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Computational lithography.pdf

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    1
    Computational Lithography 计算光刻
    Computational Lithography
    Contents
    Preface
    Acknowledgments
    Acronyms
    1 Introduction
    1.1 OPTICAL LITHOGRAPHY
    1.1.1 Optical Lithography and Integrated Circuits
    1.1.2 Brief History of Optical Lithography Systems
    1.2 RAYLEIGH’S RESOLUTION
    1.3 RESIST PROCESSES AND CHARACTERISTICS
    1.4 TECHNIQUES IN COMPUTATIONAL LITHOGRAPHY
    1.4.1 Optical Proximity Correction
    1.4.2 Phase-Shifting Masks
    1.4.3 Off-Axis Illumination
    1.4.4 Second-Generation RETs
    1.5 OUTLINE
    2 Optical Lithography Systems
    2.1 PARTIALLY COHERENT IMAGING SYSTEMS
    2.1.1 Abbe’s Model
    2.1.2 Hopkins Diffraction Model
    2.1.3 Coherent and Incoherent Imaging Systems
    2.2 APPROXIMATION MODELS
    2.2.1 Fourier Series Expansion Model
    2.2.2 Singular Value Decomposition Model
    2.2.3 Average Coherent Approximation Model
    2.2.4 Discussion and Comparison
    2.3 SUMMARY
    3 Rule-Based Resolution Enhancement Techniques
    3.1 RET TYPES
    3.1.1 Rule-Based RETs
    3.1.2 Model-Based RETs
    3.1.3 Hybrid RETs
    3.2 RULE-BASED OPC
    3.2.1 Catastrophic OPC
    3.2.2 One-Dimensional OPC
    3.2.3 Line-Shortening Reduction OPC
    3.2.4 Two-Dimensional OPC
    3.3 RULE-BASED PSM
    3.3.1 Dark-Field Application
    3.3.2 Light-Field Application
    3.4 RULE-BASED OAI
    3.5 SUMMARY
    4 Fundamentals of Optimization
    4.1 DEFINITION AND CLASSIFICATION
    4.1.1 Definitions in the Optimization Problem
    4.1.2 Classification of Optimization Problems
    4.2 UNCONSTRAINED OPTIMIZATION
    4.2.1 Solution of Unconstrained Optimization Problem
    4.2.2 Unconstrained Optimization Algorithms
    4.3 SUMMARY
    5 Computational Lithography with Coherent Illumination
    5.1 PROBLEM FORMULATION
    5.2 OPC OPTIMIZATION
    5.2.1 OPC Design Algorithm
    5.2.2 Simulations
    5.3 TWO-PHASE PSM OPTIMIZATION
    5.3.1 Two-Phase PSM Design Algorithm
    5.3.2 Simulations
    5.4 GENERALIZED PSM OPTIMIZATION
    5.4.1 Generalized PSM Design Algorithm
    5.4.2 Simulations
    5.5 RESIST MODELING EFFECTS
    5.6 SUMMARY
    6 Regularization Framework
    6.1 DISCRETIZATION PENALTY
    6.1.1 Discretization Penalty for OPC Optimization
    6.1.2 Discretization Penalty for Two-Phase PSM Optimization
    6.1.3 Discretization Penalty for Generalized PSM Optimization
    6.2 COMPLEXITY PENALTY
    6.2.1 Total Variation Penalty
    6.2.2 Global Wavelet Penalty
    6.2.3 Localized Wavelet Penalty
    6.3 SUMMARY
    7 Computational Lithography with Partially Coherent Illumination
    7.1 OPC OPTIMIZATION
    7.1.1 OPC Design Algorithm Using the Fourier Series Expansion Model
    7.1.2 Simulations Using the Fourier Series Expansion Model
    7.1.3 OPC Design Algorithm Using the Average Coherent Approximation Model
    7.1.4 Simulations Using the Average Coherent Approximation Model
    7.1.5 Discussion and Comparison
    7.2 PSM OPTIMIZATION
    7.2.1 PSM Design Algorithm Using the Singular Value Decomposition Model
    7.2.2 Discretization Regularization for PSM Design Algorithm
    7.2.3 Simulations
    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
    10.2.1 Boundary Layer Model in Coherent Imaging Systems
    10.2.2 Boundary Layer Model in Partially Coherent Imaging Systems
    10.3 LITHOGRAPHY PRELIMINARIES
    10.4 OPC OPTIMIZATION
    10.4.1 Topological Constraint
    10.4.2 OPC Optimization Algorithm Based on BL Model Under Coherent Illumination
    10.4.3 Simulations
    10.5 PSM OPTIMIZATION
    10.5.1 Topological Constraint
    10.5.2 PSM Optimization Algorithm Based on BL Model Under Coherent Illumination
    10.5.3 Simulations
    10.6 SUMMARY
    11 Conclusions and New Directions of Computational Lithography
    11.1 CONCLUSION
    11.2 NEW DIRECTIONS OF COMPUTATIONAL LITHOGRAPHY
    11.2.1 OPC Optimization for the Next-Generation Lithography Technologies
    11.2.2 Initialization Approach for the Inverse Lithography Optimization
    11.2.3 Double Patterning and Double Exposure Methods in Partially Coherent Imaging System
    11.2.4 OPC and PSM Optimizations for Inverse Lithography Based on Rigorous Mask Models in Partially Coherent Imaging System
    11.2.5 Simultaneous Source and Mask Optimization for Inverse Lithography Based on Rigorous Mask Models
    11.2.6 Investigation of Factors Influencing the Complexity of the OPC and PSM Optimization Algorithms
    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
    Computational Lithography XU MA AND GONZALO R. ARCE
    Computational Lithography
    WILEY SERIES IN PURE AND APPLIED OPTICS Founded by Stanley S. Ballard, University of Florida EDITOR: Glenn Boreman, University of Central Florida, CREOL & FPCE BARRETT AND MYERS · Foundations of Image Science BEISER · Holographic Scanning BERGER-SCHUNN · Practical Color Measurement BOYD · Radiometry and The Detection of Optical Radiation BUCK · Fundamentals of Optical Fibers, Second Edition CATHEY · Optical Information Processing and Holography CHUANG · Physics of Optoelectronic Devices DELONE AND KRAINOV · Fundamentals of Nonlinear Optics of Atomic Gases DERENIAK AND BOREMAN · Infrared Detectors and Systems DERENIAK AND CROWE · Optical Radiation Detectors DE VANY · Master Optical Techniques ERSOY · Diffraction, Fourier Optics and Imaging GASKILL · Linear Systems, Fourier Transform, and Optics GOODMAN · Statistical Optics HOBBS · Building Electro-Optical Systems: Making It All Work, Second Edition HUDSON · Infrared System Engineering IIZUKA · Elements of Photonics, Volume I: In Free Space and Special Media IIZUKA · Elements of Photonics, Volume II: For Fiber and Integrated Optics JUDD AND WYSZECKI · Color in Business, Science, and Industry, Third Edition KAFRI AND GLATT · The Physics of Moire Metrology KAROW · Fabrication Methods for Precision Optics KLEIN AND FURTAK · Optics, Second Edition MA AND ARCE · Computational Lithography MALACARA · Optical Shop Testing, Third Edition MILONNI AND EBERLY · Lasers NASSAU · The Physics and Chemistry of Color: The Fifteen Causes of Color, Second Edition NIETO-VESPERINAS · Scattering and Diffraction in Physical Optics OSCHE · Optical Detection Theory for Laser Applications O’SHEA · Elements of Modern Optical Design OZAKTAS · The Fractional Fourier Transform PRATHER, SHI, SHARKAWY, MURAKOWSKI, AND SCHNEIDER · Photonic Crystals: SALEH AND TEICH · Fundamentals of Photonics, Second Edition SCHUBERT AND WILHELMI · Nonlinear Optics and Quantum Electronics SHEN · The Principles of Nonlinear Optics UDD · Fiber Optic Sensors: An Introduction for Engineers and Scientists UDD · Fiber Optic Smart Structures VANDERLUGT · Optical Signal Processing VEST · Holographic Interferometry VINCENT · Fundamentals of Infrared Detector Operation and Testing WEINER · Ultrafast Optics WILLIAMS AND BECKLUND · Introduction to the Optical Transfer Function WYSZECKI AND STILES · Color Science: Concepts and Methods, Quantitative Data and Formulae, XU AND STROUD · Acousto-Optic Devices YAMAMOTO · Coherence, Amplification, and Quantum Effects in Semiconductor Lasers YARIV AND YEH · Optical Waves in Crystals YEH · Optical Waves in Layered Media YEH · Introduction to Photorefractive Nonlinear Optics YEH AND GU · Optics of Liquid Crystal Displays, Second Edition Theory, Applications, and Fabrication Second Edition
    Computational Lithography XU MA AND GONZALO R. ARCE
    Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permission. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic formats. For more information about Wiley products, visit our web site at www.wiley.com. 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. Semiconductors–Etching–Mathematics. 5. Resolution (Optics) Gonzalo R. II. Title. Photolithography–Mathematics. 4. I. Arce, TK7872.M3C66 2010 621.3815’31–dc22 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 2009049250
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