Experimentally Validated Hopping-Transport Model for Energetically Disordered Organic Semiconductors

Abstract

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, such as 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) is 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 is integrated in a freeware driftdiffusion solver. The mobility model is 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-and n-type devices. We find a critical ratio of a NN /α (mean intersite distance:localization radius) of about three, 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.

Enhancing Open‐Circuit Voltage in Gradient Organic Solar Cells by Rectifying Thermalization Losses

“…The base value for the energetic disorder, 75 meV, used in this article is rather modest for classic polymer:fullerene systems, though highly relevant for state-of-the-art nonfullerene systems. [32][33][34] Thus, gradient-engineering of OPV is a plausible and in principle generally applicable route to improved device performance. However, it is very well possible that unintentional gradients, for example, due to different surface and interfacial energies of the donor and acceptor materials causing a spontaneous stratification during layer deposition, already exist and play a role in optimized OPV systems, as alluded to by several authors, e.g., the Introduction section.…”

General Rules for the Impact of Energetic Disorder and Mobility on Nongeminate Recombination in Phase-Separated Organic Solar Cells

“…The kMC algorithm has been introduced in previous works. [36][37][38][39][40][41] Details can be found in the Supporting Information. In brief, we consider a cubic lattice with lattice parameter 𝑎 𝑁𝑁 = eV and HOMO of -5.5 eV, -5.9 eV for donor and acceptor, respectively.…”

Slow Relaxation of Photogenerated Charge Carriers Boosts Open-Circuit Voltage of Organic Solar Cells

“… 10 , 38 In a recent work, we investigated the energetic disorder in a range of OPV blends and found Gaussian disorder values σ ranging from 45 to 80 meV, without any clear correlation between σ and V OC . 39 For the PM6:Y6 system, σ HOMO ≈ 89 meV and σ LUMO ≈ 68 meV were found. Because these numbers are much higher than the thermal energy kT ≈ 25 meV at room temperature and well exceed the thresholds we previously found for disorder to become negligible, 20 one should expect the phenomena discussed above to be relevant for this NFA system as well.…”