The Effective Silicon Mobility

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Table of contents

1 The need of Temperature-Aware Circuits 
1.1 Circuits Reliability in Harsh Environments
1.2 Context of Temperature Considerations in Circuits
1.3 Contributions
1.3.1 Journal Papers
1.3.2 International Conferences
1.3.3 National Colloquium
1.3.4 Open Source Journals and Libraries
2 Transistor Temperature Effects 
2.1 Semiconductor Temperature Effects
2.1.1 Band Gap Temperature dependency
2.1.2 Carriers Concentration
2.1.3 The Fermi Level
2.1.4 Doping
2.2 MOSFET
2.3 The MOS Electrostatics
2.3.1 Carriers Transport on MOSFETs
2.3.2 MOSFET Models
2.3.3 The Effective Silicon Mobility
2.3.4 The Charge Sheet Approximation
Regional Approximations of the Charge Sheet Model
2.3.5 Vth Temperature effects
VFB Temperature Variation
B Temperature Dependency
2.3.6 Current ZTC Point
2.3.7 Small Channel Effects in Analog Design
Velocity Saturation
Channel Length Modulation (CLM)
Drain Induced Barrier Lowering (DIBL)
2.4 Transistor Compact Models
2.4.1 Symmetric Linearization Models
Temperature Effects
2.4.2 Inversion Charge Linearization Based Models
Solutions to Charge Linearization Models
2.4.3 The UICM model
2.4.4 The BSIM 6 Model
2.5 The gm=ID methodology gm=ID Temperature Modeling on Compact Models
2.5.1 Pao-Sah and Brews gm=ID description
3 A Temperature-Aware design Methodology 
3.1 Zero Temperature Coefficients (ZTC) Point
3.1.1 The gm ZTC Bias
3.2 Temperature analysis of gm=ID Parameters
3.2.1 Gate Transconductance Ratio
3.2.2 Parasitic Source/Drain Diodes
3.2.3 Self Gain
Drain Induced Barrier Lowering
Velocity Saturation
Channel Length Modulation
The gm=gds Model
Temperature Analysis
3.3 Temperature Analysis of MOSFET Capacitances
3.3.1 Varicap Temperature Analysis
Depletion and Inversion Analysis
Accumulation Mode Analysis
3.3.2 Cgs Temperature analysis
3.4 Conclusion
4 A Temperature-Aware Methodology Applications: A Study Case 
4.1 Bandgap Voltage Reference
4.1.1 Temperature Analysis
4.1.2 Results
4.1.3 Conclusions
4.2 Differential Amplifier
4.2.1 Voltage Gain Temperature Analysis
4.2.2 Amplifier Gain-Bandwidth Product
4.2.3 Comparison to Strong Inversion Solution
4.2.4 Results
4.2.5 Temperature Sensitivity in Closed-Loop Operation
4.2.6 Conclusion
4.3 Active Inductance VCO
4.3.1 Active Inductance Temperature Analysis
4.4 Results
4.4.1 Conclusion
4.5 Conclusion
5 Conclusion and Perspectives 
5.1 Work Conclusions
5.2 Research Perspectives
5.2.1 Multi-Objective Optimization
5.2.2 System Level Optimization
5.2.3 Technology Shrink
6 Résumé Étendu en Français 
6.1 Contexte
6.2 Proposition
6.3 Résultats
6.4 Conclusion
Appendices 
A Crystal Structures Statistics 
A.1 Classical Statistical Mechanics
B Fermi Distribution 
B.1 Fermi Level
C Drift-Diffusion Equation 
C.1 Scattering and the Relaxation Time Approximation
D Effective Mobility and Matthiessen’s Rule 
D.1 Mobility with Multiple Scattering Mechanisms