Maximum a posteriori estimation of activation energies that control silicon self-diffusion

Charlotte T.M. Kwok, Kapil Dev, Edmund G. Seebauer, Richard D. Braatz

Research output: Contribution to journalArticle

Abstract

Self-diffusion in crystalline silicon is controlled by a network of elementary steps whose activation energies are important to know in a variety of applications in microelectronic fabrication. The present work employs maximum a posteriori (MAP) estimation to improve existing values for these activation energies, based on self-diffusion data collected at different values of the loss rates for interstitial atoms to the surface. Parameter sensitivity analysis shows that for high surface loss fluxes, the energy for exchange between an interstitial and the lattice plays the leading role in determining the shape of diffusion profiles. At low surface loss fluxes, the dissociation energy of large-atom clusters plays a more important role. Subsequent MAP analysis provides significantly improved values for these parameters.

Original languageEnglish (US)
Pages (from-to)2241-2247
Number of pages7
JournalAutomatica
Volume44
Issue number9
DOIs
StatePublished - Sep 1 2008

Keywords

  • Bayesian estimation
  • Parameter estimation
  • Rapid thermal processing
  • Semiconductor processes

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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