Two-dimensional simulations of temperature and current-density distribution in electromigrated structures

We report on the application of a feedback-controlled electromigration technique for the formation of nanometre-sized gaps in mesoscopic gold wires and rings. The effect of current density and temperature, linked via Joule heating, on the resulting gap size is investigated. Our experiments include in situ measurements of the evolution of the electrical resistance and of the structure of the device during electromigration. Experimentally, a good thermal coupling to the substrate turned out to be crucial to reach electrode spacings below 10 nm and to avoid overall melting of the nanostructures. This finding is supported by numerical calculations of the current-density and temperature profiles for structure layouts subjected to electromigration. The numerical method can be used for optimizing the layout so as to predetermine the location where electromigration leads to the formation of a gap.