Spontaneous formation of nanostructures on crystal surfaces

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We present a brief overview of physical mechanisms of the spontaneous formation of arrays of strained islands (quantum dots). We focus on discussing the relative importance of thermodynamic and kinetic effects on formation of arrays of islands. We consider single-sheet arrays of islands having predominantly two-dimensional (2D) shape (planar disks), single-sheet arrays of three-dimensional (3D) islands (e.g., pyramids), and multisheet arrays of both 2D and 3D islands. For single-sheet arrays of 3D islands we demonstrate the existence of two regimes: depending on material system, the thermodynamic equilibrium may correspond either to an array of islands of an optimum volume or to a single huge cluster formed as a result of Ostwald ripening of the islands. We show that the temperature behavior of arrays of 2D islands is due to the entropy effects which ensure the shrinkage of the islands with temperature. We demonstrate that the geometry of multisheet arrays of islands is determined, to a large extent, by elastic anisotropy of the crystal. The latter results in alternating between vertical correlation and vertical anticorrelation in the relative arrangement of the islands of the neighboring sheets, controlled by the thickness of the spacer layer.