Fractional theory for transport in disordered semiconductors

The article is devoted to theoretical description of charge carrier transport in disordered semiconductors. The main idea of the approach lies in the use of fractional calculus. The physical reasons of introducing fractional derivatives in semiconductor theory are discussed, the process of derivation of fractional differential equations is demonstrated, the tied link of their solutions with non-Gaussian stable processes is shown. The last section of the article contains solutions of some concrete problems: multiple trapping, transient photocurrent and drift mobility, dispersive transport percolation model of semiconductors, transport in bilayer semiconductor and so on. Some numerical results are obtained and their agreement with experimental data is demonstrated.