Size calibration of self-assembled nanoparticles in a model of strained epitaxy with passive substrate

Abstract

We argue that a transient size calibration of self-assembled nanoparticles during strained epitaxy can be caused by forces interior to the growing islands without substrate-propagated interparticle interactions or intermixing with the substrate. The role of substrate in our mechanism is only to provide the intraparticle elastic strain. Our arguments are based on kinetic Monte Carlo simulations of the ͑1+1͒-dimensional model of strained epitaxy of Ratsch and Zangwill ͑RZ͒ ͓Surf. Sci. 293, 123 ͑1993͔͒. It has been found that while the energetics of the RZ model predicts indefinite ripening of the islands, in the simulations their linear dimensions saturated at intermediate times near some finite coverage-dependent values. Simultaneously statistical distributions of their widths and heights narrowed, thus providing improved size calibration. The size distributions obtained are qualitatively similar to those observed experimentally in the growth of ultrasmall supported metallic clusters. The applicability of the model to such systems is briefly discussed.

Nucleation of size calibrated three-dimensional nanodots in atomistic model of strained epitaxy: a Monte Carlo study

“…As is seen, the reduced energy in the square dot is equal to twice the energy in a linear 1D chain of stacks of atoms of height h [28,38,18]. This is because each atom in the island belongs to two orthogonal chains, the interactions within which are independent due to the approximations used.…”

“…Therefore, atomistic models have been developed with the aim of addressing this important problem with the use of the exact kinetic Monte Carlo (KMC) simulations [14][15][16][17][18][19][20][21][22]. The main difficulty hampering the microscopic simulations is posed by the long-range forces due to the epitaxial strain caused by the lattice size mismatch between the substrate and the overlayer.…”

In‐Situ Transmission Electron Microscopy Observation of Germanium Growth on Freestanding Graphene: Unfolding Mechanism of 3D Crystal Growth During Van der Waals Epitaxy

“…Since the lattice mismatch between the two materials is very large, the FM mode confirms that there are likely few, if any, covalent bonds between the Ge layer and the underlying graphene, confirming the VdW bonding nature of our system. [18][19] The weak bond strength, typical of VdW, favors the elastic relaxation of the Ge germs. It is worth to note that the 2D nature of the germs is corroborated by the fact that we did not notice any multilayer germs or layer stacking (except for the case where the second layer is on the opposite surface of the SLG).…”

Self-assembled Sn nanoplatelets on Si(1 1 1)- 2\sqrt 3 \times 2\sqrt 3 -Sn surfaces

“…Some attribute it to straininduced equilibrium states while others propose that the island edge effect induces a stable island size against ripening [4,5]. Besides the factors external to growing islands, it has also been shown that the size selection of islands could be achieved via the forces confined to the interiors of the islands [6]. For metals, the size distribution of 3D metal islands is broad in general [7][8][9][10] in spite of some reports on uniform 3D metal islands such as Au on TiO 2 surface and Fe on the NaCl(0 0 1) surface [11,12].…”