TY - JOUR

T1 - An algorithm for smoothing three-dimensional Monte Carlo ion implantation simulation results

AU - Heitzinger, Clemens

AU - Hössinger, Andreas

AU - Selberherr, Siegfried

N1 - Funding Information:
The authors acknowledge support from the “Christian Doppler Forschungsgesellschaft,” Vienna, Austria, and by Austrian Program for Advanced Research and Technology (APART) from the “Österreichische Akademie der Wissenschaften.”
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.

PY - 2004/6/29

Y1 - 2004/6/29

N2 - We present 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. This algorithm is important for joining various simulations of semiconductor manufacturing process steps, where data have to be smoothed or transferred from one grid to another. Furthermore different grids must be used since using ortho-grids is mandatory because of performance reasons for certain Monte Carlo simulation methods. The algorithm is based on approximations by generalized Bernstein polynomials. This approach was put on a mathematically sound basis by proving several properties of these polynomials. It does not suffer from the ill effects of least squares fits of polynomials of fixed degree as known from the popular response surface method. The smoothing algorithm which works very fast is described and in order to show its applicability, the results of smoothing a three-dimensional real world implantation example are given and compared with those of a least squares fit of a multivariate polynomial of degree 2, which yielded unusable results.

AB - We present 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. This algorithm is important for joining various simulations of semiconductor manufacturing process steps, where data have to be smoothed or transferred from one grid to another. Furthermore different grids must be used since using ortho-grids is mandatory because of performance reasons for certain Monte Carlo simulation methods. The algorithm is based on approximations by generalized Bernstein polynomials. This approach was put on a mathematically sound basis by proving several properties of these polynomials. It does not suffer from the ill effects of least squares fits of polynomials of fixed degree as known from the popular response surface method. The smoothing algorithm which works very fast is described and in order to show its applicability, the results of smoothing a three-dimensional real world implantation example are given and compared with those of a least squares fit of a multivariate polynomial of degree 2, which yielded unusable results.

KW - Bernstein polynomials

KW - Ion implantation

KW - Monte Carlo simulation

KW - Smoothing operator

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U2 - 10.1016/j.matcom.2003.11.010

DO - 10.1016/j.matcom.2003.11.010

M3 - Article

AN - SCOPUS:2942633319

VL - 66

SP - 219

EP - 230

JO - Mathematics and Computers in Simulation

JF - Mathematics and Computers in Simulation

SN - 0378-4754

IS - 2-3

ER -