Almost a year ago, I already discussed the photocurrent in organic bulk heterojunction solar cells. Also, recently I posted about the difficulties to determine the dominant loss mechanism from the short circuit current density dependence on the light intensity. Today, I would like to extend these statements to the photocurrent in somewhat more general terms.
The figure to the right contains the simulated photocurrent for a bulk heterojunction solar cell of 100nm thickness at room temperature. Parameters were chosen according to typical experimentally determined values for P3HT:PCBM solar cells: Bimolecular Langevin recombination with a reduction factor of 0.1 and electron and hole mobility of 10-4m2/Vs were assumed (is it possible I never discussed this reduction really? Seems so, just mentioned it with references here). The top graph shows the photocurrent, in the lower graph the photocurrent was divided by the illumination density in terms of suns (thus, the current densities given on the y-axis are only correct for 1 sun). Consequently, if the photocurrent scales linearly with the light intensity, all curves should coincide. Let me remind you that this was interpreted by different groups (Street et al. among them, but not the first to follow this explanation) as a sign of first order recombination.
For up to one sun, however, despite the fact that only bimolecular recombination is considered, the photocurrent does not clearly deviate from the linear scaling. Slightly above one sun, a deviation becomes apparent for the photocurrent close to the quasi flatband voltage (or the point of optimum symmetry, if you like [Ooi 2008,Limpinsel 2010]. This can also be seen in the inset. The short circuit current deviates even later.
The reason for these difficulties to pinpoint the bimolecular recombination mechanism just by looking at the photocurrent becomes a little clearer when considering the relative charge carrier losses. In the figure to the right, the illumination density is now on the log x-axis, the reduction factor was varied (different traces). For the typical 0.1 Langevin reduction factor, a charge carrier loss of 10% is only seen at about 10 suns; the corresponding slope of the short circuit current vs. light intensity plot corresponds to 0.9 at this point (where 1 is classically interpreted as meaning 1st order recombination (some would say monomolecular), and 0.5 second order (… bimolecular)). The losses have to go to around 30% until the slope becomes 0.75. For the parameters considered, this jsc vs generation rate slope actually never goes to 0.5, despite the present bimolecular recombination. Thus, in analogy to the previous post, the point is that even from the light intensity dependence of the photocurrent it is very difficult for many typical conditions to unambiguously determine the dominant loss mechanism.
If you want to know the juicy details, read on here. It is a comment to a recent paper of Bob [Street 2010], which I sent to him before submitting it. I was very positively surprised to see him answer within a day, in a very polite and openminded way! [Update 2.11.2010] Our comment and the reply of Street are now online!
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.
Now, following the definition typically used by physical chemists (as far as I know), I state that a bimolecular loss process is one where two nongeminate particles recombine. In case that one type of them is much more abundant than the other, for instance because of being trapped, this process may become a first order process instead of the second order process if the concentrations are similar. Nevertheless, I find it more logical (though longer) and more precise to call this process a (of decay) instead of monomolecular recombination. In constrast, I use the latter only for geminate recombination processes. Nevertheless, this distinction is a matter of opinion only. In different books or articles, you’ll find both terms for the same, so beware.