The role of Joule heating in the formation of nanogaps by   electromigration
  We investigate the formation of nanogaps in gold wires due to electromigration. We show that the breaking process will not start until a local temperature of typically 400 K is reached by Joule heating. This value is rather independent of the temperature of the sample environment (4.2-295 K). Furthermore, we demonstrate that the breaking dynamics can be controlled by minimizing the total series resistance of the system. In this way, the local temperature rise just before break down is limited and melting effects are prevented. Hence, electrodes with gaps < 2 nm are easily made, without the need of active feedback. For optimized samples, we observe quantized conductance steps prior the gap formation. 
M. L. Trouwborst, S. J. van der Molen and B. J. van Wees