Discrepancy-Based Genetic Algorithm Optimization of Quasi-Random Nanostructures for Broadband Light Reflection Mitigation

Periodic nanostructures have previously been used to increase the absorption of various semiconductors, but they mainly provide improvement in a specific spectrum. On the other hand, random nanostructures can increase the adsorption over a broad range of frequencies without a targeted frequency. Instead, quasi-random nanostructures have shown broad spectrum improvements and targeted spectrum enhancement compared to both periodic and random nanostructures. Considering an infinite number of quasi-random nanostructures, it is challenging to design or optimize a quasi-random structure pattern via traditional simulations (i.e., Finite Difference Time Domain (FDTD), Finite Element Analysis, Rigorous coupled-wave analysis). Discrepancy is a method of measuring surface randomness of a structure. Previous work has shown that a higher star discrepancy, and there for a higher surface randomness, of a quasi-random structure reduces surface reflection and increases optical path length, resulting in a higher absorption for semiconductors. Therefore, discrepancy calculations allow a quasi-random nanostructure to be evaluated more efficiently than running a FDTD simulation. In this paper, we used a genetic algorithm (GA) to optimize the discrepancy of quasi-random nanostructures instead of running thousands of optical simulations for the optimization. The optimized quasi-random sequence is compared with a classical quasi-random Fibonacci sequence. The star discrepancy, or the maximum absolute discrepancy was measured and found to be 0.0026 for a Fibonacci sequence and 0.0387 for the GA generated sequence, an order of magnitude enhancement. The FDTD simulations show that the GA-based quasi-random nanostructure shows a 20% absorption improvement over the Fibonacci sequence at 450 nm wavelength and additionally shows a doubling of absorption in the near-infrared region, suggesting a better antireflection performance.