## 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. 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”

## Pseudosymmetry of the photocurrent physically relevant?

Two days ago, a paper considering the role of the “quasiflat band” case in bulk heterojunction solar cells by device simulations was published online [Petersen 2012]. It is critical of the pseudosymmetric photocurrent found and interpreted by [Ooi 2008] and later also ourselves [Limpinsel 2010]. In order to focus on the physical relevance of the (non)symmetry of the photocurrent, the paper by Petersen et al neglects a field dependent photogeneration. As some good points are raised, read the new paper if you are interested in the photocurrent.

[Update 2.4.2012] Another paper showing that band bending is not needed to explain the particular shape of the photocurrent: [Wehenkel 2012].

I will come back to field dependent photogeneration later, it is still intruiging: also here, the photocurrent should (and will be) complemented by pulsed measurements such as time delayed collection field, see e.g. [Kniepert 2011].

## Charge transport in disordered organic matter: hopping transport

As I won a proposal today, I feel up to contributing once again some physics to this blog… I know, it has been a long long wait. So today it is time to consider some fundamentals of charge transport, as this is not only important for the extraction of charge carriers from the device (see earlier posts on mobility and efficiency, surface recombination velocity and photocurrent) but also the nongeminate recombination (see e.g. photocurrent part 2 and 3).

In disordered systems without long range order – such as an organic semiconductor which is processed into a thin film by sin coating – in which charge carriers are localised on different molecular sites, charge transport occurs by a hopping process. Due to the disorder, you can imagine that adjacent molecules are differently aligned and have varying distances across the device. Then, the charge carriers can only move by a combination of tunneling to cover the distance, and thermal activation to jump up in energy. In the 1950s, Rudolph A. Marcus proposed a hopping rate (jumps per second), which is suitable to describe the local charge transport. By the way, he received the 1992 Nobel prize in chemistry for his contributions to this theory of electron transfer reactions in chemical systems. Continue reading “Charge transport in disordered organic matter: hopping transport”

## Photocurrent again

I covered the photocurrent already before, for instance here. I pointed out that from the light intensity dependence of the short circuit current, it is impossible for many typical conditions to unambiguously determine the dominant loss mechanism or even the recombination order (1st (often called monomolecular, but not my favourite term;-) or 2nd order of decay).

If, however, you know (or guess) that the recombination order is two, you can use the above mentioned $j_{sc}$ vs. $P_L$ data to determine which fraction of charges is lost to bimolecular recombination, $\eta_{br}$. This was shown recently by [Koster 2011]. For $j_{sc} \propto P_L^\alpha$, they found $\eta_{br} = \alpha^{-1}-1$. Although I was not able to follow the exact derivation ([Update 5.4.2011] it can be derived by solving a simple differential equation, $\alpha=(1-dR/dG)/(1-R/G)=(1-\eta_{br}')/(1-\eta_{br})$), it seems to work. Easy method, although make sure not to have too much space charge in your device – even at the contacts, induced by low (ohmic) injection barriers (we compared it to our device simulation, and then you get significant deviations)! In my opinion, the latter point is not stressed enough in the paper, despite the nice approach. Continue reading “Photocurrent again”

## Hot CT complexes and Geminate Recombination

Lately, the notion that geminate recombination in organic solar cells is a major loss mechanism is more and more under fire. Street et al present an “experimental test” for geminate recombination [Street 2010a]. They investigate P3HT:PC60BM nor PCDTBT:PC70BM bulkheterojunction solar cells with a transient current technique at 200K and 300K between -1 and 1V external voltage bias. The authors conclude that neither exhibit significant geminate recombination, while pointing out that

Since the relative importance of geminate or nongeminate recombination depends on the specific materials comprising the cell and possibly on the method of preparation, other cells may or may not have a larger geminate recombination contribution.

## Efficiencies and other notes

I mentioned the record bulkheterojunction solar cell from Solarmer recently: 8.13%, although on a small area of 0.1cm2. The evporated small molecule solar cells had almost 6% on a ~10 times larger area. On the SPIE Optics&Photonics conference in August in San Diego I heard inofficially that Heliatek achieved more than 6%, but now on foil. Even better: more than 7% (active area efficiency; about one percent-point less for the complete area) on a module with more than 70cm2! This one is not flexible, I believe. Amazing if you consider that the evaporation is by point sources. If these modules are encapsulated, they are said to have an extrapolated lifetime exceeding 10 years.

## Brief Ad: Organic Solar Cell Review Online [Update]

If interested, find it here (Reports on Progress in Physics 73, 096401 (2010)). Included: how do bulk heterojunctions and bilayers work, how to improve the performance, how to mass print, and a brief section on the cost. I am happy it is finally “on air”:) Free from IOP for the first 30 days, if you register. Otherwise, choose the arXiv version or drop me a line. As I am on vacation, expect some delay…

[Update 30.8.2010 ] Back from vacation for already a week: was very relaxing:) In order to avoid another “ad post”, I just extend this one a bit: the progress report on charge transfer complexes (submitted to Advanced Materials already in February) is now published online. You will not find this one on arXiv, so if you cannot access it, ask me to send you the preprint. As always, I am interested in your opinion and/or criticism!

## Photocurrent in organic solar cells – Part 2 [Update]

Almost a year ago, I already discussed the photocurrent in organic bulk heterojunction solar cells. Also, recently I posted about the difficulties to determine the dominant loss mechanism from the short circuit current density dependence on the light intensity. Today, I would like to extend these statements to the photocurrent in somewhat more general terms.

The figure to the right contains the simulated photocurrent for a bulk heterojunction solar cell of 100nm thickness at room temperature. Parameters were chosen according to typical experimentally determined values for P3HT:PCBM solar cells: Bimolecular Langevin recombination with a reduction factor of 0.1 and electron and hole mobility of 10-4m2/Vs were assumed (is it possible I never discussed this reduction really? Seems so, just mentioned it with references here). The top graph shows the photocurrent, in the lower graph the photocurrent was divided by the illumination density in terms of suns (thus, the current densities given on the y-axis are only correct for 1 sun). Consequently, if the photocurrent scales linearly with the light intensity, all curves should coincide. Let me remind you that this was interpreted by different groups (Street et al. among them, but not the first to follow this explanation) as a sign of first order recombination.
Continue reading “Photocurrent in organic solar cells – Part 2 [Update]”

## Type of Polaron Recombination under Short Circuit Conditions [Update]

As promised, here a glimpse of why I believe that recombination in organic bulk heterojunction solar cells under short circuit conditions (and also at Voc) is not necessarily monomolecular.

Sometimes, the short circuit current density vs light intensity is measured, and from the linear scaling a dominant monomolecular recombination is concluded. In (partial) answer, we have performed some relevant device simulations (thanx to wapf). In short, we varied the generation of free charges over four orders of magnitude, assuming different polaron recombination mechanisms.