Analytically Solvable Model for Polarons Trapping Kinetics in Iron-Doped Lithium Niobate Crystal

The problem of the kinetic description of a light-induced, small-electron polaron population decay in a lithium niobate crystal (LiNbO₃, LN) doped with Fe is considered on the basis of the Marcus–Holstein hopping model for polaron migration and trapping. Starting from the possible reaction channels involving the different polaron species in LN (free polarons, bound polarons and Fe traps), we compose closed kinetic equations for the concentration of reactants and pair distribution functions describing the dynamics of correlations arising during reactions. Analytical solutions are then obtained for the rate constants of a multistage reaction controlled by polaron mobility, for the trapping kinetics of polarons and their lifetimes. The temperature and composition dependences of the observed quantities are analyzed. Finally, our results were used to fit experimental decay kinetics and lifetimes obtained by time-resolved Light Induced Transient Absorption spectroscopy determining poorly known parameters such as the polaron diffusion coefficient and the characteristic lengths of Marcus–Holstein hopping probabilities.