On smoothing three-dimensional Monte Carlo ion implantation simulation results

Clemens Heitzinger, Andreas Hössinger, Siegfried Selberherr

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)879-883
Number of pages5
JournalIEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Volume22
Issue number7
DOIs
StatePublished - Jul 2003
Externally publishedYes

Fingerprint

Ion implantation
Polynomials
Joining
Simulators
Acoustic waves
Monte Carlo simulation

Keywords

  • Approximation methods
  • Integrated circuit ion implantation
  • Monte Carlo methods
  • Polynomials

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Hardware and Architecture
  • Computer Science Applications
  • Computational Theory and Mathematics

Cite this

On smoothing three-dimensional Monte Carlo ion implantation simulation results. / Heitzinger, Clemens; Hössinger, Andreas; Selberherr, Siegfried.

In: IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 22, No. 7, 07.2003, p. 879-883.

Research output: Contribution to journalArticle

Heitzinger, Clemens ; Hössinger, Andreas ; Selberherr, Siegfried. / On smoothing three-dimensional Monte Carlo ion implantation simulation results. In: IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems. 2003 ; Vol. 22, No. 7. pp. 879-883.
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