Geometric heat trapping in niobium superconductor–insulator– superconductor mixers due to niobium titanium nitride leads

We analyze the current–voltage characteristics of a Nb superconductor–insulator–superconductor mixer with NbTiN leads to identify the heating processes in this device. We argue that the electron–electron interaction is much faster than the electron–phonon interaction, and show that the heat flow to the bath temperature is limited by the electron–phonon interaction time in the junction. A solution is suggested to considerably reduce the heating.