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Published March 2002 | public
Journal Article

A micromechanical model of surface steps


The surface of an epitaxial thin film typically consists of terraces separated by steps of atomic height and it evolves largely by the motion of steps. Steps are sources of stress that interact with other residual stress fields, and these interactions have a profound effect on surface evolution. A model of the elastic field arising from a two-dimensional step is presented as a departure from the commonly used half-plane point-multipole model. The field is calculated asymptotically for small step height up to second order in terms of 'structural' parameters that can be determined from empirical data or atomistic calculations. Effects of a lattice mismatch and surface stress are included. The model is shown to be in remarkable agreement with atomistic predictions. It is demonstrated that second-order terms are necessary for understanding non-trivial step–step interactions, and that these second-order fields cannot be described by point sources on a half-plane.

Additional Information

© 2002 Elsevier Science Ltd. Received 11 August 2000; received in revised form 3 May 2001; accepted 3 May 2001. The authors are grateful to Prof. Alonso Peralta at SUNY, Stony Brook for sharing his atomistic data, and R.V.K. also thanks Prof. Peralta for many stimulating discussions. The authors wish to thank one of the referees for suggesting several references and making a number of constructive comments. This research was completed in part while R.V.K. held a post-doctoral position at the California Institute of Technology. The financial support of the National Science Foundation and Defense Advanced Research Project Agency through cooperative agreement number DMS-9615858 in their joint Virtual Integrated Prototyping initiative is gratefully acknowledged.

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