High Tc coplanar resonators for microwave applications and scientific studies

PHYSICA ELSEVIER

Physica C 282-287 (1997) 395-398

H i g h Tc c o p l a n a r resonators for m i c r o w a v e applications and scientific studies C. E. Gough, A. Porch, M.J. Lancaster, J.R. Powell, B. Avenhaus, J.J. Wingfield, D. Hung and R.G. Humphreysa Superconductivity Research Group, University of Birmingham, Birmingham B 15 2TT, UK. Defence Research Agency, Malvern, Worcestershire, WRI4 3PS, UK, We briefly introduce the use of microwave HTS coplanar resonators for measurements of absolute values of L(T,B) and microwave losses with examples of temperature, static-field and power dependences. A number of applications are described including slow-wave resonators, current-switchable band-stop filters, and an ultrasensitive ESR cavity. All these structures are easy to fabricate and offer substantial advantages over conventional technologies.

1.

The coplanar resonator

Coplanar transmission line structures can be patterned very conveniently from high quality HTS films. A particularly simple in-line coplanar resonator structure is shown in Fig. 1. The inductance per unit length of the transmission line is very approximately ~ ~ [s + (~L2/t) f(XL/t,S,w)l/w, where s is the gap between the central conductor and ground planes, w is the width of the centre conductor, t is the film thickness and f is a geometric factor of order unity. The second term is the kinetic inductance associated with the supercurrents flowing near the planar edges. Porch et al. [1] have used numerical techniques to determine the current profile for a number of coplanar geometries, as illustrated in Fig.2, and hence obtain values for the kinetic inductance as a function of LL/t.

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2. Resonator measurements By fabricating resonators with different spacings from the same HTS film, and assuming the same temperature dependence of LL(T) for both resonators, it is relatively straightforward to extract absolute values for LL(T)/t using the calculated current distributions, and hence the temperature dependent penetration depth [2], provided the film thickness is known. Measurements of the temperature dependent resonant frequencies and Q-values of two resonators with different spacings, therefore, enables absolute determination of ~L(T) and ch (and hence Ks).

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Fig.2. The current distribution on the resonator cross section [ll.

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C.E. Gough et al./Physica C 282-287 (1997) 395-398

Figure 3 below shows the frequency shift as a function of temperature for two resonators with different line spacings (10 and 73 ~tm), from which we evaluate absolute values of LL(T), as plotted at low temperatures in Fig.4.

ence for thin films is probably associated with the high density of defects in thin film samples, smearing out the nodes in the energy gap. However, in a detailed study o f - 2 0 thin film resonators, no correlation was observed between residual losses and the magnitude of the T 2 dependence [41.

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Fig. 5 illustrates the expected co2-dependence of R~ derived from the Q-factors and ~,L(T). There is often considerable variation in performance of films from a single source; however, the best films have comparable performances irrespective of growth route[5] with values identical to those obtained by dielectric resonator measurements of the surface impedance on unpatterned films. The superconducting properties are therefore not significantly degraded by the currents flowing close to the lithographically patterned edges. Coplanar resonators with their high Q-values are ideally suited to mixed state measurements of microwave properties, providing useful information on vortex pinning and viscous losses [6]. As an example, Fig. 6, shows the dependence of surface reactance Xs on static magnetic field perpendicular to the film, derived using the double coplanar resonator method7: a similar field dependence is observed for 1~. The linear field dependence im-

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C.E. Gough et aL/Physica C 282-287 (1997) 395-398

plies strong pinning of flux lines with little evidence of magnetic interactions between flux lines up to -4T. For fields up to 4T parallel to the planes, there is very little additional loss below ~50K, and a relatively small increase in losses even at liquid nitrogen temperatures.

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critical current o f - 10 7 Acm 2. Unlike conventional superconductors, microwave flux enters the film edges when the edge-current density exceeds J~ because of the very small coherence length and relative ease of vortex nucleation. In poorer quality films, non-linearity can set in at much lower current densities [5], but there is no correlation with the quality of the film measured by residual surface resistance. 3. Applications Coplanar structures are used extensively as the basis of a number of planar microwave circuits. We describe three examples: a switchable band-stop filter, a fractal slow-wave resonator, and a coplanar resonator for ultra-sensitive ESR measurements. 3.1 Switchable filter Small, low frequency, coplanar, interdigital resonators can readily be patterned using HTS films [8]. For example, a LC lumped-element resonator can be made by a number of interdigital capacitors of capacitance C between two conducting plates with a parallel inductive strip, which can be driven normal by a dc current. A switchable band-stop filter can then be realised by adjusting the current through a cascaded series of such resonators with

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C.E. Gough et aL /Physica C 282-287 (1997) 395-398

different widths (10-16 Ixm) of central conductors: the response of one such filter is shown in Fig 8. 3.2 Slow-wave resonator A natural extension of the above idea is to use the high interdigital capacitance to fabricate a slowwave resonator, in which the space between the

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3.3 ESR resonator. Our final example makes use of the very high concentration of electromagnetic field in the small spacing s between the central conductor and ground planes in a simple, straight coplanar resonator. The effective resonant volume of the resonant "cavity" is therefore - s21, compared to 13 for a conventional ESR cavity, where 1 - L f~oo~pa¢o/2 . For a small sample of size < s, the effective filling factor (which determines the size of the ESR signal) is therefore increased by a factor (l/s) 2, which could be as large as (lcm/10~tm) 2 - 106. At the field required for 10GHz ESR measurements (--4).3T), there is relatively little increase in microwave losses for fields parallel to the film, so that Q > 1000 can still be achieved. The cavity can then be integrated in a conventional ESR spectrometer configuration to provide a very sensitive system for small samples. Initial results, in a far from optimised system, are shown in Fig. 10 for a small sample of DPPH (-1014 spins) - already comparable with the best commercial systems ll0].

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Frequency (GHz) Fig.9 Fractal coplanar resonator and its frequency response; at 2 GHz and 16K the Q is -10,000. central conductor and ground plane is filled by a matrix of interdigital capacitors to increase the effective capacitance per unit length C above the TEM value (c2L) 1 . In this way, the phase velocity along the line can be reduced by a factor as large as 10, enabling a ten-fold reduction in fundamental frequency for a given resonator length. A four-fold reduction is shown for a fractal interdigital geometry in Fig.9, where the fundamental resonant frequency has been lowered from - 8 to 2 GHz. HTS allows miniaturisation without the associated loss encountered using conventional material[9].

F i g l0 ESR signal for a small DPPH sample at 77K using an HTS coplanar resonator. ACKNOWLEDGMENTS This research has been support by the EPSRC and an ESPRIT - Supermica programme. REFERENCES 1. A. Porch et al., IEEE-MTT 43 (1995) 306 2. A. Porch et al.o IEEE-ASC 3 (1993) 1719 3. D.A. Bonn et al., Phys.Rev.B 50 (1994) 4051 4. A. Porch et al., Physica B 194-196 (1994) 1605 5. B. Avenhaus et al., IEEE-ASC 5 (1995) 1737 6 M.W. Coffey et al., Phys.Rev.Lett. 67 (1991) 2219 7. J.R. Powell et al., Proc. EUCAS-95, pl 119 8. B. Avenhaus et al., Electronics Lett. 31 (1995) 985 9. M.J.Lancaster et al., IEEE-MTT 44 (1996) 1339 10. J.J. Wingfield et al., Proc. EUCAS-95, p1087