Accurate and analytical strain mapping at the surface of Ge/Si(0 0 1) islands by an improved flat-island approximation

We propose an extension of the well-known flat-island approximation in (1 + 1) dimensions which, while keeping simple analytical relations, allows one to better describe the strain field on the facets of steeper islands, and on the wetting layer between them. The results of atomistic molecular dynamics simulations using the Tersoff potential are used as a benchmark. The simple continuum approach is also shown to predict the correct trend of the strain gradients characterizing closely-spaced interacting islands, which has been recently observed to produce lateral motion of large Ge dots on Si(0 0 1).