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 Ψ(t). A packet, generated with a Ψ(t) characteristic of hopping in a disordered system [e.g., Ψ(t)∼t^-(1+α), 0<α<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 Ψ(t) is related to a first-principles calculation. It is to be emphasized that these Ψ(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.