INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 13 (2001) 8217–8234 PII: S0953-8984(01)24213-1 Effective dielectric response of a shape-distributed particle system A V Goncharenko 1 , V Z Lozovski and E F Venger Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, 45 prospect Nauki, 03028 Kyiv, Ukraine E-mail: avg@isp.kiev.ua Received 24 April 2001, in final form 6 July 2001 Published 16 August 2001 Online at stacks.iop.org/JPhysCM/13/8217 Abstract To calculate the effective dielectric response of a dilute composite, a generalization of the Maxwell Garnett theory for small nonspherical particles distributed in shape is proposed. Various types of distribution function are analysed and the applicability of the simplest (steplike) distribution is discussed. It is shown that the use of the steplike distribution is more valid for particles having a higher imaginary part of the permittivity in the actual region. Besides, an alternative approach to the problem based on the spectral representation is also considered. As an illustration, the effective dielectric response of a system of semiconductor (SiC) and metal (Al) ellipsoidal particles is calculated. 1. Introduction The dielectric response is one of the most important quantities describing the electrical and op- tical properties of materials. It is of particular interest when studying composite systems. They are the mainstay of advanced engineering structures and their importance continues to grow. It is well known that most theories on the dielectric response of composite systems use spherical models. Up to now such theories as the Maxwell Garnett (MG) and Bruggeman ones, in spite of their limitations, have been widely used in practical calculations (see, e.g., [1–18]). Their application, however, is under scrutiny rather frequently. Below the MG theory will be considered that is usually applied to dilute suspensions of uniform spheres. Since the first appearance of the MG theory [19], various corrections to its initial form have been proposed. It is known that this theory completely neglects fluctuations of the local field. Many works take these fluctuations into account [20]. It should be noted that if these fluctuations are strong, then mean-field theories collapse and other approaches to description of the optical properties of composites are to be applied (see, e.g., [21] and [22]). A theory of linear and nonlinear dielectric responses of the Maxwell Garnett composites based on a spectral 1 Corresponding author. 0953-8984/01/358217+18$30.00 © 2001 IOP Publishing Ltd Printed in the UK 8217