Charge carrier mobility of disordered organic semiconductors with correlated energetic and spatial disorder

Abstract

Low charge carrier mobility is one key factor limiting the performance and applicability of devices based on organic semiconductors. Theoretical studies on mobility using the kinetic Monte Carlo or master equation are mainly based on a Gaussian energetic disorder and regular cubic lattices. The dependence of mobility on the electric field, temperature and charge carrier density is well studied for the Gaussian disorder model. In this work, we investigate the influence of spatially correlated site energies and spatial disorder in the lattice sites on the mobility using kinetic Monte Carlo simulations. Our analysis is based on both a regular cubic and a non-cubic Voronoi lattice. The latter is used to include spatial disorder in order to study its influence on the mobility for amorphous organic materials. Our results show that charge carrier mobility is strongly influenced by correlations in the site energies. Strong correlations even invert the field dependence of the mobility as observed experimentally in semi-crystalline polymers such as P3HT. Evaluation of local currents between localized states reveals the formation of current filaments with increasing correlation. Furthermore, the influence of the electric field and the energy landscape on the transport energy is studied by evaluation of active sites. A strong correlation between the transport energy, filaments in the local currents and the charge carrier mobility is observed. Our studies on the spatial disorder model do not indicate an inversion of the field dependence as observed by other researchers. The negative field-dependence in semi-crystalline materials may be explained by a higher correlation in the site energies as shown in a strongly correlated energetic landscape.

Generalized Kinetic Monte Carlo Framework for Organic Electronics

“…Using this correlation mechanism, we have shown that a high correlation in the site energies gives rise to filamentary structures of the local currents [39]. For distances below 2 nm, the correlation function obtained by atomistic simulations [73] has been reproduced with our mechanism, while for long-range hopping, other procedures, e.g., a dipole-based correlation [36], give better results.…”

“…We present a simple weighted average approach in Section 3.2. The Voronoi tessellation and the correlation procedure have been discussed recently in more detail [39]. As they are part of our generalized kMC model, we provide a concise summary.…”

“…For a representative model of the active organic layer, the use of the Voronoi tessellation generalizes the cubic lattice model [39,46]. Using the Voronoi cell library of Rycroft [47], next-neighbors of each lattice site, as well as the distance and all face-areas are computed.…”

“…This is avoided with the Voronoi tessellation. The tessellation furthermore allows the computation of local current and charge densities as a well-defined area of the faces, and the volume of the Voronoi cells is obtained [39]. Besides all the advantages, it still needs to be considered that the cell boundaries are purely based on the distance between centroids and do not contain any physical information, which, depending on the modeled system, has to be evaluated carefully for the computation of local quantities.…”

Charge Pair Separation Dynamics in Organic Bulk‐Heterojunction Solar Cells

“…[30][31][32] Furthermore, models based on continuum approaches are not sufficient to describe the spatial and energetic disorders, [33] as well as the impact of Coulomb correlation, [34] especially when time-dependent processes are to be investigated. OSC device models have emerged to simulate current-voltage characteristics, [37,38] the effect of blend morphology, [39,40] charge mobility extractions, [41,42] as well as CP separation, [30,[43][44][45][46][47][48] and its competing process, geminate recombination. [35] The kinetic Monte Carlo (kMC) method is a powerful simulation technique to model the time-dependent behavior of physical systems.…”