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Comparison of Josephson Series-Array Voltage Standards

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Metrologia

Ll, 41 -

52 (1990)

met rolog ia C Spnnger-Verlag 1990

Comparison of Josephson Series-Array Voltage Standards J. Niemeyer ’, L. Grimm ’, W. Meier T. Funck ’, E W. Dunschede E. Ausbuttel ’, J. U. Holtoug 2 , and J. Mygind

’

’

Physikalisch-Technische Bundesanstalt, Bundesallee 100, D-3300 Braunschweig, Federal Republic of Germany

’ Ddnish Institute of Funddmental Metrology B322, Lundtoftevej 100, DK-2800 Lyngby, Denmark Received Jul! 17. 1989 and in revised form October 30, 1989

Abstract A precision comparison between the Josephson seriesarray voltage standards of the Danish Institute of Fundamental Metrology (DFM) and of the Physikalisch-Technische Bundesanstalt (PTB) has been made at the one volt level by calibrating the same Zener reference standard with both instruments. Within 2.5 nanovolts (1 a), the same reference voltage has been obtained from the experiments. The calibrated Zener instrument has at the same time been used to measure the average output voltage of the PTB’s main group of Weston cells.

1. Introduction

The Josephson junction is an ideal frequency-to-voltage converter with the quotient of two fundamental constants relating the internal Josephson oscillation frequency f, to the voltage V across the element,

constant-voltage steps. Unfortunately, the maximum reference voltages are only a few millivolts (cf. Fig. 1). Traditional voltage standards therefore have to make use of a voltage divider to raise the relatively small voltages to the 1 V level. The instabilities and the imperfect and complicated calibration procedure of these voltage dividers has limited the reproducibility of traditional Josephson voltage standards to a few parts in 10’. There are two obvious ways to raise the voltage. First, one may increase the pump frequency. But apart from the fact that the very high-frequency equipment is expensive and difficult to operate, the maximum voltage at a single junction for constant-voltage steps is determined by the energy gap voltage, i.e. by the strong current increase in the d.c.-characteristic around 2.7 mV (Fig. 1). In practice, steps with a current width large enough to be used for the purposes of a standard, reach about three times the gap voltage. The maximum voltage therefore cannot be significantly increased by using higher pump

V=(h,’2e) f,. When the Josephson oscillator is phase-locked to an external oscillator with the frequency f , the I-V characteristic shows constant voltage steps [l] at,

K = n ( h ’ 2 e ) f’,

n=O, 1, 2, ... .

These constant-voltage steps are an ideal reference voltage the reproducibility of which is dependent only on the stability of the external microwave frequency which may be controlled for short periods with a relative uncertainty of by modern atomic clocks. Therefore Josephson junctions together with precision voltage dividers have been used in traditional standard instruments to maintain the unit volt [2-41. Figure 1 shows a tunnel junction d.c. characteristic without microwave radiation and with microwave radiation applied at relatively large r.f. power. In this case the d.c. characteristic is shifted towards the normal state characteristic by photon-induced excess currents and shows a large number of classic

.-> 9 4 0

0 hl

0 0

1 mVldiv

Fig. 1. The I-V characteristic of a Josephson tunnel junction without microwave radiation and with microwave radiation applied at a frequency of 70 GHz. The curve traced under microwave influence shows classic microwave-induced steps. Steps of up to V, z 6 mV can be obtained

42

frequencies. Only the number of steps in a given voltage range is lowered and the step amplitude is increased. Consequently, the highest frequency used with a traditional Josephson voltage standard is only 70 GHz [4]. Another possibility is to series-connect a large number of Josephson elements individually biased on highnumber r.f.-induced steps. In practice, however, the bias network with the large number of current sources becomes very complex and the maximum voltage achieved is 100 mV with 20 junctions [ 5 ] . In 1977 Levinsen [6] suggested another type of Josephson array voltage standard using zero-current constant-voltage steps (Fig. 2a, b). In comparison with traditional r.f.-induced steps zero-current steps cross the voltage (zero-current) axis, so that there is, in principle, no need for any d.c. current feed. For a single tunnel junction made of commonly used superconductors like the alloys of lead or niobium, zero-current steps reach about half the gap voltage. At higher voltages photon induced excess currents shift the characteristic moving the steps away from the zero-current axis (Fig. 2 b). The voltage range of stable zero-current step operation is adjusted by optimizing the microwave power applied. Zero-crossing steps overlap in a wide range. Thus, for a series-array of Josephson junctions in the zero-crossing step mode, a much larger critical current spread is tolerable than is the case for a series array in the traditional mode of operation, provided both arrays are biased by a single current source. The minimum critical current Icmin is determined by the condition that the corresponding step with A I , must be large enough to allow a stable bias in the presence of external noise. It has been found experimentally that Icmin z 100 FA is sufficient in a properly shielded system. The upper limit for the critical currents, I , m a x , is defined by the condition that the external frequency f must be considerably larger than the plasma frequency f , of the tunnel junctions [7], or the phase-lock between the junction oscillators and the external oscillator will be broken by chaos or by subharmonic generation [8]. This limit should be seen in connection with the requirement that the junction dimensions must be small enough not to sustain geometrical resonances at the frequency of the external drive and not to cause inhomogeneous r.f. and d.c. current distributions over the junction area by self-magnetic field effects. In Table 1 some junction data for the series-arrays used in this experiment are listed. They show that I,,,, may be about three times as large as I , min z 100 PA, which is much more than would be tolerable for a single biased series-array Josephson voltage standard in the traditional mode of operation. The external microwave power must be distributed so evenly over the series-array that i) the smallest amount of microwave power for an arbitrary junction of the array is large enough to provide a tight phase-lock between the external microwave and Josephson oscillations and ii) the largest amount of power a junction receives does not cause photon induced excess currents at low voltages which would shift the zero-current step mode to the traditional step mode. A feasible concept for providing an even distribution of the millimeter wave power to all Josephson junctions

c, j , max

a, /AL2 La, w,, ‘,ax

dI7,,,

(PF/cm2) (A/cmZ) (n”) (P4 (Pm) (PA) (PA)

P b In Au/ P b In oxide/ P b Au

Nb/ NW,/ Pb In Au

3 21 150/150 24 67 340 224

24 168 SOjl50 15

30 450 297

43

Fig.3. a Photograph of the PTB-chip. b Diagram of the NIST chip

ence voltages with chips including 14 184 junctions in 8 parallel lines [ 1 I], or 18 992 junctions in 16 parallel lines [12]. In order to improve durability and resistance against repeated thermal cycling, great effort has been made to use an all-niobium or niobium-nitride junction technologY [I 31. The PTB chip used for this experiment is shown in Fig. 3 a. I t is completely fabricated by a technique which places a lead alloy on Si-substrates [lo] The stripline is divided into 8 microwave paths, all connected in parallel to the finline antenna which transforms the microwave signal from the waveguide mode to a stripline mode. The series array contains 2002 junctions. The single junction area is 25 pm x 46 pm. The average critical current is 400 pA. With a specificjunction capacitance of C,= 3 pF/ cm2, and ,f = 70 GHz, the ratio of external drive frequency ,f to the Josephson junction plasma frequency f, is f / , f p= 2.4. This relatively small ratio is believed to cause the short stability time - max. 5 min - for a step biased near onc volt on this special chip. The maximum step amplitude is about 50 pA between about + 1.5 V and - 1.5 V (Fig. 4.1). The NIST chip (NIST 235-05) used in the DFM instrument consists of a Nb/Nb-oxide/PbInAu sandwich on a silicon wafer with a niobium groundplane for the 6.7 Q micro-strip transmission lines. The average critical current is 175 pA and with f =70 GHz, the ratio of external drive frequency and plasma frequency is

f / f ,= 4.4. The 12.7 x 6.3 mm2 chip contains 3020 Nb/Nboxide/PbInAu junctions series-connected in 4 parallel microstrip transmission lines (Fig. 3 b). The junction area is 24 pm x 12 pm. Pumped around 70 GHz with less than 5 mW at the input flange of the microwave mount, it produces about 30 000 steps between + 2 V and -2 V. The current width of the step, and hence the maximum applicable step voltage, is somewhat frequency dependent within the tuning range of 69-73 GHz of the DFM setup. Oscillographs of typical 4.2 K d.c. characteristics taken with and without microwave radiation being applied are shown in Fig. 4.2. Near 1.1 V the voltage steps are 70 pA wide and may be stable for 30 min or longer with the set-up operated under the usual experimental laboratory conditions which place the cryoprobe in a standard helium transport dewar outside the electrically shielded room.

2* Experimenta1 Set-up 2.1. Description of the Array Standard Instruments

a ) The PTB Instrument. The PTB system has been briefly described in [14]. For this comparison, instead of the source-locking EIP counter in the transportable

44

Fig. 4.1 a, b. The I-V characteristics of PTB's 2000 junction series array uscd in this cxpcrimcnt: a without microwave radiation, and b with 70 G H z microwave radiation

voltage standard we used a more elaborate phase-lock loop to control the 70 GHz klystron drive frequency. A block diagram of the complete system is shown in Fig. 5a. The fine adjustment of the standard voltage is made by tuning the frequency. The VRE 2101 klystron for the 70GHz supply is phase-locked to a 10 MHz quartz oscillator in two steps: A standard frequency (f,), coupled to the quartz oscillator, is phase-locked to the output of a 10 GHz klystron (flo) which in turn is phaselocked to the series array drive frequency of the 70 GHz klystron (f,o). In this system, the uncertainty of the 10 MHz quartz oscillator determines the uncertainty of the 70 GHz drive frequency. The long-term stability is controlled by means of the PTB frequency standard and a phase monitor to within 1 part in 10" over 24 h. The short-term stability was determined by a computing counter (HP-5360A) in a separate experiment. For a measuring time of z = 1 s the short-term stability results in D ( T ) = IO-'' which is also the resolution of the experiment. With the help of the stable quartz frequency, a standard frequency generator produces standard frequencies between 430 MHz and 1000 MHz, adjustable in steps of 10MHz. The output frequency of a synthesizer - adjustable between 20 MHz and 30 MHz - is added to obtain a very stable output frequency tunable in small steps. The first phase-lock loop converts the standard frequency to the frequency of the x-band klystron:

fio = 11 fi + 10 MHz . This klystron frequency is larger by 10MHz than the 1 1 th harmonic of the standard frequency generator. The seventh harmonic of the 10 GHz klystron is mixed with the output frequency of the 70 GHz klystron, which is stabilized at the frequency, f70=7f10+30 MHz,

Fig. 4.2a, b. The I-V characteristics of DFM's 3020 junction series array (NIST 235-05): a without microwave radiation, and b with 72.4 GHz microwave radiation. Note the step structure extending to voltages above 2 V

by a 30 MHz phase-lock loop. Besides the frequency stabilization (fine adjustment) and the Josephson series-array, the PTB voltage standard has two other main parts: the voltage calibration device and the coarse adjustment device. At 300 K the voltage calibration component compares the voltage to be calibrated with the Josephson reference voltage at 4.2 K using an EM N l a electronic nanovoltmeter to measure the remaining differences between the unknown voltage and the reference voltage. The electrical switching is performed by means of a special low thermal e.m.f. switch box. The voltage leads are permanently connected to small copper blocks electrically insulated from a common solid copper frame by thin PVC foils. All parts are in good thermal contact. The entire switch is thermally insulated from the environment. Its large heat capacity stabilizes the temperature of the switch. The switches are closed by inserting copper cones between two adjacent copperblocks. The wires leading to the 4.2 K series array are electrically filtered by feed-through capacitances (1.5 nF) located in a closed metal box on top of the sample holder. The voltage leads, made of low thermal e.m.f. copper, are kept in good thermal contact with each other to keep the ther-

45

Fig. 5. a Rlock diagram of the PTR serics array voltage standard. b Block diagram of the DFM multi-junction Josephson (MJJ) voltagc standard

46

mal e.m.f. differences between the leads as small as possible. They are thermally insulated from the cold He vapour by a double-walled stainless steel tube to prevent sudden changes of the temperature gradient at the wires. By this means the thermal e.m.f. differences can be kept stable. The remaining thermal e.m.f. difference of about 200 nV is compensated while biasing the series-array in the zero-voltage state. Any offset of the nanovoltmeter can also be compensated in this way. The measured total drift of thc compensated zero voltage does not exceed 6 nV/h [IO]. The leads are connected to the series array by superconducting contacts. The sample mount is surrounded by a p-metal screen and, to prevent flux trapping in the series array, is made of material free of magnetic impurities. The coarse adjustment device allows that constantvoltage step, closest to the unknown voltage, to be selected. The array is shunted by a resistor of 25 R that forms a staircase-likc d.c. characteristic by superimposing its characteristic on the completely overlapping constantvoltage steps. This allows a certain voltage step to be selected by tuning the bias current offset at the low noise current source. The search procedure is facilitated by adding a small modulating current. The oscilloscope screen shows a small number of steps close to the desired reference voltage and hence easily allows the bias current to be adjusted to the center of the constant voltage step selected. The voltage difference between two adjacent steps is 145 pV for a drive frequency of 70 GHz, so the step number is determined unambiguously using a digital voltmeter. The insulation resistance of the lines and the switches has been found to be 5 x 10” R and that of the nanovoltmeter 5 x IOl3 R. To correct for offsets and thermal e.m.f. drifts, three voltage comparison measurements were carried out by reversing the reference voltage twice (cf. Fig. 6). In the case of the PTB instrument, it was possible to adjust the null detector precisely to zero because of the high resolution of the frequency adjustment. The integration time of a single measurement is estimated to be 20 s. h ) Tlie D F M Instrument. Figure 5 b shows the DFM

Multi-Josephson Junction (MJJ) set-up. The system includes a cryoprobe with the array mount, a microwave source to power it, a counter/diplexer with an external mixer to control the frequency, and an oscilloscope with plug-ins for current-bias [I 51 and voltage-monitoring of the I-I/ characteristic. From the chip there is a separate cable to the manually operated switch box connected to the Zener reference and the digital voltmeter. An analogue nanovoltmeter is used as a low-noise preamplifier to increase the sensitivity, but only for measurements of the noise of Weston cells and Zener references (see below). The cryoprobe is designed to fit into a standard 50 mm diameter liquid helium storage dewar. A sliding flange and a simple bellows system allows the array to be slowly cycled between 4.2 K and ambient temperature in a protective helium gas atmosphere. Evaporated helium gas cools thc waveguide and the wires leading to the chip mount. The liquid helium consumption is less than 1 1 per 24 h. The hold-time in the 60 1 storage dewar is more than

Fig. 6. Three null measurements and two reversals of the array voltage are used in the calibration algorithm to correct for offset and linear drift in the DFM multi-junction Josephson (MJJ) set-up. A, Z and N are voltages. In case of the PTB instrument, N could to bc adjusted to zero because the resolution of the frequency tuning was fine enough

3 weeks. The shielding against external noise is provided by filters contained in the r.f.-shielded box on top of the cryoprobe. The problems with the thermal voltage caused by the temperature gradient between 4.4 K and 300 K are minimized by using leads made of high-grade, silver coated copper. In spite of this, we observed thermal e.m.f.s of a few pV, which are corrected for in the calibration procedure discussed below. The leakage resistance between the reference voltage leads including the switch box is above 250 GO. A cryogenic magnetic shield surrounds the chip mount and prevents flux-trapping in the array. There are two delicate operations involved in using the set-up: i) the step structure around the desired voltage must be optimized by simultaneously tuning the frequency and power of the Gunn oscillator; ii) the array must be biased on a step within less than 50 pV from the reference voltage. The latter restriction enables the computer to calculate the step number and to adjust the frequency automatically to a value which nearly nulls the reading of the digital meter. A perfect null cannot be achieved because of the limited resolution (10 kHz) of the counter. With the exception of these operations and the handling of the switch box, the calibration procedure is run by the computer via the IEEE bus. As with the PTB instrument, the practical selection and biasing on a particular step is done by shunting the

41

array by a finite source resistance. The bias supply has been modified to include a logarithmic potentiometer by means of which the slope of the load line can be varied over a wide range. With the smallest value of the parallel resistor ( I O SZ) we span a group of approximately 30 steps. The voltage of the selected group can be shifted along the voltage axis by tuning the current offset on the bias supply. By simultaneously reading the voltage difference between the array and the Zener reference on the digital voltmeter, we are able to identify the correct step and centre it on the oscilloscope display. Less than 5 min are usually needed to shift to a new reference voltage. The reversal of the array voltage on the same step number takes only about 30 s. In order to correct for offset and linear drift, three difference measurements and two array voltage reversals are performed in the calibration procedure shown in Fig. 6. The correction voltage I/ ( t )= V, Y t , which is assumed to have a linear time dependence, includes the thermal voltage and the offset voltage of the null meter. In the simple algorithm shown it is assumed that the measurements are carried out sequentially at equal time intervals A t . Typically. an average over 120 readings of the digital voltmeter, each with an integration time of 0.5 s, is made in each reversal.

r-Main Group of Weston Cells

a

+

PTB 1 V Array Set -Up

PTB

+Low Them1 + Zener

Reference

EMF Switch Box

b

2.2. Measuring Procedure

The schematic diagram in Fig. 7 illustrates three different comparisons tried out in this series of experiments. Scheme a) shows the first experiment where two Zener references nominally at 1.018 000 V and 1.018 647 V were connected manually to the series-array standards. The latter Zener reference was adjusted to permit a direct comparison with the PTB's main group of Weston cells. These Zener references were permanently installed in PTB's shielded and temperature-stabilized room. The major reason for using them as transfer standards was to protect the Weston cells against electric shocks caused by unintentional switching between steps in the Josephson voltage standards. The results obtained over a day showed a relatively large spread (20-50 nV) and a deviation of up to even 100 nV was obtained between the values from the PTB array and the D F M array. This was found to be caused by the thermal voltages, or perhaps mechanical stress, generated when we manually attached the wires to the terminals of the Zener references. It was therefore decided to use only one transfer standard and to establish a permanent connection to this Zener reference (Fluke 732A, PTB 358, 1.018 547 V). The copper blocks in the PTB low thermal switch then served as terminals for the measurements carried out following Scheme b) in Fig. 7. The results of this comparison are described in Section 4. Scheme c) describes the attempt to make a direct comparison of the two different series-array standards. This failed because an independent biasing on constantvoltage steps of the two series-array standards proved impossible because of incompatibilities in the ground connections of the two systems. The D F M instrument is designed to float with respect to ground. During the ex-

I

I

I C

Fig. 7a-c. Scheme of the three measuring procedures used for comparisons at the PTB. Central components are the PTB low thermal e.m.f. switch box and the Zener reference used as transfer standard. a First comparison: permanent connections (full lines) to the switch box, and manual alternation of the connections to the terminals on the Zener reference. b Second comparison: all connections permanent, switching only by the switch box. c Third comparison: an attempt to make a direct comparison of the two Josephson set-ups was frustrated by incompatibility of ground connections

periment, however, a marked leakage was observed and, because the current source of the D F M instrument is integrated into its oscilloscope electronics, it proved impossible at short notice to perform a direct comparison. This experiment will therefore be repeated on another occasion. The measurements were performed in a shielded room at the PTB the temperature of which is stabilized at 20.5 "Cwithin f0.1 "C.The main group of Weston cells is located in the basement under the shielded room, thus requiring a 4 m long permanently-installed connection between the Zener transfer standards in the shielded room and the Weston cells in the basement. The temperature of the enclosure with the main group of Weston cells [16]. The thermal is controlled at 20°C within f 10-4cC e.m.f. differences on the connecting lines were measured and found to be less than 20 nV with a drift of less than 5 nV/h. The PTB's common 10 MHz reference frequency

48

was used to control the series-array drive frequencies of both the DFM and the PTB instruments. The uncertainty of the reference frequency is better than 1 part in lo1' for a measuring time of 1 s. 3. Uncertainties

80 nV 40

0

a ) The PTB Instrument

When Josephson series-array potentiometers are used for a voltage calibration, the main sources of uncertainty derive usually from the inherent noise of the voltage references to be calibrated [13]. Figure 8 shows the voltage noise of a Weston cell and a Zener diode as recorded in a direct comparison with a series-array reference voltage. Another important source of uncertainty is the low thermal e.m.f. switch box used for connecting the voltage source to be calibrated to the series-array standard. Perturbations caused by actuating this switch are recorded in Fig. 9. The trace is recorded with the calibrating device of the system illustrated in Fig. 5 a while biasing the series-array to the critical current (zero voltage) and compensating the thermal e.m.f. differences and a possible nanovoltmeter offset. The fractional stability of the frequency reference is better than lo-'' for an integration time of 1 s (cf. Sect. 2.1). The total uncertainty budget of the PTB instrument (cf. Sect. 2.1 a) is listed in Table 2a.

=40

-80 0

0,5

Source of uncertainty

Weston cell Guildline 9154 D SP500 471-1

DFMINIST 2076 array chip 0.1 at 4.2 K (frequency, long-term stability) Uncorrected thermal voltage drift 1 in lines, filters and switch box Offset current in pre-amplifier 0.1 (EM, Nla) Insulation resistance in lines, filters, 2 and switch box

Series array Josephson standard at 4.2 K - Frequency drift - Thermal e.m.f. drift - Thermal e.m.f. of the switches - Offset current drift of the nanometer N l a - Insulation resistance of the lines and switches - Insulation resistance of the nanovoltmeter N l a - Noise of the Weston cell (500 R,0.9 n V / m ) - Noise of the electronic reference standard (8 n V / m ) - Noise of the nanovoltmeter N l a (0.47 n V / m at 500 R) (0.9 n V / m at lo00 R)

0.001

0.001

0.5 0.4 0.1

0.5 0.4 0.2

0.1

0.2

0.01

0.02

Relative uncertainty (1 a) without measuring time dependent noise

0.65

-

Total relative uncertainty (1 a) for 0.1 Hz bandwidth

Zener reference Fluke 732A DFM 156

0.1

1

0.2 4

Measuring time-dependent uncertainties:

0.9

8 0.47

Noise of Weston cell, Fig. 11, 500 R,0.25 s Noise of Zener reference, Fig. 11, 1000 Q, 0.25 s Noise of pre-amplifier, EM Nla, 500 R source resistance, 0.25 s Noise of pre-amplifier, EM Nla, lo00 R source resistance, 0.25 s

5

Relative uncertainty (1 a) without measuring time-dependent noise

2.5

4.1

Total relative uncertainty (1 a) for 4 Hz bandwidth

6.4

17.1

Noise voltage at nominal 1.018 V with integration time 60 s

0.4 nV

1.1 nV

Measured noise voltage with DFM MJJ set-up at 1.018 with integration time 60 s

0.4 nV

1.7 nV

16 3.2 4.5

0.9 0.7 1.2

8.1

1

Relative uncertainty in

Measuring time-independent uncertainties:

Weston cell Electronic reference standard, Fluke 732 A/AC

time

Table 2 b. Uncertainty budget for the DFM multi-junction Josephson voltage standard

son voltage standard. Relative uncertainty in lo-'

-

Fig. 8. Voltage noise of a Weston standard cell and a Zener reference (Fluke 732 AC), as measured with the PTB series array standard. The bandwidth of the measurement is 0.1 Hz

Table 2a. Uncertainty budget for the PTB multi-junction JosephSource of uncertainty

h

49

A comparison between the PTB’s series-array standard and the main group of Weston cells can be made with a standard deviation of better than 20 nV. (Fig. 10). This total 1 (T uncertainty comprises the drifts of the thermal e.m.f. differences on the 4 m lines from the seriesarray standard to the main group, the uncertainties from the internal calibration procedure of the main group, the temperature drifts of the Weston cell enclosure, and the uncertainties from the series-array standard (cf. Table 2 a). The latter is negligible compared with the uncertainty caused by the main group itself. h ) The D F M Tnsfrument

fore recording these curves. With an averaging time of one minute, the measured standard deviation on the average value is 1.7 nV for the Zener reference and 0.4 nV for the Weston cell. The noise found in the Zener reference and in the Weston cell (Guildline 91 54 D) compares well with similar measurements recently performed at the PTB [14] if the different integration times used in the respective experiments (cf. Fig. 8 and Fig. 11) are taken into account. The microvave source in the D F M MJJ set-up is frequency-locked to the external frequency reference only via the millimeter-wave counter (EIP 578 in Fig. 5 b). This means that the Josephson step voltage fluctuates in proportion to the spectral linewidth (short-term instability,

Figure 1 1 demonstrates the measured voltage noise in a Zener reference and in a Weston cell at the 1.018 V level. The offset voltage is supplied by the Josephson array and the integration time of 0.25 s is set by the filter in the pre-amplifier (EM Nla, see Fig. 5). Calibrations with the multi-junction set-up were carried out immediately be-

Fig. 9. Thermal e.m.f. changes at the PTB low thermal e.m.f. switch when actuated several times (arrows denote the time of switching)

Fig. 10. Results of the comparisons between the mean e.m.f. of PTBs main group of Weston cells V , and the Josephson series array standard over a period of three years. V , is a fictitious voltage whose value is updated after a certain time interval. The last set of points is from the experiment described in this paper (cf. Fig. 13). The open circles are the results ofa comparison ofthe reference voltage output

Fig. 11a, b. Noise from a a Weston cell (Guildline 9154D, S P 500471-1) and b a Zener reference (Fluke 732A, DFM 156) measured with the D F M MJJ set-up in a separate experiment. The integration time is 0.25 s. The corresponding standard deviations found with the MJJ set-up are 1.7 nV and 0.4 nV, respectively, when averaging for one minute. The scales of Fig. 11 a, b are the same

from another NIST chip, which is part of the first DFM series array standard, with the average of the PTB’s main group of Weston cells. Each open circle represents the average or 5 to 8 singlc measurcments carried out with three different Zener diode transfer standards. Crosses denote single measurements with NIST chips and full circles single measurements with PTB chips

50

Reference Calibration ( NlSTlDFM ARRAY ) 1,018 V 3000 h

2

2000

v

7

.-c

g

1000

o -1000

t"c -2000

0 '.-= -3000 CU

>

0" -400017-Jan.

27-Jan.

06-Feb.

16-Feb.

26-Feb.

Date ( 1989 ) Fig. 12. Examples of long-term drift in potential across the nominal 1.018 V terminals of six Zener references (Fluke 732 A, DFM 094, DFM 153, DFM 154, DFM 155, DFM 156, and DFM 157) monitored by the DFM MJJ set-up using the 3020-junction array

(NIST 235-05). Most of the variation is ascribed to the drift and noise of the Zener references which are kept in a laboratory without thermal stabilization

3 dB power width of 137 kHz at 72.4 GHz) of the Gunn oscillator. This should not lead to systematic errors in voltage comparisons but it may influence the array stability and also contribute to the measured standard deviation. Linear thermal drift is compensated as described above in Fig. 6. We have estimated the uncorrected thermal voltages and drift, originating chiefly from the switch box (Guildline 9145 A5 in Fig. 5 b), to be about 1 nV. The offset current drift in the pre-amplifier (EM, NI a in Fig. 5 b) is 2 pA/"C and the variation in the room temperature is less than f O . l "C (cf. Section 2.2). The influence of the insulation resistance of the digital voltmeter (HP 3457A in Fig. 5b) can be neglected [17]. The insulation resistance of the lines, filters and the switch box was measured and exceeds 200 GR. The internal resistance of the Zener reference and the Weston cell used is approximatly 1000 R and 500 R, respectively. The present DFM MJJ set-up was used at DFM throughout the first months of 1989 after a new Gunn oscillator had been installed. Figure 12 shows the drift of DFM's six Zener references as calibrated with the DFM MJJ set-up. Using the estimated partial uncertainties listed in Tables 2 a and 2 b we can calculate the total uncertainty in the indirect comparison between the two Josephson array voltage standards and the main PTB group of Weston cells. It is assumed that the noise in all four set-ups - the PTB 1 V set-up, the Zener reference, the PTB Weston cell group, and the DFM MJJ set-up - are uncorrelated and hence can be estimated independently and added quadratically.

Zener reference measured in a round robin with the PTB 2000-junction Josephson voltage standard, the DFM multi-junction Josephson set-up, and the main group of Weston cells at PTB. The latter measurements were each repeated three times and the bars indicate the mean and standard deviation of each comparison. The results are not corrected for thermal voltage in the long line connecting the room with the main group of Weston cells. When averaging over all measurements, we find a mean value of 1.018 647 624 V with a standard deviation of 11 nV. The large systematic difference of 69 nV between the Zener reference output and the average output of the main group is due to the long term drift of the Weston cells in the main group against the fictitious output voltage V, (cf. Fig. IO). For practicability in standard calibration procedures, V, is fitted to the measured output voltage only when the values differ by more than 100nV. This was done at the end of 1988 (Fig. IO). At the time when the comparison described here was made, V, was 69 nV larger than the average output voltage of the main group as measured with the Josephson series-array. This is just the systematic difference of 69 nV in Fig. 13. The calibration of a Zener reference with the PTB Josephson voltage standard has a total uncertainty of 8.1 nV at a bandwidth of 0.1 Hz (Table 2a). The standard deviation in the measurements with the DFM MJJ set-up derived from 120 readings of the HP digital voltmeter with an integration time of 0.5 s was 9-14 nV for a single reading, reflecting the noise of the digital voltmeter. With a total integration time of 60 s for the 120 readings, the uncertainty for the DFM MJJ set-up amounts to less than 2 nV. For the comparison between the two Josephson standards, the real problem in using the Zener reference as transfer standard is the observed 20 nV peak-to-peak fluctuation (dashed line in Fig. 13),presumably caused by thermal disturbances when people left or entered the shielded room. This thermal voltage may be in the line

4. Results and Discussion

The results obtained with the scheme shown in Fig. 7 b are given in Fig. 13. The vertical axis is the voltage of the

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1,018 647 640

>

v

620

W

0 U

3

600

9 W

za

580

a W a

560

0 W U

W

5 N

540

9

10

11

12

13

14

15

TIME ( HOURS )

Fig. 13. Intercomparison between two Josephson array voltage standards and the main group of Weston cells at the PTB. Plotted is the voltage across the nominal 1.018 647 V terminals of a Zener reference (Fluke 732A, PTB 358) measured with the (triangles) PTB 2002-junction chip, (squares) D F M N I S T 3020-junction array and (circles) the main Weston cell group at the PTB. See Scheme 2 in Fig. 7. The voltage differences between sequential pairs of measurements of the

two Josephson array standards were only 1-2 nV. This confirms the uncertainty budget of the intercomparison. The difference of 69 nV between the Zener output voltages calibrated with the series array standards on one hand and with the main group on the other is due to the uncorrected difference between the calibrated output voltage of the main group and the assumed output voltage V ,

to the Zener reference, in the terminals themselves, in the resistive divider, or even in the temperature stabilization of the Zener element. From the fact that the voltage difference between successive measurements with the two Josephson standards differs by only 1-2 nV, we infer that the comparison corroborates the uncertainty budgets for the two very different set-ups. From a direct calculation of the data we find that the two Josephson array voltage standards agree within 0.68 nV (difference between the averages of the two sets of measurements) with a standard deviation of 6.0 nV. This standard deviation is derived by averaging over all measurements at the Zener reference, which means that the uncertainties related to the Zener drift and the e.m.f. drift between the actual measurements are included. Because the difference between a pair of measurements, one carried out with the PTB array standard the other one with the D F M MJJ set-up, is much smaller (except for the first two pairs, where a large delay between the measurements has to be considered), the reproducibility of both series-array standards is considered to be much better than 6 nV (rems.of the D F M array set and the PTB array set of measurements). The standard deviation of the differences between the two sequential points of a pair of measurements is only 2.5 nV if all measurements are included. If the first measurement is omitted, this value falls to only 1.4 nV. This result appears inconsistent with the 8 nV standard deviation of the Zener calibration with the PTB array standard. This figure, however, is valid for a bandwidth of 0.1 Hz, which corresponds to an integration time of about 2 s. During the present measurements a precise zero adjustment of the nanovoltmeter was performed manually by tuning the drive frequency. A complete adjustment extended over a time period of about 20 s. If this is considered to be the effective integration time it gives a

standard deviation for a Zener diode calibration with the PTB array standard of about 2.5 nV. This is in good agreement with the experimental results. 5. Conclusions

The D F M multi-junction Josephson standard including the 3020-junction NIST 235-05 chip is a stable and practical instrument for calibrating Zener references and Weston cells. It is compact and easy to transport by car, making it also a good candidate as a transfer standard for audits and comparisons at the primary level. The intercomparison between the PTB 2002-junction array Josephson standard and the D F M MJJ set-up showed an agreement at the level of a few nanovolts using a Zener reference as transfer standard. We also tried to make a direct comparison between these very different Josephson standards, as only a direct comparison between series-array voltage standards would allow the reproducibility of this type of instrument to be determined without being influenced by less accurate voltage sources like Zener references or Weston cells. Our first attempt at the PTB in January 1989 was frustrated by incompatible ground connections. It is important to repeat the experiment and possibly also to compare two single-junction Josephson voltage standards. A comparison at the DFM between a copy of the Finnish single-junction standard [3] and the D F M MJJ set-up is planned for the near future. A similar comparison has already been made at the PTB [19]. An interesting application of the 1- 10 V series-array is its use as a precision potentiometer for calibrating the linearity of the new 8 %-digit digital voltmeters, measuring the voltage across quantum Hall-effect samples . .. etc. The array may also

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be used as a precision voltage source with multiple outputs that can be tuned quasi-continuously from, say, 0.2-10 V with fixed and, in principle, infinitely accurate ratios. Acknowledgements. This work was funded by the Danish Research Academy and the National Metrology Council of Denmark. The DFM group is indebted to H. Nilsson, Statens Proveningsanstalt, Boris, Sweden for lending us the Weston cell enclosure used in the noise measurements. We gratefully acknowledge the assistance of C. Hamilton in establishing the DFM MJJ set-up. We also would like to thank Francis L. Lloyd and C. Hamilton for preparing the NIST chip of the DFM set-up.

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5. T. Endo, M. Koyanagi, A. Nakamura: IEEE Trans. Instr. Meas. IM-32, 267 (1983) 6. M. T. Levinsen, R. Y. Chiao, M. J. Feldmann, B. A. Tucker: Appl. Phys. Lett. 31, 776 (1977) 7. R. L. Kautz: Appl. Phys. Lett. 36, 386 (1980); R. L. Kautz: J. Appl. Phys. 52,3528 (1981);R. L. Kautz: J. Appl. Phys. 62,198 (1987) 8. N. E Pedersen, A. Davidson: Appl. Phys. Lett. 39, 830 (1981) 9. J. Niemeyer, J. H. Hinken, R. L. Kautz: Appl. Phys. Lett. 45,478 (1984) 10. J. Niemeyer, L. Grimm, W. Meier, J. H. Hinken, E. Vollmer: Appl. Phys. Lett. 45, 478 (1984) 11. E L. Lloyd, C. A. Hamilton, J. A. Beall, D. Go, R. H. Ono, R. E. Harris: IEEE Electron Device Lett. EDL-8, 449 (1987) 12. E L. Lloyd, C. A. Hamilton, K. Chieh: Proc. CPEM/88,8 (1988) 13. J. Niemeyer, Y. Sakamoto, E. Vollmer, J. H. Hinken, A. Shoji, S . Takada, S . Kosaka: Jpn. Journ. Appl. Phys. 25, L343 (1986) 14. J. Niemeyer, L. Grimm: Metrologia 25, 135 (1988) 15. C. A. Hamilton, R. L. Kautz, E L. Lloyd, R. L. Steiner, B. F. Field: IEEE Trans. Instr. Meas. IM-36, 258 (1987) 16 K. Becker, E Melchert: PTB-Mitteilungen 86, 248-252 (1976) 17 C. A. Hamilton: Series Array Voltage Standard, Theory and Operating Instruction, preprint (1987) 18. J. -Niemeier, V. Sienknecht, L. Grimm, E W. Dunschede, E. Ausbuttel , H. Seppa, P. Immonen: to be published