Analysis and Verification of Position Error of Reticle Stage Based on Planar Grating

Chunxiao Hao; Wentao Zhang; Xianying Wang; Xunzhi Huang

doi:10.3788/LOP56.231202

Laser & Optoelectronics Progress, Volume. 56, Issue 23, 231202(2019)

Analysis and Verification of Position Error of Reticle Stage Based on Planar Grating

Chunxiao Hao1,*... Wentao Zhang1,2, Xianying Wang2 and Xunzhi Huang2 |Show fewer author(s)

¹School of Electronic Engineering and Automation, Guilin University of Electronic Technology, Guilin, Guangxi 541004, China

²Shanghai Micro Electronics Equipment (Group) Co., Ltd., Shanghai 201203, China

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Figures & Tables(13)

Fig. 1. Schematic of measurement optical paths of planar grating and laser interferometer

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Fig. 2. Installation layout of planar grating and laser interferometer of reticle stage

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Fig. 3. Analytical diagrams of model errors. (a) Abbe error; (b) cosine error

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Fig. 4. Error analysis diagrams of degree of freedom R_x with respect to degree of freedom in y direction

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Fig. 5. Error analysis diagrams of degree of freedom R_z with respect to degree of freedom in y direction

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Fig. 6. Error analysis diagrams of degree of freedom R_y with respect to degree of freedom in y direction

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Fig. 7. Error analysis diagrams of degree of freedom R_z with respect to degree of freedom in y direction

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Fig. 8. Error analysis diagrams of degrees of freedom y and R_x with respect to degree of freedom in y direction

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Fig. 9. Simulation results of Y-direction coupling coefficient. (a) First-order coupling coefficient; (b) high-order coupling coefficient

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Fig. 10. Experimental system for reticle stage measurement

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Table 1. Ranges of degree of freedom of reticle stage
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Table 1. Ranges of degree of freedom of reticle stage
Degree of freedom Range Step
X 1.6 mm 5
Y 240 mm 3
R_z 1. 6 mrad 3

Table 2. Coupling coefficients of three degrees of freedom of planar grating

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Table 2. Coupling coefficients of three degrees of freedom of planar grating

Degree of freedom coefficient /(mm·mrad^-1)	1	2	3
ξ_Rx₂_x	-0.381	-0.365	-0.367
ξ_Ry₂_x	-55.667	-55.653	-55.496
ξ_Rz₂_x	-22.860	-22.843	-22.849
ζ_Ry.y₂_x	-0.128	-0.090	-0.115
ξ_Rx₂_y	43.853	43.850	43.834
ξ_Ry₂_y	3.943	3.922	3.924
ξ_Rz₂_y	-7.063	-7.049	-7.069
ζ_Rx.y₂_y	-14.843	-14.758	-14.764
ξ_Rz₂_Rx	1.636	1.773	1.773
$\begin{matrix} ξ_{Rz 2 R_{y}} \end{matrix}$	0.607	0.682	0.682
ξ_Rz₂_x	3.622	3.965	3.965
ζ_Rx.y₂_Rx	-2.966	-4.096	-4.096

Table 3. Comparison of position accuracy between laser interferometer and planar gratingmm

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Table 3. Comparison of position accuracy between laser interferometer and planar gratingmm

Instrument	Physical location					3σ
Instrument		-120	-60	0	60	120
Laser interferometer	-119.999	-59.999	-1.04485×10^-7	60.000094	120.000092	1. 818×10^-4
Planar grating 1	-120.000009	-59.999998	-4.811×10^-6	60.000013	120.000004	3. 812×10^-6
Planar grating 2	-120.000003	-60.2312021	-1.316×10^-5	60.000006	120.000003	3. 897×10^-5
Planar grating 3	-120.2312021	-60.2312021	-1.429×10^-7	60.000001	120.2312021	4. 892×10^-6

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Chunxiao Hao, Wentao Zhang, Xianying Wang, Xunzhi Huang. Analysis and Verification of Position Error of Reticle Stage Based on Planar Grating[J]. Laser & Optoelectronics Progress, 2019, 56(23): 231202

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