On the assessment by grazing-incidence small-angle X-ray scattering of replica quality in polymer gratings fabricated by nanoimprint lithography

Self-assembly of block copolymers under non-isothermal annealing conditions as revealed by grazing-incidence small-angle X-ray scattering

An accurate knowledge of the parameters governing the kinetics of block copolymer self-assembly is crucial to model the time- and temperature-dependent evolution of pattern formation during annealing as well as to predict the most efficient conditions for the formation of defect-free patterns. Here, the self-assembly kinetics of a lamellar PS-b-PMMA block copolymer under both isothermal and non-isothermal annealing conditions are investigated by combining grazing-incidence small-angle X-ray scattering (GISAXS) experiments with a novel modelling methodology that accounts for the annealing history of the block copolymer film before it reaches the isothermal regime. Such a model allows conventional studies in isothermal annealing conditions to be extended to the more realistic case of non-isothermal annealing and prediction of the accuracy in the determination of the relevant parameters, namely the correlation length and the growth exponent, which define the kinetics of the self-assembly.

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.

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.

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.

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

Grazing-incidence small-angle X-ray scattering (GISAXS) is increasingly used for the metrology of substrate-supported nanoscale features and nanostructured films. In the case of line gratings, where long objects are arranged with a nanoscale periodicity perpendicular to the beam, a series of characteristic spots of high-intensity (grating truncation rods, GTRs) are recorded on a two-dimensional detector. The intensity of the GTRs is modulated by the three-dimensional shape and arrangement of the lines. Previous studies aimed to extract an average cross-sectional profile of the gratings, attributing intensity loss at GTRs to sample imperfections. Such imperfections are just as important as the average shape when employing soft polymer gratings which display significant line-edge roughness. Herein are reported a series of GISAXS measurements of polymer line gratings over a range of incident angles. Both an average shape and fluctuations contributing to the intensity in between the GTRs are extracted. The results are critically compared with atomic force microscopy (AFM) measurements, and it is found that the two methods are in good agreement if appropriate corrections for scattering from the substrate (GISAXS) and contributions from the probe shape (AFM) are accounted for.

Determining the shape and periodicity of nanostructures using small-angle X-ray scattering

The semiconductor industry is exploring new metrology techniques capable of meeting the future requirement to characterize three-dimensional structure where the critical dimensions are less than 10 nm. X-ray scattering techniques are one candidate owing to the sub-Å wavelengths which are sensitive to internal changes in electron density. Critical-dimension small-angle X-ray scattering (CDSAXS) has been shown to be capable of determining the average shape of a line grating. Here it is used to study a set of line gratings patternedviaa self-aligned multiple patterning process, which resulted in a set of mirrored lines, where the individual line shapes were asymmetric. The spacing between lines was systematically varied by sub-nm shifts. The model used to simulate the scattering was developed in stages of increasing complexity in order to justify the large number of parameters included. Comparisons between the models at different stages of development demonstrate that the measurement can determine differences in line shapes within the superlattice. The shape and spacing between lines within a given set were determined to sub-nm accuracy. This demonstrates the potential for CDSAXS as a high-resolution nanostructure metrology tool.