We recently introduced laminate metamaterials composed of a dielectric ABC layer sequence made by atomic-layer deposition. The ABC sequence breaks inversion symmetry, allowing for second-harmonic generation. Here, we discuss 3D polymeric woodpile photonic crystals conformally coated with such ABC laminate metamaterials (unpublished). In our experiments on such meta-crystals with 24 layers and 600 nm rod spacing at around 800-900 nm fundamental wavelength, we find up to 1000-fold enhancement of the second-harmonic conversion efficiency as compared to the same ABC laminate on a planar glass substrate (for 45 degrees angle of incidence with respect to the substrate and p-polarization).
To clarify the underlying mechanism, we have performed extensive numerical calculations based on solving the full-wave problem for the fundamental wave, computing the second-harmonic 3D source-term distribution assuming tensor elements for the ABC laminate as found previously, and numerically computing the resulting emitted second-harmonic wave. This analysis indicates that the enhancement is consistent with guided-mode resonant excitations at the fundamental wavelength inside of the 3D meta-crystal slab, leading to a standing-wave behavior providing beneficial local-field enhancements.
The availability of optimum textures for the purpose of light trapping in solar cells is at stake. Here, we discuss how they can be obtained with a large-area scalable bottom-up approach that utilizes as a template monolayers of densely packed nanospheres from a colloidal solution with tailored size distribution.
Theoretically, we show that the surface textures' geometry can be predicted and tuned from a colloidal solution with given nanosphere sizes and relative occurrence probability. With only simple monolayers comprised of two nanosphere size species, we show that one can already obtain a useful scattering pattern relevant for rear scattering light trapping textures. We proceeded to study the application of such textures in thin-film crystalline silicon (c-Si) solar cells. Such monolayers can be tuned to provide diffraction patterns, which form an annulus in Fourier space such that stronger scattering occurs at oblique angles. For such two species nanosphere monolayers, the nanosphere sizes dominantly influence the diffraction efficiency and minimum and maximum scattering angles. The relative occurrence probability of each nanopshere species influences the amount of diffraction states accessible, which translates to how broad the annulus region in Fourier space can be. The simplicity of the monolayer and the behavior of the scattering response allows to easily estimate nanosphere size ranges of interest by considering the radiation condition in c-Si and in air.
In optimizing the monolayer parameters to obtain optimum rear scattering light trapping textures, we inspect approaches that avoid the severe computational costs, which typically follow the modeling of random scattering geometries. In particular, we investigate the applicability of utilizing the surface texture's Power Spectral Density (PSD) and alternatively rigorous diffraction calculations in a semi-infinite c-Si superstrate to deduce net short-circuit current enhancement dependence on the monolayer parameters. The widely used PSD based prediction is shown to significantly deviate in important parameter ranges, where an optimal response can be obtained. This is related to the limitation of the PSD to be used as a predictor for the scattering response at textures with a notable height modulation. In the regime where the PSD fails to be predictive, an excellent prediction on the short-circuit current enhancement can be obtained with minimal computational costs by only examining the diffraction efficiencies in a selected wavelength range where light trapping has its largest impact. We show that the integrated diffraction in the directions of interest at the wavelength of 700 nm is sufficiently representative for the considered 1 μm thin-film c-Si cell and light trapping scheme. Fullwave simulations reveal that the integrated diffraction at 700 nm and the short-circuit current have coinciding trends in their dependency on the nanosphere size distribution.
We furthermore explore the usage of the nanosphere monolayer template to obtain front surface textures, which provide mainly anti-reflection properties. This is done by considering an inverse pattern of the template to make use of the needle-like structures that emerge from the inverted nanosphere monolayer. The conditions needed for the monolayer parameters in order to ensure broadband suppression of reflection are discussed.