Preface ........................................................ xv
1. Introduction to Semiconductor Lithography .................... 1
1.1. Basics of 1С Fabrication ................................ 2
1.1.1. Patterning ....................................... 2
1.1.2. Etching .......................................... 3
1.1.3. Ion Implantation ................................. 5
1.1.4. Process Integration .............................. 6
1.2. Moore'. s Law and the Semiconductor Industry ............ 7
1.3. Lithography Processing ................................. 12
1.3.1. Substrate Preparation ........................... 14
1.3.2. Photoresist Coating ............................. 15
1.3.3. Post-Apply Bake ................................. 18
1.3.4. Alignment and Exposure .......................... 19
1.3.5. Post-exposure Bake .............................. 23
1.3.6. Development ..................................... 24
1.3.7. Postbake ........................................ 25
1.3.8. Measure and Inspect ............................. 25
1.3.9. Pattern Transfer ................................ 25
1.3.10.Strip ........................................... 26
Problems .................................................... 26
2. Aerial Image Formation - The Basics ......................... 29
2.1. Mathematical Description of Light ...................... 29
2.1.1. Maxwell's Equations and the Wave Equation ....... 30
2.1.2. General Harmonic Fields and the Plane Wave in
a Nonabsorbing Medium ........................... 32
2.1.3. Phasors and Wave Propagation in an Absorbing
Medium .......................................... 33
2.1.4. Intensity and the Poynting Vector ............... 36
2.1.5. Intensity and Absorbed Electromagnetic Energy ... 37
2.2. Basic Imaging Theory ................................... 38
2.2.1. Diffraction ..................................... 39
2.2.2. Fourier Transform Pairs ......................... 43
2.2.3. Imaging Lens .................................... 45
2.2.4. Forming an Image ................................ 47
2.2.5. Imaging Example: Dense Array of Lines and
Spaces .......................................... 48
2.2.6. Imaging Example: Isolated Space ................. 50
2.2.7. The Point Spread Function ....................... 51
2.2.8. Reduction Imaging ............................... 53
2.3. Partial Coherence ...................................... 56
2.3.1. Oblique Illumination ............................ 57
2.3.2. Partially Coherent Illumination ................. 58
2.3.3. Hopkins Approach to Partial Coherence ........... 62
2.3.4. Sum of Coherent Sources Approach ................ 63
2.3.5. Off-Axis Illumination ........................... 65
2.3.6. Imaging Example: Dense Array of Lines and
Spaces. Under Annular Illumination .............. 66
2.3.7. Kohler Illumination ............................. 66
2.3.8. Incoherent Illumination ......................... 69
2.4. Some Imaging Examples .................................. 70
Problems .................................................... 71
3. Aerial Image. Formation - The Details ....................... 75
3.1. Aberrations ............................................ 75
3.1.1. The Causes of Aberrations ....................... 75
3.1.2. Describing Aberrations: the Zernike
Polynomial ...................................... 78
3.1.3. Aberration Example - Tilt ....................... 81
3.1.4. Aberration Example - Defocus, Spherical and
Astigmatism ..................................... 83
3.1.5. Aberration Example - Coma ....................... 84
3.1.6. Chromatic Aberrations ........................... 85
3.1.7. Strehl Ratio .................................... 90
3.2. Pupil Filters and Lens Apodization ..................... 90
3.3. Flare .................................................. 91
3.3.1. Measuring Flare ................................. 92
3.3.2. Modeling Flare .................................. 94
3.4. Defocus ................................................ 95
3.4.1. Defocus as an Aberration ........................ 95
3.4.2. Defocus Example: Dense Lines and Spaces and
Three-Beam Imaging .............................. 98
3.4.3. Defocus Example: Dense Lines and Spaces and
Two-Beam Imaging ............................... 100
3.4.4. Image Isofocal Point ........................... 102
3.4.5. Focus Averaging ................................ 103
3.4.6. Reticle Defocus ................................ 104
3.4.7. Rayleigh Depth of Focus ........................ 105
3.5. Imaging with Scanners Versus Steppers ................. 106
3.6. Vector Nature of Light ................................ 108
3.6.1. Describing Polarization ........................ 111
3.6.2. Polarization Example: ТЕ Versus TM Image of
Lines and Spaces ............................... 113
3.6.3. Polarization Example: The Vector PSF ........... 114
3.6.4. Polarization Aberrations and the Jones Pupil ... 114
3.7. Immersion Lithography ................................. 117
3.7.1. The Optical Invariant and Hyper-NA
Lithography .................................... 118
3.7.2. Immersion Lithography and the Depth of Focus ... 120
3.8. Image Quality ......................................... 121
3.8.1. Image CD ....................................... 121
3.8.2. Image Placement Error (Distortion) ............. 123
3.8.3. Normalized Image Log-Slope (NILS) .............. 123
3.8.4. Focus Dependence of Image Quality .............. 125
Problems ................................................... 126
4. Imaging in Resist: Standing Waves and Swing Curves ......... 129
4.1. Standing Waves ........................................ 130
4.1.1. The Nature of Standing Waves ................... 130
4.1.2. Standing Waves for Normally Incident Light in
a Single Film .................................. 131
4.1.3. Standing Waves in a Multiple-Layer Film
Stack .......................................... 135
4.1.4. Oblique Incidence and the Vector Nature
of Light ....................................... 137
4.1.5. Broadband Illumination ......................... 141
4.2. Swing Curves .......................................... 144
4.2.1. Reflectivity Swing Curve ....................... 144
4.2.2. Dose-to-Clear and CD Swing Curves .............. 148
4.2.3. Swing Curves for Partially Coherent
Illumination ................................... 149
4.2.4. Swing Ratio .................................... 151
4.2.5. Effective Absorption ........................... 154
4.3. Bottom Antireflection Coatings ........................ 156
4.3.1. В ARC on an Absorbing Substrate ................ 157
4.3.2. ВARCs at High Numerical Apertures .............. 160
4.3.3. В ARC on a Transparent Substrate ............... 164
4.3.4. BARC Performance ............................... 165
4.4. Top Antireflection Coatings ........................... 167
4.5. Contrast Enhancement Layer ............................ 170
4.6. Impact of the Phase of the Substrate Reflectance ...... 170
4.7. Imaging in Resist ..................................... 173
4.7.1. Image in Resist Contrast ....................... 173
4.7.2. Calculating the Image in Resist ................ 177
4.7.3. Resist-Induced Spherical Aberrations ........... 179
4.7.4. Standing Wave Amplitude Ratio .................. 181
4.8. Defining Intensity .................................... 183
4.8.1. Intensity at Oblique Incidence ................. 183
4.8.2. Refraction into an Absorbing Material .......... 184
4.8.3. Intensity and Absorbed Energy .................. 187
Problems .............................................. 188
5. Conventional Resists: Exposure and Bake Chemistry .......... 191
5.1. Exposure .............................................. 191
5.1.1. Absorption ..................................... 191
5.1.2. Exposure Kinetics .............................. 194
5.2. Post-Apply Bake ....................................... 199
5.2.1. Sensitizer Decomposition ....................... 200
5.2.2. Solvent Diffusion and Evaporation .............. 205
5.2.3. Solvent Effects in Lithography ................. 209
5.3. Post-exposure Bake Diffusion .......................... 210
5.4. Detailed Bake Temperature Behavior .................... 214
5.5. Measuring the ABC Parameters .......................... 217
Problems ................................................... 219
6. Chemically Amplified Resists: Exposure and Bake
Chemistry .................................................. 223
6.1. Exposure Reaction ..................................... 223
6.2. Chemical Amplification ................................ 224
6.2.1. Amplification Reaction ......................... 225
6.2.2. Diffusion ...................................... 227
6.2.3. Acid Loss ...................................... 230
6.2.4. Base Quencher .................................. 232
6.2.5. Reaction-Diffusion Systems ..................... 233
6.3. Measuring Chemically Amplified Resist Parameters ...... 235
6.4. Stochastic Modeling of Resist Chemistry ............... 237
6.4.1. Photon Shot Noise .............................. 237
6.4.2. Chemical Concentration ......................... 239
6.4.3. Some Mathematics of Binary Random Variables .... 241
6.4.4. Photon Absorption and Exposure ................. 242
6.4.5. Acid Diffusion, Conventional Resist ............ 246
6.4.6. Acid-Catalyzed Reaction-Diffusion .............. 247
6.4.7. Reaction-Diffusion and Polymer Deblocking ...... 251
6.4.8. Acid-Base Quenching ............................ 253
Problems .............................................. 254
7. Photoresist Development .................................... 257
7.1. Kinetics of Development ............................... 257
7.1.1. A Simple Kinetic Development Model ............. 258
7.1.2. Other Development Models ....................... 261
7.1.3. Molecular Weight Distributions and the
Critical Ionization Model ...................... 264
7.1.4. Surface Inhibition ............................. 265
7.1.5. Extension to Negative Resists .................. 267
7.1.6. Developer Temperature .......................... 267
7.1.7. Developer Normality ............................ 268
7.2. The Development Contrast .............................. 270
7.2.1. Defining Photoresist Contrast .................. 270
7.2.2. Comparing Definitions of Contrast .............. 274
7.2.3. The Practical Contrast ......................... 276
7.2.4. Relationship between /and rmax/rmin ............ 277
7.3. The Development Path .................................. 278
7.3.1. The Euler-Lagrange Equation .................... 279
7.3.2. The Case of No z-Dependence .................... 280
7.3.3. The Case of a Separable Development Rate
Function ....................................... 282
7.3.4. Resist Sidewall Angle .......................... 283
7.3.5. The Case of Constant Development Gradients ..... 284
7.3.6. Segmented Development and the Lumped
Parameter Model (LPM) .......................... 286
7.3.7. LPM Example - Gaussian Image ................... 287
7.4. Measuring Development Rates ........................... 292
Problems ................................................... 293
8. Lithographic Control in Semiconductor Manufacturing ........ 297
8.1. Defining Lithographic Quality ......................... 297
8.2. Critical Dimension Control ............................ 299
8.2.1. Impact of CD Control ........................... 299
8.2.2. Improving CD Control ........................... 303
8.2.3. Sources of Focus and Dose Errors ............... 305
8.2.4. Defining Critical Dimension .................... 307
8.3. How to Characterize Critical Dimension Variations ..... 309
8.3.1. Spatial Variations ............................. 309
8.3.2. Temporal Variations and Random Variations ...... 311
8.3.3. Characterizing and Separating Sources of CD
Variations ..................................... 312
8.4. Overlay Control ....................................... 314
8.4.1. Measuring and Expressing Overlay ............... 315
8.4.2. Analysis and Modeling of Overlay Data .......... 317
8.4.3. Improving Overlay Data Analysis ................ 320
8.4.4. Using Overlay Data ............................. 323
8.4.5. Overlay Versus Pattern Placement Error ......... 326
8.5. The Process Window .................................... 326
8.5.1. The Focus-Exposure Matrix ...................... 326
8.5.2. Defining the Process Window and DOF ............ 332
8.5.3. The Isofocal Point ............................. 336
8.5.4. Overlapping Process Windows .................... 338
8.5.5. Dose and Focus Control ......................... 339
8.6. H-V Bias .............................................. 343
8.6.1. Astigmatism and H-V Bias ....................... 343
8.6.2. Source Shape Asymmetry ......................... 345
8.7. Mask Error Enhancement Factor (MEEF) .................. 348
8.7.1. Linearity ...................................... 348
8.7.2. Defining MEEF .................................. 349
8.7.3. Aerial Image MEEF .............................. 350
8.7.4. Contact Hole MEEF .............................. 352
8.7.5. Mask Errors as Effective Dose Errors ........... 353
8.7.6. Resist Impact on MEEF .......................... 355
8.8. Line-End Shortening ................................... 356
8.8.1. Measuring LES .................................. 357
8.8.2. Characterizing LES Process Effects ............. 359
8.9. Critical. Shape and Edge Placement Errors ............. 361
8.10.Pattern Collapse ...................................... 362
Problems ................................................... 366
9. Gradient-Based Lithographic Optimization: Using the
Normalized Image Log-Slope ................................. 369
9.1. Lithography as Information Transfer ................... 369
9.2. Aerial Image .......................................... 370
9.3. Image in Resist ....................................... 377
9.4. Exposure .............................................. 378
9.5. Post-exposure Bake .................................... 381
9.5.1. Diffusion in Conventional Resists .............. 381
9.5.2. Chemically Amplified Resists - Reaction Only ... 383
9.5.3. Chemically Amplified Resists - Reaction-
Diffusion ...................................... 384
9.5.4. Chemically Amplified Resists - Reaction-
Diffusion with Quencher ........................ 391
9.6. Develop ............................................... 393
9.6.1. Conventional Resist ............................ 397
9.6.2. Chemically Amplified Resist .................... 399
9.7. Resist Profile Formation .............................. 400
9.7.1. The Case of a Separable Development Rate
Function ....................................... 400
9.7.2. Lumped Parameter Model ......................... 401
9.8. Line Edge Roughness ................................... 404
9.9. Summary ............................................... 406
Problems ................................................... 408
10.Resolution Enhancement Technologies ........................ 411
10.1.Resolution ............................................ 412
10.1.1.Defining Resolution ............................ 413
10.1.2.Pitch Resolution ............................... 416
10.1.3.Natural Resolutions ............................ 418
10.1.4.Improving Resolution ........................... 418
10.2.Optical Proximity Correction (OPC) .................... 419
10.2.1.Proximity Effects .............................. 419
10.2.2.Proximity Correction - Rule Based .............. 422
10.2.3.Proximity Correction - Model Based ............. 425
10.2.4.Subresolution Assist Features (SRAFs) .......... 427
10.3.Off-Axis Illumination (OAI) ........................... 429
10.4.Phase-Shifting Masks (PSM) ............................ 434
10.4.1.Alternating PSM ................................ 435
10.4.2.Phase Conflicts ................................ 438
10.4.3.Phase and Intensity Imbalance .................. 439
10.4.4.Attenuated PSM ................................. 441
10.4.5.Impact of Phase Errors ......................... 445
10.5.Natural Resolutions ................................... 450
10.5.1.Contact Holes and the Point Spread Function .... 450
10.5.2.The Coherent Line Spread Function (LSF) ........ 452
10.5.3.The Isolated Phase Edge ........................ 453
Problems ................................................... 454
Appendix A. Glossary of Microlithographic Terms ............... 457
Appendix B. Curl, Divergence, Gradient, Laplacian ............. 491
Appendix С. The Dirac Delta Function .......................... 495
Index ......................................................... 501
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