Solid State Communications, Vol. 101, No. 1, pp. 45-50, 1997 Copyright 0 1996 Else&r Science Ltd Printed in Great Britain. All rights reserved 0038-1098/97 $17.00+.00 PII: zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA SOO38-1098(96)00558-3 OPTICAL PROPERTIES OF COMPOSITE MATERIALS AT HIGH TEMPERATURES H.-P. Chiang, P.T. Leung” and W.S. Tse Institute of Physics, Academia Sinica, Taipei 11529, Taiwan, R.O.C. zyxwvutsrqponmlkjihgfedcbaZYX (Received 22 August 1996; accepted 9 September 1996 by S.G. Louie) The optical properties of composite materials are studied theoretically as a function of temperature via a phenomenological model for temperatures up to the melting points of the materials. Both the Maxwell-Garnett and Bruggeman models are considered and the temperature variation of the optical constants of the metallic particles is obtained with an account of the dependence of both the electron-phonon and electron-electron scattering on temperature. The results show that the extinction coefficient of the composite generally increases with temperature and that the Maxwell-Garnett and Bruggeman models can give very different results at certain optical frequency. Transmittance through a thin composite film is calculated providing a means for a simple experimental study of the various modeling results. Copyright 0 1996 Elsevier Science Ltd Keywords: A. disordered systems, A. thin films, D. electron-electron interactions, D. electron-phonon interactions, D. optical properties. INTRODUCTION The optical properties of composite materials such as cermet have been studied intensively for the past two decades [l]. Most of these materials contain a metal- insulator composite which have interesting properties in the infrared and optical frequencies. Theoretically, there exists many models which can describe these properties adequately under different structural conditions of the composite. These include, for example, various mean field [2-41 and fractal-cluster [5] theories as well as computational approach via various simulation schemes [6]. Nevertheless, most of the previous experimental and theoretical studies were limited to room temperature condition and thus optical properties of such composite materials at elevated temperatures are rarely reported in the literature [7]. On the other hand, it is not unrealistic to expect that there are technological applications of these materials under which the composite system will be subject to high temperatures. It is the purpose of the present communication to study the temperature dependence of the optical constants of a metal-insulator * Corresponding author. Permanent address at: Depart- ment of Physics, Portland State University, P.O. Box 751, Portland, OR 97207-0751, USA. composite via a simple phenomenological model. To begin, it is reasonable to assume that such dependence originates mainly from change in the metallic optical properties and those for the insulating host medium can be assumed to be constant with temperature change [8]. Hence, we shall first briefly review and adapt an adequate model for describing the temperature dependence of the metallic optical constants which accounts for both the electron-phonon and electron-electron collision pro- cesses in the metal. We shall then apply it to calculate the optical properties of the composite as a function of temperature. For the purpose of model calculations here, we shall adopt the simple existing effective medium theories including the Maxwell-Garnett and Bruggeman models for the optical functions of the composite. TEMPERATURE DEPENDENCE OF OPTICAL CONSTANTS For simplicity, we shall assume a Drude model metal which will be adequate for certain simple and noble metals within the appropriate ranges of light frequencies. Hence we write the metal dielectric function as: 2 e=l- zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM OP w(w + iw,) ’ (1) 45