Elastic Interaction Between Modulated Steps on a Vicinal Surface

(Received 28 November 1994, revised 14 February 1995, accepted 6 March 1995)

Abstract
We study in this paper the elastic interaction between modulated steps, in both homoepitaxy and heteroepitaxy. The influence of this interaction on the step fluctuation spectrum is discussed. There are two important consequences that emanate from our analysis, i) in the homoepitaxy case the elastic interaction favors a modulated step profile. However, the gain in the elastic interaction does not generally overcome the line tension effect and ii) more importantly, for the heteroepitaxial case the elastic contribution to the energy modulation is of the same order as that of the line tension part. Elasticity results in an effective line tension (but singular), which may be either positive or negative depending on the phase shift between two adjacent steps. This analysis shows that the elastic contribution for non-zero wavevectors should be incorporated in any statistical theory of fluctuating steps, if one wants to account properly for experimental observations. We point out similarities between this problem, and others arising in quite different systems. We suggest that, in general, tensorial (dipolar and multipolar) interactions between lines, surfaces, etc. of electrostatic, magnetic, hydrodynamic, etc. nature, should lead to the same generic behaviour.