Different shape normal metal interlayers between niobium based SIS junctions and niobium titanium nitride leads and their influence on the electron temperature

In this paper we demonstrate the reduction of heating in a niobium superconductor-insulator-superconductor (SIS) junction with aluminum-oxide tunnel barrier embedded in a niobium-titanium-nitride circuit. Nonequilibrium quasiparticles which are created due to the Andreev trap at the interface between the niobium and the niobium-titanium-nitride layers are relaxed by inserting a normal-metal conductor of gold between these two layers. In an earlier work we explained the observed relaxation of nonequilibrium quasiparticles due to the geometrically assisted cooling effect. In this paper we investigate this cooling effect in dependence of the normal-metal layer shape and size. We expect that an adapted normal-metal layer is necessary for implementation in practical terahertz SIS heterodyne mixer circuits. We observe in DC-measurements of a large number of devices a clear relation between the volume of the gold layer and the effective electron temperature in the device. Our central finding is that the shape of the gold layer does not influence the cooling provided that the volume is sufficient.