Investigation on the properties of a laminar grating as a soft x-ray beam splitter

Ying Liu; Hans-Jörg Fuchs; Zhengkun Liu; Huoyao Chen; Shengnan He; Shaojun Fu; Ernst-Bernhard Kley; Andreas Tünnermann

doi:10.1364/AO.49.004450

Applied Optics
Vol. 49,
Issue 23,
pp. 4450-4459
(2010)
•https://doi.org/10.1364/AO.49.004450

Investigation on the properties of a laminar grating as a soft x-ray beam splitter

Ying Liu, Hans-Jörg Fuchs, Zhengkun Liu, Huoyao Chen, Shengnan He, Shaojun Fu, Ernst-Bernhard Kley, and Andreas Tünnermann

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Ying Liu, Hans-Jörg Fuchs, Zhengkun Liu, Huoyao Chen, Shengnan He, Shaojun Fu, Ernst-Bernhard Kley, and Andreas Tünnermann, "Investigation on the properties of a laminar grating as a soft x-ray beam splitter," Appl. Opt. 49, 4450-4459 (2010)

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Table of Contents Category
- Diffraction and Gratings
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About this Article
History
- Original Manuscript: March 16, 2010
- Revised Manuscript: July 11, 2010
- Manuscript Accepted: July 12, 2010
- Published: August 6, 2010

Abstract

Laminar-type gratings as soft x-ray beam splitters for interferometry are presented. Gold-coated grating beam splitters with $1000 lines / mm$ are designed for grazing incidence operation at $13.9 nm$ . They are routinely fabricated using electron beam lithography and ion etching techniques. The laminar grating is measured to have almost equal absolute efficiencies of about 20% in the zeroth and $- 1$ st orders, which enables a fringe visibility up to 0.99 in the interferometer. The discrepancy of the grating profiles between the optimized theoretical and the experimental results is analyzed according to the comparison of the optimized simulation results and the measurement realization of the grating efficiencies. By a precise control of the grating profile, the grating efficiency in the $- 1$ st order and the fringe visibility could be improved to 25% and 1, respectively.

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	Fill Factor	Depth (nm)	$η_{0}$ (%)	$η_{- 1}$ (%)	V
Optimized parameter	$0.28 - 0.32$	23	24	24	1.0
Fabrication tolerance 1	0.36	$23_{- 4}^{+ 5}$	$24_{- 4}^{+ 12}$	$24_{- 4}^{- 1}$	$> 0.90$
		$23_{+ 1}^{+ 5}$	$24_{- 4}^{+ 1}$	$24_{- 4}^{- 1}$	1.0
Fabrication tolerance 2	0.40	$23_{- 3}^{+ 4}$	$24_{- 1}^{+ 11}$	$24_{- 4}^{- 1}$	$0.94 - 0.98$
		$23_{+ 1}^{+ 4}$	$24_{- 0}^{+ 3}$	$24_{- 4}^{- 2}$	0.98

	Grating Number
Characteristic	$A_{1}$	$B_{1}$
Fill factor from SEM	0.40 (photoresist grating)	0.43 (after coating)
Incidence angle in the measurement	$83.5 °$	$84 °$
Measured efficiency for TE polarization	20% (zeroth order), 18% ( $- 1$ st order)	25% (zeroth order), 14% ( $- 1$ st order)
Measured TE efficiency ratio of the $- 1$ st to the zeroth order	0.90	0.55
Final deduced groove depth from the efficiency measurement (nm)	27	31
Predicted nonpolarized efficiency	23% in the zeroth order, 20% in the $- 1$ st order	25% in the zeroth order, 13% in the $- 1$ st order
Predicted fringe visibility	0.99	0.83

	Fill Factor	Depth (nm)	$η_{0}$ (%)	$η_{- 1}$ (%)	V
Optimized parameter	$0.28 - 0.32$	23	24	24	1.0
Fabrication tolerance 1	0.36	$23_{- 4}^{+ 5}$	$24_{- 4}^{+ 12}$	$24_{- 4}^{- 1}$	$> 0.90$
		$23_{+ 1}^{+ 5}$	$24_{- 4}^{+ 1}$	$24_{- 4}^{- 1}$	1.0
Fabrication tolerance 2	0.40	$23_{- 3}^{+ 4}$	$24_{- 1}^{+ 11}$	$24_{- 4}^{- 1}$	$0.94 - 0.98$
		$23_{+ 1}^{+ 4}$	$24_{- 0}^{+ 3}$	$24_{- 4}^{- 2}$	0.98

	Grating Number
Characteristic	$A_{1}$	$B_{1}$
Fill factor from SEM	0.40 (photoresist grating)	0.43 (after coating)
Incidence angle in the measurement	$83.5 °$	$84 °$
Measured efficiency for TE polarization	20% (zeroth order), 18% ( $- 1$ st order)	25% (zeroth order), 14% ( $- 1$ st order)
Measured TE efficiency ratio of the $- 1$ st to the zeroth order	0.90	0.55
Final deduced groove depth from the efficiency measurement (nm)	27	31
Predicted nonpolarized efficiency	23% in the zeroth order, 20% in the $- 1$ st order	25% in the zeroth order, 13% in the $- 1$ st order
Predicted fringe visibility	0.99	0.83

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Applied Optics