Shape and stability of self-assembled surface domains

Area of Science:

• Surface Science
• Materials Science
• Nanotechnology

Background:

• Two-dimensional (2D) nanostructure shapes are governed by boundary energies and long-range interactions (elastic, electrostatic, magnetic).
• Long-range interactions are known to cause shape bifurcation, an abrupt symmetry change at critical sizes.
• A comprehensive description of shape evolution with size, integrating azimuthal boundary energy dependence and long-range interactions, was previously lacking.

Purpose of the Study:

• To develop a general description for the continuous evolution of nanostructure shape with size.
• To incorporate the azimuthal dependence of boundary energy and long-range interactions into shape evolution models.
• To investigate the role of boundary curvature in stabilizing surface nanostructures.

Main Methods:

• Unconstrained shape relaxation calculations, including boundary curvature effects.
• Quantitative determination of the azimuthal dependence of boundary energy.
• Analysis of energy gain from boundary curvature relaxation.

Main Results:

• A novel, continuous shape transition from convex (small size) to concave (large size) was observed.
• Boundary curvature relaxation was identified as a crucial factor for stabilizing surface nanostructures.
• For 7x7 domains on Si(111), boundary curvature reduced formation free-energy by up to 50%.

Conclusions:

• Boundary curvature is a key factor in the continuous shape evolution and stabilization of 2D surface nanostructures.
• The findings provide a more general description of shape evolution, accounting for both boundary energy anisotropy and long-range interactions.
• This work offers insights into controlling and predicting nanostructure morphology for advanced material applications.