1. Transistors and Atoms
J.Dqhrowski, E.R.Weber, H.-J.Mussig, W.Schroter ........... 1
1.1. Introduction ............................................... 1
1.2. MOS Technology ............................................. 4
1.2.1. The MOS Transistor .................................. 4
1.2.2. Technological MOS Processes ......................... 6
1.2.3. Trends in CMOS Miniaturization ...................... 9
1.3. Technological Progress and Challenges for Modeling ........ 10
1.3.1. Crystal Growth ..................................... 10
1.3.2. Lithography ........................................ 11
1.3.3. Implantation and Diffusion ......................... 12
1.3.4. Gate Oxides ........................................ 14
1.3.5. Deposition and Etch ................................ 15
1.3.6. Contacts and Interconnects ......................... 16
1.3.7. Yield and Contamination Control .................... 18
1.3.8. Planarization ...................................... 20
1.3.9. Assembly and Packaging ............................. 21
1.4. The Environment for Process Simulation .................... 21
1.5. What TCAD Can Deliver and What it Can Not ................. 24
1.6. Atomistic Theory .......................................... 27
1.6.1 Accuracy in Ab-initio Methods ....................... 29
1.7. Conclusions ............................................... 31
References ..................................................... 32
2. Atomistic Simulations of Processes at Surfaces
P.Kratzer ................................................ 39
2.1. Introduction .............................................. 39
2.2. Simulation Methods ........................................ 44
2.3. Total-energy and Force Calculations ....................... 45
2.3.1. Analytical Potentials .............................. 47
2.3.2. Tight-binding Molecular Dynamics ................... 49
2.3.3. Density-Functional Theory and Other
Quantum-Chemical Ab-initio Methods ................. 51
2.4. Selected Applications of Molecular Dynamics Simulations ... 56
2.4.1 Molecular Dynamics Simulations of Surface Melting ... 56
2.4.2 Molecular Dynamics Simulations of Surface
Reactions ........................................... 57
2.5. Kinetic Monte Carlo Simulations for Modeling
of Molecular Beam Epitaxy ................................. 60
2.6. Concluding Remarks ........................................ 68
References ..................................................... 69
3. Atomistic Simulations in Materials Processing
M.Jaraiz ................................................. 73
3.1. Introduction .............................................. 73
3.2. The Facts: Diffusion and Defects in Silicon ............... 74
3.2.1. Si Self-Defects .................................... 75
3.2.2. V and I Point Defects .............................. 75
3.2.3. Foreign Atoms ...................................... 84
3.2.4. Deep Sub-Micron Si Device Processing ............... 85
3.3. The Models: Atomistic Kinetic Monte Carlo ................. 86
3.3.1. The KMC Concept .................................... 86
3.3.2. An Atomistic KMC Simulator (DADOS) ................. 88
3.4. Benchmarking: Simulation Examples ......................... 98
3.4.1. Ion Implantation: The "+1" Model ................... 98
3.4.2. {311} Defects and Dislocation Loops ............... 100
3.4.3. Amorphization and Recrystallization ............... 101
3.4.4. Impurity Diffusion/Clustering Mechanisms .......... 102
3.4.5. Fermi Level Effects ............................... 105
3.4.6. Device-Size Simulations ........................... 105
3.4.7. Conclusions ....................................... 107
References .................................................... 107
4. Atomistic Simulation of Decanano MOSFETs
A.Asenov, A.R.Brown, S.Kaya ............................. 1ll
4.1. Introduction ............................................. 1ll
4.2. Random Dopant Fluctuations ............................... 113
4.2.1. Fluctuation Problem ............................... 114
4.2.2. Simulation Approach ............................... 117
4.2.3. Conventional Structures ........................... 124
4.2.4. Fluctuation Resistant Architectures ............... 129
4.2.5. The Effect of the Poly-Si Gate .................... 130
4.2.6. Quantum Mechanical Corrections .................... 132
4.2.7. Comparative Analysis .............................. 135
4.3. Single Charge Trapping ................................... 139
4.3.1. Simulation Approach ............................... 139
4.3.2. Continuous Doping ................................. 140
4.3.3. Discrete Dopant Simulations ....................... 141
4.4. Oxide Thickness Variations ............................... 143
4.4.1. Interface Reconstruction .......................... 144
4.4.2. Implications for Decanano MOSFETs ................. 145
4.5. Line Edge Roughness ...................................... 150
4.6. Challenges Ahead ......................................... 152
4.7. Conclusions .............................................. 152
4.8. List of Acronyms and Symbols ............................. 154
References .................................................... 154
5. Modeling and Simulation of Heterojunction Bipolar
Transistors
H.Unlu .................................................. 157
5.1. Introduction ............................................. 157
5.2. An Overview of Charge Transport in HBTs .................. 160
5.3. Heteroemitter Energy Band Properties ..................... 163
5.3.1. Temperature, Strain, and Composition Effects ...... 164
5.3.2. Conduction and Valence Band Offsets ............... 172
5.4. Charge Transport and Boundary Conditions ................. 175
5.4.1. Conservation of Charge and Trap Levels ............ 177
5.4.2. Boundary Conditions for Electric Potential ........ 178
5.4.3. Boundary Conditions for Carrier Products .......... 182
5.4.4. Boundary Conditions for Quasi-Fermi Levels ........ 183
5.5. The Modeling of Current Transport ........................ 184
5.5.1. The Heterojunction Recombination Current .......... 184
5.5.2. The Minority Carrier Diffusion Currents ........... 185
5.6. The Modeling of Current Fluctuations ..................... 188
5.7. Results and Discussion ................................... 189
5.8. Summary and Future Trends ................................ 195
References .................................................... 197
6. Gate Oxide Reliability: Physical and Computational
Models
A.Ghetti ................................................ 201
6.1. Introduction ............................................. 201
6.2. Gate Oxide Reliability ................................... 203
6.2.1. Basic Statistical Concepts ........................ 203
6.2.2. The Industry Problem .............................. 206
6.2.3. General Model ..................................... 207
6.3. Electrical Stress and Carrier Energy ..................... 210
6.3.1. Tunneling ......................................... 210
6.3.2. Self-Consistent Potential Profile ................. 211
6.3.3. The Transmission Probability ...................... 212
6.3.4. Tunneling Current Components ...................... 215
6.3.5. Fowler-Nordheim Tunneling ......................... 216
6.3.6. Carrier Separation Experiments .................... 218
6.3.7. Trap-Assisted Tunneling ........................... 221
6.3.8. Interface State Assisted Tunneling ................ 224
6.3.9. Hot Carriers ...................................... 225
6.4. Critical Trap Density .................................... 227
6.4.1. Experimental Evidence ............................. 227
6.4.2. Percolation ....................................... 229
6.4.3. Area and Percentile Scaling ....................... 232
6.5. Defect Generation and Lifetime Extrapolation ............. 234
6.5.1. The Anode Hole Injection Model .................... 235
6.5.2. The Anode Hydrogen Release Model .................. 242
6.5.3. The Thermochemical Model .......................... 244
6.5.4. Phenomenological Models ........................... 245
6.5.5. Reliability Projections ........................... 246
6.6. The Breakdown Mode ....................................... 248
6.7. Summary and Conclusions .................................. 252
References .................................................... 253
7. High-if Dielectrics: The Example of Pr2О3
H.J.Osten, J.Dabrowski, H.-J.Mussig, A.Fissel,
V.Zavodinsky ............................................ 259
7.1. Introduction ............................................. 259
7.2. Alternative (High-AT) Dielectrics ........................ 261
7.2.1. General Requirements .............................. 261
7.2.2. Available Materials ............................... 262
7.2.3. Praseodymium Oxide ................................ 265
7.3. Experimental and Theoretical Approach .................... 267
7.4. Results of Structural Investigations ..................... 268
7.4.1. Initial Growth .................................... 268
7.4.2. Thicker Films ..................................... 271
7.5. Interface Formation ...................................... 275
7.6. Layer Stability .......................................... 282
7.7. Electrical Properties of Pr203 on Si(OOl) ................ 287
7.7.1. Band Structures ................................... 287
7.7.2. Gate Capacitance and Gate Leakage Current ......... 289
7.7.3. Gate Dielectric Reliability ....................... 291
7.7.4. Thermal Stability ................................. 291
7.7.5. Process Integration ............................... 291
7.8. Outlook .................................................. 292
References .................................................... 293
8. Atomistic Simulation of SisN4 CVD from Dichlorosilane
and NH3
A.A.Bagatur'yants, A.K.Minushev, K.P.Novoselov,
A.A.Safonov, S.Ya. Umanskii, A.S.Vladimirov,
A.Korkin ................................................ 295
8.1. Introduction ............................................. 295
8.2. Theoretical Study of the Mechanism and Kinetics
of Gas-Phase Reactions ................................... 297
8.2.1. Introduction ...................................... 297
8.2.2. Computational Details ............................. 298
8.2.3. Results and Discussion ............................ 309
8.2.4. Summary and Conclusions ........................... 329
8.3. Theoretical Study of the Si3N4 Surface Structures
and Mechanisms of Some Essential Surface Reactions ....... 330
8.3.1. Introduction ...................................... 330
8.3.2. Computational Details ............................. 330
8.3.3. Results and Discussion ............................ 331
8.3.4. Conclusions ....................................... 343
8.4. Kinetic Monte Carlo Atomic Scale Simulation
of Chemical Vapor Deposition of Silicon Nitride Film ..... 344
8.4.1. Introduction ...................................... 344
8.4.2. Method of Kinetic Monte Carlo Simulation
of Film Growth .................................... 344
8.4.3. Reaction Rate Calculations for Elementary
Surface Reactions ................................. 346
8.4.4. Results of Calculations ........................... 349
8.4.5. Conclusions ....................................... 351
8.5. General Conclusions and Outlook .......................... 352
References .................................................... 352
9. Interconnects and Propagation of High Frequency Signals
R.Sabelka, C.Harlander, S.Selberherr .................... 357
9.1. Introduction ............................................. 357
9.2. Interconnect Modeling .................................... 359
9.3. Parasitics Extraction .................................... 362
9.3.1. Capacitance Extraction ............................ 363
9.3.2. Resistance Extraction ............................. 367
9.3.3. Substrate Resistance .............................. 368
9.3.4. Inductance Extraction ............................. 369
9.4. Partial Element Equivalent Circuits ...................... 372
9.5. Transmission Line Models ................................. 373
9.6. Three-Dimensional Analysis ............................... 374
9.7. Model Order Reduction .................................... 376
9.8. Reliability .............................................. 377
9.9. Design ................................................... 378
9.10.Software ................................................. 380
9.11.Conclusion and Outlook ................................... 381
References .................................................... 382
10.Modeling of Electromigration in Interconnects
V.Petrescu, W.Schoenmaker ............................... 387
10.1.Introduction ............................................. 387
10.1.1.The Physical Basis of Electromigration ............ 388
10.1.2.The Influence of Al Microstructure ................ 391
10.1.3.Mechanical Stress; Critical Stress ................ 392
10.1.4.Elastic Properties of Materials ................... 393
10.1.5.Thermal Stress .................................... 393
10.1.6.Electromigration in Multilayer Metallization
Structures ........................................ 394
10.1.7.The Blech Length Concept .......................... 396
10.1.8.Resistance Change in the Early Phase
of Electromigration ............................... 397
10.1.9.Change of Resistance under Hydrostatic Stress ..... 398
10.1.10.The Effect of Cu Precipitation on Resistance ..... 398
10.2.Modeling of Electromigration ............................. 399
10.2.1.Modeling Aspects of Electromigration
and Stress Migration .............................. 401
10.2.2.Stress Generation in a Vacancy Diffusion Model .... 403
10.2.3.Vacancies in Equilibrium .......................... 407
10.2.4.The Flux of Vacancies ............................. 408
10.2.5.Kirchheim's Vacancy Continuity Equation ........... 410
10.2.6.Kirchheim's Model: Simulation Results ............. 411
10.2.7.The Model of Electromigration and Stress
Migration of Clement and Thompson ................. 413
10.2.8.Hydrodynamic Model ................................ 417
10.2.9.Vacancies, Stress and Early Resistance Changes .... 420
10.3.Simulation of Electromigration ........................... 421
10.3.1.Scaling of the Constitutive Equations ............. 422
10.3.2.The Discretization Technique ...................... 425
10.3.3.Simulation Results ................................ 430
10.3.4.Proof of Blech Length ............................. 430
10.4.Experimental Validation .................................. 437
10.4.1.Early Resistance Change Measurements .............. 438
10.4.2.The Experimental Set-Up ........................... 439
10.4.3.The Influence of Cu Addition on the Early
Resistance Changes of Al Lines .................... 442
10.4.4.Precipitation in Aluminum-Copper Alloys ........... 442
10.4.5.Samples Fabrication ............................... 443
10.4.6.Measurement Results ............................... 443
10.4.7.Precipitation Hardening ........................... 446
10.4.8.The Dislocation-Solute Atoms Interaction .......... 447
10.4.9.Proof of Blech Length ............................. 449
10.5.Conclusion ............................................... 453
References .................................................... 453
11.Predictive Modeling of Transition Metal Gettering:
Applications and Materials Science Challenges
A.A.Istratov, W.Huber, E.R.Weber ........................ 457
11.1.Introduction ............................................. 457
11.1.1.Mathematical Basis for Computer Modeling
of Gettering ...................................... 458
11.1.2.Examples of Applications of the Gettering
Simulations ....................................... 460
11.2.The Road from Qualitative to Predictive Modeling:
Materials Science Challenges ............................. 462
11.3.Conclusion ............................................... 466
References .................................................... 466
Index ......................................................... 469
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