Anomalous transit-time dispersion in amorphous solids

Measurements of the transient photocurrent I (t) in an increasing number of inorganic and organic amorphous materials display anomalous transport properties. The long tail of I (t) indicates a dispersion of carrier transit times. However, the shape invariance of I (t) to electric field and sample thickness (designated as universality for the classes of materials here considered) is incompatible with traditional concepts of statistical spreading, i. e. , a Gaussian carrier packet. We have developed a stochastic transport model for I (t) which describes the dynamics of a carrier packet executing a time-dependent random walk in the presence of a field-dependent spatial bias and an absorbing barrier at the sample surface. The time dependence of the random walk is governed by hopping time distribution (t). A packet, generated with a (t) characteristic of hopping in a disordered system e. g. , (t) t^- (1+), 0<<1, is shown to propagate with a number of anomalous non-Gaussian properties. The calculated I (t) associated with this packet not only obeys the property of universality but can account quantitatively for a large variety of experiments. The new method of data analysis advanced by the theory allows one to directly extract the transit time even for a featureless current trace. In particular, we shall analyze both an inorganic (a-As₂Se₃) and an organic (trinitrofluorenone-polyvinylcarbazole) system. Our function (t) is related to a first-principles calculation. It is to be emphasized that these (t) 's characterize a realization of a non-Markoffian transport process. Moreover, the theory shows the limitations of the concept of a mobility in this dispersive type of transport.