The transient localization scenario for charge transport in crystalline organic materials

Abstract: Charge transport in crystalline organic semiconductors is intrinsically limited by the presence of large thermal molecular motions, which are a direct consequence of the weak van der Waals inter-molecular interactions. These lead to an original regime of transport called \textit{transient localization}, sharing features of both localized and itinerant electron systems. After a brief review of experimental observations that pose a challenge to the theory, we concentrate on a commonly studied model which describes the interaction of the charge carriers with inter-molecular vibrations. We present different theoretical approaches that have been applied to the problem in the past, and then turn to more modern approaches that are able to capture the key microscopic phenomenon at the origin of the puzzling experimental observations, i.e. the quantum localization of the electronic wavefuntion at timescales shorter than the typical molecular motions. We describe in particular a relaxation time approximation which clarifies how the transient localization due to dynamical molecular motions relates to the Anderson localization realized for static disorder, and allows us to devise strategies to improve the mobility of actual compounds. The relevance of the transient localization scenario to other classes of systems is briefly discussed.

• The paper introduces a transient localization model that explains the dual nature of charge carriers oscillating between localized and itinerant states.
• It employs a relaxation time approximation to connect static disorder models with dynamic transport using key parameters like transfer integrals and coupling strength.
• The study suggests optimizing molecular packing and reducing thermal fluctuations as strategies to enhance charge mobility in organic semiconductor devices.

The Transient Localization Scenario for Charge Transport in Crystalline Organic Materials

The investigation into charge transport within crystalline organic semiconductors has elucidated a scenario that diverges from conventional models applied in inorganic semiconductors, primarily due to the peculiar interactions typical of organic materials. In this context, the study headed by Fratini, Mayou, and Ciuchi explores the transient localization scenario—a regime that aptly describes the unique charge transport mechanisms in these materials where traditional band transport approaches fail.

Overview of Charge Transport in Organic Semiconductors

Crystalline organic materials, employed in devices like organic field-effect transistors (OFETs), exhibit charge transport characterized by relatively low mobility, often falling beneath the Mott-Ioffe-Regel limit. This low mobility is largely due to the pronounced thermal motions of molecules dictated by weak van der Waals forces, contrary to the stronger covalent bonds found in inorganic substances. These vibrational motions introduce dynamic disorder, leading to a phenomenon termed as transient localization, where carriers experience localization on timeframes shorter than typical molecular motions. The intrinsic properties of these carriers—oscillating between localized and itinerant states—pose a challenge for traditional approaches like the semi-classical Boltzmann transport equation and Marcus theory.

Investigating Transient Localization

The transient localization model synthesizes several theoretical frameworks and experimental observations, providing a more refined description of the transport mechanism. It considers:

• Localized vs. Itinerant Regimes: It describes a dual nature of charge carriers where, within certain bands, carriers demonstrate itinerant characteristics, while near band edges, they exhibit localization due to disorder.
• Microscopic Parameters: The study discusses the electron-lattice coupling through inter-molecular vibrations, quantified by parameters such as the transfer integral (J) and the coupling strength (λ). Importantly, it addresses the intrinsic thermal disorder via a static model that serves as a reference for understanding the dynamic disorder.
• Relaxation Time Approximation (RTA): In circumventing the limitations of previous theories, the RTA offers a path to compute mobility by connecting the static models of disorder to dynamic conditions. It hinges on pivotal concepts like the elastic scattering time (τ).

Implications and Future Directions

The transient localization scenario has significant implications, suggesting that charge transport within these semiconductors is not merely governed by traditional conductive mechanisms but by a complex interaction with thermal molecular movements. This indicates a need for refined fabrication and material selection strategies aiming at enhancing mobility, potentially by minimizing molecular fluctuations or optimizing the orientation and packing of molecules to augment π-overlap.

Furthermore, the theoretical treatment emphasizes that transient localization is not only pertinent to organic semiconductors but may also extend its relevance to other low-dimensional systems and materials under strong dynamical disorder. As such, future research might explore these analogies, potentially uncovering broader applications where the transient localization model could apply.

The insights derived from this study underscore a pivotal shift in understanding charge dynamics within organic semiconductors and signal towards evolutionary paths in both theoretical models and practical implementations in organic electronics.