Analytical approach to calculating the effective dielectric characteristics of heterogeneous textured materials with randomly shaped inclusions

Analytical expressions for calculating the tensor of the effective permittivity of a matrix-type heterogeneous medium with inclusions of random ellipsoidal shape, which are a small deviation from the average spheroidal shape, are obtained. The orientations of the inclusions are probabilistically distributed; rotation group representations are used for their consideration. It is shown that the developed method is a generalization of the Maxwell–Garnett approximation for the given medium type. Based on this method, the frequency- induced dielectric properties of porous silicon are simulated in the range of 10 3 –10 8 Hz.