Position dependant critical thickness in finite epitaxial systems

During the growth of an epitaxial overlayer, interfacial misfit dislocations become energetically favourable on exceeding the critical thickness. In the case of finite systems (i.e. either the substrate or the epitaxial overlayer is finite), different positions along the interface are not equivalent and the critical thickness will be position dependent. Minimum of these thickness values can be visualized as the global critical thickness. The current work aims at simulating the stress state of a growing epitaxial overlayer on a finite substrate using finite element method and further use the numerical model to calculate the position dependent critical thickness along the interface. Eigenstrains will be imposed in selected regions in the domain towards this end. The variation of shear stress along the interface will be computed from the model to understand the issues related to the mechanism of formation of misfit dislocations. This includes the important question: “why interfacial dislocations cannot ‘punch-in’ directly from the free lateral surface?” The simulation methodology and associated concepts can readily be extended to other finite epitaxial systems like stripes and islands.