We utilize drift-diffusion modeling to investigate the cause of S-shaped current-voltage curves in organic solar cells. We find that even a many order-of-magnitude mismatch of the carrier mobilities is insufficient to generate S-shaped J-V curves. Instead, S-shaped J-V curves result when a sigmoid-shaped electron mobility profile is entered into the calculation. This suggests that S-curves in bulk heterojunction photovoltaics are caused by factors that affect the extraction of electrons near the device cathode. Such factors could include surface recombination, partially blocking contacts caused by interfacial layers, or vertical phase separation of the fullerenes away from the cathode interface.

Time-domain current measurements are widely used to characterize semiconductor material properties, such as carrier mobility, doping concentration, carrier lifetime, and the static dielectric constant. It is therefore critical that these measurements be theoretically understood if they are to be successfully applied to assess the properties of materials and devices. In this paper, we derive generalized relations for describing current-density transients in planar semiconductor devices at uniform temperature. By spatially averaging the charge densities inside the semiconductor, we are able to provide a rigorous, straightforward, and experimentally relevant way to interpret these measurements. The formalism details several subtle aspects of current transients, including how the electrode charge relates to applied bias and internal space charge, how the displacement current can alter the apparent free-carrier current, and how to understand the integral of a charge-extraction transient. We also demonstrate how the formalism can be employed to derive the current transients arising from simple physical models, like those used to describe charge extraction by linearly increasing voltage (CELIV) and time-of-flight experiments. In doing so, we find that there is a nonintuitive factor-of-2 reduction in the apparent free-carrier concentration that can be easily missed, for example, in the application of charge-extraction models. Finally, to validate our theory and better understand the different current contributions, we perform a full time-domain drift-diffusion simulation of a CELIV trace and compare the results to our formalism. As expected, our analytic equations match precisely with the numerical solutions to the drift-diffusion, Poisson, and continuity equations. Thus, overall, our formalism provides a straightforward and general way to think about how the internal space-charge distribution, the electrode charge, and the externally applied bias translate into a measured current transient in a planar semiconductor device.

The active layers of most OPV devices are constructed from a blend of two organic compounds. The two materials spontaneously segregate into pure component phases during device fabrication, creating a bicontinuous network of conduction pathways that are selective for electron or hole charge carriers. The morphological distribution of these materials within the active layer has long been known to influence charge transport and resulting device performance. In addition to the two purecomponent phases present in these devices, a third, mixed-composition phase exists at the interface between the two pure phases. The exact effects of this mixed-composition phase on OPV device performance are not well understood, although it has been argued that the presence of a mixed phase is necessary for optimal device operation. In this work, we probe the effects of having a mixed-composition, interfacial phase on the performance and charge transport characteristics of organic photovoltaic (OPV) devices through a series of drift-diffusion model simulations. We start with set of model morphologies with only pure component phases and then introduce an interfacial, mixed-phase in a controllable fashion. Our simulations show that a modest amount of mixing initially improves device efficiency by reducing the tortuosity of the device's conduction pathways and easing morphological traps. However, an excessive amount of mixing can actually degrade highconductivity pathways, reducing photovoltaic performance. The point at which mixing switches from being beneficial to instead detrimental to OPV performance differs depending on the average domain size of a device's morphology. Devices with smaller feature sizes are more susceptible to the debilitating effects of overmixing, so that the presence of a mixed-phase may either raise power conversion efficiency by as much as 100% or lower it by as much as 50%, depending on the average domain size and the extent of mixing. This suggests that variations in the amount of mixed-composition phase with different processing conditions is one of the key factors that makes optimizing bulk heterojunction OPV devices difficult.

We probe the effects of structural disorder on the performance of organic photovoltaic (OPV) devices via Drift-Diffusion (D-D) modeling. We utilize ensembles of spatially disordered 1-dimensional mobility profiles to approximate the 3-dimensional structural disorder present in actual devices. Each replica in our ensemble approximates one high-conductivity pathway through the threedimensional network(s) present in a polymer-based bulk heterojunction solar cell, so that the ensemble-averaged behavior provides a good approximation to a full 3-dimensional structurally disordered device. Our calculations show that the short circuit current, fill factor and power conversion efficiency of simulated devices are all negatively impacted by the inclusion of structural disorder, but that the open circuit voltage is nearly impervious to structural defects. This is in contrast to energetic disorder, where previous studies found that spatial variation in the energy in OPV active layers causes a decrease in the open circuit voltage. We also show that structural disorder causes the greatest detriment to device performance for feature sizes between 2 nm and 10 nm. Since this is on the same length scale as the fullerene crystallites in experimental devices, it suggests both that controlling structural disorder is critical to the performance of OPV devices and that the effects of structural disorder should be included in future D-D modeling studies of organic solar cells.

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