Computational Lithography (Wiley Series in Pure and Applied by Xu Ma

By Xu Ma

A Unified precis of the types and Optimization tools utilized in Computational LithographyOptical lithography is without doubt one of the so much tough parts of present built-in circuit production expertise. The semiconductor is depending extra on solution enhancement strategies (RETs), considering the fact that their implementation doesn't require major alterations in fabrication infrastructure. Computational Lithography is the 1st publication to handle the computational optimization of RETs in optical lithography, offering 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 ebook starts off with an advent to optical lithography platforms, electrical magnetic box rules, and the basics of optimization from a mathematical perspective. It is going directly to describe intimately varieties of optimization algorithms to enforce RETs. many of the algorithms constructed are in response to the appliance of the OPC, PSM, and OAI methods and their combos. Algorithms for coherent illumination in addition to partly coherent illumination platforms 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 records for the entire RET tools defined within the e-book make it effortless for readers to run and examine the codes which will comprehend and observe 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 learn and improvement actions of their educational or commercial agencies. An accompanying MATLAB® software program consultant can also be integrated. An accompanying MATLAB® software program advisor is integrated, and readers can obtain the software program to exploit with the advisor at for either entry-level and skilled readers, Computational Lithography is intended for school, graduate scholars, and researchers, in addition to scientists and engineers in commercial businesses whose learn or profession box is semiconductor IC fabrication, optical lithography, and RETs. Computational lithography attracts from the wealthy thought of inverse difficulties, optics, optimization, and computational imaging; as such, the publication can be directed to researchers and practitioners in those fields.

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Efficient algorithms do not need excessive running time and memory. Accurate algorithms can obtain a solution close to the minimum or minimum without being overly sensitive to the errors. These properties of good algorithms are sometimes in conflict. Thus, a user should keep a balance among these properties. 2 Classification of Optimization Problems According to the domain of the variable vector x, the optimization problems can be classified into continuous optimization problems and discrete optimization problems.

3 are illustrated in Fig. 11a and b, respectively. 6 are illustrated in Fig. 12a and b, respectively. 3. 6. It is noted that for the illuminations having small partial coherence factors, the eigenvalues decay very rapidly. 5, a partially coherent imaging system may be approximated to within 10% error by the first-order coherent approximation [58]. 3 Average Coherent Approximation Model The average coherent approximation model for the partially coherent imaging system was introduced by Salik et al.

Since the Fourier series expansion model is based on direct discretization of the Hopkins diffraction model, they have the same accuracy. Taking the annular illumination as an example, the complex degree of coherence is γ(r) = where r = 2 J (2πr/2D ) J1 (2πr/2Dcu ) Dcu 1 cl − 2 , 2πr/2Dcu Dcl 2πr/2Dcl x2 + y2 . 21) where Dcl and Dcu are the coherent lengths of the inner and outer circles, respectively. σinner = 2DclλNA and σouter = 2Dcuλ NA are the corresponding inner and outer partial coherence factors.

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