Return of the transport resistance: what Jphoto vs. Veff really tells you

The last two times I wrote about transport resistance as a voltage-loss (or, depending on how you like to look at it, current-loss) mechanism in organic solar cells – in 2022 and 2025 – I mostly talked about fill factor: how a low active-layer conductivity bends the illuminated j(V) curve around V_\mathrm{oc}, and how the resulting gap between FF and pseudo-FF is often larger than the recombination loss itself, even in record-efficiency devices. Moon over Hoher Ifen from Hirschegg.This time I want to show you that a plot that is very common in today’s literature does not make much sense for today’s high-efficiency organic solar cells. I am talking about the plot of photocurrent – the difference between illuminated and dark current of a solar cell – vs what is called “effective voltage”, i.e., J_\mathrm{ph} vs. V_\mathrm{eff}. I mentioned this in a talk on transport resistance that I gave at the SAMSEC in Berlin in July 2025. I want to write this post to address potential misconceptions concerning this plot.

If you look at the current–voltage characteristics of state-of-the-art organic solar cells, as shown in the plot below, you can observe that dark and illuminated j(V) curves cross. The voltage at which they cross is often called V_0: it is the compensation voltage, and by definition, the photocurrent there is zero, J_\mathrm{ph}=0. It is important to point out that in the ideal diode equation (briefly mentioned in this earlier post, equation “(*)”), this case never occurs: there, due to the superposition principle, the illuminated curve is just a shifted-down version of the dark current, by the generation current density J_\mathrm{gen}. Thus, in the ideal case, dark and illuminated curve never meet! Fig0 JVT dark+illum pm6y6.

So, the question I hear you asking: why do the experimental dark and illuminated current densities cross?

For the field of organic photovoltaics, this question was first addressed by the Blom group, in Mihailetchi 2004. At this time, organic solar cells reached power conversion efficiencies of only 2 or 3%. So, Valentin Mihailetchi plotted the photocurrent density of a PPV:PCBM organic solar cell, J_\mathrm{ph} = J_\mathrm{illum} - J_\mathrm{dark}, against the effective voltage V_\mathrm{eff} = V_0 - V, where V is the applied voltage. As result, one gets a photocurrent curve that rises steeply and then flattens into a plateau which corresponds to the solar cells’ maximum photocurrent. The authors interpreted this result as follows:

“The photocurrent in conjugated polymer-fullerene blends is dominated by the dissociation efficiency of bound electron-hole pairs at the donor–acceptor interface. A model based on Onsager’s theory of geminate charge recombination explains the observed field and temperature dependence of the photocurrent in PPV:PCBM blends. At room temperature only 60% of the generated bound electron-hole pairs are dissociated and contribute to the short-circuit current.”

Continue reading “Return of the transport resistance: what Jphoto vs. Veff really tells you”