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-ofthe-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.
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.
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 applying the DWF are found depending on whether or not the roughness is normally distributed.
To ensure consistent and high-quality semiconductor production, additional metrology tools are needed to measure the smallest structures. Due to its high statistical power and the well-known X-ray optical constants, small-angle X-ray scattering (SAXS) is being considered for this purpose. Compared to transmission SAXS, signal intensities can be enhanced dramatically by using small incidence angles in reflection geometry (Grazing-Incidence SAXS, GISAXS), enabling quick measurements. The capability to reconstruct average line shapes from GISAXS measurements of gratings has already been proven. However, GISAXS has so far not been used to reconstruct line shapes of gratings with pitches smaller than 50 nm, which are standard in current-generation semiconductor manufacturing. In this paper, GISAXS is used to reconstruct the line profile of a grating with 32 nm pitch produced by self-aligned quadruple patterning (SAQP). It is found that the reconstructed shape is generally in agreement with previously published SAXS results. However, the reconstructed line height and line width show deviations of 1.0(2) nm and 2.0(7) nm, respectively. Additionally, a series of grating samples with deliberately introduced pitchwalk was measured. Here, it is found that GISAXS yields the pitchwalk in agreement with the SAXS results, with uncertainties ranging from < 0.5 nm for small pitchwalks (< 2 nm) up to ≈ 2 nm for larger pitchwalks.
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.
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