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Register a new userExperimentally Validated Hopping-Transport Model for Energetically Disordered Organic Semiconductors
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Added by
Dorothea Scheunemann
Publication date
2021
fields
Physics
and research's language is
English
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Charge transport in disordered organic semiconductors occurs by hopping of charge carriers between localized sites that are randomly distributed in a strongly energy dependent density of states. Extracting disorder and hopping parameters from experimental data like temperature dependent current-voltage characteristics typically relies on parametrized mobility functionals that are integrated in a drift-diffusion solver. Surprisingly, the functional based on the extended Gaussian disorder model (eGDM) has been extremely successful at this, despite it being based on the assumption of nearest neighbor hopping (nnH) on a regular lattice. We here propose a variable range hopping (VRH) model that has been integrated in a freeware drift-diffusion solver. The mobility model has been calibrated using kinetic Monte Carlo calculations and shows good agreement with the Monte Carlo calculations over the experimentally relevant part of the parameter space. The model is applied to temperature-dependent space charge limited current (SCLC) measurements of different systems. In contrast to the eGDM, the VRH model provides a consistent description of both p-type and n-type devices. We find a critical ratio of aNN/$alpha$ (mean inter-site distance / localization radius) of ~3 below which hopping to non-nearest neighbors becomes important around room temperature and the eGDM cannot be used for parameter extraction. Typical (Gaussian) disorder values in the range 45-120 meV are found, without any clear correlation with photovoltaic performance when the same active layer is used in an organic solar cell.
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Using analytical arguments and computer simulations we show that the dependence of the hopping carrier mobility on the electric field $mu(F)/mu(0)$ in a system of random sites is determined by the localization length $a$, and not by the concentration of sites $N$. This result is in drastic contrast to what is usually assumed in the literature for a theoretical description of experimental data and for device modeling, where $N^{-1/3}$ is considered as the decisive length scale for $mu(F)$. We show that although the limiting value $mu(F rightarrow 0)$ is determined by the ratio $N^{-1/3}/a$, the dependence $mu(F)/mu(0)$ is sensitive to the magnitude of $a$, and not to $N^{-1/3}$. Furthermore, our numerical and analytical results prove that the effective temperature responsible for the combined effect of the electric field $F$ and the real temperature $T$ on the hopping transport via spatially random sites can contain the electric field only in the combination $eFa$.
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.
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Long-range and fast transport of coherent excitons is important for development of high-speed excitonic circuits and quantum computing applications. However, most of these coherent excitons have only been observed in some low-dimensional semiconductors when coupled with cavities, as there are large inhomogeneous broadening and dephasing effects on the exciton transport in their native states of the materials. Here, by confining coherent excitons at the 2D quantum limit, we firstly observed molecular aggregation enabled super-transport of excitons in atomically thin two-dimensional (2D) organic semiconductors between coherent states, with a measured a high effective exciton diffusion coefficient of 346.9 cm2/sec at room temperature. This value is one to several orders of magnitude higher than the reported values from other organic molecular aggregates and low-dimensional inorganic materials. Without coupling to any optical cavities, the monolayer pentacene sample, a very clean 2D quantum system (1.2 nm thick) with high crystallinity (J type aggregation) and minimal interfacial states, showed superradiant emissions from the Frenkel excitons, which was experimentally confirmed by the temperature-dependent photoluminescence (PL) emission, highly enhanced radiative decay rate, significantly narrowed PL peak width and strongly directional in-plane emission. The coherence in monolayer pentacene samples was observed to be delocalized over 135 molecules, which is significantly larger than the values (a few molecules) observed from other organic thin films. In addition, the super-transport of excitons in monolayer pentacene samples showed highly anisotropic behaviour. Our results pave the way for the development of future high-speed excitonic circuits, fast OLEDs, and other opto-electronic devices.
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