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By Xu Ma

A Unified precis of the types and Optimization equipment utilized in Computational Lithography

Optical lithography is among the such a lot demanding parts of present built-in circuit production expertise. The semiconductor is depending extra on answer enhancement options (RETs), on the grounds that their implementation doesn't require major adjustments in fabrication infrastructure. Computational Lithography is the 1st e-book to handle the computational optimization of RETs in optical lithography, delivering an in-depth dialogue of optimum optical proximity correction (OPC), section moving masks (PSM), and off-axis illumination (OAI) RET instruments that use model-based mathematical optimization approaches.

The publication starts off with an advent to optical lithography structures, electrical magnetic box rules, and the basics of optimization from a mathematical viewpoint. It is going directly to describe intimately types of optimization algorithms to enforce RETs. many of the algorithms built are in line with the appliance of the OPC, PSM, and OAI techniques and their combos. Algorithms for coherent illumination in addition to in part coherent illumination structures are defined, and diverse simulations are provided to demonstrate the effectiveness of the algorithms. furthermore, mathematical derivations of all optimization frameworks are presented.

The accompanying MATLAB® software program documents for the entire RET tools defined within the ebook make it effortless for readers to run and examine the codes with a view to comprehend and practice the optimization algorithms, in addition to to layout a suite of optimum lithography mask. The codes can also be utilized by readers for his or her examine and improvement actions of their educational or commercial agencies. An accompanying MATLAB® software program consultant is usually integrated. An accompanying MATLAB® software program advisor is integrated, and readers can obtain the software program to exploit with the advisor at

Tailored for either entry-level and skilled readers, Computational Lithography is intended for school, graduate scholars, and researchers, in addition to scientists and engineers in business companies whose examine or occupation box is semiconductor IC fabrication, optical lithography, and RETs. Computational lithography attracts from the wealthy conception of inverse difficulties, optics, optimization, and computational imaging; as such, the e-book is additionally directed to researchers and practitioners in those fields.

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These additional operations will severely increase the exposure time. 5 SUMMARY This chapter first discussed the classification of the RET methods. Subsequently, it focused on the rule-based RETs, where the rule-based OPC, PSM, and OAI approaches were described in detail. As the counterpart of the rule-based RETs, the model-based RET methods are emphasized in the book hereafter.

24) into the sum of coherent systems, the variable pairs of (p, q) and (r, u) in the argument of TCC 2 ∗ should be separated by the SVD. The result of the SVD of A is A = N k=1 αk Vk Vk , 2 where αk is the kth eigenvalue and α1 > α2 > · · · > αN 2 . The N × 1 vector Vk is the eigenfunction corresponding to αk . Thus, Eq. 24) becomes N I(m, n) = αk |˜sT Vk |2 . 26) k=1 Let S −1 (·) be the inverse column stacking operation that converts the N 2 × 1 column vector Vk into a N × N square matrix S −1 (Vk ).

In Chapter 7, OPC optimization approaches are developed for the partially coherent imaging systems based on the Fourier series expansion model. In order to reduce the computational complexity, the average coherent approximation model is applied to develop effective and more computationally efficient OPC optimization algorithms for inverse lithography. The advantages and the disadvantages of both algorithms are discussed and analyzed. Subsequently, the SVD model is used to develop computationally efficient PSM optimization algorithms under partially coherent illuminations for inverse lithography.

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