TOPIC 2

Josephson voltage standards

are based on an effect predicted in 1962 by Brian D. Josephson, a 22-year-old British student (Nobel prize in 1973).

This effect can be observed if a so called Josephson junction (two weakly coupled superconductors, e.g. two superconductors separated by an insulating layer of a few nanometers in thickness) is irradiated with microwaves.

Josephson voltage standards

Steps of constant voltage can be observed on the current-voltage characteristic of the junction:

fe

hnU

2n

where f is frequency of the microwaves,n = 1, 2, 3, ... is the step number, h is the Planck constant and

e ist the elementary charge.

Josephson voltage standards

The distance between neighbouring steps is approximately 145 µV for a typical microwave frequency of 70 GHz.

The term Josephson constant KJ is used for the quotient 2e/h . A conventional value of

KJ-90 = 483 597,9 GHz/V

has been adopted for it beginning 1 January 1990.

Josephson voltage standards

By means of Josephson junctions, voltages can be reproduced with relative uncertainties of less than one part in 1010.

Large series arrays consisting of several tens of thousands of Josephson junctions are fabricated for voltages up to more than 10 V.

Quantum Hall effect

has been discovered in 1980 by Klaus von Klitzing (Nobel prize 1985) as a result of a study of the behaviour of field effect transistors at helium temperatures and in high magnetic fields.

In contradistinction to the discovery of the Josephson effect, for which a theoretical prediction existed, the discovery of the quantum Hall effect was a triumph of experimental physics.

Quantum Hall effect

At the European High Magnetic Field Laboratrory in Grenoble, K. v. Klitzing used water-cooled copper coils with a power supply of 10 MW to generate magnetic flux densities up to 25 T.

At present, superconducting solenoids are routinely used for generating such fields at many laboratories worldwide.

QHE devices

S G D

S D

Longitudinal resistance Rx = Ux / I

Hall resistance RH = UH / I

QHE devices

In case of GaAs heterostructures, the insulator (SiO2) is replaced by a semiconductor with a large energy gap (e.g. Al0.3Ga0.7As).

Ionized donors in this semiconductor act as a positive gate voltage, so that a 2DEG may be present in the structure even if no external gate voltage is applied.

Longitudinal resistanceas function of magnetic flux

density

T = 2.2 K T = 1.6 K

0 1 2 3 4 5 6 7 8 9 10 110

200

400

600

800

1000

1200

1400

Long

itudi

nal r

esis

tanc

e [Ω

]

Magnetic flux density [T]

Negligibly small longitudinal resistance indicates a dissipationless regime.

Hall resistanceas function of magnetic flux

density

0 1 2 3 4 5 6 7 8 9 10 110

2

4

6

8

10

12

14

T = 2.2 K T = 1.6 K

Hal

l res

ista

nce

[kΩ

]

Magnetic flux density [T]

Quantized Hall resistance

RH ( 1 ) 25 812.8

RH ( 2 ) 12 906.4

RH ( 3 ) 8 604.3

RH ( 4 ) 6 453.2

etc.

i RH ( i ) = const,

i = 1, 2, 3, ...

Von Klitzing constant

where i is the plateau number,

e is the electron charge and

h is the Planck constant.

A conventional value of

RK-90 = 25 812.807 Ω

has been adopted for RK beginning 1 January 1990.

RK = i RH ( i ) = h / e2

Thompson-Lampard'scross-capacitor (TLC)

Cross-capacitor

In case of symmetry,

2ln0//2

/1

CCC

where the electric constant

Magnetic constant0 = 4 x 10 -7 H/m (exactly),

speed of light in vacuumc0 = 299 792 458 m/s (exactly),

and so

C / = 1.953 549 043 ... pF/m

200

0c

1

Cross-capacitor

The effect of possible unsymmetry:

Cross-capacitor

l /CΔC

Measurement of l by means of a built-in Fabry-Perot interferometer.

C-bridge Cx

CSIRO-NMLcross-capacitor

Equivalent circuits of resistance standards

Rs j Xs

Rp

j Xp

Gp

j Bp

Equivalent circuits of capacitance standards

Rs Cs

Cp

Rp

Cp

Gp

Dissipation (power, loss) factor

Equivalent circuits of inductance standards

Rs Ls

Lp

Rp

Dissipation and quality factor

Lp

p

s

sL

1tan

QR

L

L

R

L2

sp

L2

L2

sp

tan1

tan

tan1

LL

RR

Calculable resistors

are resistors constructed in such a way that frequency dependences of their values can be calculated, with a sufficient accuracy, from the knowledge of their constructional parameters.In these calculations, changes in resistance due to parasitic inductances and capacitances, as well as changes due to eddy currents have to be evaluated.

12 906 Ω quadrifilar resistor

Resistive element made of bare Nikrothal wire, 20 μm in diameter. Distance between adjacent parts of the wire 10 mm, folded length 730 mm. Inner diameter of the copper shield 103 mm, its wall thickness 2.5 mm.

12 906 Ω octofilar resistor

Wire radius 10 μm

Distance betweenadjacent wire elements

15 mm

Folded length ofresistive element

358 mm

Inside shield radius 51 mm

Shield thickness 2.6 mm

Frequency characteristics of the 12 906 Ω resistors

QF: quadrifilar versionOF: octofilar version

AC-DC difference = relative change of the parallel equivalent resistance from the DC value

Hamon transfer standards

C0 P0 C2 P2 Cn Pn

C1 P1 C3 P3 Cn-1 Pn-1

R1 R2

R3 Rn

Interconnection by means of zero-resistance four-terminal junctions:

Hamon transfer standards

Ca Pa

CbPb

Conversion of the array to a parallel connection by adding four "terminal fans".

Hamon transfer standards

where

A 1000 Ω / 10 ΩHamon transfer standard

Pa

Ca

Cb

Pb

equipped with 2 shorting barsand two compensation networks

Rnom = 100 Ω

r of the order of 1 Ω