The time-of-flight signal in a gaussian disordered chain

摘要

We consider a one-dimensional master equation model for the time-of-flight (TOF) experiment performed on an organic disordered material where the charge transport occurs via thermally activated hops between localized electronic states. From the model we obtain an expression for the average transit time in terms of the site energies and of the forward hopping rates. In the particular case of a bloacking cathode we are ble to perform the (Gaussian) average over the site energies and to obtain an exact expression for the transit time as a function of the applied field and of the variance of the energy distribution. We also obtain numerically the TOF signal I(t) and show that it exhibits two power-law regimes whose exponents do not sum up to 2, as in the time-dependent-random-walk model by Scher and Montroll. We investigate the dependence of the exponents with the field and with the amount of disorder. Finally, we show how the field dependence of the exact average transit time can be inferred from t_R, the time of the transition between the two power-law regimes.