Nonlinear electrophysical phenomena in ionic dielectrics
The methods of semiclassical kinetic theory are used to study the phenomena of nonlinear relaxation polarization in ionic dielectrics with a complex crystal lattice structure (layered crystals; ceramics; perovskites; vermiculites and others), characterized by high ionic conductivity. A special case of materials of this class are proton semiconductors and dielectrics (mica, talc, pyrophyllite, etc.), characterized in a fairly wide range of field parameters (100 kV/m - 1000 MV/m) and temperatures (1-1500 K), high proton conductivity. Based on the continuity equation for the ion current, a generalized kinetic equation is constructed that describes the 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 kinetic theory is “zero” in the small dimensionless parameter by an approximation to the generalized nonlinear kinetic equation. The dielectric polarization is written from the solution of the Fokker - Planck equation in the infinite approximation of perturbation theory (k = 1,2,3, ...) for an arbitrary value of the exponent of multiplicity r of multiplicity in frequency of the alternating field. The spectra of complex dielectric constant, built on the fundamental frequency of the alternating field (r = 1), taking into account all subsequent (starting from the second) approximations of the perturbation theory (k > 1), differ significantly from the classical laws of Debye dispersion (corresponding to the first approximation of the theory disturbances (k = 1)). The theoretical foundations have been laid for algorithms for computer-aided prediction of the properties and parameters of electrical materials for functional elements in microelectronic device circuits, isolation equipment, and non-volatile high-speed memory devices.