Fundamental Principles of Optical Lithography: The Science of Microfabrication CHRIS MACK www. lithoguru. com

3ICENTENNIAL

3ICENTENNIAL

John Wiley & Sons, Ltd

Contents Preface 1. Introduction to Semiconductor Lithography 1.1 Basics of IC Fabrication 1.1.1 Patterning 1.1.2 Etching 1.1.3 Ion Implantation 1.1.4 Process Integration 1.2 Moore: s Law and the Semiconductor Industry Lithog]"aphy Processing 1.3 Substrate Preparation 1.3.1 1.3.2 Photoresist Coating 1.3.3 Post-Apply Bake 1.3.4 Alignment and Exposure 1.3.5 Post-exposure Bake 1.3.6 Development 1.3.7 Postbake 1.3.8 Measure and Inspect Pattern Transfer 1.3.9 1.3.10 Strip Problems Aerial Image Formation - The Basics 2.1 Mathematical Description of Light 2.1.1 Maxwell's Equations and the Wave Equation 2.1.2 General Harmonie Fields and the Plane Wave in a Nonabsorbing Medium 2.1.3 Phasors and Wave Propagation in an Absorbing Medium 2.1.4 Intensity and the Poynting Vector 2.1.5 Intensity and Absorbed Electromagnetic Energy

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Contents

2.2

Basic Imaging Theory 2.2.1 Diffraction 2.2.2 Fourier Transform Pairs 2.2.3 Imaging Lens 2.2.4 Forming an Image 2.2.5 Imaging Example: Dense Array of Lines and Spaces 2.2.6 Imaging Example: Isolated Space 2.2.7 The Point Spread Function 2.2.8 Reduction Imaging 2.3 Partial Coherence 2.3.1 Oblique Illumination 2.3.2 Partially Coherent Illumination 2.3.3 Hopkins Approach to Partial Coherence 2.3.4 Sum of Coherent Sources Approach 2.3.5 Off-Axis Illumination 2.3.6 Imaging Example: Dense Array of Lines and Spaces Under Annular Illumination 2.3.7 Köhler Illumination 2.3.8 Incoherent Illumination 2.4 Some Imaging Examples Problems

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Aerial Image Formation - The Details 3.1 Aberrations 3.1.1 The Causes of Aberrations 3.1.2 Describing Aberrations: the Zernike Polynomial 3.1.3 Aberration Example - Tut 3.1.4 Aberration Example - Defocus, Spherical and Astigmatism 3.1.5 Aberration Example - Coma 3.1.6 Chromatic Aberrations 3.1.7 Strehl Ratio 3.2 Pupil Filters and Lens Apodization 3.3 Flare 3.3.1 Measuring Flare 3.3.2 Modeling Flare 3.4 Defocus 3.4.1 Defocus as an Aberration 3.4.2 Defocus Example: Dense Lines and Spaces and Three-Beam Imaging 3.4.3 Defocus Example: Dense Lines and Spaces and Two-Beam Imaging 3.4.4 Image Isofocal Point 3.4.5 Focus Averaging 3.4.6 Reticle Defocus 3.4.7 Rayleigh Depth of Focus

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Contents

3.5 3.6

Imaging with Scanners Versus Steppers Vector Nature of Light 3.6.1 Describing Polarization 3.6.2 Polarization Example: TE Versus TM Image of Lines and Spaces 3.6.3 Polarization Example: The Vector PSF 3.6.4 Polarization Aberrations and the Jones Pupil 3.7 Immersion Lithography 3.7.1 The Optical Invariant and Hyper-NA Lithography 3.7.2 Immersion Lithography and the Depth of Focus 3.8 Image Quality 3.8.1 Image CD 3.8.2 Image Placement Error (Distortion) 3.8.3 Normalized Image Log-Slope (NILS) 3.8.4 Focus Dependence of Image Quality Problems

Imaging in Resist: Standing Waves and Swing Curves 4.1 Standing Waves 4.1.1 The Nature of Standing Waves 4.1.2 Standing Waves for Normally Incident Light in a Single Film 4.1.3 Standing Waves in a Multiple-Layer Film Stack 4.1.4 Oblique Incidence and the Vector Nature of Light 4.1.5 Broadband Illumination 4.2 Swing Curves 4.2.1 Reflectivity Swing Curve 4.2.2 Dose-to-Clear and CD Swing Curves 4.2.3 Swing Curves for Partially Coherent Illumination 4.2.4 Swing Ratio 4.2.5 Effective Absorption 4.3 Bottom Antireflection Coatings 4.3.1 BARC on an Absorbing Substrate 4.3.2 BARCs at High Numerical Apertures 4.3.3 BARC on a Transparent Substrate 4.3.4 BARC Performance 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 4.7.1 Image in Resist Contrast 4.7.2 Calculating the Image in Resist 4.7.3 Resist-Induced Spherical Aberrations 4.7.4 Standing Wave Amplitude Ratio

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4.8

Defimng Intensity 4.8.1 Intensity at Oblique Incidence 4.8.2 Refraction into an Absorbing Material 4.8.3 Intensity and Absorbed Energy Problems

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Conventional Resists: Exposure and Bake Chemistry 5.1 Exposure 5.1.1 Absorption 5.1.2 Exposure Kinetics 5.2 Post-Apply Bake 5.2.1 Sensitizer Decomposition 5.2.2 Solvent Diffusion and Evaporation 5.2.3 Solvent Effects in Lithography 5.3 Post-exposure Bake Diffusion 5.4 Detailed Bake Temperature Behavior 5.5 Measuring the ABC Parameters Problems

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Chemically Amplified Resists: Exposure and Bake Chemistry 6.1 Exposure Reaction 6.2 Chemical Amplification 6.2.1 Amplification Reaction 6.2.2 Diffusion 6.2.3 Acid Loss 6.2.4 Base Quencher 6.2.5 Reaction-Diffusion Systems 6.3 Measuring Chemically Amplified Resist Parameters 6.4 Stochastic Modeling of Resist Chemistry 6.4.1 Photon Shot Noise 6.4.2 Chemical Concentration 6.4.3 Some Mathematics of Binary Random Variables 6.4.4 Photon Absorption and Exposure 6.4.5 Acid Diffusion, Conventional Resist 6.4.6 Acid-Catalyzed Reaction-Diffusion 6.4.7 Reaction-Diffusion and Polymer Deblocking 6.4.8 Acid-Base Quenching Problems

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Photoresist Development 7.1 Kinetics of Development 7.1.1 A Simple Kinetic Development Model 7.1.2 Other Development Models 7.1.3 Molecular Weight Distributions and the Critical Ionization Model 7.1.4 Surface Inhibition

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Contents

8.

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7.1.5 Extension to Negative Resists 7.1.6 Developer Temperature 7.1.7 Developer Normality 7.2 The Development Contrast 7.2.1 Defining Photoresist Contrast 7.2.2 Comparing Definitions of Contrast 7.2.3 The Practical Contrast 7.2.4 Relationship between yand rmJrr^n 7.3 The Development Path 7.3.1 The Euler-Lagrange Equation 7.3.2 The Case of No z-Dependence 7.3.3 The Case of a Separable Development Rate Function 7.3.4 Resist Sidewall Angle 7.3.5 The Case of Constant Development Gradients 7.3.6 Segmented Development and the Lumped Parameter Model (LPM) 7.3.7 LPM Example - Gaussian Image 7.4 Measuring Development Rates Problems

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Lithographie Control in Semiconductor Manufacturing 8.1 Defining Lithographie Quality 8.2 Critical Dimension Control 8.2.1 Impact of CD Control 8.2.2 Improving CD Control 8.2.3 Sources of Focus and Dose Errors 8.2.4 Defining Critical Dimension 8.3 How to Characterize Critical Dimension Variations 8.3.1 Spatial Variations 8.3.2 Temporal Variations and Random Variations 8.3.3 Characterizing and Separating Sources of CD Variations 8.4 Overlay Control 8.4.1 Measuring and Expressing Overlay 8.4.2 Analysis and Modeling of Overlay Data 8.4.3 Improving Overlay Data Analysis 8.4.4 Using Overlay Data 8.4.5 Overlay Versus Pattern Placement Error 8.5 The Process Window 8.5.1 The Focus-Exposure Matrix 8.5.2 Defining the Process Window and DOF 8.5.3 The Isofocal Point 8.5.4 Overlapping Process Windows 8.5.5 Dose and Focus Control 8.6 H-V Bias 8.6.1 Astigmatism and H-V Bias 8.6.2 Source Shape Asymmetry

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Contents .7

8.8

8.9 8.10

Mask Error Enhancement Factor (MEEF) 8.7.1 Linearity 8.7.2 Defining MEEF 8.7.3 Aerial Image MEEF 8.7.4 Contact Hole MEEF 8.7.5 Mask Errors as Effective Dose Errors 8.7.6 Resist Impact on MEEF Line-End Shortening Measuring LES 8.8.1 8.8.2 Characterizing LES Process Effects Critical Shape and Edge Placement Errors Pattern Collapse

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Gradient-Based Lithographie 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 9.5.1 Diffusion in Conventional Resists 9.5.2 Chemically Amplified Resists - Reaction Only 9.5.3 Chemically Amplified Resists - Reaction-Diffusion 9.5.4 Chemically Amplified Resists - Reaction-Diffusion with Quencher 9.6 Develop 9.6.1 Conventional Resist 9.6.2 Chemically Amplified Resist 9.7 Resist Profile Formation 9.7.1 The Case of a Separable Development Rate Function 9.7.2 Lumped Parameter Model 9.8 Line Edge Roughness 9.9 Summary Problems

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Resolution Enhancement Technologies 10.1 Resolution 10.1.1 Defining Resolution 10.1.2 Pitch Resolution 10.1.3 Natural Resolutions 10.1.4 Improving Resolution 10.2 Optical Proximity Correction (OPC) 10.2.1 Proximity Effects 10.2.2 Proximity Correction - Rule Based

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Contents

10.2.3 Proximity Correction - Model Based 10.2.4 Subresolution Assist Features (SRAFs) 10.3 Off-Axis Illumination (OAI) 10.4 Phase-Shifting Masks (PSM) 10.4.1 Alternating PSM 10.4.2 Phase Conflicts 10.4.3 Phase and Intensity Imbalance 10.4.4 Attenuated PSM 10.4.5 Impact of Phase Errors 10.5 Natural Resolutions 10.5.1 Contact Holes and the Point Spread Function 10.5.2 The Coherent Line Spread Function (LSF) 10.5.3 The Isolated Phase Edge Problems

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Appendix A.

Glossary of Microlithographic Terms

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Appendix B.

Curl, Divergence, Gradient, Laplacian

491

Appendix C.

The Dirac Delta Function

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Index