Hybrid Metrology for Nanostructured Optical Metasurfaces.

Metasurfaces have garnered increasing research interest in recent years due to their remarkable advantages, such as efficient miniaturization and novel functionalities compared to traditional optical elements such as lenses and filters. These advantages have facilitated their rapid commercial deployment. Recent advancements in nanofabrication have enabled the reduction of optical metasurface dimensions to the nanometer scale, expanding their capabilities to cover visible wavelengths. However, the pursuit of large-scale manufacturing of metasurfaces with customizable functions presents challenges in controlling the dimensions and composition of the constituent dielectric materials. To address these challenges, the combination of block copolymer (BCP) self-assembly and sequential infiltration synthesis (SIS), offers an alternative for fabrication of high-resolution dielectric nanostructures with tailored composition and optical functionalities. However, the absence of metrological techniques capable of providing precise and reliable characterization of the refractive index of dielectric nanostructures persists. This study introduces a hybrid metrology strategy that integrates complementary synchrotron-based traceable X-ray techniques to achieve comprehensive material characterization for the determination of the refractive index on the nanoscale. To establish correlations between material functionality and their underlying chemical, compositional and dimensional properties, TiO2 nanostructures model systems were fabricated by SIS of BCPs. The results from synchrotron-based analyses were integrated into physical models, serving as a validation scheme for laboratory-scale measurements to determine effective refractive indices of the nanoscale dielectric materials.

A new sample chamber for hybrid detection of scattering and fluorescence, using synchrotron radiation in the soft x-ray and extreme ultraviolet (EUV) spectral range.

Smaller and more complex nanostructures in the semiconductor industry require a constant upgrade of accompanying metrological methods and equipment. A central task for nanometrology is the precise determination of structural features of gratings in the nanometer range as well as their elemental composition. Scatterometry and x-ray fluorescence in the soft x-ray and extreme ultraviolet spectral ranges are ideally suited to this task. We here present a new, compact measurement chamber that can simultaneously detect the elastically scattered signal and the fluorescence, originating from nanoscale grating samples. Its geometry enables detecting scattered intensity over a wide angular range with a variable angle of incidence. We show first experiments on industry-relevant test structures from the commissioning process alongside the specifications of the setup, located at PTB's soft x-ray radiometry beamline at the synchrotron radiation facility BESSY II in Berlin.

Nanoscale grating characterization using EUV scatterometry and soft x-ray scattering with plasma and synchrotron radiation.

Modern semiconductor structures reach sizes in the nanometer regime. Optical metrology characterizes test structures for the quality assessment of semiconductor fabrication. The limits of radiation to resolve nanometer structure sizes can be overcome by shortening the wavelength. The compact source extreme ultraviolet (EUV) scatterometer presented here characterizes samples in the EUV spectral range using plasma radiation. Reference measurements with synchrotron radiation are carried out using a beamline scatterometer. A comparison including Markov chain Monte Carlo sampling shows that the compact source and beamline setups can both determine the given dimensional parameters of a nanoscale grating with uncertainties in the sub-nanometer range. Grating characterization based on soft x ray scattering has increased accuracy.

Scan-Free GEXRF in the Soft X-ray Range for the Investigation of Structured Nanosamples.

Scan-free grazing-emission X-ray fluorescence spectroscopy (GEXRF) is an established technique for the investigation of the elemental depth-profiles of various samples. Recently it has been applied to investigating structured nanosamples in the tender X-ray range. However, lighter elements such as oxygen, nitrogen or carbon cannot be efficiently investigated in this energy range, because of the ineffective excitation. Moreover, common CCD detectors are not able to discriminate between fluorescence lines below 1 keV. Oxygen and nitrogen are important components of insulation and passivation layers, for example, in silicon oxide or silicon nitride. In this work, scan-free GEXRF is applied in proof-of-concept measurements for the investigation of lateral ordered 2D nanostructures in the soft X-ray range. The sample investigated is a Si3N4 lamellar grating, which represents 2D periodic nanostructures as used in the semiconductor industry. The emerging two-dimensional fluorescence patterns are recorded with a CMOS detector. To this end, energy-dispersive spectra are obtained via single-photon event evaluation. In this way, spatial and therefore angular information is obtained, while discrimination between different photon energies is enabled. The results are compared to calculations of the sample model performed by a Maxwell solver based on the finite-elements method. A first measurement is carried out at the UE56-2 PGM-2 beamline at the BESSY II synchrotron radiation facility to demonstrate the feasibility of the method in the soft X-ray range. Furthermore, a laser-produced plasma source (LPP) is utilized to investigate the feasibility of this technique in the laboratory. The results from the BESSY II measurements are in good agreement with the simulations and prove the applicability of scan-free GEXRF in the soft X-ray range for quality control and process engineering of 2D nanostructures. The LPP results illustrate the chances and challenges concerning a transfer of the methodology to the laboratory.

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.

Determination of optical constants of thin films in the EUV.

The determination of fundamental optical parameters is essential for the development of new optical elements such as mirrors, gratings, or photomasks. Especially in the extreme ultraviolet (EUV) and soft x-ray spectral range, the existing databases for the refractive indices of many materials and compositions are insufficient or are a mixture of experimentally measured and calculated values from atomic scattering factors. Since the physical properties of bulk materials and thin films with thicknesses in the nanometer range are not identical, measurements need to be performed on thin layers. In this study we demonstrate how optical constants of various thin film samples on a bulk substrate can be determined from reflection measurements in the EUV photon energy range from 62 eV to 124 eV. Thin films with thickness of 20 nm to 50 nm of pure Mo, Ni, Pt, Ru, Ta, and Te and different compositions of NixAlx, PtTe, PtxMo, RuxTax, Ru3Re, Ru2W, and TaTeN were prepared by DC magnetron sputtering and measured using EUV reflectometry. The determination optical constants of the different materials are discussed and compared to existing tabulated values.

Nested Sampling aided determination of tantalum optical constants in the EUV spectral range.

We report on determining the optical constants of Ta in the sub-extreme ultraviolet (EUV) spectral range 5.0-24.0 nm from the angle-dependent reflectance (ADR) measured using monochromatized synchrotron radiation. Two sputtered samples with differing thicknesses were investigated. Complementarily x-ray reflectance was measured at shorter wavelengths and evaluated by Fourier transform to facilitate an unambiguous selection of a model for the data evaluation based on an inverse solution of the Fresnel's equations for a layered system. Bayesian inferences coupled with a Nested Sampling (NS) algorithm were utilized to derive the optical constants with their corresponding uncertainties. This report further emphasizes the applicability of an acclaimed NS algorithm on a high-dimensional inverse problem. We explore the possibility of addressing the correlations between the optical constants of thin films and their structural parameters based on other established studies.

Simultaneous Dimensional and Analytical Characterization of Ordered Nanostructures.

The spatial and compositional complexity of 3D structures employed in today's nanotechnologies has developed to a level at which the requirements for process development and control can no longer fully be met by existing metrology techniques. For instance, buried parts in stratified nanostructures, which are often crucial for device functionality, can only be probed in a destructive manner in few locations as many existing nondestructive techniques only probe the objects surfaces. Here, it is demonstrated that grazing exit X-ray fluorescence can simultaneously characterize an ensemble of regularly ordered nanostructures simultaneously with respect to their dimensional properties and their elemental composition. This technique is nondestructive and compatible to typically sized test fields, allowing the same array of structures to be studied by other techniques. For crucial parameters, the technique provides sub-nm discrimination capabilities and it does not require access-limited large-scale research facilities as it is compatible to laboratory-scale instrumentation.

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.

Shape- and Element-Sensitive Reconstruction of Periodic Nanostructures with Grazing Incidence X-ray Fluorescence Analysis and Machine Learning.

The characterization of nanostructured surfaces with sensitivity in the sub-nm range is of high importance for the development of current and next-generation integrated electronic circuits. Modern transistor architectures for, e.g., FinFETs are realized by lithographic fabrication of complex, well-ordered nanostructures. Recently, a novel characterization technique based on X-ray fluorescence measurements in grazing incidence geometry was proposed for such applications. This technique uses the X-ray standing wave field, arising from an interference between incident and the reflected radiation, as a nanoscale sensor for the dimensional and compositional parameters of the nanostructure. The element sensitivity of the X-ray fluorescence technique allows for a reconstruction of the spatial element distribution using a finite element method. Due to a high computational time, intelligent optimization methods employing machine learning algorithms are essential for timely provision of results. Here, a sampling of the probability distributions by Bayesian optimization is not only fast, but it also provides an initial estimate of the parameter uncertainties and sensitivities. The high sensitivity of the method requires a precise knowledge of the material parameters in the modeling of the dimensional shape provided that some physical properties of the material are known or determined beforehand. The unknown optical constants were extracted from an unstructured but otherwise identical layer system by means of soft X-ray reflectometry. The spatial distribution profiles of the different elements contained in the grating structure were compared to scanning electron and atomic force microscopy and the influence of carbon surface contamination on the modeling results were discussed. This novel approach enables the element sensitive and destruction-free characterization of nanostructures made of silicon nitride and silicon oxide with sub-nm resolution.

Grazing incidence-x-ray fluorescence for a dimensional and compositional characterization of well-ordered 2D and 3D nanostructures.

The increasing importance of well-controlled ordered nanostructures on surfaces represents a challenge for existing metrology techniques. To develop such nanostructures and monitor complex processing constraints fabrication, both a dimensional reconstruction of nanostructures and a characterization (ideally a quantitative characterization) of their composition is required. In this work, we present a soft x-ray fluorescence-based methodology that allows both of these requirements to be addressed at the same time. By applying the grazing-incidence x-ray fluorescence technique and thus utilizing the x-ray standing wave field effect, nanostructures can be investigated with a high sensitivity with respect to their dimensional and compositional characteristics. By varying the incident angles of the exciting radiation, element-sensitive fluorescence radiation is emitted from different regions inside the nanoobjects. By applying an adequate modeling scheme, these datasets can be used to determine the nanostructure characteristics. We demonstrate these capabilities by performing an element-sensitive reconstruction of a lamellar grating made of Si3N4, where GIXRF data for the O-Kα and N-Kα fluorescence emission allows a thin oxide layer to be reconstructed on the surface of the grating structure. In addition, we employ the technique also to three dimensional nanostructures and derive both dimensional and compositional parameters in a quantitative manner.

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.

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

[This corrects the article DOI: 10.1107/S2052252517006297.].

Element sensitive reconstruction of nanostructured surfaces with finite elements and grazing incidence soft X-ray fluorescence.

The geometry of a Si3N4 lamellar grating was investigated experimentally with reference-free grazing-incidence X-ray fluorescence analysis. While simple layered systems are usually treated with the matrix formalism to determine the X-ray standing-wave field, this approach fails for laterally structured surfaces. Maxwell solvers based on finite elements are often used to model electrical field strengths for any 2D or 3D structures in the optical spectral range. We show that this approach can also be applied in the field of X-rays. The electrical field distribution obtained with the Maxwell solver can subsequently be used to calculate the fluorescence intensities in full analogy to the X-ray standing-wave field obtained by the matrix formalism. Only the effective 1D integration for the layer system has to be replaced by a 2D integration of the finite elements, taking into account the local excitation conditions. We will show that this approach is capable of reconstructing the geometric line shape of a structured surface with high elemental sensitivity. This combination of GIXRF and finite-element simulations paves the way for a versatile characterization of nanoscale-structured surfaces.

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.

Interface morphology of Mo/Si multilayer systems with varying Mo layer thickness studied by EUV diffuse scattering.

We investigate the influence of the Mo-layer thickness on the EUV reflectance of Mo/Si mirrors with a set of unpolished and interface-polished Mo/Si/C multilayer mirrors. The Mo-layer thickness is varied in the range from 1.7 nm to 3.05 nm. We use a novel combination of specular and diffuse intensity measurements to determine the interface roughness throughout the multilayer stack and do not rely on scanning probe measurements at the surface only. The combination of EUV and X-ray reflectivity measurements and near-normal incidence EUV diffuse scattering allows to reconstruct the Mo layer thicknesses and to determine the interface roughness power spectral density. The data analysis is conducted by applying a matrix method for the specular reflection and the distorted-wave Born approximation for diffuse scattering. We introduce the Markov-chain Monte Carlo method into the field in order to determine the respective confidence intervals for all reconstructed parameters. We unambiguously detect a threshold thickness for Mo in both sample sets where the specular reflectance goes through a local minimum correlated with a distinct increase in diffuse scatter. We attribute that to the known appearance of an amorphous-to-crystallization transition at a certain thickness threshold which is altered in our sample system by the polishing.

Multiparameter characterization of subnanometre Cr/Sc multilayers based on complementary measurements.

Cr/Sc multilayer systems can be used as near-normal incidence mirrors for the water window spectral range. It is shown that a detailed characterization of these multilayer systems with 400 bilayers of Cr and Sc, each with individual layer thicknesses <1 nm, is attainable by the combination of several analytical techniques. EUV and X-ray reflectance measurements, resonant EUV reflectance across the Sc L edge, and X-ray standing wave fluorescence measurements were used. The parameters of the multilayer model were determined via a particle-swarm optimizer and validated using a Markov chain Monte Carlo maximum-likelihood approach. For the determination of the interface roughness, diffuse scattering measurements were conducted.

Modeling and empirical characterization of the polarization response of off-plane reflection gratings.

Off-plane reflection gratings were previously predicted to have different efficiencies when the incident light is polarized in the transverse-magnetic (TM) versus transverse-electric (TE) orientations with respect to the grating grooves. However, more recent theoretical calculations which rigorously account for finitely conducting, rather than perfectly conducting, grating materials no longer predict significant polarization sensitivity. We present the first empirical results for radially ruled, laminar groove profile gratings in the off-plane mount, which demonstrate no difference in TM versus TE efficiency across our entire 300-1500 eV bandpass. These measurements together with the recent theoretical results confirm that grazing incidence off-plane reflection gratings using real, not perfectly conducting, materials are not polarization sensitive.

Role of dynamic effects in the characterization of multilayers by means of power spectral density.

In this paper, we present measurements of angle- and wavelength-resolved diffuse scattering of EUV radiation on a Mo/Si multilayer. Our sample is optimized for high reflectivity at 13.5 nm wavelength near-normal incidence. We present a rigorous theoretical analysis of the off-specular EUV scattering on the basis of the distorted-wave Born approximation. We prove that the determination of the interface roughness power spectral density (PSD) is only possible by considering geometry-dependent and dynamic contributions. The scattering from multilayer mirrors leads to an intrinsic enhancement in off-specular intensity independent of roughness properties. The thickness oscillations in the scattering intensity (Kiessig fringes) are found to cause additional dynamic enhancement in analogy to Bragg-like peaks for grazing incidence geometry. Considering these effects, the interface PSD is consistently determined.