Shape and stability of self-assembled surface domains.
The shapes of two-dimensional (2D) nanostructures on surfaces are determined by their boundary energies as well as by long-range elastic, electrostatic or magnetic interactions. Although it is well known that long-range interactions can give rise to shape bifurcation-an abrupt change in shape symmetry at a critical size-a general description of the evolution of shape with size, systematically incorporating both the azimuthal dependence of the boundary energy and long-range interactions, has been lacking. Here we show that unconstrained shape relaxation, including previously ignored boundary curvature, leads to a novel, continuous shape change from convex at small size to concave at large size. In addition to demonstrating a method to quantitatively determine the azimuthal dependence of the boundary energy, we show that the energy gain associated with boundary curvature relaxation is a key factor in stabilizing surface nanostructures. For 7 x 7 domains on Si(111), boundary curvature reduces the formation free-energy by up to 50%.
Thayer
G E
GE
IBM Research Division, Thomas J. Watson Research Center, PO Box 218 Yorktown Heights, New York 10598, USA. gthayer@sandia.gov
Hannon
J B
JB
Tromp
R M
RM
D008422:Materials Testing; D008854:Microscopy, Electron; D036103:Nanotechnology