We study the equilibrium shapes, shape transitions and optimal volumes of small strained heteroepitaxial nanoislands with a two-dimensional atomistic model, using simple interatomic pair potentials [1]. We first numerically map out the phase diagrams for the equilibrium island shapes as a function of the island size (up to N=105 atoms) and lattice misfit f with the substrate. Such nanoscopic islands have four generic equilibrium shapes, which appear in different regimes depending on the sign of the relative substrate-adatom interaction
paramater κ.
For large N, we map out the global phase diagram on the f-κ plane. This phase diagram reveals all the well-known growth modes. In particular, for large enough misfits and attractive substrate-adatom interactions there is a Stranski-Krastanow regime, where the islands attain optimal sizes as determined by their energy balance. We analyze the various terms contributing to the total island energy in detail, and develop an analytic extrapolation scheme for the total energy of the system. We find very good agreement between the numerically and analytically calculated global phase diagrams.
[1] J. Jalkanen, O. Trushin, E. Granato, S.C Ying, T. Ala-Nissila,
Phys. Rev. B 72, 081403 (R) (2005)
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