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!
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”
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].
I just have to share these quotes of Wolfgang Pauli:
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 ;-)
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?
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.
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).
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?”
Recombination of free charge carriers in materials with a low mobility is often described with the Langevin recombination rate [Langevin 1903 (Ann. Chim. Phys. 28, 433)] (Update 3.12.2008: wrong reference previously, sorry.) Generally, if electron and holes – being potential recombination partners – wish to recombine, the effective recombination rate is proportional to
- 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. Continue reading “Recombination in low mobility semiconductors: Langevin theory”
In disordered organic semiconductors, there is no band transport, as there are no delocalised, just localised charges. Consequently, there is no simple band-band recombination of free carriers, and no Shockley-Read-Hall recombination! Of course, there is still recombination going on, a lot of it;-)
Here I’ll just quote some definitions concerning different types of recombination, and get back with details later.
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? ;-)