Thermodynamic Limits of Photon-Multiplier Luminescent Solar Concentrators

Luminescent solar concentrators (LSCs) are theoretically able to concentrate both direct and diffuse solar radiation with extremely high efficiencies. Photon-multiplier luminescent solar concentrators (PM-LSCs) contain chromophores that exceed 100% photoluminescence quantum efficiency. PM-LSCs have recently been experimentally demonstrated and hold promise to outcompete traditional LSCs. However, we find that the thermodynamic limits of PM-LSCs are different and are sometimes more extreme relative to traditional LSCs. As might be expected, to achieve very high concentration factors, a PM-LSC design must also include a free energy change, analogous to the Stokes shift in traditional LSCs. Notably, unlike LSCs, the maximum concentration ratio of a PM-LSC is dependent on the brightness of the incident photon field. For some brightnesses, but equivalent energy loss, the PM-LSC has a greater maximum concentration factor than that of the traditional LSC. We find that the thermodynamic requirements to achieve highly concentrating PM-LSCs differ from those of traditional LSCs. The new model gives insight into the limits of concentration of PM-LSCs and may be used to extract design rules for further PM-LSC design.

Popular Summary

The ability to harness and concentrate solar light using luminescent solar concentrators (LSCs) could allow photovoltaics to overcome the Shockley-Queisser limit. Recently photon-multiplier (PM) technologies which allow for one high energy photon to be converted into two lower energy photons have been incorporated into LSCs creating PM-LSCs.

This study proposes a model for the thermodynamic limits of PM-LSCs that can be used to benchmark future efforts. This study sets out the thermodynamic mechanism and possibilities for PM-LSCs and the LSC field more generally. The authors obtain insights into the physical nature of chromophores suited to PM-LSCs. Interestingly, they show that PM-LSCs may concentrate even in the limit of no energy loss, where the input and output photons are of the same energy, something not possible with traditional LSCs. This expands the achievable performance of solar energy conversion devices with direct implications in photovoltaic approaches for sustainable power.

Figure 1

Schematic of operation of a photon-multiplier luminescent solar concentrator (PM-LSC). As an input beam, $B_1$, irradiates the device, a chromophore absorbs and emits light at a longer wavelength. In a PM-LSC, maximally two photons are emitted for every incoming photon. Supposing isotropic emission, the number of photons lost through the escape cone is dependent on the ratio of the refractive indices of the outside medium ($n_1$) to the medium of the LSC ($n_2$). Photons that are emitted within the LSC are described by the second concentrated beam, $B_2$, which, during proper operation, impinges on a photovoltaic mounted on the edge of the LSC.

Figure 2

Maximum concentration factor as a function of chromophore absorption operating under terrestrial conditions. Dotted and solid lines give the maximum concentration factor, $C$, of the traditional LSC and PM-LSC, respectively, at room temperature ($T=300$ K) with $n=1$, when illuminated with light of brightness ${10}^9$ photons per second per unit bandwidth per unit area per $4\pi$ solid angle. This brightness roughly approximates a broad chromophore absorption over the terrestrial solar spectrum (see Ref. [16] for further discussion). Emission for both the PM-LSC and the traditional LSC are fixed by $h{\nu }_2=1.12$ eV, to match the band gap of silicon photovoltaics. In the PM-LSC, the onset of the photon-multiplication process occurs at ${\nu }_1=2{\nu }_2$. Under normal terrestrial conditions, the PM-LSC may concentrate at ${\nu }_1=2{\nu }_2$, since the entropic change associated with the removal and addition of photons at different wavelengths ($\mathrm{\Delta }{S}_2-\mathrm{\Delta }{S}_1$) is greater than zero. When absorbing higher-energy photons, ${\nu }_1>2{\nu }_2$, the maximum concentration factor increases as the thermal loss increases, analogous to the Stokes shift in the traditional LSC.

Figure 3

Maximum concentration factor at room temperature for a traditional LSC (dotted line) and a PM-LSC (solid line) as a function of incident brightness. Both the PM-LSC and traditional LSC concentration limits have an emission at $h{\nu }_2=1.12$ eV, which is optimized for silicon photovoltaics. Traditional LSC has a chromophore with a Stokes shift of $0.24$ eV (${\lambda }_1=912$ nm), which gives a brightness-independent maximum concentration factor, $C=7280$. PM-LSC is assumed to be 200% efficient. PM-LSC has a thermal loss matching that of the traditional LSC, i.e. $h{\nu }_1=2\times 1.12+0.24=2.48$ eV input, corresponding to monochromatic incident light of wavelength ${\lambda }_1=500$ nm.

Figure 4

Maximum concentration as function of PM efficiency and input brightness. Blue surface represents the maximum concentration factor for a PM-LSC with a variable PM efficiency, $\gamma$, under different incident brightness. $\gamma$ varies from one, which would be the maximum efficiency of a traditional LSC, to two, the maximum efficiency of PM-LSCs considered here. Emission frequency for the PM-LSC is fixed at $h{\nu }_2=1.12$ eV, to match that of silicon photovoltaics. Incident illumination is described by a monochromatic beam with wavelength $h{\nu }_1=1.12\gamma +0.15$ eV. Input brightness is plotted between ${10}^8$ and ${10}^{12}$ photons per second per unit bandwidth per unit area per $4\pi$ solid angle.