Prediction of dislocation formation in epitaxial multilayers subject to in-plane loading

Abstract

A theoretical model is described to predict equilibrium distributions of misfit dislocations in one or more anisotropic epitaxial layers of a multilayered system deposited on a thick substrate. Each layer is regarded as having differing elastic and lattice constants, and the system is subject to biaxial in-plane mechanical loading. A stress transfer methodology is developed enabling both the stress and displacement distributions in the system to be estimated for cases where the interacting dislocations are of a pure edge configuration. Energy methods are used to determine equilibrium distributions of the dislocations for given external applied stress states. It is shown that the new model accurately reproduces known exact analytical solutions for the special case of just one isotropic epitaxial layer applied to an isotropic semi-infinite substrate having the elastic constants of the substrate but differing lattice constants. The model is used to consider equilibrium dislocation distributions in capped epitaxial systems with misfit dislocations. It is shown that the simplifying assumptions often made in the literature, regarding the uniformity of elastic properties and the neglect of anisotropy, can lead to critical thicknesses being underestimated by 15–18%. The application of uniaxial tensile stresses increases the value of critical thicknesses. The model can be used to analyse dislocations in various non-neighbouring layers provided the dislocation density has the same value in all layers in which dislocations have formed. This type of analysis enables the prediction of the deformation of metallic multilayers subject to mechanical and thermal loading.

Acknowledgements

The work reported in this paper has formed part of the NPL Strategic Research Programme. The author would like to thank Professor R. Bullough for initially encouraging work on this problem, and for valuable help when comparing, for a special case, the results predicted by the layer model to those predicted by published exact analytical formulae. Drs S. A. Hannaby and L. Wright, NPL, CMSC, are acknowledged for the use in the project of software that solves the system of fourth order ordinary differential equations that arise from stress transfer mechanics. Dr D. Paul, Cavendish Laboratory, University of Cambridge, is acknowledged for technical discussions regarding semiconductors, and for advice regarding data used for modelling. Dr A. Nejim, Silvaco (Europe) is acknowledged for technical discussions and advice regarding the parameters to be used when solving the capped dislocation problem. Dr D. Mendels, NPL, and Dr E Busso, Imperial College, are acknowledged for technical comments on the typescript.

Notes

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Additional information

Notes on contributors

L. N. McCartney *

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