Vertical correlations and anticorrelations in multisheet arrays of two-dimensional islands

Abstract

The energetics of multisheet arrays of two-dimensional islands is studied where the structure of the surface sheet is determined by thermodynamic equilibrium under the constraint of a fixed structure of sheets of buried islands. For the arrangement of islands in a single surface sheet, both a one-dimensional structure of stripes and a two-dimensional structure of square-shaped islands are examined. The buried islands are considered as planar elastic defects characterized by a uniaxially anisotropic double force density, and the surface islands are considered as two-dimensional islands characterized by an isotropic intrinsic surface stress tensor. It is shown that, in cubic crystals with a negative parameter of elastic anisotropy, $\xi {=(c}_{11}-c_{12}-{2c}_{44}{)/c}_{44}<0,$ the elastic interaction between successive sheets of islands parallel to the (001) crystallographic plane exhibits an oscillatory decay with the separation between sheets. This oscillatory decay is related to generalized Rayleigh waves in elastically anisotropic crystals. By varying the distance between successive sheets of islands, a transition occurs from vertical correlations between islands where islands of the upper sheet are formed above the buried islands of the lower sheet to anticorrelations between islands where islands of the upper sheet are formed above the spacings in the lower sheet. The separation between successive sheets of islands corresponding to this transition depends drastically on the anisotropy of the double force density of buried islands. Thus an explanation for the recently observed anticorrelations in multisheet arrays of CdSe islands in the ZnSe matrix is obtained.