3.2 Finite Difference Method

The finite difference method requires an orthographic grid. In the two-dimensional case the grid points are located at horizontal and vertical lines. The points must provide a good resolution of the regions of the device where a strong variation of the quantities is expected. Fig. 3.1 shows an example of such a grid. The grid lines are more dense in the regions of strong variation of the carrier concentration, like the channel and the junctions of the source and drain doping.

Figure 3.1: Schematic representation of an orthogonal mesh discretizing the active region of a MOSFET.

Subsections

• 3.2.1 One-Dimensional TAYLOR Expansion
• 3.2.2 One-Dimensional POISSON's Equation
• 3.2.3 Final Remarks

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