Level-set-based inverse lithography for photomask synthesis

Shen, Yongming; Wong, Ngai; Lam, Edmund Y.

doi:10.1364/oe.17.023690

Cited by 71 publications

(45 citation statements)

References 39 publications

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“…Various computation techniques have been proposed to deal with this inverse problem in the literature, such as the level-set method, [5][6][7][8] the discrete cosine transform (DCT)-based method, 9 and the gradient-based method. [10][11][12][13][14][15] The level-set method treats a mask as a sophisticated continuum, [5][6][7][8] and consequently, the boundary of the mask is iteratively evolved according to an optimization algorithm. The DCT-based method transforms a mask to the frequency space using a two-dimensional DCT.…”

Section: Introductionmentioning

confidence: 99%

“…[6][7][8][10][11][12][13][14][15] The pattern error employs an approximated and continuous resist model, and it is defined as a square of the L 2 norm of the difference between the output pattern of the input mask and the desired feature, which causes pattern error to be continuous and differentiable with respect to the input mask explicitly. 10,11 However, pattern error is a dimensionless quantity and highly depends on mask feature and simulation parameters, such as simulation area and simulation resolution.…”

Section: Introductionmentioning

confidence: 99%

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Mask-filtering-based inverse lithography

Xia

Liu

2013

J. Micro/Nanolith. MEMS MOEMS

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Abstract. We propose a new regularization framework for inverse lithography that regularizes masks directly by applying a mask filtering technique to improve computational efficiency and to enhance mask manufacturability. This technique is different from the conventional regularization method that regularizes a mask by incorporating various penalty functions to the cost function. We design a specific mask filter for this purpose. Moreover, we introduce a metric called edge distance error (EDE) to guide mask synthesis and establish the correlation between pattern error and edge placement error (EPE) via EDE. We prove that EDE has the same dimension as EPE and has a continuous expression as pattern error. Simulation results demonstrating the validity and efficiency of the proposed method are presented. © 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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mask-filtering-based inverse lithography

Xia

Liu

2013

J. Micro/Nanolith. MEMS MOEMS

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“…18,19 The inverse problems have been solved by linear programming, quadratic programming, or nonlinear formulations based on the assumptions made for the optical systems. [20][21][22][23] Recently, the traditional pixel-flipping techniques have been replaced with elaborated algorithms such as gradient descent methods 24,25 and levelset 26,27 alorithms, which have also been demonstrated on large-scale layouts. Although pixel-flipping techniques could also be very efficient for inverse lithography, the techniques exhibit some known issues.…”

Section: Introductionmentioning

confidence: 99%

Wavefront-based pixel inversion algorithm for generation of subresolution assist features

Yu²,

Chao

2011

J. Micro/Nanolith. MEMS MOEMS

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The generation of subresolution assist features (SRAFs) using inverse-lithography techniques demands extensive computational resources which limits its deployment in advanced CMOS nodes. In this paper, we propose a wavefront-based pixel inversion algorithm to quickly obtain inverse masks with a high aerial image quality. Further assisted by a flexible pattern simplification technique, we present effective SRAF generation and placement based on the calculated inverse mask. The proposed approach can be easily inserted prior to a conventional mask correction flow for subsequent concurrent optimizations of both drawn patterns and SRAFs. The innovative pixel inversion and pattern simplification techniques allow quality mask corrections as produced by inverse lithography while maintaining the convenience of standardized/validated process flows currently used in the industry. C 2011 Society of Photo-Optical Instrumentation Engineers (SPIE).

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“…A periodic array of contact holes pattern is used in the numerical verification. To demonstrate effectiveness and efficiency of CGALSA, we also perform mask synthesis using gradient based algorithm (GBA) [7] and traditional level-set algorithm (TLSA) [11].…”

Section: Introductionmentioning

confidence: 99%

Mask Synthesis for Aerial Image Fidelity in Optical Lithography Using a Coarse-Grid-Approximation Level-Set Approach

2011

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Inverse lithography technique, which treats mask synthesis as an inverse problem, has been considered as a strong contender to deal with the 45 nm technology node and beyond. But one problem exists in present pixel based mask synthesis algorithms: to describe mask patterns more accurately and to obtain better image quality, usually need finer grid representation, which results in extremely intensive computations. In this paper, a new method is proposed to mitigate this issue based on level-set method. This method utilizes the coarse-grid-approximation (CGA), which means the mask pattern defined on the fine grids is approximated using a new mask defined on coarse grids. The mask optimization is then performed on coarse girds and the final result is acquired by extracting mask patterns from coarse grids to fine grids. This method is demonstrated using a periodic array of contact holes pattern. Comparing with a gradient based algorithm and the traditional levelset algorithm, this method can provide almost the same image quality, but with over 100X running speed enhancement.

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Level-set-based inverse lithography for photomask synthesis

Cited by 71 publications

References 39 publications

Mask-filtering-based inverse lithography

Mask-filtering-based inverse lithography

Wavefront-based pixel inversion algorithm for generation of subresolution assist features

Mask Synthesis for Aerial Image Fidelity in Optical Lithography Using a Coarse-Grid-Approximation Level-Set Approach

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