Dear all,
I am trying to compute the theoretical efficiency of a photovoltaic cell using the method described in the attached paper, which is based on the classical Shockley and Queisser arguments (available here: Article High Temperature Epsilon-Near-Zero and Epsilon-Near-Pole Met...
)Part of the calculation involves the efficiency factor n_rec = V_oc / Vg where V_oc is the open circuit voltage and Vg the bandgap voltage (Equation 13).
As a far as I understand, from a physical standpoint n_rec should be smaller than 1, since V_oc cannot be superior to Vg. Nevertheless, I do obtain n_rec values higher than 1 (i.e. V_oc > Vg), when I consider for instance a blackbody emitter at 6000K, a PV cell temperature = 300K, 100% radiative recombinations (f_rec = 1) and a bandgap of 1 eV.
Therefore, I am wondering: is there something wrong with my calculation ? or does the model have some limitation that I am not aware of ?
From a mathematical standpoint, I don't see what enforces V_OC < Vg, would someone be able to explain this?
Thanks a lot for your help!
Thanks a lot for your answer Preston Guynn. I had read that answer but I could not figure out why I was getting V_oc values higher than Vg.
Nevertheless I found the issue: the formula that I used to compute V_oc, which is commonly found in the literature (such as the paper I was referring to) is valid only under Boltzmann approximation, which does not hold when the solar concentration is high or the bandgap is low.
Best regards,
Quentin
Dear Quentin,
the open circuit voltage is determined by the difference of the quasi-fermi-levels. Therefrom you can differ the following cases:
- In low doped semiconductors and at low excitation levels you have V_oc/Vg < 1 as expected.
- In degenerated material you have V_oc/Vg >1 because the fermi-level lies within the bands.
- At high excitation levels (excess carrier concentration compares with the equilibrium concentration) the quasi Fermi level shifts into the bands due to the fact that the bands are filled with carriers. In this nonequilibrium case you find V_oc/Vg > 1 too.
With Regard
R. Mitdank
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