Three-dimensional towards two-dimensional coherent epitaxy initiated by surfactants
Résumé
The problem of the equilibrium shape of a three-dimensional (3D) crystal A accommodated epitaxially, with a misfit m, onto a substrate B is reconsidered by taking into account surface stress effects. An extended Wulf-Kaishew's theorem is obtained: surface free energy ~r A as well as surface stress s A contribute to the aspect ratio. Bauer's criterion of the three-dimensional towards two-dimensional (2D) growth (3D-) 2D transition) is also modified. Surface stress may drive the system either away from or towards the 3D ~ 2D transition depending on the sign of m(s A-(rA). For so-called surfactants decreasing SA and ~A, it is shown that 3D epitaxial crystals become flatter so that the 3D ~ 2D transition is initiated. For the epitaxial system Si(111) over Ge(111) we illustrate this numerically.