Preface ........................................................ xi
Acknowledgments .............................................. xiii
Acronyms ....................................................... xv
1 Introduction ................................................. 1
1.1 Optical Lithography ..................................... 1
1.1.1 Optical Lithography and Integrated Circuits ...... 2
1.1.2 Brief History of Optical Lithography Systems ..... 3
1.2 Rayleigh's Resolution ................................... 5
1.3 Resist Processes and Characteristics .................... 7
1.4 Techniques in Computational Lithography ................ 10
1.4.1 Optical Proximity Correction .................... 11
1.4.2 Phase-Shifting Masks ............................ 11
1.4.3 Off-Axis Illumination ........................... 14
1.4.4 Second-Generation RETs .......................... 15
1.5 Outline ................................................ 16
2 Optical Lithography Systems ................................. 19
2.1 Partially Coherent Imaging Systems ..................... 19
2.1.1 Abbe's Model .................................... 19
2.1.2 Hopkins Diffraction Model ....................... 22
2.1.3 Coherent and Incoherent Imaging Systems ......... 24
2.2 Approximation Models ................................... 25
2.2.1 Fourier Series Expansion Model .................. 25
2.2.2 Singular Value Decomposition Model .............. 29
2.2.3 Average Coherent Approximation Model ............ 32
2.2.4 Discussion and Comparison ....................... 34
2.3 Summary ................................................ 36
3 Rule-Based Resolution Enhancement Techniques ................ 37
3.1 RET Types .............................................. 37
3.1.1 Rule-Based RETs ................................. 37
3.1.2 Model-Based RETs ................................ 38
3.1.3 Hybrid RETs ..................................... 39
3.2 Rule-Based OPC ......................................... 39
3.2.1 Catastrophic OPC ................................ 40
3.2.2 One-Dimensional OPC ............................. 40
3.2.3 Line-Shortening Reduction OPC ................... 42
3.2.4 Two-Dimensional OPC ............................. 43
3.3 Rule-Based PSM ........................................ 44
3.3.1 Dark-Field Application .......................... 44
3.3.2 Light-Field Application ......................... 45
3.4 Rule-Based OAI ......................................... 46
3.5 Summary ................................................ 47
4 Fundamentals of Optimization ................................ 48
4.1 Definition and Classification .......................... 48
4.1.1 Definitions in the Optimization Problem ......... 48
4.1.2 Classification of Optimization Problems ......... 49
4.2 Unconstrained Optimization ............................. 50
4.2.1 Solution of Unconstrained Optimization
Problem ......................................... 50
4.2.2 Unconstrained Optimization Algorithms ........... 52
4.3 Summary ................................................ 57
5 Computational Lithography with Coherent Illumination ........ 58
5.1 Problem Formulation .................................... 59
5.2 OPC Optimization ....................................... 62
5.2.1 OPC Design Algorithm ............................ 62
5.2.2 Simulations ..................................... 64
5.3 Two-Phase PSM Optimization ............................. 65
5.3.1 Two-Phase PSM Design Algorithm .................. 65
5.3.2 Simulations ..................................... 68
5.4 Generalized PSM Optimization ........................... 72
5.4.1 Generalized PSM Design Algorithm ................ 72
5.4.2 Simulations ..................................... 75
5.5 Resist Modeling Effects ................................ 79
6 Regularization Framework .................................... 83
6.1 Discretization Penalty ................................. 84
6.1.1 Discretization Penalty for OPC Optimization ..... 84
6.1.2 Discretization Penalty for Two-Phase PSM
Optimization .................................... 86
6.1.3 Discretization Penalty for Generalized PSM
Optimization .................................... 87
6.2 Complexity Penalty ..................................... 93
6.2.1 Total Variation Penalty ......................... 93
6.2.2 Global Wavelet Penalty .......................... 94
6.2.3 Localized Wavelet Penalty ....................... 98
6.3 Summary ............................................... 100
7 Computational Lithography with Partially Coherent
Illumination ............................................... 101
7.1 OPC Optimization ...................................... 102
7.1.1 OPC Design Algorithm Using the Fourier Series
Expansion Model ................................ 102
7.1.2 Simulations Using the Fourier Series
Expansion Model ................................ 105
7.1.3 OPC Design Algorithm Using the Average
Coherent Approximation Model ................... 107
7.1.4 Simulations Using the Average Coherent
Approximation Model ............................ 111
7.1.5 Discussion and Comparison ...................... 111
7.2 PSM Optimization ...................................... 115
7.2.1 PSM Design Algorithm Using the Singular Value
Decomposition Model ............................ 116
7.2.2 Discretization Regularization for PSM Design
Algorithm ...................................... 118
7.2.3 Simulations .................................... 118
7.3 Summary ............................................... 122
8 Other RET Optimization Techniques .......................... 123
8.1 Double-Patterning Method .............................. 123
8.2 Post-Processing Based on 2D DCT ....................... 128
8.3 Photoresist Tone Reversing Method ..................... 131
8.4 Summary ............................................... 135
9 Source and Mask Optimization ............................... 136
9.1 Lithography Preliminaries ............................. 137
9.2 Topological Constraint ................................ 140
9.3 Source-Mask Optimization Algorithm .................... 141
9.4 Simulations ........................................... 141
9.5 Summary ............................................... 145
10 Coherent Thick-Mask Optimization ........................... 146
10.1 Kirchhoff Boundary Conditions ......................... 147
10.2.1 Boundary Layer Model in Coherent Imaging
Systems ....................................... 147
10.2.2 Boundary Layer Model in Partially Coherent
Imaging Systems ............................... 151
10.2 Boundary Layer Model .................................. 147
10.3 Lithography Preliminaries ............................. 153
10.4 OPC Optimization ...................................... 157
10.4.1 Topological Constraint ......................... 157
10.4.2 OPC Optimization Algorithm Based on BL Model
Under Coherent Illumination .................... 158
10.4.3 Simulations .................................... 159
10.5 PSM Optimization ...................................... 162
10.5.1 Topological Constraint ......................... 162
10.5.2 PSM Optimization Algorithm Based on BL Model
Under Coherent Illumination .................... 165
10.5.3 Simulations .................................... 165
10.6 Summary ............................................... 170
11 Conclusions and New Directions of Computational
Lithography ................................................ 171
11.1 Conclusion ............................................ 171
11.2 New Directions of Computational Lithography ........... 173
11.2.1 OPC Optimization for the Next-Generation
Lithography Technologies ....................... 173
11.2.2 Initialization Approach for the Inverse
Lithography Optimization ....................... 173
11.2.3 Double Patterning and Double Exposure
Methods in Partially Coherent Imaging System ... 174
11.2.4 OPC and PSM Optimizations for Inverse
Lithography Based on Rigorous Mask Models in
Partially Coherent Imaging System .............. 174
11.2.5 Simultaneous Source and Mask Optimization
for Inverse Lithography Based on Rigorous
Mask Models .................................... 174
11.2.6 Investigation of Factors Influencing the
Complexity of the OPC and PSM Optimization
Algorithms ..................................... 174
Appendix A: Formula Derivation in Chapter 5 ................... 175
Appendix B: Manhattan Geometry ................................ 181
Appendix C: Formula Derivation in Chapter 6 ................... 182
Appendix D: Formula Derivation in Chapter 7 ................... 185
Appendix E: Formula Derivation in Chapter 8 ................... 189
Appendix F: Formula Derivation in Chapter 9 ................... 194
Appendix G: Formula Derivation in Chapter 10 .................. 195
Appendix H: Software Guide .................................... 199
References .................................................... 217
Index ......................................................... 223
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