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Front Matter
This front matter contains an introduction, table of contents, and symbol glossary.

Library of Congress Cataloging-in-Publication Data

Mack, Chris A.

Field guide to optical lithography / Chris A. Mack.

p. cm. -- (SPIE field guides; FG06)

Includes bibliographical references and index.

1. Integrated circuits--Design and construction. 2. Microlithography. I. Title. II. Series.

TK7874.M195 2006



Published by

SPIE—The International Society for Optical Engineering

P.O. Box 10

Bellingham, Washington 98227-0010 USA

Phone: +1 360 676 3290

Fax: +1 360 647 1445

Email: spie@spie.org

Web: http://spie.org

The content of this book reflects the work and thought of the author. Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon.

Printed in the United States of America.


Introduction to the Series

Welcome to the SPIE Field Guides—a series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the SPIE Field Guides is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series.

Each SPIE Field Guide addresses a major field of optical science and technology. The concept of these Field Guides is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each Field Guide provide additional information such as related material outside the main scope of the volume, key mathematical relationships and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field.

The SPIE Field Guides are intended to be living documents. The modular page-based presentation format allows them to be easily updated and expanded. We are interested in your suggestions for new Field Guide topics as well as what material should be added to an individual volume to make these Field Guides more useful to you. Please contact us at fieldguides@SPIE.org.

John E. Greivenkamp, Series Editor

Optical Sciences Center

The University of Arizona

The Field Guide Series

Keep information at your fingertips with all of the titles in the Field Guide Series:

Field Guide to Geometrical Optics, John E. Greivenkamp (FG01)

Field Guide to Atmospheric Optics, Larry C. Andrews (FG02)

Field Guide to Adaptive Optics, Robert K. Tyson & Benjamin W. Frazier (FG03)

Field Guide to Visual and Ophthalmic Optics, Jim Schwiegerling (FG04)

Field Guide to Polarization, Edward Collett (FG05)

Field Guide to Optical Lithography, Chris A. Mack (FG06)

Field Guide to Optical Thin Films, Ronald R. Willey (FG07)

Field Guide to Optical Lithography

The material in this Field Guide to Optical Lithography is a distillation of material I have been putting together for the last 20 years or so. I have been subjecting students in my graduate-level lithography course at the University of Texas at Austin to my disorganized notes for 14 years, and have published some similar material in my first book Inside PROLITH and my column in Microlithography World called “The Lithography Expert.” However, the challenge here was not in creating the material for the book but rather deciding what material to leave out and how to make what remained as condensed as possible. As people who know me can attest, I am rarely lacking for words and brevity is not my strong suit (I am a lousy poet). I hope, however, that the kind reader will forgive me when one page on a topic of interest does not satisfy—it is an unavoidable consequence of the Field Guide format, and my own limitations as an overly verbose writer.

I thank Jeff Byers, William Howard, and Rob Jones for their help in reviewing the draft manuscript of this Field Guide. My many mistakes kept them quite busy.

This Field Guide is dedicated to my wife Susan and our daughter Sarah, who have taught me that there is indeed something more fun in this world than lithography.

Chris Mack


Table of Contents

Symbol Glossary x

The Lithography Process 1

Definition: Semiconductor Lithography 1

Overview of the Lithography Process 2

Processing: Substrate Preparation 3

Processing: Photoresist Spin Coating 4

Processing: Post-Apply Bake 5

Processing: Alignment and Exposure 6

Processing: Post-Exposure Bake 7

Processing: Development 8

Processing: Pattern Transfer 9

Image Formation 11

Maxwell’s Equations: The Mathematics of Light 11

The Plane Wave and the Phasor 12

Basic Imaging Theory 13

Diffraction 14

Fraunhofer Diffraction: Examples 15

The Numerical Aperture 16

Fourier Optics 17

Spatial Coherence and Oblique Illumination 18

Partial Coherence 19

Aberrations 20

Aberrations: The Zernike Polynomial 21

Aberrations: Zernike Examples 22

Chromatic Aberration 23

Horizontal-Vertical (H-V) Bias 24

Defocus 25

Flare 26

Vector Nature of Light 27

Polarization 29

The Optical Invariant 30

Immersion Lithography: Resolution 31

Immersion Lithography: Depth of Focus 32

Imaging into a Photoresist 33

Standing Waves: Definition 33

Standing Waves: Mathematics 34

Fresnel Reflectivity 35

Swing Curves 36

Top Antireflective Coatings (TARC) 37

Bottom Antireflective Coatings (BARC) 38

Photoresist Chemistry 39

Novolak/DNQ Resists 39

Chemically Amplified Resists 40

Absorption of Light 41

Photoresist Bleaching and the Dill Parameters 42

Exposure Kinetics 43

Measuring the Dill ABC Parameters 44

Chemically Amplified Resist Kinetics 45

Diffusion in Chemically Amplified Resists 46

Acid Loss Mechanisms 47

Post-Apply Bake Effects 48

Photoresist Development Kinetics 49

Surface Inhibition 50

Developer Temperature and Concentration 51

The Development Path 52

Lithography Control and Optimization 53

NILS: The Normalized Image Log-Slope 53

NILS: The Log-Slope Defocus Curve 54

NILS: Image Optimization 55

NILS: Exposure Optimization 56

NILS: PEB Optimization 57

NILS: Development Optimization 59

NILS: Total Process Optimization 60

Defining Photoresist Linewidth 61

Critical Dimension Control 62

Critical Dimension Control: Effect on Devices 64

Overlay Control 65

Line Edge Roughness 66

Metrology: Critical Dimension 67

Metrology: Overlay 68

The Process Window 69

Depth of Focus 71

Resolution 73

Rayleigh Criteria: Resolution 74

Rayleigh Criteria: Depth of Focus 75

Mask Error Enhancement Factor (MEEF) 76

Resolution Enhancement Technologies 77

Phase-Shift Masks 78

Phase-Shift Masks: Alternating 79

Phase-Shift Masks: Attenuated 80

Optical Proximity Effects 81

Optical Proximity Correction (OPC) 82

Off-Axis Illumination 83

Lithography Simulation 85

Moore’s Law 86

Next-Generation Lithography (NGL) 87

Equation Summary 88

Glossary 92

Index 117



Dose-dependent curvature of the CD-through-focus curve; molar absorption coefficient; constant in the Mack 4-parameter dissolution rate model


Electric field amplitude; bleachable absorption co-efficient


Arrhenius coefficient


Magnetic induction, non-bleachable absorption co-efficient


Speed of light; concentration


Photoresist exposure rate constant


Critical dimension


Shifter thickness for a phase-shift mask


Electric displacement, photoresist thickness; ARC thickness


Diffusivity of acid in photoresist


Depth of focus


Electric field, incident exposure dose


Activation energy


Dose to clear


Exposure dose at depth z in the resist


Spatial frequency


Initial PAG concentration


Planck’s constant; normalized acid concentration in a chemically amplified resist


Magnetic field; acid concentration in a chemically amplified resist


Intensity of light, aerial image


Electric current density


Propagation constant, wavenumber; chemical reaction rate constant


Normalized Rayleigh resolution


Normalized Rayleigh depth of focus


Effective gate length


Magnification; normalized unreacted site concentration in conventional or chemically amplified resists


Threshold inhibitor concentration


Photoactive compound concentration, unreacted site concentration


Initial PAC concentration


Index of refraction; dissolution selectivity parameter; diffraction order number


Complex index of refraction of layer j


Avogadro’s number


Numerical aperture


Normalized image log-slope


Optical path difference




Pupil function; photoresist exposure products; a point in x-y-z space


Photoresist dissolution rate


Dissolution rate of fully exposed positive resist


Dissolution rate of unexposed positive resist


Resin concentration; resolution; relative pupil radius position; intensity reflectivity; universal gas constant; photoresist dissolution rate


Solvent concentration


Time, exposure time


Bake time


Mask transmittance function


Transmittance; absolute temperature


Fourier transform of the mask transmittance function (diffraction pattern amplitude)


Phasor representation of the sinusoidal e-field


Process variable


Slit width, mask feature width, nominal linewidth


Normalized concentration of reacted sites in a chemically amplified resist; horizontal position


Concentration of reacted sites in a chemically amplified resist


Zernike polynomial coefficient


Maximum angle of diffraction captured by a lens; absorption coefficient


Dirac delta function; defocus distance


Dielectric constant


Angle; polar angle of pupil position; photoresist sidewall angle


Photoresist constrast


Imaginary portion of complex refractive index


Wavelength (in vacuum)


Magnetic permeability


Electric charge density


Reflection coefficient between films i and j


Conductivity; partial coherence factor; diffusion length


Transmission coefficient between films i and j


Phase of an electric field; fraction of absorbed photons producing a chemical change (quantum yield)


Frequency of monochromatic light; photoresist spin coat speed


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