Design of Non-Deterministic Quasi-random Nanophotonic Structures Using Fourier Space Representations

Abstract

Despite their seemingly random appearances in the real space, quasi-random nanophotonic structures exhibit distinct structural correlations and have been widely utilized for effective photon management. However, current design approaches mainly rely on the deterministic representations consisting two-dimensional (2D) discretized patterns in the real space. They fail to capture the inherent non-deterministic characteristic of the quasi-random structures and inevitably result in a large design dimensionality. Here, we report a new design approach that employs the one-dimensional (1D) spectral density function (SDF) as the unique representation of non-deterministic quasi-random structures in the Fourier space with greatly reduced design dimensionality. One 1D SDF representation can be used to generate infinite sets of real space structures in 2D with equally optimized performance, which was further validated experimentally using light-trapping structures in a thin film absorber as a model system. The optimized non-deterministic quasi-random nanostructures improve the broadband absorption by 225% over the unpatterned cell.

Figure 1

One-to-multiple mapping from Fourier space characterization to real-space geometries of non-deterministic quasi-random structures. (a,b) Two quasi-random structures with channel-type morphology that can be obtained from spinodal decomposition process (c) A disk-type quasi-random structure that can be obtained from nucleation based phase separation process. (d–f) The Fourier spectra of the structures in (a–c), respectively.

Figure 2

Real-space quasi-random structure reconstruction from SDF. (a) An SDF following the Gaussian distribution function. (b) An SDF following two-step function. (c) A channel-type quasi-random structure reconstructed from (a) using Gaussian random field modeling. (d) A disk-type quasi-random structure reconstructed from (a) using random packing algorithm. (e) A channel-type quasi-random structure reconstructed from (b) using Gaussian random field modeling. (f) A disk-type quasi-random structure reconstructed from (b) using random packing algorithm. (g) An SDF following a decreasing-linear function. (h) An SDF following an increasing linear function. (i) An SDF following a triple-delta function. (j) An SDF following a truncated Gaussian distribution function. (k) A channel-type quasi-random structure reconstructed from (g) using the Gaussian random field modeling. (l) A disk-type quasi-random structure reconstructed from (h) using the random packing algorithm. (m) A channel-type quasi-random structure reconstructed from (i) using the Gaussian random field modeling. (n) A disk-type quasi-random structure reconstructed from (j) using the random packing algorithm.

Figure 3

Fourier space design strategy of non-deterministic quasi-random nanophotonic structures. (a) The simulation-based design approach for optimizing quasi-random nanophotonic structures in Fourier space based on the structural characterization using SDF. (b) The schematic view of the simplified thin-film silicon solar cell model with quasi-random light-trapping structure. The cell is characterized by the thickness of the silicon layer t, and the thickness of scattering layer t₁. (c) Optimization history for designing the quasi-random light-trapping structure in the absorber (t = 600 nm, t₁ = 100 nm) at λ = 650 nm using genetic algorithm. (d–i) Six different real-space quasi-random structures reconstructed from the optimal solution, where d-f with the channel-type morphology are reconstructed using Gaussian random field modeling and (g–i) with the disk-type morphology are reconstructed using random packing algorithm. (j) The absorption performance of 50 randomly generated quasi-random light-trapping structures from the optimal solution.

Figure 4

Broadband optimization results. The optimized Fourier spectra, bitmap images, and SEM images of the quasi-random nanostructures generated differently from the same optimized SDF. (a–c) Quasi-random structure constructed by repeating a single unit cell in the dashed window. (d–f) Quasi-random structure with channel-type morphology. (g–i) Quasi-random structure with disk-type morphology. (j) Simulated absorption spectra of the three quasi-random nanostructures from the identical optimized SDF, the unpatterned cell, and the unpatterned cell with ARC layer. (k) Experimentally measured absorption spectra of the five cells. Scale bars in (c,f,i): 2 µm.