Flickering Polarons Extending over Ten Nanometres Mediate Charge Transport in High‐Mobility Organic Crystals

Samuele Giannini,Jochen Blumberger,Matthew Ellis,Antoine Carof,Orestis George Ziogos

doi:10.1002/adts.202000093

Samuele Giannini, Jochen Blumberger + Show 3 more

Open Access

https://doi.org/10.1002/adts.202000093

Copy DOI

Abstract

AbstractProgress in the design of high‐mobility organic semiconductors has been hampered by an incomplete fundamental understanding of the elusive charge carrier dynamics mediating electrical current in these materials. To address this problem, a novel fully atomistic non‐adiabatic molecular dynamics approach termed fragment orbital‐based surface hopping (FOB‐SH) that propagates the electron‐nuclear motion has been further improved and, for the first time, used to calculate the full 2D charge mobility tensor for the conductive planes of six structurally well characterized organic single crystals, in good agreement with available experimental data. The nature of the charge carrier in these materials is best described as a flickering polaron constantly changing shape and extensions under the influence of thermal disorder. Thermal intra‐band excitations from modestly delocalized band edge states (up to 5 nm or 10–20 molecules) to highly delocalized tail states (up to 10 nm or 40–60 molecules in the most conductive materials) give rise to short, ≈ 10 fs‐long bursts of the charge carrier wavefunction that drives the spatial displacement of the polaron, resulting in carrier diffusion and mobility. This study implies that key to the design of high‐mobility materials is a high density of strongly delocalized and thermally accessible tail states.

Highlights

It is extremely useful and important to have analytic theories, it is paramount to develop numerical schemes that give insight into the actual dynamics and that seamlessly bridge the gap between different mechanistic regimes. With this purpose in mind, we have developed an efficient fully atomistic non-adiabatic molecular dynamics approach, denoted fragment orbital-based surface hopping (FOB-SH),[29,30,31,32] which allows us to propagate the coupled charge-nuclear motion in realtime for condensed phase systems
We find that the density of electronic states of this Hamiltonian is in good agreement with the results from standard band structure calculations at the Kohn–Sham density functional theory (DFT) level with regards to both peak positions and bandwidth
We refer to the Experimental Section for a specific discussion of the multiple time step algorithm as well as a more efficient propagation of the electronic Schrödinger equation introduced in this work to deal with large systems

Summary

Introduction

Along with the charge carrier wavefunction, the nuclei are propagated in time on the potential energy surface (PES) of one of the valence or conduction band states (i.e., eigenstates) of the electronic Hamiltonian Equation (1) (referred to as active eigenstate a), and intra-band transitions of the nuclear dynamics (“hops”) to another band state j are included using Tully’s surface hopping probability.[37] As described in detail in our previous work,[31,32] we use FOB-SH in combination with three important extensions of the original surface hopping method: decoherence correction, removal of decoherence correction induced artificial long-range charge transfer and tracking of trivial surface crossings.

Results

Conclusion