Simulation of Composite Optical Properties Close to Percolation Threshold
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SIMULATION OF COMPOSITE OPTICAL PROPERTIES CLOSE TO PERCOLATION THRESHOLD F. BROUERS(1.2), J.P. CLERC (2), G. GIRAUD (2) (1) Institut de Physique, Universit6 de Liege, 4000 Belgium 2 Universiti de Provence, D~partement de Physique des Syst~mes Ddsordonn~s, Centre de St J6r6me - 13397 Marseille cedex 13, France ABSTRACT We analyze the optical properties of a metal-insulator composite thin film close to the percolation transition pc . Using a mean field approximation, it is possible to predict the existence of an optical threshold at a concentration p- slightly larger than pc. At that concentration defined by the vanishing of the real part of the dielectric constant and which depends of the relaxation time and therefore of the microgeometry, the composite optical absorption is frequency independent up to the near infrared frequencies. This property has been observed in a number of granular and cermet films. We show that this property is quite general and can be obtained by generalizing the percolation scaling laws to a mixture of resistors, inductors and capacitors. The quality factor is shown to be a relevant physical quantity. We report and discuss the results of simulations on real analogic LCR circuits and on computer which confirm and explicit these conclusions. 1- INTRODUCTION Conduction properties of inhomogeneous materials are often modelled by numerical simulations on networks. A number of papers have been devoted to systems with two kinds of resistors or resistors and capacitors randomly assigned to the links of a lattice. Optical properties of metal-insulator composites, granular or cermets films, have recently been modelled by RLC networks (1-4). By using such models one hopes to understand a few striking observations in particular the fact that in these films reflection, transmission and absorption are nearly independent of frequency in the vicinity of the percolation threshold (3,5,6). It has also been observed that in such systems the concentration pc at which a d.c. conductivity threshold appears and the concentration p* for which the real part of the dielectric constant changes sign (optical transition) are different. The effective medium approximation (EMA) indicates that it is at p* that the optical properties are independent of frequency for good conductors (3). Although pc and p* are very close for noble metals. They can be rather different for bad conductors (3,7,8). In that case it is more difficult to predict the frequency dependence of the optical properties. The objective of this paper is to report some recent results on the electrical and optical properties of the metal-insulator composites in the vicinity of pc and p* using the EMA and an extension of the percolation scaling theory to RCL systems. We want also to discuss what can be learned from the measurement of the impedance of analogical Mat. Res. Soc. Symp. Proc. Vol. 195. 01990 Materials Research Society
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disordered RCL circuits and computer simulations of such circuits. 2 - THE OPTICAL TRANSITION INTHE EMA To simulate the behav
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