An algorithm for smoothing three-dimensional Monte Carlo ion implantation simulation results

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 has to be smoothed or translated from one grid to another. Our algorithm sweeps a small grid over the points of the new grid and uses approximation by generalized Bernstein polynomials. This approach was put on a mathematically sound basis and does not suffer from the adverse effects of least squares fits of polynomials of fixed degree when used for approximation. The most important properties of Bernstein polynomials generalized to cuboid domains are presented, including uniform convergence and an asymptotic formula. After the description of the algorithm, the resulting values of a three-dimensional real world implantation example are shown and compared with those of a least squares fit of a multivariate polynomial of degree two, which only yielded unusable results.