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Microwave intermodulation distortion measurements in unpatterned and patterned YBCO thin films
Physica C 372–376 (2002) 692–695 www.elsevier.com/locate/physc
Microwave intermodulation distortion measurements in unpatterned and patterned YBCO thin films M. Abu Bakar a, A.V. Velichko a,*, M.J. Lancaster a, A. Porch b, J.C. Gallop c, L. Hao c, L.F. Cohen d, A. Zhukov d a
School of Electronic and Electrical Engineering, University of Birmingham, Birmingham BI5 2TT, UK b School of Engineering, University of Cardiff, Cardiff CF24 OYF, UK c National Physical Laboratory, Teddington TW11 OLW, UK d Imperial College, London SW7 2BZ, UK
Abstract We present the work on intermodulation distortion (IMD) in the unpatterned and patterned states of 1 cm2 YBCO films, employing dielectric resonator and coplanar resonator techniques, respectively. The unpatterned films are measured using rutile and sapphire dielectric resonators. Subsequently, these films are patterned into identical coplanar resonator structures. Third order IMD products vs. input power for all the films studied typically show a noticeable deviation from the conventional 3:1 scaling towards a lower slope. Third order intercept powers for unpatterned and patterned states of the films appear to be slightly different and also temperature dependent. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Third order intermodulation distortion; High-temperature superconductor; Microwave nonlinearity
1. Introduction Nonlinearity in superconducting devices is manifested by a change in the device behavior as a function of the input power [1]. One direct measure of nonlinearity is to study the RF power Prf dependence of the surface impedance. However, harmonic generation and intermodulation measurements provide a more sensitive probe of the nonlinearity at extremely low power levels, where the device response otherwise appears linear. Here,
*
Corresponding author. Fax: +44-121-414-4291. E-mail address: [email protected] (A.V. Velichko).
we focus on intermodulation distortion (IMD) measurements on high temperature superconducting (HTS) films, both in the unpatterned and patterned states to find out whether the patterning affects the appearance of the IMD products. According to the classical theory of IMD in nonlinear systems with the impedance being proportional to Hrf2 (Hrf is the microwave field amplitude), third order IMD products generally scale with the third power of the input power. This is usually referred to as the 3:1 scaling. However, recently there have been a number of reports in the literature [2–4], in which the above scaling for high quality HTS films was found to break down. Here we at first time present results on the IMD measurements in unpatterned and patterned states of the same films
0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 2 ) 0 0 8 3 3 - X
M. Abu Bakar et al. / Physica C 372–376 (2002) 692–695
that also show a similar departure from the conventional 3:1 behavior.
2. Experimental details We performed IMD measurements on three films, CH172, CH113 and DP1 at temperatures T between 12 and 60 K. CH172 and CH113 were grown by laser ablation on MgO substrates, and DP1 was deposited by the magnetron sputtering on a LaAlO3 substrate. At 12 K the unpatterned measurements were carried out using a cylindrical rutile resonator (see Fig. 1a) of 4.0 mm in diameter and 2.3 mm in height, yielding the resonant frequency of about 8 GHz in the TE0 1 1 mode. The poor temperature stability (P 300 ppm) of the rutile dielectric permittivity e did not allow us to perform measurements at T > 15 K. Those measurements are described in detail elsewhere [5].
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Therefore, for measurements at higher temperatures (40 and 60 K) a sapphire resonator of 12 mm in diameter and 5 mm in height was used as shown in Fig. 1b. The resonator is supported by a low loss quartz tube. The HTS film under test is attached to the sample holder, which is an extension of the top Cu plate. The copper housing is 36 mm in diameter. The position of the top plate with the sample is adjustable to maximize the TE0 1 1 mode quality factor and to minimize insertion loss. The resonator frequency for the TE0 1 1 mode is about 10 GHz, as calculated by using MAFIA software. The coplanar resonators on all the three films were patterned by standard photolithography and ion beam milling technique. The resonators under study have a central line width of 200 lm with gaps of 73 lm on each side and the line length of 8 mm, which results in the fundamental resonant frequencies of around 8 GHz on MgO and 5 GHz on LaAlO3 substrates, respectively. In the IMD measurements two microwave signals at frequencies f1 and f2 with a frequency separation Df of about 6–7 kHz were symmetrically placed around the resonant frequency. The sources were protected from the reflected signals by 40 dB of isolation each. The two microwave signals were combined using a power combiner and passed through a variable attenuator to the resonator loaded with the film. The third order IMD signals transmitted at the lower and upper side bands (LSB and USB, respectively) were detected using a low noise spectrum analyzer (HP8593E).
3. Results and discussion
Fig. 1. (a) Rutile resonator used in IMD measurements at 12 K and (b) sapphire resonator used in IMD measurements at 40 and 60 K.
The IMD measurements on CH172 at 12 K as a function of Prf and Hrf2 are shown in Fig. 2a and b, respectively. The power dependences of the third order IMD products in both unpatterned and patterned states exhibit the same slope of 1.6:1. Fig. 2b compares the third order intercept (TOI) of the unpatterned and patterned states in terms of Hrf2 . The TOI of the unpatterned state is 6 kA m1 and the patterned state has a TOI of 13 kA m1 . The difference in these values is probably due to the error in the extrapolation of the data to higher
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M. Abu Bakar et al. / Physica C 372–376 (2002) 692–695
Fig. 2. Fundamental tones and third order IMD products vs. (a) the input power and (b) the square of the peak magnetic field in CH172 at 12 K for the unpatterned and patterned states. The symbols used in both figures are the same.
powers. However, a slight degradation of the film at the edges due to patterning is also a possible reason. Similarly to CH172, for CH113 at 12 K the IMD products also show a slope of 1.6:1 in both unpatterned and patterned states (not shown in the figure). The TOIs of the two states are 35 nd 25 kA m1 , respectively. The difference in the TOI values in CH113 is smaller than for CH172, and probably has the same origin as that for CH113. The higher TOI values for CH113 are in line with our findings that this film has a lower residual surface resistance and better power handling compared with CH172. The IMD measurements on DP1 at 40 and 60 K are shown in Fig. 3a and b. In this case the slopes
Fig. 3. Fundamental tones and third order IMD products vs. the input power for DP1 at (a) 40 and (b) 60 K for the unpatterned and patterned states. The symbols in this figure are identical with those in Fig. 2a.
in the unpatterned and patterned states are different (2 for the patterned state, and varying from 1 to 1.5 for the unpatterned film) and also temperature dependent. Such low values of the slopes as well as their variation with temperature are indicative of a mechanism which is different from the classical nonlinear mixing mechanism giving the 3:1 behavior. Although we have used the concept of TOI in this work to estimate the relative performance of different films, the fact that none of the films exhibits a slope of 3 suggests that TOI is not an appropriate measure of performance when largescale extrapolation is required in order to estimate the intercept value. In addition the observation of predominant slopes much less than 3 suggests that the conventional nonlinear mixing behavior is not the dominant contribution that
M. Abu Bakar et al. / Physica C 372–376 (2002) 692–695
generates IMD products in these films. Currently we are developing a model (to be published elsewhere) based on global heating effects. In that model by using realistic values for the thermal resistance between HTS film and thermal reservoir we are able to predict the IMD products vs. input power slopes between 1 and 2, as generally observed in this work. In addition the dependence of the IMD level on the difference frequency Df ¼ f1 f2 may also be understood by this mechanism. In conclusion, the YBCO thin films measured here exhibit a difference in the TOI values in unpatterned and patterned states within a factor of 2. Though this difference is not dramatic, it may be indicative of a slight degradation of the film at the edges due to patterning. Besides, low values (below 2) of the slopes of the third order IMD products vs. input power and their variation with temperature suggest that the nonlinear mechanism for the films studied in this work is different from the classical nonlinear mixing mechanism, which predicts the slope of 3:1.
695
Acknowledgements We are grateful to Dr. T.J. Jackson and Dr. X. Xiong for device fabrication, and Dr. T.E. Dodgson from the ‘‘Wave Solutions’’ for providing a part of the microwave equipment used in these experiments. The work at Birmingham was supported by EPSRC grant GR/L65581/01. The work at NPL was funded by DTI under the Quantum Metrology Programme, project PF9834.
References [1] S.M. Anlage, W. Hu, C.P. Vlahacos, D. Steinhauer, B.J. Feenstra, S.K. Dutta, A. Thabawalla, F.C. Wellstood, J. Supercond. 12 (1999) 353. [2] S. Cho, C. Lee, IEEE Trans. Appl. Supercond. 9 (1999) 3998. [3] B.A. Willemsen, K.E. Kihlstrom, T. Dahm, Appl. Phys. Lett. 74 (1999) 753. [4] B.A. Willemsen, T. Dahm, B.H. King, D.J. Scalapino, IEEE Trans. Appl. Supercond. 9 (1999) 4181. [5] L. Hao, J.C. Gallop, A.J. Purnell, L.F. Cohen, J. Supercond. 14 (2001) 31.
Microwave intermodulation distortion measurements in unpatterned and patterned YBCO thin films M. Abu Bakar a, A.V. Velichko a,*, M.J. Lancaster a, A. Porch b, J.C. Gallop c, L. Hao c, L.F. Cohen d, A. Zhukov d a
School of Electronic and Electrical Engineering, University of Birmingham, Birmingham BI5 2TT, UK b School of Engineering, University of Cardiff, Cardiff CF24 OYF, UK c National Physical Laboratory, Teddington TW11 OLW, UK d Imperial College, London SW7 2BZ, UK
Abstract We present the work on intermodulation distortion (IMD) in the unpatterned and patterned states of 1 cm2 YBCO films, employing dielectric resonator and coplanar resonator techniques, respectively. The unpatterned films are measured using rutile and sapphire dielectric resonators. Subsequently, these films are patterned into identical coplanar resonator structures. Third order IMD products vs. input power for all the films studied typically show a noticeable deviation from the conventional 3:1 scaling towards a lower slope. Third order intercept powers for unpatterned and patterned states of the films appear to be slightly different and also temperature dependent. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Third order intermodulation distortion; High-temperature superconductor; Microwave nonlinearity
1. Introduction Nonlinearity in superconducting devices is manifested by a change in the device behavior as a function of the input power [1]. One direct measure of nonlinearity is to study the RF power Prf dependence of the surface impedance. However, harmonic generation and intermodulation measurements provide a more sensitive probe of the nonlinearity at extremely low power levels, where the device response otherwise appears linear. Here,
*
Corresponding author. Fax: +44-121-414-4291. E-mail address: [email protected] (A.V. Velichko).
we focus on intermodulation distortion (IMD) measurements on high temperature superconducting (HTS) films, both in the unpatterned and patterned states to find out whether the patterning affects the appearance of the IMD products. According to the classical theory of IMD in nonlinear systems with the impedance being proportional to Hrf2 (Hrf is the microwave field amplitude), third order IMD products generally scale with the third power of the input power. This is usually referred to as the 3:1 scaling. However, recently there have been a number of reports in the literature [2–4], in which the above scaling for high quality HTS films was found to break down. Here we at first time present results on the IMD measurements in unpatterned and patterned states of the same films
0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 1 - 4 5 3 4 ( 0 2 ) 0 0 8 3 3 - X
M. Abu Bakar et al. / Physica C 372–376 (2002) 692–695
that also show a similar departure from the conventional 3:1 behavior.
2. Experimental details We performed IMD measurements on three films, CH172, CH113 and DP1 at temperatures T between 12 and 60 K. CH172 and CH113 were grown by laser ablation on MgO substrates, and DP1 was deposited by the magnetron sputtering on a LaAlO3 substrate. At 12 K the unpatterned measurements were carried out using a cylindrical rutile resonator (see Fig. 1a) of 4.0 mm in diameter and 2.3 mm in height, yielding the resonant frequency of about 8 GHz in the TE0 1 1 mode. The poor temperature stability (P 300 ppm) of the rutile dielectric permittivity e did not allow us to perform measurements at T > 15 K. Those measurements are described in detail elsewhere [5].
693
Therefore, for measurements at higher temperatures (40 and 60 K) a sapphire resonator of 12 mm in diameter and 5 mm in height was used as shown in Fig. 1b. The resonator is supported by a low loss quartz tube. The HTS film under test is attached to the sample holder, which is an extension of the top Cu plate. The copper housing is 36 mm in diameter. The position of the top plate with the sample is adjustable to maximize the TE0 1 1 mode quality factor and to minimize insertion loss. The resonator frequency for the TE0 1 1 mode is about 10 GHz, as calculated by using MAFIA software. The coplanar resonators on all the three films were patterned by standard photolithography and ion beam milling technique. The resonators under study have a central line width of 200 lm with gaps of 73 lm on each side and the line length of 8 mm, which results in the fundamental resonant frequencies of around 8 GHz on MgO and 5 GHz on LaAlO3 substrates, respectively. In the IMD measurements two microwave signals at frequencies f1 and f2 with a frequency separation Df of about 6–7 kHz were symmetrically placed around the resonant frequency. The sources were protected from the reflected signals by 40 dB of isolation each. The two microwave signals were combined using a power combiner and passed through a variable attenuator to the resonator loaded with the film. The third order IMD signals transmitted at the lower and upper side bands (LSB and USB, respectively) were detected using a low noise spectrum analyzer (HP8593E).
3. Results and discussion
Fig. 1. (a) Rutile resonator used in IMD measurements at 12 K and (b) sapphire resonator used in IMD measurements at 40 and 60 K.
The IMD measurements on CH172 at 12 K as a function of Prf and Hrf2 are shown in Fig. 2a and b, respectively. The power dependences of the third order IMD products in both unpatterned and patterned states exhibit the same slope of 1.6:1. Fig. 2b compares the third order intercept (TOI) of the unpatterned and patterned states in terms of Hrf2 . The TOI of the unpatterned state is 6 kA m1 and the patterned state has a TOI of 13 kA m1 . The difference in these values is probably due to the error in the extrapolation of the data to higher
694
M. Abu Bakar et al. / Physica C 372–376 (2002) 692–695
Fig. 2. Fundamental tones and third order IMD products vs. (a) the input power and (b) the square of the peak magnetic field in CH172 at 12 K for the unpatterned and patterned states. The symbols used in both figures are the same.
powers. However, a slight degradation of the film at the edges due to patterning is also a possible reason. Similarly to CH172, for CH113 at 12 K the IMD products also show a slope of 1.6:1 in both unpatterned and patterned states (not shown in the figure). The TOIs of the two states are 35 nd 25 kA m1 , respectively. The difference in the TOI values in CH113 is smaller than for CH172, and probably has the same origin as that for CH113. The higher TOI values for CH113 are in line with our findings that this film has a lower residual surface resistance and better power handling compared with CH172. The IMD measurements on DP1 at 40 and 60 K are shown in Fig. 3a and b. In this case the slopes
Fig. 3. Fundamental tones and third order IMD products vs. the input power for DP1 at (a) 40 and (b) 60 K for the unpatterned and patterned states. The symbols in this figure are identical with those in Fig. 2a.
in the unpatterned and patterned states are different (2 for the patterned state, and varying from 1 to 1.5 for the unpatterned film) and also temperature dependent. Such low values of the slopes as well as their variation with temperature are indicative of a mechanism which is different from the classical nonlinear mixing mechanism giving the 3:1 behavior. Although we have used the concept of TOI in this work to estimate the relative performance of different films, the fact that none of the films exhibits a slope of 3 suggests that TOI is not an appropriate measure of performance when largescale extrapolation is required in order to estimate the intercept value. In addition the observation of predominant slopes much less than 3 suggests that the conventional nonlinear mixing behavior is not the dominant contribution that
M. Abu Bakar et al. / Physica C 372–376 (2002) 692–695
generates IMD products in these films. Currently we are developing a model (to be published elsewhere) based on global heating effects. In that model by using realistic values for the thermal resistance between HTS film and thermal reservoir we are able to predict the IMD products vs. input power slopes between 1 and 2, as generally observed in this work. In addition the dependence of the IMD level on the difference frequency Df ¼ f1 f2 may also be understood by this mechanism. In conclusion, the YBCO thin films measured here exhibit a difference in the TOI values in unpatterned and patterned states within a factor of 2. Though this difference is not dramatic, it may be indicative of a slight degradation of the film at the edges due to patterning. Besides, low values (below 2) of the slopes of the third order IMD products vs. input power and their variation with temperature suggest that the nonlinear mechanism for the films studied in this work is different from the classical nonlinear mixing mechanism, which predicts the slope of 3:1.
695
Acknowledgements We are grateful to Dr. T.J. Jackson and Dr. X. Xiong for device fabrication, and Dr. T.E. Dodgson from the ‘‘Wave Solutions’’ for providing a part of the microwave equipment used in these experiments. The work at Birmingham was supported by EPSRC grant GR/L65581/01. The work at NPL was funded by DTI under the Quantum Metrology Programme, project PF9834.
References [1] S.M. Anlage, W. Hu, C.P. Vlahacos, D. Steinhauer, B.J. Feenstra, S.K. Dutta, A. Thabawalla, F.C. Wellstood, J. Supercond. 12 (1999) 353. [2] S. Cho, C. Lee, IEEE Trans. Appl. Supercond. 9 (1999) 3998. [3] B.A. Willemsen, K.E. Kihlstrom, T. Dahm, Appl. Phys. Lett. 74 (1999) 753. [4] B.A. Willemsen, T. Dahm, B.H. King, D.J. Scalapino, IEEE Trans. Appl. Supercond. 9 (1999) 4181. [5] L. Hao, J.C. Gallop, A.J. Purnell, L.F. Cohen, J. Supercond. 14 (2001) 31.