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 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.
Highlights
Recent years have seen a considerable improvement in the field of organic photovoltaics (OPVs), where power conversion efficiencies exceeding 16% have been reached [1]
The functional based on the extended Gaussian disorder model is extremely successful at this, despite it being based on the assumption of nearest neighbor hopping on a regular lattice
We find a critical ratio of aNN/α of about three, below which hopping to non-nearest neighbors becomes important around room temperature and the extended Gaussian disorder model (eGDM) cannot be used for parameter extraction
Summary
Recent years have seen a considerable improvement in the field of organic photovoltaics (OPVs), where power conversion efficiencies exceeding 16% have been reached [1]. To improve upon the performance of such devices, further understanding of the underlying physics of charge transport becomes important, as the (transient) mobility of the generated charge carriers is one of the key factors that decides how efficiently the charges can escape recombination and be extracted [2,3,4,5,6]. In the following, we focus on OPV materials. Charge transport in these systems is commonly understood to occur via thermally activated tunneling, hopping, of charge carriers between localized sites. Due to the wide ( kBT) typically Gaussian or exponential distribution of
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