Matrix formalism to enhance the concept of effective dielectric constant

By using a matrix formalism, a general framework describing the effective permittivity constants of an idealized freestanding uperlattice (SL), composed of thin alternating layers is derived, as a function of the dielectric tensor of each of the N constituents. The versatile results are applied to superlattices with layers of all classes of the whole set of symmetries (triclinic, monoclinic, orthorhombic, hexagonal, tetragonal and cubic). Such an approach leads to only three new general prevalent laws for working out the whole dielectric tensor of any superlattice featuring N constituents of any symmetry. Moreover it is of noteworthy interest that such laws can be formulated as one general relationship related to the 'Vegard rules' in solid state physics. (C) 2003 Elsevier Science B.V. All rights reserved.