# Influence of Finite Surface Recombination Velocity on Efficiency vs. Mobility of Polymer Solar Cells

Just a quick addition to Mobility and Efficiency of Polymer Solar Cells. You might remember that with increasing mobility, the

open circuit voltage Voc, however, decreases steadily. Actually, the slope steepness is maximum due to our implicit assumption of ideal charge extraction ; for a realistic charge extraction (= finite surface recombination), the Voc slope with mobility is weaker… or even constant for zero surface recombination. The fill factor is maximum at intermediate charge carrier mobilities, not far from the experimentally found values!

As we were finally able to calculate the open circuit voltage with a surface recombination less than infinity (thanks to Alexander Wagenpfahl),
I can show you how it looks. ([Update 3rd March 2010] For details, have a look here: [Wagenpfahl 2010, arxiv])
In the figure, the power conversion efficiency is again plotted vs. charge carrier mobility. Here, in we made the assumption that the majorities (=electrons at the electron injecting contact, or holes at the hole injecting contact) maintain an infinite surface recombination velocity, whereas the minorities (=electrons at the hole injecting contact, and …) have a surface recombination velocity Smin of 1050m/s (=infinity in terms of the simulation) or 10-4m/s. As you can see, the assumption of infinite surface recombination for electrons and holes leads to the reduction of the power conversion efficiency. This effect comes almost exclusively from a reduction of the open circuit voltage. If the minority surface recombination velocity is lowered drastically, than the open circuit voltage does not break down for high mobilities, and the power conversion efficiency remains high… but does not increase much any more.

There is almost no work an surface recombination in organic solar cells, essentially only the model by Scott and Malliaras [Scott 1999]. For typical mobilities, the surface recombination velocity after their considerations comes out at 10-2m/s or so. Nevertheless, experimental work is lacking so far. Taking into account that conjugated polymers and such do not have dangling bonds, however, a low surface recombination velocity is certainly more probable than a high one. Thus, the publications predicting a lowering of the efficiency at high mobility [Mandoc 2007, Deibel 2008] should be reconsidered (I’d like to point out that we already mentioned the effect, but were not able to calculate it at that time… ;-). Recently, a finite surface recombination influencing the efficiency was considered by [Kirchartz 2008].

## 6 thoughts on “Influence of Finite Surface Recombination Velocity on Efficiency vs. Mobility of Polymer Solar Cells”

1. Well, that always interests me ;-) Thanks! Carsten

1. texcapprezjimmy says:

Great blog. Thanks for all of the effort.

Question about your article Phys Rev B 82 (2010) on the S-shaped current-voltage. You simulate and reproduce the S-shaped curves very nicely by modeling the anode (hole collector, ITO). But, is there any reason why similar results could be obtained for modification of the cathode (electron collector)? For instance, a degraded Aluminum layer or an insulating interfacial layer that is too thick?

I sometimes generate similar S-curves and have been trying to pin-down culprit.

Austin

1. Hi Austin, thanks. You can get s-shapes by several ways, i.e. less conductive interface layers, an energetic extraction barrier, or imbalanced electron-hole mobilities. They all lead to space charges, which are most pronounced close to the electrodes. Anode or cathode does not make a difference. Best, Carsten

2. brian zacher says:

Hello Professor Deibel,

Firstly, thank you much for this blog and your many worthy publications.

I’ve been chewing on your finite surface recombination velocity work a lot lately. What’s your feeling on the effect of injection near Pmax in an OPV? Do you think the exponential decrease in the photocurrent near Voc is i) solely reduced by electric field near Voc ii) “cancelled” by injection of charge from the electrodes near Voc or iii) a combination of the two? Asked another way, if I could give you an anode which was asymmetric for charge transfer, say with infinite majority recombination velocity while requiring a large overpotential for injection of charge……do you think this would actually have much effect on the overall J-V response?

Thank you,
-Brian

1. Hi Brian,

not Prof yet but thanks anyway;)

Do you really mean the photocurrent (difference between current under illumination and dark) and not the overall current under illumination? If yes, I am not sure what you mean with the “exponential decrease”. The overall current increases exponentially, in principle similar to the dark current, due to (dark) charge carrier injection. The photocurrent reduces when going from negative voltage bias to Voc (and beyond) due to recombination.

If you consider the recent work by the Durrant group, they were able to measure the nongeminate recombination rate $R$ in dependence on the charge carrier concentration $n$ (not needing to distinguish between photo and dark carriers) and reconstruct the current-voltage characteristics under illumination from $R(n)$ and $n(V)$ [Shuttle 2010]. For samples with an additional field dependent geminate recombination, they used transient absorption to find the relative photogeneration yield vs electric field to correct their data.

Concerning your last question, if you have perfect charge extraction and a large injection barrier at the anode, the former is of course good. Increasing the injection barrier will not change much if it remains a rather small change, maybe up to 100 or 200meV, but a further increase will reduce your Voc. The shape of the I(V) in the 4th quadrant should not change by much, I think.

Best, Carsten