To find a discrete approximation of MAXWELL's fourth equation, eqn. (2.4) is
integrated over a control volume
|
(3.18) |
Applying the theorem of GAUSS to the left hand side turns
eqn. (3.18) into
|
(3.19) |
The integrals are approximated as follows:
|
(3.20) |
where is the projection of the flux
onto the grid edge , evaluated
at the midpoint of the edge, is the boundary line which belongs to both subdomains
and
, and is the space charge density at the grid
point (Fig. 3.4).
Figure 3.4:
Control volume of grid point used for the box integration method.
|
The remaining task is to find an approximation for the projection of the dielectric flux
density . This is done by the finite difference approximation
With eqn. (3.20) and eqn. (3.21), the
discretization of POISSON's equation can be concluded.
M. Gritsch: Numerical Modeling of Silicon-on-Insulator MOSFETs PDF