Computational Lithography

Cover Page......Page 1
Title: Computational Lithography......Page 4
ISBN 9780470596975......Page 5
3 Rule-Based Resolution Enhancement Techniques......Page 7
7 Computational Lithography with Partially Coherent Illumination......Page 8
10 Coherent Thick-Mask Optimization......Page 9
Index......Page 10
Preface......Page 11
Acknowledgments......Page 13
Acronyms......Page 14
1.1 OPTICAL LITHOGRAPHY......Page 15
1.1.1 Optical Lithography and Integrated Circuits......Page 16
1.1.2 Brief History of Optical Lithography Systems......Page 17
1.2 RAYLEIGH’S RESOLUTION......Page 19
1.3 RESIST PROCESSES AND CHARACTERISTICS......Page 21
1.4 TECHNIQUES IN COMPUTATIONAL LITHOGRAPHY......Page 24
1.4.2 Phase-Shifting Masks......Page 25
1.4.3 Off-Axis Illumination......Page 28
1.4.4 Second-Generation RETs......Page 29
1.5 OUTLINE......Page 30
2.1.1 Abbe’s Model......Page 33
2.1.2 Hopkins Diffraction Model......Page 36
2.1.3 Coherent and Incoherent Imaging Systems......Page 38
2.2.1 Fourier Series Expansion Model......Page 39
2.2.2 Singular Value Decomposition Model......Page 43
2.2.3 Average Coherent Approximation Model......Page 46
2.2.4 Discussion and Comparison......Page 48
2.3 SUMMARY......Page 50
3.1.1 Rule-Based RETs......Page 51
3.1.2 Model-Based RETs......Page 52
3.2 RULE-BASED OPC......Page 53
3.2.2.1 Line Biasing......Page 54
3.2.3 Line-Shortening Reduction OPC......Page 56
3.2.4 Two-Dimensional OPC......Page 57
3.3.1 Dark-Field Application......Page 58
3.3.2 Light-Field Application......Page 59
3.4 RULE-BASED OAI......Page 60
3.5 SUMMARY......Page 61
4.1.1 Definition in the Optimization Problem......Page 62
4.1.2 Classification of Optimization Problems......Page 63
Theorem 4.1 (First-order necessary condition).......Page 64
Definition 4.6 (Convex function).\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0......Page 65
Theorem 4.5 (Taylor’s theorem).......Page 66
4.2.2.1 Line Search Strategy......Page 68
4.2.2.2 Trust Region Strategy......Page 70
4.3 SUMMARY......Page 71
5 Computational Lithography with Coherent Illumination......Page 72
5.1 PROBLEM FORMULATION......Page 73
5.2.1 OPC Design Algorithm......Page 76
5.2.2 Simulations......Page 78
5.3.1 Two-Phase PSM Design Algorithm......Page 79
5.3.2 Simulations......Page 82
5.4.1 Generalized PSM Design Algorithm......Page 86
5.4.2 Simulations......Page 89
5.5 RESIST MODELING EFFECTS......Page 93
5.6 SUMMARY......Page 96
6 Regularization Framework......Page 97
6.1.1 Discretization Penalty for OPC Optimization......Page 98
6.1.2 Discretization Penalty for Two-Phase PSM Optimization......Page 100
6.1.3 Discretization Penalty for Generalized PSM Optimization......Page 101
6.2.1 Total Variation Penalty......Page 107
6.2.2 Global Wavelet Penalty......Page 108
6.2.3 Localized Wavelet Penalty......Page 112
6.3 SUMMARY......Page 114
7 Computational Lithography with Partially Coherent Illumination......Page 115
7.1.1 OPC Design Algorithm Using the Fourier Series Expansion Model......Page 116
7.1.2 Simulations Using the Fourier Series Expansion Model......Page 119
7.1.3 OPC Design Algorithm Using the Average Coherent Approximation Model......Page 121
7.1.5 Discussion and Comparison......Page 125
7.2 PSM OPTIMIZATION......Page 129
7.2.1 PSM Design Algorithm Using the Singular Value Decomposition Model......Page 130
7.2.3 Simulations......Page 132
7.3 SUMMARY......Page 136
8.1 DOUBLE-PATTERNING METHOD......Page 137
8.2 POST-PROCESSING BASED ON 2D DCT......Page 142
8.3 PHOTORESIST TONE REVERSING METHOD......Page 145
8.4 SUMMARY......Page 149
9 Source and Mask Optimization......Page 150
9.1 LITHOGRAPHY PRELIMINARIES......Page 151
Definition 9.4 (Singular pixels).\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0......Page 154
9.4 SIMULATIONS......Page 155
9.5 SUMMARY......Page 159
10 Coherent Thick-Mask Optimization......Page 160
10.2.1 Boundary Layer Model in Coherent Imaging Systems......Page 161
10.2.2 Boundary Layer Model in Partially Coherent Imaging Systems......Page 165
10.3 LITHOGRAPHY PRELIMINARIES......Page 167
10.4.1 Topological Constraint......Page 171
10.4.2 OPC Optimization Algorithm Based on BL Model Under Coherent Illumination......Page 172
10.4.3 Simulations......Page 173
10.5.1 Topological Constraint......Page 176
Definition 10.10 (Type III singular pixel).\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0\0......Page 178
10.5.3 Simulations......Page 179
10.6 SUMMARY......Page 184
11.1 CONCLUSION......Page 185
11.2.2 Initialization Approach for the Inverse Lithography Optimization......Page 187
11.2.6 Investigation of Factors Influencing the Complexity of the OPC and PSM Optimization Algorithms......Page 188
Appendix A Formula Derivation in Chapter 5......Page 189
Appendix B Manhattan Geometry......Page 195
Appendix C Formula Derivation in Chapter 6......Page 196
Appendix D Formula Derivation in Chapter 7......Page 199
Appendix E Formula Derivation in Chapter 8......Page 203
Appendix F Formula Derivation in Chapter 9......Page 208
Appendix G Formula Derivation in Chapter 10......Page 209
Appendix H Software Guide......Page 213
References......Page 231
Index......Page 237
Back Page......Page 241