2008 NSTI Nanotechnology Conference and Trade Show - Nanotech 2008 - 11th Annual

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Clean Technology 2008

A Physics-Based Empirical Model for Ge Self Diffusion in Silicon Germanium Alloys

M.A. Rabie, Y.M. Haddara
McMaster University, CA

Keywords:
empirical model, sige, silicon germanium, diffusivity, germanium diffusivity, modeling, physics based modeling, self diffusivity, germanium self diffusivity

Abstract:
We propose a physics-based model for the Ge diffusivity in SiGe and empirically fit the model to previously reported experimental results. The self-diffusivity of Ge can be given by: DGe=D0*exp(Sx)*exp(-E/kT) where x is the Ge concentration, E is the activation energy given by 3.85 eV, S is a measure of the vacancy disorder entropy given by 11.56, D0 is the pre-exponential factor given by 0.137 cm2/sec, k is the Boltzmann constant and T is the temperature. The given values offer the best match with the published experimental data. It has been well-established in the literature that self-diffusion in pure Ge is mediated only by vacancies. It has been also shown that Ge diffusion is dominated by a vacancy mechanism at low temperatures. Since the published data on Ge diffusivity are in most cases for experiments done at temperatures lower than 1050 ºC, therefore; the only dominant mechanism for the self-diffusion of Ge is the vacancy exchange mechanism. The new term modifying the regular diffusivity equation to relate the diffusivity to the change in Ge concentration is a consequence of the change in the point defects disorder entropy as a result of adding more Ge atoms to the SiGe system.


Nanotech 2008 Conference Program Abstract