The relevance of polaronic effects to the hopping motion of charges

Abstract

Most models describing the mobility of charge carriers in the framework of electron-phonon coupling (small polarons) take into account only forward and backward jumps. A new formalism, taking into account that the hopping can occur in an isotropic way in three dimensions, has been developed to describe the influence of the applied electric field on the mobility of charge carriers in the presence of polaronic effects. While at very small applied fields it corresponds to the models developed earlier for a one-dimensional hopping model, it leads to a much slower decrease of the mobility at large applied fields by introducing the possibility of hops in a direction making an angle with the applied field. While this model can explain in a qualitative way the experimentally obtained field dependence of the mobility, it does not lead to physical relevant and consistent values of the hopping distance and reorganization energy. However the correct incorporation of the polaronic effects in the current model describing the hopping of charge carriers in a Gaussian density of states will for a physically relevant range of values of the reorganization energy influence the field and temperature dependence of the mobility to a very limited extent. The influence of the applied field on the preferential direction of an electron transfer process relative to the applied field will be compared for a one-dimensional model, a three-dimensional isotropic model and a three-dimensional cube lattice.