Print this page Share

Computational Lithography

ISBN: 978-0-470-59697-5
226 pages
September 2010
Computational Lithography  (047059697X) cover image


A Unified Summary of the Models and Optimization Methods Used in Computational Lithography

Optical lithography is one of the most challenging areas of current integrated circuit manufacturing technology. The semiconductor industry is relying more on resolution enhancement techniques (RETs), since their implementation does not require significant changes in fabrication infrastructure. Computational Lithography is the first book to address the computational optimization of RETs in optical lithography, providing an in-depth discussion of optimal optical proximity correction (OPC), phase shifting mask (PSM), and off-axis illumination (OAI) RET tools that use model-based mathematical optimization approaches.

The book starts with an introduction to optical lithography systems, electric magnetic field principles, and the fundamentals of optimization from a mathematical point of view. It goes on to describe in detail different types of optimization algorithms to implement RETs. Most of the algorithms developed are based on the application of the OPC, PSM, and OAI approaches and their combinations. Algorithms for coherent illumination as well as partially coherent illumination systems are described, and numerous simulations are offered to illustrate the effectiveness of the algorithms. In addition, mathematical derivations of all optimization frameworks are presented.

The accompanying MATLAB® software files for all the RET methods described in the book make it easy for readers to run and investigate the codes in order to understand and apply the optimization algorithms, as well as to design a set of optimal lithography masks. The codes may also be used by readers for their research and development activities in their academic or industrial organizations. An accompanying MATLAB® software guide is also included. An accompanying MATLAB® software guide is included, and readers can download the software to use with the guide at ftp://ftp.wiley.com/public/sci_tech_med/computational_lithography.

Tailored for both entry-level and experienced readers, Computational Lithography is meant for faculty, graduate students, and researchers, as well as scientists and engineers in industrial organizations whose research or career field is semiconductor IC fabrication, optical lithography, and RETs. Computational lithography draws from the rich theory of inverse problems, optics, optimization, and computational imaging; as such, the book is also directed to researchers and practitioners in these fields.

See More

Table of Contents




1 Introduction.

1.1 Optical Lithography.

1.2 Rayleigh’s Resolution.

1.3 Resist Processes and Characteristics.

1.4 Techniques in Computational Lithography.

1.5 Outline.

2 Optical Lithography Systems.

2.1 Partially Coherent Imaging Systems.

2.2 Approximation Models.

2.3 Summary.

3 Rule-Based Resolution Enhancement Techniques.

3.1 RET Types.

3.2 Rule-Based OPC.

3.3 Rule-Based PSM.

3.4 Rule-Based OAI.

3.5 Summary.

4 Fundamentals of Optimization.

4.1 Definition and Classification.

4.2 Unconstrained Optimization.

4.3 Summary.

5 Computational Lithography with Coherent Illumination.

5.1 Problem Formulation.

5.2 OPC Optimization.

5.3 Two-Phase PSM Optimization.

5.4 Generalized PSM Optimization.

5.5 Resist Modeling Effects.

5.6 Summary.

6 Regularization Framework.

6.1 Discretization Penalty.

6.2 Complexity Penalty.

6.3 Summary.

7 Computational Lithography with Partially Coherent Illumination.

7.1 OPC Optimization.

7.2 PSM Optimization.

7.3 Summary.

8 Other RET Optimization Techniques.

8.1 Double-Patterning Method.

8.2 Post-Processing Based on 2D DCT.

8.3 Photoresist Tone Reversing Method.

8.4 Summary.

9 Source and Mask Optimization.

9.1 Lithography Preliminaries.

9.2 Topological Constraint.

9.3 Source–Mask Optimization Algorithm.

9.4 Simulations.

9.5 Summary.

10 Coherent Thick-Mask Optimization.

10.1 Kirchhoff Boundary Conditions.

10.2 Boundary Layer Model.

10.3 Lithography Preliminaries.

10.4 OPC Optimization.

10.5 PSM Optimization.

10.6 Summary.

11 Conclusions and New Directions of Computational Lithography.

11.1 Conclusion.

11.2 New Directions of Computational Lithography.

Appendix A: Formula Derivation in Chapter 5.

Appendix B: Manhattan Geometry.

Appendix C: Formula Derivation in Chapter 6.

Appendix D: Formula Derivation in Chapter 7.

Appendix E: Formula Derivation in Chapter 8.

Appendix F: Formula Derivation in Chapter 9.

Appendix G: Formula Derivation in Chapter 10.

Appendix H: Software Guide.



See More

Author Information

Dr. Xu Ma received a PhD in electrical and computer engineering from the University of Delaware. He is now with the Electrical Engineering and Computer Science Department at the University of California at Berkeley. Dr. Ma's research interests include computational imaging, signal processing, and computational lithography.

Dr. Gonzalo R. Arce received a PhD degree in electrical engineering from Purdue University. He is the Charles Black Evans Distinguished Professor of Electrical and Computer Engineering at the University of Delaware and holds the Fulbright-Nokia Distinguished Chair in Information and Communications Technologies. Dr. Arce's fields of interest include nonlinear and statistical signal processing, digital printing, and computational imaging. He is a Fellow of the IEEE for his contributions to the theory and applications of nonlinear signal processing.

See More


"Computational lithography draws from the rich theory of inverse problems, optics, optimization, and computational imaging; as such, the book is also directed to researchers and practitioners in these fields. " (Consumer Electronics Net, 15 March 2011)
See More
Back to Top