Geometrical effect on dislocation nucleation at crystal surface nanostructures

Crystal surface nanostructures such as steps and trenches in microelectronic layer structures have been considered as stress concentrators that may facilitate dislocation nucleation. Quantitative characterization of the critical condition of this atomic scale process is of considerable interest for the development of high performance electronic devices. This paper addresses this issue using a multiscale approach based on the variational boundary integral formulation of the Peierls–Nabarro dislocation model. By representing the profiles of embryonic dislocations as the relative displacements between the two adjacent atomic layers along the slip planes, the critical conditions for dislocation nucleation are obtained by solving the stress dependent activation energies required to activate embryonic dislocations from their stable to unstable saddle point configurations. The geometrical effect of surface nanostructures such as steps and trenches on dislocation nucleation is ascertained quantitatively. Our results show that the atomic scale surface nanostructures can reduce the critical stress for dislocation nucleation by nearly an order of magnitude and the trench configurations are more prone to dislocation nucleation than the step configurations. Nucleation of versatile dislocations in multiple slip systems at crystal surfaces may be attributed surface nanostructures of a variety of geometries.