Abstract
Many advanced solar cell concepts propose surpassing the Shockley Queisser (SQ) limit by introducing multiple quasi-Fermi level separations that are arranged in series and/or in parallel. Exceeding the SQ limit with any parallel arrangement involves intermediate states that deliver additional charge carriers at, ideally, the same electro-chemical 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 sub-optimal 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 radiative efficiency and emission \'etendue of the individual transitions. For solar cell concepts that use Auger type carrier-carrier interactions or molecular triplet states for energetic up- or down-conversion, ideal bandgap 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.
Highlights
Solar cells that are bounded by the Shockley-Queisser (SQ) efficiency limit possess one carrier temperature and nonequilibrium carrier populations in the valence band (VB) and conduction band (CB) only
An overmatching of the quasi-Fermi-level separation (QFLS) between the IB and the VB and between the CB and the VB is required to provide a free-energy differential to drive the carrier multiplication (CM) process, a requirement that has been articulated in the molecular-singlet-fission-solar cell concept [22]
While the two concepts are completely symmetric to each other in the regime of infinite interaction rates and yield the same limiting efficiency, finite Auger interaction rates break the symmetry between the two concepts and we find that the CM solar cell is more robust to a slowdown of Auger interaction rates
Summary
Solar cells that are bounded by the Shockley-Queisser (SQ) efficiency limit possess one carrier temperature and nonequilibrium carrier populations in the valence band (VB) and conduction band (CB) only. The alternative is to contact the highest two energy bands, to what is done in the IBSC, but distinct in that carriers are excited via an Auger-assisted (AA) process [28,29] or the molecular equivalent triplet-triplet annhiliation [30], the latter having been demonstrated experimentally [31,32] In all these instances, an overmatching of the QFLS between the IB and the VB and between the CB and the VB is required to provide a free-energy differential to drive the CM process, a requirement that has been articulated in the molecular-singlet-fission-solar cell concept [22]. We analyze the open-circuit voltage of an intermediate-band material—which could be used to implement either of the parallel schemes—with the aim of elucidating the relationship between étendue, radiative efficiency, and the magnitude of the ratchet step. In the Boltzmann approximation the maximum Gibbs free energy of an electron-hole pair in an absorber with sharp threshold Eg at temperature Tc under illumination by a blackbody of temperature Ts can be written as [33,34]
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