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?
Luckily, not as bad as one might think! It turns out that a certain charge carrier mobility is important to get good power conversion efficiencies, but looking at further improvements, there are other more pressing issues. But one after the other.
- the polaron pair dissociation (Braun-Onsager theory [Braun 1984], describing the escape from the mutual Coulomb attraction)
- the charge transport
- polaron recombination (possibly Langevin recombination, but with a reduced rate, as found experimentally [Deibel 2008b, arxiv:0810.0542])
- and finally, the charge extraction (which is directly related to charge transport, and possibly influenced by surface recombination)
Using our macroscopic device simulator, we looked at the influence of charge carrier mobility on the solar cell parameters (short circuit current, open circuit voltage, fill factor, and of course the efficiency) [Deibel 2008a, arxiv:0806.2249], following the idea of [Mandoc 2007], but considering a more realistic (=reduced) polaron recombination as well as injection barriers at the electrodes. Due to polaron pair dissociation, the short circuit current jsc increases with mobility (here equal for electrons and holes) until saturation is reached. 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!
Looking at the power conversion efficiency, there is indeed a maximum value at rather low mobilities, just a bit higher as compared to the values found in state-of-the-art polymer solar cells (shown by a vertical dashed line). The parameter zeta shown in the graph is indicative of wether normal (1) or reduced (0.01) Langevin recombination has been considered.
So, what does all that mean?
- the charge carrier mobility has to be reasonable for good solar cells
- however, there is not much room for improvement; even if surface recombination is rather small (which is to be expected in materials without dangling bonds;-), the maximum efficiency is reached already at low mobilities
- this is due to very low polaron recombination rates, i.e., even though slow, the charges are extracted at some time (if they do not recombine, which they almost never do), leading to photocurrent
- a brief note: the decreasing efficiency at high mobilities is overestimated, as mentioned before; for realistic extraction, it will only be weakly decreasing or even remaining constant… but not increasing after approx. 10-6m2/Vs (10-2cm2/Vs)!
So, finally, how to get higher efficiencies? What can be optimised?
- very important, but achieved for some material combinations: a donor-acceptor phase separation which is fine-grained enough for good exciton dissociation, and coarse enough for good charge transport
- polaron pair dissociation: better at low fields than previously thought, but still limiting… more basic understanding is needed
- the narrow absorption bands are a major issue, limiting the photocurrent and thus the short circuit current
- the exciton binding energy and the relative acceptor energy offset: the energy needed for exciton dissociation limits the open circuit voltage
Some of these points I had mentioned already earlier. So, for light absorption, tandem solar cells might be a solution (with new problems arising, e.g., current matching with angle dependence of the incident light), or design/synthesis of novel materials. Same goes for exciton dissociation. But I believe there are many more ideas still out there which need to be implemented and tested;-)