The quality of the result obtained from numerical simulations and the convergence of the
numerical iteration strongly depend on the proper meshing of the simulation domain. The
simulation grid has to meet several requirements. First, it has to render the device geometry
as accurately as possible, which calls for small mesh elements where complicated geometrical
details are located. A large mesh point density is also required to resolve an abrupt change
of the solutions over a small space region. For example, the carrier concentration increases
very rapidly from the substrate towards the channel region of a MOSFET, requiring a
very fine grid spacing. The source and drain dopings also decay very steep at the
pn-junctions. On the other hand, the meshing of the body region of such a device can often
remain quite coarse to reduce computational time.
On the contrary, a too fine grid structure increases the computation time and can even make
the accuracy of the result worse because of the introduced rounding errors. Since the
discretization converts a set of differential equations into a set of algebraic equations the
accuracy and robustness of the algorithms for the solution of such a system strongly depend on
matrix properties which in turn are related with the mesh properties.

An approach to get an initial mesh is to solve POISSON's equation in the simulation
domain and refine the grid depending on the computed potential distribution [45]. The
meshes of the Devices 1 and 2 which are used in Chapter 4
were generated by using the MDRAW program [46].

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