TY - JOUR
T1 - On smoothing three-dimensional Monte Carlo ion implantation simulation results
AU - Heitzinger, Clemens
AU - Hössinger, Andreas
AU - Selberherr, Siegfried
N1 - Funding Information:
Manuscript received May 10, 2002; revised December 6, 2002. This work was supported in part by the Christian Doppler Forschungsgesellschaft, Vienna, Austria, and in part by the Austrian Program for Advanced Research and Technology (APART) from the Österreichische Akademie der Wissenschaften. This paper was recommended by Associate Editor Z. Yu.
PY - 2003/7
Y1 - 2003/7
N2 - An algorithm for smoothing results of three-dimensional (3-D) Monte Carlo ion implantation simulations and translating them from the grid used for the Monte Carlo simulation to an arbitrary unstructured 3-D 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. Furthermore, it is important for integrating the ion implantation simulator into a process flow. One reason for using different grids is that for certain Monte Carlo simulation methods, using orthogrids is mandatory because of performance reasons. The algorithm presented sweeps a small rectangular grid over the points of the new tetrahedral grid and uses approximation 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 adverse effects of least squares fits of polynomials of fixed degree as known from the response surface method. The most important properties of Bernstein polynomials generalized to cuboid domains are presented, including uniform convergence, an asymptotic formula, and the variation diminishing property. The smoothing algorithm which works very fast is described and, in order to show its applicability, the resulting values of a 3-D real world implantation example are given and compared with those of a least squares fit of a multivariate polynomial of degree two, which yielded unusable results.
AB - An algorithm for smoothing results of three-dimensional (3-D) Monte Carlo ion implantation simulations and translating them from the grid used for the Monte Carlo simulation to an arbitrary unstructured 3-D 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. Furthermore, it is important for integrating the ion implantation simulator into a process flow. One reason for using different grids is that for certain Monte Carlo simulation methods, using orthogrids is mandatory because of performance reasons. The algorithm presented sweeps a small rectangular grid over the points of the new tetrahedral grid and uses approximation 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 adverse effects of least squares fits of polynomials of fixed degree as known from the response surface method. The most important properties of Bernstein polynomials generalized to cuboid domains are presented, including uniform convergence, an asymptotic formula, and the variation diminishing property. The smoothing algorithm which works very fast is described and, in order to show its applicability, the resulting values of a 3-D real world implantation example are given and compared with those of a least squares fit of a multivariate polynomial of degree two, which yielded unusable results.
KW - Approximation methods
KW - Integrated circuit ion implantation
KW - Monte Carlo methods
KW - Polynomials
UR - http://www.scopus.com/inward/record.url?scp=0037698165&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037698165&partnerID=8YFLogxK
U2 - 10.1109/TCAD.2003.814259
DO - 10.1109/TCAD.2003.814259
M3 - Article
AN - SCOPUS:0037698165
SN - 0278-0070
VL - 22
SP - 879
EP - 883
JO - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
JF - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IS - 7
ER -