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

  • Authors:

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

  • Affiliations:

  • University of Illinois at Urbana-Champaign, Urbana, IL 61801-3602, USA;University of Illinois at Urbana-Champaign, Urbana, IL 61801-3602, USA;University of Illinois at Urbana-Champaign, Urbana, IL 61801-3602, USA;University of Illinois at Urbana-Champaign, Urbana, IL 61801-3602, USA

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2008

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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.