11. Smoothing Monte Carlo Simulation Results

In this chapter an algorithm for smoothing results of three-dimensional Monte Carlo ion implantation simulations and translating them from the grid used for the Monte Carlo simulation to an arbitrary unstructured three-dimensional grid is presented. This algorithm is important for joining various process simulation steps, where data have to be smoothed or transferred from one grid to another. In an example it is used for integrating the ion implantation simulator into the simulation flow of the complete manufacturing process. One reason for using different grids is that for certain Monte Carlo simulation methods using ortho-grids is mandatory because of performance reasons.

The algorithm sweeps a small rectangular grid over the points of the new tetrahedral grid and uses approximation by generalized Bernstein polynomials (cf. Chapter 7) and it is thus put on a mathematically sound basis. It does not suffer from the adverse effects of least squares fits of polynomials of fixed degree as known from RSM.