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Direct structural characterisation of line gratings with grazing incidence small-angle x-ray scattering
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Image of FIG. 1.
FIG. 1.

GISAXS elastic scattering geometry.

Image of FIG. 2.
FIG. 2.

Cross-sectional model profile of the examined grating structure with line width L, groove width G, grating period P = L + G, and line height H.

Image of FIG. 3.
FIG. 3.

X-ray reflectivity data (grey symbols) of the mask layer system measured at a mask position without any grating structure. Also shown is the best fit (black solid line) of an approximation by a Fresnel reflectivity model of a Ru layer on SiO2 (see inset). Parameters of the fit are displayed in Table I.

Image of FIG. 4.
FIG. 4.

(a) GISAXS scattering image in perpendicular orientation of incident beam and grating lines (E ph = 8 keV, αi = 0.8°). (b) Intensity profile along the vertical specular axis (q y = 0 nm−1) as a function of αf. The diffraction peak positions at 23.33 mrad and 30.17 mrad, respectively, are used to determine P.

Image of FIG. 5.
FIG. 5.

GISAXS analysis method. (a) GISAXS pattern of beam orientation parallel to grating lines, αi = 0.8°, E ph = 6 keV. (b) Extracted profile along the Ewald semicircle in (a) as a function of q y. For averaging, each column within a ring of 12 pixel width around the Ewald semicircle is averaged column-wise for each corresponding q y. (c) PSD of I(q y) profile (solid line in (b)) as a function of spatial period length, i.e., characteristic scattering length. Black solid lines represent peak fits with Gaussian functions. Dotted vertical lines indicate the nominal lengths of grating period P, line width L, and groove width G.

Image of FIG. 6.
FIG. 6.

Power spectral density versus spatial period length of various grating fields (“A,” “B,” and “C”) with different line-groove ratios L/G at constant grating period P and constant line height H. Dashed vertical lines indicate the positions of nominal values for L, G, and P for the respective field as specified by the manufacturer.

Image of FIG. 7.
FIG. 7.

Simulation of scattering by a grating structure with IsGISAXS using a 1D-paracrystal model (parameters see text). (a) The calculated GISAXS pattern. Depicted in (b) is the PSD of the I(q y) profile that has been obtained by averaging and extraction along the Ewald semicircle. Vertical dotted lines indicate the model parameters for the box width 2R = 250 nm, the interference function peak position D = 833 nm, and the groove width G = D − 2R = 583 nm. Black solid lines show the peak fits with Gaussian functions.

Image of FIG. 8.
FIG. 8.

GISAXS of the azimuthally rotated grating close to parallel orientation (φ = 0°), recorded at E ph = 6 keV, αi = 0.8°. GISAXS patterns at (a) φ = 2.50° azimuthal angle and (b) φ = −2.50°. (c) Superposition of 101 individual GISAXS images, each rotated by Δφ = 0.05° with respect to its predecessor in the range of φ = (−2.50°…2.50°). The white box indicates the averaging range of the extracted vertical intensity profile I(q z) shown in (d). The profile has been fitted with a Bessel function of first order (black solid line) to determine a grating line height of H = 27.3 nm.


Generic image for table
Table I.

Parameters of XRR fitting.

Generic image for table
Table II.

Mean grating parameters obtained from PSD of various GISAXS images with corresponding standard deviation.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Direct structural characterisation of line gratings with grazing incidence small-angle x-ray scattering