^{1,a)}, Frank Scholze

^{1}and Michael Krumrey

^{1}

### Abstract

Grazing incidence small-angle x-ray scattering (GISAXS) and x-ray reflectometry (XRR) have been used to investigate structural parameters, especially period length, line width, groove width, and line height, of grating test structures in the sub-micron range. The gratings are e-beam written structures on a quartz substrate with a fixed period length, but different line and groove widths, covered by a layer of ruthenium. A Ru layer thickness of 9.4 nm has been determined with XRR. GISAXS was performed in two orientations, with an incident beam alignment perpendicular and parallel to the grating lines. The scattering patterns in parallel orientation have been analysed without numerical simulation by Fourier transformation. The obtained results for line and groove width are in good agreement with nominal values. The analysis method has been validated by analysing simulated scattering data. A superposition of scattering intensities measured for different azimuthal rotation angles close to parallel alignment was used to determine the line height of a grating of 27.3 nm, which is also close to the nominal value. The Fourier analysis procedure opens up the possibility of traceable structure determination with GISAXS in the nanometre range.

The experimental contributions from Stefanie Marggraf (PTB) and Levent Cibik (PTB) are gratefully acknowledged. We would also like to thank the CMN-optics group of Dr. Uwe D. Zeitner (Fraunhofer IOF) for providing the grating test structures and Dr. Armin Hoell (HZB) for the cooperating research with the HZB SAXS instrument.

I. INTRODUCTION

II. THEORY

III. EXPERIMENTAL PROCEDURE

IV. RESULTS AND DISCUSSION

A. X-ray reflectometry

B. GISAXS in perpendicular orientation

C. GISAXS in parallel orientation

1. Grating parameter determination by Fourier analysis

2. Validation with simulated scattering data

3. Rotation around surface normal vector close to parallel orientation

V. CONCLUSIONS

### Key Topics

- Diffraction gratings
- 68.0
- X-ray scattering
- 39.0
- Position sensitive detectors
- 16.0
- Surface scattering
- 16.0
- Multiple scattering
- 11.0

## Figures

GISAXS elastic scattering geometry.

GISAXS elastic scattering geometry.

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*.

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*.

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 SiO_{2} (see inset). Parameters of the fit are displayed in Table I.

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 SiO_{2} (see inset). Parameters of the fit are displayed in Table I.

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

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

GISAXS analysis method. (a) GISAXS pattern of beam orientation parallel to grating lines, α_{i} = 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*.

GISAXS analysis method. (a) GISAXS pattern of beam orientation parallel to grating lines, α_{i} = 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*.

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.

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.

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 2*R* = 250 nm, the interference function peak position *D* = 833 nm, and the groove width *G* = *D* − 2*R* = 583 nm. Black solid lines show the peak fits with Gaussian functions.

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 2*R* = 250 nm, the interference function peak position *D* = 833 nm, and the groove width *G* = *D* − 2*R* = 583 nm. Black solid lines show the peak fits with Gaussian functions.

GISAXS of the azimuthally rotated grating close to parallel orientation (φ = 0°), recorded at *E* _{ph} = 6 keV, α_{i} = 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.

GISAXS of the azimuthally rotated grating close to parallel orientation (φ = 0°), recorded at *E* _{ph} = 6 keV, α_{i} = 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.

## Tables

Parameters of XRR fitting.

Parameters of XRR fitting.

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

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

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