Crossover from dispersive to nondispersive transport in a trap-controlled hopping model.

Abstract

We use an exactly solvable model for charge-carrier transport in amorphous solids to study the crossover from dispersive to regular transport. The model takes into account the energetic disorder; furthermore, in it the multiple-trapping approach and the continuous-time random walk are equivalent. The crossover is studied as a function of the distribution of trap energies. Thus for exponential trap distributions, which lead to long-time tails \ensuremath{\psi}(t)\ensuremath{\propto}${t}^{\mathrm{\ensuremath{-}}1\mathrm{\ensuremath{-}}\ensuremath{\alpha}}$, around the marginal value \ensuremath{\alpha}=1 strong crossover effects are found.