Theoretical modeling of charge transport in triphenylamine–benzimidazole based organic solids for their application as host-materials in phosphorescent OLEDs

Abstract

Dynamic disorder and electric field affect the charge (hole and electron) transport in host-materials for OLEDs.

Generalization on Entropy-Ruled Charge and Energy Transport for Organic Solids and Biomolecular Aggregates

“…On the other hand, when there is an applied bias, the drift-coupled diffusion is anticipated, which improves the traversing carrier energy rate in molecular devices. As reported in earlier studies, − the effect of the applied electric field, doping, and other interactions (including thermal effect) on charge and energy transport can be quantified by entropy parameters S and h S . Based on eq , one can emphasize that the variation in nonsteady energy flux strongly depends on the change in entropy due to various internal and external interactions of the system.…”

“…The generalized charge and energy transport relation for organic semiconductors can be described as 3 , 5 where is the carrier’s energy transfer rate, q is the electronic charge, n is the electron density, ε is the electric permittivity of the material, and D is the diffusion coefficient. From the above generalized charge and energy transport relation ( eq 1 ), the carrier energy rate directly depends on the charge diffusion coefficient and carrier density (electron or hole) in the concerned molecular devices.…”

“…The main corollary is that the particle flux (in terms of diffusion) causes the existence of nonsteady energy transport. According to our earlier model, 4 , 5 the rate of traversing carrier’s energy flux (i.e., nonsteady energy transport) with respect to entropy changes in the conjugated molecular sites can be related by where S is the entropy that quantifies the amount of disorder change due to randomness by thermal fluctuation, defect states, and various interactions such as phonon scattering, and k B is the Boltzmann constant. In molecular solids at high temperatures ( T > 150 K), the breakdown of the translational symmetry leads to a nonperiodic potential energy surface (PES).…”

“…The rate of traversing carrier energy in the stacked or conjugated BDHTT-BBT molecular solids reveals the existence of a nonsteady dynamical state of , which influences the nonlinear transport in dynamical systems (see Figure 4 ). Here, the energy traversing rate is calculated at a different set of Δ E ( E⃗ ) values of 0, 20, 40, 60, and 80 meV using the energy redistribution function (see refs ( 3 − 5 )). The nonlinear behavior of charge transport parameters (like diffusion, conductivity, and current density) strongly depends on the differential entropy parameter, where σ is the Gaussian disorder width.…”

“…The diffusion–mobility relation generally provides fundamental transport properties for all classes of materials, from classical to quantum systems. According to the generalized paradigm, diffusion mobility is directly related to the carrier density and thermodynamic density of states of the system. , From our earlier studies, it has been emphasized that entropy is a key parameter to study the electric field coupled with disordered transport in molecular solids. , The interesting fact is that the entropy-dependent charge density and diffusion coefficient relations are originally derived from the entropy-committed energy flux equation. , This energy flux equation explains the entropy-mediated variation in energy flux under nonsteady-state conditions. Here, the entropy-dependent charge density and diffusion relations are directly involved in charge transport calculations.…”