Stresses and first-order dislocation energetics in equilibrium Stranski-Krastanow islands

We numerically determine the state of stress in two-dimensional Stranski-Krastanow islands having equilibrium shape. These calculations reveal important generic characteristics and quantitative details of the stress state in equilibrium islands, including stress relaxation and stress concentration. We also use the stresses to determine the first-order energy of introducing dislocations of different Burgers vectors into Stranski-Krastanow islands. These results characterize the ``energy wells'' sought by dislocations to relieve the misfit stress, and suggest that misfit dislocations in islands segregate according to the orientation of their Burgers vector. This segregation allows for more efficient relief of the nonuniform strain in misfitting islands.