2.3.3 Closure

Depending on the order up to which the moment equations are taken into account, transport models of different levels of sophistication are obtained. A characteristic of the moments method is that each equation for the moment $i$ of the distribution function contains the next higher moment $i + 1$. For example eqn. (2.104) contains the sixth order moment $\ensuremath{\langle \phi_6 \rangle}$. Therefore the number of unknowns exceeds the number of equations and an expression for the highest occurring moment must be found. This can be achieved either by simplifying the equation of order $i + 1$ or by invoking some physical reasoning independent of the derivation of the moments themselves. This task is referred to as closure of the moment equations.

Subsections

• 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 $\phi _6$

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