Density-Gradient quantization models

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Table of contents

General Introduction
1 TCAD: Application and Physical’s Modeling Validity
1.1 TCAD in an industrial environment
1.2 TCAD modeling
1.2.1 Poisson equation
1.2.2 Continuity equation
1.2.3 Transport models
1.2.4 Density-Gradient quantization models
1.3 TCAD for 14FDSOI and 10FDSOI UTBB
1.3.1 Description of the simplified devices
1.3.2 Device dimensions and physical parameters
1.3.3 Source and Drain regions
1.3.4 Oxide and space charges
1.3.5 Extracted electrical quantities
1.3.6 Saturation regime and model comparison
1.3.7 14nFDSOI results
1.3.1 14pFDSOI results
1.3.2 Additional results for 14FDSOI
1.3.3 10nFDSOI predictions
1.3.4 10pFDSOI predictions
1.4 Conclusion
2 Nonlinear k.p Schrödinger-Poisson Equation with the Finite-Difference Method
2.1 Introduction
2.2 The UTOXPP solver
2.3 The Poisson Equation
2.3.1 The Boundary Conditions
2.3.2 Nonlinear Poisson Equation
2.3.3 Kerker Mixing
2.3.4 Predictor-Corrector Scheme
2.3.5 Initial Guess
2.3.6 Matrix System Solving
2.4 The Schrödinger Equation
2.4.1 No Confinement – Gas 3D
2.4.2 Confinement 1D – Gas 2D
2.4.3 Confinement 2D – Gas 1D
2.4.1 1.5D Poisson-Schrödinger
2.4.2 Mode Space
2.5 Arbitrarily Oriented Devices
2.6 Self-Consistent Simulation Flow
2.6.1 Algorithm n°1
2.6.2 Algorithm n°2
2.7 Simulation Results
2.8 Conclusion
3 Transport Models: From Classical to Quantum Drift-Diffusion
3.1 Introduction
3.2 Drift-Diffusion Model
3.2.1 Continuity Boundary Conditions
3.2.2 Self-Consistent Poisson-Continuity
3.3 Quantum Drift-Diffusion Model
3.4 Simulation Results for nFDSOI
3.5 Simulation Results for pFDSOI
3.6 Convergence Study
3.6.1 Comparison FEM vs FDM
3.7 Drift-Diffusion decoupling
3.8 Conclusion
4 Mobility Models
4.1 Introduction
4.2 Empirical Mobility Models
4.2.1 Charge-dependent Models
4.2.2 Field-dependent Models
4.2.3 Access Resistance
4.2.4 Velocity Saturation
4.3 Kubo-Greenwood Mobility Models
4.3.1 Mobility from Linearized Boltzmann Equation
4.3.2 Collision times calculation
4.3.3 Kubo-Greenwood in UTOXPP
4.4 Mobility Models study
4.4.1 Long Channel Mobility
4.4.2 Device Mobility
4.5 NEGF (Mode Space) in planar systems
4.5.1 Transverse -vector integration
4.5.2 Ballistic transport in effective mass: analytic k-points integration
4.5.3 Phonon scattering: numerical k-points integration
4.5.4 Decoupled mode-space approximation
4.6 Mobility extracted from NEGF simulations
4.7 NEGF versus QDD
4.7.1 Ballistic diffusive transport
4.7.2 Saturations effects
4.7.3 Validity of QDD model
4.8 IMEP-Lahc NEGF solver applied to 14FDSOI
4.9 Conclusion
General Conclusion
Bibliography