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A PhysicsBased 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 physicsbased model for the Ge diffusivity in SiGe and empirically fit the model to previously reported experimental results. The selfdiffusivity 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 preexponential 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 wellestablished in the literature that selfdiffusion 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 selfdiffusion 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
