## Nongeminate recombination in organic solar cells – slower than expected

In a “recent” post (just 3 posts but 10 months ago;-) I wrote once again on the derivation of the Langevin recombination rate for nongeminate recombination. The question is, is Langevin recombination really what governs the charge carrier loss rate in organic solar cells?

Recombination of electrons with holes is usually a 2nd order decay. As electrons $n$ and holes $p$ are photogenerated pair wise, the respective excess charge carrier concentrations are symmetric, $n=p$. Then a recombination rate $R$ is

$R = k n p = k n^2$,

where the recombination prefactor $k$ could be a Langevin prefactor – more on that later. In a transient experiment with a photogenerating, short laser pulse at $t=0$, the continuity equation for charge carriers (here, e.g. electrons) under open circuti conditions (no external current flow, for instance if the experiment is done on a thin film without electrodes)

$\frac{dn}{dt} = G-R$

becomes

$\frac{dn}{dt} = -R$

for $t>0$ (as the generation was only at $t=0$).

If all electrons and hole are available for recombination (i.e., can reach all other charge carriers and can be reached by them), then the recombination rate and the continuity equation for $t>0$ yield

$\frac{dn}{dt} = k n^2$ Continue reading “Nongeminate recombination in organic solar cells – slower than expected”

## Nongeminate Recombination: Langevin (again) and beyond (later;-)

Nongeminate recombination is the major loss mechanism for state-of-the-art organic solar cells. In an early blog post, I showed how the Langevin recombination was derived. Although there is more to nongeminate recombination than just this mechanism, it is still instructive and also relevant to trap-assisted recombination mechanisms, due to its mobility-containing prefactor.

[Nenashev 2010] pointed out that in the derivation of the Langevin recombination,

since the electric field scales as r−2 and the surface area of the sphere scales as 2, the value of r chosen is unimportant, leading to a simple solution with constant electron den- sity, thus justifying the neglect of diffusion.

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

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

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

## From Newton to Hawking

Via c’t: as the British Royal Society turns 350, several historical works are available online for the first time. Not only physics, but also medicine etc… In the nice timeline, you find Newton’s theory of light and colour in the year 1672. It links to Phil. Trans. 1 January 1671 vol. 6 no. 69-80 3075-3087. Quite amazing!

## Influence of Finite Surface Recombination Velocity on Efficiency vs. Mobility of Polymer Solar Cells

Just a quick addition to Mobility and Efficiency of Polymer Solar Cells. You might remember that with increasing mobility, the

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]) Continue reading “Influence of Finite Surface Recombination Velocity on Efficiency vs. Mobility of Polymer Solar Cells”

## Photocurrent in organic solar cells – Part 1

In at least two previous posts (Picture Story and How do organic solar cells function – Part 1), I highlighted the field dependence of the photocurrent in organic solar cells, and its connection to the polaron pair dissociation. Actually, there is more to it.

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].

## Mobility and Efficiency of Polymer Solar Cells

Disordered organic materials inhibit charge carrier mobilities which are orders of magnitude lower than for inorganic crystals. First thing missing in disordered matter is the regularly ordered lattice of atoms, where the charge carriers can delocalise, leading to band transport. Second thing is the generally lower interaction between adjacent molecules, which is due to weaker bonding and larger distances. The transfer integral, the value of which goes exponentially down with distance, to get from one to the other molecule is too low for delocalisation. Thus, in terms of charge carrier mobility, think 10-2cm2/Vs for disordered organics (if you are lucky) vs. at least 102cm2/Vs for ordered inorganics.

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

## Trimolecular Recombination … really?

As you might already have guessed, I am interested in loss mechanisms in organic photovoltaics. Despite considering the impact of recombination on the solar cell performance, also the physical origins are challenging… and many open questions remain.

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 n2.5-n3.5, 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.

## Picture Story – How Do Organic Solar Cells Function?

After the introductory posts about organic solar cells – split in parts zero, one and two, – I would like to present a somewhat more intuitive picture today… well, picture indeed says it all;-)

#### 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).

## A potential candidate for trimolecular recombination?

Lately, we have talked about recombination, also discussing instances where trimolecular recombination has been observed experimentally. From the different excited states observed in organic solar cells, it is not obvious which combination could be participating in a trimolecular loss process. By the way, chemists seem to know the occurance of termolecular recombination, though in different circumstances.

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.
Continue reading “A potential candidate for trimolecular recombination?”