Self-diffusion in crystalline silicon: A single diffusion activation enthalpy down to755∘C

Abstract

Self-diffusion in silicon and the contribution of vacancies and self-interstitials have been controversially discussed for 50 yr. Most recent results show that the intrinsic silicon self-diffusion coefficient deviates from an Arrhenius-type, single exponential function for temperatures below $950{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$ [Y. Shimizu, M. Uematsu, and K. M. Itoh, Phys. Rev. Lett. 98, 095901 (2007); R. Kube, H. Bracht, E. H\uger, H. Schmidt, J. L. Hansen, A. N. Larsen, J. W. Ager, E. E. Haller, T. Geue, and J. Stahn, Phys. Rev. B 88, 085206 (2013)]. This led us to propose temperature-dependent thermodynamic properties of vacancies in order to achieve full consistency to vacancy-mediated dopant diffusion in silicon. Concepts of temperature-dependent properties of native defects or distinct forms of defects with different formation entropies suggested by Cowern et al. [N. E. B. Cowern, S. Simdyankin, C. Ahn, N. S. Bennett, J. P. Goss, J.-M. Hartmann, A. Pakfar, S. Hamm, J. Valentin, E. Napolitani, D. De Salvador, E. Bruno, and S. Mirabella, Phys. Rev. Lett. 110, 155501 (2013)] question the present understanding on atomic transport in semiconductors. To verify these concepts, additional self-diffusion experiments under particular gettering conditions were performed. As a result, silicon self-diffusion was found to be accurately described by one single diffusion activation enthalpy of $(4.73\ifmmode\pm\else\textpm\fi{}0.02)$ eV down to $755{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C}$. This provides full consistency to dopant diffusion without claiming native-defect concepts that were originally proposed by Seeger and Chik in 1968 [A. Seeger and K. P. Chik, Phys. Stat. Sol. 29, 455 (1968)] and confirms most recent density functional theory calculations on the activation energy of self-diffusion via vacancies and self-interstitials. Overall, this unravels the old debate of self-diffusion in silicon with the supposed intrinsic temperature dependence.