Carrier hopping in disordered semiconducting polymers: How accurate is the Miller-Abrahams model?

TL;DR

This study critically evaluates the Miller-Abrahams model for carrier hopping in disordered polymers, revealing significant discrepancies and proposing a new, more accurate model based on atomic-level calculations of electronic and phonon states.

Contribution

The paper introduces a new model for carrier hopping that accounts for atomic structure, electronic states, and phonon interactions, improving upon the Miller-Abrahams model.

Findings

Miller-Abrahams model does not accurately predict hopping rates or mobility.

A new model based on atomic and phonon states better describes carrier hopping.

Carrier hopping depends on electronic density, phonon density, and wavefunction overlap.

Abstract

We performed direct calculations of carrier hopping rates in strongly disordered conjugated polymers based on the atomic structure of the system, the corresponding electronic states and their coupling to all phonon modes. We found that the dependence of hopping rates on distance and the dependence of the mobility on temperature are significantly different than the ones stemming from the simple Miller-Abrahams model, regardless of the choice of the parameters in the model. A new model that satisfactorily describes the hopping rates in the system and avoids the explicit calculation of electron-phonon coupling constants was then proposed and verified. Our results indicate that, in addition to electronic density of states, the phonon density of states and the spatial overlap of the wavefunctions are the quantities necessary to properly describe carrier hopping in disordered conjugated polymers.