Radiative Limit for Solar Cell Efficiencies

Since radiative recombination is tied on one side to the absorption coefficient, which should be as large as possible to facilitate the absorption of solar radiation, and on the other side to the difference between the Fermi energies fc — fV) which is the free energy per electron-hole pair and should also be as large as possible, radiative recombination is quite unavoidable. On the contrary, in a solar cell, which does not emit photons under open-circuit conditions, non-radiative recombination is dominant and causes the difference between the Fermi energies pc — fv to be too small for a sizeable emission according to (4.52). In an optimal situation, all recombination is radiative. The efficiency for this situation is the maximum efficiency a 2-band solar cell can have [6,8-10]. 

This eliminates all spurious absorption that does not lead to electron-hole pairs. It also excludes emission of low energy photons, that is, those with fko eg, the energy gap of the material. 

To keep the calculation simple, we also assume that the electrons and holes, although generated at a rate which decreases with distance from the surface, are distributed homogeneously in the material due to their good mobility. 

As for the 2-level system, we require that electrical contact be made to the 2-band system in such a way that, at one contact, which will be the negative contact of the solar cell, only electrons are exchanged with an external circuit, whereas holes are exclusively exchanged through the second contact, the positive contact of the solar cell under energy conversion conditions. As before, the charge current is 

With (4.52), this transforms as for the 2-level system into 

---