The elusive role of Nb_Libound polaron energy in hopping charge transport in Fe: LiNbO₃

Abstract

Charge transport due to small polarons hopping among defective (bound polarons) and regular (free polarons) sites is shown to depend in a non-trivial way from the value of the stabilization energy provided by the lattice distortion surrounding the charge carriers. This energy, normally not directly accessible for bound polarons by spectroscopic techniques, is here determined by a combination of experimental and numerical methods for the important case of small electron polarons bound to \mathrm{Nb}_{\mathrm{Li}} defects in the prototype ferroelectric oxide lithium niobate. Our findings provide an estimation of the \mathrm{Nb}_{\mathrm{Li}} polaron stabilization energy E_{GP}=\unit[(0.75\pm0.05)]{eV} and point out that in lithium niobate both free and bound polarons contributes to charge transport already at room temperature, explaining the fast decays of the light-induced bound polaron population observed by transient absorption spectroscopy.

Small Polaron Hopping in Fe:LiNbO3 as a Function of Temperature and Composition

“…According to the discussion reported elsewhere [17,18,22,23] it can be considered that α TA (785 nm, t) was proportional to the weighted sum of the bound and free polarons populations.…”

“…The pre-exponential factor I i, f describes the intrinsic hopping rate between the two sites and was determined by the choice of the (i, f ) combination. Using the data reported in [15,18] the hopping barrier (4) for any process and the hopping rates (3) can be calculated. This result was used in a dedicated Monte Carlo code based on a classical Gillespie algorithm.…”

“…However, if more processes with similar hopping frequency occurred in a comparable amount, the observed activation energy would somehow lie in the middle. Using Equation (4) and the known values of the polaron energies (see [18] and the references therein), it is possible to compute the characteristic hopping barriers for the different processes, reported in Figure 3. As can be verified by inserting some typical values in Equation (3), the processes requiring the longest time to hop away from an antisite were the Nb Li − Nb Li and Nb Li − Nb Nb hops, characterized by an activation energy of 0.375 eV and 0.55 eV.…”

“…This means that the polaron, initially stuck on an antisite defect, either hopped directly towards another antisite or became a free polaron (which can eventually move on the Nb Nb lattice or re-captured by an antisite, but since those processes were very fast, they did not significantly affect the polaron lifetime). (4)) calculated using the values for the different polaron energies detailed in [18]. FP, free polaron.…”

“…As a consequence, the relation (1) cannot be used in real crystals. Nevertheless, in recent works [17,18], it was shown that by an appropriate choice of a few microscopic parameters, the problem can be tackled numerically by resorting to Monte Carlo simulations incorporating the presence of defects in the lattice structure of LN. In line with those studies, one may expect that depending on the temperature and composition of the crystal, one type of hop may dominate the transport process.…”