2.3 Systematic Approach

As already discussed, the mobile charge in a device can be seen as a system comprising two interacting subsystems, namely electrons and holes [11, p.57]. The macroscopic average quantities are basically determined by the microscopic behavior of the particles constituting the systems.

Subsections

• 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

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