ABSTRACT
In the absence of disorder, the probability that a carrier will leave a hopping site is an exponential function of time. In the presence of disorder, this is no longer true. Disorder changes the transition rates between hopping sites into a statistical quantity that reflects the fact that certain sites are depopulated faster or slower than average. A technique that has been used to quantify this effect involves the assumption of a distribution function that describes the dwell times that carriers spend on hopping sites. In the absence of disorder, the time distribution is determined by a single transition rate and the distribution function is i|>(0 ~ exp (-Xt), where \ is a constant. To describe the effects of disorder, Scher (1974, 1976) and Scher and Montroll (1975) proposed the function i|t(t) ~ Here, a is a disorder parameter that has values between zero and unity. The more disordered the material, the smaller the value of a and the more dispersive the transport. The Scher-Montroll model describes the dynamics of a charge packet executing continuous-time random-walk in the presence of a field dependent spatial bias. In the original model, it was assumed that i|f(t) originates from positional disorder of the hopping sites. The model predicts that with increasing time, an increasing fraction of the carriers will encounter at least one long waiting time at some site, leading to a dispersion in transit times.
