Defect-induced instability of the surface layer involving static coupled Lamb and Rayleigh waves as a universal mechanism of the formation of an ensemble of nanodot nucleation centers

It is demonstrated that a stressed flat surface nanolayer saturated with mobile point defects exhibits a threshold (with respect to the defect concentration or mechanical stress) transition to a periodic spatially bent state with a simultaneous formation of the spatially periodic defect pile-ups at the extrema of the spontaneously emerging surface relief. In this case, the layer deformation corresponds to the displacements in a static bending Lamb wave and the deformation of the underlying elastic continuum corresponds to the displacements in the static Rayleigh wave. For the first time, we demonstrate that the analysis simultaneously involving the nonlocal character of the defect interaction with the lattice atoms and both (normal and lateral) defect-induced forces that cause the bending of the surface layer yields two maxima on the curve of the instability growth rate versus the period of the generated relief. This corresponds to the experimentally observed two scales of the surface relief modulation upon the laser and ion irradiation of semiconductors. Based on the results obtained, we propose a cooperative defect-deformational (DD) mechanism for the formation of an ensemble of the nanoparticle nucleation centers above the critical levels of the stress or the defect concentration. An approach to the calculation of a bimodal distribution function of the nanoparticle nucleation centers with respect to their size is adequately developed to the DD mechanism of nucleation which represents the distribution function in terms of the growth rate. The calculated results are compared with the experimental data for the molecular beam epitaxy of the nanodot ensemble and the pulsed laser nanostructuring of a solid surface.