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.

TY JOUR
TI Fractional differential approach to dispersive transport in semiconductors
AU Sibatov, R. T.
AU Uchaikin, V. V.
PB Physics-Uspekhi
PY 2009
JO Physics-Uspekhi
JF Physics-Uspekhi
JA Phys. Usp.
VL 52
IS 10
SP 1019-1043
UR https://ufn.ru/en/articles/2009/10/c/
ER https://doi.org/10.3367/UFNe.0179.200910c.1079