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Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step
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10.1116/1.4813781
/content/avs/journal/jvstb/31/4/10.1116/1.4813781
http://aip.metastore.ingenta.com/content/avs/journal/jvstb/31/4/10.1116/1.4813781

Figures

Image of FIG. 1.
FIG. 1.

Flowchart of TCC decomposition into analytical kernels.

Image of FIG. 2.
FIG. 2.

(Color online) (a) Desired pattern, (b) its optical image, and (c) its output pattern on the wafer with a pattern error of 16 723. (d) The synthesized mask pattern by the SD method after 81 iterations, (e) its optical image, and (f) its output pattern on the wafer with a pattern error of 4408. (g) The synthesized mask pattern by the CG method after 81 iterations, (h) its optical image, and (i) its output pattern on the wafer with a pattern error of 3670. The horizontal axis and vertical axis denote position and position of the patterns in nanometers, respectively. The two red dotted lines are CD cutlines both at the position of  = 450 nm, which will be detailed in Fig. 5(b) .

Image of FIG. 3.
FIG. 3.

(Color online) Comparison of output pattern contours. Enlarged views of three black boxes 1, 2, and 3 in (a) are shown in (b), (c), and (d) for the line-end error, the corner error, and the edge error, respectively.

Image of FIG. 4.
FIG. 4.

(Color online) Convergence of pattern error and mean EPE by the SD and CG methods, both for the desired pattern as shown in Fig. 2(a) . The red dotted–dashed line represents the 5% CD tolerance.

Image of FIG. 5.
FIG. 5.

(Color online) (a) Mean EPEs vs defocus variation for the synthesized mask pattern shown in Figs. 2(d) and 2(g) , and (b) intensity distributions along the cutlines shown in Figs. 2(e) and 2(h) .

Image of FIG. 6.
FIG. 6.

(Color online) (a) Desired pattern, (b) its optical image, and (c) its output pattern on the wafer with a pattern error of 42 066. (d) The synthesized mask pattern by the SD method after 100 iterations, (e) its optical image, and (f) its output pattern on the wafer with a pattern error of 6781. (g) The synthesized mask pattern by the CG method after 100 iterations, (h) its optical image, and (i) its output pattern on the wafer with a pattern error of 5372. The horizontal and vertical axes denote position and position of the patterns in nanometers, respectively.

Image of FIG. 7.
FIG. 7.

(Color online) Convergence of pattern error and mean EPE by the SD and CG methods, both for the desired pattern as shown in Fig. 6(a) .

Image of FIG. 8.
FIG. 8.

(Color online) (a) Synthesized mask pattern by the CG method with the Euler time step after 151 iterations, (b) its optical image, and (c) its output pattern on the wafer with a pattern error of 4785. (d) The synthesized mask pattern by the CG method with the optimal time step after 81 iteration, (e) its optical image, and (f) its output pattern on the wafer with a pattern error of 3670. The horizontal axis and vertical axis denote position and position of the patterns in nanometers, respectively.

Image of FIG. 9.
FIG. 9.

(Color online) (a) Convergence of pattern error by the CG method with the optimal time step and the Euler time step, and (b) the ratio of the optimal time step to the Euler time step during the evolution, both for the desired pattern shown in Fig. 2(a) .

Image of FIG. 10.
FIG. 10.

Cost function vs time step Δ in the extended Euler time range of [0.1Δ, 10Δ], where and denote the cost functions in the 1st and the 60th iterations, respectively, and and representing the corresponding Euler time steps.

Tables

Generic image for table
TABLE I.

Optimization comparison for some typical mask patterns by the SD and CG methods, both using an optimal time step.

Generic image for table
TABLE II.

Comparison of the pattern error and convergence performance by the CG method with different time steps.

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/content/avs/journal/jvstb/31/4/10.1116/1.4813781
2013-07-22
2014-04-17
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Level-set-based inverse lithography for mask synthesis using the conjugate gradient and an optimal time step
http://aip.metastore.ingenta.com/content/avs/journal/jvstb/31/4/10.1116/1.4813781
10.1116/1.4813781
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