Fractional Einstein relation for strongly disordered semiconductors

TL;DR

This paper introduces a fractional Einstein relation (FER) for electric conduction in disordered semiconductors, showing it outperforms previous models by accounting for detailed balance violations in hopping processes.

Contribution

The paper proposes a new fractional Einstein relation (FER) that better models conduction in disordered semiconductors by incorporating detailed balance violations.

Findings

FER agrees better with Monte Carlo simulations than GER.

FER captures the violation of detailed balance in hopping conduction.

FER provides a more accurate description of charge transport in disordered materials.

Abstract

A novel Einstein relation (fractional Einstein relation, FER) for the electric conduction in non-crystalline semiconductors is presented. FER and the generalized Einstein relation (GER) [Phys. Rev. E 8, 1296 (1998)] are compared to the result of the Monte Carlo (MC) simulation, and is confirmed that FER exhibits better agreement than GER. The cruial feature of FER is that it reflects the violation of the detailed balance in the coarse-grained hopping process, while it is preserved in the original Einstein relation or GER.