**5. Special issues for next generation standard and possible solutions**

### **5.1 About the extended use of Josephson Voltage standard in AC measurement**

The use of Josephson junctions arrays for AC measurement, while has already set up reference standards of AC voltages in defined ranges of amplitude and frequency, as described in section 2, represents also the first step of new quantum based electrical metrology and instrumentation, of which the quantum voltmeters represent an example.

A first application to AC measurement has been realized by using a programmable array to generate the AC voltage to be compared, at some frequencies, with the DC voltage of a thermal converter, through a suitable balance bridge. In such a way the determination of this standard is also linked to the e and h fundamental constant A comparison between the traditional technique and the one employing PJVS has demonstrated and the accuracy for AC voltages up to 100 Hz can be better than one part in 107.

Further improvement are expected concerning AC equivalent of the resistance: it is in fact possible to realize quantum impedance bridges, by using two separate sections of an array, or even two different arrays each separately radiated by a microwave signal, with a known and measurable phase difference. A two terminal pair impedance bridge has achieved an accuracy of one part in 108 in a frequency range from 25 Hz to 10 KHz, limited mainly by contact resistance changes at the bridge terminals [57]. Further progress is expected when a four terminal connection to the resistances can be provided..

Also quantum sampling of waveforms is made possible, by realization of Josephson DAC with quantum accuracy, and using them with a proper electronics which enclose in the same circuit conventional and quantum based DAC.

resistance *R*sg at 4.2 K and very low voltages is of the order of 0.3 Ohm which is higher but

The main contribution to this subgap enhancement may be related to Andreev reflection processes in the interlayer. Really, since the Al film thickness in SNIS junctions is comparable with the electron mean free path, the transparency of the weak link between the Nb electrodes is dominated by that of the insulating layer. Its average resistance nearly coincides with that in high-specific-conductance Nb-AlOx-Nb junctions where appearance of multiple Andreev reflections was revealed by analyzing comparatively high subgap 'leakage' currents in Nb-AlOx-Nb junctions. Hence, the explanation of the phenomenon suggested for these structures and based on the existence of a universal distribution of transparencies in dirty disordered tunnel barriers [55],[56] in the interlayer. Really, since the Al film thickness in SNIS junctions is comparable with the electron mean free path, the transparency of the weak link between the Nb electrodes is dominated by that of the insulating layer, Its average resistance nearly coincides with that in high-specific-conductance Nb-AlOx-Nb junctions where appearance of multiple Andreev reflections was revealed by analyzing comparatively high subgap 'leakage' currents in Nb-AlOx-Nb junctions . Hence, the explanation of the phenomenon suggested for these structures and based on the existence of a universal distribution of transparencies in dirty disordered tunnel barriers is appropriate to these devices as well. They do not arise from trivial pinholes because after suppressing the Josephson effect, usually no leakage

**5. Special issues for next generation standard and possible solutions 5.1 About the extended use of Josephson Voltage standard in AC measurement** 

AC voltages up to 100 Hz can be better than one part in 107.

four terminal connection to the resistances can be provided..

circuit conventional and quantum based DAC.

The use of Josephson junctions arrays for AC measurement, while has already set up reference standards of AC voltages in defined ranges of amplitude and frequency, as described in section 2, represents also the first step of new quantum based electrical metrology and instrumentation, of which the quantum voltmeters represent an example. A first application to AC measurement has been realized by using a programmable array to generate the AC voltage to be compared, at some frequencies, with the DC voltage of a thermal converter, through a suitable balance bridge. In such a way the determination of this standard is also linked to the e and h fundamental constant A comparison between the traditional technique and the one employing PJVS has demonstrated and the accuracy for

Further improvement are expected concerning AC equivalent of the resistance: it is in fact possible to realize quantum impedance bridges, by using two separate sections of an array, or even two different arrays each separately radiated by a microwave signal, with a known and measurable phase difference. A two terminal pair impedance bridge has achieved an accuracy of one part in 108 in a frequency range from 25 Hz to 10 KHz, limited mainly by contact resistance changes at the bridge terminals [57]. Further progress is expected when a

Also quantum sampling of waveforms is made possible, by realization of Josephson DAC with quantum accuracy, and using them with a proper electronics which enclose in the same

comparable with the normal-state junction resistance *RN*.

supercurrents were observed.

A further employ, presently already in progress, is the realization of standards for Johnson noise thermometry, where arrays of a small number of Josephson junctions are used to generate random white noise voltages. For this application, while the amplitude is not important, the device should extend the frequency range of quantum standard as much as possible [58].

All these aspects have been the subject of specific research projects of Euromet, named ProVolt, JAWS, Binary Josephson Array Power Standard, JOSY and future proposals of next calls.

But, considering the use of Josephson junctions for Voltage standard, the content of this chapter, what are the main goals for the next generation devices?

As mentioned above, see figure 7, both amplitude and frequency of the AC voltage must be pushed to higher values.

It should of course be observed that for people working in the AC field the value of importance is the rms voltage, while typically the output from the values mentioned for some of the mentioned devices is the maximum output DC value.

Fig. 8. Josephson programmable and pulse driven AC Voltage standard impact on measurement of AC voltages for some applications. The amplitude and the frequency extension for the time period from 2007 to 2011 is indicated. (from IMERA TP 4 Josy project extended summary).

To increase the output voltage of the arrays is a serious challenge since nowadays to have more than 106 Josephson junctions on the same chip with tolerable spread of parameters (5- 10%), is beyond the state of art of superconductive technology, As reported in a previous section, 250.000 junctions in plane or 330.000 in vertical stacks of three junctions [17], are the best result sofar.

So, waiting for a technology which can overcome this limit a different approach must be presently searched, reducing as much as possible the number N of junctions and their dimensions for a given voltage output, while keeping the desired voltage resolution.

Another relevant issue is in the possibility of operation at temperatures higher than 4.2 K, in view of the substitution of expensive liquid helium refrigeration systems with the compact cryocoolers which can lead the diffusion of voltage standards to the private companies.

This is a challenge of great importance for superconductive circuits and voltage standards apparently not to be solved in a short period by high *Tc* junctions. At present, large arrays fabricated with higher critical temperature superconductors, like YBCO or the more recent MgB2, are not yet available, since the technology of these junctions do not allow to achieve the required integration level [59]. One big problem of these junctions is the stability in time and with thermal cycling.

The most interesting results sofar have been achieved with YBCO bicrystal shunted junctions, where quantized steps have been measured near 77 K above 100 mV [60].

Concerning niobium and niobium nitride based junctions, only NbN/TiN/NbN have demonstrated operation at these temperatures, achieving a sound result such as a 11 bit DAC with 10 V output at 10 K, which were also risen at 20 V, by using two separate chip connected in series [9].

However, they are sensitive to temperature changes, requiring a stabilization of the cryocooler at 0.1 K level, have a strong demand on dissipated power and require a top-level, costly, fabrication process.

The need of the temperature stability means that small temperature variations should cause only small current changes and can be of interest for applications where a simplified refrigerator is used such as RSFQ and also voltage standard applications [19]. For example, conventional SIS junctions exhibit an excellently stable temperature range from 0 to nearly 0.6 *Tc* but a very strong *Ic-vs-T* dependence above.

A possible solution for both the above mentioned issues is to use high characteristic voltage junctions.

As reported in section 3, this is not trivial, since intrinsically overdamped junctions have Vc below 100 µV at 4.2 K.

However two different technologies have been recently proposed able to produce Vc as high as 0.5 mV and more at such temperature: Nb/NbxSi1-x/Nb SNS and Nb/Al-AlOx/Nb SNIS junctions

In the following results using SNIS are reported.

To increase the output voltage of the arrays is a serious challenge since nowadays to have more than 106 Josephson junctions on the same chip with tolerable spread of parameters (5- 10%), is beyond the state of art of superconductive technology, As reported in a previous section, 250.000 junctions in plane or 330.000 in vertical stacks of three junctions [17], are the

So, waiting for a technology which can overcome this limit a different approach must be presently searched, reducing as much as possible the number N of junctions and their

Another relevant issue is in the possibility of operation at temperatures higher than 4.2 K, in view of the substitution of expensive liquid helium refrigeration systems with the compact cryocoolers which can lead the diffusion of voltage standards to the private

This is a challenge of great importance for superconductive circuits and voltage standards apparently not to be solved in a short period by high *Tc* junctions. At present, large arrays fabricated with higher critical temperature superconductors, like YBCO or the more recent MgB2, are not yet available, since the technology of these junctions do not allow to achieve the required integration level [59]. One big problem of these junctions is the stability in time

The most interesting results sofar have been achieved with YBCO bicrystal shunted

Concerning niobium and niobium nitride based junctions, only NbN/TiN/NbN have demonstrated operation at these temperatures, achieving a sound result such as a 11 bit DAC with 10 V output at 10 K, which were also risen at 20 V, by using two separate chip

However, they are sensitive to temperature changes, requiring a stabilization of the cryocooler at 0.1 K level, have a strong demand on dissipated power and require a top-level,

The need of the temperature stability means that small temperature variations should cause only small current changes and can be of interest for applications where a simplified refrigerator is used such as RSFQ and also voltage standard applications [19]. For example, conventional SIS junctions exhibit an excellently stable temperature range from 0 to nearly

A possible solution for both the above mentioned issues is to use high characteristic voltage

As reported in section 3, this is not trivial, since intrinsically overdamped junctions have Vc

However two different technologies have been recently proposed able to produce Vc as high as 0.5 mV and more at such temperature: Nb/NbxSi1-x/Nb SNS and Nb/Al-AlOx/Nb SNIS

junctions, where quantized steps have been measured near 77 K above 100 mV [60].

dimensions for a given voltage output, while keeping the desired voltage resolution.

best result sofar.

companies.

and with thermal cycling.

connected in series [9].

costly, fabrication process.

junctions.

junctions

below 100 µV at 4.2 K.

0.6 *Tc* but a very strong *Ic-vs-T* dependence above.

In the following results using SNIS are reported.

#### **5.2 Advantages of using junctions with high characteristic voltage: a) Use of higher order steps to optimize Vmax/N**

A specific feature of SNIS junctions is the possibility of achieving high values of both *Ic* and *Vc*, see section 3.5, with current density *Jc* up to 0.5 mA/µm2 and Vc up to 0.7 mV at 4.2 K.

It is then possible to fabricate junctions with dimensions in the range of 1 µm2, with critical currents in the mA range, which ensures that adequate amplitudes of the Shapiro steps are obtained in circuits with reduced dimensions.

Concerning the step amplitude, as reported in section 3.1, the optimal value for the Shapiro steps in overdamped junctions is obtained when *f*drive *f*c = 2*e*/*h V*c , which gives values of about 0.15 mV for *f*drive = 70 GHz. The choice of *f*drive = *f*c is regarded as the best operating condition for Josephson binary arrays since it ensures the minimal demand of microwave power for equal and maximized 0 and ±1 step amplitude. In fact for many applications the step n = 0 is needed to establish zero output voltage. However, steps corresponding to higher order harmonics are enhanced for *f*c multiple of *f*drive [61]. This allows to measure voltages twice, three and also four times higher for a given number of junctions and for instance, a binary-divided arrays consisting of 8192 SNIS Josephson junction has given output voltages of 1.25, 2.5, 3.75 and 5 V [62].

Of course an increased power dissipation is required to work on higher order steps, proportional to the square of the bias current of the step, especially if the maximum amplitude of the step is searched.

In figure 9 the amplitude of the Bessel functions of order 1 to 3, to which are proportional to the corresponding steps, is plotted vs. the argument of these function, which, according to Shapiro calculations, is related to the voltage of the microwave signal of frequency *f*drive

Fig. 9. Step amplitude behavior for n=0–3, see eq. 4. Conditions for optimal 0 and 1, 0, 1 and 2 and also 0, 1, 2 and 3 are indicated.

And it must be remembered that, when higher order steps are used, the voltage resolution of the device is correspondingly reduced, since now vmin. = *f*drive × n.

Therefore it must be evaluated what is the target to be fulfilled: if maximum voltage output, circuit dimensions, power dissipation or resolution. In correspondence different type of standard can be fabricated.

An optimal solution seems achieved when using arrays made of junctions with characteristic voltage in the range between *f*drive < *f*c < 2*f*drive , where it is possible to have both first and second step enhanced.

From figure 9 the condition where the steps n=0, 1 and 2 are all optimized requires a low increment of the microwave voltage, with respect to that for optimized steps n=0 and n=1.

Experimentally, for a radiation frequency of 70 GHz, an RF power of about 40 mW, measured at the input flange of the waveguide cryoprobe for equal 1st and 2nd step (cf. Figure 10), is slightly higher of 20-25 mW for the case of n=0 and n=1. The *V*c of this array was 0.3 mV. The step amplitudes, measured with oscilloscope and with sub-microvolt techniques confirm flatness at metrological level (Figure 9 inset), while the RF power is slightly higher of 20-25 mW for the case of n=0 and n=1. The *V*c of this array was 0.3 mV. The step amplitudes, measured with oscilloscope and with sub-microvolt techniques confirm flatness at metrological level (Figure 10).

Fig. 10. Part of a binary-divided array consisting of 4096 SNIS junctions irradiated by 73 GHz microwaves. The microwave power, 40 mW at the input flange, has been optimized to have equal and wide (1 mA) 1st and 2nd steps. The insets show high resolution measurements of steps profiles. The n=1 step was traced with a precision DVM (dashed) and by array comparison (continuous).

And it must be remembered that, when higher order steps are used, the voltage resolution

Therefore it must be evaluated what is the target to be fulfilled: if maximum voltage output, circuit dimensions, power dissipation or resolution. In correspondence different type of

An optimal solution seems achieved when using arrays made of junctions with characteristic voltage in the range between *f*drive < *f*c < 2*f*drive , where it is possible to have

From figure 9 the condition where the steps n=0, 1 and 2 are all optimized requires a low increment of the microwave voltage, with respect to that for optimized steps n=0 and n=1. Experimentally, for a radiation frequency of 70 GHz, an RF power of about 40 mW, measured at the input flange of the waveguide cryoprobe for equal 1st and 2nd step (cf. Figure 10), is slightly higher of 20-25 mW for the case of n=0 and n=1. The *V*c of this array was 0.3 mV. The step amplitudes, measured with oscilloscope and with sub-microvolt techniques confirm flatness at metrological level (Figure 9 inset), while the RF power is slightly higher of 20-25 mW for the case of n=0 and n=1. The *V*c of this array was 0.3 mV. The step amplitudes, measured with oscilloscope and with sub-microvolt techniques

Fig. 10. Part of a binary-divided array consisting of 4096 SNIS junctions irradiated by 73 GHz microwaves. The microwave power, 40 mW at the input flange, has been optimized to

measurements of steps profiles. The n=1 step was traced with a precision DVM (dashed)

have equal and wide (1 mA) 1st and 2nd steps. The insets show high resolution

of the device is correspondingly reduced, since now vmin. = *f*drive × n.

standard can be fabricated.

both first and second step enhanced.

confirm flatness at metrological level (Figure 10).

and by array comparison (continuous).

The precision measurement have been carried out using different approach: i) the array voltage has been measured with a Digital Voltage Multimeter, DVM, using multi averaging to reduce noise, ii) the voltage of one half of the array was measured vs. the voltage of the other half, biased on the same step, iii) the voltage of the programmable array was compared with the 10 V DC voltage standard, biased at the appropriate voltage level. Depending on the method, the resolution ranged between 1µV and 10 nV.

Being *V* = *Nn* (*h*/2*e*) *f*drive, where *N* is the number of series connected junctions and *n* is the step order, this results in the possibility of using an array where half the number of junctions provide the same voltage output, with the same resolution, by realizing a suitable biasing electronics for 1st, and 2nd and 0 step.

As a consequence, the chip size can be reduced of a factor 2 respect to the size of the present type of programmable voltage standard .
