Ohmic and radiation losses in superconducting filmsL. Drabeck, K. Holczer, G. Grüner, and D. J. Scalapino

Citation: Journal of Applied Physics 68, 892 (1990); doi: 10.1063/1.346753 View online: http://dx.doi.org/10.1063/1.346753 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/68/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Terahertz surface impedance of thin YBa2Cu3O7 superconducting films Appl. Phys. Lett. 58, 2561 (1991); 10.1063/1.104826 Confocal resonators for measuring the surface resistance of hightemperature superconducting films Appl. Phys. Lett. 58, 2543 (1991); 10.1063/1.104821 Power and magnetic fieldinduced microwave absorption in Tlbased high T c superconducting films Appl. Phys. Lett. 58, 307 (1991); 10.1063/1.104670 YBa2Cu3O7 superconducting films with low microwave surface resistance over large areas Appl. Phys. Lett. 57, 520 (1990); 10.1063/1.104244 Microwave surface resistance in Tlbased superconducting thin films Appl. Phys. Lett. 55, 1357 (1989); 10.1063/1.102475

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Ohmic and radiation losses in superconduciing films L. Drabeck, K. Holczer, and G. GrOner Department of Physics and Solid State Science Center. University of California. Los Angeles. Los Angeles, California 90024

D. J. Scalapino Department of Physics, University a/California, Santa Barbara, Santa Barbara, California 93106

(Received 12 February 1990; accepted for publication 28 March 1990)

The losses associated with leakage through thin-film superconductors with film thickness comparable to the skin depth in the normal state, and to the penetration depth in the superconducting state, are described. The method is used to describe the surface resistance of YBa2Cu30 7 films deposited on various substrates.

Considerable effort has been devoted to the measure­ment of the surface impedance Zs = Rs + jX" where R, is the surface resistance and X, is the surface reactance of high­temperature superconductors. 1.2 Experiments conducted in the micrometer and millimeter wave spectral range have been used to answer questions concerning the symmetry of the superconducting ground state and the strength of the coupling that leads to superconductivity. The surface resis­tance R, is the parameter which is proportional to the ac losses and determines the application potential of these ma­terials in passive microwave components.

Recent experiments 1-5 have been performed on thin films deposited on various substrates. The typical film thick­ness, of the order 5000 A, is larger than the T = 0 London penetration depth ,;{ ( T = 0), but is comparable to ,;l (T) at temperatures a few degrees below Te. The normal state skin depth

( 2 )112

0= --floWCT

(1)

is, for p = 100 11ft em (a typical value for the normal-state resistivity just above Tc ), 0 = 1.6 fJ-m at 100 GHz.

It is expected, therefore, that while radiation is not transmitted through a typical film at low temperatures, around and especially above Tc radiation leakage effects oc­cur when the film is used as a resonator wall or as a shielding wall in a device. We also note that the penetration depth depends on the quaHty of the specimens,6 and ,;{ approaches the London penetration depth only in high quality material. In this communication we examine the magnitude of this radiation loss in comparison with the ohmic loss which oc­curs in the specimen.

The experiments were conducted2 on high-quality laser­ablated YBa2Cu30 7 films 7 of thickness between 4000 and 6000 A. In the experimental arrangement, the film forms the bottom surface of a TEO]] copper cavity operating at a fre­quency off = 101.6 GHz. The quality ractor Q of the reso­nance is compared with the Q measured with a eu or Pb endplate in place of the film. This gives R ~ff, the effective surface resistance, which includes both ohmic and radiation losses,

(2)

The temperature dependence of R ~ff, measured for a

d = 6000 A film on a SrTi03 substrate is displayed in Fig. 1. The superconducting transition at T""" 90 K is clearly visible and oscillations are seen above Tc due to standing waves formed in the substrate resulting from the large and strongly temperature-dependent dielectric constant of the SrTiOy

In order to describe the oscillations of the surface resis­tance in the normal state with a SrTi03 substrate, we have employed standard transmission line theory for the geome­try shown in Fig. 20 The SrTi03 substrate is characterized by the parameters 1'/s (impedance) and ks (propagation con­stant), while the film parameters are 1J(CT) and k(CT), and 1'/0 and ko describe the vacuum. The impedance at z = t and z = 0 (see Fig. 2) is given by

Zet) = (TfO cos(k,d) + il}s Sin(ksd») (3) 1Js Tfs cos(ksd) + il}o sin(ksd)

and

Z(O) = 11(0') ( Z(t)COS[k(CT)t 1 + j1](CT)sin[k(CT)t] ) 1](CT)cos[k(CT)t J + jZ(t)sin[k(u)t]

(4)

where 1'/ s = 1'/01 /E, ks = ko~€, and E is the dielectric constant of the substrate. Using an algebraic calculation, Eqo (4) can be written as

3

R, 2

~~O--~I~OO~--~15~O--~2~O~O--~25~O~~300 T (K)

FIG. I. Surface resistance of a 6ooo-A. thin film on SrTiO, (individual points). Also included are calculated curves using Eq. (4) for a substrate 1-mm-thick (solid line) and an infinitely thick film (dashed line).

892 J. Appl. Phys. 68 (2), 15 July 1990 0021-8979/90/140892-03$03000 @ 1990 American Institute of Physics 892

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Film Subil,ai. Vacuum

19Uillllll it' Cgyl\y \,

II Ia'i

FIG. 2. Impedance model used ill calculating of Eqs. (3) and (4).

Z(O) =7J(u) tanh [jk(a)t ]

Z(t) + 1](a)/tanhUk(l7)t]

x( I-tanh2[jk(U)I]).

tanh2 [jk(u)! ] (5)

The temperature dependence of the dielectric is nicely ap­proximated by the expressions

E(T) = al[coth(ToIT) - b], (6)

with a = 2.14 X 103, b = 0.905, and To = 42 K. The surface

impedance and propagation constant of the film are given by

Z{u) = UPowlu) 1/2 (7)

and

k(u) = ( - ipowa) 112,

where

In the normal state, u = Un and

(8)

(9)

Z(u) = Rn + jXn = ( P ow/2un ) 112(1 + j), (10)

with

k(u) = (/8) (1 - j).

Here a is the skin depth

0= (2Ip..o(;)On)1/2.

(11)

(12)

We will assume9 that the normal-state resistivity is propor­tional to the temperature

Pn =AT. (13)

The solid line in Fig. 1 shows the calculated results of Eq. (4) for a film thickness of 6000 A on a SrTi03 substrate of thickness 1 mm. The dashed line shows what the calcula-

893 J. Appl. Phys., Vol. 68, No.2, 15 July 1990

don would give if the film were of infinite thickness; in this limit R ~ad = 0, and consequently this limit gives Rs directly. Several things can be seen in the figure. First, the measured oscillation amplitude (maximum amplitude) increases somewhat more rapidly than the calculated oscillation am­plitude indicating perhaps a stronger than linear tempera­ture dependence for Pn or a slightly different magnitude of E( T) than that given by Eq. (6). Second, at lower tempera­tures (below 140 K) the oscillations are nicely matched with a substrate thickness of 1.1 mm while for temperatures larg­er than 140 K the oscillations are consistent with a substrate thickness of 1 mm. This is most likely due to a slightly differ­ent temperature dependence of E( n than given by Eg. (6). Third, the magnitude (peak to valley) of the measured oscil­lations are weaker than that given by the calculations. This is not surprising since the back side of the substrate is not against a pure vacuum as was modeled above, but rather has silver solder, tape, and a spongy microwave absorber on it. This will lead to a smearing of the resonance, and thus to a smaller amplitude oscillatory behavior.

In the superconducting state, for U2~ U t andjk(u) = 1/ A, wehavefrom Eg. (5) and the geometry of Fig. 2 (a film of thickness t on a substrate mounted at the end of a cavity)

Z(O) = 1]«(7) tanh(t IA)

7J(a}2 (1) - Z(t) + 1] (u)/tanh(tIA) sinh2 (tIA) ,

(14)

where

(15)

is the surface impedance of an infinite film. Z(n is the sur­face impedance of the substrate plus the medium behind the substrate. If we assume that the substrate is infinitely thick, we have

Z(n = (p..O/~()€') 112( 1 + j ~ tan8) (16)

with tan 15 = €''' IE' (the medium behind the substrate leads to a very sman correction to R ~hmi"). In order to extract the surface resistance of the thin film from our measured R ~ff, Eq. (14) has to be solved with Z(t) as given by Eg. (16). For arbitrary values of U 1 and Ci2, this leads to a complicated set of eguations lO and we have evaluated Z(O) only in the limit U2~UJ' This is valid in the entire superconducting tempera­ture range except very close to the transition temperature (within""" 1 K) .17] <u2 implies that R, <X, andX, = !-low)" In order to solve Eq. (14) in this limit, we expand and keep only terms linear in R" and also neglect the losses which occur in the dielectric [Le., Z(t) = (j.-l(/EoE') il2J. In this limit Eq. (14) can be inverted, giving

(17)

Drabeck at al. 893

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R,

l.Oc----,..----,----,-----:J

0.1

.. .. " '" .. .

" . . .. . .. -i~:o II

l't· • ,;(."

w~ .t:.~~I1~

<8A\W: II • 4000 U"lcorrec1ed

• 4000 CO".C! ••

A 6000 Uncorrected

• 6COO Co"ecteo

O.001L-__ -:-'-:,__---::-c~--~,__----' 0.80 0.85 0.90 0.95 j .00

TITc

FIG. 3. R ~If and R ~hmic vs reduced temperature for two films of diffcrent thickness.

In Fig. 3, R ~ff is displayed together with R ~hmic as ex~ tracted from the data using Eq. (17) above for a 6000-A thick YBa2Cu30 7 film on SrTi03 and a 4000-A-thick YBa2Cu30 7 film on LaAI03 • For both cases, the tempera­ture dependence of the penetration depth A ( T) is taken from Ref. 11. R ~hmic in the normal state is fully compatible with the measured de resistivity ofpn = 50-100,un em above the phase transition. As expected, R ~ad is negligible below about 80 K where A (T) is significantly smaller than the film thick­ness, but radiation losses become significant close to Tc. It is also important to note that while R ~tf is rather different for the 4000- and 6ooo-A films (as expected for larger radiation losses from smaller film thicknesses), the ohmic loss R ~hmic is practically identical. R ~hrnic shown in Fig. 3 displays the true ohmic losses in the film and its magnitude and tempera­ture dependence can be compared with calculations based on the various theories of the superconducting state. Detailed

comparisons between our experiments and theory will be given elsewhere. 12

In conclusion, we have described the radiation losses which occur when the surface resistance R ~ff of thin-film superconductors is measured. For typical YBa2Cu30 7 films, radiation losses are large close to and above Tc but negligible for high~quality films with a typical thickness of 5000 A at low temperatures.

Three of us (L.D., K.H., and G.G.) received support from the California Competitive Technology Program and the UCLA Consortium on Superconductivity. One of us (L.D.) would like to thank AT&T Bell Labs for partial sup­port. One of us (D.J.S.) would like to acknowledge support from the National Science Foundation under Contract No. DMR86-15454.

'For a review seeJ. Carini. L. Drabeck, and G. Griiner, Modern Phys. Lett. R 3, 5 (1989).

'L. Drabeck, G. Gruner, J. J. Chang, A. Inam, X. D. Wu, L. Nazer, T. Venkatesan, and D. J. Scalapino. Phys. Rev. B 40,7350 (1989). 'N. Klein etat., App!. Phys. Lctt. 54, 757 (1989). 4S. Sridhar et at., Phys. Rev. Lett. 63,1873 (1989). 5D. W. Cooke, E. R. Gray, H. Javadi, R. Houhon, N. Klein, G. Miiller, S. Orbach, H. Piel, L. Drabeck, G. Gruner, J. Iosefowicz, D. Rensch, and F. Krajenbrink, Solid State Commun. 73, 297 (1989).

6T. L. Hylton and M. R. Beasley, Phys. Rev. B 39.9042 (1989). 'IT. Vankatcsan, X. D. Wu, B. Dutta, A. Inam, M. S. Hegde, D. M. Hwang, C. C. Chang, L. Nazar, and B. 1. Wilkens, App!. Phys. Lett. 54, 581 (1989).

'E. Sawaguchi, A. Kiruchi. and Y. Kodera, J. Phys. Soc. lpn. 17, 1666 (1962).

"Experiments on films prepared under identical conditions gave Pn which is proportional to T, as given by Eq. (9) with typical resistivity values between 50 and 100 pH em just above the supercollducting transition.

JOS. Sridhar,]. App!. Phys. 63,159 (1988). "L. Krusin-Elballm, R. L. Greene, F. Holtzberg, A. P. Malozcmoff, and Y.

Yeshurun, Phys. Rev. Lett. 62, 217 (1989); A. T. Fiory, A. F. Hebard, P. M. Mankiewich, and R. E. Howard, Phys. Rev. Lett. 61,1419 (1988).

12L. Drabeck, K. Holtzer, G. Griiner, J. J. Chang, D. 1. Scalapino, A. Inam, X. D. Wu, L. Nazar, and T. Vankatesan (unpublished).

Some optical properties of infrared transmitting Bi~Ca~Sr~Cu~O glasses Haixing Zheng, Patrick Lin, Ren Xu, and J. D. Mackenzie Department of Materials Science and Engineering, University of California-Los Angeles, Los Angeles, California 90024

(Received 11 August 1989; accepted for publication 9 April 1990)

Glasses based on Si20 3, CaO, SrO, and CuO were first prepared as precursors to polycrystalline superconducting ceramics based on these oxides. These glasses were found to be transparent in the infrared to 11 ,urn. The infrared cutoff is approximately 6.5 pm, The refractive indices are surprisingly high being about 2.9.

High Tc ·Bi~Ca-Sr-Cu-o superconductors can be pre­pared from the crystallization of glasses prepared from the melting of mixtures of Hi20 3 , CaC03, SrC03 , and CuO. A great deal of research has been carried out in a period of less

than two years to investigate this novel process for supercon­ducting ceramics: They included a study of the glass forming region and glass structure, l,2 fabrication of the glasses in dif­ferent shapes,3,4 control of preferred orientation of the super-

894 J. Appl. Phys. 68 (2), 15 July 1990 0021-8979/90/140894-03$03.00 @ 1990 American Institute of Physics 894

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