Truncated Levy statistics for transport in disordered semiconductors

TL;DR

This paper models charge transport in disordered semiconductors using truncated Levy distributions, deriving fractional transport equations, and explaining how truncation affects observable transport properties, aligning well with experimental data.

Contribution

It introduces a probabilistic framework based on truncated Levy distributions for describing transition regimes in disordered semiconductor transport.

Findings

Truncated Levy distributions effectively model transition from dispersive to Gaussian transport.

Derived fractional order transport equations match experimental observations.

Truncation influences carrier packet shape and frequency-dependent conductivity.

Abstract

Probabilistic interpretation of transition from the dispersive transport regime to the quasi-Gaussian one in disordered semiconductors is given in terms of truncated Levy distributions. Corresponding transport equations with fractional order derivatives are derived. We discuss physical causes leading to truncated waiting time distributions in the process and describe influence of truncation on carrier packet form, transient current curves and frequency dependence of conductivity. Theoretical results are in a good agreement with experimental facts.