Fractional differential approach to dispersive transport in semiconductors
A novel approach using equations with fractional order derivatives to describe dispersive transport in disordered semiconductors is described. A relationship between the self-similarity of dispersive transport, stable limiting distributions,
and kinetic equations with fractional derivatives is established. It is shown that unlike the well-known Scher — Montroll and Arkhipov — Rudenko models, which are in a sense alternatives to the normal transport model, fractional differential equations provide a unified mathematical framework for describing normal and dispersive transport. The fractional differential formalism allows the equations of ambipolar dispersive transport to be written down and transport in systems with a distributed dispersion parameter to be described. The relationship between
fractional differential equations and the generalized limiting theorem reveals the probabilistic aspects of the phenomenon in which a dispersive-to-Gaussian transport transition occurs in a time-of-flight experiment as the applied voltage is decreased and/or the sample thickness increased.