Abstract
ConspectusOrganic semiconductors (OSs) are an exciting class of materials that have enabled disruptive technologies in this century including large-area electronics, flexible displays, and inexpensive solar cells. All of these technologies rely on the motion of electrical charges within the material and the diffusivity of these charges critically determines their performance. In this respect, it is remarkable that the nature of the charge transport in these materials has puzzled the community for so many years, even for apparently simple systems such as molecular single crystals: some experiments would better fit an interpretation in terms of a localized particle picture, akin to molecular or biological electron transfer, while others are in better agreement with a wave-like interpretation, more akin to band transport in metals.Exciting recent progress in the theory and simulation of charge carrier transport in OSs has now led to a unified understanding of these disparate findings, and this Account will review one of these tools developed in our laboratory in some detail: direct charge carrier propagation by quantum-classical nonadiabatic molecular dynamics. One finds that even in defect-free crystals the charge carrier can either localize on a single molecule or substantially delocalize over a large number of molecules depending on the relative strength of electronic couplings between the molecules, reorganization, or charge trapping energy of the molecule and thermal fluctuations of electronic couplings and site energies, also known as electron–phonon couplings.Our simulations predict that in molecular OSs exhibiting some of the highest measured charge mobilities to date, the charge carrier forms “flickering” polarons, objects that are delocalized over 10–20 molecules on average and that constantly change their shape and extension under the influence of thermal disorder. The flickering polarons propagate through the OS by short (≈10 fs long) bursts of the wave function that lead to an expansion of the polaron to about twice its size, resulting in spatial displacement, carrier diffusion, charge mobility, and electrical conductivity. Arguably best termed “transient delocalization”, this mechanistic scenario is very similar to the one assumed in transient localization theory and supports its assertions. We also review recent applications of our methodology to charge transport in disordered and nanocrystalline samples, which allows us to understand the influence of defects and grain boundaries on the charge propagation.Unfortunately, the energetically favorable packing structures of typical OSs, whether molecular or polymeric, places fundamental constraints on charge mobilities/electronic conductivity compared to inorganic semiconductors, which limits their range of applications. In this Account, we review the design rules that could pave the way for new very high-mobility OS materials and we argue that 2D covalent organic frameworks are one of the most promising candidates to satisfy them.We conclude that our nonadiabatic dynamics method is a powerful approach for predicting charge carrier transport in crystalline and disordered materials. We close with a brief outlook on extensions of the method to exciton transport, dissociation, and recombination. This will bring us a step closer to an understanding of the birth, survival, and annihiliation of charges at interfaces of optoelectronic devices.
Highlights
Organic semiconductors (OSs) combine many advantages that make them attractive for a host of different applications, e.g., easy chemical tunability, synthesis from renewable materials free of nonprecious elements, mechanical flexibility, and light weight
For reasons that will become clear in this Account, we prefer to call it “Transient Delocalization Regime”.3. These methods include, e.g., transient localization theory (TLT),[7,17,21,22] delocalized charge carrier hopping based on generalized Marcus theory[23] or polaron-transformed Redfield theory[24] mapped onto kinetic Monte Carlo,[25] Kubo formula solved by finite temperature time-dependent density matrix renormalization group (TD-DMRG),[26,27] or the mobility relation with the imaginary-time current−current correlation function solved using quantum Monte Carlo techniques (QMC).[28]
It is worth noting that Fragment Orbital-Based Surface Hopping (FOB-SH) is a nonperturbative method that goes beyond the linear electron−phonon coupling approximation, which is often assumed in model Hamiltonians (Holstein or Holstein−Peierl), and it incorporates nonadiabatic nuclear dynamics effects, which are usually missing in analytic charge transport theories
Summary
Organic semiconductors (OSs) combine many advantages that make them attractive for a host of different applications, e.g., easy chemical tunability, synthesis from renewable materials free of nonprecious elements, mechanical flexibility, and light weight. For reasons that will become clear in this Account, we prefer to call it “Transient Delocalization Regime”.3 These methods include, e.g., transient localization theory (TLT),[7,17,21,22] delocalized charge carrier hopping based on generalized Marcus theory[23] or polaron-transformed Redfield theory[24] mapped onto kinetic Monte Carlo,[25] Kubo formula solved by finite temperature time-dependent density matrix renormalization group (TD-DMRG),[26,27] or the mobility relation with the imaginary-time current−current correlation function solved using quantum Monte Carlo techniques (QMC).[28] direct charge propagation based on nonadiabatic dynamics schemes using either a fully atomistic[2,29−35] or a coarse grained description of the nuclear degrees of freedom[36−39] has been used to predict mobility and wave function delocalization in OSs; see Figure 1 for a summary. We summarize and discuss the design rules that should pave the way toward new ultrahigh mobility OSs and explain why covalent organic frameworks are a promising class of materials in this respect
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