Phase field model for the dynamics of steps and islands on crystal surfaces

Abstract

Surface stress and lattice strain are the essential factors on the self-organization of a surface, because they affect remarkably adatom diffusion on surfaces and at step edges and induce the elastic interaction between the surface steps. In spite of the importance, their kinetic role on the growth dynamics of the step and the islands in thin film deposition is not yet fully understood. Therefore, in this work, a continuum model is presented, which considers both elastic and entropic interactions between the steps or the islands on the crystal surface and growth dynamics of the steps or the islands. The present model is based on the Ginzburg-Landau approach on phase transition and reduces to the Gibbs-Thompson equation at the step edges. In addition, the elastic field, which is generated by the surface force, is calculated using elastic surface Green function under the assumption that the atomic displacement field decays exponentially from the surface. Using the resulting atomic displacement, the elastic interaction between the surface steps is incorporated into the model. Through numerical simulations, it is shown that the elastic interaction between the steps in our model is in good agreement with previcus theories and that the phase field model has the ability to solve the various phenomena of the step dynamics.