Influence of Quantum Effects on Dielectric Relaxation in Functional Electrical and Electric Energy Elements Based on Proton Semiconductors and Dielectrics

Abstract

Using the quasi-classical kinetic theory of dielectric relaxation, in addition to existing methods, fundamental mathematical expressions are built, which make it possible to more strictly consider the effects of the main charge carriers’ (protons’) tunneling on the numerical values of the molecular parameters (activation energy, equilibrium concentration) of protons in HBC. The formulas for calculating the statistically averaged non-stationary quantum transparency of a parabolic potential barrier for protons have been modernized by more stringent consideration of the effects of corrections caused by an external electric field. For the model of a double-symmetric potential well, a generalized nonlinear solution of the quasi-classical kinetic equation of dielectric relaxation in HBC was built. The phenomenological Bucci-Rive formula for thermally stimulated depolarization current density (TSDC) was first investigated, taking into account quantum transparency, for the case of a parabolic potential barrier. The choice of the parabolic shape of the potential barrier allowed, at a theoretical level, for the mathematical model of relaxation polarization to be brought closer to the conditions of the real spatial structure of the crystal potential field, in comparison with the rectangular potential barrier model. It has been found that quantum effects due to proton tunnel transitions significantly affect the mechanism of thermally stimulated depolarization currents in HBC, over a wide temperature range (50–550 K) and external field parameters (0.1–1 MV/m). Generalized solutions of the nonlinear kinetic equation, recorded considering the effects of field parameters on proton tunnel transitions, made it possible to significantly approximate the theoretical values of activation energies, equilibrium concentrations of protons and amplitudes of the theoretical maxima of the current density of thermally stimulated depolarization, according to their experimental values in the field of low-temperature (50–100 K) and high-temperature (350–550 K) maxima of TSDC density in HBC. For the first time, precision measurements of TSDC temperature spectra were carried out for chalcanthite crystals. The effects of alloying impurities concentrations and crystal calcination temperatures on the parameters of experimental maxima in the TSDC spectrum of chalcanthite were established. A physical mechanism of the quantum tunnel motion of protons in HBC with a complex crystal structure (crystalline hydrates, layered silicates, ferroelectric HBC (KDP, DKDP)) is described. The patterns found in this article indicate a fairly high degree of applied scientific significance for the obtained theoretical results, allowing for the further development of electrophysics and optoelectronics of heterogeneous structures (MIS, MSM) based on proton semiconductors and dielectrics (PSD) and their composites.

Physical and Mathematical Models of Quantum Dielectric Relaxation in Electrical and Optoelectric Elements Based on Hydrogen-Bonded Crystals

“…Studies of the electrophysical properties of HBC-class crystals are based on precision measurements of the temperature spectra of thermally stimulated depolarization currents (TSDC) and the frequency-temperature spectra of the dielectric loss angle tangent tgδ exp (ω, T) [75,78,[81][82][83][84][85][86][87][88][89]. In [90], the methodologies of experimental studies and semi-empirical estimates of the characteristic parameters of crystals under various external conditions of the experiment (polarization temperature; polarizing field strength; external mechanical stresses) and methods of processing samples (doping, calcination, etc.)…”

“…In [90], experimental patterns of behavior of TSDC density spectra in a model Ih-ice crystal and complex HBC crystal lattice structure (layered silicates; crystalline hydrates) on the example of the crystals of natural phlogopite KMg 3 (AlSi 3 O 10 )(OH) 2 , muscovite KAl 2 (AlSi 3 O 10 )(OH) 2 , onot talc Mg 3 (Si 4 O 10 )(OH) 2 chemically pure chalcanthite CuSO 4 •5H 2 O at temperatures above 50-550 K and at polarizing field strengths of 0.1-1 MV/m with a frequency of the polarizing field in the range of 1 kHz-10 of MHz. At the same time, in natural samples of layered minerals and crystalline hydrates, as a rule, 6-7 monorelaxation maxima [78,90] are found, caused by relaxation of the corresponding types of structure defects: Bjerrum ionization defects and complexes of the "vacation + L-defect" (VL) or "vacation + D-defect" (VD) type [1] are dipole molecules of crystallization (structural) and adsorbed (interlayer) water. A significant role in relaxation processes in HBC-type dielectrics is acquired by volume-charge polarization associated with relaxation of a mixed type (when defects of a structure of different nature are activated in an electric hollow), manifested in a region of sufficiently high temperatures (250-550 K) and characterized by high polarization nonlinearities (associated with the influence of electric field parameters on the amplitudes of TSDC density maxima and relaxation times of structure defects) [78,90].…”

“…At the same time, in natural samples of layered minerals and crystalline hydrates, as a rule, 6-7 monorelaxation maxima [78,90] are found, caused by relaxation of the corresponding types of structure defects: Bjerrum ionization defects and complexes of the "vacation + L-defect" (VL) or "vacation + D-defect" (VD) type [1] are dipole molecules of crystallization (structural) and adsorbed (interlayer) water. A significant role in relaxation processes in HBC-type dielectrics is acquired by volume-charge polarization associated with relaxation of a mixed type (when defects of a structure of different nature are activated in an electric hollow), manifested in a region of sufficiently high temperatures (250-550 K) and characterized by high polarization nonlinearities (associated with the influence of electric field parameters on the amplitudes of TSDC density maxima and relaxation times of structure defects) [78,90].…”

“…In the field of low temperatures (50-100 K), the main contribution to a dielectric relaxation of HBC is made by the quantum microscopic effects connected with tunnel transitions of ions of hydrogen (protons) inside and between ions of an anion sublattice [78,90]. The structure of an anion sublattice is formed in a certain way by the type of anions connected among themselves at the corresponding geometry of a crystal lattice: SiO 4− 4 -silicate-anions in layered silicates (micas, minerals of group of talc-pyrophyllite, clay minerals, vermiculites, allophanes, halloysites, etc.…”

“…Theoretical studies of nonlinear kinetic phenomena during polarization of layered dielectrics of the HBC-class (crystal hydrates; layered silicates) were carried out in a wide range of field parameters and temperatures and indicate the manifestation of an anomalously high dielectric constant ((1.5-2.5) million) in the region of ultralow temperatures (1-10 K) in weak fields (100-1000 kV/m) and in the region of ultra-high temperatures (550-1500 K) in strong fields (10-100 MV/m) [72][73][74][75][76][77][78].…”