D I S S E R T A T I O N


Numerical Modeling of
Silicon-on-Insulator MOSFETs


ausgeführt zum Zwecke der Erlangung des akademischen Grades
eines Doktors der technischen Wissenschaften

eingereicht an der Technischen Universität Wien
Fakultät für Elektrotechnik und Informationstechnik
von


Markus Gritsch


Buntweg 7a
A-6511 Zams, Österreich

Matr. Nr. 9326522
geboren am 5. Mai 1974 in Zams


Wien, im November 2002 .......

• Kurzfassung
• Abstract
• Acknowledgment
• Contents
• List of Acronyms
• List of Symbols
  • Notation
  • Physical Quantities
  • Constants
• List of Figures
• 1. Introduction and Overview
• 2. Semiconductor Equations
  • 2.1 MAXWELL's Equations
    • 2.1.1 POISSON's Equation
  • 2.2 Phenomenological Approach
    • 2.2.1 Balance Equations
    • 2.2.2 Drift-Diffusion Transport Model
      • 2.2.2.1 Drift Current
      • 2.2.2.2 Diffusion Current
    • 2.2.3 Carrier Continuity Equations
  • 2.3 Systematic Approach
    • 2.3.1 BOLTZMANN's Transport Equation
    • 2.3.2 Moments Method
      • 2.3.2.1 Gradient Calculation
      • 2.3.2.2 Macroscopic Relaxation Time Approximation
      • 2.3.2.3 Isotropic Distribution Function
      • 2.3.2.4 Statistical Averages
    • 2.3.3 Closure
      • 2.3.3.1 Maxwell Distribution
      • 2.3.3.2 Discussion of the Diffusion Approximation
      • 2.3.3.3 Drift-Diffusion Transport Model - Closure at $\phi _2$
      • 2.3.3.4 Energy Transport Model - Closure at $\ensuremath{\boldsymbol{\mathrm{\phi}}}_3$ and $\phi _4$
      • 2.3.3.5 Six Moments Transport Model - Closure at $\phi _6$
    • 2.3.4 Generation/Recombination Processes
      • 2.3.4.1 Thermal Equilibrium
      • 2.3.4.2 Steady State
      • 2.3.4.3 Higher Order Moments
• 3. Discretization
  • 3.1 Grid Generation
  • 3.2 Finite Difference Method
    • 3.2.1 One-Dimensional TAYLOR Expansion
    • 3.2.2 One-Dimensional POISSON's Equation
    • 3.2.3 Final Remarks
  • 3.3 Box Integration Method
    • 3.3.1 POISSON's Equation
    • 3.3.2 Six Moments Transport Model
      • 3.3.2.1 Continuity and Balance Equations
      • 3.3.2.2 Flux Equations
      • 3.3.2.3 Growth Function
    • 3.3.3 Final Remarks
• 4. Standard Energy Transport Simulations
  • 4.1 Devices Used
  • 4.2 Body and Bipolar Effect
  • 4.3 Anomalous Output Characteristic
  • 4.4 Body Contact
  • 4.5 Cause of the Effect
  • 4.6 Transient Behavior
  • 4.7 Doping Dependence
  • 4.8 Impact-Ionization
• 5. Modified Energy Transport Model
  • 5.1 Monte Carlo Simulations
    • 5.1.1 Anisotropic Distribution Function
    • 5.1.2 Non-MAXWELLian Closure
  • 5.2 Model Derivation
    • 5.2.1 Anisotropic Distribution Function
    • 5.2.2 Non-MAXWELLian Closure
  • 5.3 Combining the Modifications
• 6. Modeling and Application
  • 6.1 Temperature Tensor Modeling
  • 6.2 Closure Relation Modeling
    • 6.2.1 Six Moments Transport Model
    • 6.2.2 Bulk Case
    • 6.2.3 Inhomogeneous Case
  • 6.3 Summarizing the Models
  • 6.4 Using the Modified Energy Transport Model
  • 6.5 "Well-Tempered" SOI MOSFET
  • 6.6 Grid Matters
• 7. Summary and Conclusion
• A. Vector and Tensor Notation
• B. Driving Force Discretization
• Bibliography
• Own Publications
• Curriculum Vitae
• About this document ...

M. Gritsch: Numerical Modeling of Silicon-on-Insulator MOSFETs PDF