Abstract
The problem of 1/f noise in thin metal films and metal-insulator composites in the scaling fractal regime near percolation threshold is considered. The correspondence between a percolation transition and a second order phase transition is extended from the point of view of electronic polarization and electrical fluctuations. The charge fluctuations on finite fractal clusters are argued to be analogous to spontaneous order parameter fluctuations in phase transitions, being correlated upto percolation correlation length. The charge relaxation times are shown to be related to the cluster sizes having distribution function of the formg(τ)∝τ−b, whereb is connected to Euclidean and fractal dimensionalities and critical exponents. This produces the 1/f noise spectrum. Below percolation threshold, the nodes-links-blobs picture is invoked such that the blobs represent metallic conductances of the finite clusters and the links are tunnelling conductances between them through narrowest barrier regions. Above threshold, the finite cluster network is visualized as connected to the infinite cluster through narrowest tunnelling regions. The correlated spontaneous charge fluctuation on finite fractal clusters is held responsible for conductance fluctuation on either side of the metal-insulator transition via tunnelling processes. Finally, the scaling behaviour of noise magnitude near percolation threshold is explained.
Similar content being viewed by others
References
Van der Ziel, A.: Adv. Electron. Electron Phys.49, 225 (1979) (Flicker noise in electron devices)
Press, W.H.: Comm. Astrophys. Space Phys.7, 103 (1978) (Flicker noise in astronomy and elsewhere)
Musha, T.: Proceedings of the Sixth International Conference on Noise in Physical Systems. Meijer, P.H.E., Mountain, R.D., Soulen, R.J. (eds.), p. 143, NBS Publication No. 614, U.S. GPO, Washington, D.C. 1980
Hooge, F.N., Kleinpenning, T.G.M., Vandamme, L.K.J.: Rep. Prog. Phys.44, 479 (1981)
Dutta, P., Horn, P.M.: Rev. Mod. Phys.53, 497 (1981)
Voss, R.F.: Phys. Rev. Lett.40, 913 (1978)
Scofield, J.H., Darling, D.H., Webb, W.W.: Phys. Rev. B24, 7450 (1981)
Black, R.D., Weissman, M.B., Fliegel, F.M.: Phys. Rev. B24, 7454 (1981)
Fleetwood, D.M., Giordano, N.: Phys. Rev. B27, 667 (1983)
Purcell, W.E.: J. Appl. Phys.43, 2890 (1972)
Stoisiek, M., Wolf, D.: J. Appl. Phys.47, 362 (1976)
Rammal, R., Tannous, C., Breton, P., Tremblay, A.-M.S.: Phys. Rev. Lett.54, 1718 (1985)
Garfunkel, G.A., Weissman, M.B.: Phys. Rev. Lett55, 296 (1985)
Koch, R.H., Laibowitz, R.B., Alessandrini, E.I., Viggiano, J.M.: Phys. Rev. B32, 6932 (1985)
Mantese, J.V., Webb, W.W.: Phys. Rev. Lett.55, 2212 (1985);
Mantese, J.V., Curtin, W.A., Webb, W.W.: Phys. Rev. B33, 7897 (1986); Mantese, J.V., Goldburg, W.I., Darling, D.H., Craighead, M.G., Gibson, V.J., Buhrman, R.A., Webb, W.W.: Solid-State Commun.37, 353 (1981)
Rudman, D.A., Calabrese, J.J., Garland, J.C.: Phys. Rev. B33, 1456 (1986)
Chen, C.C., Chou, Y.C.: Phys. Rev. Lett.54, 2529 (1985)
Tremblay, A.-M.S., Feng, S., Breton, P.: Phys. Rev. B33, 2077 (1986)
Wright, D.C., Bergman, D.J., Kantor, Y.: Phys. Rev. B33, 396 (1986)
Rammal, R.: Phys. Rev. Lett.55, 1428 (1985)
Rammal, R., Tremblay, A.-M.S.: Phys. Rev. Lett.58, 415 (1987)
Landau, L.D., Liftshitz, E.M.: Statistical physics, p. 384. Oxford, New York: Pergamon 1980
Essam, J.W.: Rep. Prog. Phys.43, 833 (1980)
Stauffer, D.: Phys. Rep.54, 1 (1979)
Voss, R.F., Laibowitz, R.B., Allessandrini, E.I.: Phys. Rev. Lett.49, 1441 (1982)
Kapitulnik, A., Deutscher, G.: Phys. Rev. Lett.49, 1444 (1982)
Reference 22 p. 449
Gefen, Y., Aharony, A., Alexander, S.: Phys. Rev. Lett.50, 77 (1983) and references there in
Laibowitz, R.B., Gefen, Y.: Phys. Rev. Lett53, 380 (1984)
Efros, A.L., Shklovskii, B.I.: Phys. Status Solidi (b)76, 475 (1976)
Wilkinson, D., Langer, J.S., Sen, P.N.: Phys. Rev. B28, 1081 (1983)
Bowman, D.R., Stroud, D.: Phys. Rev. Lett.52, 299 (1984)
De Arcangelis, L., Coniglio, A., Redner, S.: Phys. Rev. B36, 5631 (1987)
Stauffer, D.: Introduction to percolation theory. London: Taylor and Francis 1985
Reference 22, p. 471, Formula 146.2. Temperature in this formula is in units of Boltzman constantk (see p. 36). The fluctuation — dissipation theorem is given on p. 387, formula 124. 14. For the analogies of order parameter and susceptibility see Sect. 123 and foot note on p. 377
Bak, P., Tang, C., Wiesenfeld, K.: Phys. Rev. Lett.59, 381 (1987)
Voss, R.F., Clarke, J.: Phys. Rev. B13, 556 (1976)
Clarke, J., Hsiang, T.Y.: Phys. Rev. B13, 4790 (1976)
Pelz, J., Clarke, J.: Phys. Rev. B36, 4479 (1987)
Feng, S., Lee, P.A., Stone, A.: Phys. Rev. Lett.56, 1960 (1986);56, 2772 (1986)
Weissman, M.B.: Phys. Rev. Lett59, 1772 (1987)
Fourcade, B., Tremblay, A.-M.S.: Phys. Rev. B34, 7802 (1986)
Celasco, M., Masoero, A., Mazetti, P., Stepnescu, A.: Phys. Rev. B17, 2553 (1978); Phys. Rev. B17, 2564 (1978)
Simmons, J.G.: J. Appl. Phys.35, 2655 (1964)
Halperin, B.I., Feng, S., Sen, P.N.: Phys. Rev. Lett.54, 2391 (1985)
Wright, D.C., Bergamon, D.J., Kantor, Y.: Phys. Rev. B33, 396 (1986)
Williams, J.L., Stone, I.L.: J. Phys. C5, 2105 (1972)
Williams, J.L., Burdett, R.K.: J. Phys. C2, 298 (1969)
Ben-Mizrahi, A., Bergamon, D.J.: J. Phys. C14, 909 (1981)
Harris, A.B.: Phys. Rev. B28, 2614 (1983)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yadava, R.D.S. A finite fractal cluster theory of 1/f noise in percolation systems near metal-insulator transition. Z. Physik B - Condensed Matter 76, 365–374 (1989). https://doi.org/10.1007/BF01321915
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01321915