A lossless solar cell operating at the Shockley-Queisser (S-Q) limit generates an open-circuit voltage (VOC) equal to the radiative limit. At VOC, the highly directional beam of photons from the sun is absorbed and subsequently externally reemitted into a 4π solid angle, providing a large photon entropy loss. Moreover, due to many total internal reflections and low internal radiative efficiency, a lot of light is lost in nonradiative recombination events. In our research, we perform a nanophotonic optimization of a semiconductor nanowire geometry with a top microlens in order to decrease the photon entropy loss and to increase the photon escape probability for the nanowire, therefore increasing the output voltage. The optimization leads us to a maximum VOC of 1178 mV which is 141 mV higher than the radiative limit and 172 mV lower than the ultimate limit. The photon entropy loss is also studied fundamentally from the thermodynamics point of view to better understand where the entropy is generated during the absorption-emission processes.
A lossless solar cell operating at the Shockley-Queisser (S-Q) limit generates an open-circuit voltage (VOC) equal to the radiative limit. At VOC, the highly directional beam of photons from the sun is absorbed and subsequently externally reemitted into a 4Ο solid angle, providing a large photon entropy loss. In our research we study the performance of a nanowire solar cell that can beat the S-Q limit and approach the 46.7% ultimate limit by placing a plano-convex lens on top of each nanowire. We have shown numerically that a 2 μm long InP tapered nanowire with the top radius of 83 nm and a tapering angle of 1.2 degrees shows a high photon escape probability of 42% due to an adiabatic expansion of the fundamental HE11 mode which is then collimated using a plano-convex lens with a diameter of 8 ΞΌm. Both effects cause the increase of the open-circuit voltage of the solar cell by 159 mV above the radiative limit which is just 154 mV below the ultimate limit. The lens concept is also studied for a planar solar cell from the thermodynamics point view in terms of local entropy generation within the cell due to absorption/emission processes and is planned to be extended to a nanowire geometry.
Our previously reported 17.8 % efficiency InP nanowire solar cell1 showed a short-circuit current πΌπ π of 29.3 ππ΄ ππ2, which is not far from the theoretical maximum πΌπ π = 34.6 ππ΄ ππ2, but the loss in the open circuit voltage with respect to the radiative limit still amounted to 272 mV. To avoid this loss and reach the radiative limit we have to increase both the internal radiative efficiency πint PL and the photon escape probability πππ π towards unity, as shown by the last term in Eq. 1. πOC = πoc Ultimate β πBπ π |ππ πin πout |β πBπ π |ππ(πint PLπππ π)| (1) We report top-down etched InP nanowires intended to both optimize the amount of light outcoupling as well as the directionality of the emitted light. The photon entropy loss is governed by the ππ πin πout term, which is responsible for a 300 mV loss in the open circuit voltage. To circumvent this loss, we need to redirect all the emitted photoluminescence from the cell back to the sun (εππ = εππ’π‘), For this purpose, we have fabricated PMMA microlenses by using a reflow process, which can be precisely positioned with respect to the InP nanowires.
III/V semiconductor solar cells feature the highest photon conversion efficiencies (PCE), but they are still too expensive for terrestrial application. Conventional nanowire (NW) solar cells already partially resolve this issue since they can be grown on a silicon substrate and feature a low filling factor (the ratio of the 180 nm NW diameter to 500 nm NW pitch, squared). We take the next step by depositing PMMA micro-lenses with a diameter of 6 ΞΌm on top of a NW-array with the same 6 μm pitch, allowing to reduce the material consumption by more than 3 orders of magnitude. According to our FDTD simulations, the material consumption can even be further decreased by reducing the NW length with a factor of 2 down to 1 μm, since the lens is focusing the solar radiation near the top of the nanowires. We also expect a significantly increased Voc due to an increased internal radiative efficiency (IRE) at a higher excitation power. Preliminary measurement show an increase in Voc of at least 50 mV for randomly positioned microlenses on top of a dense NW array with 0.5 μm pitch.
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