We use Monte-Carlo simulations to study island formation in the growth of thin semiconducting films deposited on lattice-mismatched substrates. It is known that islands nucleate with critical nuclei of about one atom and grow two dimensionally until they reach a critical size s c , when it is favorable for the islands to become three dimensional. We investigate the mechanism for this transition from two-dimensional(2D) to three-dimensional(3D) growth. Atoms at the edge of 2D islands with the critical size s c become mobile as a result of strain and are promoted to the next level. Edge atoms of the resulting island remain highly strained and are promoted to the higher layers in quick succession. This process of depletion is rapid and occurs at a sharply defined island size. We discuss why this leads to the uniformity seen in self-assembled quantum dots in highly mismatched heteroepitaxy 68.35Bs, 68.55Jk, 81.15Aa Typeset using REVT E X
The energetics of island growth on thin semiconducting films deposited on lattice-mismatched substrates is discussed in this article. Hut clusters similar to those proposed by Mo et al. [Phys. Rev. Lett. 65, 1020 (1990)] for Ge/Si(001), with (10n), (n⩾3), or (11n), (n⩾1), side facets will be analyzed. Results show that hut clusters are the energetically favorable structures during early growth, with side facets of rebonded (105) planes; at later times, larger islands with (11n)-like facets become favorable. It is found that islands nucleate with critical nuclei of about 1 atom and grow two dimensionally until they reach a critical size sc, when it is favorable for the islands to become three dimensional. There is an effective barrier at the transition from two dimensional to three dimensional growth. Beyond the barrier, there is an immediate energy gain which can be large, on the order of 5–10 meV/atom for the highly mismatched system of InAs/GaAs. It is suggested that these results are the underlying reason for the uniformity seen in self-assembled quantum dots in highly mismatched heteroepitaxy.
Motivated by the recent investigations on instabilities caused by Schwoebel barriers during growth and their effects on growth or sublimation by step flows, we have investigated, using the Stillinger-Weber potential, how this step edge barrier arises for the two high symmetry steps on 1×1 reconstructed Si(111). Relative to a barrier of 0.97 ± 0.07 eV on the surface, we find additional (Schwoebel) barriers of 0.61 ± 0.07 eV and 0.16 ± 0.07 eV for adatom migration over the [211] and the [112] steps respectively. The adatom potential energy is found to be strongly correlated with that derived from the local geometry of atoms on the adatom-free surface or step edges. This correlation preserves a strict correspondence between the barrier determining features in the spatial variation of the adatom potential energy and the same derived from the local geometry for the Si( 111) surface and the [211] step. It is therefore argued that the Schwoebel barrier on the [211] step is robust i.e. a feature that would survive in more satisfactory ab initio or tight binding calculations. Using a diffusion equation for the adatom concentration the relevance of the barrier to electromigration of steps has been explored. Data from such experiments on Si(111) has been used to place an upper bound on the Schwoebel barrier and a lower bound on the electromigration force.
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