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IMPROVEMENT OF THE STATISTICAL ACCURACY FOR THE THREE-DIMENSIONAL MONTE CARLO SIMULATION OF ION IMPLANTATION

Statistical fluctuations of three-dimensional Monte Carlo simulation results require a sophisticated postprocessing of the obtained data. We present an advanced algorithm for smoothing Monte Carlo results of ion implantation and translating them from the internal ortho-grid of the simulator to an unstructured grid which is suitable for subsequent process simulation steps. This algorithm allows a more accurate prediction of doping profiles, which is essential for an implantation treatment of deep-submicrometer device structures. Basically, the ion concentration value on a grid point of the unstructured grid is approximated by means of Bernstein polynomials, evaluated in a fast way only in the middle point of that cell which contains the new grid point. The key idea is to estimate also the concentration difference between the new point and the middle point by calculating the scalar product of the concentration gradient and the distance vector. In that way, effects based on the cell discretization can also be significantly reduced, which leads to more realistic doping profiles. The impact of the advanced smoothing procedure on the statistical accuracy for three-dimensional implantation applications is demonstrated.