We propose a model based on a Ginzburg-Landau approach to study a strain relief mechanism at a free interface of a non-hydrostatically stressed solid, commonly observed in thin-film growth. The evolving instability, known as the Grinfeld instability, is of high technological importance. It can be associated with the dislocation-free island-on-layer growth mode in epitaxy which is an essential process used in the semiconductor industry. / In our model, the elastic field is coupled to a scalar order parameter in such a way that the solid supports shear whereas the liquid phase does not. Thus, the order parameter has a transparent meaning in the context of liquid-solid phase transitions. / We show that our model reduces in the appropriate limits to the sharp-interface equation, which is the traditional formulation of the problem. Inherent in our description is the proper treatment of non-linearities which avoids the numerical deficiencies of previous approaches and allows numerical studies in two and three dimensions. / To test our model, we perform a numerical linear stability analysis and obtain a dispersion relation which agrees with analytical results. We study the non-linear regime by measuring the Fourier transform of the height-height correlation function. We observe that, as strain is relieved, interfacial structures, corresponding to different wave numbers, coarsen. Furthermore, we find that the structure factor shows scale invariance. We expect that our result on transient coarsening phenomena can be measured through microscopy or x-ray diffraction.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:QMM.35472 |
| Date | January 1998 |
| Creators | Müller, Judith. |
| Contributors | Grant, Martin (advisor) |
| Publisher | McGill University |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Format | application/pdf |
| Coverage | Doctor of Philosophy (Department of Physics.) |
| Rights | All items in eScholarship@McGill are protected by copyright with all rights reserved unless otherwise indicated. |
| Relation | alephsysno: 001658049, proquestno: NQ50225, Theses scanned by UMI/ProQuest. |
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