NDLI: On smoothing three-dimensional Monte Carlo ion implantation simulation results

Content Provider	IEEE Xplore Digital Library
Author	Heitzinger, C. Hossinger, A. Selberherr, S.
Copyright Year	1982
Abstract	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.
Sponsorship	IEEE Council on Electronic Design Automation IEEE Circuits and Systems Society
Starting Page	879
Ending Page	883
Page Count	5
File Size	704342
File Format	PDF
ISSN	02780070
Volume Number	22
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2003-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Smoothing methods Monte Carlo methods Ion implantation Polynomials Least squares approximation Least squares methods Application software Approximation algorithms Convergence Integrated circuit yield
Content Type	Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Electrical and Electronic Engineering Software

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