High-Tc superconducting thin film resonators with buffer layers

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Physica C 235-240 ( 1 9 9 4 ) 3 3 7 1 - 3 3 7 2 North-Holland

High-To Superconducting Thin Film Resonators with Buffer Layers Farhat Abbas 1, L.E.Davis 1, J.C.Gallop2 tDept, of Electrical Engineering, UMIST, P.O. Box 88, Manchester M60 1QD, UIC 2National Physical Laboratory, Teddington TWl 1 0LW, UK We show that the addition of buffer layers to HTS planar resonator structures may be used to improve Q-factor as well as solving superconductor/substrate incompatibilities.. 1. INTRODUCTION

2. THEORY

In addition to their potential for applications, microwave resonators made from high quality twosided YBCO thin films on sapphire with CeO buffer layers may provide experimental data to elucidate appropriate theoretical models for high temperature superconductivity. Here we use London's electrodynamic equations to calculate a sinusoidal solution for a planar superconducting transmission line, including the effects of buffer layers. The solution provides expressions for the phase velocity and attenuation coefficient for a range of combinations of materials properties. The Q factor of a resonator constructed from such a transmission line is also calculated and some specific cases are considered which demonstrate how the use of lowloss buffer layers may enhance the Q factr.. Such resonators may find practical application as the stabilising element in low phase noise microwave oscillators.

The structure of the resonator, shown in fig.l, consists of a pair of thin buffer layers (dielectric 1) separated by a central substmte (dielectric 2) and a pair of superconducting thin films separated by the buffer layers from the substrate. Thicknesses of the thin films, buffer Myers and central substrate are 1, d~ and d2 respectively. The dielectric regions 3 are considered to be very thick so that the fields in these regions can be assumed to decay exponentially away from the interface. The dispersion relation for the resonator of fig.1 can be written as follows [3]:

Superconductor

Dielectric I (Buffer Layer)

a2= c°2P'oe~e2 [2~,coth(/)÷2dt.hd2] (2dlz2+d2sl) ;Z Here a is the propagation constant along the z direction (taking em), 0~ is the angular frequency (assuming e i°~) e0 and Ix0 are the permittivity and permeability of free space respectively, Et~ is the dielectric constant of dielectrics 1 and 2 respectively, and c are the penetration depth and normal state conductivity of the superconductors. The total unloaded Q-factor Qo of the resonator can be writtten in terms of Q-factors arising from losses in conductors, buffer layers, dielectric substrate and radiation: Qo, Qb, Qd & Q~ respectively, as follows:

1

1

1

~_...._ +...._.. +

1

÷

1

Qo Qc Qb Qd Qr I)iclcclrit ~

I),t!lcclri~: _.2 (~tl|)~tr ale ~

Fig.1 Schematic of resonator using HTS thin films and buffer layers.

where Qo = o~/2aov s, Qb = co/2o~vg, Qd = ¢o/2aavs, vg---v22/vpand v2 ffi Re(e21Xo)"tt2where Vp is the phase velocity in the corresponding material (for details see [3]). Q, has been discussed elsewhere [4].

0921-4534/94/$07.00 © 1994 - Elsevier Science B.V. All rights reserved. SSDI 0921-4534(94)02251-8

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E Abbas et al,/Pt~vsica C 235 240 (1994) 337I 3372

3. RESULTS The temperature dependence of penetration depth and normal state conductivity o of a superconductor

1.9635

107

the f i l l s , which increases Qr. In fig.3 Qb is plotted versus thickness of buffer layers (dl) for a range of dielectric constant e, = 2,4,6,8,9 with T/To=0.5. The other parameters are the same as for fig.2 except that G=0 and tanfi~=104. Note that the values of Qb Increase as the thickness is decreased. Here the behaviour is domInated by 16OOO

1.9~3

.

.

.

.

~rI--2 1'4OOO

1.96:;Z5

eel

-

9

12ooc 1.961~ 1.961

8

600~¢ ;

600~ /

1.960:

6

6

1.gS~o~ 10 ~

Buffer Layer Thcknesses

(dl

m)

406C ~

4

200C ~

2

10 {0 e

1o 8 Buf,er Layer Thicknesses (dl

1o ~ m)

Fig.3 Qb versus thickness (d~) of buffer layers for lossless ttTS thin films Fig. 2 Computed Q factor versus thickness (d~) of lossless buffer layers can be described by any one of several different models (for a summary see [5]). Any of these models which lead to a complex conductivity may be inserted into the above analysis. Different experimental combinations for the layers of substrate/buffer/HTS have been reported in the literature and the derived expressions can be used for any combinations of superconductor and dielectrics. Let us consider an example in which the superconductors are YBCO and dielectrics 1 and 2 are taken to be MgO and sapphire respectively. Considering the losses in the superconducting films only, in fig.2 the Q¢ values are plotted versus thickness d~ of the lossless buffer layers, for a range of dielectric constants e,=2,4,6,8,9 and ea=l 0, with T/To=0.5, ~.=700nm, t~=l.7xl06(~m) -~, d2=5001xm and c0/2rt=10GHz. The values of Q¢ increase only very slightly as the buffer layer thickness is increased, arising from the small effective increase in thickness. Also values of Q¢ increase if er~ is decreased. This arises from increased internal reflection at the buffer layer/substrate interface. As the dielectric constant of the buffer layers decreases the internal reflection at the dielectric interfaces mcreases so the field at the surface of the superconductors is decreased, hence increasing Qo. This also implies a reduced radiation loss through

lossy buffer layers and as their thickness is reduced, the 'filling factor' is reduced so higher Qb values are attained. Also the Qb values are higher for higher dielectric constants because the fields in region 1 are smaller yielding lower losses since we assume tandfiI is independent of eTt. From this example we conclude that buffer layers not only overcome the problems of f i l l - substrate interactions and reduction of micro-cracks but can also be used to confine the eleclromagnetic field more effectively into the low loss dielectric region, which enhances Qr and Qc for the resonator.

REFERENCES [1] K Ohbayashi et al., Appl. Phys. Lett. 64 (3), (1994) 369 [2] S N Mao et al., Appl. Phys. Lett. 64(3) (1994) 375 [3] F Abbas et al., J.Appl. Phys. 73(9) (1993) 4494 [4] F Abbas et al., IEE Electr. Lett., 29(1) (1993) 105 [5] F Abbas et al., Physica C 215 (1993) 132