Coupled surface and bulk diffusion in crystals

We analyze point defect bulk and surface diffusion near the crystal–vacuum interface and show that bulk diffusion is coupled with surface diffusion via the atomic processes in the intermediate subsurface layer. A set of self-contained differential equations describing the interaction of self-interstitials and bulk vacancies with the surface of crystal is proposed. The results show the existence of the fundamental relation between the equilibrium concentrations of the point defects in bulk and at the surface of the crystal. For the case of silicon, the energy barrier differences that restrict the point defect fluxes between the bulk and surface of the crystal are estimated.