Low-temperature ionization of the excited<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>F</mml:mi></mml:math>center: Evidence for lattice tunneling

Abstract

Several possible ionization mechanisms of excited $F$ centers (${F}^{*}$) in alkali halides are discussed. A lattice tunneling model for the low-temperature ${F}^{*}$ ionization is proposed which implies considerable rearrangement of the lattice as a condition for a radiationless electron transfer from the ${F}^{*}$ center to a virtual polaron center in the crystal. This model rests on a configurational diagram based on experimental absorption and emission data. A recent reaction-rate theory of electron hopping in polar crystals is applied to calculate the rate constant ${k}_{12}$ of the ${F}^{*}$ ionization in the temperature range 10-160 K by the use of reasonable values of four parameters: the LO vibration frequency $\ensuremath{\nu}$, the reorganization energy ${E}_{r}$ of the lattice, the reaction heat $Q$ at zero temperature, and the resonance energy ${V}_{12}$ of the electron transfer. In this way good agreement between the theoretical results and the available experimental data for ${k}_{12}$ is obtained. In addition, an independent estimation of the "average" resonance energy, based on a simple donor-acceptor model for the electron transfer, is found to agree very well with the values of ${V}_{12}$ fitted to the experiment. The average values of the electron tunneling distance ${\overline{R}}_{t}$ and the average donor-acceptor ($F$-center---polaron-center) separation $\overline{R}$ derived from this model seem also to be quite reasonable. Some implications of the theory concerning the reverse process of electron transfer from a free polaron to an empty ion vacancy are also discussed.