Tag: organic solar cells

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”

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.

Continue reading “Transport resistance strikes back”

Pitfalls when measuring recombination lifetimes in organic solar cells

Six years ago, I came across an interesting publication by David Kiermasch and Kristofer Tvingstedt, [Kiermasch et al 2018], Frosch verlässt Seerose. titled Revisiting lifetimes from transient electrical characterization of thin film solar cells; a capacitive concern evaluated for silicon, organic and perovskite devices. It shows that particular in thin film solar cells, the time constant determined by voltage based techniques – open circuit voltage decay (OCVD), transient photovoltage (TPV), intensity modulated photovoltage spectroscopy (IMVS) – is in many cases not the recombination lifetime, but corresponds to an RC-time from the device itself. While the authors did not find this effect, they showed impressively how most modern solar cells are limited in this respect, and it has to be verified carefully whether or not the experimentally determined time constants do correspond to recombination lifetimes!

Continue reading “Pitfalls when measuring recombination lifetimes in organic solar cells”

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.

Continue reading “The transport resistance in organic solar cells”

The diode ideality factor in organic solar cells: basics

Where does one start after so long an absence — meaning only the blog abstinence; I have been working and publishing since last time;-) Passing by One of the things which have been on my mind is the ideality factor, a figure of merit for the charge carrier recombination mechanism in a semiconductor diode. In short, a diode ideality factor of 1 is interpreted as direct recombination of electrons and holes across the bandgap. An ideality factor of 2 is interpreted as recombination through defects states, i.e. recombination centres. More on that in a later post, let’s start with the basics.

A couple of years ago, I wrote about some general properties of current-voltage characteristics of organic solar cells, but did not describe the ideality factor.1 I think the ideality factor was mentioned only once, and then without details.

The Shockley diode equation describes the current–voltage characteristics of a diode,

j=j_0 \left(\exp\left(\frac{eV}{n_{id}kT}\right)-1\right) - j_{gen}.

Here, j current, V the voltage, e elementary charge, kT thermal voltage, j_0 the dark saturation current, and j_{gen} the photogenerated current. If the ideality factor n_{id} was equal to one, one could call this the ideal Shockley equation. It derivation can be found in semiconductor text books, but it can also be derived based on thermodynamic arguments (see Peter Würfel’s excellent book on the physics of solar cells).

The current j flowing out of the diode is defined to be negative. Essentially, the charge carriers which can flow out are the generated ones (e.g. j_{gen}), but reduced by the recombination current. That means,

j=\underbrace{j_0 \left(\exp\left(\frac{eV}{n_{id}kT}\right)-1\right)}_{j_{rec}} - j_{gen}.

However, the term j_{rec} contains also a negative contribution, j_0 times the -1 from the bracket. This is the thermal generation current j_{gen,th} \equiv j_0, i.e. charge carriers excited across the bandgap just by thermal energy — and therefore very little. Still, the term is very important, as it is the prefactor of the whole j(V) curve. Without light, i.e. with photocurrent j_{gen}=0, we can clarify

j=\underbrace{j_0 \exp\left(\frac{eV}{n_{id}kT}\right)}_{j_{rec,dark}} - \underbrace{j_0}_{j_{gen,th}}.

so that at negative voltages, j=-j_0.Jdark (Please note that under realistic conditions, j_0 is not only pretty small and difficult to measure in principle, it is also hidden behind shunt currents in the device. ) At zero volt, j=j_0-j_0=0. Thus, generation = recombination — or more specifically, thermal generation current = recombination current — which essentially implies that 0V correspond to the open circuit voltage in the dark.

How can one determine the ideality factor and the dark saturation current (at least in principle, see below for a better way on real devices)? It is common to neglect the thermal generation current (the term -1, multiplied by j_0), which is a good approximation for voltages some kT/e larger than 0. Then, calculate the logarithm of the dark current (j_{gen}=0),

\ln(j) = \ln(j_0) +\frac{e}{n_{id}kT}V,

so that the ideality factor can be determined from the inverse slope of the ln(current) at forward bias, and the dark saturation current from the current-axis offset. Let me already tell you that I do not recommend this approach, for reasons written below, and as explained in more detail in a recent paper of Kris Tvingstedt and myself [Tvingstedt/Deibel 2016].

Under illumination and at open circuit conditions, j(V_{oc})=0, we can rewrite the Shockley equation as

j_{gen}=j_0 \left(\exp\left(\frac{eV_{oc}}{n_{id}kT}\right)-1\right),

which has the same shape as the Shockley equation in the dark. This means that if you measure (j_{gen}, V_{oc}) pairs for a (wide) range of different illumination intensities (thus varying j_{gen}), the points should overlap with the dark j(V) curve! We’ll come back to this important point further below. Note that for solar cells with good fill factor, j_{gen} can be approximated by the short circuit current j_{sc}. Continue reading “The diode ideality factor in organic solar cells: basics”

Nongeminate recombination in organic solar cells – slower than expected

In a “recent” post (just 3 posts but 10 months ago;-) I wrote once again on the derivation of the Langevin recombination rate for nongeminate recombination. Tiger (Zoo Wuppertal)The question is, is Langevin recombination really what governs the charge carrier loss rate in organic solar cells?

Recombination of electrons with holes is usually a 2nd order decay. As electrons n and holes p are photogenerated pair wise, the respective excess charge carrier concentrations are symmetric, n=p. Then a recombination rate R is

R = k n p = k n^2,

where the recombination prefactor k could be a Langevin prefactor – more on that later. In a transient experiment with a photogenerating, short laser pulse at t=0, the continuity equation for charge carriers (here, e.g. electrons) under open circuti conditions (no external current flow, for instance if the experiment is done on a thin film without electrodes)

\frac{dn}{dt} = G-R

becomes

\frac{dn}{dt} = -R

for t>0 (as the generation was only at t=0).

If all electrons and hole are available for recombination (i.e., can reach all other charge carriers and can be reached by them), then the recombination rate and the continuity equation for t>0 yield

\frac{dn}{dt} = k n^2 Continue reading “Nongeminate recombination in organic solar cells – slower than expected”

Belectric aquires German Konarka Daughter

Related to this post on Konarka’s bankruptcy: According to a range of news sites, Bear Lake in the Rocky Mountainsincluding pv-tech.org, the german company Belectric has acquired Konarka Technologies. Find the press release here (pdf).

The system integrator Belectric is situated in Lower Franconia, less than 50km from Würzburg and less than 10km from where I live. Let’s keep our fingers crossed!

Nongeminate Recombination: Langevin (again) and beyond (later;-)

Nongeminate recombination is the major loss mechanism for state-of-the-art organic solar cells. In an early blog post, I showed how the Langevin recombination was derived. Summer in Lower FranconiaAlthough there is more to nongeminate recombination than just this mechanism, it is still instructive and also relevant to trap-assisted recombination mechanisms, due to its mobility-containing prefactor.

[Nenashev 2010] pointed out that in the derivation of the Langevin recombination,

since the electric field scales as r−2 and the surface area of the sphere scales as 2, the value of r chosen is unimportant, leading to a simple solution with constant electron den- sity, thus justifying the neglect of diffusion.

Continue reading “Nongeminate Recombination: Langevin (again) and beyond (later;-)”

Konarka bankrupt

Via Juan Bisquert’s post: solar cell company Konarka filed for bankrupty yesterday according to Businessweek. It is always hard to be the first… Konarka received its first venture capital in mid 2001.

Howard Berke, CEO of Konarka:

This is a tragedy for Konarka’s shareholders and employees and for the development of alternative energy in the U.S.

Let’s hope that our friends from Konarka find other suitable positions, and that other companies such as Heliatek take up the lead!

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Photovoltaics:

Global warming:

  • Climate sceptics on the go, via /.: Don’t Worry About Global Warming, Say 16 Scientists in the WSJ; I am no climate scientist, but what I read usually points in the other direction… at least judging from most scientists with peer reviewed publications in contrast to non-peer reviewed “scientists”. Nevertheless, the scientists cited above seem to be real ones, although (mostly?) not with scientific background related to the global climate
  • we have a similar discussion here in Germany, with RWE manager Fritz Vahrenholt writing a book trying to confute evidence of global warming, relating any temperature change to the solar activity: summary by Die Zeit (german, google translate) and an article (again Die Zeit) by Toralf Staud, refuting the seven main theses of Vahrenholt ( german, google translate).

Other stuff:

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