Computational Lithography E-Book

Xu Ma

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Wiley Series in Pure and Applied Optics
• Sprache: Englisch

Seitenzahl: 280

Veröffentlichungsjahr: 2011

Beschreibung

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.

Leseprobe

Contents

Cover

Wiley Series in Pure and Applied Optics

Title Page

Copyright

Dedication

Preface

Acknowledgments

Acronyms

Chapter 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

Chapter 2: Optical Lithography Systems

2.1 Partially Coherent Imaging Systems

2.2 Approximation Models

2.3 Summary

Chapter 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

Chapter 4: Fundamentals of Optimization

4.1 Definition and Classification

4.2 Unconstrained Optimization

4.3 Summary

Chapter 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

Chapter 6: Regularization Framework

6.1 Discretization Penalty

6.2 Complexity Penalty

6.3 Summary

Chapter 7: Computational Lithography with Partially Coherent Illumination

7.1 OPC Optimization

7.2 PSM Optimization

7.3 Summary

Chapter 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

Chapter 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

Chapter 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

Chapter 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

References

Index

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Library of Congress Cataloging-in-Publication Data:

Ma, Xu, 1983-

Computational lithography / Xu Ma and Gonzalo R. Arce.

p. cm. – (Wiley series in pure and applied optics)

Includes bibliographical references and index.

ISBN 978-0-470-59697-5 (cloth)

1. Microlithography–Mathematics. 2. Integrated circuits–Design and construction–Mathematics. 3. Photolithography–Mathematics. 4.

Semiconductors–Etching–Mathematics. 5. Resolution (Optics) I. Arce, Gonzalo R. II. Title.

TK7872.M3C66 2010

621.3815'31–dc22

2009049250

To Our Families.

Preface

Moore's law and the integrated circuit industry have led the electronics industry to make technological advances that have transformed the society in many ways. Wireless communications, the Internet, and the astonishing new modalities in medical imaging have all been realized by the availability of the computational power inside IC processors. At this pace, if Moore's law continues to hold for the next couple of decades, the computational power of integrated circuits will play a key role in unveiling the secrets of the working mechanisms behind the living brain, it will also be the enabler in the advances of health informatics and of the solutions to other grand challenges singled out by the National Academy of Engineering. Maintaining this pace, however, requires a constant search by the semiconductor industry for new approaches to reduce the size of transistors. At the heart of Moore's law is optical lithography by which ICs are patterned, one layer at a time. By steadily reducing the wavelength of light in optical lithography, the IC industry has kept pace with the Moore's law. In the past two decades, the wavelength used in optical lithography has shrunk down to today's standard of 193 nm. This strategy, however, has become less certain as wavelengths shorter than 193 nm cannot be used without a major overhaul of the lithographic process, since shorter wavelengths are absorbed by the optical elements in lithography. While new lithography methods are under development, such as extreme ultraviolet (EUV) at the wavelength of 13 nm, the semiconductor industry is relying more on resolution enhancement techniques (RETs) that aim at coaxing light into resolving IC features that are smaller than its wavelength. RETs are becoming increasingly important since their implementation does not require significant changes in fabrication infrastructure.

The laws of optical wave propagation determine that the smallest resolvable features in optical lithography are proportional to the wavelength used and inversely proportional to the numerical aperture of the underlying optical system. Reducing the optical wavelength in optical lithography and exploring new methods to increase the numerical aperture are the two ways in which the semiconductor industry has made advances to keep up with the Moore's law. A third approach is that of reducing the proportionality constant k through resolution enhancement techniques. RETs manipulate the amplitude, phase, and direction of light propagation impinging on the lithographic mask to reduce the proportionality constant. In particular, optical proximity correction (OPC) modifies the wavefront amplitude, off-axis illumination (OAI) modifies the light wave direction of propagation, and phase-shifting masks manipulate the phase. OPC methods add assisting subresolution features on the mask pattern to correct the distortion of the optical projection systems. PSM methods modify both the amplitude and phase of the mask patterns. OAI methods exploit various illumination configurations to enhance the resolution. Used individually or in combination, RETs have proven effective in subwavelength lithography.

The literature on RET methods has been growing rapidly in journals and conference articles. Most of the methods used in RET exploit the rule-based principles developed and refined by practicing lithographers. Several excellent books on optical lithography have appeared in print recently. Wong provides a tutorial reference focusing on RET technology in optical lithography systems [92]. Wong subsequently extended this previous work and provided an integrated mathematical view of the physics and numerical modeling of optical projection lithography [93]. Levinson addressed and discussed an overall view of lithography, from the specific technical details to economical costs [36]. Mack captured the fundamental principles of the incredibly fast-changing field of semiconductor microlithography from the underlying scientific principles of optical lithography [49]. While the rule-based RET methods will continue to provide a valuable tool set for mask design in optical lithography, the new frontier for RETs will be on the development of tools and methods that capitalize from the ever rapid increase of computational power available for the RET design.

This book first aims at providing an adequate summary of the rule-based RET methodology as well as a basic understanding of optical lithography. It can thus serve as a tutorial for those who are new to the field. Different from the above-mentioned textbooks, this book is also the first to address the computational optimization approaches to RETs in optical lithography. Having vast computational resources at hand, computational lithography exploits the rich mathematical theory and practice of inverse problems, mathematical optimization, and computational imaging to develop optimization-based resolution enhancement techniques for optical lithography. The unique contribution of the book is thus a unified summary of the models and the optimization methods used in computational lithography. In particular, this book provides an in-depth and elaborate discussion on OPC, PSM, and OAI RET tools that use model-based mathematical optimization in their design. The book starts with an introduction of optical lithography systems, electric magnetic field principles, and fundamentals of optimization. Based on this preliminary knowledge, this book describes different types of optimization algorithms to implement RETs in detail. Most of the optimization algorithms developed in this book are based on the application of the OPC, PSM, and OAI approaches and their combinations. In addition, mathematical derivations of all the optimization frameworks are presented as appendices at the end of the book.

The Matlab's m-files for all the RET methods described in the book are provided at ftp://ftp.wiley.com/public/sci\_tech\_med/computational\_lithography. All the optimization tools are made available at ftp://ftp.wiley.com/public/sci\_tech\_med/computational\_lithography as Matlab's m-files. Readers may run and investigate the codes to understand the algorithms. Furthermore, these codes may be used by readers for their research and development activities in their academic or industrial organizations. The contents of this book are tailored for both entry-level and experienced readers.

Xu Ma and Gonzalo R. Arce

Department of Electrical and Computer Engineering, University of Delaware

Acknowledgments

We are thankful to many colleagues for their advice and contributions. It has been our good fortune to have had the opportunity to interact and have received the guidance of some of the world's leaders in optical lithography from the Intel Corporation. In particular, we are indebted to Dr. Christof Krautschik, Dr. Yan Borodovsky, Dr. Vivek Singh, and Dr. Jorge Garcia, all from the Intel Corporation, for their guidance and support. Our contributions to this field and the elaboration of this book would not have been possible without their support. We thank Dr. Dennis Prather from the University of Delaware for insightful discussions on optics, polarization, and optical wavefront propagation. The discussions on optimization and inverse problems as applied to RET design with Dr. Yinbo Li, Dr. David Luke, Dr. Javier Garcia-Frias, and Dr. Ken Barner, all from the University of Delaware, are greatly appreciated. We also thank Dr. Avideh Zakhor from the University of California, Berkeley, and Dr. Stephen Hsu from AMSL Corporation for insightful discussions on RETs. The material in this textbook has benefited greatly from our interactions with many bright students at the University of Delaware, with special appreciation to Dr. Zhongmin Wang, Peng Ye, Yuehao Wu, Dr. Lu Zhang, Dr. Bo Gui, and Xiantao Sun. We are particularly grateful to Prof. Glenn Boreman from CREOL at the University of Central Florida for his support in including this book in the Wiley Series in Pure and Applied Optics. We would like to thank our editor George Telecki and the staff at Wiley for supporting this project from the beginning stage through that at the printing press.

Xu Ma and Gonzalo R. Arce

Department of Electrical and Computer Engineering, University of Delaware

Acronyms

ACAAAverage Coherence Approximation AlgorithmBLBoundary LayerCDCritical DimensionCMTFCritical Modulation Transfer FunctionDCTDiscrete Cosine TransformDELDouble Exposure LithographyDPLDouble Patterning LithographyDUVLDeep Ultraviolet LithographyEBLE-Beam LithographyEUVLExtreme Ultraviolet LithographyFDTDFinite-Difference Time-Domain MethodFFTFast Fourier TransformICIntegrated CircuitILTInverse Lithography TechniqueITRSInternational Technology Roadmap for SemiconductorsMOSMetal Oxide SiliconMoSiMolybdenum SilicideMTFModulation Transfer FunctionNANumerical ApertureOAIOff-Axis IlluminationOPCOptical Proximity CorrectionPACPhotoactive CompoundPCIPartially Coherent IlluminationPSFPoint Spread FunctionPSMPhase-Shifting MaskRETResolution Enhancement TechniqueSMOSimultaneous Source and Mask OptimizationSNRSignal-to-Noise RatioSOCSSum of Coherent SystemSR1Symmetric Rank OneSVDSingular Value DecompositionWGWaveguide Method

Chapter 1

Introduction

1.1 Optical Lithography

Complex circuitries of modern microelectronic devices are created by building and wiring millions of transistors together. At the heart of this technology is optical lithography. Optical lithography technology is similar in concept to printing, which was invented more than 3000 years ago [92]. In optical lithography systems, a mask is used as the template, on which the target circuit patterns are carved. A light-sensitive polymer (photoresist) coated on the semiconductor wafer is used as the recording medium, on which the circuit patterns are projected. Light is used as the writing material, which is transmitted through the mask, thus optically projecting the circuit patterns from the mask to the wafer. The lithography steps are typically repeated 20–30 times to make up a circuit, where each underprinting pattern must be aligned to the previously formed patterns. After a lengthy lithography process, a complex integrated circuit (IC) structure is built from the interconnection of basic transistors. Moore's law, first addressed by Intel cofounder G. E. Moore in 1965, describes a long-term trend in the history of computing hardware. Moore's law predicted that the critical dimension (CD) of the IC would shrink by 30% every 2 years. This trend has continued for almost half a century and is not expected to stop for another decade at least. As the dimension of IC reduces following Moore's law, optical lithography has become a critical driving force behind microelectronics technology. During the past few decades, our contemporary society has been transformed by the dramatic increases in electronic functionality and lithography technology. Two main factors of optical lithography attract the attention of scientists and engineers. First, since lithography is the cardinal part of the IC fabrication process, around 30% of the cost of IC manufacturing is attributed to the lithography steps. Second, the advance and ultimate performance of lithography determine further advances of the critical size reduction in IC and thus transistor speed and silicon area. Both of the above aspects drive optical lithography into one of the most challenging places in current IC manufacturing technology. Current commercial optical lithography systems are able to image features smaller than 100 nm (about one-thousandth the thickness of human hair) of the IC pattern. As the dimension of features printed on the wafer continuously shrinks, the diffraction and interference effects of the light become very pronounced resulting in distortion and blurring of the circuit patterns projected on the wafer. The resolution limit of the optical lithography system is related to the wavelength of light and the structure of the entire imaging system. Due to the resolution limits of optical lithography systems, the electronics industry has relied on (RETs) to compensate and minimize mask distortions as they are projected onto semiconductor wafers. There are three RET techniques: optical proximity correction (OPC), phase-shifting masks (PSMs), and off-axis illumination (OAI). OPC methods add assisting subresolution features on the mask pattern to correct the distortion of the optical projection systems. PSM methods modify both the amplitude and phase of the mask patterns. OAI methods exploit various illumination configurations to enhance the resolution.