Characterization of the shape and line-edge roughness of polymer gratings with grazing incidence small-angle X-ray scattering and atomic force microscopy

Artificial fingerprints engraved through block-copolymers as nanoscale physical unclonable functions for authentication and identification

Besides causing financial losses and damage to the brand's reputation, counterfeiting can threaten the health system and global security. In this context, physical unclonable functions (PUFs) have been proposed to overcome limitations of current anti-counterfeiting technologies. Here, we report on artificial fingerprints that can be directly engraved on a wide range of substrates through self-assembled block-copolymer templating as nanoscale PUFs for secure authentication and identification. Results show that morphological features can be exploited to encode fingerprint-like nanopatterns in binary code matrices representing a unique bit stream of information characterized by high uniqueness and entropy. A strategy based on computer vision concepts for authentication/identification in real-world scenarios is reported. Long-term reliable operation and robust authentication/identification against thermal treatment at cryogenic and high temperatures of the PUF have been demonstrated. These results pave the way for the realization of PUFs embracing the inherent stochasticity of self-assembled materials at the nanoscale.

Challenges of grazing emission X-ray fluorescence (GEXRF) for the characterization of advanced nanostructured surfaces

The grazing emission X-ray fluorescence (GEXRF) technique offers a promising approach to determining the spatial distribution of various chemical elements in nanostructures. In this paper, we present a comparison with grazing incidence small-angle X-ray scattering (GISAXS), an established method for dimensional nanometrology, on periodic TiO₂ nanostructures fabricated by a self-aligned double patterning (SADP) process. We further test the potential of GEXRF for process control in the presence of residual chromium on the structures. The angle-resolved fluorescence emission as well as the scattered radiation from the surface are collected with photon-counting hybrid pixel area detectors using scanning-free detection schemes. By modelling the X-ray standing wave (XSW) field in the vicinity of and inside the nanostructure, it is possible to obtain both the angle-resolved fluorescence intensities and the far-field scattering intensities from the same model. The comparison also illustrates that for ensemble photon-based measurement methods, accounting for roughness effects and imperfections can be essential when modelling advanced nanostructured surfaces.

Effect of sidewall roughness on the diffraction efficiency of EUV high aspect ratio freestanding transmission gratings

Manufacturing-induced sidewall roughness has a significant impact on the diffraction efficiency of extreme ultraviolet (EUV) gratings and masks, which could be evaluated by a Debye-Waller damping factor. The rough profile models of line structures are always parallel to the surface for the reflective elements. In this manuscript, a model of rough lines along the thickness direction is established, which cannot be ignored for high aspect ratio transmission gratings. Numerical calculations are carried out using both a rigorous model and a Fraunhofer approximation model. The two models agree with each other on the low-order transmission efficiencies, and the fitted Debye-Waller factor indicates a larger roughness value than that of the model due to the absorption of EUV irradiation for 90° sidewall angle. When the sidewall angle is smaller than 88°, an extra degree of freedom is introduced to the traditional Debye-Waller factor-based formula. The +1-order transmission efficiency and absorptivity with smooth and rough sidewalls are also analyzed, as well as the effect of incidence angle, wavelength and grating thickness.

Uncertainties in the reconstruction of nanostructures in EUV scatterometry and grazing incidence small-angle X-ray scattering

Increasing miniaturization and complexity of nanostructures require innovative metrology solutions with high throughput that can assess complex 3D structures in a non-destructive manner. EUV scatterometry is investigated for the characterization of nanostructured surfaces and compared to grazing-incidence small-angle X-ray scattering (GISAXS). The reconstruction is based on a rigorous simulation using a Maxwell solver based on finite-elements and is statistically validated with a Markov-Chain-Monte-Carlo sampling method. It is shown that in comparison to GISAXS, EUV allows to probe smaller areas and to reduce the computation times obtaining comparable uncertainties.

Applicability of the Debye-Waller damping factor for the determination of the line-edge roughness of lamellar gratings

Periodic nanostructures are fundamental elements in optical instrumentation as well as basis structures in integrated electronic circuits. Decreasing sizes and increasing complexity of nanostructures have made roughness a limiting parameter to the performance. Grazing-incidence small-angle X-ray scattering is a characterization method that is sensitive to three-dimensional structures and their imperfections. To quantify line-edge roughness, a Debye-Waller factor (DWF), which is derived for binary gratings, is usually used. In this work, we systematically analyze the effect of roughness on the diffracted intensities. Two different limits to the application of the DWF are found depending on whether the roughness is normally distributed or not.

Direct Imaging of Interfacial Fluctuations in Confined Block Copolymer with in Situ Slow-Scan-Disabled Atomic Force Microscopy

Using environmentally controlled, high-speed atomic force microscopy (AFM), we examine dynamic fluctuations of topographically confined poly(styrene-block-methyl methacrylate) (PS-b-PMMA) cylinders. During thermal annealing, fluctuations drive perturbations of the block copolymer (BCP) interface between polymer domains, leading to pattern roughness. Whereas previous investigations have examined roughness in room-temperature and kinetically quenched samples, we directly visualize the dynamics of PS/PMMA interfaces in real space and time at in situ temperatures above the glass transition temperature, T_g. Imaging under these experimentally challenging thermal annealing conditions is critical to understanding the inherent connection between thermal fluctuations and BCP pattern assembly. Through the use of slow-scan-disabled AFM, we dramatically improve the imaging time resolution for tracking polymer dynamics. Fluctuations increase in intensity with temperature and, at high temperatures, become spatially coherent across their confining potential. Additionally, we observe that topographic confinement suppresses fluctuations and correlations in the proximity of the guiding field. In situ imaging at annealing temperatures represents a significant step in capturing the dynamics of chain mobility at BCP interfaces.

Distortion analysis of crystalline and locally quasicrystalline 2D photonic structures with grazing-incidence small-angle X-ray scattering

In this study, grazing-incidence small-angle X-ray scattering (GISAXS) is used to collect statistical information on dimensional parameters in an area of 20 × 15 mm on photonic structures produced by nanoimprint lithography. The photonic structures are composed of crystalline and locally quasicrystalline two-dimensional patterns with structure sizes between about 100 nm and 10 µm to enable broadband visible light absorption for use in solar-energy harvesting. These first GISAXS measurements on locally quasicrystalline samples demonstrate that GISAXS is capable of showing the locally quasicrystalline nature of the samples while at the same time revealing the long-range periodicity introduced by the lattice design. The scattering is described qualitatively in the framework of the distorted-wave Born approximation using a hierarchical model mirroring the sample design, which consists of a rectangular and locally quasicrystalline supercell that is repeated periodically to fill the whole surface. The nanoimprinted samples are compared with a sample manufactured using electron-beam lithography and the distortions of the periodic and locally quasiperiodic samples are quantified statistically. Owing to the high sensitivity of GISAXS to deviations from the perfect lattice, the misalignment of the crystallographic axes was measured with a resolution of 0.015°, showing distortions of up to ±0.15° in the investigated samples.

X-ray characterization of contact holes for block copolymer lithography

The directed self-assembly (DSA) of block copolymers (BCPs) is a promising low-cost approach to patterning structures with critical dimensions (CDs) which are smaller than can be achieved by traditional photolithography. The CD of contact holes can be reduced by assembling a cylindrical BCP inside a patterned template and utilizing the native size of the cylinder to dictate the reduced dimensions of the hole. This is a particularly promising application of the DSA technique, but in order for this technology to be realized there is a need for three-dimensional metrology of the internal structure of the patterned BCP in order to understand how template properties and processing conditions impact BCP assembly. This is a particularly challenging problem for traditional metrologies owing to the three-dimensional nature of the structure and the buried features. By utilizing small-angle X-ray scattering and changing the angle between the incident beam and sample we can reconstruct the three-dimensional shape profile of the empty template and the residual polymer after self-assembly and removal of one of the phases. A two-dimensional square grid pattern of the holes results in scattering in both in-plane directions, which is simplified by converting to a radial geometry. The shape is then determined by simulating the scattering from a model and iterating that model until the simulated and experimental scattering profiles show a satisfactory match. Samples with two different processing conditions are characterized in order to demonstrate the ability of the technique to evaluate critical features such as residual layer thickness and sidewall height. It was found that the samples had residual layer thicknesses of 15.9 ± 3.2 nm and 4.5 ± 2.2 nm, which were clearly distinguished between the two different DSA processes and in good agreement with focused ion beam scanning transmission electron microscopy (FIBSTEM) observations. The advantage of the X-ray measurements is that FIBSTEM characterizes around ten holes, while there are of the order of 800 000 holes illuminated by the X-ray beam.

Ionic Liquids as Additives to Polystyrene- Block-Poly(Methyl Methacrylate) Enabling Directed Self-Assembly of Patterns with Sub-10 nm Features

Polystyrene- block-poly(methyl methacrylate) (PS- b-PMMA) is one of the prototypical block copolymers in directed self-assembly (DSA) research and development, with standardized protocols in place for processing on industrially relevant 300 mm wafers. Scaling of DSA patterns to pitches below 20 nm using PS- b-PMMA, however, is hindered by the relatively low Flory-Huggins interaction parameter, χ. Here, we investigate the approach of adding small amounts of ionic liquids (ILs) into PS- b-PMMA, which selectively segregates into the PMMA domain and effectively increases the χ parameter and thus the pattern resolution. The amount of IL additive is small enough to result in limited changes in PS- b-PMMA's surface and interfacial properties, thus maintaining industry-friendly processing by thermal annealing with a free surface. Three different ILs are studied comparatively regarding their compositional process window, capability of increasing χ, and thermal stability. By adding ∼3.1 vol % of the champion IL into a low-molecular-weight PS- b-PMMA ( M_n = 10.3k- b-9.5k), we demonstrated DSA on chemically patterned substrates of lamellar structures with feature sizes <8.5 nm. Compatibility of the PS- b-PMMMA/IL blends with the standardized processes that have been previously developed suggests that such blend materials could provide a drop-in solution for sub-10 nm lithography with the processing advantages of PS- b-PMMA.

Characteristic diffuse scattering from distinct line roughnesses

Lamellar gratings are widely used diffractive optical elements; gratings etched into Si can be used as structural elements or prototypes of structural elements in integrated electronic circuits. For the control of the lithographic manufacturing process, a rapid in-line characterization of nanostructures is indispensable. Numerous studies on the determination of regular geometry parameters of lamellar gratings from optical and extreme ultraviolet (EUV) scattering highlight the impact of roughness on the optical performance as well as on the reconstruction of these structures. Thus, a set of nine lamellar Si gratings with a well defined line edge roughness or line width roughness were designed. The investigation of these structures using EUV small-angle scattering reveals a strong correlation between the type of line roughness and the angular scattering distribution. These distinct scattering patterns open new paths for the unequivocal characterization of such structures by EUV scatterometry.

Reconstructing detailed line profiles of lamellar gratings from GISAXS patterns with a Maxwell solver

Laterally periodic nanostructures have been investigated with grazing-incidence small-angle X-ray scattering (GISAXS) by using the diffraction patterns to reconstruct the surface shape. To model visible light scattering, rigorous calculations of the near and far field by numerical solution of Maxwell's equations with a finite-element method are well established. The application of this technique to X-rays is still challenging, owing to the discrepancy between the incident wavelength and the finite-element size. This drawback vanishes for GISAXS because of the small angles of incidence, the conical scattering geometry and the periodicity of the surface structures, which allows a rigorous computation of the diffraction efficiencies with sufficient numerical precision. To develop metrology tools based on GISAXS, lamellar gratings with line widths down to 55 nm were produced by state-of-the-art electron-beam lithography and then etched into silicon. The high surface sensitivity of GISAXS in conjunction with a Maxwell solver allows the detailed reconstruction of the grating line shape for thick non-homogeneous substrates as well. The reconstructed geometric line-shape models are statistically validated by applying a Markov chain Monte Carlo sampling technique which reveals that GISAXS is able to reconstruct critical parameters like the widths of the lines with sub-nanometre uncertainty.

Grazing-incidence small-angle X-ray scattering (GISAXS) on small periodic targets using large beams

Grazing-incidence small-angle X-ray scattering (GISAXS) is often used as a versatile tool for the contactless and destruction-free investigation of nano-structured surfaces. However, due to the shallow incidence angles, the footprint of the X-ray beam is significantly elongated, limiting GISAXS to samples with typical target lengths of several millimetres. For many potential applications, the production of large target areas is impractical, and the targets are surrounded by structured areas. Because the beam footprint is larger than the targets, the surrounding structures contribute parasitic scattering, burying the target signal. In this paper, GISAXS measurements of isolated as well as surrounded grating targets in Si substrates with line lengths from 50 µm down to 4 µm are presented. For the isolated grating targets, the changes in the scattering patterns due to the reduced target length are explained. For the surrounded grating targets, the scattering signal of a 15 µm × 15 µm target grating structure is separated from the scattering signal of 100 µm × 100 µm nanostructured surroundings by producing the target with a different orientation with respect to the predominant direction of the surrounding structures. As virtually all litho-graphically produced nanostructures have a predominant direction, the described technique allows GISAXS to be applied in a range of applications, e.g. for characterization of metrology fields in the semiconductor industry, where up to now it has been considered impossible to use this method due to the large beam footprint.