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

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

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

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

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