We know that the "driving force" that separates photo-generated charge carriers in a solar cell is not merely the built-in potential of the junction, but the gradient of the electrochemical potential which takes into account both electrostatic potential and concentration gradient of charge carriers.
If we consider now the absorption of a single photon within the space charge region of a solar cell p-n junction, this locally creates a small increase of charge carrier concentrations and thereby also a splitting of the quasi Fermi energies (=electrochemical potentials, Fn,p) of electrons and holes. Is it possible to draw the quasi Fermi levels, for example under short-circuit conditions?
My problem is that I do not understand how a separation of the e-h pair can happen when considering the electrochemical potentials. I am aware that, since the excitation takes place within the built-in electric field of the junction, the carriers will drift into their respective majority regions. But from the electrochemical point of view, there should only appear a "delta-like" peak in Fn and Fp, and since there is no gradient of the quasi Fermi levels, no directed current can result..
1. I don't think you can calculate the quasi-Fermi level (QFL) splitting for one e-h pair because Fermi levels are based on statistics that are only valid for many carriers.
2. I think, but am not sure, that under short-circuit conditions there is no QFL splitting.
3. Carriers within a standard Si solar cell move by diffusion. I.e, there is random motion within either n or p-type material until the carriers reach the contact and are extracted. That's why such large diffusion lengths are required.
4. I'd recommend reading "Physics of Solar Cells" by Peter Würfel. It explains most of these issues rather nicely.
Dear Manuel,
thank you for your answer. Actually, I've been reading Würfel's book, and his remarks on the working principle of the solar cell made me think about this. But maybe I will find something on this subject when I keep reading....
The cells I work with are not 'standard' Si cells, but UV-active cells where absorption takes place mostly in the depleted region of the absorber. That is why I am so interested in the mechanism that, based on Würfel's thermodynamic arguments, leads to charge carrier separation. But I guess these arguments can only be applied in the case of a large amount of photo-generated carriers...?
If you're interested in cells where absorption takes place in the depletion region you can look at the literature on a-Si:H solar cells. These usually have a p-i-n structure because the inbuilt field is needed to improve the carrier extraction process. I am also unsure how that works without consuming some of the electrochemical driving force but maybe you can find the answer by reading the literature on these cells. I think there are some good transport mechanism papers by Crandall and Merten.
Thank you again for answering! I've gone through some important chapters in Würfel's book several times now, and I think I got rid of some (seemingly very common) misconceptions of the working principle of a solar cell. Especially with regard to the built-in electric field, which actually has no meaning for the collection of photo-generated carriers... Würfel's reasonings is so coherent. I wonder why there are so many textbooks and websites telling us differently.
I completely agree with you.
I wondered about photonic effects. What would happen to the Fermi-levels, if the absorption is made up by hot spots in a thin-film ? Could this create peaks ?
I guess this would create locally different quasi-Fermi levels looking like peaks. The charge carriers would then be driven into the 'inactive' regions of the thin film by drift and diffusion. But what do you mean by 'photonic effects'?
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