Sverdlov Strain-Induced Effects in Advanced MOSFETs

1. Auflage 2011
ISBN: 978-3-7091-0382-1
Verlag: Springer Vienna
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 252 Seiten

Reihe: Computational Microelectronics

Strain is used to boost performance of MOSFETs. Modeling of strain effects on transport is an important task of modern simulation tools required for device design. The book covers all relevant modeling approaches used to describe strain in silicon. The subband structure in stressed semiconductor films is investigated in devices using analytical k.p and numerical pseudopotential methods. A rigorous overview of transport modeling in strained devices is given.

Autoren/Hrsg.

Sverdlov, Viktor

Inhaltsverzeichnis

1;Strain-Induced Effectsin Advanced MOSFETs;3
1.1;Preface;7
1.2;Contents;9
1.3;List of Symbols;13
1.4;Chapter 1:
Introduction;15
1.5;Chapter 2:
Scaling, Power Consumption, and Mobility Enhancement Techniques;18
1.5.1;2.1 Power Scaling;18
1.5.2;2.2 Strain Engineering;19
1.5.3;2.3 Global Strain Techniques and Substrate Engineering;21
1.5.4;2.4 Local Stress Techniques;23
1.5.5;2.5 Advanced Stress Techniques;25
1.5.6;2.6 Hybrid Orientation Technology and Alternative Channel Materials;27
1.5.7;References;29
1.6;Chapter 3:
Strain and Stress;36
1.6.1;3.1 Strain Definition;36
1.6.2;3.2 Stress;38
1.6.3;3.3 Relation Between Strain and Stress Tensor in Silicon and Germanium;40
1.6.4;3.4 Strain and Stress Tensors: Examples;41
1.6.4.1;3.4.1 Uniform All-Around Compression;41
1.6.4.2;3.4.2 Biaxial Strain Resulting From Epitaxial Growth;42
1.6.4.3;3.4.3 Uniaxial Stress;45
1.6.5;References;47
1.7;Chapter 4:
Basic Properties of the Silicon Lattice;48
1.7.1;4.1 Crystal Structure of Silicon and Germanium;48
1.7.2;4.2 Reciprocal Lattice and First Brillouin Zone;52
1.7.3;4.3 Particle in a Periodic Potential;54
1.7.4;References;57
1.8;Chapter 5:
Band Structure of Relaxed Silicon;58
1.8.1;5.1 Conduction and Valence Bands;58
1.8.2;5.2 First-Principle Band Structure Calculations;59
1.8.3;5.3 Pseudopotential Band Structure Calculations;62
1.8.4;5.4 Semi-Empirical Tight Binding Method;69
1.8.5;5.5 Comparison Between Different Numerical Methods;71
1.8.6;References;74
1.9;Chapter 6:
Perturbative Methods for Band Structure Calculations in Silicon;76
1.9.1;6.1 The kp Method for a Non-Degenerate Band;76
1.9.2;6.2 Effective Mass Theory for Non-Degenerate Bands;77
1.9.2.1;6.2.1 Electron Effective Mass in Relaxed Silicon;79
1.9.2.2;6.2.2 Approximations for the Conduction Band Dispersion at Higher Energies;80
1.9.3;6.3 Valence Band;83
1.9.3.1;6.3.1 Spin–Orbit Coupling in the Valence Band;85
1.9.3.2;6.3.2 Dispersion of the Valence Band in Silicon;88
1.9.3.3;6.3.3 Luttinger Parameters;89
1.9.4;References;93
1.10;Chapter 7:
Strain Effects on the Silicon Crystal Structure;95
1.10.1;7.1 Strain-Induced Symmetry Reduction of Silicon Crystal Lattice;95
1.10.1.1;7.1.1 Oh Symmetry;95
1.10.1.2;7.1.2 D4h Symmetry;96
1.10.1.3;7.1.3 D3d Symmetry;97
1.10.1.4;7.1.4 D2h Symmetry;97
1.10.1.5;7.1.5 C2h Symmetry;98
1.10.2;7.2 Internal Strain Parameter;98
1.10.3;7.3 Strain and Symmetry of the Brillouin Zone;100
1.10.4;References;102
1.11;Chapter 8:
Strain Effects on the Silicon Band Structure;103
1.11.1;8.1 Linear Deformation Potential Theory;103
1.11.1.1;8.1.1 Conduction Band;103
1.11.1.2;8.1.2 Valence Band;105
1.11.1.3;8.1.3 Stress-Induced Band Splitting of the Valence Bands;106
1.11.2;8.2 Inclusion of Strain into Perturbative Band Structure Calculations;109
1.11.3;8.3 Empirical Pseudopotential Method with Strain;114
1.11.4;References;115
1.12;Chapter 9:
Strain Effects on the Conduction Band of Silicon;116
1.12.1;9.1 Limitation of the Effective Mass Approximationfor the Conduction Band of Silicon;116
1.12.2;9.2 The Two-Band kp Model;118
1.12.2.1;9.2.1 Valley Shift Due to Shear Strain;119
1.12.2.2;9.2.2 Stress-Dependent Transversal Effective Masses;122
1.12.2.3;9.2.3 Dependence on Strain of the Longitudinal Effective Mass;123
1.12.2.4;9.2.4 Stress and Non-Parabolicity;126
1.12.2.5;9.2.5 Comparison of the Two-Band kp Model with Strain to the Empirical Pseudo-Potential Calculations;129
1.12.3;References;131
1.13;Chapter 10:
Electron Subbands in Silicon in the Effective Mass Approximation;133
1.13.1;10.1 Arbitrary Substrate Orientation;133
1.13.2;10.2 Substrate Orientation (001);136
1.13.3;10.3 Substrate Orientation (110);137
1.13.4;10.4 Substrate Orientation (111);138
1.13.5;References;139
1.14;Chapter 11:
Electron Subbands in Thin Silicon Films;140
1.14.1;11.1 Numerical Methods for Subband Structure Calculations;140
1.14.2;11.2 ``Linear Combination of Bulk Bands'' Method;141
1.14.3;11.3 Unprimed Subbands in (001) Films: Analytical Consideration;146
1.14.3.1;11.3.1 Dispersion Relations from an Auxiliary Tight-Binding Model;150
1.14.4;11.4 Strain-Induced Valley Splitting;153
1.14.4.1;11.4.1 Small Strain Values;153
1.14.4.2;11.4.2 High Values of Shear Strain;153
1.14.4.3;11.4.3 Numerical Solutions;154
1.14.5;11.5 Effective Mass of the Unprimed Subbands;156
1.14.6;11.6 Valley Splitting in Magnetic Field and Point Contacts;161
1.14.6.1;11.6.1 Valley Splitting in Magnetic Fields;163
1.14.6.2;11.6.2 Valley Splitting in a Point Contact;163
1.14.7;11.7 Primed Subbands in Ultra-Thin (001) Silicon Films;164
1.14.7.1;11.7.1 Effective Mass of Primed Subbands;165
1.14.8;11.8 Substrate Orientations Different from (001);166
1.14.8.1;11.8.1 Rotation of the Hamiltonian;167
1.14.8.2;11.8.2 Thin (110) Oriented Silicon Films;168
1.14.9;11.9 Appendix;171
1.14.9.1;11.9.1 Re-Expressing X1 as a Function of X2;171
1.14.9.2;11.9.2 Expressing the Dispersion Equations in Terms of X1 X2;173
1.14.10;References;174
1.15;Chapter 12:
Demands of Transport Modeling in Advanced MOSFETs;177
1.15.1;12.1 TCAD Tools: Technological Motivation and General Outlook;177
1.15.1.1;12.1.1 Brief History of TCAD Transport Modeling;179
1.15.1.2;12.1.2 Transport Modeling: Formulation of the Problem;180
1.15.2;12.2 Semi-Classical Transport;181
1.15.2.1;12.2.1 From Drift-Diffusion to Higher Moments Equations;182
1.15.2.2;12.2.2 Model Verification;186
1.15.3;12.3 Mobility in Strained Silicon;190
1.15.3.1;12.3.1 Mobility and Piezoresistance;191
1.15.3.2;12.3.2 Compact Mobility Modeling;192
1.15.3.3;12.3.3 Monte Carlo Methods for Transport Calculations;195
1.15.4;12.4 Mixed Quantum-Semi-Classical Description and Quantum Corrections in Current Transport Models;200
1.15.4.1;12.4.1 Subband Monte Carlo and Degeneracy Effects;203
1.15.4.2;12.4.2 Simulation Results for Mobilities in Single- and Double-Gate FETs;208
1.15.4.3;12.4.3 Electron Mobility Enhancement in FETs with Ultra-Thin Silicon Body;214
1.15.4.4;12.4.4 Stress-Induced Mobility and DriveCurrent Enhancement;215
1.15.5;12.5 Quantum Transport Models;216
1.15.5.1;12.5.1 Ballistic Transport and Tunneling;217
1.15.5.2;12.5.2 Quantum Transport Models with Scattering;224
1.15.5.3;12.5.3 Non-Equilibrium Green's Function Method;230
1.15.5.4;12.5.4 Conclusion and Trends;234
1.15.6;References;236
1.16;Author Index;246
1.17;Subject Index;258