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

Abstract

Progress 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.

Impact of Nanoscale Morphology on Charge Carrier Delocalization and Mobility in an Organic Semiconductor

“…[ 8–11 ] We have recently shown, using advanced quantum dynamical simulations, that charge carriers in single‐crystalline OS form “flickering polarons,” objects that are half‐way between waves and particles. [ 12–14 ] We found they are delocalized over up to 10–20 molecules in the most conductive crystals and constantly change their shape and extension under the influence of the thermal motion of the atoms (crystal vibrations). [ 12 ] Taking the example of bulk crystalline pentacene, we found that the excess hole is typically delocalized over 17 molecules, [ 12,13 ] in excellent agreement with experimental estimates from electron spin resonance data.…”

“…[ 12–14 ] We found they are delocalized over up to 10–20 molecules in the most conductive crystals and constantly change their shape and extension under the influence of the thermal motion of the atoms (crystal vibrations). [ 12 ] Taking the example of bulk crystalline pentacene, we found that the excess hole is typically delocalized over 17 molecules, [ 12,13 ] in excellent agreement with experimental estimates from electron spin resonance data. [ 15 ] The computed mobility, of 9.6 cm 2 V −1 s −1 , [ 13 ] is also in good agreement with experiment, 5.6 cm 2 V −1 s −1 .…”

Delocalised kinetic Monte Carlo for simulating delocalisation-enhanced charge and exciton transport in disordered materials

“…Existing methods can be broadly divided into atomistic ones and those based on effective Hamiltonians. Atomistic calculations track the dynamics of both the nuclear degrees of freedom (usually using molecular mechanics) and the electronic ones (using quantum equations of motion) [31][32][33][34][35][36][37]. Atomistic simulations do not have adjustable parameters, but they suffer from the considerable cost of tracking the atomic motion.…”

“…1 ps [34][35][36][37]. These capabilities enable remarkable simulations of layered organic crystals, which admit a twodimensional simulation and are ordered enough that mobilities converge rapidly.…”

Exciton Diffusion in Highly-Ordered One Dimensional Conjugated Polymers: Effects of Back-Bone Torsion, Electronic Symmetry, Phonons and Annihilation

“…While beyond the scope of this article, we note that the 2 1 A g – state exhibits a lower transition dipole moment than 1 1 B u + 7 ,. 37 Given that the annihilation cross-section of a state is proportional to its transition dipole moment 38 − 40 this may explain why the 2 1 A g – symmetry excitons do not exhibit significant annihilation effects. 41 A similar effect has been observed in H- and J-aggregate systems.…”