III-V solar cells dominate the high efficiency charts, but with significantly higher cost than other solar cells. Ultrathin III-V solar cells can exhibit lower production costs and immunity to short carrier diffusion lengths caused by radiation damage, dislocations, or native defects. Nevertheless, solving the incomplete optical absorption of sub-micron layers presents a challenge for light-trapping structures. Simple photonic crystals have high diffractive efficiencies, which are excellent for narrow-band applications. Random structures a broadband response instead but suffer from low diffraction efficiencies. Quasirandom (hyperuniform) structures lie in between providing high diffractive efficiency over a target wavelength range, broader than simple photonic crystals, but narrower than a random structure. In this work, we present a design method to evolve a simple photonic crystal into a quasirandom structure by modifying the spatial-Fourier space in a controlled manner. We apply these structures to an ultrathin GaAs solar cell of only 100 nm. We predict a photocurrent for the tested quasirandom structure of 25.3 mA/cm$^2$, while a planar structure would be limited to 16.1 mA/cm$^2$. The modified spatial-Fourier space in the quasirandom structure increases the amount of resonances, with a progression from discrete number of peaks to a continuum in the absorption. The enhancement in photocurrent is stable under angle variations because of this continuum. We also explore the robustness against changes in the real-space distribution of the quasirandom structures using different numerical seeds, simulating variations in a self-assembly method.
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