Pressure and stress effects on the diffusion of B and Sb in Si and Si-Ge alloys

Abstract

The hydrostatic pressure dependence of the diffusivity of B and Sb in Si and of B in ${\mathrm{Si}}_{89}{\mathrm{Ge}}_{11}$ has been measured. The diffusivity of Sb in Si is retarded by pressure, characterized by an apparent activation volume of ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}}_{\mathrm{Sb}}=+0.06\ifmmode\pm\else\textpm\fi{}0.04$ times the Si atomic volume $\ensuremath{\Omega}$. The diffusivity of B is enhanced by pressure, characterized by an apparent activation volume of ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}}_{\mathrm{B}}$ of $(\ensuremath{-}0.16\ifmmode\pm\else\textpm\fi{}0.05)\phantom{\rule{0.3em}{0ex}}\ensuremath{\Omega}$. The diffusivity of B in strain-relaxed ${\mathrm{Si}}_{89}{\mathrm{Ge}}_{11}$ is imperceptibly pressure dependent, characterized by an apparent activation volume of $(+0.03\ifmmode\pm\else\textpm\fi{}0.03)\phantom{\rule{0.3em}{0ex}}\ensuremath{\Omega}$. ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}}_{\mathrm{B}}$ in Si is close to the activation volume for the interstitialcy mechanism calculated for B in Si by ab initio methods. ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{V}}_{\mathrm{Sb}}$ is close to some values inferred from atomistic calculations for a vacancy mechanism; problems of interpretation are discussed. A phenomenological thermodynamic treatment of diffusion under hydrostatic and nonhydrostatic stress is developed for sample configurations in which virtually all point defect equilibration occurs at the free surface of a hydrostatically or biaxially strained thin film stack. Relationships are predicted between the effects of hydrostatic and biaxial stress on diffusion normal to the surface. The prediction for Sb diffusion agrees reasonably well with measured behavior for Sb diffusion in biaxially strained Si and Si-Ge films, lending additional support to the conclusion that the vacancy mechanism dominates Sb diffusion, and supporting the nonhydrostatic thermodynamic treatment. The same analysis is used to compare hydrostatic boron results with ab initio calculations and with literature values for the biaxial strain effect on diffusion, and the resulting agreements and disagreements are discussed critically. Predictions for the effect of biaxial strain on diffusion parallel to the surface are made using these results and analyses.