Measurements of the transient photocurrent $I\left(t\right)\mathrm{}$ in an increasing number of inorganic and organic amorphous materials display anomalous transport properties. The long tail of $I\left(t\right)\mathrm{}$ indicates a dispersion of carrier transit times. However, the shape invariance of $I\left(t\right)\mathrm{}$ 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 $I\left(t\right)\mathrm{}$ 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 $\Psi \mathrm{}\left(t\right)\mathrm{}$. A packet, generated with a $\Psi \mathrm{}\left(t\right)\mathrm{}$ characteristic of hopping in a disordered system [e.g., $\Psi \mathrm{}\left(t\right)\mathrm{}\sim t^{-(1+\alpha )}$, $0<\mathrm{}\alpha <1\mathrm{}$], is shown to propagate with a number of anomalous non-Gaussian properties. The calculated $I\left(t\right)\mathrm{}$ 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 ($a-{\mathrm{As}}_2{\mathrm{Se}}_3$) and an organic (trinitrofluorenone-polyvinylcarbazole) system. Our function $\Psi \mathrm{}\left(t\right)\mathrm{}$ is related to a first-principles calculation. It is to be emphasized that these $\Psi \mathrm{}\left(t\right)\mathrm{}$'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.

• Received 13 January 1975

DOI:https://doi.org/10.1103/PhysRevB.12.2455