High-speed microlithography aerial image contour generation without images

Szu-kai Lin; Charlie Chung Ping Chen; Lawerence S. Melvin III

doi:10.1117/12.814420

16 March 2009 High-speed microlithography aerial image contour generation without images

Szu-kai Lin, Charlie Chung Ping Chen, Lawerence S. Melvin III

Proceedings Volume 7274, Optical Microlithography XXII; 727436 (2009) https://doi.org/10.1117/12.814420
Event: SPIE Advanced Lithography, 2009, San Jose, California, United States

Abstract

To evaluate the quality of microlithography result, massive aerial images are often generated for careful inspection using applications such as OPC LCC (Lithography Compaliance Check). The number of the pixels used in a 2D aerial image is in the order of O(n * n), where n is the image resolution, which means the runtime scales in a n² fashion. However, most of the quality indexes such as CDs or EPE (Edge Placement Error) can be readily observed using contours only and the number of pixels in a specific contour is around O(n) in general. Therefore, there is a huge waste (at least O(n)) of both computation time and memory in most microlithography aerial image simulation tools. The question is: "how to compute an image contour without explicitly generate images?". In this paper, we show that it is indeed feasible to know the image contour with an explicit image formation. The concept is to represent the image in an implicit way. In our algorithm, we utilize hierarchical region-wise function such as 2D polynomials to fit the aerial image kernels instead of using a bitmap type fit. Therefore, any LUT (Look-up-table) operation can be transformed into a polynomial look up and mathematical operations. Since there are only additive and subtractive operations during aerial image generation, we only need to apply same operations to the polynomial coefficients. Once the LUT operation is done,

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Szu-kai Lin, Charlie Chung Ping Chen, and Lawerence S. Melvin III "High-speed microlithography aerial image contour generation without images", Proc. SPIE 7274, Optical Microlithography XXII, 727436 (16 March 2009); https://doi.org/10.1117/12.814420

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KEYWORDS

Optical lithography

Computer simulations

Image resolution

Light sources

Photomasks

Convolution

Imaging systems

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