Microscopic theory of dispersive transport in disordered semiconductors

A theory of dispersive transport based on the microscopic master equation is presented. The theory agrees with previous approaches and unifies them but is much more general. By means of the two-site effective medium approximation of Movaghar et al. we derive a generalised master equation for the averaged propagator of the carriers the kernel of which can be calculated directly from the microscopic transfer rates and distribution functions. We give analytic expressions for the transient current i(t) including the conditions for the transition from dispersive to Gaussian transport for three relevant hopping models. The influence of multiple trapping is treated by means of the coherent potential approximation. We find the same results for trapping with an exponentiak trap depth distribution and fixed-range hopping over energy barriers with an exponential barrier height distribution.