the most practical and appropriate for the standardization at present. However, several sources of error are expected in this method. We focused on asymmetry in coupling and the parasitic coupling eect and then discussed the precision and accuracy of the
0921-4534/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 1 ) 0 0 5 3 3 - 0
1512
H. Obara et al. / Physica C 357±360 (2001) 1511±1515
measurements. We also performed a round robin test which is essential to standardization of measurements. The observed Rs in three institutes gave good agreement. Some of the experimental results are re¯ected in the working draft of the International Electrotechnical Commission Technical Committee 90 (IEC/TC90).
2. Experimental The Rs of high-Tc ®lms was measured with a dielectric resonator using two sapphire rods [1,2]. Fig. 1 shows the apparatus for the measurement of Rs . A high-quality sapphire rod was sandwiched between two superconducting ®lms (2-in. diameter), which were pressed together with a spring. The diameter of the sapphire rod for the 12-GHz resonator was about 12 mm. Magnetic dipole coupling was achieved by a pair of coaxial cables with a loop at the end. To eliminate the ambiguity of the loss tangent, tan d of sapphire rods, we used two sapphire rods which have the same diameter and dierent height: one is for a TE0 1 1 mode resonator and the other is for a TE0 1 3 mode resonator. The tan d value of the sapphire rods and the Rs value of the superconducting ®lms can be determined separately from the resonance frequencies and unloaded Q value, Qu . The measured samples were coevaporated YBa2 Cu3 Oy (YBCO) ®lms deposited on MgO-(1 0 0) substrates, fabricated by THEVA. The YBCO ®lms were c-axis-oriented with a 2-in. diameter and the typical thickness of the ®lms was 500 nm. The dielectric rods were c-axis-oriented high-purity single-crystal sapphire obtained from Union
Carbide and cut and polished to appropriate sizes. Two sapphire rods were used, with dimensions of 11:8 mm diameter 5:49 mm (length), and 11:8 mm diameter 16:47 mm (length). For measurements of superconductor ®lms, the resonator must be cooled below the critical temperature of the ®lms. We designed a cryostat system which enables us to introduce the He exchange gas for uniform temperature distribution in sample space and is almost free from the vibration of the refrigerator.
3. Results and discussion Qu of the resonator was calculated using loaded Q, QL and insertion attenuation. This technique assumes that the coupling on both loop antennas of the resonator is symmetric. Asymmetry of the coupling occurs frequently because of the dierent characteristics of the loop antennas, movement of the sapphire rod during measurement and other assembly-dependent eects. To measure the asymmetry of the resonator, the re¯ection coecient method is known to be useful [3]. Qu calculated using a conventional insertion attenuation method is QL ; 1 At At 10 IAdB=20 ;
Qu
1
where IA is insertion attenuation. An alternative method, a re¯ection coecient method for extracting unloaded Qu is calculated by
Fig. 1. Dielectric resonator for surface resistance measurement of superconductor ®lms.
H. Obara et al. / Physica C 357±360 (2001) 1511±1515
Qu QL 1 b1 b2 ; 1 S11 ; S11 S22 1 S22 b2 ; S11 S22 b1
2
where S11 and S22 are S-parameters of re¯ection on each port. Fig. 2 shows determination of S-parameter from multifrequency measurements around the resonance. A simple method to determine S-parameter is measuring magnitude of re¯ection coecient at the resonance frequency. Another method is ®tting the S-parameter data to a circle in complex plane [4]. This procedure is more precise when the background signal of S11 and S22 is not ¯at. The calculated Qu values at
Fig. 2. Determination of re¯ection S-parameters. The inset shows circle ®tting in complex plane.
1513
several temperatures in TE0 1 3 mode measurement using the insertion attenuation method and the re¯ection coecient method with circle ®tting are summarized in Table 1. The dierence between Qu values from both measurements was less than 3% even though asymmetry of coupling was observed in our resonator. The re¯ection coecient method with circle ®tting is the best technique to determine Qu and does not require the additional step of through calibration. However, this method takes time to ®t and calculate data, and needs to maintain a resonator at constant temperature. The asymmetry eect is considered to cause large errors in strong coupling. In our case, the coupling was about 20 dB at low temperatures and the error due to the asymmetry eect is considered to be small. Expected error of the simple insertion attenuation method was less than 3% in our experimental setup. A round robin testing was done using the insertion attenuation method with increasing temperature. The obtained data was checked using the re¯ection coecient method at several temperatures. Parasitic coupling to an unwanted mode existing outside the resonator is known to aect the Qu value of the open-type resonator. In the present study, the sizes of the resonator and sapphire rod were carefully designed. However, we observed a variation of Qu value which is considered to be due to the parasitic coupling to the case mode. RF shield ®lms attached to the case of the sample space were eective for the reduction of parasitic coupling to the case mode. Additional coupling to the other mode, for example, the mode excited in the copper base of the resonator and the coaxis cable, was not eliminated by this RF shield. Fig. 3 shows temperature dependencies of Qu in dierent types of resonator. Higher Qu was observed in closed-type resonator which indicates
Table 1 Calculated re¯ection S-parameters and Q values of TE0 1 3 mode measurements at several temperatures T (K)
S11
S22
QL (106 )
Qu (106 ) (insertion attenuation method)
Qu (106 ) (re¯ection method)
22.6 39.4 64.9
0.85142 0.89488 0.92827
0.8519 0.92947 0.94912
4.0851 2.9623 2.0609
4.7513 3.3099 2.2270
4.6610 3.2476 2.1955
1514
H. Obara et al. / Physica C 357±360 (2001) 1511±1515
Fig. 3. Temperature dependences of Qu in dierent type of resonators.
that the additional loss occurred in open-type resonator. The disadvantage of a closed-type resonator is the possible damage to the superconducting ®lms due to the direct contact of the conductor plate to the superconducting ®lms. A round robin test was performed using the identical ®lms and sapphire rods. Each sapphire rod was selected from two rods which have the same physical dimensions. Choice of sapphire rod is quite important in the dielectric resonator method using two sapphire rods because we assume that tan d values of two sapphire rods are the same. Measurements were done in three institutes. The range of observed Qu values of the TE0 1 3 mode was from 4:2 106 to 6:4 106 at 20 K. The Qu values of the TE0 1 1 mode were also variant in three institutes, from 2:1 106 to 3:7 106 at 20 K. Two Institutes used open-type resonators and another institute used a close-type resonator. The Qu of the close-type resonator was higher than that of the open-type resonator. The Rs of ®lms is calculated using the following equation, Rs A
1 Qu
B tan d ;
3
Fig. 4. Results of the round robin test in three institutes. Temperature dependences of Rs .
where A and B are geometrical factors. tan d of sapphire rod was estimated from the measured values of Qu in TE0 1 1 and TE0 1 3 mode measurements. 1 3 1 tan d ; 4 2B Qu3 Qu1 where Qu3 and Qu1 are Qu values in TE0 1 1 and TE0 1 3 mode measurements, respectively. Calculated Rs values of the round robin test are shown in Fig. 4. The Rs values coincided well even though Qu values diered. In the open-type resonator, lower Qu was observed in TE0 1 1 and TE0 1 3 indicating that the additional loss occurs, i.e. 1 Rs 1 B tan d ; Qu Qopen A
5
where Qopen is quality factors due to the additional loss in open-type resonator. Possible mechanism of the loss is parasitic coupling eect. If Qopen values of TE0 1 1 and TE0 1 3 mode resonator are the same, this factor is canceled in Eqs. (3) and (4). The results of the round robin test suggest that the additional loss in the open-type resonators is
H. Obara et al. / Physica C 357±360 (2001) 1511±1515
canceled using TE0 1 1 and TE0 1 3 mode measurements. However, the loss in dierent mode measurements is not necessarily the same. Moreover, tan d of sapphire rods for TE0 1 1 and TE0 1 3 mode measurements may be dierent. The ambiguity still exists in the dielectric resonator measurements and further study is needed for standardization of the measurements. 4. Conclusion In the present work, we have discussed several sources of error which aect the precision and accuracy of dielectric resonator measurements. The re¯ection coecient measurement is useful to check the Qu values obtained from the conventional insertion attenuation method. The results of the round robin test in three institutes showed a good agreement in Rs values. However, a variety of Qu values was observed in the dierent-type resonators.
1515
Acknowledgements We are grateful to R. Ono of NIST and C. Wilker of DuPont for their helpful comments on the re¯ection measurements. This work was performed as an activity of Japanese National Committee of IEC/TC90 and supported by the VAMAS (Versailles Project on Advanced Materials and Standards) pre-standardization work on the thin ®lm properties of superconductors. References [1] Y. Kobayashi, T. Imai, H. Kayano, IEEE Trans. Microwave Theory Tech. 39 (1991) 1530. [2] Z. Shen, C. Wilker, P. Pang, W.L. Holstein, D. Face, D.J. Kountz, IEEE Trans. Microwave Theory Tech. 40 (1992) 2424. [3] C. Wilker, Z.-Y. Shen, V.X. Nguyen, M.S. Brenner, IEEE Trans. Appl. Supercond. 3 (1993) 1457. [4] J. Mazierska, C. Wilker, IEEE Trans. Appl. Supercond., submitted for publication.