Method for optical proximity correction based on&#x00A0;a vector imaging model

Ruixuan Wu; Ruixuan Wu; Lisong Dong; Lisong Dong; Lisong Dong; Lisong Dong; Yayi Wei; Yayi Wei; Yayi Wei

doi:10.1364/AO.518578

Applied Optics
Vol. 63,
Issue 10,
pp. 2719-2727
(2024)
•https://doi.org/10.1364/AO.518578

Method for optical proximity correction based on a vector imaging model

Ruixuan Wu, Lisong Dong, and Yayi Wei

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Ruixuan Wu, Lisong Dong, and Yayi Wei, "Method for optical proximity correction based on a vector imaging model," Appl. Opt. 63, 2719-2727 (2024)

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Abstract

Optical proximity correction (OPC) has become an indispensable step in integrated circuit manufacturing. It requires a huge amount of calculation to obtain a sufficiently accurate OPC model and implement pattern correction. In this paper, the authors proposed an edge-based OPC method built on a vector imaging model, where the analytical correlation between the cost function and movement of each edge segment is established by the chain rule. First, the mask pattern is segmented and downsampled to get the mask image in order to reduce the total data. Second, the aerial image, various parameters on each evaluating point, and the final cost value are obtained in proper sequence. In each part of the OPC process, the procedures of solution and derivation are both recorded. After obtaining the cost value, the chain rule is applied, by which the differential relation between the cost value and movement of each segment is built. According to this differential relation, the next movement of each segment is decided under a quasi-Newton method. All results obtained by the proposed method are compared with results from commercial software. The comparison shows that the proposed OPC method has good OPC accuracy in few iterations.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Object	Submodule	Parameter
Optics	Illumination	Wavelength: 193 nm
		Point source
	Projection	$N A = 1.1$
		$R e d u c t i o n = 4$
Mask	Mask type	Bright-field
Mask	Critical dimension	180 nm on mask/45 nm on wafer

Target Patterns	Contours from nmOPC	Total EPE Total ${E P E}^{2}$	Contours of Proposed Method	Total EPE Total ${E P E}^{2}$
		71.2 nm $131.52 {n m}^{2}$		76.4 nm $148.28 {n m}^{2}$
		98.4 nm $168.56 {n m}^{2}$		95.2 nm $157.64 {n m}^{2}$
		114.4 nm $191.56 {n m}^{2}$		116.4 nm $211.08 {n m}^{2}$
		139.2 nm $228.88 {n m}^{2}$		149.8 nm $260.84 {n m}^{2}$

Test Patterns
Difference of total EPE	7.30%	−3.25%	1.75%	7.61%
Difference of total ${E P E}^{2}$	12.74%	−6.48%	10.19%	13.96%

Object	Submodule	Parameter
Optics	Illumination	Wavelength: 193 nm
		Point source
	Projection	$N A = 1.1$
		$R e d u c t i o n = 4$
Mask	Mask type	Bright-field
Mask	Critical dimension	180 nm on mask/45 nm on wafer

Target Patterns	Contours from nmOPC	Total EPE Total ${E P E}^{2}$	Contours of Proposed Method	Total EPE Total ${E P E}^{2}$
		71.2 nm $131.52 {n m}^{2}$		76.4 nm $148.28 {n m}^{2}$
		98.4 nm $168.56 {n m}^{2}$		95.2 nm $157.64 {n m}^{2}$
		114.4 nm $191.56 {n m}^{2}$		116.4 nm $211.08 {n m}^{2}$
		139.2 nm $228.88 {n m}^{2}$		149.8 nm $260.84 {n m}^{2}$

Abstract

Data availability

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Equations (17)

Applied Optics