Analytical procedures for the modelling of hopping transport in disordered semiconductors

Abstract

The transient and steady-state electronic and optoelectronic properties of disordered semiconductors involve interactions of charge carriers with localized states distributed over a range of energies. Where the concentration of such states is sufficiently high, the transport mechanism can be dominated by hopping (quantum-mechanical tunnelling) transitions directly between them. In the analysis of the above situation, one easily applicable approach is to replace a continuous energy distribution with a 'ladder' of energetically discrete sets of traps. This can greatly simplify calculations, but a serious limitation is that the resulting properties depend extremely sensitively upon the slice width selected. In this letter, two variants of a new approach, based upon simple concepts of differential probability and detailed balance, and applicable to an arbitrary energy distribution of trapping centres, are introduced. The capabilities of the procedures are demonstrated by their application to the calculation of effective hopping rates in an exponential energy distribution of localized states. Finally, to illustrate the application of the techniques, the effective rates are coupled to the corresponding hopping distances. This allows the results to be employed (as a preliminary example) in the calculation of the time dependence of the transient photocurrent within an exponential band tail.