Critical island size for a shape transition in strained Cu/Ni(100) islands

We examine the shape instability of dislocation-free strained islands in heteroepitaxial growth, using continuum elasticity theory. Using the dipole interaction approximation for the strain-energy proposed by Pimpinelli and Villain, we have calculated the critical island size at which the shape instability may occur, and found that our expressions for the strain-energy and corresponding critical island size are very similar to those obtained by Li, Liu, and Lagally (Phys. Rev. Lett. 85 (2000) 1922). In addition, for the case of Cu/Ni(100) submonolayer islands we have carried out a direct comparison between the continuum elasticity predictions for the force monopole density and dipole interaction energy and atomistic calculations. Our results indicate that while the continuum elasticity expressions significantly underestimate both the force monopole density and the dipole interaction energy, the use of atomistic calculations leads to reasonable agreement between the two approaches. Our results also confirm that the experimentally observed ramified islands in Cu/Ni(100) submonolayer growth cannot be explained by equilibrium energetics arguments.