This in the case of an organic solar cell and high open circuit voltage.
Well for different materials this is quite normal. A larger band gap leads to higher (potential) Voc and lower Jsc. Or are you talking about nominally identical cells from the same material?
In fact, I used P3HT:PCBM blend and I get a very good current, but low Voc. and I test another layer for optamizing my Voc ( organic layer with small band gap) I get for this layer a very good Voc and a bad Jsc. when I combine both layer in one device I obtained a good Voc and the current still low.
So despite my affiliation I'm not an expert on this but the one thing I can think of that is consistent with a lower Voc and higher Jsc is shunts, i.e. a decreased parallel resistance Rp.
I hope my understanding can give an explanation. A change in voltage may be related to anode and cathode. Let's consider that from cathode. A voltage drop means a Fermi energy level improvement of cathode. As a result, cathode transfer electrons to shuttle (or other things like this) easier with a higher effeciency. This finally leads to a current increase.
Second with Dr. Schnabel, generally shunt. And you could check the cross section of your device. or you could detect possible shunting by Dark lock-in thermography imaging as reported in the following article:
http://www.hindawi.com/journals/aoe/2008/532351/
cheers.
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