Theoretical Efficiency Comparison between Carrier Multiplication and Down-Conversion 3rd Generation Solar Cell Designs

Methods of exceeding the detailed balance limit for a single junction solar cell have included down-converting high energy photons to produce two photons; and carrier multiplication, whereby high energy photons produce more than one electron-hole pair. Both of the 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 that there is no thermodynamic difference between the two methods. Here, we compare the two methods using a generalized approach based on Kirchhoff's 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 modifies the existing literature on entropy generation limits in solar cells, and creates a new distinction among 3rd generation photovoltaic technologies.