Conceptual Frameworks Disorder-Based Models

In an extended version of the hopping concept, positional ( off-diagonal ) disorder in addition to energetic ( diagonal ) disorder has been introduced [54,63]. The simplest ansatz was to incorporate this by allowing the electronic overlap parameter 2ya to vary statistically. Operationally, one splits this parameter into two site contributions, each taken from a Gaussian probability density, and defines a positional disorder parameter I, in addition to the energetic disorder parameter cr. 

Monte Carlo simulations [54], analytical effective medium theory [64], and stochastic hopping theory [46] predict a dependence of the charge carrier mobility as a function of temperature and electric field given in (3)  

Equation (3) implies that the field dependence of the mobility can become negative if a E in (3a) or if E 1.5 in (3b). This is a signature of positional disorder. The reason is the following. Suppose that a migrating charge carrier encounters a site from which the next jump in field direction is blocked because of poor electronic coupling. Under this condition the carrier may find it easier to circumvent that blockade. If the detour involves jumps against the field direction it 

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