Model-based study of a nanowire heating and dynamic axisymmetric necking by surface electromigration

Axisymmetric solid-state necking of a single-crystal metallic nanowire in a thermal contact with a substrate and subjected to a surface electromigration current is accompanied by a local current crowding and a sharp rise of a resistivity of a wire material in a thinning neck. This results in a temperature spike at the neck, which feedback affects the necking via thermomigration and the temperature-dependent surface diffusivity of the adatoms. A model that incorporates these effects and couples the nonlinear dynamics of a wire temperature and a wire radius for a necking wire is presented. Conditions on the physical parameters are derived that ensure a straight wire is in the solid state prior to an onset of a morphological instability that ultimately breaks a wire via a pinch-off. The impacts of a wire radius and a wire length on the temperature spike at the break junction are studied.