Surface stress stabilizes vicinal surfaces

Vicinal surfaces have been used as a model for improving our fundamental understanding of the stability of self-organized surfaces. Steps on vicinal surfaces and their regularity result from the repulsive interaction between steps. According to the Marchenko–Parshin (MP) model, this interaction varies as 1/L2, where L is the distance between steps. Here, I show (1) that the interaction between steps in the MP model is actually attractive and is due to second order deformations within the bulk material, (2) that the MP model does not correctly account for surface stress σ0yy, and (3) that the repulsion between steps results from first order deformations and from one negative step stress σSyy. The latter interaction is more important than that proposed by the MP model. To the first approximation, it varies with σSyyεyy(0), where εyy(0) is the deformation at the step position including two interaction terms which vary as u1/L and u2/L2.