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].

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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.The equation he proposed for the hopping rate from site i to site j across the distance is

.

Here, is the transfer integral, i.e. the wavefunction overlap between sites i and j, which is proportional to the tunnelling contribution. is the reorganisation energy related to the polaron relaxation, which is sometimes called self-trapping: the molecule is distorted by the charge, which leads to a (lattice) polarisation, lowering the site energy. is the thermal energy and is due to different energetic contributions, in particular the energy difference between the two sites. In disordered systems, the density of states is often approximated by an exponential or Gaussian distribution, so that the energy of each site is from this distribution. Integrating over all site energies just yields the chosen energy distribution, e.g. a Gaussian, once again. Then, is just the energy difference of the two chosen sites. Thus, jumping from one molecular site to the next is proportional to the tunneling term and an exponential term proportional to the site energy difference and the self-trapping of the charge on the initial molecular site.

For a given molecule, the arrangement can be calculated by molecular dynamics, and the transfer integrals between different possible pairs of molecules, constituting sites i and j, respectively, can be calculated by quantum chemistry. A nice application of this approach is shown in [Kirkpatrick 2007] for discotic liquid crystals, without considering molecular dynamics in a qualitative way look at [Stehr 2011].

A simpler but more generic way to calculate a hopping rate is the so-called Miller-Abrahams hopping rate

.

Here, the contributions of tunnelling and thermal activation are even more explicit. is the maximum hopping rate, sometimes called attempt-to-escape frequency. is the inverse localisation radius, stating how well charge carriers can tunnel across the distance between site i and j. Indeed, the first term denotes the tunneling contribution. The thermal activation comes from a Boltzmann term, where hopping upwards in energy, i.e. >0: if the hopping process is from an initial state i lower in energy than the final state j, it is made difficult by an exponential penalty. Hopping downwards in energy (<0) is approximated to be always similarly easy: the complete second term, the Boltzmann term, is replaced by . In the Miller-Abrahams rate, the molecular details are usually neglected, so instead of transfer integrals only the attempt-to-escape frequency is approximated. Instead of the reorganisation energy, only energetic site differences derived from a (often Gaussian) density of states distribution are considered.

Both models, Marcus and Miller-Abrahams hopping rate, are used in different context and are not exactly equivalent, but will yield similar results under many conditions. Nevertheless, it is probably safe to state that the former has a higher scientific applicability.

Now why is it important to be able to calculate a hopping rate when considering charge transport in organic matter? – If one knows the number of molecular sites across the device length , which is the conservative estimate of the number of jumps needed to travel through the whole device, and the time needed per jump , one can calculate the velocity . Here, is the average distance crossed per single jump. If the velocity is known, also the charge carrier mobility is known, which is a very important figure of merit in semiconductor physics. The mobility relates the drift velocity to its driving force, the electric field , so that . A lot of essential information on charge transport is included in this inconspicuous parameter , especially if disorder is considered.

The charge carrier velocity can, thus, be calculated by knowledge of the hopping rate as well as the time for each hop and the number of hops. Also, can alternatively be determined experimentally by measuring the transit time of charge carriers through a device of known thickness. Thus, a direct comparison of experiment and simulation is possible and desired for grasping how charge transport works. A suitable and very straight forward experiment is the transient photocurrent, also called time-of-flight (TOF) measurement. A fitting computer model is based on a kinetic Monte Carlo simulation, in which a certain spatial and energetic distribution of sites is assumed and the Marcus or Miller-Abrahams hopping rates are calculated.

Next time, I will explain the TOF experiment, and then Monte Carlo simulations. Both together allowed (and still alow) to much better understand charge transport in disordered organic semiconductors.

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Here are two or three which might interest you (well, they got my attention;-) but there is more to be found on the above mentioned web site – although I had to modify the settings of my ad blocker to be able to watch. No, there are no ads; still…

Before you scroll down, let me mention some other “findings” of potential interest:

• How Google Went Solar by Dan Auld about Big G’s 1.65MW array, and how to get most out of it.
• Then, a nice rant on the climate debate and how news media, trying to be biased, do become very biased… read Diamond planets, climate change and the scientific method by Matthew Bailes. You can see it as a kind of (inofficial) editorial for the last linked article, Who’s your expert? The difference between peer review and rhetoric by Ove Hoegh-Guldberg.
• Another one on organic photovoltaics, Paper solar cells by 2015 (Disclaimer: I was involved in one of these projects. Um .
• Totally unrelated, PhDComics on Writing and Figures…
• Even more unrelated, and not funny: Sitting and Standing at work, finally.

• The most efficient flexible solar cells are not organic, but made from CIGS: Highly efficient Cu(In,Ga)Se2 solar cells grown on flexible polymer films (Nat Mater).
• Alternatively, Silicon Ink can be used, as Bill Scanlon writes.

• Stephen Wolfram on the Advance of the Data Civilization: A Timeline
  

• Some lessons learned by Chris Dixon; while being about getting a job or your startup funded, it is somewhat applicable to carreers in science.
• The Scientist on the Perfect Poster.
• Nature News on the The reasons for retraction.

But now to these SPIE presentations [Update: WordPress does not accept the embedded vidos, so here just the links to the videos].

James Durrant, Imperial: Charge photogeneration and recombination in organic solar cells

Jenny Nelson, Imperial: Modelling charge transport and recombination in organic photovoltaic materials

Craig Peters, Stanford: High-efficiency polymer-based OPV with lifetimes approaching 7 years; liked especially the PDS spectra about the impact of degradation on CT states (around position 19min):

Wei You, UNC: Molecular engineering of conjugated polymers for highly efficient bulk-heterojunction solar cells on molecular engineering of conjugated polymers, penne vs spaghetti, reorganisation, and high efficiencies.

Also, there is one from yours truly;-) Impact of trap-assisted recombination on the performance of polymer-fullerene bulk-heterojunction solar cells. Never realised I say “um” so much… Here the slides also on Slideshare.

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If, however, you know (or guess) that the recombination order is two, you can use the above mentioned vs. data to determine which fraction of charges is lost to bimolecular recombination, . This was shown recently by [Koster 2011]. For , they found . Although I was not able to follow the exact derivation (is it missing?!), 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.Concerning my discussion with Robert Street (see the links in the previous photocurrent blog post) if the dominant nongeminate recombination mechanism is monomolecular or bimolecular, he recently published another paper [Street 2011]. In this one, Bob claims that the recombination mechanism at short circuit and open circuit conditions are different. This is in opposition to our understanding. Also, the Durrant group is able to reconstruct the whole current-voltage characteristics of state-of-the-art organic solar cells (in which geminate recombination is negligible) by measuring the carrier concentration dependent carrier lifetime, and mapping it on the voltage dependent carrier concentration – I will not go into detail, have a look at their papers [Shuttle 2011]. Coming back to Bob Street, in order to explain why he believes that the recombination mechanism is differnt at open and short circuit, he explains

The TPV response is approximately a simple exponential decay, which is strikingly different from the power-law form of the TPC. The time constant decreases from ∼1 ms to 18 “μs for Voc increasing from 0.269 to 0.516 V. Again, this is a completely different result from the form of the photocurrent transients, which have a different magnitude of response time, depend much less on the voltage, and the voltage dependence is in the opposite direction.

As you may know, TPV=transient photovoltage, measured at open circuit, whereas TPC=transient photocurrent is determined under short circuit. One point against his argument is: TPV is a small-signal method, in which Voc is changed only by a few percent due to a (sufficiently weak) laser pulse in addition to bias illumination. Therefore, it decays monoexponentially. In contrast, TPC is a large signal. Bob Street points out that TPC at short circuit decays with a power law. Let me add that is similar to the large-signal method at open circuit, namely the time dependent open circuit voltage. The latter also decays with a power law, and not monoexponentially. Thus, no principal difference between recombination at short circuit and open circuit.

Finally, a nice publication concerning these topics is [Dibb 2011]. From the abstract,

We show that it is only safe to infer a linear recombination mechanism from a linear dependence of corrected photocurrent on light intensity under the following special conditions: (i) the photogenerated charge carrier density is much larger than the dark carrier density and (ii) the photogenerated carrier density is proportional to the photogeneration rate.

Indeed, it all depends;-)

And lastly (does this come after finally? a few links I found over the weeks. From the Coronene Blog, an excellent parody of how to publish high impact papers. An insightful article on mistakes in scientific programming by Zeeya Merali in Nature News. A list of the Top 100 Material Scientists, from Thomson Reuters based on impact factor etc – despite that, interesting;-) What’s wrong with scholarly publishing? How it used to be on petermr’s blog. Then: Is there a point in publishing corrections to articles? It seems not (Scholarly Kitchen)! Infodocket: Google Scholar Citations launched. On Nature Chemistry: The art of abstracts (similar to some others, behind the wall…). You know that I like preprint servers, as they are barrierless: arXiv just turned 20, written by Paul Ginsparg himself for Nature. Then nice pic: how people in science see each other…as always, there is some truth to simplifications;-) Nice article by Ben Coldacre on paywalls for science, Academic publishers run a guarded knowledge economy (Guardian).

That’s it. If you wonder why I have time to write, I have one month “off”: we call it parent time in Germany, it is my part 2 (part 1 was directly after the birth). See you again, still have to finish this other science thing…

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Many things I want to write about I have not had time to handle in the recent months. For now, let me start with just briefly revisiting what I have written. Hints of what I will add in the coming weeks and months are to come soon (soon meaning: worst case mid February, as one proposal is submitted by then, lecture is finished and project meeting / seminar talk marathon “finished”;-).

Find the overview below.All the best, Carsten

Introduction to

• Disordered Organic Semiconductors and some Definitions for excited states
• Basic Function of Organic Solar Cells, Part 0, Part 1, Part 2 and as cartoon
• Efficiency estimates and optimisation, also for Tandem solar cells
• Current-Voltage Characteristics
• Some Definitions for Recombination, which are slightly outdated, and an Introduction to Langevin Theory
• Find all of this in concise form in [Deibel 2010 Review]

Descriptions of

• Impact of Mobility on Efficiency, also considering Finite Surface Recombination
• Photocurrent in organic solar cells, Part 1 and Part 2

(Critical) Comments on

• Estimates on the Efficiencies of Organic Tandem Solar Cells
• Primary Photoexcitation in Polymer:Fullerene Blends
• Trimolecular Recombination
• Type of Polaron Recombination under Short Circuit Conditions
• Hot CT complexes and Geminate Recombination

News on

• Efficiencies: Plextronics 5.94% (August 2008), Heliatek 5.9%/6.07% (July 2009), Solarmer 7.9% (December 2009), Solarmer 8.13% (August 2010), Heliatek 7.7% (already shown in April);
  actually, now they are at 8.3% on >1 cm² (Heliatek with Tandem, 10/2010, and Konarka with single junction, 11/2010) [Solar Cell Efficiency Tables V37]
• Degradation: Improved Lifetime
• Production: organic roll-to-roll, inkjet printing of inorganic solar cells, organic inks, Company Funding, Heliatek starts production in 2012
• Materials: Buckyball polymers

Links to

• Scientific Writing and Publishing: Writing Style, How to publish, How to Publish a Scientific Comment, Metrics, Publish like a Pro
• Academic Productivity: Science 3.0?, Talking vs Doing

Personal news

• Married…, and again

Concerning Organic Photovoltaic Publications, the trend continues (using the same search phrases), see the graph.

Not exponential any more, but still growing steeply… it is more difficult to measure the quality, though.

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The first products should be coming onto the market at the start of 2012.

Good!

Second, you may remember my post on photocurrent in organic solar cells back in July. It was inspired by a comment I wrote on a paper by Street et al, who proposed monomolecular recombination to dominate the loss of free charges in organic bulk heterojunction solar cells. My comment and Bob Street’s reply to it are now online at Phys Rev B. I’ll not comment this interesting exchange any further (unless requested by you;-), so read and think for yourself!

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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.

Another recent paper investigates the role of hot charge transfer complexes for the separation yield of photogenerated polaron pairs – an alternative explanation for the high charge generation efficiency in organic bulk. Lee et al. consider the subgap quantum efficiency and other measures of P3HT:PCBM and PPV:PCBM solar cells [Lee 2010]. Their conclusion:

By varying the excitation wavelengths through the CT band we show that it is the thermally relaxed CT states, not hot CT states, which mediate the conversion between excitons and free charge carriers.

The latter finding contradicts the experiments of Imperial College [e.g., Clarke 2009], in which an exponential dependence of the charge generation yield on the excess energy of CT complexes after singlet exciton dissociation was reported (for optical thin films: no voltage bias).

As you may remember, we suggested last year – based on Monte Carlo simulations – that the driving force for charge separation is mainly due to delocalisation of charges along the conjugated segments of polymer chains (or, possibly, PCBM nanocrystals) [Deibel 2009]. We also did some photocurrent experiments [Limpinsel 2010]. In both cases, we found that the field dependence of the polaron pair dissociation is very weak in the working regime of organic solar cells at room temperature. The latter two points are important, and another one might be added: for good solar cells. We found that at open circuit, the CT complex dissociation probabilty for a given parameter set was about 50%, whereas it was 60% at short circuit. Clearly, a weak field dependence, but nevertheless: 40% “field-independent” loss due to geminate recombination within the narrow field range determined by the fourth quadrant of the current-voltage characteristics.

Our results thus confirm the findings of Street et al, but also (in my opinion) put them in a somewhat larger perspective. Concerning the 2nd paper on hot excitons, I am sure that more work will necessary to determine if (as the work from Imperial college implies) either Voc or jsc can be optimised for a given material, but not both. I am more positive about it (for instance, see [Deibel 2010 CT-review]), nevertheless: experiments to come on the field dependence of charge generation, also at low temperature and also for “bad” solar cells will, be interesting for seeking a more general understanding of polaron pair dissociation and, thus, geminate recombination.

Thanks to Thomas K for pointing me to the Lee paper.

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[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!

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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.

In the first figure, we assumed monomolecular recombination with different polaron lifetimes, so that the continuity equation for electrons reads . In all cases, even with negligible monomolecular recombination (longer lifetimes), is the scaling linear.

In the second figure we assumed bimolecular (Langevin type) recombination, using the continuity equation . Here, is the Langevin recombination prefactor, proportional to the charge carrier mobility, and is the experimentally found reduction factor [Deibel 2009]. The static part of the latter (for details read the paper) is about 0.1. In the graph we used a range of up till 100. This number (actually, everything above 1) is completely unphysical; we just used it here in order to boost the bimolecular recombination. The simulated open circuit voltage vs light intensity (expressed as generation rate) under standard conditions ( =0.1 (updated 15th May: 10 was typo) and illumination of 1 sun, i.e., G=10²⁸m^-3s^-1) shows very much a slope 1 behaviour. However, there is no monomolecular recombination present in this simulation. Only at 100 suns you see a slight deviation from slope 1 for the typical value of . Only by boosting the bimolecular recombination unnaturally, can the slope 1/2 behaviour be observed at high illumination intensities.

By the way, experimentally the recombination mechanism in these devices is usually found to be bimolecular. See for instance [Shuttle 2008], [Foertig 2009] or as an overview the review [Deibel 2010] – the latter is now accepted by Reports on Progress in Physics with minor revisions

My conclusion: under typical conditions and for the bulk heterojunction solar cells I know, is it impossible to distinguish from the short circuit current vs light intensity whether or not recombination is monomolecular or bimolecular, respectively. I am interested in your comments!

[Update 2.7.2010] I moved my previous comment from here to a new blog post, with a brief overview on whether or not the whole voltage-dependent photocurrent, as opposed to the short circuit current, gives information on the dominant type of loss in bulk heterojunction solar cells.

For details about the simulation, have a look at these papers [Deibel 2008, Wagenpfahl 2010].

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Is Organic PV the Future of Solar?.

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Reviews seem to be pretty subjective, and I am sure there are many omissions, but hopefully not too many inconsistencies. If there are any particular things you do like or do not like, or which are plain wrong: I am happy about every bit of constructive criticism! I submitted the article to Rep. Prog. Phys. It will be peer-reviewed, and I am pretty sure the referees’ comments will make the current version much less final as I’d like it to be;-)

[Update 25.6.2010] The review was accepted after some minor revisions, and is scheduled for publication by Rep. Prog. Phys. in September (2010).

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Heliatek will be utilizing the new funding primarily to build an initial production facility in Dresden. In this step and right through to mass production, the company will be using its proprietary tandem technology to efficiently produce, flexible and very lightweight PV modules on a film substrate. Their weight will be merely 500 grams per square meter, instead of today’s customary 20 kilograms per square meter. This will open up a forward-looking market for mobile applications, for architectural solutions and for independently supplying regions with weak infrastructures.

Indeed, interesting times for OPV – particularly in view of the commercial aspects! The science aspects are also getting more and more interesting, but unfortunately I thus have less and less time to write about them here…

P.S. Another company Solexant just starts the production of hybrid solar cells after the process developed by the group of Paul Alivisatos at Berkeley, as reported by Technology Review.

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