Field-induced trapping as a probe of dimensionality in molecular crystals

The combined effect of an electric field and reduced dimensionality on the hopping motion of a charge carrier in an anisotropic molecular crystal is determined. New, exact expressions for S(t), the number of distinct sites occupied by a carrier in time t, are presented for two-dimensional and three-dimensional anisotropic lattices. The general results are used to model the unusual phenomenon of field-induced charge carrier trapping reported to occur in a quasi-one-dimensional molecular crystal. An analytic expression for the carrier lifetime tau, as a function of the anisotropy in the molecular hopping rates and electric field, is developed and is shown to be in excellent agreement with experimental results. A major conclusion of the theory is that E(c), the electric field characterizing the E dependence of tau, can be a more direct probe of the intrinsic anisotropy than is the observed mobility ratio.