Nanoscale faceting due to elastic interactions and crystal shapes near Si(1 1 3)

The consequences of Marchenko’s demonstration that striction effects lead to elimination of edges in equilibrium shapes of crystals are explored in detail. The shape of the curved portion of the crystal replacing the edge is explicitly given, and the treatment is extended to the case of step-bunched surfaces vicinal to Si(1 1 3), recently studied in a series of experiments by Song et al. and Yoon et al. A key feature that emerges from our analysis is a novel transition point, which we call the rounded Pokrovsky–Talapov (RPT) point, that separates regions of the crystal surface that are uniformly stepped and regions that contain step-bunches. On the basis of this new observation, earlier interpretations of the experimental results in terms of tricritical points and first-order transitions are shown to be incorrect. Orientational phase diagrams that incorporate the RPT points are given, including a new type of critical point, the Marchenko point, which replaces the tricritical point. It is also shown that the corrugated surfaces emerging from Marchenko’s analysis are rough.