Drift of Charge Carriers in Crystalline Organic Semiconductors

TL;DR

This study models charge carrier drift in crystalline organic semiconductors under electric fields using a quantum-classical approach with decoherence corrections, revealing field-dependent mobility behavior and restoring the Einstein relation.

Contribution

It introduces a unified quantum-classical framework with decoherence corrections to accurately simulate charge transport in organic semiconductors, capturing field effects and energy relaxation.

Findings

Drift velocity peaks and then decreases at high fields due to Wannier-Stark localization.

Mobility exhibits negative electric-field dependence.

The Einstein relation is maintained up to high electric fields.

Abstract

We investigate the direct-current response of crystalline organic semiconductors in the presence of finite external electric fields by the quantum-classical Ehrenfest dynamics complemented with instantaneous decoherence corrections (IDC). The IDC is carried out in the real-space representation with the energy-dependent reweighing factors to account for both intermolecular decoherence and energy relaxation by which conduction occurs. In this way, both the diffusion and drift motion of charge carriers are described in a unified framework. Based on an off-diagonal electron-phonon coupling model for pentacene, we find that the drift velocity initially increases with the electric field and then decreases at higher fields due to the Wannier-Stark localization, and a negative electric-field dependence of mobility is observed. The Einstein relation, which is a manifestation of the fluctuation-dissipation theorem, is found to be restored in electric fields up to ~$10^5$ V/cm for a wide temperature region studied. Furthermore, we show that the incorporated decoherence and energy relaxation could explain the large discrepancy between the mobilities calculated by the Ehrenfest dynamics and the full quantum methods, which proves the effectiveness of our approach to take back these missing processes.