Reconstructing Detailed Line Profiles of Lamellar Gratings from GISAXS Patterns with a Maxwell Solver

Abstract

Laterally periodic nanostructures were 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 numerically solving Maxwell's equations with a finite-element method are well established. The application of this technique to X-rays is still challenging, due to the discrepancy between incident wavelength and finite-element size. This drawback vanishes for GISAXS due to 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 dimensional metrology tools based on GISAXS, lamellar gratings with line widths down to 55 nm were produced by state-of-the-art e-beam lithography and then etched into silicon. The high surface sensitivity of GISAXS in conjunction with a Maxwell solver allows a detailed reconstruction of the grating line shape also for thick, non-homogeneous substrates. The reconstructed geometrical line shape models are statistically validated by applying a Markov chain Monte Carlo (MCMC) sampling technique which reveals that GISAXS is able to reconstruct critical parameters like the widths of the lines with sub-nm uncertainty.

References in corpus (4)

• Grazing Incidence Small Angle X-Ray Scattering (GISAXS) on Small Targets Using Large Beams
• Analytical modeling and 3D finite element simulation of line edge roughness in scatterometry
• Correlated Diffuse X-ray Scattering from Periodically Nano-Structured Surfaces
• hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures

Cited by in corpus (11)

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• Applicability of the Debye-Waller damping factor for the determination of the line-edge roughness of lamellar gratings
• Grazing incidence-X-ray fluorescence for a dimensional and elemental characterization of well-ordered nanostructures
• On uncertainties in the reconstruction of nanostructures in EUV scatterometry and grazing incidence small-angle X-ray scattering
• Extracting Dimensional Parameters of Gratings Produced with Self-Aligned Multiple Patterning Using GISAXS
• Using Gaussian process regression for efficient parameter reconstruction
• Distortion analysis of crystalline and locally quasicrystalline 2D photonic structures with GISAXS
• Hybrid approach to reconstruct nanoscale grating dimensions using scattering and fluorescence with soft X-rays
• Polygon-based unified Fourier-modal approach for diffractive optics simulations