Equilibrium shapes of strained islands with non-zero contact angles

Oleg E. Shklyaev, Michael J. Miksis*, P. W. Voorhees

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


The equilibrium morphology of a strained island on an elastic substrate is determined. The island is assumed to partially wet the substrate (Volmer-Weber growth) and thus makes a non-zero contact angle with the surface. Both isotropic and anisotropic misfit strain are allowed. Two- and three-dimensional equilibrium island shapes are determined by using expressions for the elastic strain energy in the small-slope approximation. In this limit, the problem can be reduced to a singular integral-differential equation for the island thickness. We find that when there is a non-zero contact angle, all island shapes, for a given ratio of the elastic stress to surface energy, attain a form that is independent of the specific contact angle under an appropriate scaling. We show that for islands with non-zero contact angles, as the island volume increases, the shape approaches the geometry of a completely wetting island. But when the volume decreases, these islands approach a point while islands with a zero contact angle, approach a finite length line segment of zero volume. Multiple-hump equilibrium shapes are found. Single-humped islands are shown to have a lower chemical potential than multiple-humped islands, implying that they are the most stable. This conclusion is shown to be consistent with a stability analysis of the two-dimensional case. The effects of a tetragonal misfit strain on the three-dimensional island shape is investigated.

Original languageEnglish (US)
Pages (from-to)2111-2135
Number of pages25
JournalJournal of the Mechanics and Physics of Solids
Issue number10
StatePublished - Oct 2006


  • Asymptotic analysis
  • Boundary integral equations
  • Microstructures
  • Quantum dots

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'Equilibrium shapes of strained islands with non-zero contact angles'. Together they form a unique fingerprint.

Cite this