Wave hierarchy interpretation of a multiple-trapping model

We consider a generalized multiple-trapping model for charge transport in a disordered material. The model is defined in terms of a set of coupled differential equations, in which each type of trap is characterized by a capture rate and a release rate. We rescale and recast the multiple-trapping equations, and interpret the motion of charge carriers as a hierarchy of waves. This approach leads to estimates of the mean-transit time which involve appropriate restricted sums. Using previously determined trap parameters for $a$-Se, we show how the superlinear dependence of the mean-transit time on material thickness follows naturally from the wave hierarchy interpretation of the multiple-trapping model.