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: 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 K J is used for the quotient 2e/h. A conventional value of K J-90 = ,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 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 SGD SD Longitudinal resistance R x = U x / I Hall resistance R H = U H / I

QHE devices In case of GaAs heterostructures, the insulator (SiO 2 ) is replaced by a semiconductor with a large energy gap (e.g. Al 0.3 Ga 0.7 As). 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 resistance as function of magnetic flux density T = 2.2 K T = 1.6 K Longitudinal resistance [Ω] Magnetic flux density [T] Negligibly small longitudinal resistance indicates a dissipationless regime.

Hall resistance as function of magnetic flux density T = 2.2 K T = 1.6 K Hall resistance [kΩ] Magnetic flux density [T]

Quantized Hall resistance R H ( 1 )   R H ( 2 )   R H ( 3 )   R H ( 4 )   etc. i R H ( 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 R K-90 = Ω has been adopted for R K beginning 1 January 1990.

Thompson-Lampard's cross-capacitor (TLC)

Cross-capacitor In case of symmetry, where the electric constant Magnetic constant  0 = 4  x H/m (exactly), speed of light in vacuum c 0 = m/s (exactly), and so C / = pF/m

Cross-capacitor The effect of possible unsymmetry:

Cross-capacitor Measurement of  l by means of a built-in Fabry-Perot interferometer. C-bridge CxCx

CSIRO-NML cross-capacitor

Equivalent circuits of resistance standards RsRs jXsjXs RpRp jXpjXp GpGp jBpjBp

Equivalent circuits of capacitance standards RsRs CsCs CpCp RpRp CpCp GpGp Dissipation (power, loss) factor

Equivalent circuits of inductance standards RsRs LsLs LpLp RpRp Dissipation and quality factor

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.

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.

Ω octofilar resistor

Frequency characteristics of the Ω resistors QF: quadrifilar version OF: octofilar version AC-DC difference = relative change of the parallel equivalent resistance from the DC value

Hamon transfer standards C0C0 P0P0 C2C2 P2P2 CnCn PnPn C1C1 P1P1 C3C3 P3P3 C n-1 P n-1 R1R1 R2R2 R3R3 RnRn Interconnection by means of zero- resistance four-terminal junctions:

Hamon transfer standards CaCa PaPa CbCb PbPb Conversion of the array to a parallel connection by adding four "terminal fans".

Hamon transfer standards where

A 1000 Ω / 10 Ω Hamon transfer standard PaPa CaCa CbCb PbPb equipped with 2 shorting bars and two compensation networks R nom = 100 Ω r of the order of 1 Ω