**Name of the standard:** National standard of DC electrical resistance

**Code name:** ECM 230-1/08-043

**Year of announcement:** 2008

**Workplace:** department 1011 ČMI OI Praha

**Guarantor:** Ing. Jan Kučera, Ph.D.

**Number of CMC lines to be provided:** 3

The national standard of DC electrical resistance is a standard of the highest metrological quality and serves as a basis for ensuring the uniformity of all other standards of the relevant quantity in the country.

Expanded uncertainties of the national standards members:

Quantity | Nominal value | Rel. uncertainty (k = 2) |
---|---|---|

DC electrical resistance | 1 Ω | 0.060 μΩ/Ω |

DC electrical resistance | 100 Ω | 0.012 μΩ/Ω |

DC electrical resistance | 10 kΩ | 0.034 μΩ/Ω |

The quantum Hall effect (QHE), together with high-temperature superconductivity, represent the two greatest discoveries in solid-state physics in the last 20 years of the last century. The main application of QHE is in metrology, as it allows the realization of an accurate, perfectly stable and highly reproducible quantum standard of electrical resistance. The quantum Hall effect was discovered by Klaus von Klitzing while investigating the electron transport properties of silicon, field-effect Si-MOSFET transistors at very low temperatures *(T *< 0.1 K) and in strong magnetic fields (*B *= 18 T).

Starting from 1 January 1990, it is recommended to all member countries of *the General Conference on Weights and Measures (CGPM)*, i.e. also the Czech Republic, to link their national electrical resistance standards to quantum standards. The uniformity of measurements in different countries and at the same time the most accurate possible agreement of the resistance unit obtained in this way with the ohm, defined in the SI system, is achieved by introducing the exact value of the *von Klitzing constant R*_{K}. In the integer QHE mode, the following relation applies to the value of the Hall resistance in the *i-th *plateau region:

Thus, the value of the Hall resistance of the quantum structure inside the QHE plateau is determined only by the fundamental natural constants *h *(Planck's constant) and *e *(the charge of the electron).

*R*_{H }is the Hall resistance, the quantity *h/e ^{2}* is called the

*von Klitzing constant, i*is the plateau number. For metrology purposes, based on the redefinition of SI units as of 20 May 2019, the value of the von Klitzing constant from which the value of the quantum Hall resistance on the second plateau is derived is in accordance with CODATA 2018 and is:

*R*_{H} (2) = 12 906.403 73 Ω

*R*_{H} (i) = *R*_{K} /i = 25 812.807 459 3045 Ω

In practice, the reference values *R*_{H } (2) and *R*_{H } (4) are used:

*R*_{H} (2) = *R*_{K} /2 = 12 906.403 73 Ω

*R*_{H} (4) = *R*_{K} /4 = 6 453.201 86 Ω

The national DC electrical resistance standard is derived from the primary quantum standard using a cryogenic current comparator (CCC) or the MI 6010 Q automatic resistance bridge.

The basic element of the primary quantum standard is a semiconductor structure that exhibits QHE at very low temperatures (0.35 K to 4.2 K) and strong magnetic field in the cryostat of the CRYOGENIC QHR 2010 system with a superconducting magnet (10 T). Through long-term theoretical and experimental work in 2003-2008, the etalon was prepared for the announcement of the national standard, which was successfully established in 2008.

The next stage of building the primary DC electrical resistance metrology includes theoretical and experimental work carried out since September 2014 after the delivery of the new cryogenic current comparator and the related electronics from MAGNICON. On the basis of the Proposal for approval of the update of the state standard (No. 1011-ZV-C0001-16), a successful defense of the update of the national standard with the new MAGNICON measurement system was carried out on January 24, 2017. Next update of the national standard related to redefinition of SI units, name of the standard and storage conditions was carried out on January 6, 2020.

The assembly of the national standard:

- CRYOGENIC QHR 2010 measuring system with a cryostat with a superconducting magnet, with a semiconductor (quantum) structure and a cryogenic current comparator MAGNICON CCC-1.
- MI 6010 Q (Quant Ω) Automatic Ratio Resistance Bridge.
- A set of classical DC electrical resistance standards of nominal values 1 Ω, 100 Ω, 10 kΩ.

Resistance standards of nominal value 1 Ω (2 pcs) of classical design, type NML, manufacturer CSIRO (Australia) are placed in a low ohmic DC electrical resistance laboratory in an oil thermostat at a temperature of (23.00 ± 0.02)ºC.

Resistance standard of nominal value 100 Ω of classical design, type 5685A, manufactured by Tinsley (England) is located in the primary quantum laboratory of the DC electrical resistance in the air thermostat of the QHR 2010 measuring system at a temperature of 31.500 ºC with a mid-term stability of ±0.005 ºC.

A resistance standard of nominal value 10 kΩ of classical design, type SR 104, manufacturer ESI (USA) is placed in a low ohmic DC electrical resistance laboratory in an air thermostat at a temperature of (23.00 ± 0.05)ºC.

The linkage of all members of the national resistance standard (1 Ω, 100 Ω, 10 kΩ) is carried out 1 to 2 times a year by sequential transfer of the value from the Hall resistance of the quantum structure on the 2nd plateau to the individual members of the national standard, by measuring the ratio of resistances, by means of classical reference resistance standards of 10 Ω and 1000 Ω values, using the CCC or the classical automatic ratio resistance bridge MI 6010 Q (Quant Ω).

Other metrological characteristics of the national standard:

**Implementation of QHR**

QHR value | Rel. uncertainty (k = 2) |
---|---|

R_{H} (2) | 0.0040 μΩ/Ω |

**Resistance ratios using CCC-1**

Measured ratios | Rel. uncertainty (×10^{-6} ) (k = 2) |
---|---|

100Ω / R_{H} (2) | 0.011 |

1Ω /100 Ω | 0.0066 |

10 kΩ /100 Ω | 0.0084 |

**Resistance ratios with MI 6010Q**

Measured ratios | Rel. uncertainty (×10^{-6} ) (k = 2) |
---|---|

1 kΩ / R_{H} (2) | 0.040 |

100Ω /1 kΩ | 0.040 |

10 kΩ /1 kΩ | 0.040 |

10Ω /100 Ω | 0.040 |

1Ω /10 Ω | 0.040 |

Between 2003 and 2017, the national standard successfully participated in key comparisons under the KCDB:

2004: EUROMET EM-K10: 100 Ω

2007 to 2008: BIPM.EM-K13.a: 1 Ω

2008: BIPM.EM-K13.b: 10 kΩ

2015: BIPM.EM-K13.a: 1 Ω, BIPM.EM-K13.b: 10 kΩ

2017: BIPM.EM-K12: On-site comparison of quantum Hall resistance realized by CMI and BIPM – realization of *R*_{H} (2) with the ratio *R*_{H} (2)*/R*_{100}Ω and the ratios *R*_{10k}Ω* /R*_{100}Ω_{, }* R*_{100}Ω* /R*_{1}Ω