The unit Ampere (A) for the electric current, named after the French physicist André-Marie Ampère (1775 - 1836), is one of the seven traditional basic units in the International System of Units (SI).
In the historical development of the SI, since 1948 the ampere was defined by the force effect between two conductors through which current flows. This "classical" definition based on electromagnetism implicitly established the value for the magnetic constant μ0 = 4 π.10-7 H.m-1 = 4π.10-7 m.kg.s-2.A-2. Direct practical implementations of the ampere according to this SI definition were based on complex electro-mechanical apparatus such as e.g. the "current balance". The accuracy of such realizations was limited to a few parts in ten million, insufficient for the requirements of modern metrology.
According to recommendations of the CIPM (International Comité des Poids et Mesures), since 1990 all electrical voltage and resistance calibrations were related to the electrical quantum standards for the electrical voltage, i.e. the Josephson effect, and for the electrical resistance, i.e. the quantum Hall effect. Exactly fixed numerical values for the Josephson constant related to the Josephson effect (KJ-90 = 483 597.9 GHz/V90) and for the von-Klitzing constant related to the quantum Hall effect (RK-90 = 25 812.807 Ω90) were introduced.
The use of these "conventional" reference values for the von-Klitzing and Josephson constants had considerable practical advantages in terms of maintenance and dissemination of the electrical units. It enabled reproducing the electrical units with significantly improved accuracy of down to one part in a billion. However, it also meant that the electrical units derived from the "conventional" units V90 and Ω90 were no longer compliant with the valid International System of Units (SI).
On May 20, 2019, a revision of the SI came into force according to which SI values for the Josephson constant KJ = 2e/h and for the von-Klitzing constant RK = h/e2 using exactly defined values for the elementary charge e and the Planck constant h are derived. Thus, the realization of the ohm and the volt within the SI is now possible by using the corresponding quantum effects. By using the relationship I = U / R or 1 A = 1 V/Ω, respectively (i.e. "Ohm’s law"), the electrical current or the unit ampere can be traced to the two electrical quantum effects for the volt and the ohm indirectly, but in full conformity to the SI.
The SI revision of 2019 in principle offers yet another possibility for the direct realization of the ampere, which is based on the exact value for the elementary charge e. This uses the definition of the current I as amount of charge ΔQ transported through a conductor per unit time Δt, i.e. I = ΔQ/Δt. Understanding the transported charge as the number N of charge carriers with the charge e (e.g. electrons), one obtains I = N∙e/Δt or I = N∙e∙f, respectively, with f being the frequency of the electrons passing a cross section of the conductor. This gives the possibility of directly and elegantly realizing the current or the ampere by "counting" the number of electrons that pass through one conductor cross section per second. A corresponding implementation is possible by means of single-electron pumps, producing electrical currents via the clocked, controlled transport of single electrons. These currents are - due to physical limitations of the pumps - currently still very small (less than 1 nm = 10-9 A). In addition, the single-electron transport is subject to errors caused by statistical fluctuations. Therefore, the control of the single-electron transport by "counting" of error events is necessary. This is possible by single-electron transistors.
For further reading:
- H. Scherer and H. W. Schumacher, “Single-Electron Pumps and Quantum Current Metrology in the Revised SI,” Ann. Phys., vol. 531, no. 5, p. 1800371, 2019.