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Narrow-bandwidth solar upconversion: Case studies of existing systems and generalized fundamental limits
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43.See supplementary material at http://dx.doi.org/10.1063/1.4796092 for (1) a discussion of the energy levels and optimization routine used to model the upconversion process, (2) calculation of currents in each cell, (3) a discussion of the relationship between upconverter relaxation energy and upconverter bandwidth, (4) a table of the spectral parameters used to model upconversion in the bimolecular and lanthanide nanoparticle case studies, and (5) a brief note on solar cell non-idealities. [Supplementary Material]
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FIG. 1.

Schematics outlining the solar cell/upconverter system under consideration. (a) Above-bandgap light is absorbed by the solar cell, which iselectrically isolated from the upconverter. Sub-bandgap light is transmitted by the solar cell, absorbed by the upconverter, and re-radiated backinto the cell as above-bandgap light. (b) The upconverter is equivalent to a circuit containing two low bandgap solar cells (C3 and C4) in series with a high bandgap photodiode (C2). (c) Energy level diagram indicating the relevant transitions. Eg , E 3, and E 4 represent the effective band edges for cells C2, C3, and C4, respectively (Eg is also the solar cell bandgap). A 2, A 3, and A 4 are the centroids of the upconverter emission and absorption lorentzians; the absorption and emission peaks for each cell comprising the upconverter (C2, C3, and C4) are coincident, thus allowing the non-radiative relaxation energy ER to account for all non-radiative loss in the upconverter. The solar cell conduction and valence bands extend to positive and negative infinity, respectively.

Image of FIG. 2.

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FIG. 2.

Ideal solar cell with an ideal upconverter. (a) The maximum power conversion efficiency is calculated as a function of cell bandgap and upconverter bandwidth for the optimal relaxation energy of 0.48 eV. The Shockley-Queisser limit is thus generalized to include a narrow-band upconverter. (b) The absolute increase in cell efficiency is computed as a function of upconverter relaxation energy for a 0.1 eV bandwidth upconverter; the dotted line indicates the relaxation energy at which the maximum increase is achieved.

Image of FIG. 3.

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FIG. 3.

Calculated optimal spectral locations for the low energy absorption peaks in the upconverter, determined using both the solar Planck spectrum (fine lines) and the AM1.5G solar irradiance spectrum (thicker lines). The emitter position is fixed relative to each bandgap. The AM1.5G spectrum is plotted (relative to the upper horizontal axis) for reference.

Image of FIG. 4.

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FIG. 4.

Case studies of existing upconverting systems with different UC efficiencies are shown. The absorption and emission spectra and associated lorentzian fits (a), the raw efficiency (b), and the absolute increase in efficiency (c) for the bimolecular system (PdOEP + DPA). Analogous plots (d)–(f) for the lanthanide-based system (IR806-sensitized oleylamine-coated β-NaYF4:Yb,Er nanoparticles). The axes in the bimolecular spectra plot extend to 900 nm for better spectral comparison.

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/content/aip/journal/jap/113/12/10.1063/1.4796092
2013-03-29
2014-04-18

Abstract

Upconversion of sub-bandgap photons is a promising approach to exceed the Shockley-Queisser limit in solar technologies. Calculations have indicated that ideal, upconverter-enhanced cell efficiencies can exceed 44% for non-concentrated sunlight, but such improvements have yet to be observed experimentally. To explain this discrepancy, we develop a thermodynamic model of an upconverter-cell considering a highly realistic narrow-band, non-unity-quantum-yield upconverter. As expected, solar cell efficiencies increase with increasing upconverter bandwidth and quantum yield, with maximum efficiency enhancements found for near-infrared upconverter absorption bands. Our model indicates that existing bimolecular and lanthanide-based upconverters will not improve cell efficiencies more than 1%, consistent with recent experiments. However, our calculations show that these upconverters can significantly increase cell efficiencies from 28% to over 34% with improved quantum yield, despite their narrow bandwidths. Our results highlight the interplay of absorption and quantum yield in upconversion, and provide a platform for optimizing future solar upconverter designs.

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Scitation: Narrow-bandwidth solar upconversion: Case studies of existing systems and generalized fundamental limits
http://aip.metastore.ingenta.com/content/aip/journal/jap/113/12/10.1063/1.4796092
10.1063/1.4796092
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