To find a discrete approximation of MAXWELL's fourth equation, eqn. (2.4) is
integrated over a control volume
Applying the theorem of GAUSS to the left hand side turns
eqn. (3.18) into
The integrals are approximated as follows:
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 is the space charge density at the grid
point (Fig. 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