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.
Autorentext
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.
Zusammenfassung
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.
Inhalt
Preface xi
Acknowledgments xiii
Acronyms xv
1 Introduction 1
1.1 Optical Lithography 1
1.1.1 Optical Lithography and Integrated Circuits 2
1.1.2 Brief History of Optical Lithography Systems 3
1.2 Rayleigh's Resolution 5
1.3 Resist Processes and Characteristics 7
1.4 Techniques in Computational Lithography 10
1.4.1 Optical Proximity Correction 11
1.4.2 Phase-Shifting Masks 11
1.4.3 Off-Axis Illumination 14
1.4.4 Second-Generation RETs 15
1.5 Outline 16
2 Optical Lithography Systems 19
2.1 Partially Coherent Imaging Systems 19
2.1.1 Abbe's Model 19
2.1.2 Hopkins Diffraction Model 22
2.1.3 Coherent and Incoherent Imaging Systems 24
2.2 Approximation Models 25
2.2.1 Fourier Series Expansion Model 25
2.2.2 Singular Value Decomposition Model 29
2.2.3 Average Coherent Approximation Model 32
2.2.4 Discussion and Comparison 34
2.3 Summary 36
3 Rule-Based Resolution Enhancement Techniques 37
3.1 RET Types 37
3.1.1 Rule-Based RETs 37
3.1.2 Model-Based RETs 38
3.1.3 Hybrid RETs 39
3.2 Rule-Based OPC 39
3.2.1 Catastrophic OPC 40
3.2.2 One-Dimensional OPC 40
3.2.3 Line-Shortening Reduction OPC 42
3.2.4 Two-Dimensional OPC 43
3.3 Rule-Based PSM 44
3.3.1 Dark-Field Application 44
3.3.2 Light-Field Application 45
3.4 Rule-Based OAI 46
3.5 Summary 47
4 Fundamentals of Optimization 48
4.1 Definition and Classification 48
4.1.1 Definitions in the Optimization Problem 48
4.1.2 Classification of…