Spontaneous pattern formation in reverse epitaxy


Spontaneous pattern formation in reverse epitaxy

Facsko, S.; Ou, X.

In molecular beam epitaxy (MBE) the continuous deposition of atoms can lead to growth of self-organized 3D nanostructures. One of the possible surface instability, which is responsible for this kind of growth is caused by the Ehrlich-Schwoebel (ES) barrier, i.e. an additional diffusion barrier for ad-atoms to cross terrace steps [1]. The arriving atoms are trapped on a terraces and can again nucleate to form new terraces. This mechanism leads to the growth of pyramidal mounds on the surface with facets corresponding to energetically favored crystal planes. An analogous mechanism is also observed on ion irradiated surfaces. However, ion sputtering leads to the erosion of the surfaces and at room temperature semiconductor surfaces become amorphous. At these conditions periodic patterns are observed which are oriented perpendicular or parallel to the ion beam direction or are isotropic dot or hole patterns for normal incidence of the ion beam [2].
At temperatures above the recrystallization temperature of the material, bulk defects are dynamically annealed and amorphization is prevented. Now, ion sputtering is creating vacancies on the crystalline surface and the surfaces morphology is determined primarily by vacancy kinetics. The diffusion of vacancies is also biased by the ES barrier like the diffusion of ad-atoms. Consequently, the 3D growth turns into a 3D erosion. The resulting structures are inverse pyramids which are growing into the material [3]. The symmetry of these patterns is given by the crystal symmetry of the surface. Hence, checkerboard patterns appear for instance on the Ge (001) surface, oriented in the <100> directions. On the other hand, on the Ge (111) surface facets with a three fold symmetry evolve. For high ion fluences the patterns also exhibit facets, which correspond to low index crystal planes [3].
For the description of the pattern formation and evolution in reverse epitaxy a continuum equation can be used, which combines the effects of ion irradiation and effective diffusion currents due to the ES barrier on the crystalline surface. By including also a conserved Kardar-Parisi-Zhang term a remarkable qualitative agreement to the experiments is achieved [3].
[1] P. Politi, G. Grenet, A. Marty, A. Ponchet, J. Villain, Phys. Rep. 324, 271 (2000).
[2] A. Keller, S. Facsko, Materials 3, 4811 (2010).
[3] X. Ou, A. Keller, M. Helm, J. Fassbender, S. Facsko, Phys. Rev. Lett. 111, 016101 (2013).

Keywords: reverse epitaxy; pattern formation; nanostructures; ion irradiation

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