Electronic transport and quantum localization effects in organic semiconductors

Abstract

We explore the charge transport mechanism in organic semiconductors based on a model that accounts for the thermal intermolecular disorder at work in pure crystalline compounds, as well as extrinsic sources of disorder that are present in current experimental devices. Starting from the Kubo formula, we develop a theoretical framework that relates the time-dependent quantum dynamics of electrons to the frequency-dependent conductivity. The electron mobility is then calculated through a relaxation time approximation that accounts for quantum localization corrections beyond Boltzmann theory, and allows us to efficiently address the interplay between highly conducting states in the band range and localized states induced by disorder in the band tails. The emergence of a "transient localization" phenomenon is shown to be a general feature of organic semiconductors, that is compatible with the bandlike temperature dependence of the mobility observed in pure compounds. Carrier trapping by extrinsic disorder causes a crossover to a thermally activated behavior at low temperature, which is progressively suppressed upon increasing the carrier concentration, as is commonly observed in organic field-effect transistors. Our results establish a direct connection between the localization of the electronic states and their conductive properties, formalizing phenomenological considerations that are commonly used in the literature

The Transient Localization Scenario for Charge Transport in Crystalline Organic Materials

“…[52,62] have shown that at intermediate values of the ratio s/J, corresponding to the experimentally relevant temperature range, both extended "band-like" carriers and incoherent excitations coexist in different regions of the excitation spectrum: carriers with a markedly itinerant character are mostly located within the bulk of the band, while the most dramatic effects of inter-molecular fluctuations are instead concentrated around the band tails, where they cause the states to have a more localized character. The origin of the long-standing controversy on the microscopic identity of the charge carriers in organic semiconductors comes from the fact that different experimental probes will see alternatively one feature or the other, or a mixture of both.…”

“…As was studied systematically both theoretically [52] and experimentally [25], extrinsic sources of disorder can affect carrier transport even in the purest samples available nowadays, especially when these are placed in FET geometries. Static disorder causes the mobility to degrade at low temperature in the best cases, and wash out the intrinsic transport regime completely in the worst cases, leading to a thermally activated behavior.…”

“…The origin of the long-standing controversy on the microscopic identity of the charge carriers in organic semiconductors comes from the fact that different experimental probes will see alternatively one feature or the other, or a mixture of both. [52]). Tails of localized states with spread ≈ a emerge beyond the band edge, whose width is controlled by the temperature via the parameter s = √ 4λJk B T .…”

“…This was done in Refs. [62] and [52] by solving exactly the model Eq. (1) in the limit of static molecular displacements.…”

Crossover from Super- to Subdiffusive Motion and Memory Effects in Crystalline Organic Semiconductors

“…In order to overcome this difficulty the fluctuations of the lattice vibrations, completely neglected in the adiabatic approximation (it becomes exact when ω 0 → 0 and the ionic mass M → ∞ keeping k = M ω 2 0 constant [17]), have to be taken into account. To this aim it has been proposed: i) to employ mixed quantum-classical simulations based on the Ehrenfest coupled equations [14]; ii) to neglect vertex corrections in the OC calculation [18]; iii) to introduce an ad hoc energy broadening of the system energy levels [15]. All these approximated approaches, although able to reproduce a power law dependence of mobility vs temperature, do not restore the conductivity values quantitatively.…”