Random walk theory of a trap-controlled hopping transport process.

A random walk theory of hopping motion in the presence of a periodic distribution of traps is presented. The solution of the continuous-time random walk equations is exact and valid for arbitrary intersite interactions and trap concentration. The treatment is shown to be equivalent to an exact solution of the master equation for this trapping problem. These interactions can be a general function of electric field and are not restricted to nearest neighbors. In particular, with the inclusion of trap-to-trap interactions, as well as trap-to-host interactions, an exact treatment of the change from one hopping channel to another has been obtained. The trap-modulated propagator has been derived in terms of a type of Green's function that is introduced. The results are specialized to spatial moments of the propagator, from which expressions for the drift velocity and diffusion coefficient are obtained. Numerical results for the drift velocity are presented and shown to account for the change in hopping channels in recent transport measurements in mixed molecularly doped polymers.