Geminate electron–cation recombination in disordered solids

Abstract

A theory of a geminate electron–cation recombination has been developed using the percolation approach to the description of the electron transport in disordered solids. Following this approach all trapping sites are separated into two groups. The first group forms a diffusion cluster responsible for the macroscopic charge transfer in disordered media whilethe second group consists of isolated traps playing the role of origins and sinks for mobile electrons. In the framework of such a model an equation has been derived describing the electron motion in the Coulomb field of a parent cation. The solution of this equation in the long time limit shows that the recombination rate decreases vs time as t −(1+α/2) with α being a positive constant or a very weak function of t. In the particular case of Gaussian diffusion α=1 and the kinetic law obtained reduces to that predicted by the well‐known Onsager–Smoluchowski theory. However for the dispersive (non‐Gaussian) transport in highly disordered systems α<1 and its value depends on the type of disorder, on the energy level structure of trapped electrons and on the specific mechanism of electron migration through the medium.