Bez nadpisu

1

• TOPIC 2

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.

3
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.
4
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.

5
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.

6
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.

7
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.

8
QHE devices

Longitudinal resistance Rx Ux / I Hall
resistance RH UH / I
9
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.

10
Longitudinal resistance

• as function of magnetic flux density

Negligibly small longitudinal resistance
indicates a dissipationless regime.
11
Hall resistance

• as function of magnetic flux density

12
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, ...

13
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 O
• has been adopted for RK beginning 1 January 1990.

14
Thompson-Lampard'scross-capacitor (TLC)

15
Cross-capacitor
In case of symmetry,

where the electric constant
Magnetic constant ?0 4 ? x 10 -7 H/m
(exactly), speed of light in vacuum c0 299 792
458 m/s (exactly), and so C / 1.953 549 043
... pF/m
16
Cross-capacitor
The effect of possible
unsymmetry

17
Cross-capacitor

Measurement of ? l by means of a built-in
Fabry-Perot interferometer.
18
CSIRO-NMLcross-capacitor

19
Equivalent circuits of resistance standards

20
Equivalent circuits of capacitance standards

Dissipation (power, loss) factor
21
Equivalent circuits of inductance standards

Dissipation and quality factor
22
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.
23
12 906 O 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.
24
12 906 O octofilar resistor
25
Frequency characteristics of the 12 906 O
resistors
QF quadrifilar version OF octofilar version
AC-DC difference relative change of the
parallel equivalent resistance from the DC value
26
Hamon transfer standards
Interconnection by means of zero-resistance
four-terminal junctions
27
Hamon transfer standards
Conversion of the array to a parallel connection
by adding four "terminal fans".
28
Hamon transfer standards
where
29
A 1000 O / 10 OHamon transfer standard
equipped with 2 shorting bars and two
compensation networks
Rnom 100 O r of the order of 1 O