Dimensions Of Nanostructures Research Articles

Optimization of hierarchical textured PDMS film with wide-angle broadband anti-reflection for light trapping in solar cells

We developed a hierarchical random pyramid (HRP)-polydimethylsiloxane (PDMS) film as an antireflective layer for metal halide perovskite solar cells (PSCs). To create the HRP structure on the PDMS surface, we first patterned the Si surface using alkaline etching and Ag-assisted chemical etching (Ag-ACE) and then transferred the pattern onto the PDMS surface. The resulting PDMS exhibited hierarchical structures of inverted micro-pyramids with nano-scale surface features. The optical performance of the textured PDMS film was observed across the entire wavelength range of visible light (λ = 300–800 nm), attributed to the enhanced light-trapping effect resulting from the increased fractal dimensions (Df) of the hierarchical nanostructures. Under optimal conditions, an average reflectance of 3.13 % was observed, along with a 14 % improvement in transmittance compared to that of the reference. Finite difference time-domain simulations were used to investigate the origins of these optical enhancements, conclusively linking them to the HRP structures. The optimized structures also showed superhydrophobicity with a contact angle (θCA) of approximately 155.2°. When applied to PSCs (MAPbI3), the optimized textured PDMS film led to a 12 % increase in short-circuit current density (Jsc) from approximately 23.1 to 25.98 mA/cm2. Furthermore, the power conversion efficiency of the MAPbI3 p-i-n structured devices was enhanced by 18.21 %, representing a 13 % improvement. Our results confirm that the HRP-PDMS film enhances superhydrophobicity and light trapping, while mitigating the transmittance loss due to changes in the incident angle. This study suggests potential strategies for overcoming the limitations of light absorption in solar cell applications.

Engineering amphiphilic alkenyl lipids for self-assembly in functional hybrid nanostructures

The development of biocompatible hybrid nanosystems for advanced functional applications presents significant challenges to the research community. Key obstacles include the poor solubility of these nanosystems in water and the difficulty of precisely controlling their nanostructure dimensions and composition. A promising approach to overcoming these challenges is the self-assembly of surfactant-based building blocks into well-ordered hybrid nanostructures. In this study, we explore the relationship between structure and self-assembly in novel low molecular weight amphiphilic molecules to produce stable and biocompatible hybrid nanostructures. We investigated the self-assembly behavior of two families of amphiphiles derived from alkenyl lipids with one or two double bonds, leading to distinct hybrid supramolecular structures facilitated by the incorporation of hydrophobic iron oxide nanoparticles (IONPs) as templates. The presence of double bonds in the lipid tail and the morphology of the amphiphile influence the arrangement on the hydrophobic NPs. Amphiphiles with a single double bond in the lipid tail form highly water-soluble, well-ordered micellar-like structures on the IONP surfaces, while those with two double bonds create disordered lipid nanoparticles. Furthermore, these amphiphilic molecules can self-organize into higher-order hybrid supramolecular structures, such as vesicles, with potential applications in magnetic resonance imaging (MRI).

Quasi-visualizable detection of deep sub-wavelength defects in patterned wafers by breaking the optical form birefringence

Abstract In integrated circuit (IC) manufacturing, fast, nondestructive, and precise detection of defects in patterned wafers, realized by bright-field microscopy, is one of the critical factors for ensuring the final performance and yields of chips. With the critical dimensions of IC nanostructures continuing to shrink, directly imaging or classifying deep-subwavelength defects by bright-field microscopy is challenging due to the well-known diffraction barrier, the weak scattering effect, and the faint correlation between the scattering cross-section and the defect morphology. Herein, we propose an optical far-field inspection method based on the form-birefringence scattering imaging of the defective nanostructure, which can identify and classify various defects without requiring optical super-resolution. The technique is built upon the principle of breaking the optical form birefringence of the original periodic nanostructures by the defect perturbation under the anisotropic illumination modes, such as the orthogonally polarized plane waves, then combined with the high-order difference of far-field images. We validated the feasibility and effectiveness of the proposed method in detecting deep subwavelength defects through rigid vector imaging modeling and optical detection experiments of various defective nanostructures based on polarization microscopy. On this basis, an intelligent classification algorithm for typical patterned defects based on a dual-channel AlexNet neural network has been proposed, stabilizing the classification accuracy of λ/16-sized defects with highly similar features at more than 90%. The strong classification capability of the two-channel network on typical patterned defects can be attributed to the high-order difference image and its transverse gradient being used as the network’s input, which highlights the polarization modulation difference between different patterned defects more significantly than conventional bright-field microscopy results. This work will provide a new but easy-to-operate method for detecting and classifying deep-subwavelength defects in patterned wafers or photomasks, which thus endows current online inspection equipment with more missions in advanced IC manufacturing.

Dendritic copper nanostructures for ultrasensitive detection of rhodamine 6G and Congo red

Surface-Enhanced Raman Scattering (SERS) is a fast-responding and non-destructive ultra-sensitive detection technique that can replace traditional chromatographic and spectroscopic analysis techniques. In this experiment, dendritic copper nanostructures were prepared by the solid-state ionics method and the vacuum hot evaporation process with an applied current of I=9μA. Using them as a SERS substrate, Raman detection was performed on the dye molecules Rhodamine 6G (R6G) and Congo Red (CR) to determine SERS enhancement performance. It is found that the growth of the prepared copper nanostructures has a top-end dominant phenomenon. The fractal dimension of the copper nanostructure was calculated using fractal theory, and it was revealed to be 1.560. Scanning electron microscopy (SEM) results showed that a large number of 60-80 nm regularly arranged copper nanoparticles were attached to the surface of the dendritic copper nanostructure. This is beneficial to increase the surface roughness of the substrate and improve the detection level of dye molecules. Subsequently, copper nanostructures can sensitively detect R6G and CR solutions as low as 1×10-13 mol/L and 1×10-7 mol/L, reaching single-molecule levels. The Raman mapping experiment showed that the mean relative standard deviation (RSD) values of R6G and CR were 12.3% and 12.9%, indicating high uniformity and reproducibility of the structure. This structure effectively achieves the fusion of uniformity, repeatability, and sensitivity, and shows broad application prospects in food detection.

Harnessing the potential of electrospun TiO2 nanofibers and nanoparticles enriched with natural dyes: a path towards affordable aolutions for low-cost electronic devices

Abstract This study evaluates the morphological effects of TiO2 nanoparticles, nanofibers, and a bilayer configuration on electronic devices, such as Dye-Sensitized Solar Cells (DSSCs) and UV sensors. Cost-efficient natural dyes—curcumin, coffee beans, and banana peel—were used as sensitizers for nanomaterial films. TiO2 nanoparticles were synthesized using the sol–gel technique, while nanofibers were produced via electrospinning. Characterization techniques, including Scanning Electron Microscopy (SEM), Energy Dispersive x-ray Spectroscopy (EDS), and x-ray Diffraction (XRD), confirmed the formation and dimensions of the TiO2 nanostructures. UV–visible spectroscopy was used to determine the optical properties of the samples. TiO2 nanofibers and nanoparticles exhibited high surface-area-to-volume ratios, with nanofibers having a diameter of 20 nm and particles measuring 50 nm. A binder-free, low-temperature paste was prepared using TiO2 nanoparticles and nanofibers to develop thin films. The turmeric dye showed peak absorption at 470 nm with a band gap energy of 2.06 eV when loaded on a TiO2 bilayer film. This study aims to develop electronic devices that reduce costs and enhance performance by using low-cost, efficient, and economically viable dyes. TiO2 nanofiber and nanoparticle films show promise for cost-effective and high-performance electronic devices.

Colloidal Quasi-2D Methylammonium Lead Bromide Perovskite Nanostructures with Tunable Shape and High Chemical Stability.

Control over the lateral dimensions of colloidal nanostructures is a complex task which requires a deep understanding of the formation mechanism and reactivity in the corresponding systems. As a result, it provides a well-founded insight to the physical and chemical properties of these materials. In this work, the preparation of quasi-2D methylammonium lead bromide nanostripes and discuss the influence of some specific parameters on the morphology and stability of this material is demonstrated. The variation in the amount of the main ligand dodecylamine gives a large range of structures beginning with 3D brick-like particles at low concentrations, nanostripes at elevated and ultimately nanosheets at large concentrations. The amount of the co-ligand trioctylphosphine can alter the width of the nanostripe shape to a certain degree. The thickness can be adjusted by the amount of the second precursor methylammonium bromide. Additionally, insights are given for the suggested formation mechanism of these anisotropic structures as well as for stability against moisture at ambient conditions in comparison with differently synthesized nanosheet samples.

Comparison of In Vitro and In Vivo Biological Screening of Nano‐Palladium (II) and Platinum (II)‐Based Compounds With DFT and Molecular Docking Study

ABSTRACTWithin the current challenges in medicinal chemistry, the creation of novel and improved therapeutic agents stands out. 2‐Cyano‐3‐(thiophen‐2‐yl)prop‐2‐enethioamide (CTPTA) ligand was complexed with palladium (II) and platinum (II) ions within the nanoscale with the molecular formula [M (CTPTA)Cl2]. H2O. The CTPTA ligand and its complexes were characterized by elemental analysis, UV–Vis spectra, FTIR, mass spectra, TGA, magnetic measurement, and the molar conductance technique. Analysis with a scanning electron microscope (SEM) revealed that the nanostructure dimension of both complexes is predominantly between 10 and 30 nm. The CTPTA ligand functions as a bidentate ligand, utilizing thione sulfur, and cyanide nitrogen atoms. Density functional theory was employed to analyze the geometric structure properties of the CTPTA ligand and its complexes. Natural population (NPA) and Mulliken population (MPA) methods were used to calculate the charge distribution. The cytotoxic impact results of all compounds on human liver cancer (HepG2) cell line were satisfactory. The ligand and its complexes were also tested against gram‐negative and gram‐positive bacteria in vitro. The findings of the molecular docking study supported the cytotoxicity and antibacterial effects. The antioxidant and anti‐inflammation activities of synthesized palladium (II) and platinum (II) complexes had a great spectrum of activity. The preclinical pharmacokinetic studies on albino rats revealed that the newly studied complexes achieved excellent antitumor results. This was clear in the investigated parameters, especially the amelioration of AFP levels, liver weight, oxidative stress, and lobular hepatic architecture injury.

Substrate-induced hybridization of plasmon modes in the composite nanostructure of nanodisk array/thin film for spectrum modulation.

Hybridization coupling among plasmon modes is an effective approach to manipulate near-field properties thus optical spectral shapes of plasmonic nanostructures. Generally, mode hybridization coupling is achieved by modifying the topography and dimensions of nanostructures themselves, with few concerns about substrate-induced manipulation. Herein, we propose a composite nanostructure consisting of a gold (Au) nanodisk array and a thin Au film supported by a dielectric substrate. In this configuration, both the refractive index of the dielectric substrate and thin gold film's thickness mediate the interaction of plasmon modes supported by upper and lower interfaces of the composite nanostructure, resulting in two hybridized plasmon modes. We systematically investigate the relationship between optical fields at the top surface of plasmon modes before and after the hybridization coupling. Specifically, the near-field amplitude at the top surface of the unhybridized modes is stronger than that of individual hybridized mode, and lower than the near-field summation of these two hybridized modes. This work not only provides a straightforward strategy for generating two plasmon modes in a nanostructure but also elucidates the variation of the optical field during the hybridization process, which is of crucial significance for applications, such as upconversion enhancement and multi-resonance sensing.

Enhancing THz radiation by optimizing the dimensioning of metallic nanostructures

A scheme of nonlinear terahertz (THz) radiations from gas atoms in spatially inhomogeneous fields induced by an intense monochromatic laser and an array of bow-tie shaped metallic nanostructures is proposed and theoretically investigated. Our simulations are based on the finite-difference time-domain method (FDTD) and time-dependent Schrödinger equations. The results demonstrate that the collective motion of ionized electrons within the inhomogeneous field generates intense transient currents. Asymmetrical electron motion leads to a net current, thereby generating strong THz radiation. By modulating the geometric dimensions of the metallic nanostructures, control over the distribution of the inhomogeneous field is achieved, enabling modification of the generated THz radiation.

Magnetic field effects on electronic and optical properties in variant toroidal quantum ring: A comparative study of GaN, GaAs, and CdSe materials

In this work, we have examined the electronic and optical properties of three Variant Toroidal Quantum Ring (VTQR) materials, GaN, GaAs, and CdSe, in the presence of an axial magnetic field. Using an infinite potential model and based on the effective mass approximation, we calculated eigenvalues and eigenvectors using the three-dimensional finite difference method. This research aims to improve our understanding of the impact of the magnetic field on VTQRs of different sizes fabricated from various materials, such as GaAs, GaN, and CdSe. We simultaneously studied the geometrical parameters of VTQR nanostructures and the influence of the axial magnetic field on electronic energy, donor energy, electron-donor binding energy, magnetic shift, diamagnetic susceptibility, bandgap energy, and optical band gab. Our results show a strong correlation between electron-impurity binding energy, geometric parameters, and the presence of a magnetic field. CdSe consistently displays the highest binding energy, indicating superior stability under the study conditions. The effects of the magnetic field on these materials vary, with CdSe exhibiting increased sensitivity and GaAs demonstrating the lowest sensitivity. Nanostructure dimensions, including radii and curvature angles, play a central role in modulating the effects of binding energy and magnetic field, reflecting distinct electronic properties.

Cross-shaped nanoaperture nanoantennas inside plasmonic nanorings for large SERS enhancement and multiple hotspots

We have designed a novel nanostructure consisting of a cross-shaped nanoaperture nanoantenna inside plasmonic nanorings for achieving very large values of electric field enhancement, as well as large theoretical surface-enhanced Raman scattering (SERS) enhancement factor, towards the center of the nanostructure. In this work, we employed Finite-difference-time-domain (FDTD) numerical modeling to simulate the plasmonic (gold) nanostructures present on silica substrates. We found that the nanostructures being proposed by us show very high localized electric field enhancements as well as multiple hotspots in which the electric field is enhanced and localized. We observed that these hotspots have large electric field enhancements (and therefore large theoretical SERS enhancement factors) at more than one wavelength. Thus, the proposed nanostructure can be used to achieve a multiple wavelength SERS response. The electric field enhancements and the resonance wavelengths of nanostructures can be tuned in the visible and the NIR region by modifying the nanostructure dimensions like the gap between the tips in the central nanoaperture structure, height of nanostructure, and tip angle variation. It is observed that as the number of gold nanorings increase, the electric field enhancement (as well as the theoretical SERS enhancement factor) also increase due to the focusing of light towards the center of nanostructure, and after the addition of a few rings, the electric field enhancement becomes almost constant. We also studied the polarization dependence of the nanostructure by varying the angle of polarization of the incident light to check the variation of the electric field of the nanostructure, and observed that the proposed nanostructures did not have much polarization dependence. Moreover, due to the symmetric nature of the plasmonic nanostructure, the position of the hotspot region shifts to the adjacent corner on rotating the incident field polarization. We optimized all the dimensional parameters to get the best possible theoretical SERS enhancement factor of ∼ 1010. Moreover, we simulated a periodic array of these plasmonic nanostructures on the silica substrates, having equal periodicity in X and Y directions, and achieved a theoretical SERS enhancement factor of ∼ 1011.

Application of Nanostructured Parylene‐C Films for Improved Optical Characteristics of Organic Light‐Emitting Diodes

AbstractAnti‐reflection (AR) characteristics on the display surface and light outcoupling efficiency are significant factors for controlling external and internal light in organic light‐emitting diodes (OLEDs), respectively. This paper presents the fabrication of moth‐eye nanostructured parylene‐C films that simultaneously achieve optimized AR characteristics and enhanced OLED performance. AR performance is optimized by varying the nanostructure dimensions, resulting in a nanostructured film with a reflectance of <1%. Furthermore, applying this nanostructured film to OLEDs improved the light outcoupling efficiency by 40% compared with the reference device. Therefore, employing nanostructured parylene‐C films to enhance the optical characteristics of OLEDs is proposed.

Surface modification using nanostructures and nanocoating to combat the spread of bacteria and viruses: Recent development and challenges

Apart from transmission through the respiratory droplet, the surface contact route is another major mode of viral transmission. The recent pandemic is neither the first nor the last; hence, it is a big challenge for a surface engineer to combat the transmission of microbes and viruses through the contact route. In this topical review, we have comprehensively summarized the possible techniques of surface modification for making surfaces antiviral and the respective antiviral mechanisms. Will the anti-biofouling, superhydrophobic, structured surfaces be enough to roll down viruses with water droplets? If so, there could be critical dimensions of nanostructures that need to be fabricated using a precise micro-nano manufacturing method, and the same has been discussed in this review. The surface structuring using functional nanomaterials (copper and copper alloy, gold nanoparticles, silver nanoparticles, titanium dioxide, zinc dioxide, etc.) against different types of viruses and viruses belonging to the coronavirus family has been compared in detail with their merits and demerits. Finally, we foresee that among these surface modification techniques, the nanospike structures combined with an antiviral coating could be the most effective way to combat the transmission of viruses (e.g., COVID-19) through the contact route.

Effect of surface structure on fluid flow and heat transfer in cold and hot wall nanochannels

Nanochannels consisting of hot and cold walls with periodic rectangular and triangular nanostructures were simulated by molecular dynamics in this paper, the periodic size dimensionless parameters φ was defined to describe the dimension of nanostructures on the wall. The results show that the addition of nanostructures leads to the variation of mass density distribution of fluid near the wall. A hot wall with nanostructures can promote the appearance of a fluid high-potential area near it. The discrepant attraction for fluid from the wall caused by the different wall conditions leads to different flow characteristics in nanochannels. Fluid velocity growth rate near the hot wall is 10.5% higher than that near the cold wall. Average velocity of the fluid near the hot wall is 5.1% higher than that of fluid near the cold wall. A wall with rectangular nanostructures at φ = 0.28 shows minimum flow resistance among rough hot walls, while a wall with triangular nanostructures at φ = 0.14 has minimum flow resistance among rough cold walls. Heat is transferred from the hot wall to the cold wall through fluid flow. Wall conditions impact the heat transfer situation of fluid in flow boundary by changing the fluid mass density contribution. The addition of nanostructures and decrease of nanostructures size is beneficial for heat transfer while unfavorable for fluid flow, convective heat transfer was influenced by their combination. For a wall with 300 K, the addition of rectangular nanostructures at φ = 0.07 has the best convective heat transfer performance. For a wall with 200 K temperature, increasing triangular nanostructures at φ = 0.14 on the wall can reach the best convective heat transfer capacity. This paper can provide a theoretical foundation for the optimization of nanochannels to achieve best convective heat transfer ability.

Tuning the dimensional order in self-assembled magnetic nanostructures: theory, simulations, and experiments.

A major obstacle to building nanoscale magnetic devices or even experimentally studying novel nanomagnetic spin textures is the present lack of a simple and robust method to fabricate various nano-structured alloys. Here, theoretical and experimental investigations were conducted to understand the underlying physical mechanisms of magnetic particle self-assembly in zero applied magnetic field. By changing the amount of NaOH added during the synthesis, we demonstrate that the resulting morphology of the assembled FeCo structure can be tuned from zero-dimensional (0D) nanoparticles to one-dimensional (1D) chains, and even three-dimensional (3D) networks. Two numerical simulations were developed to predict aspects of nanostructure formation by accounting for the magnetic interactions between individual magnetic nanoparticles. The first utilized the Boltzmann distribution to determine the equilibrium structure of a nanochain, iteratively predicting the local deviation angle θ of each particle as it attaches to a forming chain. The second simulation illustrates the differences in nanostructure arrangement and dimensionality (0D, 1D, or 3D) that arise from random interactions at various nanoparticle densities. The simulation results closely match the experimental findings, as seen from SEM images, demonstrating their ability to capture the system's structural properties. In addition, magnetic hysteresis measurements of the samples were performed along two orthogonal directions to show the influence of dimensional order on the magnetic behavior. The normalized remanence (MR/MS||) of the FeCo alloys increases as the dimensions of nanostructures are increased. Of the three cases, the FeCo 3D network structures exhibit the highest normalized nanostructure remanence of 0.33 and an increased coercivity to above 200 Oe at 300 K. This combined numerical and experimental investigation aims to shed light on the preparation of FeCo nanostructures with tailorable dimensional order and it opens new avenues for exploring the complex spin textures and coercive behavior of these multi-dimensional nanomagnetic structures.

Performance of laser patterned copper plasmonic photocathodes

We study ultrafast laser surface nanopatterning as an alternative to improve the photo-emissive properties of metallic photocathodes. By tailoring the physical dimensions of these surface nanostructures, one can localize the optical field intensity and exploit plasmonic effects occurring in such nanostructures. As a result, this surface nanopatterning technique can become a great tool for improving metallic photocathodes photoemission behavior enabling their use for next generation high brightness electron sources. Our goal is to investigate such surface-plasmon assisted photoemission processes with a view on simplifying the photocathode production at CERN while extending the lifetime of existing photoinjectors. The performance of two different femtosecond laser nanopatterned plasmonic photocathodes was analyzed by measuring the quantum yield with a 65kV DC electron gun utilizing 266nm laser excitation generated by a nanosecond laser with 5ns pulse duration and 10Hz repetition rate. By comparing the electron emission of the copper surface nanostructured areas with that of a flat area, our results suggest quantum yield enhancements of up to a factor of 5.

Synthesis and characterization of LiCo1-xNixO2 nanoparticles by urea route as cathode for lithium-ion battery

LiCo1-xNixO2 (x = 0, 0.25, 0.5, 0.75, 1) powders are synthesized using the urea; the crystalline structure and surface morphology of the prepared powders are investigated through XRD, FTIR, FE-SEM, and EDX analyses. X-ray diffraction indicates a hexagonal crystal structure for the LiCoO2 phase, Additionally, the XRD pattern of prepared LiCoO2 doped with Ni metal (x = 0.25) shows the formation of a cubic LiCoO2 nanostructure, FTIR spectra analysis of LiCoO2 and LiCo1-xNixO2 revealed several vibrational modes, such as (C=O and O–H). FESEM results indicate that all samples have nanostructure dimensions, An EDX spectrum reveals the presence of transition metals (Co) in LiCoO2, transition metals (Co and Ni) in LiCo1-xNixO2, and transition metals (Ni) in LiNiO2.

Structural and Magnetic Properties of MnxZn1-xFe2O4 Prepared via Sol-Gel Method

Manganese-zinc ferrite MnxZn1-xFe2O4 (MnZnF) powder was prepared using the sol-gel method. The morphological, structural, and magnetic properties of MnZnF powder were studied using X-ray diffraction (XRD), atomic force microscopy (AFM), energy dispersive X-ray (EDX), field emission-scanning electron microscopes (FE-SEM), and vibrating sample magnetometers (VSM). The XRD results showed that the MnxZn1-xFe2O4 that was formed had a trigonal crystalline structure. AFM results showed that the average diameter of Manganese-Zinc Ferrite is 55.35 nm, indicating that the sample has a nanostructure dimension. The EDX spectrum revealed the presence of transition metals (Mn, Fe, Zn, and O) in Manganese-Zinc Ferrite. The FE-SEM results of MnZnF showed uniform spherical structures. VSM was used to study the change in magnetization, the saturation magnetization, (Ms) value of the samples. The measurement of VSM indicated that the MnZnF exhibits ferromagnetic behavior with coercivity Hc (0.0014 Gauss), remanent magnetization (Mr) (0.202 emu/gr), and saturation magnetization Ms (2.69 emu/g).

Effect of contact interface type in charge transfer mechanism and visible-light photocatalytic activity of ZnO-g-C3N4 heterostructures

The dimension of semiconductor nanostructures is an effective parameter in their applications as photocatalysts, catalysts, sensors, etc. This effect of semiconductor nanostructures is more significant in heterostructures with different applications. In detail, we investigate the dimensional effect of ZnO nanostructures on the contact interface type of heterostructures and the number of created electron transfer channels at the contact place. In this work, heterostructures were designed and prepared by merging one component with fixed dimension (2D g-C3N4) and one component with variable dimension (0D ZnO, 1D ZnO, 2D ZnO, and 3D ZnO). Then, the accuracy of their structure was confirmed by various analyzes such as SEM, TEM, XRD, XPS, and Raman. Also, the charge transfer efficiency and photocatalytic properties were explored via electrochemical study, optical analysis, and photocatalytic tests for the degradation of organic pollutants. Examining the effect of dimension parameters on the interface area and charge transfer properties of carbon-based heterostructures showed that the heterostructures with more interface area create higher transfer channels for electron transfer to the surface and provide greater charge transfer efficiency. Among the prepared heterostructures with different dimensions, the 2D-2D heterostructure with more interface area between the two components has more electron transfer channels on all over of contact interface (surface-to-surface contact) and trapped more charge on the surface; thus, it shows a higher charge transfer efficiency and photocatalytic properties.

Virtual experiments for the assessment of data analysis and uncertainty quantification methods in scatterometry

Geometrical dimensions in nanostructures can be determined through indirect optical measurements carried out by a scatterometer. This includes solving a non-linear regression task in which a physical model is fitted to the observed optical diffraction pattern. We developed a virtual experiment which produces simulated diffraction patterns in coherent Fourier scatterometry measurements including perturbations due to various error sources. We utilize this virtual experiment to assess the suitability of data analysis and uncertainty quantification methods employed in scatterometry. In addition to investigating relevant physical parameters we explore the impact of deviations between the regression model utilized for the analysis and the scatterometry model used to produce the virtual diffraction pattern. We choose coverage probabilities of interval estimates of the geometrical dimensions as the main metric for the assessment. One of our findings is that the discretization level, expressed as the number of retained Fourier orders, can be relaxed up to order 9 in our case study, which is relevant as calculation times strongly depend on this parameter. Another result is that the least-squares approach considered here for solving the regression task in combination with the propagation of variances yields uncertainties which have somewhat lower coverage probabilities than the envisaged 95%. It turned out that it was critically important to model the oxide layer in order to get proper estimates of the width, or ‘critical dimension’, of the sample, while the uncertainty of the side wall angle had the largest impact on the uncertainty of the measurands. Our findings can help establishing traceability of Fourier scatterometry and underline the usefulness of high-quality virtual experiments in connection with complex measurement principles. At the same time the presented case study can be seen as a generic approach that could be followed for assessing uncertainty quantifications in other applications as well.