Pixelated source and mask optimization for immersion lithography

Ma, Xu; Han, Chunying; Li, Yanqiu; Dong, Lisong; Arce, Gonzalo R.

doi:10.1364/josaa.30.000112

Cited by 72 publications

(27 citation statements)

References 32 publications

(42 reference statements)

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“…We approximate J sum as a constant for simplicity during the derivation of Eq. (12), since our extensive simulations show that this approximation makes the optimization procedure more stable [7,31]. The gradient of the cost function with respect to the mask pattern is calculated as…”

Section: B Optimization Proceduresmentioning

confidence: 99%

“…To further exploit the degree of freedom during SMO, the fundamental theory of pixel-based source optimization was developed by Granik [2], and then, a set of pixelated SMO methods had been introduced for improving lithography performance [3][4][5][6][7][8]. However, all of these traditional SMO methods are based on an ideal lithography system, thus sensitive to the nonideal factors of the actual scanners.…”

Section: Introductionmentioning

confidence: 99%

“…Then, a statistical method is adopted to establish an optimization framework, which treats the source blur and flare as random variables and takes their statistical properties in account. Finally, the HSMO algorithm described in [7] is used to solve the optimization framework, because it takes full advantages of source optimization, simultaneous SMO and mask optimization. The simulation results demonstrate our proposed robust HSMO approach effectively improves the robustness of the pattern fidelity and process window (PW) against the source blur and flare.…”

Section: Introductionmentioning

confidence: 99%

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Robust hybrid source and mask optimization to lithography source blur and flare

Han

et al. 2015

Appl. Opt.

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As a promising resolution enhancement technique, a set of pixelated source and mask optimization (SMO) methods has been introduced to further improve the lithography at 45 nm node and beyond. Recently, some papers studied the impact of the scanner errors on SMO, and the results revealed that the source blur and flare seriously impact on the lithography performance of the optimal source and mask resulting from SMO. However, current SMO methods did not propose an effective method to compensate for the impact of these nonideal factors of the actual scanners. To overcome this drawback, this paper focuses on developing a robust hybrid SMO (HSMO) method where the sensitivities of the aerial image to source blur and flare are introduced into the cost function. Simulation results are compared with traditional SMO to demonstrate the benefit of the proposed source blur-flare-aware HSMO method in pattern fidelity and process window.

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Section: B Optimization Proceduresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust hybrid source and mask optimization to lithography source blur and flare

Han

et al. 2015

Appl. Opt.

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“…The two acceleration methods used in [12,31] are adopted to speed up the proposed algorithm. The first one is the electric field caching technique (EFCT), which means that we only calculate E wafer p x s ; y s once in each iteration, and repetitively use it to calculated Z and ∇FΘ in Eq.…”

Section: Ztfmgmentioning

confidence: 99%

Block-based mask optimization for optical lithography

Song

et al. 2013

Appl. Opt.

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Pixel-based optical proximity correction (PBOPC) methods have been developed as a leading-edge resolution enhancement technique (RET) for integrated circuit fabrication. PBOPC independently modulates each pixel on the reticle, which tremendously increases the mask's complexity and, at the same time, deteriorates its manufacturability. Most current PBOPC algorithms recur to regularization methods or a mask manufacturing rule check (MRC) to improve the mask manufacturability. Typically, these approaches either fail to satisfy manufacturing constraints on the practical product line, or lead to suboptimal mask patterns that may degrade the lithographic performance. This paper develops a block-based optical proximity correction (BBOPC) algorithm to pursue the optimal masks with manufacturability compliance, where the mask is shaped by a set of overlapped basis blocks rather than pixels. BBOPC optimization is formulated based on a vector imaging model, which is adequate for both dry lithography with lower numerical aperture (NA), and immersion lithography with hyper-NA. The BBOPC algorithm successively optimizes the main features (MF) and subresolution assist features (SRAF) based on a modified conjugate gradient method. It is effective at smoothing any unmanufacturable jogs along edges. A weight matrix is introduced in the cost function to preserve the edge fidelity of the printed images. Simulations show that the BBOPC algorithm can improve lithographic imaging performance while maintaining mask manufacturing constraints.

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“…Recently, we proposed a pixelated SMO based on a vector imaging model that significantly improved the simulation precision for lithography at the 45-nm node and beyond. 11,12 Previous SMO methods fixed the NA and fell short in considering the mutual impact of the NA with respect to the source and mask. Prior work has demonstrated that a larger NA could realize a higher resolution, but the DOF would decrease because of the relation DOF ¼ k 2 · λ∕ðNAÞ 2 , 13 where λ is the wavelength and k 2 is the process factor.…”

Section: Introductionmentioning

confidence: 99%

Parametric source-mask-numerical aperture co-optimization for immersion lithography

Guo

Dong

et al. 2014

J. Micro/Nanolith. MEMS MOEMS

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Abstract. Source mask optimization (SMO) is a leading resolution enhancement technique in immersion lithography at the 45-nm node and beyond. Current SMO approaches, however, fix the numerical aperture (NA), which has a strong impact on the depth of focus (DOF). A higher NA could realize a higher resolution but reduce the DOF; it is very important to balance the requirements of NA between resolution and the DOF. In addition, current SMO methods usually result in complicated source and mask patterns that are expensive or difficult to fabricate. This paper proposes a parametric source-mask-NA co-optimization (SMNO) method to improve the pattern fidelity, extend the DOF, and reduce the complexity of the source and mask. An analytic cost function is first composed based on an integrative vector imaging model, in which a differentiable function is applied to formulate the source and mask patterns. Then, the derivative of the cost function is deduced and a gradient-based algorithm is used to solve the SMNO problem. Simulation results show that the proposed SMNO can achieve the optimum combination of parametric source, mask, and NA to maintain high pattern fidelity within a large DOF. In addition, the complexities of the source and mask are effectively reduced after optimization. © The Authors. Published by SPIE under a Creative Commons Attribution 3.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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Pixelated source and mask optimization for immersion lithography

Cited by 72 publications

References 32 publications

Robust hybrid source and mask optimization to lithography source blur and flare

Robust hybrid source and mask optimization to lithography source blur and flare

Block-based mask optimization for optical lithography

Parametric source-mask-numerical aperture co-optimization for immersion lithography

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