Theory of Dispersive Transport in Amorphous Semiconductors

Abstract

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The distribution of functional of a trajectory of a particle executing a random walk in a disordered medium

“…is the probability that the particle is in transport state n at time t ; ) (t Q n is the probability that the particle is in trap n at time t ; mn  is the transition rate from transport state n to transport state m ; n  and n  are, respectively, the transitions rates from the n -th transport state to the n -th trap and back. As a result of averaging of this equations over the ensemble of configurations and passing to the continuum limit, the authors of [7,15,18] obtained following equation for the averaged probability density of finding a particle at the point x at the time t ) , ( t x  :…”

“…These functions can be calculated in different approximations. The works [7,15,18], proposed methods for finding functions ) (s  in EMA (effective medium approximation) and ) (s  in CPA (coherent potential approximation). In this paper, specific forms of these functions will not be used.…”

“…Particle is not necessary in transport state at the initial time Equation (2.3) is obtained under the assumption that the particle is in the transport state at the initial time [7,15,18,21]. However, this assumption is not always satisfied.…”

“…For this purpose the parameters of these equations, in particular, memory functions ( ) t  and ( ) t  must be chosen so that the theoretical distribution of functional coincide with the experimental one. Having these memory functions, and knowing the dependence of these functions on the parameters characterizing the structure of the medium (see [7,15,18]), it is possible, in principle, to find these medium structure parameters.…”

Feynman-Kac Equations for Random Walks in Disordered Media

“…Thus, if the self-averaging property holds, the problem reduces to finding the averaged over the ensemble of configurations solutions of equation (1.4). In this paper we obtain the equations which this averaged solutions must satisfy within the Schirmacher model [7,15,18].…”