Voltage Matching, Etendue, and Ratchet Steps in Advanced-Concept Solar Cells

Many advanced solar cell concepts propose surpassing the Shockley-Queisser limit by introducing multiple quasi-Fermi-level separations that are arranged in series and/or in parallel. Exceeding the Shockley-Queisser limit with any parallel arrangement involves intermediate states that deliver additional charge carriers at, ideally, the same electrochemical potential as the other elements in the parallel network. This can be thought of as voltage matching individual parallel components, and in intermediate-band materials is intricately linked to solar concentration and etendue mismatch between absorption and emission. Generally, to achieve voltage matching under suboptimal conditions, an additional degree of freedom in the absorption thresholds of the material through a carrier relaxation or ratchet step is required. We explain why the ideal ratchet step decreases with solar concentration and how it depends on the radiative efficiency and emission etendue of the individual transitions and provide illustrative examples. The ideal ratchet step at 1 sun is largely given by the etendue mismatch between incoming sunlight and emitted light, which results in a step on the order of 270 meV that increases logarithmically with the ratio of luminescence-extraction efficiencies of the transitions. For solar cell concepts that use Auger-type carrier-carrier interactions or molecular triplet states for energetic up-conversion or down-conversion, the ideal band-gap combinations and achievable efficiencies also depend on interaction rates. We show that Auger-assisted solar cells suffer more strongly from finite interaction rates than carrier-multiplication devices.