Notes on Disordered Matter

In the beginning 90s, a novel concept was introduced, accounting for the low exciton diffusion length in disordered organic semiconductors, as well as the required thickness for a sufficient light absorption: the so-called bulk heterojunction solar cell [Heeger 1995]. This approach features a distributed junction between donor and acceptor material: both components interpenetrate one another, so that the interface between them is not planar any more, but spatially distributed. It is implemented by spincoating a polymer:fullerene blend, or by coevaporation of conjugated molecules. Bulk heterojunctions have the advantege of being able to dissociate excitons very efficiently over the whole extent of the solar cell, and thus generating polaron pairs anywhere in the film. The disadvantage is that it is somewhat more difficult to separate these polaron pairs due to the increased disorder, or that percolation to the contacts is not always given in the disordered material mixtures. Also, it is more likely that trapped charge carriers recombine with mobile ones. However, the positive effects outweigh the negative. Read the rest of this entry »

As an in-between, we’ll talk about a topic which will hopefully become more and more recognised by the organic photvoltaics community: the shortcomings of the established Shockley model, made for crystalline inorganic diodes, when applied on fitting organic solar cells.

The most important figures of merit describing the performance of a solar cell are the open circuit voltage, the short circuit current, the fill factor and the (power conversion) efficiency. The fill factor is given by the quotient of maximum power (yellow rectangle in the figure) and the product of open circuit voltage and short circuit current (white rectangle); it therefore decribes the “squareness” of the solar cell’s current-voltage characteristics. The efficiency is the ratio of maximum power to incident radiant power – typically radiated by the sun. E.g., a well-known detailed balance calculation for inorganic single gap solar cells gives a theoretical maximum of about 30% power conversion efficiency [Shockley 1961]. The upper limit for organic solar cells is somewhat lower, but that’s another story.

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The first organic solar cells where based on an active layer made of a single material. By the absorption of light, strongly Coulomb-bound electron hole pairs where created, singlet excitons. As described in part zero, these have to be split in order to finally generate a photocurrent. In order to overcome the binding energy, one has to either hope on the thermal energy, or dissociate the exciton at the contacts. Unfortunately, both processes have a rather low efficiency: under normal conditions, the temperature is not high enough, and the sample thickness is much thicker than the exciton diffusion length. The consequence: excitons are mostly not dissociated, but recombine instead. This leads to luminescence, and light emitting solar cells do not belong to the most efficient… there is just not enough current output.

The introduction of a second layer was a quantum leap in terms of power conversion efficiency (though still on a low level): organic bilayer solar cells, presented in the mid eighties [Tang 1986]. The light is usually absorbed mainly in the so-called donor material, a hole conducting small molecule. The photogenerated singlet excitons now can diffuse within the donor towards the interface to the second material, the acceptor, which is usually strongly electronegative. A prominent example for an electron acceptor material is the buckminsterfullerene (C60).

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In a classical inorganic solar cell, pairs of charge carrier – an electron and a hole – are generated by the absorbed sunlight. These two oppositely charged carriers are only weakly Coulomb bound, due to the screening being rather efficient in this material class. The potential drop at the interface between a p- and an n-doped semiconductor layer (the pn junction), leads to their separation and subsequent transport to the respective contacts: a current flows. In organic semiconductors, things are somewhat different.

Here, the screening of opposite charges is much weaker as the dielectric constant is lower. This leads to a much stronger interaction of the photogenerated positive and negative charges. Therefore, the primary optical excitation in organic materials is called (singlet) exciton, i.e., a strongly bound electron-hole pair. As this binding is more difficult to be overcome as compared to inorganic systems, the concept of organic solar cells has to be different… which we will come back to later.

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