Scaling spontaneous fluctuations in high-Tc superconductor films

Physica B 172 (1991) 441-444 North-Holland

Scaling spontaneous fluctuations in high-T superconductor films*

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L.B. Kiss a, P. Svedlindh b, L. Lundgren b, J. H u d n e r c, H. Ohls6n, L. Stolt and Z. Gingl a aJA TE University, Institute for Experimental Physics, D6m TOr 9., Szeged, H-6720 Hungary hUniversity of Uppsala, Department of Solid State Physics, P.O. Box 534, S-75121 Uppsala, Sweden CDepartment of Solid State Electronics, Royal Institute of Technology, P.O. Box 1298, S-16428 Kista, Sweden dSwedish Institute of Microelectronics, P.O. Box 1084, S-16421 Kista, Sweden Received 14 March 1991

Spontaneous conductivity fluctuations in high-Tc superconducting films on sapphire and SrTiO 3 substrates have been measured through the superconducting transition. It is found that the normalized spectrum for the sapphire film is two orders of magnitude larger than for the SrTiO3 film, due to a stronger disorder. At sufficiently low temperatures, the normalized spectrum scales with the conductivity, which proves the existence of a percolation superconducting network.

Studies of spontaneous conductivity fluctuations in high-T c superconducting materials [1] may yield important information about the physics [2] of the transition, e.g. on the onset of the several stages of the transition, the intergrain critical currents and their dependence on magnetic field, the role of inhomogeneities and other types of disorder and the dynamics of vortex motion. Such investigations may also become an important tool for material characterization, and an increased understanding of the noise mechanisms may eventually facilitate a suppression of noise in high-T~ superconducting devices. Conductivity fluctuation measurements by Testa et al. [3] on bulk samples of Y - B a - C u - O and E r - B a - C u - O and an independent study by Ricketts et al. [4] on bulk samples of Y - B a - C u O gave the following main results: (i) no noise is found in the superconducting state, (ii) in the normal state the noise is large, comparable in magnitude to that found in metal-insulator composites, and (iii) the temperature dependence of

* Originally submitted for LT-19, Brighton, but not included in the proceedings for technical reasons.

the normalized noise and of the resistivity are opposite, unlike both metals and semiconductors. Furthermore, (iv) the non-normalized noise was reported to increase in the transition region. Testa et al. [3] found that the non-normalized spectra of the fluctuations were proportional to the square of the temperature-derivative of the resistivity. In this paper, conductivity fluctuation measurements on Y - B a - C u - O thin film samples are reported. Thin YBa2Cu307 films on SrTiO 3 and sapphire substrates were fabricated in an ultra-high vacuum coevaporation system (Balzers UMS 500P), (for further details, see refs. [5] and [6]). The conductivity fluctuation measurements were carried out on samples of dimensions 10 x 3 x 0.001 mm. Standard four-terminal conductance noise measurements were applied with silver paste contacts. Details are described elsewhere [5]. In fig. l(a), the square of the resistance R(T) and the strength of its mean-square fluctuation S(f, T) are plotted for the sapphire film. S(f, T) is plotted at 125 Hz, but the same temperature dependence of S(f, T) is obtained for other

0921-4526/91/$03.50 (~ 1991- Elsevier Science Publishers B.V. (North-Holland)

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85 90 95 100 T(K) 75 80 Fig. 1. Temperature dependence of logl0(R2) and logL0(S), where R is the resistance and S is the resistance fluctuation per unit bandwidth. Numerical values on the right hand scale correspond to normalized R2-values while log~0(S) has been arbitrarily displaced along the vertical axis. a) Sapphire film, l = l m A and f=l.25Hz, b) SrTiO3 film, l=7mA and f = 10.5 Hz.

frequencies (1 H z - 1 0 kHz). In fig. l(b), the same results for the SrTiO 3 film are plotted. The qualitative form of the temperature dependence of the fluctuations in the transition for the SrTiO 3 film is also frequency independent. Comparing the temperature dependencies of the fluctuations with the results by Testa et al. [3] obtained for bulk samples, we can see that in the low temperature end of the transition, the fluctuations disappear, which is consistent with the results obtained for bulk samples. Furthermore, the spectral density is less dependent on the temperature than the square of the resist-

ance, that is the normalized fluctuations increase with decreasing temperature which is also in accordance with the bulk results. However, the non-normalized fluctuations are monotonically decreasing in the transition, a result in apparent contradiction with previous results. It is likely that the origin of this contradiction is that by our careful way of controlling the temperature [5] we can avoid a noise increase caused by temperature fluctuations. The dependence of the measured fluctuations on the current was checked by varying the driving current in the range of 0 . 6 - 4 m A for the sapphire film sample and 2 - 7 mA for the SrTiO 3 film. No deviation from a quadratic dependence of the measured noise voltage spectrum on the current was found, which implies that these measuring current densities do not significantly influence the conductivity fluctuations. To compare the strength of the spectral density ( 1 / f noise) with other existing data, we can take the Hooge formula in the following form applied for metals and metal-insulator composites [7-11]: S(f, T)/R2(T)

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Fig. 2. Normalized mean-square fluctuations vs. resistance on a log-log scale. The values given for the resistance have been normalized at 95 K while the values given for the normalized mean-square fluctuations correspond to real values. (a) Sapphire film, I = 1 mA and f = 125 Hz. The solid line corresponds to a slope of -1.05. (b) SrTiO3 film, I= 7 mA and f = 10.5 Hz. The solid line corresponds to a slope of -0.72. found. This scaling with the inverse of the resistance seems to be universal for these samples since the normalized spectrum of the SrTiO 3 film (fig. 2(b)) has this dependence in the whole transition range. H e r e we present a brief interpretation (for details, see ref. [5]). According to Tinkham and Lobb [2], high-T c materials should have a twostage transition by means of a modified Kosterlitz-Thouless transition. First, at higher temperatures, the grains become superconducting and the sample resistance drops. In the second stage, at lower temperatures, where k T becomes

443

less than the Josephson coupling energy between the grains, the phases of the superconducting wave functions of neighbouring grains lock together to give long-range coherence and a macroscopic superconducting state. Regarding the sapphire film [5], we can naturally assume that the very strong excess noise found in the upper part of the transition is a McWorther-like surface noise [7-11] generated by the grain-boundary surfaces. In the second stage, or near to it, the sample resistance and the fluctuations will be dominated by the Josephsonlike junctions between the grains. Considering the effect of spatial inhomogenities on the coupling energies, the phase locking (of the superconductor wave functions) between the neighbouring grains will occur in an inhomogeneous way and we get a spatially random resistor network (fig. 3) which is well known to have a normalized fluctuation which roughly scales with a power function of the sample conductance. More exact predictions need the application of percolation theories [15, 16]. Note that according to these theories not only the geometrical dimension is important but also the fractal dimension of the network. For that reason it is important to experimentally study the magnetic field dependence of the power factor. Regarding the SrTiO 3 film [5], the disorders are much weaker. For that reason, the McWorther-like surface noise is much smaller and the

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Fig. 3. A computer-generated network modellingconductorsuperconductor composites. The short-circuits are representing phase-lockings between neighbouring grains.

444

L . B . Kiss et al. ! Fluctuations in high-T c superconductor films

Josephson-like coupling is much stronger. To decide whether the inhomogeneities in the Josephson coupling or the inhomogeneities in the critical temperature of the grains are important, one would need results from noise measurements in magnetic field and/or using currents close to the critical current density of the sample. In conclusion, we have used measurements of conductivity fluctuations of the normal conducting subvolumes of the sample as a probe of the inhomogeneities in the superconducting transition. Conductivity noise measurements in highTc materials (with possible extension of the investigations to include measurements of fluctuations in a magnetic field and/or using currents approaching the critical current) seem to be a powerful tool to determine the role of imperfections, as well as to characterize high-To superconductors during material development.

Acknowledgements The financial support from the Swedish Natural Science Research Council, the Swedish Board for Technical Development, the National Energy Administration and the (Hungarian) OTKA Foundation are gratefully acknowledged.

References [1] J.G. Bednorz and K.A. M/iller, Z. Phys. B. 64 (1986) 189. [2] M. Tinkham and C.J. Lobb, Solid State Phys. 42 (1988) 91. [3] J.A. Testa, Yi Song, X.D. Chen, J. Golben, S.-I. Lee, B.R. Patton and J.R. Gaines, Phys. Rev. B 38 (1988) 2922. [4] B.W. Ricketts, R. Driver and H.K. Welsh, Solid State Commun. 67 (1988) 133. [5] L.B. Kiss, P. Svedlindh, L. Lundgren, J. Hudner, H. Ohls6n and L. Stolt, Solid State Commun. 75 (1990) 747. [6] H. Ohls6n, J. Hudner and L. Stolt, J. Less-Common Met. 151 (1989) 317. [7] F.N. Hooge, T.G.M. Kleinpenning and L.K.J. Vandamme, Rep. Prog. Phys. 44 (1989) 479. [8] P. Dutta and P.M. Horn, Rev. Mod. Phys. 53 (1981) 497. [9] Sh. M. Kogan, Sov. Phys. Usp. 28 (1985) 170. [10] M.B. Weissman, Rev. Mod. Phys. 60 (1988) 537. [11] L.B. Kiss, Rev. Solid State Sci. 2 (1988) 659. [12] L.B. Kiss, K. Tompa, I. Hevesi, Gy. Treffin, G. G6vay and A. Lovas, Solid State Commun. 66 (1988) 525. [13] J.W. Mantese, W.A. Curtin and W.W, Webb, Phys. Rev. B 33 (1986) 7897. [14] A. Ambr6zy, E. Hahn, L.B. Kiss and Gy. Tref~n, Active and Pasive Electr. Comp. 13 (1989) 191, and references therein.

[15] D.C. Wright, D.J. Bergrnan and B 33 (1986) 396, and references [16] A.-M.S. Tremblay, B. Fourcade A 157 (1989) 89, and references

Y. Kantor, Phys. Rev. therein. and P. Breton, Physica therein.