Theoretical efficiency of 3rd generation solar cells: Comparison between carrier multiplication and down-conversion

Two of the methods of exceeding the detailed balance limit for a single junction solar cell are down-converting high energy photons to produce two photons and carrier multiplication, whereby high energy photons produce more than one electronhole pair. Both methods obey the conservation of energy in similar ways, and effectively produce a higher current in the solar cell. Due to this similarity, it has been assumed in the literature that there is no thermodynamic difference between the two methods. Here, we analyzed the two methods using a generalized approach based on Kirchhoffs law of radiation and develop a new model for carrier multiplication. We demonstrate that there is an entropic penalty to be paid for attempting to accomplish all-in-one splitting in carrier multiplication systems, giving a small thermodynamic and therefore efficiency advantage to spectral splitting prior to reaching the solar cell. We show this analytically using a derivation of basic thermodynamic identities; numerically by solving for the maximal efficiency; and generally using heat-generation arguments. Our result provides a new limit of entropy generation in solar cells beyond the existing literature, and a new distinction among 3rd generation photovoltaic technologies.