spontaneously ordered nanostructures (rus. наноструктуры, спонтанно упорядоченные) — periodic spatially ordered nanostructures that spontaneously evolve on the surface of solid matters and in epitaxy films in the process of growth or annealing.


Four classes of spontaneously ordered nanostructures have been distinguished (see fig.):

1. structures with periodic composition modulation in epitaxy films of solid semiconductor solutions;

2. periodically faceted surfaces;

3. periodic structures of planar domains (e.g., monolayer islands);

4. ordered arrays of three-dimensional coherently strained islands in heteroepitaxy systems.

Spontaneous evolution of structures with modulated composition in solid solutions occurs as a result of instability of homogeneous solid solutions to spinodal decomposition. The end state of a decomposing solid solution is represented by a one-dimensional lamellar network of concentrated elastic domains alternating along one direction of the slightest compression.

Spontaneous faceting of crystal’s planar surface is determined by the orientation dependence of free surface energy. A planar surface with greater specific surface energy will spontaneously transform into a structure of hills and grooves, which reduces the full free energy of the surface despite the increased surface area. Periodically faceted structures occur due to capillary phenomena on the surface of solid state matter.

Planar domain structures evolve when different phases coexist on one surface. In this case, forces creating an elastic field occur at the domain interface, and the full energy of a planar domain system always has a minimum value at a certain optimum period.

Ordered arrays of coherently strained islands are formed in heteroepitaxy systems like InGaAs/GaAs(001) and InAs/GaAs(001) due to surface exchange of matter between islands. If the change in a system’s surface energy during the formation of one island is negative, the system has no tendency for coalescence, meaning that a balanced array of islands with some optimum size and ordered in a square lattice may exist.


Spontaneously ordered nanostructures with the period D: а — structures with modulation of solid s

Spontaneously ordered nanostructures with the period D: а — structures with modulation of solid solution A1–xBxC composition from x1 to x2; b — periodically faceted surfaces; c — periodic structures of flat elastic domains; d — ordered blocks of three-dimensional coherently stressed islands on a substrate.


  • Gusev Alexander I.


  1. Ledentsov N.N. et al. Quantum-dot heterostructure lasers: obtaining, features, lasers (in Russian) // FTP. 1998. V. 32. p. 385–410.
  2. Gusev A. I. Nanomaterials, Nanostructures, and Nanotechnologies (in Russian) // Fizmatlit, Moscow (2007) - 416 pp.

Contact us