Surface steps: From atomistics to continuum

The elastic interaction between surface steps biases growth and can have a dominant influence on growth modes of thin films. A new continuum solution is presented that takes into account the actual geometry of the steps. It is shown that even in the absence of external stress, the interaction energy contains a logarithmic dependence not previously reported in the literature. This additional term is of the same order of magnitude as the ones contained in the solution of Marchenko and Parshin that has been generally used during the past twenty years. Opposite and similar steps are investigated and closed-form expressions for the relevant elastic fields and interaction energies are derived. Results compare favorably with the ones obtained from embedded atom method (EAM) simulations and a recent elastic lattice model.