Optical refrigeration for ultra-efficient photovoltaics
SPIE, March 25, 2015
We studied endothermic PL experimentally at high temperatures7 and have shown how, in accordance with theory, the PL photon rate is conserved with increasing temperature, while each photon is blue-shifted (becomes more energetic). A further rise in temperature leads to an abrupt transition to thermal emission where the photon rate increases sharply. In addition, we found that endothermic PL generates photons orders of magnitude more energetic than thermal emission at similar temperatures. Relying on these observations, we have proposed and studied thermally enhanced PL for highly efficient solar-energy conversion. Here, solar radiation is absorbed by a low-bandgap PL material. The dissipated heat is emitted by endothermic PL, and harvested by a higher-bandgap photovoltaic cell. While such a device operates at much lower temperatures than STPV due to the optical refrigeration effect, it has similar theoretical maximal efficiencies that approach 70%.
Recent research in optical refrigeration has demonstrated cryogenic temperatures with quantum efficiency approaching unity. At such low temperatures, thermal excitation is negligible with respect to the PL excitation. In contrast, at high temperatures, the PL and thermal excitation compete for dominance. In general, PL requires directional energy transfer from the excited to the emitting modes. This only occurs if the excitation rate is above the rate of thermal excitation where directional energy transfer is canceled by thermal equilibrium. This tradeoff is expressed by the generalized Planck’s law, suggested by Würfel, describing the spontaneous emission rate of a bandgap material.8Far from lasing conditions, this PL radiation (R) can be approximated as Planck’s thermal emission, εR0, enhanced by μ, the chemical potential: R=εR0eμ/KBT where ε is the emissivity, KB is the Boltzmann constant, and T is the temperature. With a constant pump rate and quantum efficiency, thermodynamics sets the emitted photon rate to be constant when μ>0, independent of the temperature.
Solving the above radiation equation for constant PL photon rate and energy conservation under increased heat load shows that, in contrast to thermal emission where photon rate increases with temperature, for PL emission an increase in temperature has no effect on the photon rate but the emitted photons are blue-shifted. At the critical temperature, where μ=0, only energy is balanced: the emission becomes thermal and the emitted photon rate increases sharply at all wavelengths. These results are shown in Figure 1.