3.1 Grid Generation

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