Nonlinear Electrophysical Phenomena in Ionic Dielectrics with a Complicated Crystal Structure

Abstract

The methods of quasi-classical kinetic theory are used to study the phenomena of nonlinear relaxation polarization in ionic dielectrics with a complicated crystal lattice structure (layered crystals, ceramics, perovskites, vermiculites, etc.) characterized by high ionic conductivity. A special case of materials of this class are proton semiconductors and dielectrics (mica, talc, pyrophyllite, etc.) characterized by high proton conductivity in fairly wide ranges of field parameters (100 kV/m – 1000 MV/m) and temperatures (1–1500 K). Based on the continuity equation for the ion current, a generalized kinetic equation is constructed that describes transfer of electric charge in ionic dielectrics in an alternating polarizing field with blocking electrodes. The nonlinearity of the mathematical model is ensured by the dependences of the diffusion coefficients and ion mobility on the parameters of the inhomogeneous electric field in the dielectric. It is shown that the Fokker–Planck equation, known in the kinetic theory, is a zero approximation of the generalized nonlinear kinetic equation with respect to a small dimensionless parameter. The dielectric polarization is written from the solution of the Fokker–Planck equation in the infinite approximation of the perturbation theory (k = 1, 2, 3, ...) for an arbitrary value of the multiplicity factor r over the alternating field frequency. The spectra of a complex dielectric permittivity constructed at the fundamental frequency of the alternating field (r = 1) taking into account all subsequent (starting from the second one) approximations of the perturbation theory (k > 1) differ significantly from the classical laws of the Debye dispersion (corresponding to the first approximation of the perturbation theory (k = 1)). The theoretical foundations have been laid for the program algorithms of computer prediction of properties and parameters of electrical materials for the functional elements of the microelectronic device circuits, isolation technology, and non-volatile high-speed memory devices.