Permittivity of lossy heterostructures: effect of shapeanisotropy

Abstract

The complex values of the permittivity of two-component lossy(deterministic) heterostructures, composed of inclusions of permittivityε1 embedded in a host matrix of permittivity ε2, arerigorously evaluated with the use of the field calculation package PHI3D andthe resolution of boundary integral equations. Numerical results are providedconcerning spherical and rod-like inclusions with various radius-to-lengthratios, of finite conductivity, periodically arranged in a simple-cubiclattice configuration. For illustrative purposes, a single set ofpermittivities is investigated: ε1 = 80-i102 andε2 = 2-i0. The conduction threshold volume concentration isstrongly dependent on the shape of the inclusions. Increasing theradius-to-length ratio by one order of magnitude has the effect of shiftingthe conduction threshold upwards by two decades. The exponents which determinehow the real and imaginary parts of the effective permittivity scale with thedistance from the conduction threshold are determined and are compared withthe scaling predictions of the percolation theory for infinitethree-dimensional (random) lattices of insulator-normal metal compositesystems and the self-consistent effective-medium approximation. We also foundthat the data concerning the imaginary part of the effective permittivitycollapse on a single scaling plot over the range of aspect ratio investigated.The effect of the orientation of the rod-like inclusions is further studied.We observed that the conduction transition is shifted towards higherconcentrations as the angle between the rod axis and the direction of theapplied electric field increases.