Effect of elastic interaction on self-assembled island spatial arrangement

Self-assembled islands are spontaneously formed during the heteroepitaxial growth of InAs on GaAs substrate. The island formation creates strain fields in the substrate and this leads to elastic interaction between the islands. We calculate the strain energy of the array of InAs islands on the GaAs substrate by the finite element method, and extract the elastic interaction between the islands from the variation of the energy with the distance between the islands. The interaction decays with the third power of the inter-island distance, in agreement with our previous work. The effect of the interaction on the correlation of the island positions is examined by comparing the coefficient of the interaction with the phase transition criteria of the two-dimensional dipole system. When the island size is large enough, depending on the island density, an array of islands can be in either a liquid phase where the islands are randomly distributed or in a solid phase where the islands form a two dimensional lattice. Only the liquid phase exists when the island size is small.