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.
