Report from August 18: Disorder and Aggregation in Polymer Films

Ben Hoffman, a student in my group, reported Monday on a Nature Materials article (link here, subscription required) that combines optical spectroscopy, carrier mobility, and X-ray diffraction measurements to help understand how strongly disordered polymer films transport charge.

I consider disorder to be the most intellectually interesting aspect of organic electronics so having this paper presented was high on my list of priorities for the journal club.  In almost any organic film, relatively weak intermolecular interactions lead to a low energetic cost for creating defects, polymorphs, etc.  In the extreme case, organic solids may be essentially amorphous glasses.  However, even in the case where materials are semicrystalline (or have semicrystalline regions) disorder is crucial to consider for modeling charge transport.  Seminal work by Bassler showed how it can impact the electric field and temperature dependence of carrier mobility.  Noriega and Salleo, two authors of the paper from Monday,  have a pretty good book chapter on these topics in chapter 3 here.  In addition, a longer review aimed at a theoretical audience is given by Tessler.  Baldo and Forrest and later Burin and Ratner illustrated important impacts of disorder on charge injection at contacts.

 The paper presented this week touches on most of the important concepts relating to disorder in solids.  This includes the idea (that I love) that a simple 1D tight binding model can be used as an insightful tool to study disordered solids.  If you allow the tight binding matrix elements to be random, you recover important results such as eigenvector localization and "gap states" as shown for a specific case in Figure 3 of the paper.

This paper introduced me to the concept of "paracrystallinity" (compare with paramagnetism).  This is essentially a measure of the statistical spread in lattice spacings in a disordered solid.  For example, on a 1D lattice, if the site spacings are pulled from a Gaussian statistical distribution with mean a and standard deviation s, then the paracrystallinity is s/a (see work from some of the same authors in ref 32).

Overview:
The motivation for this paper is a set of recent observations indicating that even strongly disordered polymeric solids can have quite high field effect mobilities (1cm2/Vs or larger).  How can this be since strong disorder is known to lead to "localized" wave functions that don't transport charge very well?  This is mysterious enough that Nature Materials published a perspective article accompanying the paper that Ben presented this week.

The answer, supported in part by the paper Ben presented, may be that transport is dominated by charge motion along the polymer backbone.  Polymer materials with high molecular weight are strongly disordered but have lots of long backbones for good transport.  This invokes the usual picture of conjugated polymers as "molecular wires".


Methods:
The paper begins with an optical and optoelectronic study of mixtures of pre-aggregated regioregular  P3HT with regiorandom P3HT.  Particular attention is paid to electroluminescence spectroscopy since this measurement requires the motion of polarons injected electrically from contacts (i.e. like an OLED) which then recombine to give off light.

It then illustrates a tight-binding calculation for paracrystalline pi stacks of P3HT.  This consists of diagonalizing a fairly large random matrix and evaluating the statistical distribution of eigenvalues and eigenvector decay lengths.  It uses DFT results as input for the tight-binding matrix elements. (this is the downside of tight-binding: you need additional inputs from either experiment or first-principles theory to get any numbers out).

Finally, the paper uses a somewhat non-standard (but internally validated) method of extracting paracrystallinity from diffraction peak widths.  This sounds trivial but is really the bane of diffraction people studying organics.  It is really hard to deconvolve intrinsic disorder from domain size effects, as I understand it.  Typically one uses higher order diffraction peaks, but this is not always possible with polymer films so the authors had to do something slightly different.  I do not understand this and have not yet had the motivation to work at it.

Results:
The paper opens with a stunning result:  In a blend that is 90% disordered P3HT and 10 % aggregated P3HT electroluminescence ONLY occurs from the aggregated material at low currents (~ 1mA).  A weak electroluminesence from the disordered matrix occurs only at large currents.  By contrast, photoluminesence occurs from all of the regions.

I have the following view of what happens, which I admit was hard to extract directly from the paper:  We see in Figure 1a that EL from neat RRa  films occurs even at the low current of 1 mA.  To explain Figure 1b (90:10 RRa:RR mixture) we have to say that transfer from RRa to RR is quite efficient, but that when it happens the recombination rate in RR is high enough that most emission occurs from there.  (i.e. charges are more likely to recombine that to go back to the RRa domain - this is the barrier to charges moving back to RRa that the paper mentions).

Next the paper moves on to apply the well-known (see Ch. 11 of Plischke and Bergerson) 1D disordered tight binding model to the case of P3HT pi stacks.  They show that the usual results of strongly localized gap states are obtained for values of paracrystallinity approaching 10%, implying essentially amorphous material.

The final results are a new study of different P3HT films and an extensive survey of the polymer electronics literature that correlates disorder (extracted from WAXS line shapes) with molecular weight (MW) and also carrier mobility with molecular weight.  Both paracrystallinity and mobility start to saturate at about the same MW.  This suggests a dominant role for long conjugated chains in providing electrical connections across a polymer device.

Nevertheless, the penultimate section of the paper is called "paracrystallinity governs charge transport".  How do we reconcile this with Figure 4 where the causal variable seems to be MW ?  I think this section is pointing out that disorder and paracrystallinity still plays a significant role in determining activation barriers to charge migration.  It is still clear, despite this caveat,that the key to good mobility in dosordered materials is the necessity of long conjugated chains to interconnect aggregates across the film.  The barrier part is relatively minor in comparison.

I happen to be very interested in small molecules and the authors include one case (TIPS-pentacene) in their survey of paracrystallinity to show that a "monomeric" film has small paracrystallinity. It is important to note that this material has a field effect mobility of more than 1cm^2/Vs in solution-cast FET's.  This is far from the mobility trend for polymers in Figure 4.  The whole mechanism of backbone transport is NOT operative for such a material and so the picture encoded in the correlations in Figure 4 doesn't capture much about transport in small molecules, as far as I can tell.

Conclusions:

The paper concludes that high molecular weight polymers exhibit increased disorder, but also increased carrier mobility.  This is attributed to very mobile transport along conjugated chains.  An important by-product of this conclusion is that pi stacking is NOT necessarily the crucial determining factor in charge carrier mobility for polymer films.  One can have very good mobilities with very poor pi stacking if transport along polymer backbones is efficient.  The authors are careful to remark that " no single microsctructural feature is entirely responsible for electronic performance".  However, I consider the diminished impact of pi-stacking an important conclusion that needs to be considered.  Ade group members have commented to me that this idea has been floating around the polymer world for a while.

Criticism:

The data in Figure 1 is extremely interesting, but I cannot identify a clear connection to the conclusions about molecular weight and the message of the rest of paper.  The new result really seems to be that rapid charge migration from RRa to RR occurs (but not the reverse due to rapid recombination in RR).
Conclusive results related to the main message of the paper would need to expand Figure 1 to consider the effect of molecular weight on the EL physics (similar to the MW study for P3HT in Figure 4).

As usual, I hope for comments on this article.

Report from August 13: Time Delayed Collection Field and Recombination Currents

Yesterday, Josh Carpenter from Ade group presented this article (subscription required as usual) that describes a variety of pulsed electrical measurements aimed at clarifying recombination effects in organic photovoltaics (OPVs).  The Ade group has been particularly interested in the time delayed collection field (TDCF) approach to measuring recombination processes occuring at different time scales.  I'll describe this below.

Overview:

This article continues our discussion of "loss mechanisms" in OPV's.  To aid in this discussion, we  always seem to need a glossary:

Exciton:  Bound state of a photoexcited electron and the hole it left behind (typically though of as localized on a single molecule or short part of polymer chain)

Charge Transfer Exction:  Bound state across an interface of an electron in the acceptor and hole in the donor

Geminate Recombination:  recombination of an electron and hole that come from the same initial exciton state

Polaron:  Electron or hole in a solid combined with the polarization of the solid surroundings (electron and ion charges)

Bimolecular recombination:  nongeminate recombination of uncorrelated polarons that do not come from the same initial excited state

Josh Carpenter made a nice two column overview of important loss mechansims associated with the conceptual steps in the photocurrent generation process.  I reproduce it here partly in my own words as transcribed from Josh's talk and my notes.  Josh also had pictures.

Step in Photocurrent Generation Process	Important Loss Mechanism
Light absorption to make a neutral exciton	Exciton decay (is this not considered "geminate"?), e.g. by light emission
Diffusion of the exciton to D-A interface to create a charge transfer exciton	Geminate recombination of the CT exciton
Charge Separation of the CT exciton to make polarons	Non-geminate "bimolecular" recombination of polarons
Hopping of polarons to the electrodes to finally make a photocurrent	Surface recombination and/or current leakage

The paper uses TDCF in combination with other related tools to clarify the contribution of geminate and bimolecular recombination to the non-ideality (i.e. FF<1) of the I/V curves of 3 different solar cells.

Methods:

The experimental tools used in this paper are somewhat uncommon in the field.  In part this is the reason for focusing on this paper: Can we start to evaluate these tools and whether we or others should be using them?

I want to focus on only TDCF in detail.  The other two unusual tools of bias-assisted charge extraction (BACE) and photocharge extraction by linearly increasing voltage (photo-CELIV) are too much for a blog post (I'm tending already to a TLDR regime here!).

In TDCF, you apply a "prebias" to your device.  You then hit it with a pulsed laser (Nd:YAG, 650 nm) that creates a population of photoexcitations.  Next, you wait a short delay time before applying a large (reverse) collection bias that sweep all charges out of the device.

The authors state that for delay times of 10 ns or less, the total charge collected at the last step of TDCF reflects only geminate recombination losses (since they are fast compared to non-geminate).  If you then do TDCF for different pre-biases, you get the voltage dependence of geminate recombination.  TDCF at longer times probes bimolecular recombination and the authors have a model (you need to dig  into the past literature to find details unfortunately) for how to extract bimoleuclar recombination rates from the long time TDCF.

The paper reports photo-I/V curves for three solution-processed small molecule solar cells.  They use the D-A combination p-DTS(FBTTH2)2:PC71BM (3:2 by weight) in as-cast from chlorobenzene (CB), annealed at 125 deg C after casting, and cast from CB with diodooctance (DIO) additive.  The DIO additive is widely believed to enhance crystallinity in the OPV's.  Devices cast with a DIO additive show the best OPV performance (PCE =7.1%).

Results:

I think Figure 2B is the key result of the paper.  The voltage dependence of geminate recombination in the 3 different device reflects the identical trend that is seen in their respective I/V curves under AM1.5G illumination.  The DIO dependence is basically flat and this is argued to result in a better Fill factor for this device.

In the other Figures, the authors present long-time TDCF and BACE, CELIV results that establish a role for bimolecular recombination in the devices.  Then finally in Figure, they attmept to show the relative contributions of geminate recombination and bimolecular recombination to the total I/V curve deviation from FF=1.  It is great that they over-plot the I-V curves with the geminate recombination current measured by TDCF at 10ns.  However, it was not clear why they could not also use their direct measurements of bimolecular recombination to separately quantify  its contribution to the I/V curve.  It seems they have simply (plausibly) attributed all deviations from ideality not encompassed by geminate recombination to bimolecular. It would be much better to use data to prove this quantitatively using data and I'd like to understand if there is a reason why this is not possible (comment section anyone?). 

Conclusions:

TDCF can deconvolve different recombination mechanisms contributing to OPV non-ideality.  The good performance of DIO-processed solar cells using p-DTS(FBTTH2)2:PC71BM materials is reflected in a voltage-independent geminate recombination rate.  In addition, bimolecular recombination currents are small. 

At the microscopic level, both of these factors are explained by the improvement in crystallinity afforded by the DIO additive.  Better crystallinity results in more efficient dissociation at the interface that is independent of internal field (flat TDCF at 10 ns).  In addition, it reduces bimolecular recombination by increasing carrier mobility.  This allows polarons to get to the electrode without recombining.

The consensus in the journal club was that it is very hard to evaluate the results and methods in this paper as it stands on its own.  Josh did a lot of digging through other work to find details about TDCF, BACE, and CELIV and associated modeling.  It is certainly not obvious that any of us should drop what we are doing to assemble these tools.  Perhaps the more pressing issue is how to critically evaluate new results coming from such unfamiliar tools. I do not personally feel comfortable with this.

Journal Club Report from August 6: The Role of Spin of excited states in OPV losses

Masoud Ghasemi, a graduate student who recently joined Ade group, presented this article (subscription required) and included some tutorial information on the nature of singlet and triplet excited states.  This is crucial background: photoexcitation in molecular solids results in bound states between the excited electron and the hole it leaves behind that are called "excitons".  If the spins of the excited electron and the remaining electron (in what used to be the ground state) are opposite, we have a singlet exciton.  If the spins are aligned we have a triplet exciton.  These excited states differ in energy due to exchange interactions that are fundamentally Coulombic in origin (note well:  magnetostatic interactions between spin dipole moments are way too small to matter here).  Photoexcitation dominantly makes singlet excitons (initially) due to dipole selection rules (spin is conserved upon light absorption).

Overview:
The big question in the paper is how to identify and mitigate the important mechanisms of "losses" in organic photovoltaics (OPV's).  A loss mechanism is any way that a photoexcited state ends up not creating a free charge that can be used for electrical power.  The key result from the paper is that the creation of triplet excitons formed by  bimolecular recombination of dissociated carriers (with random spins) is one of these loss mechanisms, but that it can be minimized by "wave function delocalization" that tends to favor dissociated charges.  As an aside, "The Role of Spin..." that appears in the title seems to me like a bit of a red herring.  The spin in the loss channel causes it to be slowly-evolving and helps distinguish it in the experiments, but is not crucial in the final message relating to "wave function delocalization".

This paper touches on some of the perennial questions of the ORaCEL journal club.  Note that the word "polaron" has come up immediately.  When a charge (i.e. an electron or hole) is injected into a solid it must often be considered not as a free charge but rather as a "quasiparticle" that consists of the injected charge modified by the polarization that it induces in the other electrons in the solid and in the positions of nuclei in the solid.  In briefer terms, polaron = (charge + complicated polarization response of the solid environment)

Methods:
The experimental technique used in the paper is an ultrafast pump-probe spectroscopy called Transient Absorption (TA) where an initial laser "pump" pulse creates an excited state and a slightly later "probe" pulse measures the excited state.  By varying the delay between pump and probe people have learned a lot about excited state dynamics in a wide variety of systems.  In the paper, TA is applied to a range of polymer/fullerene bulk heterojunction (BHJ) blends.  The donor polymer "PIDT-PhanQ" is specially chosen to have polaron (specifically "hole polaron") and triplet exciton features that are distinct.  As a result TA evolution of these separate excitations can be observed over the course of nanoseconds can be used to track recombination effects.

Comparison of the triplet and polaron dynamics when PIDT is blended with different fullerene acceptor derivatives provides the evidence used to generate new ideas about the supression of bimolecular recombination to triplets.  We noted that the authors use a special "genetic algorithm" to deconvolve triplet and polaronic contributions to the total TA signal.  This is probably similar to a principle component analysis, though no one in our journal club was familiar with the details.

Key results and details:

The basic result is that TA evolution shows polarons evolving to triplet excitons with different kinetics for different blends. Figure 2 and 4 show the following comparisons:

• PIDT:PCBM (1:3) blends (good OPV performance) :  TA shows only ONE excited state species (has to be polarons, which in all cases are created "within the response time of the instrument")
• PIDT:ICBA or ICMA blends (poor OPV performance) :  TA shows a change in evolution indicating one excited state evolving to another.  Specifically, early-time polarons recombine to form triplet excitons (the triplet is identified based on the fact that it is a long lived excitation at lower energy than the polaron) that form after a nansecond or so.
• PIDT:PCBM (1:1) blends (poor fullerene aggregation OPV performance) :  TA shows polaron to triplet evolution.
• PCPDTBT:PCBM (1:2) blends (modest OPV performance):  TA shows polaron to triplet evolution

Quantitative analysis of deconvolved polaron and triplet evolution in ICBA and ICMA blends is carried out with a kinetic model that supports the simple picture that triplet are created as polarons decay.  In addition, light intensity dependence of the triplet feature is used as the "smoking gun" that bimolecular recombination is the root cause of the creation of these low energy excitations.  This is an argument that I am aware of being made in the OPV literature but that I would like to have clarified (comments anyone?).

The temperature dependence of the kinetics is also argued to be consistent with a bimolecular recombination process.  Charge (i.e. polaron) diffusion is slower at low temperatures and it is observed that the triplet population arises more slowly (Figure 3c) at lower temperatures.

All of the systems that show evolution of polarons to triplet excitons suffer from poor fullerene aggregation.  Thus, it is concluded that fullerene aggregation is important in minimizing this loss mechanism.  The microscopic explanation advanced in the paper is that larger fullerene aggregates are more crystalline and allow better wave function delocalization.  This, in turn, makes it more likely that polarons interacting in a charge transfer exciton state re-dissociate to polarons again rather than recombine to a triplet exciton.
*Note that the direct experimental connection with crystallinity is NOT made in the paper.  This is a weak point and place for further work.

Conclusions:
Polarons are created very rapidly in a BHJ but they can be lost due to the formation of triplet exctions via triplet charge transfer states.  Large fullerene aggregates, with presumably good crystallinity, promote wavefunction delocalization in the charge-transfer state that in turn promotes re-dissociation to polarons rather than formation of triplets.  The practical message is that you need large fullerene aggregates to prevent this loss mechanism.  I would have liked to see another example of large fullerene aggregates with no triplet formation in the TA.  The paper shows multiple cases of polaron-to-triplet recombination but only 1:3 PIDT:PCBM shows the supression of this loss channel.

I hope that the comment section of this blog can be used to help clarify any misunderstandings and further the discussion about the article and related topics.

Journal club introduction and background

  This blog is planned as a record of journal club activities at the NC State Organic and Carbon Electronics Lab (ORaCEL). ORaCEL was created in 2014 to organize and solidify research efforts in  multiple departments focused on organic/polymer electronics and graphene and carbon nanotubes.

  We've had an organic electronics (OE) journal club in the physics department at NC State for about four years now that has moved this summer to the ORaCEL facilities on Centennial campus.  It all started after discussions between Ade, Dougherty, and Gundogdu about the meaning of the word "polaron" and whether it is used consistently in the organic electronics literature.  We decided we'd better have a regular meeting to clarify this and the journal club was born.  I think it is safe to say that we've all learned a lot about polarons, excitons, etc in the intervening years.  We still often revert to our initial discussion:  What IS a polaron? What do THESE authors mean by polaron? I'll hopefully have science discussions related to this in future posts, though Doug Natelson has pretty much covered the non-technical points about the topic in his blog post here.

  More recently, the journal club has been led by graduate students and post-docs and has occasionally featured delicious pizza.  In the summer of 2014, after some significant student turnover (PhD's awarded !) , the newer students organized a series of tutorials covering the basics of organic electronics.  Topics included:

• Organic materials and how to make thin film samples
• Molecular Orbital Theory
• Basic organic devices (OPV's, OTFT's, OLED's) and device measurements
• Singlet  and Triplet excitons
• Interfacial band alignment

We're now back in the mode of presenting important new articles and we realized we want a written record.  So far, the following articles have been presented:

  Fill Factor in Organic Solar Cells (presented by Andy Barrette)

  Role of Spin in Kinetic Control of Recombination in Organic Photovoltaics (presented by Masoud Ghasemi)

The first blog post will summarize key points (from my perspective) from the second paper.