Quantum properties of proton subsystem in proton semiconductors

Abstract

The quantum mechanism of the relaxation motion of the most mobile charge carriers (protons) in crystals with hydrogen bonds (HBC) in the range of low temperature (70-100 K) is studied. The energy spectrum of the proton in the unperturbed potential field of a crystal lattice modeled as a one-dimensional periodic potential relief of a rectangular shape is investigated in the quasi-classical approximation by the Wentzel – Kramers – Brillouin method (WKB-method) at ohmic contacts at the crystal boundaries (the work function of the proton from the crystal is assumed to be finite). The band structure of the energy spectrum of lowtemperature relaxers (protons) in proton materials was discovered, the word parameters of the band structure (width of the forbidden zone, «bottom» and «ceiling» of the energy zone minimum and maximum distances between two fixed energy bands). The populations of quasi-discrete energy levels (within the limits of the corresponding energy bands) by protons are calculated using an balanced (equilibrium) density matrix constructed on the basis of Boltzmann's quantum statistics for protons tunneling through a rectangular potential barrier. With the help of a quasi-stationary equilibrium density matrix, an expression is constructed for the polarization of the proton subsystem perturbed by an external homogeneous harmonic time-varying electric field.