Tag: transport resistance

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.”

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Transport resistance strikes back

Since the last time that I wrote on transport resistance as a voltage loss mechanism in organic solar cells, due to low active layer conductivities, we have continued working on it. double rainbow seen from the institute of physics in Chemnitz
While we learnt from our valued colleague Prof. Chang-Qi Ma that MoOx diffusion contributes strongly to fill factor losses by thermal degradation – they had published their convincing results in [Qin 2023], under our radar – we also understand better how to recognise and comprehend transport resistance losses.

The simplest way to characterise transport resistance is to determine the difference between a normal current density–voltage curve under 1 sun, and the suns-Voc curve. The latter is the pair-wise combination of generation current density and open-circuit voltage that is giving one current density-voltage point per light intensity: doing this for a wide range of light-intensities results in a pseudo-JV curve. To compare this suns-Voc curve to the current density–voltage curve under 1 sun, it has to downshifted so that the open-circuit voltage of both curves coincide on one point: j(V) = (0, V_{oc}). The result could look like the scheme shown in the figure below. I have adapted this figure from Maria’s new publication on transport resistance losses in organic solar cells [Saladina 2025] (the title is Transport resistance strikes back: unveiling its impact on fill factor losses in organic solar cells ;-). The j(V_\mathrm{external}) curve (blue) is the normal JV curve under illumination, where V_\mathrm{external} is the applied voltage. The down-shifted suns-Voc curve corresponds to the j(V_\mathrm{implied}) (red); the implied voltage is the voltage without any series-resistance imposed drops. In other words, the externally applied voltage drops over the diode and all series resistances, the external series resistance as well as the transport resistance that comes from a low active layer (or transport layer) conductivity. The implied voltage, as measured by the open-circuit voltage (at zero current, where series resistances do not play a role), corresponds to the voltage without drops over series and transport resistance. If a solar cell has a low active layer conductivity and is transport resistance limited, than the measurement of the suns-Voc curve to construct the j(V_\mathrm{implied})-curve allows to evaluate the performance of that solar cell as if it did not have any transport resistance losses. One could also say: while the measured j(V_\mathrm{external}) curve is transport resistance limited, the pseudo-j(V_\mathrm{implied}) curve corresponds to the case of infinite conductivity, but contains the same recombination as the measured curve.

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The transport resistance in organic solar cells

In one of my last posts on the diode ideality factor (6 years ago…), I promised to talk about the transport resistance in organic solar cells. Cornudella de MontsantI came across it already during my time at IMEC in Leuven, Belgium, around 2004: my colleagues and I worked on an analytic model of the open circuit voltage in organic bilayer solar cells. The corresponding paper was published a few years later, [Cheyns et al 2008], but I have to admit that I did not grasp its importance as a relevant loss mechanism for organic solar cells in general, focussing on geminate and nongeminate recombination – until this paper by [Würfel/Neher et al 2015] came out. I think now I have;)

The transport resistance is an internal resistance in the active layer (or transport layer(s)) of the solar cell, acting like an internal series resistance: It changes the slope of the current density–voltage characteristics – for instance around the open circuit voltage – and thus reduces the fill factor.

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