Finite Elements

One of the most important steps in the process of semiconductor device simulation, or any other numerical simulation based on finite elements, finite differences or similar standard techniques, is the discretisation of the domain of the problem. A mesh must be generated, and its properties determine the stability of the numerical solver, computational time and quality of the solution.

We have developed two different mesh generation algorithms for the discretisation of the simulation domains. The first one is based on the use of an octree and is optimised for the discretisation of Manhattan type structures. The flexibility in the specification of the refinement is especially appropriate to simulate spatially localised effects producing sharp variations in magnitudes such as electrostatic potential or carrier density.

The second algorithm is based on placing a node of the mesh in every position of an atom of the crystal lattice. These meshes can be used, for example, to place the dopants in their exact positions without being limited by the mesh size or structure.

Finally, we have developed an adaptive refinement algorithm based in the bisection method. This algorithm can use different variables to guide the refinement. Its use improves the convergence without the necessity to rebuild the mesh and saving nodes.