Reflective EUVL tool design with generalized Gaussian constant mathematics

Li-Jen Hsiao; Hoang Yan Lin

doi:10.1364/AO.57.005884

Applied Optics
Vol. 57,
Issue 20,
pp. 5884-5892
(2018)
•https://doi.org/10.1364/AO.57.005884

Reflective EUVL tool design with generalized Gaussian constant mathematics

Li-Jen Hsiao and Hoang Yan Lin

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Li-Jen Hsiao and Hoang Yan Lin, "Reflective EUVL tool design with generalized Gaussian constant mathematics," Appl. Opt. 57, 5884-5892 (2018)

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Abstract

This study aims to develop a systematic design procedure for extreme ultraviolet lithography tools. Through analysis using generalized Gaussian constants, relationships between optical properties and requirements can be obtained, and can be used to help ensure that optical system properties required for the tool are upheld during the design process. As verification of the design method, an eight-mirror 0.4 NA tool design has been demonstrated.

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Surface	Description
0	Object (mask)
1	Input surface of lens module 1
2	Output surface of lens module 1
3	Aperture stop
4	Input surface of lens module 2
5	Output surface of lens module 2
6	Image (wafer)

Specifications
Magnification	0.25
Numerical aperture	0.2
Chief ray angle (mask)	4°
Chief ray angle (wafer)	0°
Total tract length	1000 mm
Working distance (mask)	200 mm
Working distance (wafer)	100 mm
Minimum obstruction clearance	10 mm

Module		Thickness
* ${EF}_{a}$	800 mm	$t_{ob}$	600 mm
${FF}_{a}$	1320 mm	* ${thc}_{a}$	−400 mm
${BF}_{a}$	−242.4 mm	$t_{s - 1}$	395.8 mm
${EF}_{b}$	−182.8 mm	$t_{s}$	304.2 mm
${FF}_{b}$	−304.2 mm	* ${thc}_{b}$	−300 mm
${BF}_{b}$	290.2 mm	$t_{im}$	400 mm
$M_{a}$	−0.146
* $M_{b}$	0.6

Properties	(mm)	Surface	R (mm)	T (mm)
${EF}_{a}$	1038.80	Object	—	531.76
${FF}_{a}$	−781.14	1	−6994.42	−331.76
${BF}_{a}$	940.25	2	2675.11	698.77
${EF}_{b}$	245.21	Stop	—	1.23
${FF}_{b}$	−1.23	4	1428.16	−243.56
${BF}_{b}$	328.84	5	489.57	343.56

Surf	$R$ (mm)	$T$ (mm)	$K$	$A_{4}$
Obj	—	328.1	—	—
1	−1639.0	−303.4	3.110	$- 6.3 e - 10$
2	−647.6	415.3	8.503	$- 1.7 e - 9$
Stop	−579.9	−384.4	−0.483	$3.4 e - 10$
4	−942.7	778.0	19.12	$- 3.2 e - 9$
5	−632.1	−258.3	0.040	$2.8 e - 11$
6	−879.9	312.9	−6.818	$- 3.5 e - 10$
7	459.6	−352.9	1.055	$- 6.2 e - 10$
8	484.8	419.8	0.371	$- 5.5 e - 11$
Surf	$A_{6}$	$A_{8}$	$A_{10}$	$A_{12}$
1	$- 4.0 e - 16$	$3.4 e - 21$	$- 6.7 e - 26$	$3.9 e - 31$
2	$9.1 e - 16$	$4.9 e - 19$	$- 1.8 e - 23$	$9.5 e - 28$
Stop	$2.8 e - 15$	$6.8 e - 21$	$- 4.3 e - 25$	$7.5 e - 30$
4	$- 1.4 e - 14$	$- 4.3 e - 19$	$1.7 e - 23$	$- 1.2 e - 28$
5	$1.5 e - 17$	$8.1 e - 23$	$8.5 e - 28$	$- 5.9 e - 33$
6	$- 2.5 e - 16$	$1.1 e - 20$	$- 2.7 e - 25$	$1.8 e - 30$
7	$- 6.4 e - 14$	$9.6 e - 19$	$- 1.8 e - 23$	$6.6 e - 27$
8	$- 8.5 e - 18$	$2.1 e - 22$	$- 1.0 e - 27$	$- 4.0 e - 32$

Field No.	RMS Error	$Z_{3}$	$Z_{4}$
1	0.0707	−0.0324	−0.0379
2	0.0666	0.0042	0.0097
3	0.0717	0.0045	0.0188
4	0.0707	−0.0322	−0.0379
5	0.0665	0.0041	0.0097
6	0.0672	0.0001	0.0136

Abstract

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Equations (45)

Applied Optics