1 Introduction to Semiconductor Lithography

1.1 Basics of IC Fabrication

1.2 Moore’s Law and the Semiconductor Industry

1.3 Lithography Processing



2 Aerial Image Formation–The Basics

2.1 Mathematical Description of Light

2.2 Basic Imaging Theory

2.3 Partial Coherence

2.4 Some Imaging Examples Problems



3 Aerial Image Formation – The Details

3.1 Aberrations

3.2 Pupil Filters and Lens Apodization

3.3 Flare

3.4 Defocus

3.5 Imaging with Scanners Versus Steppers

3.6 Vector Nature of Light

3.7 Immersion Lithography

3.8 Image Quality



4 Imaging in Resist: Standing Waves and Swing Curves

4.1 Standing Waves

4.2 Swing Curves

4.3 Bottom Antireflection Coatings

4.4 Top Antireflection Coatings

4.5 Contrast Enhancement Layer

4.6 Impact of the Phase of the Substrate Reflectance

4.7 Imaging in Resist

4.8 Defining Intensity



5 Conventional Resists: Exposure and Bake Chemistry

5.1 Exposure

5.2 Post-Apply Bake

5.3 Post-exposure Bake Diffusion

5.4 Detailed Bake Temperature Behavior

5.5 Measuring the ABC Parameters Problems



6 Chemically Amplified Resists: Exposure and Bake Chemistry

6.1 Exposure Reaction

6.2 Chemical Amplification

6.3 Measuring Chemically Amplified Resist Parameters

6.4 Stochastic Modeling of Resist Chemistry



7 Photoresist Development

7.1 Kinetics of Development

7.2 The Development Contrast

7.3 The Development Path

7.4 Measuring Development Rates Problems



8 Lithographic Control in Semiconductor Manufacturing

8.1 Defining Lithographic Quality

8.2 Critical Dimension Control

8.3 How to Characterize Critical Dimension Variations

8.4 Overlay Control

8.5 The Process Window

8.6 H–V Bias

8.7 Mask Error Enhancement Factor (MEEF)

8.8 Line-End Shortening

8.9 Critical Shape and Edge Placement Errors

8.10 Pattern Collapse Problems



9 Gradient-Based Lithographic Optimization: Using the Normalized Image Log-Slope

9.1 Lithography as Information Transfer

9.2 Aerial Image

9.3 Image in Resist

9.4 Exposure

9.5 Post-exposure Bake

9.6 Develop

9.7 Resist Profile Formation

9.8 Line Edge Roughness

9.9 Summary Problems



10 Resolution Enhancement Technologies

10.1 Resolution

10.2 Optical Proximity Correction (OPC)

10.3 Off-Axis Illumination (OAI)

10.4 Phase-Shifting Masks (PSM)

10.5 Natural Resolutions



Appendix A Glossary of Microlithographic Terms

Appendix B Curl, Divergence, Gradient, Laplacian

B.1 Cross Product

B.2 Dot Product

B.3 Curl

B.4 Divergence

B.5 Gradient

B.6 Laplacian

B.7 Some Useful Identities

B.8 Spherical Coordinates

Appendix C The Dirac Delta Function

C.1 Definition

C.2 Properties and Theorems



British Library Cataloguing in Publication Data

To Susan, Sarah and Anna


There was a time when I was sure this book would never be finished. Believe it or not, I began working on it about 18 years ago, and for a long time it seemed that each year left me farther from completion (a consequence of working in a rapidly changing field). Several things conspired to finally make this book a reality. Ron Hershel, the closest person to a mentor I have known, gave me sage advice on writing a book: Dons’t try to write it all at once–instead, write and publish pieces of your book as journal articles over time, then collect them up when you have written enough. That advice has served me well, especially since I have been writing a quarterly column for Microlithography World since 1992. That approach helped me finish my first book, Inside PROLITH: A Comprehensive Guide to Optical Lithography Simulation, in 1997.

While I enjoyed finishing and publishing Inside PROLITH, my ambition was to write a more comprehensive university textbook on the topic of semiconductor lithography. I have been teaching a graduate level class on optical lithography at the University of Texas at Austin since 1991, using handouts in place of a real book. Each year I strove to add more material to make those notes more complete. But I ran into the same problem as before–new material in this quickly changing field was needed at a faster rate than I was writing.

I solved this problem in two ways. First, I began to focus solely on fundamental principles needed to understand the science of lithography. While lithography practice changes quickly, the fundamental principles underlying that practice do not. The result, though, is that this book has very little ‘practical’ advice, that is, descriptions of best practices in the industry. While such practical descriptions can be very useful, they also become dated very quickly. I hope that by focusing on fundamentals this book might be useful to the reader many years after it is purchased.

Secondly, I quit my job and worked on this book full-time (well, almost full time) for the final year before its completion. I hope that this admission doesn’t scare off the earnest would-be author, but the reality was, for me at least, that dedicated effort was required

to complete the project. Much of the material contained herein is, of course, a tutorial review of the published literature on lithography and related sciences. But a significant portion is new work, having never before been published. Thus, I hope that this book will contribute to the body of lithography literature mostly as a convenient repository of a useful portion of the collective knowledge in this field, but also as a repository for the information contained in various notebooks, files and scraps of paper scattered around my cluttered office.

While the length of the final book surprised even me, still, there are many fascinating and important topics in lithography that have been excluded for lack of space. In particular, rigorous treatment of electromagnetic scattering through the topography of a photomask is extremely important in lithography today, but goes without even a mention in the book. With respect to photoresist, etch resistance, spin coat rheology, adhesion, shelf life and quality control, resist formulations and defects all receive short shrift, and nothing is mentioned of top surface imaging or the various multilayer and nontraditional resist schemes. For those interested in imaging tools, the topics of geometrical optics, lens design, aberration measurement and tool component functions such as alignment, autofocus, stage motion, etc., are essentially ignored. The world of mask making is left to other books, as are the topics of chip design and design for manufacturability, despite their obvious impact on the field of lithography. Metrology, especially critical dimension metrology, is extremely important to lithography, since data from these measurements drive much of our knowledge of how lithography behaves. However, even though metrology deserves an entire chapter, I have left it out almost completely. Surprisingly to some, I have chosen not to cover an aspect of lithography very dear to me–lithography simulation. While the use of simulation is illustrated throughout the book, and of course a scientific description of lithography must necessarily serve as the foundation of a lithographic simulator, I have avoided the topic of the numerical solutions to the equations presented in the book as well as to the topics of model speed, accuracy and calibration. Finally, there is no effort to describe research into next generation lithography technologies, and no description of the many lithographic approaches that dons’t use projection optical imaging. Despite these glaring omissions, I still might be criticized for making the book too long, with too many topics, for use as a university text. I can only say that I have successfully covered most of the information contained in the book in a one semester course, with only the usual amount of grumbling from the affected students.

I am indebted to many, many people for their help with this book. In the 24 years that I have worked in the field of lithography I have been taught by many, many people. I couldns’t possible begin to count, let alone recount, the published works that have so greatly contributed to my understanding in this field. In fact, I will here issue a blanket apology to all those whose important works I have relied on but did not include in the references in the book. The lack of proper references is, I think, the biggest failure of this work, though I hope to be forgiven based on its format as a university textbook. I would also like to thank the students at the University of Texas at Austin and at Notre Dame whom I punished with early drafts of this book. Their feedback and experiences, good and bad, helped me to greatly improve the material and make it more suitable for the classroom.

There are many people who helped by reviewing chapters and providing feedback: Gary Bernstein, John Biafore, Robert Bunch, Jeff Byers, John Kulp and John Petersen

among others that I am sure I am forgetting. I would especially like to thank Warren Grobman who carefully read every chapter in the book and provided invaluable feedback, and Trey Graves who bravely defied Finmans’s Law of Mathematics and re-derived many of the equations in Chapters 2 and 3. I am indebted to Chris Sallee and KLA-Tencor for allowing me the use of the lithography simulator PROLITH, which I employed extensively in generating many of the figures found throughout the book.

As a final note, I encourage the interested reader to visit the web page for this book: There I will post errata and other information that might be useful to the reader, and information that might prove valuable to the professor interested in using this text as the basis for a university course.

                                                                                                                    Chris A. Mack

                                                                                                                    Austin, Texas

                                                                                                                   June, 2007