A polaron is a charge, i.e., an electron or a hole, plus a distortion of the charge’s surroundings. In a crystalline inorganic material, setting a charge onto a site does not change the surroundings, as the crystal lattice is rigid. Not so in many disordered organic materials. Putting a charge onto a certain molecular site can deform the whole molecule. Moving the charge from this to another molecule means that first the energy for the deformation – the polaron binding energy or reorganisation energy – has to be mustered. The implication is that charge transport becomes more difficult, the charge carrier mobility becomes lower, … This process is also described as self-trapping. As a side note, it is often difficult to distinguish between the influence of polaronic self-trapping and of gaussian disorder, as both have a similar impact on the charge transport properties. This similarity is also reflected in the corresponding hopping rates used to calculate charge transport: Marcus theory is a function of the reorganisation energy, where as the Miller Abrahams rate [Miller 1960] is related to the energetic disorder of the density of states. The polaronic deformation can be quantified in terms of a (lattice) polarisation, or a phonon cloud, or just as the above-mentioned polaron binding energy. Mostly, however, when hearing polaron, think charge;-) See also what wikipedia has to say about polarons.
Recombination of free charge carriers in materials with a low mobility is often described with the Langevin recombination rate [Langevin 1903 (Ann. Chim. Phys. 28, 433)] (Update 3.12.2008: wrong reference previously, sorry.) Generally, if electron and holes – being potential recombination partners – wish to recombine, the effective recombination rate is proportional to
- the “direct” recombination rate
- finding each other
In high mobility semiconductors, the former is dominant. However, in disordered solids, and particularly disordered organic semiconductors, the low mobility limits the effective recombination rate. The process of finding each other can be described as diffusion limited, which is proportional to the charge carrier mobility when considering the Einstein relation. Continue reading “Recombination in low mobility semiconductors: Langevin theory”
In disordered organic semiconductors, there is no band transport, as there are no delocalised, just localised charges. Consequently, there is no simple band-band recombination of free carriers, and no Shockley-Read-Hall recombination! Of course, there is still recombination going on, a lot of it;-)
Here I’ll just quote some definitions concerning different types of recombination, and get back with details later.
For a general classification we take a look at Kwan-Chi Kao’s book “Dielectric Phenomena in Solids“.
Looking for monomolecular recombination, we find
The recombination that involves one free carrier at a time, such as indirect revombination through a recombination center (e.g., an electron captures by a recombination center and then recombined with a hole, each process involving only one carrier), is generally referred to as monomolecular recombination.
In organic semiconductors, a recombination centre can for instance be a trapped hole, localised in a deep state; it can induce a monomolecular recombination with a mobile electron. Even knowing this, it still feels like bimolecular recombination, doesn’t it? ;-)
It seems that one prominent discussion in organic photovoltaics has officially ended, the one about the primary photoexcitation in disordered organic solar cells being excitons (with a binding energy clearly above 100meV) or free charges (with excitons having binding energies in the range of the thermal energy, i.e. <<100meV). Hwang, Moses and Heeger, have just published a paper on polymer:fullerene blends [Hwang 2008] where they describe the charge generation as
Mobile carriers are generated via a two-step process: initial ultrafast charge separation to an intermediate charge transfer (CT) bound state, followed by the transfer of carriers onto the bicontinuous networks.
They explicitly mention
[…] indicating ultrafast dissociation of the singlet excitons at the polymer-PCBM interface and the build-up of the initial CT state.
The paper is nice but in itself not that remarkable, except that previously, Moses and Heeger always claimed the primary photoexcitation to be free charges instead of bound excitons. Their measurements yielded exciton binding energies in the range of the thermal energy, i.e., no donor acceptor interface being necessary for charge separation. To quote an older paper [Moses 2000],
Thus, carriers are photoexcited directly and not generated via a secondary process from exciton annihilation.
Now I have to mention that in the new paper they use P3HT:PCBM, and in the old one MEH-PPV:PCBM. But as they do not mention this in the new paper, I assume that either I missed something, or they changed their point of view concerning the primary photoexcitation.
Ideally, tandem solar cell made of a series connection of two subcells work as follows. Both sub cells generate their own photocurrent by absorbing light and generating charges (as described for single layer cells in here), and have their own open-circuit voltage. Of course, as the two cells are connected in series, they influence each other. The photogenerated holes of cell 1 are extracted by the ITO, but where to the electrons go? They have to recombine with photogenerated holes from cell 2: that is what the intermediate recombination layer is for. If the photocurrent of sub cells 1 and 2 is initially unbalanced, the electric field is redistributed, such that the photocurrent becomes balanced… at a lower value, approximately determined by the worse of the two cells. The open-circuit voltage is aproximately the sum of both sub cells’ open circuit voltages. Of course, in cases of field redistribution, that does not quite hold true. So, what approximately happens in a tandem solar cell of subcells 1 and 2:
- open circuit voltage Voc = Voc1 + Voc2
- short circuit current Isc = min(Isc1, Isc2)
- fill factor is more difficult, but as a rough guide lets stick to the minimum of both as well
So for an ideal tandem solar cell, complementary absorption ranges, and balanced photocurrents are needed.
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. Continue reading “How Do Organic Solar Cells Function? – Part Two”
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.
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).
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.