Strain-Induced Effects in Advanced MOSFETs (eBook)

Strain-Induced Effectsin Advanced MOSFETs 3
Preface 7
Contents 9
List of Symbols 13
Chapter 1: 
15 
Chapter 2: 
18 
2.1 Power Scaling 18
2.2 Strain Engineering 19
2.3 Global Strain Techniques and Substrate Engineering 21
2.4 Local Stress Techniques 23
2.5 Advanced Stress Techniques 25
2.6 Hybrid Orientation Technology and Alternative Channel Materials 27
References 29
Chapter 3: 
36 
3.1 Strain Definition 36
3.2 Stress 38
3.3 Relation Between Strain and Stress Tensor in Silicon and Germanium 40
3.4 Strain and Stress Tensors: Examples 41
3.4.1 Uniform All-Around Compression 41
3.4.2 Biaxial Strain Resulting From Epitaxial Growth 42
3.4.3 Uniaxial Stress 45
References 47
Chapter 4: 
48 
4.1 Crystal Structure of Silicon and Germanium 48
4.2 Reciprocal Lattice and First Brillouin Zone 52
4.3 Particle in a Periodic Potential 54
References 57
Chapter 5: 
58 
5.1 Conduction and Valence Bands 58
5.2 First-Principle Band Structure Calculations 59
5.3 Pseudopotential Band Structure Calculations 62
5.4 Semi-Empirical Tight Binding Method 69
5.5 Comparison Between Different Numerical Methods 71
References 74
Chapter 6: 
76 
6.1 The kp Method for a Non-Degenerate Band 76
6.2 Effective Mass Theory for Non-Degenerate Bands 77
6.2.1 Electron Effective Mass in Relaxed Silicon 79
6.2.2 Approximations for the Conduction Band Dispersion at Higher Energies 80
6.3 Valence Band 83
6.3.1 Spin–Orbit Coupling in the Valence Band 85
6.3.2 Dispersion of the Valence Band in Silicon 88
6.3.3 Luttinger Parameters 89
References 93
Chapter 7: 
95 
7.1 Strain-Induced Symmetry Reduction of Silicon Crystal Lattice 95
7.1.1 Oh Symmetry 95
7.1.2 D4h Symmetry 96
7.1.3 D3d Symmetry 97
7.1.4 D2h Symmetry 97
7.1.5 C2h Symmetry 98
7.2 Internal Strain Parameter 98
7.3 Strain and Symmetry of the Brillouin Zone 100
References 102
Chapter 8: 
103 
8.1 Linear Deformation Potential Theory 103
8.1.1 Conduction Band 103
8.1.2 Valence Band 105
8.1.3 Stress-Induced Band Splitting of the Valence Bands 106
8.2 Inclusion of Strain into Perturbative Band Structure Calculations 109
8.3 Empirical Pseudopotential Method with Strain 114
References 115
Chapter 9: 
116 
9.1 Limitation of the Effective Mass Approximationfor the Conduction Band of Silicon 116
9.2 The Two-Band kp Model 118
9.2.1 Valley Shift Due to Shear Strain 119
9.2.2 Stress-Dependent Transversal Effective Masses 122
9.2.3 Dependence on Strain of the Longitudinal Effective Mass 123
9.2.4 Stress and Non-Parabolicity 126
9.2.5 Comparison of the Two-Band kp Model with Strain to the Empirical Pseudo-Potential Calculations 129
References 131
Chapter 10: 
133 
10.1 Arbitrary Substrate Orientation 133
10.2 Substrate Orientation (001) 136
10.3 Substrate Orientation (110) 137
10.4 Substrate Orientation (111) 138
References 139
Chapter 11: 
140 
11.1 Numerical Methods for Subband Structure Calculations 140
11.2 ``Linear Combination of Bulk Bands'' Method 141
11.3 Unprimed Subbands in (001) Films: Analytical Consideration 146
11.3.1 Dispersion Relations from an Auxiliary Tight-Binding Model 150
11.4 Strain-Induced Valley Splitting 153
11.4.1 Small Strain Values 153
11.4.2 High Values of Shear Strain 153
11.4.3 Numerical Solutions 154
11.5 Effective Mass of the Unprimed Subbands 156
11.6 Valley Splitting in Magnetic Field and Point Contacts 161
11.6.1 Valley Splitting in Magnetic Fields 163
11.6.2 Valley Splitting in a Point Contact 163
11.7 Primed Subbands in Ultra-Thin (001) Silicon Films 164
11.7.1 Effective Mass of Primed Subbands 165
11.8 Substrate Orientations Different from (001) 166
11.8.1 Rotation of the Hamiltonian 167
11.8.2 Thin (110) Oriented Silicon Films 168
11.9 Appendix 171
11.9.1 Re-Expressing X1 as a Function of X2 171
11.9.2 Expressing the Dispersion Equations in Terms of X1 X2 173
References 174
Chapter 12: 
177 
12.1 TCAD Tools: Technological Motivation and General Outlook 177
12.1.1 Brief History of TCAD Transport Modeling 179
12.1.2 Transport Modeling: Formulation of the Problem 180
12.2 Semi-Classical Transport 181
12.2.1 From Drift-Diffusion to Higher Moments Equations 182
12.2.2 Model Verification 186
12.3 Mobility in Strained Silicon 190
12.3.1 Mobility and Piezoresistance 191
12.3.2 Compact Mobility Modeling 192
12.3.3 Monte Carlo Methods for Transport Calculations 195
12.4 Mixed Quantum-Semi-Classical Description and Quantum Corrections in Current Transport Models 200
12.4.1 Subband Monte Carlo and Degeneracy Effects 203
12.4.2 Simulation Results for Mobilities in Single- and Double-Gate FETs 208
12.4.3 Electron Mobility Enhancement in FETs with Ultra-Thin Silicon Body 214
12.4.4 Stress-Induced Mobility and DriveCurrent Enhancement 215
12.5 Quantum Transport Models 216
12.5.1 Ballistic Transport and Tunneling 217
12.5.2 Quantum Transport Models with Scattering 224
12.5.3 Non-Equilibrium Green's Function Method 230
12.5.4 Conclusion and Trends 234
References 236
Author Index 246
Subject Index 258