ANOMALOUS KINETICS OF CHARGE CARRIERS IN DISORDERED SOLIDS: FRACTIONAL DERIVATIVE APPROACH

Abstract

Anomalous (non-Gaussian) kinetics is often observed in various disordered materials, such as amorphous semiconductors, porous solids, polycrystalline films, liquid-crystalline materials, polymers, etc. Recently the anomalous relaxation-diffusion processes have been observed in nanoscale systems: nanoporous silicon, glasses doped by quantum dots, quasi-one-dimensional (1D) systems, arrays of colloidal quantum dots, and some others. The paper presents a review of new approach, based on fractional kinetic equations. We give a physical basis for some fractional equations deriving them from their classical counterparts by means of averaging over statistical ensemble of disordered media. We consider self-similarity as the main feature of these processes, and explain memory phenomena in frameworks of hidden variables conception.