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

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 ψ(t)∝$t^{\mathrm{-}1\mathrm{-}\alpha }$, around the marginal value α=1 strong crossover effects are found.