简介
An officer of a lithography company who teaches a graduate-level course on optical lithography (U. of Texas at Austin) presents a review of the published literature on lithography and related sciences, plus previously unpublished work in the field. Focusing on the application of lithography in the fabrication of semiconductor integrated circuits, Mack opted to leave out solutions to the equations presented and such topics as metrology, lithographic simulation, and approaches that do not use projection optical imaging. The text includes diagrams, chapter problems, a glossary of microlithographic terms, and technical appendices. Annotation 漏2008 Book News, Inc., Portland, OR (booknews.com)
目录
Contents 9
Preface 17
1: Introduction to Semiconductor Lithography 21
1.1 Basics of IC Fabrication 22
1.1.1 Patterning 22
1.1.2 Etching 23
1.1.3 Ion Implantation 25
1.1.4 Process Integration 26
1.2 Moore\u2019s Law and the Semiconductor Industry 27
1.3 Lithography Processing 32
1.3.1 Substrate Preparation 34
1.3.2 Photoresist Coating 35
1.3.3 Post-Apply Bake 38
1.3.4 Alignment and Exposure 39
1.3.5 Post-exposure bake 43
1.3.6 Development 44
1.3.7 Postbake 45
1.3.8 Measure and Inspect 45
1.3.9 Pattern Transfer 45
1.3.10 Strip 46
Problems 46
2: Aerial Image Formation \u2013The Basics 49
2.1 Mathematical Description of Light 49
2.1.1 Maxwell\u2019s Equations and the Wave Equation 50
2.1.2 General Harmonic Fields and the Plane Wave in a Nonabsorbing Medium 52
2.1.3 Phasors and Wave Propagation in an Absorbing Medium 53
2.1.4 Intensity and the Poynting Vector 56
2.1.5 Intensity and Absorbed Electromagnetic Energy 57
2.2 Basic Imaging Theory 58
2.2.1 Diffraction 59
2.2.2 Fourier Transform Pairs 63
2.2.3 Imaging Lens 65
2.2.4 Forming an Image 67
2.2.5 Imaging Example: Dense Array of Lines and Spaces 68
2.2.6 Imaging Example: Isolated Space 70
2.2.7 The Point Spread Function 71
2.2.8 Reduction Imaging 73
2.3 Partial Coherence 76
2.3.1 Oblique Illumination 77
2.3.2 Partially Coherent Illumination 78
2.3.3 Hopkins Approach to Partial Coherence 82
2.3.4 Sum of Coherent Sources Approach 83
2.3.5 Off-Axis Illumination 85
2.3.6 Imaging Example: Dense Array of Lines and Spaces Under Annular Illumination 86
2.3.7 K枚hler Illumination 86
2.3.8 Incoherent Illumination 89
2.4 Some Imaging Examples 90
Problems 92
3: Aerial Image Formation \u2013The Details 95
3.1 Aberrations 95
3.1.1 The Causes of Aberrations 95
3.1.2 Describing Aberrations: the Zernike Polynomial 98
3.1.3 Aberration Example \u2013 Tilt 101
3.1.4 Aberration Example \u2013 Defocus, Spherical and Astigmatism 103
3.1.5 Aberration Example \u2013 Coma 104
3.1.6 Chromatic Aberrations 105
3.1.7 Strehl Ratio 110
3.2 Pupil Filters and Lens Apodization 110
3.3 Flare 111
3.3.1 Measuring Flare 112
3.3.2 Modeling Flare 114
3.4 Defocus 115
3.4.1 Defocus as an Aberration 115
3.4.2 Defocus Example: Dense Lines and Spaces and Three-Beam Imaging 118
3.4.3 Defocus Example: Dense Lines and Spaces and Two-Beam Imaging 120
3.4.4 Image Isofocal Point 122
3.4.5 Focus Averaging 123
3.4.6 Reticle Defocus 124
3.4.7 Rayleigh Depth of Focus 125
3.5 Imaging with Scanners Versus Steppers 126
3.6 Vector Nature of Light 128
3.6.1 Describing Polarization 131
3.6.2 Polarization Example: TE Versus TM Image of Lines and Spaces 133
3.6.3 Polarization Example: The Vector PSF 134
3.6.4 Polarization Aberrations and the Jones Pupil 134
3.7 Immersion Lithography 137
3.7.1 The Optical Invariant and Hyper-NA Lithography 138
3.7.2 Immersion Lithography and the Depth of Focus 140
3.8 Image Quality 141
3.8.1 Image CD 141
3.8.2 Image Placement Error (Distortion) 143
3.8.3 Normalized Image Log-Slope (NILS) 143
3.8.4 Focus Dependence of Image Quality 145
Problems 146
4: Imaging in Resist: Standing Waves and Swing Curves 149
4.1 Standing Waves 150
4.1.1 The Nature of Standing Waves 150
4.1.2 Standing Waves for Normally Incident Light in a Single Film 151
4.1.3 Standing Waves in a Multiple-Layer Film Stack 155
4.1.4 Oblique Incidence and the Vector Nature of Light 157
4.1.5 Broadband Illumination 161
4.2 Swing Curves 164
4.2.1 Reflectivity Swing Curve 164
4.2.2 Dose-to-Clear and CD Swing Curves 168
4.2.3 Swing Curves for Partially Coherent Illumination 169
4.2.4 Swing Ratio 171
4.2.5 Effective Absorption 174
4.3 Bottom Antireflection Coatings 176
4.3.1 BARC on an Absorbing Substrate 177
4.3.2 BARCs at High Numerical Apertures 180
4.3.3 BARC on a Transparent Substrate 184
4.3.4 BARC Performance 185
4.4 Top Antireflection Coatings 187
4.5 Contrast Enhancement Layer 190
4.6 Impact of the Phase of the Substrate Reflectance 190
4.7 Imaging in Resist 193
4.7.1 Image in Resist Contrast 193
4.7.2 Calculating the Image in Resist 197
4.7.3 Resist-Induced Spherical Aberrations 199
4.7.4 Standing Wave Amplitude Ratio 201
4.8 Defining Intensity 203
4.8.1 Intensity at Oblique Incidence 203
4.8.2 Refraction into an Absorbing Material 204
4.8.3 Intensity and Absorbed Energy 207
Problems 208
5: Conventional Resists: Exposure and Bake Chemistry 211
5.1 Exposure 211
5.1.1 Absorption 211
5.1.2 Exposure Kinetics 214
5.2 Post-Apply Bake 219
5.2.1 Sensitizer Decomposition 220
5.2.2 Solvent Diffusion and Evaporation 225
5.2.3 Solvent Effects in Lithography 229
5.3 Post-exposure Bake Diffusion 230
5.4 Detailed Bake Temperature Behavior 233
5.5 Measuring the ABC Parameters 237
Problems 239
6: Chemically Amplified Resists: Exposure and Bake Chemistry 243
6.1 Exposure Reaction 243
6.2 Chemical Amplification 244
6.2.1 Amplification Reaction 245
6.2.2 Diffusion 247
6.2.3 Acid Loss 250
6.2.4 Base Quencher 252
6.2.5 Reaction\u2013Diffusion Systems 253
6.3 Measuring Chemically Amplified Resist Parameters 255
6.4 Stochastic Modeling of Resist Chemistry 257
6.4.1 Photon Shot Noise 257
6.4.2 Chemical Concentration 259
6.4.3 Some Mathematics of Binary Random Variables 261
6.4.4 Photon Absorption and Exposure 262
6.4.5 Acid Diffusion, Conventional Resist 266
6.4.6 Acid-Catalyzed Reaction\u2013Diffusion 267
6.4.7 Reaction\u2013Diffusion and Polymer Deblocking 271
6.4.8 Acid\u2013Base Quenching 273
Problems 274
7: Photoresist Development 277
7.1 Kinetics of Development 277
7.1.1 A Simple Kinetic Development Model 278
7.1.2 Other Development Models 281
7.1.3 Molecular Weight Distributions and the Critical Ionization Model 284
7.1.4 Surface Inhibition 285
7.1.5 Extension to Negative Resists 287
7.1.6 Developer Temperature 287
7.1.7 Developer Normality 288
7.2 The Development Contrast 290
7.2.1 Defining Photoresist Contrast 290
7.2.2 Comparing Definitions of Contrast 294
7.2.3 The Practical Contrast 296
7.2.4 Relationship Between g and rmax/rmin 297
7.3 The Development Path 298
7.3.1 The Euler\u2013Lagrange Equation 299
7.3.2 The Case of No z-Dependence 300
7.3.3 The Case of a Separable Development Rate Function 302
7.3.4 Resist Sidewall Angle 303
7.3.5 The Case of Constant Development Gradients 304
7.3.6 Segmented Development and the Lumped Parameter Model (LPM) 306
7.3.7 LPM Example \u2013 Gaussian Image 307
7.4 Measuring Development Rates 312
Problems 314
8: Lithographic Control in Semiconductor Manufacturing 317
8.1 Defining Lithographic Quality 317
8.2 Critical Dimension Control 319
8.2.1 Impact of CD Control 319
8.2.2 Improving CD Control 323
8.2.3 Sources of Focus and Dose Errors 325
8.2.4 Defining Critical Dimension 327
8.3 How to Characterize Critical Dimension Variations 329
8.3.1 Spatial Variations 329
8.3.2 Temporal Variations and Random Variations 331
8.3.3 Characterizing and Separating Sources of CD Variations 332
8.4 Overlay Control 334
8.4.1 Measuring and Expressing Overlay 335
8.4.2 Analysis and Modeling of Overlay Data 337
8.4.3 Improving Overlay Data Analysis 340
8.4.4 Using Overlay Data 343
8.4.5 Overlay Versus Pattern Placement Error 346
8.5 The Process Window 346
8.5.1 The Focus\u2013Exposure Matrix 346
8.5.2 Defining the Process Window and DOF 352
8.5.3 The Isofocal Point 356
8.5.4 Overlapping Process Windows 358
8.5.5 Dose and Focus Control 359
8.6 H\u2013V Bias 363
8.6.1 Astigmatism and H\u2013V Bias 363
8.6.2 Source Shape Asymmetry 365
8.7 Mask Error Enhancement Factor (MEEF) 368
8.7.1 Linearity 368
8.7.2 Defining MEEF 369
8.7.3 Aerial Image MEEF 370
8.7.4 Contact Hole MEEF 372
8.7.5 Mask Errors as Effective Dose Errors 373
8.7.6 Resist Impact on MEEF 375
8.8 Line-End Shortening 376
8.8.1 Measuring LES 377
8.8.2 Characterizing LES Process Effects 379
8.9 Critical Shape and Edge Placement Errors 381
8.10 Pattern Collapse 382
Problems 386
8: Lithographic Control in Semiconductor Manufacturing 317
8.1 Defining Lithographic Quality 317
8.2 Critical Dimension Control 319
8.2.1 Impact of CD Control 319
8.2.2 Improving CD Control 323
8.2.3 Sources of Focus and Dose Errors 325
8.2.4 Defining Critical Dimension 327
8.3 How to Characterize Critical Dimension Variations 329
8.3.1 Spatial Variations 329
8.3.2 Temporal Variations and Random Variations 331
8.3.3 Characterizing and Separating Sources of CD Variations 332
8.4 Overlay Control 334
8.4.1 Measuring and Expressing Overlay 335
8.4.2 Analysis and Modeling of Overlay Data 337
8.4.3 Improving Overlay Data Analysis 340
8.4.4 Using Overlay Data 343
8.4.5 Overlay Versus Pattern Placement Error 346
8.5 The Process Window 346
8.5.1 The Focus\u2013Exposure Matrix 346
8.5.2 Defining the Process Window and DOF 352
8.5.3 The Isofocal Point 356
8.5.4 Overlapping Process Windows 358
8.5.5 Dose and Focus Control 359
8.6 H\u2013V Bias 363
8.6.1 Astigmatism and H\u2013V Bias 363
8.6.2 Source Shape Asymmetry 365
8.7 Mask Error Enhancement Factor (MEEF) 368
8.7.1 Linearity 368
8.7.2 Defining MEEF 369
8.7.3 Aerial Image MEEF 370
8.7.4 Contact Hole MEEF 372
8.7.5 Mask Errors as Effective Dose Errors 373
8.7.6 Resist Impact on MEEF 375
8.8 Line-End Shortening 376
8.8.1 Measuring LES 377
8.8.2 Characterizing LES Process Effects 379
8.9 Critical Shape and Edge Placement Errors 381
8.10 Pattern Collapse 382
Problems 386
9: Gradient-Based Lithographic Optimization: Using the Normalized Image Log-Slope 389
9.1 Lithography as Information Transfer 389
9.2 Aerial Image 390
9.3 Image in Resist 397
9.4 Exposure 398
9.5 Post-exposure Bake 401
9.5.1 Diffusion in Conventional Resists 401
9.5.2 Chemically Amplified Resists \u2013 Reaction Only 403
9.5.3 Chemically Amplified Resists \u2013 Reaction\u2013Diffusion 404
9.5.4 Chemically Amplified Resists \u2013 Reaction\u2013Diffusion with Quencher 411
9.6 Develop 413
9.6.1 Conventional Resist 417
9.6.2 Chemically Amplified Resist 419
9.7 Resist Profile Formation 420
9.7.1 The Case of a Separable Development Rate Function 420
9.7.2 Lumped Parameter Model 421
9.8 Line Edge Roughness 424
9.9 Summary 426
Problems 428
10: Resolution Enhancement Technologies 431
10.1 Resolution 432
10.1.1 Defining Resolution 433
10.1.2 Pitch Resolution 436
10.1.3 Natural Resolutions 438
10.1.4 Improving Resolution 438
10.2 Optical Proximity Correction (OPC) 439
10.2.1 Proximity Effects 439
10.2.2 Proximity Correction \u2013 Rule Based 442
10.2.3 Proximity Correction \u2013 Model Based 445
10.2.4 Subresolution Assist Features (SRAFs) 447
10.3 Off-Axis Illumination (OAI) 449
10.4 Phase-Shifting Masks (PSM) 454
10.4.1 Alternating PSM 455
10.4.2 Phase Conflicts 458
10.4.3 Phase and Intensity Imbalance 459
10.4.4 Attenuated PSM 461
10.4.5 Impact of Phase Errors 465
10.5 Natural Resolutions 470
10.5.1 Contact Holes and the Point Spread Function 470
10.5.2 The Coherent Line Spread Function (LSF) 472
10.5.3 The Isolated Phase Edge 473
Problems 474
Appendix A Glossary of Microlithographic Terms 477
Appendix B Curl, Divergence, Gradient, Laplacian 511
Appendix C The Dirac Delta Function 515
Index 521
Preface 17
1: Introduction to Semiconductor Lithography 21
1.1 Basics of IC Fabrication 22
1.1.1 Patterning 22
1.1.2 Etching 23
1.1.3 Ion Implantation 25
1.1.4 Process Integration 26
1.2 Moore\u2019s Law and the Semiconductor Industry 27
1.3 Lithography Processing 32
1.3.1 Substrate Preparation 34
1.3.2 Photoresist Coating 35
1.3.3 Post-Apply Bake 38
1.3.4 Alignment and Exposure 39
1.3.5 Post-exposure bake 43
1.3.6 Development 44
1.3.7 Postbake 45
1.3.8 Measure and Inspect 45
1.3.9 Pattern Transfer 45
1.3.10 Strip 46
Problems 46
2: Aerial Image Formation \u2013The Basics 49
2.1 Mathematical Description of Light 49
2.1.1 Maxwell\u2019s Equations and the Wave Equation 50
2.1.2 General Harmonic Fields and the Plane Wave in a Nonabsorbing Medium 52
2.1.3 Phasors and Wave Propagation in an Absorbing Medium 53
2.1.4 Intensity and the Poynting Vector 56
2.1.5 Intensity and Absorbed Electromagnetic Energy 57
2.2 Basic Imaging Theory 58
2.2.1 Diffraction 59
2.2.2 Fourier Transform Pairs 63
2.2.3 Imaging Lens 65
2.2.4 Forming an Image 67
2.2.5 Imaging Example: Dense Array of Lines and Spaces 68
2.2.6 Imaging Example: Isolated Space 70
2.2.7 The Point Spread Function 71
2.2.8 Reduction Imaging 73
2.3 Partial Coherence 76
2.3.1 Oblique Illumination 77
2.3.2 Partially Coherent Illumination 78
2.3.3 Hopkins Approach to Partial Coherence 82
2.3.4 Sum of Coherent Sources Approach 83
2.3.5 Off-Axis Illumination 85
2.3.6 Imaging Example: Dense Array of Lines and Spaces Under Annular Illumination 86
2.3.7 K枚hler Illumination 86
2.3.8 Incoherent Illumination 89
2.4 Some Imaging Examples 90
Problems 92
3: Aerial Image Formation \u2013The Details 95
3.1 Aberrations 95
3.1.1 The Causes of Aberrations 95
3.1.2 Describing Aberrations: the Zernike Polynomial 98
3.1.3 Aberration Example \u2013 Tilt 101
3.1.4 Aberration Example \u2013 Defocus, Spherical and Astigmatism 103
3.1.5 Aberration Example \u2013 Coma 104
3.1.6 Chromatic Aberrations 105
3.1.7 Strehl Ratio 110
3.2 Pupil Filters and Lens Apodization 110
3.3 Flare 111
3.3.1 Measuring Flare 112
3.3.2 Modeling Flare 114
3.4 Defocus 115
3.4.1 Defocus as an Aberration 115
3.4.2 Defocus Example: Dense Lines and Spaces and Three-Beam Imaging 118
3.4.3 Defocus Example: Dense Lines and Spaces and Two-Beam Imaging 120
3.4.4 Image Isofocal Point 122
3.4.5 Focus Averaging 123
3.4.6 Reticle Defocus 124
3.4.7 Rayleigh Depth of Focus 125
3.5 Imaging with Scanners Versus Steppers 126
3.6 Vector Nature of Light 128
3.6.1 Describing Polarization 131
3.6.2 Polarization Example: TE Versus TM Image of Lines and Spaces 133
3.6.3 Polarization Example: The Vector PSF 134
3.6.4 Polarization Aberrations and the Jones Pupil 134
3.7 Immersion Lithography 137
3.7.1 The Optical Invariant and Hyper-NA Lithography 138
3.7.2 Immersion Lithography and the Depth of Focus 140
3.8 Image Quality 141
3.8.1 Image CD 141
3.8.2 Image Placement Error (Distortion) 143
3.8.3 Normalized Image Log-Slope (NILS) 143
3.8.4 Focus Dependence of Image Quality 145
Problems 146
4: Imaging in Resist: Standing Waves and Swing Curves 149
4.1 Standing Waves 150
4.1.1 The Nature of Standing Waves 150
4.1.2 Standing Waves for Normally Incident Light in a Single Film 151
4.1.3 Standing Waves in a Multiple-Layer Film Stack 155
4.1.4 Oblique Incidence and the Vector Nature of Light 157
4.1.5 Broadband Illumination 161
4.2 Swing Curves 164
4.2.1 Reflectivity Swing Curve 164
4.2.2 Dose-to-Clear and CD Swing Curves 168
4.2.3 Swing Curves for Partially Coherent Illumination 169
4.2.4 Swing Ratio 171
4.2.5 Effective Absorption 174
4.3 Bottom Antireflection Coatings 176
4.3.1 BARC on an Absorbing Substrate 177
4.3.2 BARCs at High Numerical Apertures 180
4.3.3 BARC on a Transparent Substrate 184
4.3.4 BARC Performance 185
4.4 Top Antireflection Coatings 187
4.5 Contrast Enhancement Layer 190
4.6 Impact of the Phase of the Substrate Reflectance 190
4.7 Imaging in Resist 193
4.7.1 Image in Resist Contrast 193
4.7.2 Calculating the Image in Resist 197
4.7.3 Resist-Induced Spherical Aberrations 199
4.7.4 Standing Wave Amplitude Ratio 201
4.8 Defining Intensity 203
4.8.1 Intensity at Oblique Incidence 203
4.8.2 Refraction into an Absorbing Material 204
4.8.3 Intensity and Absorbed Energy 207
Problems 208
5: Conventional Resists: Exposure and Bake Chemistry 211
5.1 Exposure 211
5.1.1 Absorption 211
5.1.2 Exposure Kinetics 214
5.2 Post-Apply Bake 219
5.2.1 Sensitizer Decomposition 220
5.2.2 Solvent Diffusion and Evaporation 225
5.2.3 Solvent Effects in Lithography 229
5.3 Post-exposure Bake Diffusion 230
5.4 Detailed Bake Temperature Behavior 233
5.5 Measuring the ABC Parameters 237
Problems 239
6: Chemically Amplified Resists: Exposure and Bake Chemistry 243
6.1 Exposure Reaction 243
6.2 Chemical Amplification 244
6.2.1 Amplification Reaction 245
6.2.2 Diffusion 247
6.2.3 Acid Loss 250
6.2.4 Base Quencher 252
6.2.5 Reaction\u2013Diffusion Systems 253
6.3 Measuring Chemically Amplified Resist Parameters 255
6.4 Stochastic Modeling of Resist Chemistry 257
6.4.1 Photon Shot Noise 257
6.4.2 Chemical Concentration 259
6.4.3 Some Mathematics of Binary Random Variables 261
6.4.4 Photon Absorption and Exposure 262
6.4.5 Acid Diffusion, Conventional Resist 266
6.4.6 Acid-Catalyzed Reaction\u2013Diffusion 267
6.4.7 Reaction\u2013Diffusion and Polymer Deblocking 271
6.4.8 Acid\u2013Base Quenching 273
Problems 274
7: Photoresist Development 277
7.1 Kinetics of Development 277
7.1.1 A Simple Kinetic Development Model 278
7.1.2 Other Development Models 281
7.1.3 Molecular Weight Distributions and the Critical Ionization Model 284
7.1.4 Surface Inhibition 285
7.1.5 Extension to Negative Resists 287
7.1.6 Developer Temperature 287
7.1.7 Developer Normality 288
7.2 The Development Contrast 290
7.2.1 Defining Photoresist Contrast 290
7.2.2 Comparing Definitions of Contrast 294
7.2.3 The Practical Contrast 296
7.2.4 Relationship Between g and rmax/rmin 297
7.3 The Development Path 298
7.3.1 The Euler\u2013Lagrange Equation 299
7.3.2 The Case of No z-Dependence 300
7.3.3 The Case of a Separable Development Rate Function 302
7.3.4 Resist Sidewall Angle 303
7.3.5 The Case of Constant Development Gradients 304
7.3.6 Segmented Development and the Lumped Parameter Model (LPM) 306
7.3.7 LPM Example \u2013 Gaussian Image 307
7.4 Measuring Development Rates 312
Problems 314
8: Lithographic Control in Semiconductor Manufacturing 317
8.1 Defining Lithographic Quality 317
8.2 Critical Dimension Control 319
8.2.1 Impact of CD Control 319
8.2.2 Improving CD Control 323
8.2.3 Sources of Focus and Dose Errors 325
8.2.4 Defining Critical Dimension 327
8.3 How to Characterize Critical Dimension Variations 329
8.3.1 Spatial Variations 329
8.3.2 Temporal Variations and Random Variations 331
8.3.3 Characterizing and Separating Sources of CD Variations 332
8.4 Overlay Control 334
8.4.1 Measuring and Expressing Overlay 335
8.4.2 Analysis and Modeling of Overlay Data 337
8.4.3 Improving Overlay Data Analysis 340
8.4.4 Using Overlay Data 343
8.4.5 Overlay Versus Pattern Placement Error 346
8.5 The Process Window 346
8.5.1 The Focus\u2013Exposure Matrix 346
8.5.2 Defining the Process Window and DOF 352
8.5.3 The Isofocal Point 356
8.5.4 Overlapping Process Windows 358
8.5.5 Dose and Focus Control 359
8.6 H\u2013V Bias 363
8.6.1 Astigmatism and H\u2013V Bias 363
8.6.2 Source Shape Asymmetry 365
8.7 Mask Error Enhancement Factor (MEEF) 368
8.7.1 Linearity 368
8.7.2 Defining MEEF 369
8.7.3 Aerial Image MEEF 370
8.7.4 Contact Hole MEEF 372
8.7.5 Mask Errors as Effective Dose Errors 373
8.7.6 Resist Impact on MEEF 375
8.8 Line-End Shortening 376
8.8.1 Measuring LES 377
8.8.2 Characterizing LES Process Effects 379
8.9 Critical Shape and Edge Placement Errors 381
8.10 Pattern Collapse 382
Problems 386
8: Lithographic Control in Semiconductor Manufacturing 317
8.1 Defining Lithographic Quality 317
8.2 Critical Dimension Control 319
8.2.1 Impact of CD Control 319
8.2.2 Improving CD Control 323
8.2.3 Sources of Focus and Dose Errors 325
8.2.4 Defining Critical Dimension 327
8.3 How to Characterize Critical Dimension Variations 329
8.3.1 Spatial Variations 329
8.3.2 Temporal Variations and Random Variations 331
8.3.3 Characterizing and Separating Sources of CD Variations 332
8.4 Overlay Control 334
8.4.1 Measuring and Expressing Overlay 335
8.4.2 Analysis and Modeling of Overlay Data 337
8.4.3 Improving Overlay Data Analysis 340
8.4.4 Using Overlay Data 343
8.4.5 Overlay Versus Pattern Placement Error 346
8.5 The Process Window 346
8.5.1 The Focus\u2013Exposure Matrix 346
8.5.2 Defining the Process Window and DOF 352
8.5.3 The Isofocal Point 356
8.5.4 Overlapping Process Windows 358
8.5.5 Dose and Focus Control 359
8.6 H\u2013V Bias 363
8.6.1 Astigmatism and H\u2013V Bias 363
8.6.2 Source Shape Asymmetry 365
8.7 Mask Error Enhancement Factor (MEEF) 368
8.7.1 Linearity 368
8.7.2 Defining MEEF 369
8.7.3 Aerial Image MEEF 370
8.7.4 Contact Hole MEEF 372
8.7.5 Mask Errors as Effective Dose Errors 373
8.7.6 Resist Impact on MEEF 375
8.8 Line-End Shortening 376
8.8.1 Measuring LES 377
8.8.2 Characterizing LES Process Effects 379
8.9 Critical Shape and Edge Placement Errors 381
8.10 Pattern Collapse 382
Problems 386
9: Gradient-Based Lithographic Optimization: Using the Normalized Image Log-Slope 389
9.1 Lithography as Information Transfer 389
9.2 Aerial Image 390
9.3 Image in Resist 397
9.4 Exposure 398
9.5 Post-exposure Bake 401
9.5.1 Diffusion in Conventional Resists 401
9.5.2 Chemically Amplified Resists \u2013 Reaction Only 403
9.5.3 Chemically Amplified Resists \u2013 Reaction\u2013Diffusion 404
9.5.4 Chemically Amplified Resists \u2013 Reaction\u2013Diffusion with Quencher 411
9.6 Develop 413
9.6.1 Conventional Resist 417
9.6.2 Chemically Amplified Resist 419
9.7 Resist Profile Formation 420
9.7.1 The Case of a Separable Development Rate Function 420
9.7.2 Lumped Parameter Model 421
9.8 Line Edge Roughness 424
9.9 Summary 426
Problems 428
10: Resolution Enhancement Technologies 431
10.1 Resolution 432
10.1.1 Defining Resolution 433
10.1.2 Pitch Resolution 436
10.1.3 Natural Resolutions 438
10.1.4 Improving Resolution 438
10.2 Optical Proximity Correction (OPC) 439
10.2.1 Proximity Effects 439
10.2.2 Proximity Correction \u2013 Rule Based 442
10.2.3 Proximity Correction \u2013 Model Based 445
10.2.4 Subresolution Assist Features (SRAFs) 447
10.3 Off-Axis Illumination (OAI) 449
10.4 Phase-Shifting Masks (PSM) 454
10.4.1 Alternating PSM 455
10.4.2 Phase Conflicts 458
10.4.3 Phase and Intensity Imbalance 459
10.4.4 Attenuated PSM 461
10.4.5 Impact of Phase Errors 465
10.5 Natural Resolutions 470
10.5.1 Contact Holes and the Point Spread Function 470
10.5.2 The Coherent Line Spread Function (LSF) 472
10.5.3 The Isolated Phase Edge 473
Problems 474
Appendix A Glossary of Microlithographic Terms 477
Appendix B Curl, Divergence, Gradient, Laplacian 511
Appendix C The Dirac Delta Function 515
Index 521
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- 大小
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