**5.3 Advantages of high characteristic voltage: b) Operation of voltage references above 4.2 K**

The high value of Vc at 4.2 K is also a tool for operation of the arrays above 4.2 K, since the scaling of the electrical parameters with temperature, still allows to use them at higher temperatures.

However a further requirement to the junctions is set by the temperature stability of the electrical parameters, especially above 4.2 K. For a superconductive junctions in fact several non-equilibrium phenomena arise when the operating temperature approaches Tc

The stability of Vc mainly depends from the critical current dependence on temperature, since the junction resistance is almost constant in that temperature range for the majority of metallic and insulating barriers. In particular an evaluation of the temperature stability can be made considering the temperature derivative of the current, normalized to the value at T = 0 , vs. the incremental temperature, normalized to Tc: / 0/ / *cc c d(I (T) I ( )) d(T T )*

In figure 11 the relation is plotted for different type of Josephson junctions.

For hysteretic SIS junctions, whose temperature behavior is described according to the Ambegaokar and Baratoff theory, curve AB, a strong change is observed especially above 4.2. On the contrary for SNS junction, described by a Kulik and Omelianchuk formulation, curve KO, a less prononunced dependence can be observed, but it must not be ignored that in the majority of case these junctions have quite low Vc values already at 4.2 K [63].

In the figure are also shown three calculated curves for SNIS junctions, where by changing the N/S relative thickness in the Nb/Al first electrode, through the parameter of the parameter eff, the temperature dependence can be properly tailored.

In particular, the dotted curve, corresponding to a thickness of the aluminum film about 100 nm, shows a a very small change from 0.7 T/Tc.

Thus, it is possible to engineer the temperature stability of 4-layered structure by increasing the thickness of the different layers and changing, as a result, the shape of supercurrent-vstemperature characteristics [64].

Experiments on single junctions and small array of 10 junctions demonstrated the operation up to temperatures near junction *T*c [65].

Fig. 11. Normalized temperature derivative of the critical supercurrent calculated for conventional SIS (the AB curve) and SNS (the curve KO) junctions and the SNIS devices with eff = 2, 10, and 20 (dashed, dashed-dotted, and dotted lines respectively).

Fig. 12. Voltage step at 1.25 V measured at T = 6.3 K on a binary-divided array of 8192 JJ. The inset shows detail of the quantized step, 0.25 mA wide.

Of course when using more complex circuits, as the programmable arrays described above, non-uniformities in the fabrication and in the distribution of the microwave signal reduce the maximum temperature, especially if the device is operated in gas.

Figure 12 show steps at 1.25 V, 0.25 mA of a binary array, measured at T = 6.3 K Wider steps, 0.5 to 1 mA, have been measured up to 7.2 K on subsections of the arrays.

It is expected that the results will be improved by improving fabrication homogeneity, microwave signal coupling and using a cryocooler setup.
