Numerical Modeling of Sub-Wavelength Anti-Reflective Structures for Solar Module Applications

Process and optical modeling of black silicon

Black silicon is relevant for the photovoltaic industry when searching for low-reflectance, low-defect front surface, which is the goal of this work. We have fabricated samples using reactive ion etching (RIE) plus chemical etching for the smoothing, characterized them, and built modeling tools capable of reproducing the resulting geometric features, based on the process parameters. Reflectance is simulated using a proprietary rigorous coupled wave analysis (RCWA)-based tool, and compared with the experimental results. A good matching was achieved using a simple unit cell, and a better agreement when using a 0.5 square microns sample. Finally, an optimum trade-off between low reflectance and low thickness has been achieved.

Modeling of the synergistic anti-reflection effect in gradient refractive index films integrated with subwavelength structures for photothermal conversion

Photothermal materials generally suffer from challenges such as low photothermal conversion efficiency and inefficient full-spectrum utilization of solar energy. This paper proposes gradient refractive index transparent ceramics (GRITCs) integrated with subwavelength nanostructure arrays and simulates the synergistic anti-reflection effect by an admittance recursive model. An innovative subwavelength structure, possessing a superior light-trapping capability, is initially crafted based on this model. Subsequently, various intelligent optimization algorithms including genetic algorithm, particle swarm optimization, and simulated annealing are employed to optimize the structure of gradient refractive index films respectively. Finally, the photothermal conversion efficiencies of devices based on different photothermal materials are calculated. The simulations and finite-difference time-domain calculations demonstrate that the three-layer GRITCs integrated with an optimal SNA exhibit outstanding full-spectrum and omnidirectional anti-reflection performance. The solar transmittance of the devices can exceed 97% for light wavelengths ranging from 300 to 2500 nm over the full angle of incidence. Our results reveal that the synergistic anti-reflection effect in the SNAs and GRITCs can enhance the photothermal conversion efficiency by more than 20%.

Neural Inverse Design of Nanostructures (NIDN)

In the recent decade, computational tools have become central in material design, allowing rapid development cycles at reduced costs. Machine learning tools are especially on the rise in photonics. However, the inversion of the Maxwell equations needed for the design is particularly challenging from an optimization standpoint, requiring sophisticated software. We present an innovative, open-source software tool called Neural Inverse Design of Nanostructures (NIDN) that allows designing complex, stacked material nanostructures using a physics-based deep learning approach. Instead of a derivative-free or data-driven optimization or learning method, we perform a gradient-based neural network training where we directly optimize the material and its structure based on its spectral characteristics. NIDN supports two different solvers, rigorous coupled-wave analysis and a finite-difference time-domain method. The utility and validity of NIDN are demonstrated on several synthetic examples as well as the design of a 1550 nm filter and anti-reflection coating. Results match experimental baselines, other simulation tools, and the desired spectral characteristics. Given its full modularity in regard to network architectures and Maxwell solvers as well as open-source, permissive availability, NIDN will be able to support computational material design processes in a broad range of applications.

Efficient Rigorous Coupled-Wave Analysis Simulation of Mueller Matrix Ellipsometry of Three-Dimensional Multilayer Nanostructures

Mueller matrix ellipsometry (MME) is a powerful metrology tool for nanomanufacturing. The application of MME necessitates electromagnetic computations for inverse problems of metrology determination in both the conventional optimization process and the recent neutral network approach. In this study, we present an efficient, rigorous coupled-wave analysis (RCWA) simulation of multilayer nanostructures to quantify reflected waves, enabling the fast simulation of the corresponding Mueller matrix. Wave propagations in the component layers are characterized by local scattering matrices (s-matrices), which are efficiently computed and integrated into the global s-matrix of the structures to describe the optical responses. The performance of our work is demonstrated through three-dimensional (3D) multilayer nanohole structures in the practical case of industrial Muller matrix measurements of optical diffusers. Another case of plasmonic biosensing is also used to validate our work in simulating full optical responses. The results show significant numerical improvements for the examples, demonstrating the gain in using the RCWA method to address the metrological studies of multilayer nanodevices.

Enhanced light management and optimization of perovskite solar cells incorporating wavelength dependent reflectance modeling

Perovskite Solar Cells (PSCs) are the most promising candidates for low-cost and high-efficiency devices in the future photovoltaic market. PSCs are also used as the top cell in tandem devices with silicon bottom cells. However, research in PSCs is still at an early stage while racing towards a promising future. Along with experimental research, numerous simulation studies are conducted with PSCs aiming to analyze new materials and optimize their performance. Here, a wavelength-dependent model is implemented to account for the reflected part of irradiance from the cells, which is ignored in most SCAPS-1D based PSC simulated models. This model optimizes the MgF₂ anti-reflective coating in SCAPS-1D simulation to allow maximum photons to pass inside the device. A simple structured PSC (MgF₂/Glass/ITO/ZnO/CH₃NH₃PbI₃/Spiro-OMeTAD/Au) is simulated and optimized optically as well as electrically with this model’s modified spectrum. The device was optimized for layer thickness, defects, and doping. Moreover, the effects of temperature and device resistances are discussed. The optimized device yields 21.62% power conversion efficiency, which can be further improved to reach over 25% through better processing schemes. Finally, the optimized device was compared with other devices having different ETL/absorber/HTL combinations and the pathway to achieving higher efficiencies was discussed. This article aims at improving the credibility of simulated devices by incorporating top surface reflection with electrical optimization.

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Simulation of Perovskite solar cells with MgF2 ARC to optimize light management.

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Improving the simulation of SCAPS-1D based solar cell studies by incorporating reflectance modelling, which is ignored in all previous studies.

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Detailed analysis of loss of photons from non-radiative recombination in PSC studies.

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Optimization of the device to improve the efficiency to greater than 20%.

Broadening the absorption bandwidth based on heavily doped semiconductor nanostructures

Broadband light absorption is a basis for the proper functionality of various materials, microstructures, and devices. Despite numerous studies, however, many aspects of broadband absorption remain uncovered. In this paper, we demonstrate an inverse-problem approach to designing nanostructures with a very low optical reflection and high absorption through a frequency band. Particular emphasis is made on a subwavelength transparent film as a top layer and anisotropic substrate. The polarization-dependent metamaterial absorber based on a subwavelenth semiconductor multicomponent multilayer structure is proposed and numerically investigated. For an illustration, we consider a four-component heavily doped silicon lattice with a thin undoped silicon top layer. The dielectric response of the structure is engineered by controlling the free carrier density and filling factor of each layer. A simulation study reveals a power law dependence of the bandwidth on the maximum reflectivity within the band.

Textured Stainless Steel as a Platform for Black Mg2Si/Si Heterojunction Solar Cells with Advanced Photovoltaic Performance

This paper reports on a facile bottom-up method for the direct integration of a silicon (Si)-magnesium silicide (Mg₂Si) heterojunction solar cell (HSC) with a textured rear reflector made of stainless steel (SS). Modified wet chemical etching and post processing of SS substrates resulted in the formation of both a rough surface texture and diffusion barrier layer, consisting of magnetite (Fe₃O₄) with reduced optical reflection. Then, Si, Mg₂Si and CaSi₂ layers were stepwise thermally evaporated onto the textured SS surface. No traces of Fe and Cr silicide phases were detected by Raman spectroscopy, confirming effective suppression of impurity diffusion from the SS to the upper layers at least at temperatures required for Si deposition, as well as Mg₂Si and CaSi₂ formation. The obtained black-SS/Fe₃O₄/Si/Mg₂Si/CaSi₂ sample preserved, to some extent, its underlying textured morphology and demonstrated an averaged reflection of 15% over the spectral range of 200-1800 nm, while its prototype HSC possessed a wideband photoresponse with a photoelectric conversion efficiency of 7.5% under AM1.5 illumination. Moreover, Si layers deposited alone onto a black-SS substrate demonstrated competitive antireflection properties compared with black Si (b-Si) obtained by traditional top-down etching approaches, and hybrid b-Si/textured-SS structures with a glue-bonded interlayer.

Ultrabroadband suppression of mid-infrared reflection losses of a layered semiconductor by nanopatterning with a focused ion beam

Moth-eye structures are patterned onto gallium selenide surfaces with sub-micrometer precision. In this way, Fresnel reflection losses are suppressed to below one percent within an ultrabroad optical bandwidth from 15 to 65 THz. We tune the geometry by rigorous coupled-wave analysis. Subsequently, ablation with a Ga⁺ ion beam serves to write optimized structures in areas covering 30 by 30 μm. The benefits are demonstrated via optical rectification of femtosecond laser pulses under tight focusing, resulting in emission of phase-stable transients in the mid-infrared. We analyze the performance of antireflection coating directly in the time domain by ultrabroadband electro-optic sampling.

Enhanced Transmission from Visible to Terahertz in ZnTe Crystals with Scalable Subwavelength Structures

The zinc blend nonlinear crystal of zinc telluride (ZnTe) is currently one of the most commonly used electro-optical material for terahertz (THz) probe and imaging. We report herein how to engineer the surface behavior of a ZnTe single crystal to design subwavelength structures (SWSs) for enhancing ultrabroadband transmission. Polystyrene (PS) nanoparticle monolayers with a maximum coverage of 85.2% were produced on the ZnTe crystal by an eccentric spin-coating technique combined with surface wettability engineering. Subsequently, the well-defined conical SWS arrays were fabricated on the ZnTe crystal by reactive ion etching over the PS monolayer template, with the size of the SWS arrays customized by optimizing the etching process. Finally, we demonstrated ultrabroadband antireflection on the surface structured ZnTe crystals in the visible-near-infrared, infrared, and terahertz regions with transmittance increase of 11.6%, 10.0%, and 24.8%, which are attributed to the decrease of surface Fresnel reflection by SWS. Notably, in 0.2-1.0 THz, the transmittance reached over 70%. Our work provides a new strategy to enhance the THz generation efficiency and detection sensitivity based on ZnTe crystals by surface engineering.

Comparison of absorption simulation in semiconductor nanowire and nanocone arrays with the Fourier modal method, the finite element method, and the finite-difference time-domain method

For the design of nanostructured semiconductor solar cells and photodetectors, optics modelling can be a useful tool that reduces the need of time-consuming and costly prototyping. We compare the performance of three of the most popular numerical simulation methods for nanostructure arrays: the Fourier modal method (FMM), the finite element method (FEM) and the finite-difference time-domain (FDTD) method. The difference between the methods in computational time can be three orders of magnitude or more for a given system. The preferential method depends on the geometry of the nanostructures, the accuracy needed from the simulations, whether we are interested in the total, volume-integrated absorption or spatially resolved absorption, and whether we are interested in broadband or narrowband response. Based on our benchmarking results, we provide guidance on how to choose the method.

Numerical and Experimental Investigation into LWIR Transmission Performance of Complementary Silicon Subwavelength Antireflection Grating (SWARG) Structures

This paper presents a detailed comparison between the long wave infrared (LWIR) transmission performances of binary, silicon based, structurally complementary pillar and groove type antireflective gratings that can be used for wafer level vacuum packaging (WLVP) of uncooled microbolometer detectors. Both pillar and groove type gratings are designed with various topological configurations changing in various period sizes (Λ) from 1.0 μm to 2.0 μm, various heights/depths (h) from 0.8 μm to 1.8 μm, and various pillar/groove width-to-period (w/Λ) ratios from 0.6 to 1.0. The transmission performance of gratings is simulated with a hybrid simulation technique based on the modification of the reflection term within the Fresnel transmission equation, which combines both numerical and analytical approaches in a unique way for the first time in literature. Simulation results are experimentally verified with 19 different fabricated structures where a spectral agreement is achieved with an absolute root-mean-square (RMS) error less than 5.4% within the subwavelength (SW) regime, proving the effectiveness of the proposed hybrid technique. These results show first time in the literature that both pillar and groove type silicon based gratings present similar spectral IR transmission characteristics, and they are also structurally complementary when optimum configurations are employed to maximize the transmission.

Fabrication of broadband anti-reflective layers by mask-free etching TiO2 films

We present a simple way to make TiO₂ anti-reflective layers on top of silicon substrates. Surfaces of TiO₂ films have been modified by radio frequency plasma with CF₄ as an etchant. Mask-free etching process on the polycrystalline films leads to the formation of random sub-wavelength textures. The reflection of the etched samples are significantly suppressed in the wavelength range of 400~800 nm (2.9~4.6%, 3% compared with 34% on bare silicon at the wavelength of 600 nm). We have numerically simulated the optical properties of TiO₂ layers using the finite-difference time-domain method. The anti-reflective effects are attributed to random roughness on TiO₂ surfaces. The etching porcess increases the surface roughness, therefore, the gradient of refractive index between air and silicon substrate is reduced. As a result, the Fresnel reflection is supressed. Our results demonstrate an efficient way of anti-reflective coating for solar cells.

Tailoring diamond's optical properties via direct femtosecond laser nanostructuring

We demonstrate a rapid, accurate, and convenient method for tailoring the optical properties of diamond surfaces by employing laser induced periodic surface structuring (LIPSSs). The characteristics of the fabricated photonic surfaces were adjusted by tuning the laser wavelength, number of impinging pulses, angle of incidence and polarization state. Using Finite Difference Time Domain (FDTD) modeling, the optical transmissivity and bandwidth was calculated for each fabricated LIPSSs morphology. The highest transmission of ~99.5% was obtained in the near-IR for LIPSSs structures with aspect ratios of the order of ~0.65. The present technique enabled us to identify the main laser parameters involved in the machining process, and to control it with a high degree of accuracy in terms of structure periodicity, morphology and aspect ratio. We also demonstrate and study the conditions for fabricating spatially coherent nanostructures over large areas maintaining a high degree of nanostructure repeatability and optical performance. While our experimental demonstrations have been mainly focused on diamond anti-reflection coatings and gratings, the technique can be easily extended to other materials and applications, such as integrated photonic devices, high power diamond optics, or the construction of photonic surfaces with tailored characteristics in general.

Moth-Eye-Inspired Biophotonic Surfaces with Antireflective and Hydrophobic Characteristics

In nature, in order to prevent attention from predators, the eyes of night-flying moths have evolutionarily developed an antireflective ability. The surfaces of their eyes are covered with a layer of a sub-wavelength structure that eliminates reflections of visible light. This layer allows the eyes of moths to escape detection in darkness, without reflections that could reveal the position of the moths to potential predators. In this study, we proposed a novel procedure for manufacturing a non-close-packed polystyrene (PS) nanosphere monolayer by combining the Langmuir-Blodgett (LB) deposition technique and oxygen plasma treatment. An antireflective structure was replicated from the sub-wavelength structure of moth eyes onto the surface of a glass substrate by nano-imprinting lithography; the structure also displayed hydrophobic properties. The Fresnel reflection of the replicated sub-wavelength structure is near the theoretical prediction from the effective medium theory model. The biomimetic moth-eye structure can be applied to solar cells, monitors, light-emitting diodes, and other optical devices in the future.

Optical modeling and optimizations of Cu2ZnSnSe4 solar cells using the modified transfer matrix method

The fast and computationally inexpensive Modified Transfer Matrix Method (MTM) is employed to simulate the optical response of kesterite Cu₂ZnSnSe₄ solar cells. This method can partially take into account the scattering effects due to roughness at the interfaces between the layers of the stack. We analyzed the optical behavior of the whole cell structure by varying the thickness of the TCO layer (iZnO + ITO) between 50 and 1200 nm and the buffer CdS layer between 0 and 100 nm. We propose optimal combinations of the TCO/CdS thicknesses that can locally maximize the device photocurrent. We provide experimental data that qualitatively confirm our theoretical predictions.

General optimization of tapered anti-reflective coatings

An efficient, general optimized method is outlined that achieves antireflective tapers using lossless, non-dispersive dielectrics. The method modifies the derivative of a perfect antireflective wave amplitude distribution rather than the index of refraction distribution. Modifying the derivative of the wave amplitude distribution minimizes the potential index of refraction distributions and ensures perfect antireflection at one frequency, incidence angle, and linear polarization combination. Additional combinations of frequency, incident angle, and linear polarization can be targeted at a particular reflection coefficient within the optimization. After the method is outlined, three examples are shown with one being fabricated and validated at radiofrequencies.

Antireflective Coatings for Glass and Transparent Polymers

Antireflective coatings (ARCs) are applied to reduce surface reflections. We review coatings that reduce the reflection of the surface of the transparent substrates float glass, polyethylene terephthalate, poly(methyl methacrylate), and polycarbonate. Three main coating concepts exist to lower the reflection at the interface of a transparent substrate and air: multilayer interference coatings, graded index coatings, and quarter-wave coatings. We introduce and discuss these three concepts, and zoom in on porous quarter-wave coatings comprising colloidal particles. We extensively discuss the four routes for introducing porosity in quarter-wave coatings through the use of colloidal particles, which have the highest potential for application: (1) packing of dense nanospheres, (2) integration of voids through hollow nanospheres, (3) integration of voids through sacrificial particle templates, and (4) packing of nonspherical nanoparticles. Finally, we address the remaining challenges in the field of ARCs, and elaborate on potential strategies for future research in this area.

Optimized moth-eye anti-reflective structures for As2S3 chalcogenide optical fibers

We computationally investigate moth-eye anti-reflective nanostructures imprinted on the endfaces of As₂S₃ chalcogenide optical fibers. With a goal of maximizing the transmission through the endfaces, we investigate the effect of changing the parameters of the structure, including the height, width, period, shape, and angle-of-incidence. Using these results, we design two different moth-eye structures that can theoretically achieve almost 99.9% average transmisison through an As₂S₃ surface.

Irradiance enhancement and increased laser damage threshold in As₂S₃ moth-eye antireflective structures

It has been experimentally observed that moth-eye antireflective microstructures at the end of As2S3 fibers have an increased laser damage threshold relative to thin-film antireflective coatings. In this work, we computationally study the irradiance enhancement in As2S3 moth-eye antireflective microstructures in order to explain the increased damage threshold. We show that the irradiance enhancement occurs mostly on the air side of the interfaces and is minimal in the As2S3 material. We give a physical explanation for this behavior.

Enhancing near-infrared light absorption in PtSi thin films for Schottky barrier IR detectors using moth-eye surface structures

Si-based Schottky barrier infrared detectors typically use thin (1-10 nm) PtSi or Pd₂Si layers grown on Si substrates as an absorption medium. Herein, we demonstrate the use of sub-wavelength moth-eye (ME) structures on the Si substrate of such detectors to enhance absorption of near infrared (NIR) light in the active PtSi layer to increase detector efficiency. Absorbance enhancement of 70%-200% in the λ=1-2.5  μm range is demonstrated in crystalline PtSi films grown via electron beam evaporation of Pt and subsequent vacuum annealing. Low total reflectance (<10%) was measured for ME films, demonstrating the efficacy of the ME effect. Effective medium approximation calculations show that absorption enhancement at short wavelengths is partially due to forward scattering, which increases the effective optical path length in PtSi. Results also suggest that ME structuring of substrates is a general and low-cost method to enhance absorption in a variety of IR material platforms used for back-illuminated detectors.

Low-cost & low-temperature curable solution-processed silica-based nanostructured antireflective coatings on CuIn1−xGaxSe2thin film solar cells

A simple, low-cost and low-temperature curable silica-based antireflective coating (ARC) deposited by a solution-based process has been investigated for Cu(In,Ga)Se₂(CIGS) solar cells for the first time.