• From December 2011, but nevertheless interesting: critical comment by Joerg Heber, senior editor of Nature Materials, on Organic Solar Cells.
• Criticism of publisher Elsevier becomes louder again (some history of it in the previous link = Wikipedia entry): the mathematician Gowers speaks out in his blog post Elsevier — my part in its downfall (and a follow up post here), and PZ Myers rants Elsevier = Evil in his blog. There is even a website where you can sign upto protest against Elsevier’s practices of driving prices for their journals very high, thecostofknowledge.com. I have to admit I did not do it; just now a book was released by Academic Press (which is an Elsevier brand) with a chapter by me, and also I’d somehow feel strange to boycott one of the few journals (or even the only one?) on organic electronics by Elsevier, the one with just that name. Nevertheless, I agree that information should be made widely available, specifically if funded with public money. That is one of the reasons why I upload most of our articles to the arXiv.org e-print archive.
• Essay by Santiago Alvarez on the wide range of different arrows chemists use… Chemistry: A Panoply of Arrows.
• Adv Funct Mater editorial by Dave Flanagan: More Fundamental Understanding In Materials Science
• Nature News by Jim Giles, Going paperless: The digital lab on using Ipad as your notebook with commercial labbook software.
• Did I link to this nature education piece on English communication for scientists already? I particularly liked the comic on the first page;-)
• The voice of science: let’s agree to disagree by Daniel Sarewitz about the importance of disagreements.

Next week a round of referees will come to Würzburg to decide on another set of grant proposals, so I’ll go back to my preparations now…

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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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I have collected a few links which might or might not interest you. Also, I plan to start with some scientific (background) posts again. Let’s see how this works out:-)

Press release of Heliatek: Heliatek achieves new world record for organic solar cells with certified 9.8 % cell efficiency. Evaporated small molecule tandem with area above 1cm². Very good! Also, Mitsubishi Chemical has reached 10.1% efficiency on solution processed small molecules.

Nature looks back at the science year 2011: 365 days: Images of the year.

Interesting, although not related to physics: Syllabus for David Foster Wallace’s class “English 102-Literary Analysis: Prose Fiction Fall ’94″. Clear rules, yeah! Forgot who linked to it, sorry.Editorial of Nature Physics: How to be popular, i.e. how to write popular science articles for a general non-scientific audience. If you are at talks, also consider to read the requirements of Richard Stallman, free software advocate, for his speeches.

Citation science: about the Temporal Effects in the Growth of Networks via physics.aps.org

Tim Vines: Is Peer Review a Coin Toss? – good question. Also: Quality Reviewing Declines with Experience by Phil Davis.

Quirin Schiermeier & Katrin Kohnert from Nature: Germany: Renewables revolution

The myth of renewable energy by the Bulletin of the Atomic Scientists… bit of propaganda, but always some truth there.

Collection of Newton’s work at Cambridge Digital Library.

Via Maxine Clarke, Nautilus blog: Howy Jacobs receives a letter – how a director of human services at a university handles cricital feedback in a most kindly manner… impressive.

Mobile science by maninchem.org: iphone apps for scientists (mostly chemists, though;-) Also, 10 cool things you can do with Wolfram Alpha and Siri by Erica Sadun at tuaw.com.

More on the funny side:

A review article proposes smoking for endurance athletes via Kent Anderson, the scholarly kitchen.

Reference to a nice paper by Dennis Upper on “The unsuccessul self-treatment of a case of writer’s block” as pdf.

Chemist jokes… without comment, find them at the chemistry world blog.

Quotes:

T. H. Huxley via #naturenews:

The great tragedy of Science — the slaying of a beautiful hypothesis by an ugly fact

Oscar Wilde:

What is a cynic? A man who knows the price of everything and the value of nothing.

Daniel Patrick Moynihan:

Everyone is entitled to his own opinion, but not his own facts.

Lawrence J. Peter:

The way to avoid mistakes is to gain experience. The way to gain experience is to make mistakes.

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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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I have looked in the mirror every morning and asked myself: “If today were the last day of my life, would I want to do what I am about to do today?” And whenever the answer has been “No” for too many days in a row, I know I need to change something.

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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The 2010 impact factors were just released by Thomson Reuters, as most of you will know due to the mails sent by almost all publishers to tell about recent boosts of impact for their journals. A sober post was written by Jörg Heber, editor of Nature materials. A brief quote

So what use is the impact factor number? Well, being cynical one could say it is a quick measure for those that don’t read the journals but still want to know how good they are on average. The danger is of course that this is then used as a kind of metric to assess the quality of research or to decide on the career of researchers.

Maybe not so surprisingly, the recent Nature material’s editorial is about the impact factor as well. It also includes a link to Eigenfactor, which is open and also weights from how “good” a journal the reference to the measured publication was made. There, only the 2009 results are up presently.

Concerning organic photovoltaics, the race for higher efficiencies briefly had seemed to have taken another step upwards as compared to the recent non-certified above 9% power conversion efficiency to almost 12%, but I heard that this was a mistake. New competition for organics comes from a startup Alta devices, which makes solar cells of GaAs by epitaxial liftoff to reduce cost. Does not sound so cost effective, but if they go on to prove it, it’s ertainly impressive with the above 28% efficiency shown by them recently, as reported by Technology Review. Along these lines, flexible CIGS solar cells have hit 18.7% end of May by the EMPA researchers around Prof. Tiwari. Indium price may be a limiting factor here, but otherwise this thin film polycrystalline technique is another strong competitor. Thus, enough driving force to go bexond 10% for organic solar cells soon:-)

Finally, a nonphysical, but nevertheless important read: Traumatic brain injuries in illustrated literature: experience from a series of over 700 head injuries in the Asterix comic books – enjoy Thanks to Julien for the hint.

With that, bye for now. Next entry will not be a news summary, I hope, but something more physics related again…

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I received this statement,

Blue suits the lecturer better than pink

as one of the results of the lecture evaluation (Atom Physics for “Teachers to be”). Yes, I also received some other comments, most positive, some negative, all useful (including that one?;-)

Just to say that I am still amongst the living, here some bits and pieces I found during the last weeks, when time allowed.You may have heard of the rumors concerning a new efficiency record. I heard this by way of a discussion on LinkedIn, the information was also on CrunchGear. 9.2 or 9.3% is the word, made by Mitsubishi Chemical in cooperation with the University of Tokyo, probably the group of Nakamura. Not sure if this is certified, but it is certainly a follow-up of this cell. Artificial leafs where also in the news, see Nature News.

PhD Comics finally tells us how grant applications work… how true! A bit dry reading in comparison may be the European Peer Review Guide, as reported by Nature News.

Via Slashdot: Experimental Error: Forging a Head by “scientist-comedian” Adam Ruben. Quite nice:-)

Organic solar cells can become cheaper, as ITO is replaced by printed nano-silver. This step may reduce the cost of the electrode by up to 90%, according to Konarka as reported by Technology Review (in german, translation here). By the way, Germany had a new record for the installed power from renewables, as reported by Renewable Energy World. Well, massive funding helps… and may be a good way to get started.

Two sad but interesting stories about two scientists leaving the world of fundamental research to move on: Getting a life (devicerandom blog) and Falling Off the Ladder: How Not to Succeed in Academia
(published in Science Careers). However, if you decide to stay – which I hope… I will:-) – consider to read this Guardian article on Good Science Writing by Tim Radford.

So long, maybe at some point some physics is to come again – there is always hope;-)

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Tomorrow is abstract deadline for the SPIE Optics and Photonics 2011, including the session Organic Photovoltaics XII. See you there:-)

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For unrelated reading, but following up some other notes on publishing and peer review (see overview of posts here), an insightful post by Cameron Neylon: What is it with researchers and peer review? or; Why misquoting Churchill does not an argument make. If you are researcher, peer review is (and will remain) important. Therefore, staying up to date is not only interesting (e.g., you get to see the real Churchill quote;) but also useful to see its pros and cons more clearly. Interesting may be this Nature Materials editorial on Transparency in peer review (free with registration). Out of curiosity I just checked: I reviewed 21 papers in 2010, so a couple more than I (or a coauthor) actually submitted, but a lot less than I was asked to review…

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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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• You are only as good as your last paper – previous success does not guarantee future acceptance.
• You’ve got to hook the editor with the abstract.
• Don’t delete those files. Keep every version. You never know what aspect you can use for some other piece of writing.
• Writing is an amazingly long learning curve. many authors say that they’re still getting better as a writer after several decades.
• The most significant work is improved by subtraction. Keeping the clutter away allows a central message to be communicated with a broader impact.
• Write every day if possible.
• once you’ve written what you wanted to convey, end it there.

These go hand in hand with this earlier post, although Kendall’s article does not stop there. Therefore, read it!

Personally, what I need for writing is a quiet, non-distracting environment with the internet switched off.

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Sherlock Holmes never said “Elementary, my dear Watson.” Neither Ingrid Bergman nor anyone else in “Casablanca” says “Play it again, Sam”; Leo Durocher did not say “Nice guys finish last”; Vince Lombardi did say “Winning isn’t everything, it’s the only thing” quite often, but he got the line from someone else. Patrick Henry almost certainly did not say “Give me liberty, or give me death!”; William Tecumseh Sherman never wrote the words “War is hell”; and there is no evidence that Horace Greeley said “Go west, young man.” Marie Antoinette did not say “Let them eat cake”; Hermann Göring did not say “When I hear the word ‘culture,’ I reach for my gun”; and Muhammad Ali did not say “No Vietcong ever called me nigger.”

In order to have one that was said – Daniel Patrick Moynihan:

Everyone is entitled to his own opinion, but not his own facts.

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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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Several other topics I originally planned to write about are already outdated in as far as they have been published as papers. It seems that many groups present only work which had been submitted to a journal beforehand – not a bad thing, as these results are not known to the general public then.

Currently, there is a smaller annual Conference on Organic Photovoltaics taking place in Würzburg. Some well-known invited speakers are here, such as Jenny Nelson (Imperial), Christoph Brabec (Nürnberg), Serdar Sariciftci (LIOS), Vladimir Dyakonov (Würzburg), Peter Erk (BASF), Paul Blom (Holst Centre), Mats Andersson (Chalmers University, Sweden), Frederik Krebs (Risoe), Jens Hauch (Konarka), Martin Pfeiffer (Heliatek) and others. That’s why I have to stop writing now and start listening;-) So maybe see you here next year on 22nd September 2011.

[Update 17.9.2010] Martin Pfeiffer, CTO of Heliatek, presented the above mentioned efficiencies in his talk at yesterday’s conference. The 7.2% module consists of 7 stripes, each of which yielding about 7.7% individually: clearly, the upscaling losses are quite low. The active material seems to be based on thiophene oligomers. As for the future plans, they plan a proof-of-principle production line with 30cm width roll-2-roll, and throughput of 1 metre per minute. The system is anticipated to be up and running in mid 2011. Also, Pfeiffer promised news concerning higher efficiencies to be presented soon. We are waiting eagerly:-)

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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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Jack London:

You can’t wait for inspiration. You have to go after it with a club.

William Gibson:

The future is here. It’s just not evenly distributed.

Niels Bohr:

I try never to write more clearly than I am able to think.

John von Neumann:

There is no sense in being precise when you don’t even know what you are talking about.

Henry Ford:

If I’d listened to customers, I’d have given them a faster horse.

Peter Drucker:

What everybody knows is frequently wrong.

Do not believe that it is very much of an advance to do the unnecessary three times as fast.

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I am also here, my talk will be on wednesday afternoon – but do not expect any breakthroughs in terms of performance from me:-) Maybe there will be more news here in the days to come.

In June and July, I was visiting scientist in the group of Mike McGehee at Stanford University for five very interesting weeks. Thanks again for hosting me, and for the interesting discussions we had! I also had a brief visit to PARC, the Palo Alto Research Center, for an interesting discussion with Robert Street about the photocurrent in organic solar cells. We finally agreed to disagree on some issues, but from my point of view, that’s absolutely fine.

During my Stanford visit, there was fortunately time enough for hiking in the Foothill Mountains as well! Highly recommended. Thanks to Andreas and Verena as well as Matthias for getting me started.

Another bit, highly unrelated, which you should skip if you are not interested in software related stuff: you may know that I am a Mac user, and since the MRS meeting back in April also a happy iPad owner. One of the favourite programs, exclusively for Mac, is Papers, a program to organise and read your scientific articles. It is also available for iPhone/iPad, and includes sync to your Mac (WLAN or via iTunes) and online backups (if you like). I mention it now as of last week, the iPhone/iPad version has the ability to add annotations and highlights to the pdfs. As far as I know, these annotations cannot yet be synced, but I am sure it is a top priority for the next version. Just one of the many useful programs assisting scientists to get their work done:-) If you wonder what other software I use, you will notice that I do not mind paying for good software, although a lot of very good freeware is around is well on Macs. My top ten is (disordered;-) TeXshop, Daylite, DevonThink Pro Office (or Journler), Textexpander, Cornerstone (or svnX), MarsEdit, Launchbar (or Quicksilver), Intaglio, Dropbox, and Textmate (or TextWrangler). The alternative option is brackets are the programs which are free or shareware programs, whereas I use commercial ones. The ones without alternatives have none (or are free or shareware;-)

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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.
For up to one sun, however, despite the fact that only bimolecular recombination is considered, the photocurrent does not clearly deviate from the linear scaling. Slightly above one sun, a deviation becomes apparent for the photocurrent close to the quasi flatband voltage (or the point of optimum symmetry, if you like [Ooi 2008,Limpinsel 2010]. This can also be seen in the inset. The short circuit current deviates even later.

The reason for these difficulties to pinpoint the bimolecular recombination mechanism just by looking at the photocurrent becomes a little clearer when considering the relative charge carrier losses. In the figure to the right, the illumination density is now on the log x-axis, the reduction factor was varied (different traces). For the typical 0.1 Langevin reduction factor, a charge carrier loss of 10% is only seen at about 10 suns; the corresponding slope of the short circuit current vs. light intensity plot corresponds to 0.9 at this point (where 1 is classically interpreted as meaning 1st order recombination (some would say monomolecular), and 0.5 second order (… bimolecular)). The losses have to go to around 30% until the slope becomes 0.75. For the parameters considered, this jsc vs generation rate slope actually never goes to 0.5, despite the present bimolecular recombination. Thus, in analogy to the previous post, the point is that even from the light intensity dependence of the photocurrent it is very difficult for many typical conditions to unambiguously determine the dominant loss mechanism.

If you want to know the juicy details, read on here. It is a comment to a recent paper of Bob [Street 2010], which I sent to him before submitting it. I was very positively surprised to see him answer within a day, in a very polite and openminded way! [Update 2.11.2010] Our comment and the reply of Street are now online!

As a small bonmot, and to point out that I changed the definitions I use describing recombination as compared to an older post, where I quoted from [Kwan-Chi Kao 2004 (Book)]

The recombination that involves one free carrier at a time, such as indirect revombination through a recombination center (e.g., an electron captures by a recombination center and then recombined with a hole, each process involving only one carrier), is generally referred to as monomolecular recombination.

Now, following the definition typically used by physical chemists (as far as I know), I state that a bimolecular loss process is one where two nongeminate particles recombine. In case that one type of them is much more abundant than the other, for instance because of being trapped, this process may become a first order process instead of the second order process if the concentrations are similar. Nevertheless, I find it more logical (though longer) and more precise to call this process a (of decay) instead of monomolecular recombination. In constrast, I use the latter only for geminate recombination processes. Nevertheless, this distinction is a matter of opinion only. In different books or articles, you’ll find both terms for the same, so beware.

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Short note: my short review finally came online. Coauthors are Vladimir Dyakonov and Christoph Brabec. In case you have access to IEEE, find the paper here.

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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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Many interesting talks, too many to go into more detail in the given time!;-) Anyway, it was nice to meet Alex (glidera) and his colleague Bertrand in person, and spend time with Andy B and Tom!

It was difficult (if not impossible) to agree with Alan Heeger and Robert Street on their propositions that monomolecular recombination is the limiting factor for organic bulk heterojunction solar cells at short circuit current under one sun illumination. Thus, despite both of them being well-known and highly respected, I allow myself to express my strong belief (supported by transient experiments and macroscopic simulations;-) that bimolecular polaron recombination is the dominant loss mechanism for free polarons, instead of monomolecular polaron recombination. Maybe more on this later.

During the conference, and featured in the talk of Karl Leo, Heliatek announced another efficiency record for small molecule solar cells, enhancing their recent achievements to now 7.7% certified efficiency for a tandem cell with 1.1cm². Again, my congratulations, great stuff!

[Update 17.5.2010] here the embedded slides:

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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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It is quality, not quantity, which matters.

Good point. Nevertheless, although the publish and perish mentality lately became quite tiring, I wonder if (how quickly) these new conditions will change the mentality of the researchers in general, and in particular the ones who are reviewing the proposals and are sitting in the committees for professorship appointment;-)

[Update 25.2.2010] Find the original DFG statement here (pdf, german).

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Every second spent blogging, chatting on FriendFeed, or leaving comments on a PLoS paper is a second taken away from other activities. Those other activities have direct rewards towards advancement.

Actually, this is one of the reasons for the low activity in recent months: I just do not have time for the blog right now – I believe I can write again end of March or so. Nevertheless, I am active, having written proposals (1 won, 1 open) as well as two review-like papers. One of them is on Organic Bulk Heterojunction Solar Cells, the other on the Role of the Charge Transfer State for Organic Photovoltaics. Writing a third one right now… Once they are published (if they ever are), I will link to them. You are likely to find some figures etc familiar from the blog… and finally something to properly reference

[Update 25th March 2010] 2nd proposal won as well;-) Also, the CT review was accepted by Adv Mater: if you are interested in the preprint, drop me a line.

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Whenever a theory appears to you as the only possible one, take this as a sign that you have neither understood the theory nor the problem which it was intended to solve.

If we are uncritical we shall always find what we want: we shall look for, and find, confirmations, and we shall look away from, and not see, whatever might be dangerous to our pet theories.

Science may be described as the art of systematic over-simplification — the art of discerning what we may with advantage omit.

In his book Making Things Happen, the above-mentioned Scott Berkun summarizes Karl Popper as saying that there are only two kinds of theories: those that are wrong and those that are incomplete.

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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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• Part 1
• Part 2
• Part 3
• Part 4

The Nature Journal liked it, as apparent from their blog post According to Jorge Cham, their general comment was:

Use this comic for procrastination or decompression, as you see fit.

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Recently, I linked to some PLOS editorials about Ten simple rules for nearly everything, including writing papers.

Along this line, the presentation given by the Phys. Rev. Lett. Editor Manolis Antonoyiannakis in Japan end of last year, is very interesting. In addition to hints for using the right phrasing when writing about scientific results, he also gives some insight – from the viewpoint of the Editorial Office of a high impact phyics journal – into the inner workings of paper predecision (by Editor) and general acceptance rate. Antonoyiannakis also mentions additional sources, for instance What editors want by Lynn Worsham (Subscription required; summary here) and Writing a Paper by George M. Whitesides.

[Update 3.9.2009] Other interesting resources: two PRL editorials, Successful Letters (Mar 13, 2008) and Is PRL Too Large to Have an Impact? (Feb 13, 2009), interview with Gene Sprouse, Editor-in-Chief of APS publications.

[Update 17.9.2009]: recently published researcher perspective at ArsTechnica.

Afterwards, the only thing left to do is performing significant research, and writing a paper…

[Update 8.10.2009] Another question is where to publish. Interesting insights are given by Martin Heintzelman and Diego Nocetti in their paper on Where should we submit our paper? An analysis of journal submission strategies (via the blog The Great Beyond).

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open circuit voltage Voc, however, decreases steadily. Actually, the slope steepness is maximum due to our implicit assumption of ideal charge extraction ; for a realistic charge extraction (= finite surface recombination), the Voc slope with mobility is weaker… or even constant for zero surface recombination. The fill factor is maximum at intermediate charge carrier mobilities, not far from the experimentally found values!

As we were finally able to calculate the open circuit voltage with a surface recombination less than infinity (thanks to Alexander Wagenpfahl),
I can show you how it looks. ([Update 3rd March 2010] For details, have a look here: [Wagenpfahl 2010, arxiv])
In the figure, the power conversion efficiency is again plotted vs. charge carrier mobility. Here, in we made the assumption that the majorities (=electrons at the electron injecting contact, or holes at the hole injecting contact) maintain an infinite surface recombination velocity, whereas the minorities (=electrons at the hole injecting contact, and …) have a surface recombination velocity S_min of 10⁵⁰m/s (=infinity in terms of the simulation) or 10^-4m/s. As you can see, the assumption of infinite surface recombination for electrons and holes leads to the reduction of the power conversion efficiency. This effect comes almost exclusively from a reduction of the open circuit voltage. If the minority surface recombination velocity is lowered drastically, than the open circuit voltage does not break down for high mobilities, and the power conversion efficiency remains high… but does not increase much any more.

There is almost no work an surface recombination in organic solar cells, essentially only the model by Scott and Malliaras [Scott 1999]. For typical mobilities, the surface recombination velocity after their considerations comes out at 10^-2m/s or so. Nevertheless, experimental work is lacking so far. Taking into account that conjugated polymers and such do not have dangling bonds, however, a low surface recombination velocity is certainly more probable than a high one. Thus, the publications predicting a lowering of the efficiency at high mobility [Mandoc 2007, Deibel 2008] should be reconsidered (I’d like to point out that we already mentioned the effect, but were not able to calculate it at that time… . Recently, a finite surface recombination influencing the efficiency was considered by [Kirchartz 2008].

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The field dependence of the photocurrent is due to different contributions:

• polaron pair dissociation (bulk heterojunctions and bilayers)
• polaron recombination (mostly bulk heterojunctions)
• charge extraction (bulk heterojunctions and bilayers)

An experimental curve of the photocurrent of a P3HT:PCBM solar cell is shown in the figure (relative to the point of optimum symmetry, as described by [Ooi 2008]. The symbols show our experimental data, the green curve a fit with two of the contributions mentioned above: polaron pair dissociation (after [Braun 1984]) and charge extraction (after [Sokel 1982]). Both models are simplified, but more on that later. Polaron recombination has been covered before (here and here); it is pretty low in state-of-the-art bulk heterojunction solar cells, and has therefore been neglected. For now, lets concentrate on the contribution from polaron pair dissociation. For the sample shown in the figure, the separation yield approaches 60% at short circuit current (at about 0.6V on the rescaled voltage axis, 0V corresponding to the flatband case). The question is, why is it so high in polymer-fullerene solar cells, considering that a charge pair has a binding energy og almost half an electron Volt at 1 nm distance, and that recombination is on the order of nanoseconds [Veldman 2008].

A powerful way to gain new insight into the mechanisms governing polaron pair dissociation is by using Monte Carlo simulations. We recently applied this technique to explain the origin of the high polaron pair dissociation yield found experimentally in polymer-fullerene solar cells [Deibel 2009a]. We will give an introduction to Monte Carlo simulations another time – for now only stating that some information can be found in our paper, and more details on the principle in [Houili 2006] – and focus on the physics for now.

In the figure below, the simple cubic lattice representing the donor-acceptor blend is shown on the left hand side. Polaron pairs are generated by setting a positive charge on the polymer (the donor), and a certain distance away (e.g., the nearest neighbour distance of 1nm) a negative charge on the fullerene (the acceptor). Every site has a certain energy chosen from a Gaussian distribution of states, and charges are subject to the external electric field and the Couloumbic attraction (or repulsion). The charges move by a hopping process as described by the Miller-Abrahams hopping rate [Miller 1960]. On the right hand side, the polaron pair dissociation yield is shown in dependence on the electric field (log-log Plot). The simulated curves (dotted) are shown for two different effective polaron pair lifetimes, the solid red line corresponds to the polaron pair contribution as extracted from the photocurrent in the topmost figure. The yellow rectangle denotes the internal field under solar cell short circuit conditions, i.e., the highest field usually found in a working organic solar cell. Clearly, the simulations underestimate the polaron pair separation yield by more than one order of magnitude.

Why is the discrepancy between simulation and experiment so large? What is the origin of the high experimental polaron pair dissociation yield?

Several possible explanations come to mind,

• a high local mobility could have a stronger impact, either due to fullerene nanocrystals [Veldman 2008] on which charges are delocalised, or – as the evidence for fullerene nanocrystals is somewhat debated [Deibel 2009a] – polymer chains [Hoofman 1998 (exp)]
• excess energy from hot polaron pairs [Ohkita 2008 (exp)]
• local dielectric constant [Szmytkowski 2009 (analytic)]

One group has performed a Monte Carlo simulation to check the influence of nanocrystals on polaron pair dissociation,

• high local mobility of charges in nanocrystals [Groves 2008 (sim)],

considering ordered domains in the otherwise disordered, low-mobility donor-acceptor blends. However, while the high experimental yield could almost be reached, the donor and acceptor “grains” were very large, and the polaron-pair lifetimes orders of magnitude higher than determined experimentally.

In order to contribute to this issue, we considered

• delocalisation of charges along the effective conjugation length polymer chains [Deibel 2009a (sim)],

following the experiments of Hoofman et al. We modified our Monte Carlo simulation accordingly, as shown in the figure below:

The long polymer chains are shown schematically on the left hand side, the resulting field-dependent polaron-pair dissociation yield (log-log) is shown on the right hand side. An effective conjugation length (CL) of 4 or 10 monomer units, which is easily reached in the current synthesis of conjugated polymers, yields a strong increase of the separation yield up to 60% to 90% dissociation yield at moderate fields of below 10⁷ V/m, as found in working organic solar cells.

Thus, the highly efficient polaron-pair dissociation can be explained by delocalised charge carriers within conjugated segments of the polymer chain. The resulting local charge carrier mobility is much larger than the macroscopic one. Together with the reduced Coulomb attraction due to the accordingly increased initial polaron-pair radius, the high on-chain mobility is essential to explain the high polaron- pair separation yield. These values correspond to recent experimental findings, as also indicated by the solid red line, the polaron pair contribution as extracted from the photocurrent in the topmost figure. Thus, we believe the delocalisation along the conjugated polymer chains to be a dominant contribution to polaron pair separation, although other contributions listed above can certainly also play a role.

More on photocurrent, polaron pair dissociation and Monte Carlo simulations later;-)

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On the 11th of July 2009, Anja and I celebrated our church wedding. After the civil wedding last December in my home town Wuppertal, we now married in Anja’s home village Schwebheim in Lower Frankonia. It was a wonderful ceremony, and a very nice festivity afterwards (I believe… but I might be biased;-).

The only reason I am already back at my computer is that the beginning of our honey moon is somewhat delayed, as both of us have very interesting but also demanding jobs. Well, postponed is not abandoned!

All the best,

Carsten

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The claim “new world record: efficiency of organic solar cell increased to 5.9%” should be preceded by “almost”, or succeeded by “based on small molecules”, because less than 2 months ago, Konarka had a press release about a certified efficiency of 6.4% for an organic bulk heterojunction solar cell. Although not mentioned in the press release, this one is probably not a tandem cell.

[Update 3.9.2009] After talking to Moritz Riede, a researcher from Dresden, I understood that the world record is unique in as far as the area is above one square-centimeter: 2 cm², whereas the Konarka cell has only 0.76 cm² – almost at, but not quite above “unity”. This distinction comes from the solar cell efficiency tables by Green et al. (see for instance [Green 2009]).
Thus, the 5.9% are best for small molecule based solar cells, and the best organic solar cells above one cm²: congratulations!

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All models are wrong, but some are useful.

The article takes the provocative stance that we do not need models any more to describe the world, as petabyte data clouds combined with massive computing power are able to correlate data.

Data without a model is just noise. But faced with massive data, this approach to science — hypothesize, model, test — is becoming obsolete. [...] Correlation supersedes causation, and science can advance even without coherent models, unified theories, or really any mechanistic explanation at all.

I humbly disagree. Understanding needs models, predictions need models. Of course, in order to find models, correlations – probably found by using computers – can show the way.

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Some of the centers will focus on photovoltaic energy conversion, partly with a strong focus on organics!

• Center for Interface Science: Hybrid Solar-Electric Materials, University of Arizona (Director: Neil R. Armstrong)
• Center for Inverse Design, National Renewable Energy Laboratory in Colorada (Director: Alex Zunger)
• Center for Excitonics, Massachusetts Institute of Technology (Director: Marc Baldo)
• Polymer-Based Materials for Harvesting Solar Energy, University of Massachusetts (Director: Thomas Russell)
• Solar Energy Conversion in Complex Materials, University of Michigan (Director: Peter Green)
• Solar Fuels and Next Generation Photovoltaics, University of North Carolina (Director: Thomas Meyer)
• The Center for Advanced Solar Photophysics, Los Alamos National Laboratory (Director: Victor Klimov)
• Re-Defining Photovoltaic Efficiency Through Molecule-Scale Control, Columbia University (Director: James Yardley)
• Understanding Charge Separation and Transfer at Interfaces in Energy Materials and Devices, University of Texas (Director: Paul Barbara)

The list can be found here, and there are also details available.

Well, strong competition coming up for us European researchers… but what could be better for driving a field forward?

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Thanks go to Jens for the link!

P.S. Juan had this already last month: sorry for being late;-)

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Two other useful programs: a periodic table, The Chemical Touch: Lite Edition) and PhD Comics (very useful – and also available directly on the web Enjoy.

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One shouldn’t work on semiconductors, that is a filthy mess; who knows if they really exist!

God created the solids, the devil their surfaces.

I don’t mind your thinking slowly; I mind your publishing faster than you think.

This isn’t right. It’s not even wrong.

Excellent… and certainly applicable to the fields of organic solar cells and disordered semiconductors

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Yesterday, a new report on the future prospects of the organic photovoltaics business was presented by the analyst firm Nanomarkets. It is said to include a roadmap for improvements in organic solar cell lifetimes and efficiencies, as well as forecast of volume and price of relevant materials over the course of eight years.

I cannot comment on the analysts’ expertise, although they are specialised on market research for organic and printable electronics – which has pros (they know what they are talking about) and cons (they might be pretty subjective), I reckon;-) See their press release here. All in all, a promising future is just what we need:-)

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Of course, I am very happy that my figures are liked and used, and also happy that I was referenced (my name and the blog are mentioned below the respective figures, and really also appear in the list of references . However, I was somewhat surprised about not having been asked for the permission of the images’ reproduction. I even could have supplied them in high resolution.

By the way, if you want to have a look at the book (yes, free advertisement… maybe I get a copy of the book as appreciation;) , you can find it at google books (hope the links works..) and also at Scribd, although for the latter link, I am pretty sure that the book pdf is published without Wiley’s permission! Disclaimer: all links go to external sites, they are just for your information. [Update 7.7.2009: the book pdf on Scribd was deleted at the request of John Wiley and Sons.]

So, once again, I am happy if you use my material and give me credit, even if you do not ask. But please do!

P.S. One of my photos from this blog (saved at flickr) was also published (with my permission;-) in the Schmap Boston Guide.

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Personally, I like the Mac version of Papers a lot: it is really an innovative program, although for me it has never been very stable (this, however, seems not to be a common problem according to the forums. Still, apologies to mek for never mentioning my instabilities to him .

Update 27.2.2009 P.S. After I posted this, I wrote the Papers developer, mek, about my instability problem, and he answered within a few hours. It is a known issue having to do with Smart Lists. Now, my Papers version is responsive and stable!

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So from the generation side, there were several key messages about where we should be putting our money: go with solar, increase efficiencies using nanoparticles, find a way to use cheap and abundant raw materials, and think seriously about thermoelectric materials.

The German physical society published a study about climate, energy, and what related research is needed back in 2005, yet still contains uptodate concepts and ideas. But I still wonder: Do Europeans actually have an organisation similar to the AAAS mentioned above, or similar meetings?

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As fellow blogger with common interest:

Welcome!

I am looking forward to reading your posts.

Carsten

Update 20.2.2009: At the same time, another new blog from the same university started; same topic, different style.

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How much does a weak charge transport limit the performance of organic solar cells? How bad is it?

Luckily, not as bad as one might think! It turns out that a certain charge carrier mobility is important to get good power conversion efficiencies, but looking at further improvements, there are other more pressing issues. But one after the other.

Several processes in organic solar cells (the function of which was detailed before in three parts) do strongly depend on the mobility:

• the polaron pair dissociation (Braun-Onsager theory [Braun 1984], describing the escape from the mutual Coulomb attraction)
• the charge transport
• polaron recombination (possibly Langevin recombination, but with a reduced rate, as found experimentally [Deibel 2008b, arxiv:0810.0542])
• and finally, the charge extraction (which is directly related to charge transport, and possibly influenced by surface recombination)

Using our macroscopic device simulator, we looked at the influence of charge carrier mobility on the solar cell parameters (short circuit current, open circuit voltage, fill factor, and of course the efficiency) [Deibel 2008a, arxiv:0806.2249], following the idea of [Mandoc 2007], but considering a more realistic (=reduced) polaron recombination as well as injection barriers at the electrodes. Due to polaron pair dissociation, the short circuit current j_sc increases with mobility (here equal for electrons and holes) until saturation is reached. The open circuit voltage V_oc, however, decreases steadily. Actually, the slope steepness is maximum due to our implicit assumption of ideal charge extraction; for a realistic charge extraction (= finite surface recombination), the Voc slope with mobility is weaker… or even constant for zero surface recombination. The fill factor is maximum at intermediate charge carrier mobilities, not far from the experimentally found values!

Looking at the power conversion efficiency, there is indeed a maximum value at rather low mobilities, just a bit higher as compared to the values found in state-of-the-art polymer solar cells (shown by a vertical dashed line). The parameter zeta shown in the graph is indicative of wether normal (1) or reduced (0.01) Langevin recombination has been considered.

So, what does all that mean?

• the charge carrier mobility has to be reasonable for good solar cells
• however, there is not much room for improvement; even if surface recombination is rather small (which is to be expected in materials without dangling bonds;-), the maximum efficiency is reached already at low mobilities
• this is due to very low polaron recombination rates, i.e., even though slow, the charges are extracted at some time (if they do not recombine, which they almost never do), leading to photocurrent
• a brief note: the decreasing efficiency at high mobilities is overestimated, as mentioned before; for realistic extraction, it will only be weakly decreasing or even remaining constant… but not increasing after approx. 10^-6m²/Vs (10^-2cm²/Vs)!

So, finally, how to get higher efficiencies? What can be optimised?

• very important, but achieved for some material combinations: a donor-acceptor phase separation which is fine-grained enough for good exciton dissociation, and coarse enough for good charge transport
• polaron pair dissociation: better at low fields than previously thought, but still limiting… more basic understanding is needed
• the narrow absorption bands are a major issue, limiting the photocurrent and thus the short circuit current
• the exciton binding energy and the relative acceptor energy offset: the energy needed for exciton dissociation limits the open circuit voltage

Some of these points I had mentioned already earlier. So, for light absorption, tandem solar cells might be a solution (with new problems arising, e.g., current matching with angle dependence of the incident light), or design/synthesis of novel materials. Same goes for exciton dissociation. But I believe there are many more ideas still out there which need to be implemented and tested;-)

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on organic solar cell and organic light emitting diodes (OLED), specifically the conductive inks and process technologies that enable those and other similar applications.

I mentioned Plextronics already last year, as they presented the (up to now, I believe) highest certified power conversion efficiency for an organic solar cell.

Indeed, industry news again… for next time, I promise more fundamentals;-)

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Just married !

On the 20^th of December 2008, Anja and I celebrated our civil wedding, our “way into happiness” as we call it, in my home town Wuppertal! Afterwards we spent two very relaxing weeks on vacation, enjoying togetherness, thus regaining vigour and inspiration after a laborious year.

That news given, you will certainly believe me that for us this will be an excellent new year 2009, with many more as good ones to follow. Please accept my best wishes for a healthy, funny, splendid year to come.

All the best,

  Carsten

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A somewhat older press release (see here and here) by the belgian research institute IMEC shows how they managed to improve the stability of the donor material, a conjugated polymer. The improvement is apparent from electrical characteristics and TEM images.

Not being quite as fancy as efficiency improvements, the lifespan of organic solar cells is probably more important for a ssuccessful commercialisation. As you know now that we are “officially” involved, stay tuned: this topics interests me from a fundamental research perspective.

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In a significant milestone in the deployment of flexible, printed photovoltaics, Konarka, a solar-cell startup based in Lowell, MA, has opened a commercial-scale factory, with the capacity to produce enough organic solar cells every year to generate one gigawatt of electricity, the equivalent of a large nuclear reactor.

Read it here, or the corresponding Konarka press release.

Thanks to Henning for the link.

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Just a view days ago, there was another publication about recombination of free polarons (free carriers) – also called nongeminate recombination *¹ – more specifically, trimolecular recombination. You might remember that, a while ago, I already mentioned third order recombination, including a reference to private communications with Prof. Juska and another recent paper by the Durrant group [Shuttle 2008]) as well as a potential candidate for its origin. The new paper [Juska 2008] uses three different experimental methods, including photo-CELIV, to measure the temperature dependence of the trimolecular recombination rate in polymer:fullerene solar cell. The authors mention very briefly a possible mechanism responsible for the third order recombination, Auger processes. Shuttle et al. argue in their paper that a bimolecular recombination with a carrier concentration dependent prefactor could be the origin, in particular as they observe a decay law proportional to n^2.5-n^3.5, depending on the sample. We are also in the game, an accepted APL awaiting its publication (preprint here) Update 20.10.2008: now published online [Deibel 2008b]. We rather tend to believe the explanation by Shuttle, but that’s just an assumption at the present stage: the generally low recombination rate could also be due to a rather improbable process.

Disregarding the physical origin for a moment, it is important to note that the nongeminate polaron recombination rate is very low in solution-processed polymer:fullerene solar cells. We believe – and can also show with macroscopic solar cell simulations – that it is not a major limiting factor for the solar cell performance.

As a concluding remark, the differences between recombination in ordered inorganic semiconductors and disordered organic semiconductors also imply that the ideality factor n to describe the exponential part of the current-voltage characteristics, as applied in the Shockley equation, has a different meaning for organic solar cells. To my (limited) knowledge, this has never been openly discussed. (Update 14.10.2008: I should have known better, as I knew these two papers discussing the ideality factor, [Harada 2005, Koster 2005]. IMHO, these are not yet the complete answers, but I might be wrong;-) Some other deficiencies of applying the Shockley equation to disordered organic semiconductor devices I have scribbled down in this post.

*¹ The term geminate tells us something about the history of a carrier pair: geminate pairs originate from the same (photoexcited) precursor state, such as a polaron pair generated by the dissociation of a singlet exciton. Nongeminate pairs, on the other hand, are unrelated carriers of usually opposite charge that can interact and recombine. They could either be injected in to the organic semiconductor, or originate from successfully dissociated polaron pairs.

P.S. Thanks to Martijn and Thomas for pointing me to the new Juska article:)

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Today I heard a talk by Darin Laird, Plextronics. Using an undisclosed organic donor material (well, they call their product Plexcore OS 2000 [Update below], as opposed to their P3HT OS 1000 or so) blended with the usual suspect PCBM, they managed to process an NREL certified lab scale (0.1cm²) solar cell with 5.94% power conversion efficiency! Fill factor was almost 72%, I believe, with the major improvement as compared to the reference material P3HT coming from an increased open-circuit voltage.

The corresponding solar cell module, 15×15 cm² large, has an efficiency of 1.1% (or 2.3% active area efficiency, if you consider that only 46% of the module are active area). These numbers are brand new, but generally, uptodate solar cell efficiencies can be found in the efficiency tables (V32) by Martin Green.

So, who’s next to boost the organic solar cell efficiencies?  

P.S. As there sadly was a history of overestimated efficiencies published, followed by letters to the editors by watchful scientists and statements, a solar cell characterised by a certified institute is important to regain the trust.

P.P.S. Of course, not every university group can afford to spend 1000 bucks on a certified solar cell measurement. Still, at least some effort can be put into doing the current-voltage characterisations carefully. In January, Jan Kroon gave an interesting talk about measuring organic solar cells properly; find the video here.

Update (5.9.2008): The donor Plexcore OS 2100 available at Sigma Aldrich is not the one with which the 5.9% efficiency where achieved. The undisclosed donor material used is not yet available commercially, it seems.

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Too much physics here anyway… have a nice day!

Step 1: Light Absorption => Exciton Generation

• light is absorbed in the donor material, e.g., a conjugated polymer
• excitons are thus created, strongly bound electron-hole pairs on the polymer chain
• very high absorption coefficient, device thickness on ~100nm scale, as compared to the inorganic polycrystalline semiconductor CuInSe₂ (~1 micron) and crystalline Silicon (~100 micron)
• but: only narrow absorption bands, as shown for two conjugated polymers P3HT and PCPDTBT in comparison to CuInSe₂. This drawback could be circumvented by synthesis of novel materials, or multijunction concepts (tandem solar cells).

Step 2: Exciton Diffusion => to Acceptor Interface

• the photogenerated excitons are strongly Coulomb bound due to the low dielectric constant in organic materials, and the correspondingly low screening length: charges can ‘see’ each other very well
• electrically neutral excitons can only move by diffusion
• in order to disociate into an electron-hoe pair, it has to find an acceptor site (e.g., fullerene molecule)
• short exciton diffusion length of only a few nanometres
• therefore, no bilayer concept, instead bulk heterojunction solar cells of intermixed donor and acceptor materials (shown in the figure), such as conjugated polymers blended with fullerene derivatives

Step 3: Exciton Dissociation => Polaron Pair Generation

• excitons dissociate only at energetically favourable acceptor molecules such as the fullerenes, when the energy gain is larger than the exciton binding energy
• then, an electron transfer (or charge transfer) takes place, dissociating the exciton into an electron on the fullerene acceptor, and a hole remaining on the polymer
• this electron-hole pair is still Coulomb bound, and is called geminate pair or polaron pair

Step 4: Polaron Pair Dissociation => Free Electron–Hole Pairs!

• the polaron pairs are Coulomb bound
• they also need to be dissociated, this time by an electric field ( = built-in voltage + applied voltage)
• therefore, the photocurrent in organic solar cells depends strongly on the applied voltage
• this is a major loss mechanism in organic solar cells

Step 5: Charge Transport => Photocurrent!

• the electrons and holes are transported to the respective electrodes, driven by the electric field, and moved by a hopping transport process
• hopping: very slow charge transport, low carrier mobility, at least a factor of 1000 smaller than for crystalline Silicon… while the power conversion efficiency of organic solar cells is only factor 4 worse;-)
• indeed, our current research indicates that a loss of free charge carriers by nongeminate recombination during the charge transport to the contacts is only marginal
• and, higher mobility does not improve the power conversion efficiency significantly. Will be covered in a later post;-)

So much for now, see you later.

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In case you want to reproduce the graph, I used the topic

“organic photovoltaic cell” or “organic photovoltaics” or “organic solar cell*”

for organic photovoltaics and related phrases, and

“bulk heterojunction solar cell*” or “bulk-heterojunction solar cell*” or “polymer photovoltaic” or “polymer fullerene photovoltaic” or “polymer solar cell*” or “polymer fullerene solar cell*” or “polymer-fullerene solar cell*” or “polymer-fullerene solar cell*”

Web of Science can also combine search sets in the history, so that publications matching both sets are not counted twice; the result is shown as the curve “both” in the graph. Probably, by a more appropriate choice of search terms, even some more papers can be found. For instance, I should have included small molecules.

The result is not strictly growing exponentially, but the interest still is increasing continuously. Let’s hope that the commercial interest will have similar growth rates soon;-)

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One candidate for an excitation involving three species it the so called trion. Coming from inorganic semiconductor physics, and meaning charged exciton, it has been described for organic matter already more than 20 years ago [Pope 1984] as

bound exciton plus hole (excitonic ion)

In this review (including the references therein, in particular [Agranovich 1979]), an attractive interaction between exciton and charge is described.
The respective binding energy is linearly proportional to the change in the molecular polarisability of the excited molecule,
.
(Note: all in CGS unit system, therefore a pain… for me;-) The binding energy is about 500 cm^-1, calculated for a polarisability of 15×10^-24cm³, which was – for the matter of obtaining an estimate – taken from the polarizability of the lowest lying singlet exciton state in the rather rigid molecules tetracene or anthracene. Furthermore, epsilon=3 and r=0.5nm where assumed. This corresponds to about 60meV binding energy. For polymers, this estimate looks quite different: Taking also polarisabilities for the lowest lying singlet state for polythiophene [van der Horst 2001], which seems to be 2 orders of magnitude higher (please correct me if I messed up something… 1.6×10³Angstrom³ was given in the paper;-) , the binding energy would be on the order of a few eV… which is just an estimate, and hopefully not wrong.

With these rather high binding energies, trions seem to be rather stable entities. Also, they might be the candidate for trimolecular recombination, even though a possible mechanism could also be proportional to singlet density times charge density, i.e., bimolecular again. I am not sure myself, so let’s wait and see … or measure and think;-)

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A polaron is a charge, i.e., an electron or a hole, plus a distortion of the charge’s surroundings. In a crystalline inorganic material, setting a charge onto a site does not change the surroundings, as the crystal lattice is rigid. Not so in many disordered organic materials. Putting a charge onto a certain molecular site can deform the whole molecule. Moving the charge from this to another molecule means that first the energy for the deformation – the polaron binding energy or reorganisation energy – has to be mustered. The implication is that charge transport becomes more difficult, the charge carrier mobility becomes lower, … This process is also described as self-trapping. As a side note, it is often difficult to distinguish between the influence of polaronic self-trapping and of gaussian disorder, as both have a similar impact on the charge transport properties. This similarity is also reflected in the corresponding hopping rates used to calculate charge transport: Marcus theory is a function of the reorganisation energy, where as the Miller Abrahams rate [Miller 1960] is related to the energetic disorder of the density of states. The polaronic deformation can be quantified in terms of a (lattice) polarisation, or a phonon cloud, or just as the above-mentioned polaron binding energy. Mostly, however, when hearing polaron, think charge;-) See also what wikipedia has to say about polarons.

A polaron pair is a Coulomb bound pair of a negative and a positive polarons, situated on different molecules. Usually, polaron pairs are the intermediate step from an exciton to a pair of free polarons &ndash far enough apart not to feel the attraction of one another &ndash and therefore important in order to understand photogeneration in organic semiconductors.

An exciton is an excited quasiparticle in a solid, which is formed by a Coulomb-bound electron-hole pair. It is more prominent in organic semiconductors as compared to their inorganic counterparts: as the dielectric constant is lower in organics, the screening length is larger. In this case, the name Frenkel exciton is applied, whereas the weakly bound type is called Wannier-Mott. Thus, in organic materials, the two charges feel a strong mutual attraction, and usually reside on one molecule. There seem to be special cases, however, in which the two particles reside on adjacent molecules – of the same kind, in contrast to polaron pairs. The spin-state of the two charges is quite important. Without going into too much detail: when the two spin-vectors add up to zero, we have a singlet exciton. Singlet excitons are the only ones which are generated upon illumination, which is due to the specific selection rules. The other exciton type, triplet excitons, have a nonzero spin vector, which is possible in three different combinations – thus the name triplet. Singlet and triplet excitons can also be formed due to interaction following charge injection; theoretically, this follows a one-to-three ratio, i.e., only a quarter is of singlet type. Some features of singlet excitons and their relevance for organic photovoltaics was discussed here. The exciton binding energy of singlets is around 0.3eV in organics (compared to ~0.01eV in classical semiconductors). Excitons have a certain lifetime, typically of the order of ns in organic semiconductors, after which they recombine radiatively; this is called photoluminescence. Triplet excitons generally have lower energies and longer lifetimes. For photovoltaics, they are not yet import (though might be following some novel concepts), instead they can act as loss mechanisms (by intersystem crossing or electran back transfer) under certain conditions as their energy is too low to generate free charge carriers. Radiative recombination after the triplet long lifetime of maybe some milliseconds – the transition is actually spin forbidden – phosphorescence occurs. As a side note, phosphorescence can be applied to high usefulness in so called triplet emitters, being an important concept for organic light emitting diodes. Maybe we’ll detail this another time. Wikipedia on excitons here.

An exciplex is just an exciton which is located at the interface of its “host” molecular material – indeed it still resides on one molecule – as indicated in the image. Due to the influence of the surface, the exciplex experiences a different environment as compared to a bulk exciton. This leads to photoluminescence which is slighlty red shifted. Also, the lifetime can be prolonged in comparison to the bulk exciton, as it is stabilised by the surface states.

Did you miss bipolarons? I didn’t;-)

Thanks to JG for the exciplex!

[Update 27.4.2010 to answer the question of Jenna] In organic bulk heterojunction solar cells, the path from singlet excitons in P3HT to free charges usually goes via charge transfer complexes of the donor-acceptor system. (See for instance here.) I often refer to these as polaron pairs. However, naming conventions are not that simple. Here a brief excerpt from an unpublished review I recently wrote (accepted for publication by Adv Mater).

The commonly used names for CT states and complexes are diverse, either used alternatively or to define special cases. Examples are polaron pairs, [Dyakonov 1998] intermolecular radical pairs (with the radical cation on the polymer and the radical anion on the fullerene) [ Scharber2003], interfacial charge pairs [Westenhoff 2008], geminate pairs [Arkhipov2003], charge transfer excitons [Veldman2008] and exciplexes [Morteani2004].

Huang et al. [Huang 2008] found by theoretical considerations for polymer-polymer heterojunctions that a range of Coulombically bound CT states with both, emissive and non-emissive character, exist. The different states are a result of the specific features of the intermolecular overlap between donor and acceptor moieties. In order to strive for a more precise nomenclature, they point out that polaron pairs can be considered as one special instance of the more general exciplex. From this point of view, the distincitve property of the polaron pair excitation is that it is due to a complete charge transfer from donor to acceptor, as opposed to a partial CT. Thus, an exciplex can generally be regarded as a hybrid state with partly CT character and a certain fraction of a local excitation on one (or both) molecules of the donor–acceptor system. Already earlier, Gould et al. [Gould 1994] pointed out that the character of the emitting species of an exciplex depends on the relative contributions of pure ion-pair and locally excited states. In their definition, an exciplex with beyond 90% CT character represents a pure contact radical-ion pair. They suggested that it can be identified experimentally by verifying that the emission maximum lies about 5000/cm (100meV) below the singlet exciton photoluminescence.

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• the “direct” recombination rate
• finding each other

In high mobility semiconductors, the former is dominant. However, in disordered solids, and particularly disordered organic semiconductors, the low mobility limits the effective recombination rate. The process of finding each other can be described as diffusion limited, which is proportional to the charge carrier mobility when considering the Einstein relation.The idea is as follows (after [Pope & Swenberg 1999]): we assume a negative charge to be fixed, and a positive mobile charge (moving with mobility of electron plus hole), both being attracted by the Coulomb force. The hole can avoid recombination at zero field only if the thermal energy is sufficient to overcome the Coulomb potential. As demarcation line, the Coulomb radius is defined by equating

as

If we consider now a drift current density for the mobile hole,

bearing in mind that electric field is the spatial derivative of the potential (energy), we get

Now considering that recombination of the two charges takes only place if they find each other, i.e., the hole comes to within the Coulomb radius, we can calculate the hole recombination current. That is the current density flowing into the sphere of radius around the electron,

with gamma being the Langevin recombination strength

Now, indeed, the recombination is proportional to the charge carrier mobility of electron and hole, i.e., to the two carriers finding each other.

The Langevin recombination strength time electron density times hole density is then the Langevin recombination rate, as used in a typical continuity equation

with generation term G0, a monomolecular recombination term, and the bimolecular Langevin recombination rate.

Bimolecular recombination in disordered plastic solar cells is usually described with the Langevin theory. There seem to be some adjustments to be made, which we’ll discuss another time;-)

(Update 3.2.2009: support by WordPress, excellent! My splendid MarsEditblog editor transfers it, but does not parse it… but that would have been asked too much indeed! No, I am glad it works as is:-)

(Update 18.1.2011: Wapf asks, Carsten answers;-) The thermal energy with is only an estimate as compared to the for three degrees of freedom. Also, if you are wondering why , but : I did not transform into Concerning : consider that a current . Therefore “disappears” going from current to continuity equation. Concerning the “appearing” : the recombination current as calculated by Langevin considers particles which flow into the -Sphere around the center charge. By definition of Langevin, all charges (here, holes) flowing into the sphere recombine with the center center charge (here, one electron). Going from microscopic consideration to macroscopic equation, this one charge of course has to be translated to a charge density, as this can happen with every electron. (And all of this is of course true for the opposite case, electrons flowing into the “hole sphere”, but this is generalised already in the final rate equation.)

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For a general classification we take a look at Kwan-Chi Kao’s book “Dielectric Phenomena in Solids“.
Looking for monomolecular recombination, we find

The recombination that involves one free carrier at a time, such as indirect revombination through a recombination center (e.g., an electron captures by a recombination center and then recombined with a hole, each process involving only one carrier), is generally referred to as monomolecular recombination.

In organic semiconductors, a recombination centre can for instance be a trapped hole, localised in a deep state; it can induce a monomolecular recombination with a mobile electron. Even knowing this, it still feels like bimolecular recombination, doesn’t it?

Bimolecular recombination reads as

The recombination that involves two free carriers simultaneously, such as direct band-to-band recombination, is generally referred to as bimolecular recombination.

As mentioned above, direct band-band recombination of free carriers does not exist as such in organic disordered semiconductors. Generally speaking, in a hopping system with localised charges, the two oppositely charged carriers “wishing” to recombine first have to find each other. This is described by the Langevin recombination rate, which is therefore proportional to the carrier mobility of both, and is often applied to low mobility semiconductors.

Finally, trimolecular recombination is defined in the book as

The recomination that involves three free carriers simultaneously, such as a three-body collision in the Auger intrinsic recombination (in which one electron in the conduction band recombines with a hole in the valence band and the energy released is taken up by a third particle-electron), is generally referred to as trimolecular recombination or three-body recombination (or simply as Auger or impact recombination).

Auger recombination seems to be negligible in organic solids. However, recently, there was an article claiming to observe a trimolecular recombination signature in polymer:fullerene devices [Shuttle 2008]. Other researchers also observed recombination proportional to the third order of charge carrier density [Juska and Pivrikas, private communications 2008]. They told me they were still looking for an explanation before publishing it. Shuttle et al. instead published without giving an explanation: The specific nature of trimolecular recombination in the polymer:fullerene system is not yet known;-)

I’ll come back to recombination soon, this post serving just as a starting point to delve deeper into the topic;-)

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Mobile carriers are generated via a two-step process: initial ultrafast charge separation to an intermediate charge transfer (CT) bound state, followed by the transfer of carriers onto the bicontinuous networks.

They explicitly mention

[...] indicating ultrafast dissociation of the singlet excitons at the polymer-PCBM interface and the build-up of the initial CT state.

The paper is nice but in itself not that remarkable, except that previously, Moses and Heeger always claimed the primary photoexcitation to be free charges instead of bound excitons. Their measurements yielded exciton binding energies in the range of the thermal energy, i.e., no donor acceptor interface being necessary for charge separation. To quote an older paper [Moses 2000],

Thus, carriers are photoexcited directly and not generated via a secondary process from exciton annihilation.

Now I have to mention that in the new paper they use P3HT:PCBM, and in the old one MEH-PPV:PCBM. But as they do not mention this in the new paper, I assume that either I missed something, or they changed their point of view concerning the primary photoexcitation.

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• open circuit voltage Voc = Voc₁ + Voc₂
• short circuit current Isc = min(Isc₁, Isc₂)
• fill factor is more difficult, but as a rough guide lets stick to the minimum of both as well

So for an ideal tandem solar cell, complementary absorption ranges, and balanced photocurrents are needed.

Recently, Kim et al. presented 6.5% efficient organic tandem solar cells [Kim 2007]. The samples were made of two series connected sub cells of polymer:fullerene blends. The anode was indium tin oxide on a glass substrate. The top cell (in terms of incident light) was PCPDTBT:PC60BM, the recombination layer was of TiO_x and a special PEDOT:PSS, and the bottom cell P3HT:PC70M. The cathode was made of TiO_x and Aluminum. The absorption ranges of these two material combinations complement each other quite nicely. By adjusting the thickness of the two sub cells, the photocurrent was balanced in order to get a high resulting photocurrent.

Only a short time later, Dennler et al. [Dennler 2007] presented optical simulations by considering thin film interference effects using a transfer matrix algorithm (and another one). They verify that Kim et al. indeed used an advantageous thickness combination for both subcells (approx. 180 and 130nm) in order to optimise the photocurrent by balancing it. They continue to consider other thickness combinations with balanced photocurrent, and find higher charge carrier generation rates by increasing the thickness of both cells. Finally, Dennler et al. claim that by going as far as 565nm for the P3HT based cell, and 225nm for the PCPDTBT based sub cell, the efficiency can be as high as 9% power conversion efficiency.

I would like to comment on the last claim. In my humble opinion, one detail is neglected which is worth to be looked at more closely. The authors essentially calculate the energy dissipation in the tandem solar cell, and convert all the energy into photocurrent. This assumption becomes worse the thicker the active layer becomes. As I have pointed out in a previous post, the separation of Coulomb bound polaron pairs is strongly field dependent, one needs a rather high electric field in order to efficiently dissociate the pairs into free charges. The effective field in the active layer is (external voltage minus built in potential) / thickness. If the two voltages remain the same, and the thickness is increased (here from approx. 300nm to almost 800nm), the field decreases accordingly (by factor 2.5 or so!). Now as photocurrent is only generated by free charges, the photocurrent decreases significantly. That means even though the generation of excitons is much higher for the two thicker sub cells as calculated by Dennler et al., the charge generation will not increase in linear proportion, as assumed in the paper. Actually, I reckon that the power conversion efficiency will not exceed the one of the “thin” tandem device. Of course, there is no exact theory yet to consider the field dependence of the polaron pair dissociation realistically, but in order to not generate unrealistic expectations using “extrapolation by simulation”, a short note by the authors concerning the shortcomings of their model would be appropriate.

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In the figure, the schematic energy level diagram of a bilayer solar cell is shown. The anode is made of TCO (transparent conductive oxide), then follow donor and acceptor, and finally the metal cathode. The exciton is photogenerated in the donor, which can diffuse to and dissociate at the interface to the acceptor. The resulting polaron pair then is energetically separated by the effective band gap of the organic solar cell, Eg.The smaller the LUMO-LUMO offset & – which still has to be larger than the exciton binding energy – the larger Eg: the open circuit voltage is maximised, as it equals Eg minus band bending BB and the injection barriers phi [Cheyns 2008].

As a side note, recently there was a report that claims that the polaron pair dissociation yield is exponentially proportional to the LUMO-LUMO offset [Ohkita 2008]. This implies that always a trade-off between short circuit current and open circuit voltage will have to be made. Please note, however, that the photoinduced absorption measurements by Shuttle et al. are done without the application of an external (or internal for that matter, the samples being optical thin films without electrodes) electric field; so there is still hope;-)

But back to absorption and its impact on the power conversion efficiency: you may know the detailed balance calculation of Shockley and Queisser for inorganic solar cells, power conversion efficiency vs band gap, which has been mentioned recently. It is shown in the left figure as black solid line. For organic solar cells, there is no complete analytic theory to describe all parameters proportional to the properties, therefore I made an estimate based on a couple of assumptions:

• quantum efficiency 100% within absorption band of 200 (blue) or 400nm (red) width
• fill factor 80%
• thickness 200nm
• open circuit voltage after [Koster 2005] with recombination strength gamma either 10^-15m³/s (as in the article, even if not explicitly mentioned) or a reduced recombination strength of 10^-18m³/s (green); the other parameters are as in the paper.
• Koster’s Eg is set to “Energy Gap” (as in “x axis”) minus exciton binding energy Eb of 0.3eV

Clearly, disordered organic solar cells have a lot of potential in view of manufacturing by roll-to-roll printing, but the maximum power conversion efficiencies which can be reached are lower as compared to inorganic solar cells… unless a clever chemist (actually, we need a genius here;-) manages to make suitable donor and acceptor materials with wider absorption ranges… Of course, higher intrinsic absorption is not the only route for higher organic photovoltaic performances: another possibility are (solution-processed!) multijunction solar cells, thus combining different absorption ranges of already existing materials.

Update 24.3.2008: I exchanged the wrong reference Shuttle 2008 by Ohkita 2008. Apologies!

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Next time, we’ll be looking a bit closer into advanced device architectures. Stay tuned;-)

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The most important figures of merit describing the performance of a solar cell are the open circuit voltage, the short circuit current, the fill factor and the (power conversion) efficiency. The fill factor is given by the quotient of maximum power (yellow rectangle in the figure) and the product of open circuit voltage and short circuit current (white rectangle); it therefore decribes the “squareness” of the solar cell’s current-voltage characteristics. The efficiency is the ratio of maximum power to incident radiant power – typically radiated by the sun. E.g., a well-known detailed balance calculation for inorganic single gap solar cells gives a theoretical maximum of about 30% power conversion efficiency [Shockley 1961]. The upper limit for organic solar cells is somewhat lower, but that’s another story.

As you may know, the Shockley diode equation

(which is older than 1961 but also used in the paper) looks as in the equation below when corrected for real inorganic devices with series and shunt resistance:

In the Shockley equation for “real” diodes, an optional photocurrent is included by a parallel shift of the current-voltage curve down the current axis: this is the (constant) photocurrent jph. Now, many people have fitted the current-voltage characteristics of organic solar cells under illumination with this equation, but as one can clearly see from the figure above, the shown j(V) curve for a typical organic solar cells has a strongly field dependent photocurrent. There is for example a crossing point of dark and illuminated curve at approx. 700mV which cannot be explained by the Shockley equation. The reason is, as explained in “How Do Organic Solar Cells Function? – Part One“, that the Coulomb bound polaron pairs (approximately: electron-hole pairs) have to be split by the externally applied electric field. At 700mV (in this instance), however, the internal electric field, which is the contact potential difference minus the external electric field, is zero. That means flat band conditions, and therefore there is not enough driving force for the polaron pairs to be separated: there has to be a crossing point. (Actually, even in inorganic compound semiconductors such as CuInSe2 there are similar crossing points, but their origin is different.)

As you can also see from the upper figure, it sometimes happens that the maximum photocurrent is not reached at 0 Volts, i.e., under short circuit conditions, but only at more negative bias, corresponding to a higher internal field. This happens in organic solar cells where the polaron pair dissociation is more difficult, e.g. if the active layer is thicker, and therefore at the same (external) voltage the (internal) field at zero bias is lower.

The details of polaron pair dissociation are not completely understood. Right now, the so called Onsager theory [Onsager 1938] and its somewhat more modern incarnation [Braun 1984] are used to describe its field dependence. According to me, however, the last word is not yet spoken… which might not mean much;-)

Coming back to the Shockley equation. A positive bias leads to the injection of charge carriers into the solar cell: the current increases exponentially, we see a rectifying (=diode-like) behaviour in the ideal case. In real solar cells, however, there are losses, considered in the second equation above by two resistors. The so called series resistance R_s – in series with the diode – describes (amongst others) contact resistances such as injection barriers and sheet resistances. In contrast, the parallel resistance covers the influence of local shunts (=short circuits) between the two electrodes, i.e., additional current paths circumventing the diode. Works nicely in silicon solar cells, but in organic solar cells some problems appear: the “parallel resistance” now seems to depend on the voltage and illumination intensity, the “series resistance” also also changes with voltage.

Unfortunately, there is no analytic equation yet to properly describe the peculiarities of organic solar cells. what we’ll settle for now is to describe the known differences between Shockley and real organic cells. As organic semiconductors are usually not as conductive as their inorganic counterparts, at higher voltages (and sometimes also at higher negative internal fields under illumination, even in the 4th quadrant!) space charges can build up, leading to space charge limited currents. Here, the current is proportional to the square of the voltage (an not linearly proportional to the voltage as for resistors). (Actually, in organics, the well-known Childs law or Mott-Gurney law with j being proportional to V² is also not strictly correct… maybe more on this another time;-) This can lead to the determination of apparently voltage dependent resistors. As mentioned above, space charges under illumination, which can be induced for instance by trapped charges, can superimpose with the “parallel resistance”, which than becomes voltage (and light) dependent as well. And of course, shunts and contact resistances do also exist in organic solar cells.

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The introduction of a second layer was a quantum leap in terms of power conversion efficiency (though still on a low level): organic bilayer solar cells, presented in the mid eighties [Tang 1986]. The light is usually absorbed mainly in the so-called donor material, a hole conducting small molecule. The photogenerated singlet excitons now can diffuse within the donor towards the interface to the second material, the acceptor, which is usually strongly electronegative. A prominent example for an electron acceptor material is the buckminsterfullerene (C60).

The energy difference between the electron level of the donor and the corresponding acceptor level has to be larger than the exciton binding energy, in order to initiate a charge transfer from donor to acceptor material. If an exciton moves – by diffusion, as it is neutral – towards the donor-acceptor heterojunction, it is energetically favourable if the electron is transferred to the acceptor molecule. This charge transfer, or electron transfer, is reported to be very fast (can be faster than 100fs in polymer-fullerene systems) and very efficient, as the alternative loss mechanisms are much slower [Sariciftci 1992]. The hole stays on the polymer: the exciton is dissociated, the charge carriers are now spatially separated. Even though residing on two separate materials now, electron and hole are still Coulomb bound, even though the recombination rate is clearly lowered (lifetime: micro to milliseconds) as compared to the singlet exciton (lifetime: nanoseconds). Therefore, a further step is necessary for the final charge pair dissociation. Here, an electric field is needed to overcome the Coulomb attraction, and this dependence becomes manifest in the typical, strongly field dependent photocurrent of organic solar cells, also influencing fill factor and short circuit current. The basic steps from light generation / exciton generation to photocurrent are shown in the figure.

If no or just a low electric field is applied, the so-called monomolecular recombination of the charge carrier pair is very probable. As a brief sidenote, important here is not directly the externally applied field, but the internal field, which is influenced by the built-in potential due to the work function difference of the electrodes. But back to the dissociation: only if the field supported charge carrier separation is successfull, can electron and hole hop towards their respective contacts, in order to generate a photocurrent. C.W. Tang (cited above), who reported the first organic bilayer solar cell made of two conjugated small molecules, achieved a power conversion efficiency of about 1 percent. The limiting factor in this concept is that for a full absorption of the incident light, a layer thickness of the absorbing material is to be of the order of the absorption length, approx. 100nm. This is much more than the diffusion length of the excitons, about 10nm. In this example, maybe 100 percent of the incoming photons (within the absorption band) can be absorbed, but only 10 percent of these could reach the donor-acceptor interface and be dissociated to charge carrier pairs (also called polaron pairs). As mostly the exciton diffusion length is much lower than the absorption length, the potential of the bilayer solar cell is difficult to exploit. Fortunately, there are advanced concepts, e.g. the so called bulk heterojunction solar cell, which we will talk about the next time [Update 16.6.2009: link]. See you then;-)

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Here, the screening of opposite charges is much weaker as the dielectric constant is lower. This leads to a much stronger interaction of the photogenerated positive and negative charges. Therefore, the primary optical excitation in organic materials is called (singlet) exciton, i.e., a strongly bound electron-hole pair. As this binding is more difficult to be overcome as compared to inorganic systems, the concept of organic solar cells has to be different… which we will come back to later.

Another difference between organic and inorganic solar cells is less principal, but also has significant consequences. About 95% of the silicon solar cells produced every year are made of crystalline silicon, in which the atoms are ordered (almost) perfectly well, and the charges can travel quickly after they have been photogenerated. In contrast, organic semiconductors interesting for electronics applications are rather amorphous, polycrystalline at best. (Now there also exist amorphous silicon as well as organic crystals, but in terms of applications, the statement above describes the usual case.) The advantage with disordered stuff is, and that is also true for inorganics, it is easier to make. Unfortunately, not all is so well: charge transport is more difficult: crystals are like the autobahn for charges, whereas disordered matter are country roads at best. Due to the lack of long-range order, the electrical transport in disordered semiconductors usually takes place by hopping from one localised state to the next, instead of gliding quasi-freely through the carrier band of crystalline semiconductors.

So, up to now we have been talking about two issues making life more difficult for designing an efficient organic solar cell. Positive, however, is the ability to synthesise tailor-made organic substances, which – at least in principle – allow fine tuning of the absorption range, the charge transport properties, and maybe additionally allow for self-assembly… which is almost as good crystallinity;-) Of course, even hard working chemists (and many of them are) have difficulty to judge just from the chemical formula if every aspect of the designed substance is as intended. And that is why chemists and physicists still have to do trial-and-error, in the hope if finding the optimum materials for organic solar cells. One feature which is mostly good is the absorption length. That means that already very thin organic films can absorb all the light shone on them (within their absorption range). We are talking about 100nm or so, 100x thinner than hair. So only very little material is needed… compare this to crystalline silicon, standard wafers being 300 micron thick, i.e., several hairs on top of each other (by diameter, not length;) Considering world domination of photovoltaics (ok, unrealistic), this makes quite a difference in material use. Of course, clever scientists work also on making silicon solar cells much thinner, and there are interesting alternatives such as derivatives of the inorganic compound semiconductor CuInSe₂, which is usually polycrystalline and has an absorption length below 1 micron. Not as thin as organics, but certainly not bad! But then, we don’t do inorganic solar cell bashing here;-)

So stay tuned for the next parts, starting with the basic function of how light is converted to current in organic photovoltaics, and the secrets of how to realise a printed multijunction organic solar cell on a flexible substrate!

P.S. If you wish, continue with Part 1 [Update 16.6.2009].

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Well, there are some drawbacks in terms of the application… though not for researchers;-) Printing semiconductors usually leads to rather disordered films, which have very low charge carrier mobilities as compared to Silicon and other inorganic semiconductors, and are thus not suitable for high-frequency applications. However, for photovoltaic devices, the low mobilities are not that much of a drawback. That said, organic solar cells are still at below 7% power conversion efficiencies… for very small areas. Single crystalline Silicon, on the other hand, sees already above 20% for modules.

In my opinion, while organic solar cells probably never reach the performance of these Silicon devices – which might limit their suitability for rooftop applications – there is still a good chance to get printed low cost photovoltaic modules on flexible substrates with good energy balances. A prerequisite for achieving this goal is to do not only trial-and-error device development, but also fundamental research of the properties of disordered materials.

Speaking of which, from the point of view of basic research (physicist, o brother, where art thou), disordered materials are just… complex and very interesting… beautiful. So we just need the applications as an excuse to do what we like to do in any case;-)

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