You are right, polaron pair dissociation is improved by a higher charge carrier mobility (if there is anything to improve), but at some point you have perfect photogeneration and even higher mobility does not make a difference any more. Thus, this is indeed unrelated to the reduction of Voc at high mobilities.

More crucial is the nongeminate recombination, which (as pointed out above) influences the carrier concentration and also its gradient. It is important to understand that the open circuit voltage corresponds to a current free situation, _not_ a field free case. Thus, you certainly can have a finite internal electric field at open circuit. The injection barriers play an important role here. For low injection barriers and thus good injection, the electron injecting contact will determine the carrier concentration at this side (similar for the hole contact): this high concentration is not influenced by recombination! Recombination will of course lower the overall carrier concentration, and due to the boundary condition of injection at the same time the carrier concentration gradients will become steeper. Simultaneously, Voc will be reduced.

It is important to point out that our 2008 paper considered only Braun-Onsager for photogeneration and Langevin recombination for already free charge carriers. The latter was taken into account even for charge carrier mobilities beyond about 1 cm²/Vs, although for high mobilities the finding of charge carriers is not the step limiting the recombination rate any more: Langevin is only valid for low mobility materials. Therefore, check out our 2009 followup paper, also considering surface recombination in addition to bulk recombination: [Wagenpfahl 2009]. Best,

Carsten

I have a doubt regarding this post. You mention that the Voc decreases with increasing mobility because the concentraion gradient of charge carriers increases. I understand why a more steep concentration gradient would lead to a lower Voc. What I do not get is why there is a concentration gradient at Voc (no internal electric field)?

This is what I think about Voc and mobility (after reading some literature):

At low mobilities the probability for polaron pair dissociation is low, so decaying polaron pairs will reduce the quasi-Fermi level splitting. However, a low bimolecular recombination at low mobiliies compensates for this loss, and a high Voc is obtained at low mobilities. As you increase the mobilitiy the polaron pair dissociation process is more efficient, but the bimolecular recombination also increases. The increased bimolecular recombination at high mobility reduces the quasi-Fermi level splitting. Even if the polaron pair dissociation is very efficient at high mobilities, the high bimolecuar recombination outweights it and results in lower quasi-Fermi level splitting and hence a low Voc. Is this correct?

Thanks for the links, and good luck with your grant applications.

-AA

Cheers and greetings to my home area Lower Franconia
Miriam

(1) In polymer (P3HT) : PCBM devices, the geminate recombination of the CT state is the dominant loss mechanism, correct?

(2) Is that recombination radiative or non-radiative? Nobody seems to talk about the possibility of it being non-radiative.

transient photovoltage is on an illuminated (with, say, 1 sun) solar cell under steady state conditions. You set the voltage to the open circuit voltage Voc, current=0. An additional laser pulse will change Voc by a small amount dVoc. Make sure that the laser pulse is small enough so that dVoc << Voc (say, 5%, but depends). The excess charge carriers will recombine until the steady state Voc is reached again. As dVoc is small, the decay is exponential, with an effective lifetime tau which is valid for the illumination intensity, here 1 sun. If you do this experiment for different illumination intensities (corresponding to generation rate G), you get a set of effective lifetimes tau(G). Second step: transient photocurrent or charge extraction experiment to determine the carrier concentration n at Voc for the different G, so that you get n(G). Thus, you now have two sets which you can combine, tau(n(G)), thus tau(n). This corresponds to a recombination rate R=n/tau(n), which is usually not a first order process as tau is not a constant with increasing n. If you compare to the recombination rate written in other terms, , you can find from your above measurement.

The order of decay is a function of temperature. A very good starting point to read about this is [Shuttle 2010]. The authors find that at room temperature, $R(n)=k n^{\lambda+1}\propto \mu(n) n^2$, thus 2nd order bimolecular recombination with a concentration dependent mobility responsible for increasing the recombination order above the expected value of two. However, we think the results need to be generalised if you look at lower temperatures, but that is a bit more complicated. For a first glimpse, you could have a look at these slides of ours, Deibel 2011 nanopv presentation, especially slides 15-18.

Regards, Carsten

Best wishes, Linda

Question about your article Phys Rev B 82 (2010) on the S-shaped current-voltage. You simulate and reproduce the S-shaped curves very nicely by modeling the anode (hole collector, ITO). But, is there any reason why similar results could be obtained for modification of the cathode (electron collector)? For instance, a degraded Aluminum layer or an insulating interfacial layer that is too thick?

I sometimes generate similar S-curves and have been trying to pin-down culprit.

Thanks for your time,
Austin

BTW, do you happen to have an English version of the paper Langevin 1903 (Ann. Chim. Phys. 28, 433)? I want to read the original paper. Thanks.

I was thinking some holes may have multiple choices (path) to choose which electron to “marry” to, which causes overestimate of the current. Do this term account for this or for other reasons? Thanks.

the Koster model is fine, , only the application of the Braun-Onsager part was criticised for the use of polaron pair (geminate) lifetimes on the microsecond instead of the experimentally measured nanosecond scale. Alternatively, you can have a look at [Deibel 2009] and references therein.

Geminate recombination and why it is almost field independent in the fourth I-V quadrant of most solar cells: see previous blogpost on geminate recombination and [Kniepert 2011 ]. Thus, indeed, you can neglect Braun-Onsager for getting started.

Nongeminate recombination and why the Langevin prefactor is reduced, see previous blogpost on nongeminate recombination, or [Deibel 2009] or for an overview my review.

Carsten

You said that “I’d start without Braun-Onsager and concentrate on nongeminate recombination.” did you mean that geminate recombination play a minor role? and the net generation rate is as following: U=G-R ? please sir if you have a buplication speaking about that ,could you let me know??

I apologize for the inconvenience,olso excuse me for my poor english
with my thaks advance

yours sincerly

I thoroughly enjoyed your presentation

Where can I find more information on the large-signal method at open circuit?

Thank you
Regards
Nissy

.

thanks; Carsten (without any title) will do;-) You are right: geminate recombination describes a recombination in which the recombination partners come from the same precurcor state. Consequently: nongeminate recombination, different precursors. The former is for instance recombination of a singlet exciton or a charge transfer exciton, which is first order recombination usually on a time scale of below 1 to 10ns. Nongeminate recombination implies that first two different precursors states need to dissociate to generate free species which then find one other to recombine. Sounds more complicated, also takes longer: usually more than 1 to 10ns, and usually 2nd (or higher) order recombination. I belive this is also explained in my review, in which you might find useful references as well. Best,

Carsten

Your blog is quite helpful! However, I still have a silly question on geminate recombination and nongeminate recombination. What is the difference between the two indeed? I hear that the former involves electron and hole polarons originally from the same exciton while the latter from two different excitons. Is it correct? I am also wondering how you can experimentally recognize these two recombination mechanisms? I read some papers on that but didn’t have a clue. Thanks very much~!

i am graduate student and new to this field. It would be great if you could find some time for giving an insight into the capacitance vs Voltage behavior of Organic bulk Hetero junction Solar Cell eg. P3HT:PCBM). I have a low frequency CV data ( @ 100Hz) from -1.0 Volt to +0.5 volt. But I am confused how to interpret it. How to calculate Built In potential and total defect states in P3HT. what is the physics behind it. Is there any concept of Depletion width in Bulk hetero junction? How can we get a complete picture of Built in voltage and depletion width in organic bulk hetero junction.

Waiting for your response.

Thanks

Joydeep

However, you are probably more interested in finding the maximum of the open circuit voltage. Here, you could determine Voc(T) and extrapolate to 0K, as done in [Vandewal 2010] or [Rauh 2011]. This measurement determines the effective bandgap which goes into the equation for the open circuit voltage [Cheyns 2008]. This equation and the measurements given are directly about the effective bandgap. The actual HOMO(A)-LUMO(D) gap, as determined by the single-particle energies as mentioned above, is actually larger. It was used by [Scharber 2006] as upper limit for Voc (q Voc = HOMO(A)-LUMO(D) – 0.3 eV), but that is rather an empirical relation.

Best, Carsten

With My best Regards

António

Durrant et al are right: for many “good” organic solar cells at room temperature, the charge generation seems to be field independent. The same is seen by Street et al (PRB 2010, do not have the reference at hand). There are not that many studies on this field. We were able to model the photocurrent of P3HT:PCBM solar cells by a charge generation yield of 60% at short circuit and 50% under open circuit conditions, which is also almost field independent [Limpinsel 2010].

Space charge build up happens in low mobility materials in the (dark) injection regime (see my reference in the previous comment in this thread), and sometimes also in the photocurrent [Mihailetchi 2005] [Wagenpfahl 2010]. I do not think that the “charge buildup” seen by the Durrant group is similar, but have not checked their papers again to make sure.

Our phys stat sol RRL was made under the condition that even at high mobilities the recombination occurs with the Langevin recombination rate. This is not a very good assumption, I am sorry to say. Please find a more applicable simulation here [Wagenpfahl 2010a]. In any case, it is difficult to get into this high mobility regime with organic semiconductors. Concerning your studies, more important to Voc are probably the energy of the charge transfer complex (the “effective bandgap” or “maximum Voc”) which is, in view of Voc, reduced by charge carrier recombination. What do you mean with “charge buildup” in view of the linear Voc dependence on light intensity? The term does not quite fit here, it seems to me, more important is the recombination regime (1st order recombination or 2nd order, and even then it depends on the “strength” of the recombination”. Details on request;-) Best, C

Space charge limited currents (SCLC, with Child’s law as the trap-free case) is unrelated to recombination. For details, have a look at [Arkhipov 2001], in which the behaviour is well explained for gaussian DOS. The principle is the same for exponential DOS.

Best, C

Thank you so much for posting so many important terms in your blog, which is really helpful.

I have a question to ask here about the excitons generation due to charge injection. In this page, as well as in your paper (Rep. Prog. Phys. 73 (2010) 096401), you mentioned “Singlet and triplet excitons can also be formed due to interaction following charge injection”. I’m really curious about how this process happens, because it’s very important to understand the carrier transport at equilibrium and steady state.

Thank you so much and look forward to your reply.

Kejia

In the dark, you do have free charges available in an organic semiconductor device, no matter if made of one semiconductor (e.g., LED) or two (a solar cell). Usually, these carriers are not intrinsic, but injected. If you can inject both electrons and holes, you may have a certain fraction of them interacting, generating excitons (singlet excitons and CT singlet excitons for diode and solar cell, respectively). The latter may recombine, also radiatively. This is the basis for organic light emitting diodes, where the resulting emission is significant. For solar cells, you will also have radiative recombination, but that cannot be seen by eye only, you will probably need a good detector;-) This emission is called electroluminescence, as it results from injection, not photoexcitation.

Concerning radiation, I do not think that you will have a (significant) discrepancy between the “thermodynamic” measurement and the photon flux on the solar cell surface. Solar irradiation is based on a distribution of photon energies, thus a spectral distribution, with a certain flux depending on the photon energy. For solar irradiation, black body radiation of 5000K or so works pretty well, therefore your detector does not need to measure every part of the spectral range separately. Best, Carsten

Now we have supp. info. for nearly every paper, I can’t see there being any problem with publishing the review process in full, as a guide to readers. Of course, you don’t need to publish reviewers’ names, but if reviewers are worried their reviews will look bad to the public , then this can only be a positive force for improvement. It’s not the peer review system which is imperfect; only the peers who do the reviews. Also, if the review is published freely, a disagreement between author and reviewer can be left open.. let the readers decide if the reviewer is making a fair criticism or not.

I will definitely try and put my review in the Supp of my next paper.

Kejia

Once again, thank you and have a great 2011.

Regards,
Kim Hai

1 (Voc) The maximum Voc depends on the effective bandgap, which is indeed very close to the LUMO(A)-HOMO(D) gap. This value is reduced by band bending in the bulk as well as the injection barriers. Band bending is proportional to the steady state carrier concentration, which can be increased by photogeneration and decreased by recombination. Thus far, similar to inorganics. A difference is in the answer to

2 (junction): we simulate the bulk heterojunction as an effective medium, as we have a one-dimensional simulation. If you want to approximate the distributed heterojunction, you need at least a 2D simulation. The effective medium approach works pretty well, only thing missing is that for large phase donor-acceptor separation, the local band bending is neglected in our 1D approach. What are we missing with that? The local band bending can partly compensate for effects reducing the Voc. The extreme case is the bilayer solar cell, for which you can increase the injection barriers a lot without decreasing Voc… the latter is compensated by the band bending at the planar D-A heterojunction. In large phase separated bulk heterojunctions, this effect will be weaker, and therefore we do not consider it.

3 (concentration): the organics we work with are usually semiconductors or even insulators. Mostly, everything can be well described if you consider zero doping. Thus charges come from injection (thermionic emission model with maybe 0.1eV injection barriers or so at anode and cathode) and photogeneration (generation rate of around . So, open for discussion:-)

Best, Carsten

I have three questions about your electrical modeling of organic solar cells (OSCs). Hope those won’t bother you.

1. According to most papers of OSCs, the Voc just depends on the difference of LUMO(acceptor) and HOMO(donor). But based on my modeling experience of “inorganic” solar cells, the Voc will depend on the “band barriers” of conduction band and valence band for heterojunction. Although the bimolecular recombination also controls the point of Voc, the band barrier still dominates.

Would you please make some comments on that difference of Voc mechanism between inorganic and organic solar cells.

For OPV:
Band barrier for conduction band: LUMO(donor)-LUMO(acceptor)
Band Barrier for valence band: HOMO(acceptor)-HOMO(donor)

2. In your simulation, do you consider the heterojunction effects? Or just simplify your model into “HOMOJUNCTION” with effective materials?

3. Do you have to set the carrier concentration of donor(p-type) and acceptor(n-type)? Would you please give me rough numbers as reference?

I really appreciate you spend much time establishing this fruitful discussion panel, which helps me fast broaden my organic material knowledge.

In fact, even though I’m interested in electrical working mechanism of organic solar cells, I can’t learn those knowledge efficiently since our group is focusing on nanostrcuture fabrication for “inorganic” solar cells.
(http://www.ieo.nctu.edu.tw/gpl/mainForEnglish.php)I hope you don’t mind putting the link here.:P

Anyway, really thanks for your kind patience.
(p.s. I also think the bimolecular recombination dominate the recombination mechanisms in OSC system, since inorganic solar cells have similar properties.)

Mark

I am just curious how large those deviations could be? I mean the values of

Of course your question was more precise and deserves a better answer than that! CIGS is nice, and I hope it will gain market share. Its two only severe problems I see are (1) the complex material combination with four to five elements (in addition to Cu, In, Ga, Se also often sulfur, and Na also having an important role) in the active layer. And (2), in comparison to organic solar cells, it needs higher processing temperatures (e.g., sputtering and rapid thermal annealing, maybe at 550 degree C), but can even be printed.

Polymer-fullerene solar cells or organics in general are in my opinion not thought as replacement for the more established inorganic solar cell technologies. However, they can be printed at high speed at room temperature, suitable for mass production, and thus have the potential to be processed more cheaply. Also, if required, the colour of the active layer can be adjusted – which is rather a niche market, but as I said, it is not thought to replace other technologies. Last not least, the chemistry and physics involved are very interesting from a fundamental point of view (which is, incidentally, my point of view;-)

Best, C

Best Robert

Your question concerning the last equation is a bit unclear to me. The last equation is , thus the recombination rate is proportional to Langevin recombination strength times electron density times hole density.

Best, C

I have a few questions. Calculating the Langevin recombination strength we assume that the hole is moving in an electric field equal to that generated by two point charges seperated by Coulumb radius? Why? I realise if they don’t get within Coulumb radius then thermal energy is sufficient to escape recombination and if they do get within Coulumb radius then they recombine. Is that so? Could you clarify this point to me, thank you
And in the last formula why is the recombination proportional to langevin recombination strength times electron density n? Why not n^2? I realise it should depend on both carrier densities but why a simple multiplication?

thank you

I have done my bachelor on C60/CuPc solar cells. I’ll keep reading this blog!

My advice for getting your work published in a high impact journal, build your networks, if your peers know your name, I think it makes a big difference.

Thanks for the post. If you haven’t seen it already, you may be interested in the following paper: J. Materials Chemistry (2009), 19, 4609.

They deposit P3HT onto ZnO and SAM-modified ZnO and find that the crystallinity of P3HT in proximity to the ZnO layer is changed dramatically, and they argue that the recombination dynamics are modified accordingly. I only just glanced at it, but it seems these findings support the conclusions of your earlier simulations. Hope all is well.

-AA

Concerning monomolecular recombination, is indeed only an approximation. I believe that I explained this somewhere, but did not find it just yet. Your suggestion is in principal the way to go, but is not that easily defined. Should equilibrium carriers not be able to recombine? Equilibrium actually included recombination. So, no … Thinking about it, charge carriers always need some recombination partner, therefore a recombination of only electrons or holes by themselves is not possible AFAIK. Consequently, there is no monomolecular bulk recombination for free charge carriers, only for excitons, CT complexes etc. We use this simplification only to show the consequences on the device characteristics, even if physically not existant;-)

Looking forward to see you around! C

I’m a graduate student and now doing some research on the free polaron lifetime of bulk heterojunction solar cell. You blog helps a lot for me.

Regarding the continuity equation, I think the monomolecular recombination rate should be (n-n0)/tao, where n0 is the negative polaron’s density at the equilibrium condition and tao is the lifetime of negative polaron. What do you think?

Thank you for letting me know that it has a term of 1/q*(dJ/dx). What about the Eq. 14 in the reference PHYSICAL REVIEW B 80, 075203
2009? Is it a typo?

Thank you.

For bimolecular recombination (BR), the photocurrent curves coincide for “normal conditions”, i.e. 1 sun or less illumination (although slight deviations are already seen) and typical recombination conditions. For higher illumination densities or thicker cells, the photocurrent will show the bimolecular signature more clearly — in case BR is the loss mechanism — and the Hecht equation as given by Street et al cannot be fitted to the data any more. For 1st order recombination, whatever the reason, and also for no or weak recombination of any kind, the slope d(ln(Jph))/d(ln(Plight)) is always one.

If you consider instead the voltage dependence, for 1st order recombination the Hecht equation seems pretty capable of fitting the photocurrent (but you can also fit it to cases where the recombination is low — any type — or off; just mu tau does not have any real meaning then). For sufficiently low recombination, the extraction length d_c > film thickness d will usually imply that almost all charges are extracted. Thus, indeed, dJ/dV will be zero at short circuit – if the polaron pair dissociation is not (or only weakly) voltage dependent, and there is no minor shunt in the device. The latter is certainly unlikely. The former is a first order process, but it is a geminate recombination: certainly possible.

So what to make of this? Let’s wrap up. The light intensity dependence shows slope 1, but that does not mean much under the measurement conditions (< 0.3 suns, thin devices). dJ/dV is certainly nonzero, which is the sign for recombination (or shunt), but does not tell us whether that is 1st order or second order nongeminate recombination, or even geminate recombination. Again, you cannot tell just from the photocurrent curves alone.

Concerning my comment: my point was just to show that the steady state techniques used by Street et al. do not make it easy to distinguish between 1st order and second order recombination under the measurement conditions used. Instead, I was taking up the cudgels on behalf of transient techniques;-) My point was not to rule out 1st order recombination for the material system studied. With PCPDTBT-based devices, I do not have much experience. I do not believe that there will be monomolecular nongeminate recombination, I do believe there will be bimolecular recombination, but I do not know (in contrast, for P3HT:PCBM I do know that BR is dominant!). I am just pretty sure that different measurement techniques should be used to investigate the recombination mechanism.

HTH. Carsten

I have read almost all of your archives about BHJ organic solar cells and I found it is so helpful (from your discussion on the archives, I have learned something i am not able to acquire from papers:) )..

I have a question: you question Street’s paper by simulaiton first figure in this achieve. From your simulaiton, it is clear that even for bimolecular recombination, all curve concide.

I am wondering, is that because at short circuit, dJ/dV=0, which means around short circuit, I-V curve is flat. Therefore, at Isc, extraction is sufficient (n,p in the device is very small) and recombinaiton, whatever bimolecular or monomolecular, is neglegible. The slope is 1 between log(Jph) and log( I) because no recombination, only extraction and extraction is monomolecular form. I am wondering, if dJ/dv is not zero at Isc (at short circuit, extraction is not so efficient), there will be recombination and Street’s claim in PRB 2010 could be right.

Your curiosity was very close, although I am not in the Bittner Group, I am an Irish graduate student based in Houston doing some work on organic solar cells.

Thanks again,

Nigel

[Kurrle 2008] Determination of exciton diffusion length on an organic crystal. Better even is to combine this method with an optical model (transfer matrix algorithm or so)

[Ineverwantedtobeasciencistiwantedtobealumberjack 2010] 27nm for P3HT, wow, probably only possible for the optimised synthesis routes, because earlier measurements gave much lower values, such as 8nm in [Shaw 2008]. If not for a long exciton diffusion length, however, Alex would not have had success with his solution processed bilayer [Ayzner 2009]. Regards, C

P.S. from Bittner group? only temporarily? Forgive my (potential) indiscretion, just curiosity;)

How do you measure the exciton diffusion length and what is theoretical basis for such a measurement?

Concerning the reduced prefactor: indeed, 1d simulation implies an effective medium without real world morphology. The latter, i.e. donor-acceptor phase separation will certainly influence the recombination prefactor.

Two other factors are carrier concentration gradients [Deibel 2009] (already mentioned in the post), which is present even in 1d, and the temperature dependence of mobility and polaron pair lifetime [Hilczer 2010]. A nice mix of all three will be pretty close to reality. Unfortunately, all these contributions are not that easily accessible.

In my opinion the reduced prefactor of bimolecular recombination may originate from the 1D modeling. It will be interesting to compare the reduced prefactor of 1D version of drift-diffusion model to the 3D one.

Shuttle [Shuttle 2008] and also we [Foertig 2009] have published recombination with order of decay larger than two, and explain this by bimolecular recombination (order two) plus trapped charges. If the latter do not actively participate much in the recombination process with the mobile charges, they are detrapped at some point during the measurement and extracted. Therefore, this is not recombination via traps as intermediate states I disussed before.

With band-to-band, a term used for crystalline inorganics, I mean direct recombination of mobile carriers.

Never mind asking questions! Now, concerning the drinks…

Apologies for the stupid chemist questions. I’d really love to ply a few people from your side of the field with drinks until they explain things in more accessible terms, but I haven’t found anyone suitable yet.

First, let me point out that I use the term monomolecular recombination as in first order charge carrier decay, where the recombination rate is proportional to either electron or hole. Similarly, I consider bimolecular recombination to be proportional to the product of electron and hole concentration.

Monomolecular recombination (MR) “=” geminate recombination (GR) is almost right, but not quite… Indeed, GR is monomolecular, but MR is not necessarily geminate. Recombination of a free, mobile electron with a trapped hole can be an example for nongeminate recombination which is monomolecular (actually, the latter is similar to SRH recombination… have to consider this at some point more carefully!)

Shockley-Read-Hall recombination (SRH) is to my knowledge typically found in inorganic crystalline semiconductors (where, just as an additional note, the term (non)geminate loses its importance). In contrast to (bimolecular) band-band recombination or (bimolecular) Langevin recombination, SRH is recombination via an energy level due to impurity or defect. The rate of SRH is generally ; thus, although it depends on the product of electron and hole concentration, it is practically monomolecular (see details here and elsewhere, or keep up the discussion;-)

Concerning Cheyns, I also believe that SRH is very questionable in our disordered organic systems (despite the fact that I am coathour of that – otherwise nice – paper

I would be very interested to see your simulated Voc vs. log intensity plots. That is where I’ve seen interesting behavior in the past in direct disagreement with the work of Blom and company from either 2005 or 2003. I think you may have mentioned their work in your MRS talk. In any case, I’m guessing you may be writing that work up so any time after you guys submit would be great. =)

Cheyns, et. al., whom I know for a fact you mentioned in your talk, predicted a slope change in Voc vs. log intensity depending on whether bimolecular or Shockley-Hall-Read recombination was dominant. By the way, I am of the opinion that it should be debated whether the SHR model can be applied to disordered semiconductors with potentially no mobility edge and hence no extended states at all (unless we’re talking crystalline P3HT, etc.). Anyway, I would also be very interested to see the results of yours guys’ simulations of how the Voc vs. log intensity response changes as you vary the relative contributions of the two recombination processes.

That’s my two cents. Thanks again for sharing your thoughts.

Firstly, thank you for your blog! I’m finding it very useful as I’ve just started a PhD in organic solar cells.

I have a question on exciton-types. Hopefully you might be able to shed some light on my confusion. I’m looking at systems in which Frenkel and Charge-Transfer exctions have been found but I’m trying to get my head round exactly what a CT exciton is. In my (maybe simplified view) it was simply an exciton created when the electron from one material (e.g. polymer) was promoted to (close to) the LUMO level of another material (e.g. fullerene). The article below mentions them but in context of CT states being filled by Frenkel excitons.

With regards to your diagram would the CT exciton be equivalent to the polaron pair? I presumed it wasn’t or else they’d call it a polaron! It is definitely something shared between materials and no on one molecule so it isn’t an exciplex. Can the polaron pair be generated directly by light absorption?

http://www3.interscience.wiley.com/cgi-bin/fulltext/122630062/PDFSTART

If you can clarify this at all I’ll be very grateful!

Jenna

-Alex

I have never investigated hybrids myself, and have only limited insight. If you look at the systems around, it seems to me that charge transfer itself works… at least for the hybrids with beyond 2% efficiency;-) The open circuit voltage is sometimes better than for polymer:fullerene systems. Taking one example, CdSe/APFO-3, which had a short circuit current density of 7.2 mA/cm² (EQE 40%) and an open circuit voltage of almost 1 V… [Wang 2006]. Everything is ok, even PL quenching, only the fill factor is a bit low. Therefore, I believe in the morphology as major reason. (What I do not know, though, is how unbalanced the electron and hole mobilities are…) The question is, can it be better controlled, or can modification of either donor or functionalisation of the inorganic help in optimising it? To me, there is no fundamental reason that hybrids should not be beyond 5%!

Greetings to Paul, and good luck;-) and success to you!

nb:I really like your blog, keep it up, It’s open my eyes, ,
I found that you were working in IMEC with Prof. Paul Heremans, He will become my co-promotor for my PhD at KUL.

I am not sure if I will be attending or not, hopefully I will go though. I will look out for you if I do go!

Thanks for giving us a forum to have these discussions.

I believe the spikes in the PL spectrum from the Adv. Funct. Materials paper are only observed at the high fullerene loading and are in fact due to PCBM emission. I apologize, but I will have to embark on a completely thorough CTE literature exploration at some later time, so I can’t directly comment at the moment on the JACS paper you referred to.

In terms of the fullerene energy levels, yes it’s very possible that the bulk HOMO level for PCBM is around 6.1 eV. But presumably the transition from interfacial energetics to the bulk is continuous, so I guess I don’t see it as that troubling that once the barrier is lowered and the applied bias high enough, one could achieve SCL currents. At the same time, I would not call an interface with any significant barrier Ohmic by definition. Again, that doesn’t mean injection from gold to C60 requires overcoming a barrier because once the two interfaces are brought into contact, I believe that the nominal barriers calculated from UPS-type measurements are simply not applicable to the states that emerge due to the interaction between the two layers. Check out this one out of a gazillion papers on the subject: http://pubs.acs.org/doi/abs/10.1021/la981114f

You have some good comments, I relish the challenge. Yes I asked for PL, but I asked for PL to match the EL, preferably all from the same group in the same paper. In any case the PL from the Adv. Funct. Mater. paper for MDMOPPV:PCBM doesnt seem to match the PL from MDMOPPV:PCBM in the JACS paper. In the Adv.Funct. Mater. paper the supposedly CT peak is at 1.35-1.40 eV (885 -915 nm) while the CT peak in the JACS paper is 960-970 nm. I don’t think that the shape of the emission is similar neither. You may think that 50 nm is only a small shift but really given the precision of the equipment it makes you doubt. (Given the similar loadings of PCBM – it cannot be ascribed to any red-shift)

There is a similar story in the RR-P3HT:PCBM CT state emission, in JACS the peak is at 1200 nm while in Adv.Funct.Mater the peak is at 1000 nm??? ( data is unclear here – anyway its not at 1200 nm). Another question is why JACS dont mention a problem in seeing P3HT:PCBM CT while Adv.Funct.Mat. say it is difficult to see.

Inconsistency in reports of CT is one reason why I find it hard to believe.

You asked about why CT emission should not shift with PCBM concentration. These are soft materials and prefer to localise charges, relaxing their electornic structure and shape. For a neighbouring molecule to begin to distort a CT state it would have to be able to offer greater stabilisation for the polaron first and then secondly it would have to offer enough stabilisation to offset the decrease in coulombic attraction that would happen when you move the charges become further apart on average. Given the large binding energy in these soft materials (say 0.5 eV) and the weak interaction between fullerene molecule in the crystal I doubt that neighbouring fullerenes have an influence (although I wouldn’t bet my house on that). I would say that the physical spread in distances between hole and electron is more likely to control the emission energy. Which bring us nicely to the next point, as CT emission is typically so broad and featureless, why does CT emission in Adv.Funct.Mater. seem to have fine structure. If you look at Fig.2 the emission clearly has spikes? shoulders which is not like CT emission at all, and is more like emission seem from a rigid molecule, like for instance fullerene.

You asked about the intensity of the CT emission versus intensity of PCBM emission, the answer is the authors know because they measured them both. They dont tell us so as a sceptic I assume they are similar and so didn’t provide any additional evidence either way. Anyway I doubt if PCBM emission is negligible, I can measure it here on an old RT fluorimeter (although I must admit it doesnt look as clear as that.)

Regiorandom versus regioregular , I would say that the regioregular data is so unclear that it is almost worthless. If you stare at that data for long enough you will see anything you want. Furthermore the JACS paper doesnt seem to be having a problem seeing P3HT:PCBM CT emission, although of course they see it at a different wavelength.

You asked about peak shifts as a function of polymer, there is little evidence for any peak shift in the Adv.Funct.Mater paper (at least negligible to what the see in the JACS paper).

You asked about organic-metal interfaces. I agree who knows what goes on at those kind of interfaces, and most knowledge at this point is only speculation. Personally I think the first layer of organic on a metal undergoes a CT reaction and basically is changed. Whether that first layer can then distort the second layer however is more difficult. The point is that while the interface between metal-organic is probably doped, the bulk property of C60 at 6.1eV remains unchanged. How does a metal-organic electrode shift holes into that at space charge limited current? Or more potently, if 1 eV barrier is not a problem for getting ohmic contacts with organics then why do we see evidence for this in the literature. I have only a casual interest in metal organic interfaces however so I don’t know much.

First, with your permission let me ask you a couple of questions about some of the points you brought up in your earlier discussion with deibel. You mentioned that one would expect a CT band to not shift with PCBM concentration. I don’t see this as that obvious, because one could easily imagine that the polarization that a charge experiences at a polymer-fullerene interface may be different if you have one or two fullerene molecules participating in the complex, especially if they have polar sidechains. Also, what is so peculiar about having a CTE state between polymer and a nanoscale aggregate of PCBM, which could have a modified band structure and thus a shifted CT band?

Now on to your criticisms of the paper I suggested. You say that what lets you dismiss the authors is that Fig. 2 shows PCBM emission in the red. While this is
certainly true, keep in mind that fullerene emission has a very small quantum yield, so to see PCBM emission takes a sizable amount of fullerene. I personally think it’s very hard to reconcile the intensity of what they assign to CTE emission (relative to the albeit significantly quenched MDMO-PPV PL) with the very low quantum yield of PCBM at the relatively low 20% PCBM weight ratio.

Next comes the question of regiorandom vs. regioregular P3HT CTE emission. If you claim the red emission is due to the in-gap PCBM defect state, then why would the intensity of this emission be so sensisitve to the polymer self-organization? To me, to explain that you have to invoke some interaction between this defect state that you say is intrinsic to PCBM and the polymer. In that case, this rogue state isn’t as native to the fullerene as you suggest and might itself give rise to new polymer-fullerene CTE-type states. These authors also observe a shift in the “CTE” emission that at least goes in the right direction upon going from a PPV to a polythiophene. Again, why would the energy of the defect emission be so sensitive to the polymer if it’s intrinsic to the fullerene? I will grant you that the authors could have done better in terms of control samples. I would have loved to have seen PL of PCBM in an inert PMMA or polystyrene-type matrix as a function of fullerene loading to isolate the effects of PCBM emission.

Finally, your statement that C60 can be used as a hole-transporting material in conjuction with gold does not necessitate invoking the existance of a mid-gap state. The energy levels that you quote were measured in ultrahigh vacuum conditions, and the penetration depth in those experiments isn’t that large so the 6.1 eV number measured for the top several layers in contact with vacuum may not at all be representative of the energetics at the buried fullerene-metal interface, with its own charge-transfer processes. Similarly, the workfunction of gold is likely no longer 5 eV when in contact with one or more fullerene layers.

Further criticism, although I don’t think its relevant to the data. They measured the PL spectra in air. Why didn’t they realise that any defect emission could obscure there desired signal, why test in air?? Also if they are using the lamp, why didn’t they provide us with an excitation spectra for the emission? (preferably for different emission wavelengths as well).

You are right in that the midbandgap states could be coming from the sidechain but actually I see plenty of evidence that C60 also has midbandgap states. Take for instance that C60 will form an ohmic contact with metal such as gold. Workfunction of gold is 5.0eV , while the HOMO of C60 is 6.1 eV. Thats a big difference over which to form an ohmic contact unless of course there is a midgap state with which to push electrons into/out of. Plus researchers now in OLED are starting to use C60 as a HOLE injecting material because its so good.

Here is another recent paper on CT excitons that after a quick scan I think deibel might have missed (forgive me if I’m wrong): Adv. Funct. Mater. 2009, 19, 1–7. It is all about the emission band that’s red of the emission of the individual components, and it arises only in the blend. Here, I believe you’d be hard-pressed to argue that the effective interfacial area over which one expects to observe CT exciton states is small.

Your ideas about defect states being intrinsic to fullerenes are certainly interesting. PCBM has been shown to assume a weakly H-bonded motif through the ester groups when assembled as a monolayer on a (cold!) Cu surface. While this is far from the spin-coated BHJ conditions, it at least suggests that there could be aggregates of PCBM with varying degrees of these sidechain interactions, which could lead to differing degrees of local polarization and thus site energies for the various nanocrystallites. I’ve yet to see anyone take these thoughts any further.

Yes I think the red-edge to IPCE spectra comes from PCBM. I cant really explain it well here more than I have above, did you have some specific question in mind? If you look in the literature you will see parallels with C60, and there is a lot more data there on c60 than PCBM. The nature of the midbandgap states in fullerene , I have no idea (C60 and PCBM both show the same evidence for midbandgap states). It could be intercalated compounds or gases in the C60 crystal (that add their electrons), it could be intercalated compounds in the bucky ball, it could be C60 polymerised defects, or least likely it could be natural for C60 to have midbandgap states. I want to say that it is somekind of intercalated compounds, because otherwise the energy models for C60 will all be wrong, but I have a horrible sinking feeling that it is natural.

CT states are fairly common, I agree but we should be careful about the degree of charge transfer. I did not know that CT states were common at organic organic interfaces, how can you eaily measure something which is only one layer thick?

Anyway the evidence I want to see is easy to get. I would like to see the EL data shown in the papers mentioned above repeated with PL measurements. There should be no difficulty in doing so, under the current given explanation, right?

To deibel, I’ve finally signed up for an account, but I’ve been reading your blog that I’d accidentally discovered for some time now. Just wanted to let you know that I’ve really enjoyed your posts.

I have just read the papers you mentioned. It seems the story to CTC states has changed a little since I remember, or at least for these papers. Now there is no longer need to find CT absorption as now we are more interested in CT emission (Tvingstedt JACS 2008) as CT emission is all that is important and radiative recombination decay is the principal recombination mechanism that controls Voc.

Or is it actually? The Nat.Mater paper closes by saying ‘Therefore to improve Voc, the exact origin of these non-radiative recombination pathways should be investigated.’ So in other words , the radiative recombination doesn’t mean much at all as there are other recombination pathways. So in fact it is likely that
non-radiative recombination controls Voc which in turn controls the CT emission. Not the other way around.

Even this last part, that Voc controls CT emission is an open question. Why is the CT emission band higher in energy than the Voc of the device? Assuming some exciton binding for hole and electron, the emission should be at lower energy than that required to push the initial charges into the device (Voc). I believe its true for OLED’s, can’t get blue emission out of a device which has only a 2 eV bias across it!? Could it be that this CT emission is actually coming out of defects. (e.g photochemically bound polymer and fullerene), hence the higher emission energy than expected and the need for a larger driving force. Defects could be discounted if PL could be seen matching the EL, as then the electrons and hole recombination would be occuring at the same site as photo-induced charge carrier generation. With just EL we could be looking at voltage driving current to unusual places that are not a D-A junction. Defect emission and Voc could be related because one half of the defect is the polymer and has a changing HOMO.

I may not be making sense because I just had a cup of strong coffee and I have the jitters but basically I don’t see the significance of these findings. CT absorption is probably from PCBM and weak emission could be from anything. There is a correlation true but it doesn’t tell you what controls what.

Anyway I will be staying well clear of any discussion of CT states in my papers. I only pray that reviewers leave me in peace to do my work. My idea with PCBM is interesting but its main focus is not CT states , its why you can’t make a good organic solar cell using a polymer with a HOMO higher than 5.3 eV. This is experimentally validated but nobody knows yet why this is and I think I know. It is purely a thought experiment (there is enough literature evidence) and would be happy to publish it on your blog as an exclusive! Ha ha.

Even from the data shown, if I make a linear superposition of P3HT and PCBM single phase data shown in Fig. 1, and compare it to the blend data, I see that the low energy part in the blend is a new feature. Actually, the results from electroluminescence are similar (Tvingstedt, JACS 2008 and Vandewal, Nature Materials 2009). As a CT state is a hybrid, the donor-acceptor properties have an influence. For instance, the constant dielectric of the blend is increased when raising the PCBM fraction, as PCBM has epsilon of about 4 and P3HT of only 3.5 or so. Thus, changed screening, changed CT binding energy, changed CT energy.

Nevertheless, I hear your criticism loud and clear… Maybe you should finally write a paper about it;-) Most people (indeed, including myself) are pretty convinced of the CT story, at the latest since the above mentioned Nat Mater in which CT EQE, CT emission and injection current to drive the emission are used to predict the open circuit voltage! The latter is based on the Shockley–Queisser detailed balance limit, adapted 2007 by Rau (Phys Rev B). I reckon your controversial view will raise the interest in your paper-to-be;-)

Figure 4 and Figure 5, the tail in EQE down to low wavelengths just seems to correlate to how efficient the device is, with a more efficient device showing higher EQE at long wavelengths, which is not surprising. Unfortunately they cannot deconvolute absorption out of the EQE directly and so it is very feasible that all blends have the same absorption but that they only see heightened EQE at low wavelengths for the best devices. An equally likely explanation to the one they give is that PCBM is absorbing down to 1 eV in all devices and that how high the EQE gets depends on how good the device is.

Figure 6 they anneal the films causing PCBM crystallisation heightening its absorption in the region around 1 eV causing the observed change (note the absorption comes from the PCBM aggregate and not the molecule, molecule band gap is fixed at 1.7 eV).

Figure 7 increasing PCBM content causes more PCBM aggregates but also again, the more efficient device would show greater EQE at the long wavelength region. The explanation for this effect in the paper is particularly weak. How exactly is adding more PCBM meant to shift a CT state energy? A CT state is an interaction between one molecule and the next. Adding a higher concentration of one component should not shift the CT absorption band. If adding more PCBM shifts the PCBM LUMO, then suddenly we have a CT state between one polymer and a PCBM aggregate?

I have seen similar evidence like this elsewhere also for reports on absorption but the underlying factor in all of this is the PCBM; no-one yet is to show CT state evidence that goes lower than 1 eV beyond the tail of absorption in PCBM, and all this despite the fact that below 1eV is where we all expect the CT absorption to be. The energy of the CT state in PPV:PCBM should be 0.8eV and P3HT:PCBM at 0.6eV the same as the device voltage (HOMO donor-LUMO acceptor gap) but in this paper they dont even look there which is weird.

Furthermore they overlook the fact that the CT states could be coming from anything else but PCBM and MDMOPPV. The CT absorption is only weak, the absorption could be coming from an PPV defect complexing to a PCBM defect, nothing to do with PCBM and polymer at all.

Moving back to the point of why I think there is no CT interaction between , say, PCBM and P3HT, is because, if there was some CT character, then recombination of charges across the PCBM-P3HT heterojunction should give rise to CT emission. We can detect single photons of emission however to my knowledge no one has reported seeing emission from P3HT-PCBM at the expected CT wavelength of around 0.6 eV. If there is no emission (even accounting for non-radiative decay losses) there likewise can be no absorption, as absorption and emission are linked by the Einstein relation. Hence although I cannot rule out any CT absorption (anything is possible with defects etc) I doubt that it plays any significant role in the device operation.

I have seen lots of papers to date on CT states between a polymer and PCBM, however most of these reports have weaknesses. One common weakness is that it is not well known that PCBM shows absorption down as low as around 1 eV because it has midbandgap states. As an example, if you look at the IPCE spectra of a P3HT:PCBM device you will see photogenerated current (albeit small) for wavelengths down to around 900 nm. I see it at least a few times a week. That is from absorption in the PCBM. These midbandgap states are very important to the properties of fullerene however I havent had time to write up any of my ideas.

Anyway sorry for talking your ear off – congratulations on your grants!

Thanks

If you are interested I did my thesis on charge recombination in polymer-fullerene solar cells monitored using pump -probe transient absorption spectroscopy. The data is unpublished as of yet but you are welcome to look at it.

http://www.lulu.com/content/375725
(download is free)

Skip straight to chapter 3 on recombination in P3HT:PCBM. Not sure the other chapters will interest you much however.

Voc drops with higher mobility, as the charge extraction becomes more and more efficient. This means that in steady state, e.g., holes at the cathode have very low concentrations, but high concentrations at the anode (which is hole injecting). This steep gradient concentration translates into a strongly bent band due to the Poisson equation. In a steep band, however, the quasi-Fermi levels cannot be splitted very far (see Fig. 4(c) in [Deibel 2008a]). Therefore, the higher the mobility, the lower the Voc. However, as mentioned in the post already, this was calculated for ideal charge extraction. The Voc will decrease less (but still will decrease) when the extraction is more realistic.

Very brief (and incomplete;-) explanation for why the fill factor peaks: for the extreme cases, low mobility and high mobility, respectively, you have either zero voltage or zero current. Both mean zero fill factor. The maximum is inbetween.

Thickness: higher thickness means higher absorption (mor excitons) and lower internal field (less polaron pair dissociation). This means that there is an optimum thickness… which is a trade-off once again;-) This does change some values, but not the general behaviour of efficiency vs mobility.

Concerning polaron recombination, indeed mobility alone does not determine it in a two-phase system. However, there is no single model to explain the experimental recombination rates right now. We use a prefactor (zeta) which “manually”, but in accordance with experiment, reduces the Langevin recombination rate. Part of zeta’s origin might be due to the D-A interface. Another part certainly is energetic (and spatial) disorder: Langevin just considered a continuum, no hopping system. This or that way, our macroscopic model considers a blend as a single effective, ambipolar material, with a linear correction for the Langevin recombination.

If you have more information on recombination, I’d be glad to hear it.

Why does the fill factor peak?

How does this change with thickness? You know if devices could be thicker then a lot more light could be absorbed.

Personally I have seen evidence that charge recombination is not mobility controlled but instead D-A interface surface area limited. Does your model account for that possibility?

Thanks for the blog, I never thought such a blog could exist and now its my favourite read.