Substrate Thickness Research Articles

On the Peculiarities of Wire-Feed Electron Beam Additive Manufacturing (WEBAM) of Nickel Alloy–Copper Bimetal Nozzle Samples

In order to gain insight into the unique characteristics of manufacturing large-scale products with intricate geometries, experimental nozzle-shaped samples were created using wire-feed electron beam additive technology. Bimetal samples were fabricated from nickel-based alloy and copper. Two distinct approaches were employed, utilizing varying substrate thicknesses and differing fabrication parameters. The two approaches were the subject of analysis and comparison through the examination of the surface morphology of the samples using optical microscopy, scanning electron microscopy, and X-ray diffraction analysis. It has been demonstrated that the variation in heat flux distributions resulting from varying the substrate thicknesses gives rise to the development of disparate angles of grain boundary orientation relative to the substrate. Furthermore, it is demonstrated that suboptimal choice of the fabrication parameters results in large disparities in the crystallization times, both at the level of sample as a whole and within the same material volume. For example, for the sample manufacturing by Mode I, the macrostructure of the layers is distinguished by the presence of non-uniformity in their geometric dimensions and the presence of unmelted wire fragments. In order to characterize the experimental nozzle-shaped samples, microhardness was measured, uniaxial tensile tests were performed, and thermal diffusivity was determined. The microhardness profiles and the mechanical properties exhibit a higher degree of strength than those observed in pure copper samples and a lower degree of strength than those observed in Inconel 625 samples obtained through the same methodology. The thermal diffusivity values of the samples are sufficiently close to one another and align with the properties of the corresponding materials in their state after casting or rolling. The data discussed above indicate that Mode II yields the optimal mechanical properties of the sample due to the high cooling rate, which influences the structural and phase state of the resulting products. It was thus concluded that the experimental samples grown by Mode II on a thinner substrate exhibited the best formability.

Ultrathin Transistors and Circuits for Conformable Electronics.

Adapting electronics to perfectly conform to nonplanar and rough surfaces, such as human skin, is a challenging task, which could open up new applications in fields of high economic and scientific interest, ranging from health to robotics, human-machine interface, and Internet of Things. The key to success lies in defining a technology that can lead to ultrathin devices, exploiting ultimately thin materials, with high mechanical flexibility and excellent electrical properties. Here, we report a hybrid approach for the development of high-performance, ultrathin and conformable electronic devices, based on the integration of semiconducting transition metal dichalcogenides, i.e., MoS2, with organic gate dielectric material, i.e., polyvinyl formal (PVF) combined with inkjet printed PEDOT:PSS electrodes. Through this novel approach, transistors and simple digital and analogue circuits are fabricated by a sequential stacking of ultrathin (nanometer) layers on a few micrometers thick polyimide substrate, which guarantees the high flexibility mandatory for the targeted applications.

Screen-printing high/low resistance using only a single silver nanowire ink: Resistance-gradient metasurface application for broadband microwave absorption and optical transparency

Transparent metasurface absorbers are highly sought after for their diverse applications, but achieving broad absorption bandwidths without sacrificing optical transparency remains a challenge. Traditionally, enhancing absorption involves increasing substrate thickness, which reduces transmittance. We address this by introducing a resistance-gradient metasurface (RGM) that combines broad absorption with high optical transparency. Unlike conventional methods requiring various inks for different resistances, our approach uses a single silver nanowire ink and screen-printing to create multiple resistances. This technique allows for flexible design and multiple resonances within the metasurface, achieving broad absorption even with a thin substrate. The RGM demonstrates an absorption bandwidth from 8.68 to 11.48 GHz with a substrate thickness of just 0.045 λ0, and optical transmittance of 66.3 % at 550 nm. This innovation promises to enhance both substrate efficiency and bandwidth in transparent metasurface absorbers, broadening their application potential in advanced devices.

Numerical simulation of the temperature excursions of porous substrates during atomic layer deposition

Atomic layer deposition (ALD) processes are usually highly exothermic. For ALD on substrates with high specific surface area, the reaction heat per ALD cycle may lead to a substantial temperature rise of the substrates. The novelty of this study lies in quantifying the temperature excursions of porous substrates during ALD via numerical simulation and further addresses the issue of tuning this type of thermal effect. A comprehensive model has been developed and validated to investigate the ALD thermal effect with accounting for the roles of the precursor transport phenomena within the ALD reactor system, and the coupling among the precursor diffusion, heat transfer, film deposition, reaction heat generation within the porous substrates. The results show that the thermal effect of the sub-saturated ALD can change with different substrate thickness, precursor partial pressure profile, heat transfer coefficient, and kinetic parameters. In contrast, for saturated ALD with adiabatic condition, the maximum temperature rise of the substrate is a deterministic value, independent of the substrate thickness and precursor partial pressure profile. The thermal effect with the porous substrates can influence the ultimate deposit amount and its distribution for sub-saturated ALD and change the time required for attaining saturation for saturated ALD. The temperature rises of certain common substrates during typical half-ALD cycles have been simulated to demonstrate the capability of the present model in predicting the thermal effect of ALD.

A graphene-based IR Fresnel lens formed on a multiple-internal-reflection substrate

We report on the adjustable lensing effect and switchable mode performance of a graphene-based Infrared (IR) Fresnel zone plate (FZP) formed on a double-side polished Si substrate. The focusing characteristics of the graphene FZP in the IR wavelength range have been systematically investigated as a function of the Fermi energy (EF) of the multilayer graphene rings and the thickness of the Si substrate using the Finite-Difference Time-Domain method. This graphene FZP lens enhances the focal intensity of incident light at wavelengths where the multiple internal reflections in the Si substrate is periodically maximized. Also, the contrast ratios of reflectance and transmittance between the regions with and without graphene rings, which affects the focusing performance, are effectively controlled through intraband transitions depending on the EF of graphene FZP pattern. Specifically, the 8-layer graphene FZP lens transmits the incident light with a wavelength of 8 μm when the EF of the graphene is lower than 0.2 eV, while it operates as both transmissive and reflective Fresnel lens when the EF exceeds 0.2 eV. By directly depositing Ag nanoparticles on this graphene FZP to enable Ef control of graphene rings without the need for electrodes, we have experimentally confirmed the focusing performance and mode conversion properties.

Daytime radiative cooling using pattern free metal dielectric coating

Radiative coolers, which dumps the excess heat to the cold outer space by releasing the thermal radiation through the atmospheric window, have offered an alternate and feasible solution to the conventional coolers that are fueled on the electricity produced by either using renewal or non-renewal sources like fossil fuels. Particularly, daytime passive radiative coolers have paved the way for many energy free technology that are used in reducing the temperature of building tops, power plants, and water harvesting. In this, we propose a pattern free and large area scalable bi-layered thin film based daytime radiative cooler. The proposed design illustrates an average reflectivity of 98.5% for the solar spectrum, while showing average emittance of 91% within the atmospheric window (8-13μm). The design consists of thin films of transparent dielectrics such as ZnS or BaF2 placed on top of a thick glass substrate, that is backed by a thin film silver. We theoretically obtained a cooling power of 119 W.m−2 with a temperature reduction of 9 °C below the ambient.

Broadband metamaterial polarizers with high extinction ratio for high-precision terahertz spectroscopic polarimetry

The demand for precise polarizers is increasing to investigate the polarization characteristics of materials non-invasively in the terahertz region. Recently, to address the low extinction ratio and fragile nature of conventional wire-grid polarizers, plasmonic structures and metasurfaces have been proposed. However, the challenge of achieving low transmittance compared to a high extinction ratio, along with the bulky structure due to a thick substrate, remains to be addressed. Here, we present high-efficiency broadband metamaterial polarizers consisting of cross-aligned double-layers of subwavelength metallic slit arrays, leveraging the extraordinary optical transmission and funneling effects. We obtained extinction ratios exceeding 70 dB over a broad frequency range, from 0.2 to 2.5 THz, reaching a maximum extinction ratio of ∼90 dB at 0.7 THz. To investigate the influence of high extinction ratio polarizers on actual measurement results, we measured a non-Hermitian metasurface with asymmetric polarization conversion and analyzed them using the Jones matrix formalism. The results confirmed that the extinction ratio of the polarizer has a significant impact on precise polarization-dependent measurements, especially on cross-polarization measurements. The enhanced performance of our polarizers offers significant potential for sensitive THz systems, paving the way for advancements in polarization analysis of emerging materials and chiral sensing.

Investigation of a Hydrophobic Sputtered Cu Electrode to Electrocatalyze CO2 Towards a C2+ Product: The Effect of Substrate and Catalyst Thickness

The overuse of fossil fuels has resulted in massive CO2 emissions, causing global environmental problems. Renewable energy-driven electrocatalysis, which can convert CO2 into fuels and chemicals, is considered an emerging technology for carbon resource recycling. Cu-based catalysts sputtered on hydrophobic carbon paper and a polytetrafluoroethylene (PTFE) membrane were comparatively investigated, while the effect of the thickness of the Cu sputtering layer on the electrocatalytic CO2 reduction performance was investigated. Additionally, the effect of substrate properties on the distribution and morphology of sputtered Cu metal was investigated by SEM and XRD. With carbon paper as the substrate, the highest FEC2+ achieved was 70% at 200 mA/cm2, while the maximum value of FEC2+ on the Cu/PTFE electrode was realized with a Cu thickness of 400 nm (72%). Additionally, the PTFE substrate demonstrated a better inhibiting effect on HER, with a lower FEH2 and high FEC2+ over different applied current densities.

Characterization and simulation of AlSi10Mg reinforcement structures by direct energy deposition by means of laser beam and powder

Among metal additive manufacturing technologies, direct energy deposition (DED) processes have the advantage to be easily integrable in a manufacturing chain with other conventional technologies. This characteristic can be exploited by designing reinforcement structures to be added by DED onto pre-existing subcomponents to tailor the part’s mechanical properties while keeping the part lightweight. This study focuses on DED by means of laser beam and powder process optimization to improve material quality and geometrical accuracy of AlSi10Mg reinforcement structures while preventing excessive thermal deformations and material dilution into the substrate. These results are compared with finite elements numerical simulations of the deposition process, comprising thermo-elastic deformation and material deposition, to predict the bending and reinforcement of the processed substrate. In particular, the model includes the deterministic prediction of the deposition profile as a function of the process parameters and a few condition-specific coefficients: once calibrated, the model was used to compare the numerical and experimental residual deformation of the reinforced sample, obtaining promising agreement. The reinforcement provided to a 1.5 mm thick substrate by a single wall of deposited materials, with cross-sectional dimensions of 2 mm in width and 2.5 mm in height, was evaluated by three points bending. With the reinforcement on the tensile side of the stresses, the energy absorbed by the material plastic deformation increased by 2.4% as compared to the substrate alone, while with the reinforcement on the compression side of the stresses the energy absorption increased by 75.8% on average.

Finite element simulations of quartz crystal microbalances (QCM): from Sauerbrey to fractional viscoelasticity under water

2D finite element simulations are performed on QCM working in the thickness-shear mode and loaded with different homogeneous films. They include a purely elastic film, a viscoelastic Maxwellian liquid, viscoelastic-Voigt solid, and the fractional viscoelastic (power-law) version of each case. Unlike single-relaxation kind models, fractional viscoelasticity considers the relaxation-time spectrum often found in polymeric materials. The films are tested in air or covered with liquids of different viscosities. Two substrate thicknesses are tested: 100 nm and 500 nm, the latter being close to the condition that promotes the resonance of the adsorbed film. In all cases the simulations are compared with small-load approximation theory (SLA). The 100 nm films follow the theory closely, although significant deviations of the SLA are observed as the overtone number n increases, even in purely elastic films. We also show that it is possible to identify the viscoelastic ‘fingerprint’ of the 100 nm films in air using raw data and Sauerbrey’s equivalent thickness obtained with the QCM in the 3 < n < 13 range. These numerical data are validated by experimental measurements of crosslinked polydimethylsiloxane films with thicknesses ∼150 nm. In contrast, the 500 nm films deviate notoriously from the SLA, for all viscoelastic models and overtones, with the largest deviation observed in the elastic film. When a liquid layer covers the QCM without an adsorbed film, the only overtone that numerically reproduces the theoretical value is the fundamental, n = 1. For n > 1, strong coupling between the solid and liquid is detected, and the original vibration modes of the crystal are altered by the presence of the liquid. Finally, the numerical simulations suggest that it is possible to detect whether a viscoelastic film is formed under a liquid layer using only the information from n = 1. In these film/liquid systems we also observe the so-called missing-mass effect, although the theory and simulations exhibit different levels of impact of such effect when the liquid viscosity is high.

A novel strategy for activation technique for 6H-SiC substrates in electroless Ni-P plating processes

This study proposes a novel iron wire activation method for electroless Ni-P plating on 6H-SiC substrates, offering a sustainable alternative to traditional metal activation techniques, focusing on the surface roughness effect on the microhardness and Ni-P plating efficiency of 6H-SiC substrates. This experimental approach reveals insights into the relationship between substrate morphology and plating characteristics. It is found that the plating thickness (33.82 μm) of the non-polished substrates closely matched the expected (33.26 μm), with a deposition rate of 6.65 μm/h, which underscores the precision regulation of the plating process. In contrast, despite the faster deposition rate of 9.20 μm/h of the polished S500 substrate, it exhibited a minor thickness discrepancy, suggesting a saturation point in the deposition dynamics on fully polished surfaces. The research additionally sheds light on the adhesion characteristics of the plated layers, particularly emphasizing the role of surface roughness. Remarkably, non-polished substrates demonstrated better adhesion, categorized as HF3, indicating a significantly stronger bond compared to the polished substrates, which were categorized as HF4 to HF6. This distinction in adhesion categories underlines the critical influence of substrate morphology on the quality of the Ni-P layer's adherence.

MONOCRYSTALLINE DIAMOND MEMBRANES WITH A THICKNESS OF 10 MICRONS, MANUFACTURED BY PLASMA ETCHING

New applications of high-quality synthetic diamond in sensors and integrated photonic circuits, which are being rapidly developed nowdays, often demand freestanding diamond membranes with a thickness of about 10 microns as a substrate. However, the process of thin single-crystal diamond membranes fabrication, as well as their subsequent processing are challenging due to the high hardness, chemical resistance and brittleness of the material. Our work demonstrates a method for creating freestanding diamond membranes mounted on a thick diamond substrate using reactive ion etching of single-crystalline diamond wafers in plasma with mechanical protective masks. The optimal thickness of a diamond wafer for membranes etching is determined in the range from 100 to 120 µm with mandatory plane-parallel polishing of the sides. We experimentally studied the interaction of RF discharge SF6 based plasma with diamond surface during deep etching with mechanical protective masks of various shapes. It was found that the use of thick masks leads to an uneven rate of diamond etching over the entire area of the formed membrane. We have assessed ion sputtering resistance of various mask materials in SF6 based plasma, and found the most promising mask materials for deep diamond etching (steel, copper, diamond). We have fabricated diamond membranes with a thickness of 11,5 µm (and more), mounted on a durable 60 µm (and more) thick frames, and studied their characteristics. After etching membrane surface roughness was less than 25 nm, and the unevenness of their thickness did not exceed 20%. Also, we compare different methods for controlling the depth of diamond etching and the thickness of the resulting membranes, including mechanical measurements, IR spectral reflectometry, optical profilometry and electron microscopy. For citation: Golovanov A.V., Yun M.I., Bondarenko M.G., Prosin A.A., Tarelkin S.A. Monocrystalline diamond membranes with a thickness of 10 microns, manufactured by plasma etching. ChemChemTech [Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol.]. 2024. V. 67. N 10. P. 55-64. DOI: 10.6060/ivkkt.20246710.1y.

Size effects and optimization during laser directed energy deposition on high thermal conductivity copper alloys

High-copper alloy/nickel-based high-temperature alloy bimetallic structures are widely utilized in critical components, such as thrust chambers of liquid rocket engines, water cooling circuits for fusion reactor deflectors, and electromagnetic railguns. Among various methods for fabricating Cu/Ni bimetallic structures, laser directed energy deposition (LDED) is considered one of the most promising techniques for depositing nickel-based high-temperature alloys onto high-copper alloy surfaces. In the LDED fabrication process, substrates with uneven thicknesses are a common. The process is characterized by its multi-parameter, high-sensitivity, and non-equilibrium solidification characteristics. Consequently, variations in substrate size can significantly affect molten pool morphology and fabrication stability. This study examines the size effect of a single track of LDED Inconel 718 (In718) on a CuCr0.8 high-copper alloy substrate. The results indicate a pronounced size effect when using a high thermal conductivity CuCr0.8 substrate, particularly regarding substrate thickness. By reducing the thermal conductivity of the CuCr0.8 substrate, the size effect is mitigated, improving the process adaptability of LDED. These findings provide valuable data for the laser processing of surfaces with uneven thickness and high thermal conductivity. They are expected to support the fabrication of variable thrust liquid rocket engines and advance the field of interplanetary exploration.

Halvorsen chaotic system based microwave absorber modelling for fighter jet stealth technologies

This study focuses on the development and detailed analysis of a broadband microwave absorber utilizing Halvorsen chaotic dynamics, that focuses at enhancing stealth capabilities for fighter jets. The investigation begins by exploring the mathematical formulation of the Halvorsen chaotic system and conducting a parametric sweep of its control parameters to generate distinct two-dimensional and three-dimensional chaotic attractor plots. These plots are then post-processed using Julia set theory to develop intricate fractal patterns, which serve as the foundation for the absorber design. Image processing techniques, including filtering and thresholding, are employed to refine the patterns by removing artifacts and noise, ensuring they are suitable for practical implementation. The refined fractal patterns are then imported into a computational electromagnetic simulation environment where they are patterned onto a 0.035 mm thick copper sheet. Moreover, the Magtrex 555 substrate with a thickness of 1.52 mm, is selected for its high permittivity and low-loss characteristics. A comprehensive series of parametric studies are conducted to evaluate the influence of various design parameters such as side length, unit cell geometry, and substrate thickness on the absorber’s electromagnetic performance. Important parameters include the effects of chaotic control parameter optimization and the electromagnetic boundary conditions applied during the simulations. Extensive simulations are performed across the 2–20 GHz frequency range to evaluate absorption efficiency, focusing on key metrics like absorptivity, surface current distribution, and electric field distribution. The final design achieves over 90 % absorption efficiency within the target frequency band when the chaotic control parameters are optimized. Finally, comparative analysis using different commercially available substrates, including FR-4 and Rogers RO3003, reveals that Magtrex 555 offers superior absorption performance. The study concludes with a detailed presentation of the final absorber design, alongside an indepth discussion of the frequency range, parametric variations, and the impact of chaotic system dynamics on the absorption properties. This research provides crucial insights into the design and optimization of chaotic-system-based microwave absorbers, that advances the development of stealth technology in military applications.

Plasmonic Coupling for High‐Sensitivity Detection of Low Molecular Weight Molecules

This article presents a novel plasmonic sensing platform designed for the detection of low molecular weight molecules, offering significant advancements in diagnostic applications. The platform features a periodic array of gold nanodisks on a 20 nm thin silica layer, supported by a 100 nm thick gold substrate. By leveraging the coupling between localized and propagating surface plasmon resonances, this design significantly enhances the sensitivity and specificity of molecular detection. Finite element method simulations are conducted to characterize the optical properties and reflectance response of the nanodisks array in the visible to near‐infrared range. Ellipsometric analysis is performed to measure the reflectance of the sample at various angles. Additionally, scanning near‐field optical microscopy in reflectance mode validates the design by revealing well‐defined plasmonic hot spots and interference patterns consistent with the simulated results. The findings demonstrate the platform's effectiveness in amplifying optical signals, achieving a limit of detection of 50 μM for molecules with a molecular weight of less than 1 KDa. This high sensitivity and specificity highlight the potential of the proposed plasmonic platform to advance the development of highly sensitive sensors for low molecular weight molecules, making it a valuable tool for diagnostics and precise molecular detection.

Advanced Metamaterial-Integrated Dipole Array Antenna for Enhanced Gain in 5G Millimeter-Wave Bands

A metamaterial-based non-uniform dipole array antenna is presented for high gain 5G millimeter-wave applications with a wideband characteristic. Initially, a non-uniform dipole array is designed on a 0.202 mm thick Rogers RO4003C substrate, offering a wide operating bandwidth ranging from 23.1 GHz to 44.8 GHz. The dipole array antenna emits unidirectional end-fire radiation with a maximum gain of 8.1 dBi and an average gain of 6.7 dBi. Subsequently, to achieve high gain performance, a 5 × 7 metamaterial structure is designed in the direction of the antenna radiation. The implemented metamaterial structure is optimized for the operating frequency, enhancing the directivity of the antenna radiation and resulting in a gain increment of more than 3 dBi compared to the dipole array alone. The developed metamaterial-integrated dipole array antenna offers an operating bandwidth (S11 &lt; −10 dB) of more than 21 GHz (63.92%), ranging from 23.1 GHz to 44.8 GHz, covering the most commonly used 5G millimeter-wave frequency bands (n257, n258, n259, n260, and n261). Furthermore, the presented antenna yields a stable high gain with a peak gain of 11.21 dBi and a good radiation efficiency of more than 64%. The proposed antenna is an excellent option for millimeter-wave 5G systems due to its overall properties, particularly its high gain and end-fire radiation characteristics, combined with a wide operating bandwidth.

Microwave absorber surface design for 5G energy harvesting applications

This study presents a high-efficiency microwave absorber for energy harvesting in 5G frequencies. Initially, a unit cell was designed in four stages to efficiently absorb in the targeted frequency region. The results obtained for each stage of the design were analyzed, and additional investigations were conducted for substrate material and thickness based on the optimum performance of the unit cell structure. A unit cell absorber designed on an FR4 a flame-resistant fiberglass/epoxy-based composite, commonly utilized in printed circuit boards due to its favorable electrical insulation properties and low cost. With a thickness of 1.5 mm, the absorber achieved a 98.04% absorption at 3.8 GHz according to simulation results. Subsequently, this unit cell was separately designed and simulated with different periodic arrays to transform into an absorber surface. As a result, high absorption rates of 98.94% and 98.35% were achieved at 3.8 GHz and 4.2 GHz, respectively, in the 2 × 2 array. It was observed that the structure absorbs over 85% within a 1 GHz bandwidth between 3.5 GHz and 4.5 GHz. Finally, a prototype of the absorber surface was manufactured, and measurements were taken in the laboratory environment. Significant agreement was found between the data obtained from these measurements and the simulation results. The results indicate that the suggested absorber surface is well-suited for energy harvesting within the n77 (3.3 GHz to 4.2 GHz) and n78 (3.3 GHz to 3.8 GHz) bands of 5G communication.

Analysis and Guideline for Determining Piezoelectric Coefficient for Films With Substrate Constraint.

Piezoelectric films including coatings are widely employed in various electromechanical devices. Precise measurement for piezoelectric film properties is crucial for both piezoelectric material development and design of the piezoelectric devices. However, substrate constraint on the deformation of piezoelectric films could cause significant impacts on the reliability and accuracy of the piezoelectric coefficient measurement. Through both theoretical finite element analysis (FEA) and experimental validation, here we have identified three important factors that strongly affect the measurement results: ratio of Young's modulus of substrate to piezoelectric film, ratio of electrode size to substrate thickness, and test frequency. Our investigations show that a relatively smaller substrate's Young's modulus to film, and a larger ratio of electrode size to substrate thickness would cause a larger substrate bending effect and thus potentially more significant measurement errors. Moreover, intense transversal displacement fluctuation can be excited at excessively high frequencies, leading to unreliable measurements. Various well-established piezoelectric measurement methods are compared with outstanding measurement issues identified for those commonly used piezoelectric films and substrates. We further establish the guidelines for piezoelectric coefficient measurements to achieve high reliability and accuracy, thus important to the wide technical community with interests in electromechanical active materials and devices.

Particle swarm optimization for performance enhancement of cadmium telluride thin film solar cells by embedded nano-grating structures with a plasmonic metal coating layer

As the demand for energy in world is increasing rapidly and there is pursuit for renewable energy sources which is cheap, easy to generate and requires low maintenance, solar energy is a top contender. The world is in dire need of photovoltaic solar cells that can aid in keeping up with the hiking energy demands. However, thin film solar cells (TFSCs) which are developed for cost effectivity, suffer in performance due to reduced thickness. Therefore, this computational study uses Finite-Difference Time-Domain (FDTD) and delves into the scope of using a 1-D nano-grating structure embedded into absorbing layer of cadmium telluride TFSC to enhance the optoelectronic performance. A unique nano-grating structure with SiO2 at its core and aluminium coating aims to enhance the performance of CdTe TFSC with cost effectivity and ease of fabricability as the main motifs. Additionally, an evolutionary computational technique, Particle Swarm Optimization (PSO), was used to determine the optimal parameters of nano-gratings on CdTe TFSCs, i.e., nano-grating height, angle, duty cycle, aluminium coating thickness and grating substrate thickness. The PSO algorithm resulted in a nano-grating structure that yielded an efficiency increase of 52.86% and increase in short-circuit current density of 25.45% with respect to bare CdTe TFSCs. Subsequently, the performance of the optimal nano-grating structure was also observed to be insensitive to variation of wide range of incidence angle of light, a key feature preferred for versatile application of TFSCs.

Wrinkling of differentially growing bilayers with similar film and substrate moduli

Growth-induced surface wrinkling in constrained bilayers comprising a thin film attached to a thick substrate is a canonical model for understanding pattern formation in many biological systems. While the bilayer model has received much prior attention, the nonlinear behaviour for arrangements with similar film and substrate properties, or substrate growth that outpaces film growth, remains poorly understood. This paper therefore focuses on these cases in which the substrate’s elasticity dominates surface wrinkling. By combining analytical modelling and finite element simulations incorporating advanced path-following techniques, we characterise critical wrinkling states and explore the initial and advanced post-buckling behaviour for a wide range of film-to-substrate modulus and growth rate ratios. It is shown that the classical leading-order asymptotic expression for the critical strain is not of sufficient accuracy for film-to-substrate modulus ratios below 50, and higher order correction terms are presented. Leveraging a weakly nonlinear analytical model, we introduce a phase diagram categorising stable and unstable post-buckling regimes. Advanced path-following simulations are employed to unveil the evolution of wrinkling patterns, from initial sinusoidal instabilities to complex formations involving period doubling, quadrupling, and eventual surface creasing. These comprehensive phase diagrams, parameterised by film-to-substrate modulus and growth rate ratios, provide new insights into the rich dynamics of surface wrinkling. Finally, we demonstrate the existence of multi-stability in the advanced post-buckling regimes for bilayers experiencing substrate-dominated growth. This work contributes to the understanding of the mechanics underlying pattern formation in growing bilayers over the entire parameter regime, with potential implications for explaining biological morphogenesis and informing the development of novel diagnostic tools and artificial flexible electronic skins.