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Topic Name: Important Milestone on the Way to the Setup of a New Standard for Capacitance using a Single-Electron Pump

Category: Electronics

Research persons: PTB Scientists

Location: Physikalisch-Technische Bundesanstalt (PTB), Germany

Details

Physikalisch-Technische Bundesanstalt (PTB) scientists achieved to transfer very small charge "packets", comprising a well-defined number of few electrons, between metallic electrons precisely by using a single-electron pump. A single-electron transistor, being able to resolve charge variations of a single electron or less, served as a charge detector to monitor the charge movement. The successful experiment is an important milestone on the way to the setup of a new standard for capacitance, where a capacitor is charged by a well-known number of electrons. The corresponding voltage can be measured using a Josephson voltage standard. Tracing the capacitance to a resistance via the quantum-Hall effect finally allows the realisation of the so-called "Quantum Metrological Triangle", which establishes a link between all three electrical quantum effects. The precision aimed at in the experiment requires the demonstrated manipulation of charge on the scale of a single electron.

Task of this metrology project is the implementation of a new capacitance standard which is based on the quantization of electrical charge in units of the elementary charge e.

The basic idea of the experiment is to charge a capacitor with a well-known number of n electrons and to measure the resulting electrical voltage U. Thus, the capacitance C of the capacitor is determined by C = ne / U. Accurate "counting" of the electrons occurs with the help of a special Single-Electron Tunneling (SET) circuit, a so-called SET-pump. If the voltage U is measured by using a Josephson voltage standard (U = ifh / 2e), the capacitance C can be expressed exclusively in terms of the fundamental constants e and h, the frequency f and integer numbers (n and i). Thus, the experiment enables electrical capacitance metrology on quantum basis, as it is already usual for the electrical voltage U (using the Josephson effect) and the electrical resistance R(using the quantum Hall effect).

If the experiment is performed with a relative uncertainty of 10^-7 (0.1 ppm), it opens a way to realize the "quantum metrological triangle" which is a consistency test for the three electrical quantum effects involved. The results of this experiment will impact on a future system of units which will be based on fundamental constants.

Note for Josephson Effect
The Josephson effect is the phenomenon of current flow across two weakly coupled superconductors, separated by a very thin insulating barrier. This arrangement—two superconductors linked by a non-conducting barrier—is known as a Josephson junction; the current that crosses the barrier is the Josephson current. The terms are named after British physicist Brian David Josephson, who predicted the existence of the effect in 1962. It has important applications in quantum-mechanical circuits, such as SQUIDs.
The Josephson effect has found wide usage, for example in the following areas:
SQUIDs, or superconducting quantum interference devices, are very sensitive magnetometers that operate via the Josephson effect. They are widely used in science and engineering. (See main article: SQUID.)
In precision metrology, the Josephson effect provides an exactly reproducible conversion between frequency and voltage. Since the frequency is already defined precisely and practically by the caesium standard, the Josephson effect is used, for most practical purposes, to give the definition of a volt (although, as of July 2007, this is not the official BIPM definition).
Single-electron transistors are often constructed of superconducting materials, allowing use to be made of the Josephson effect to achieve novel effects. The resulting device is called a "superconducting single-electron transistor".

Note for Quantum Hall Effect
The quantum Hall effect (or integer quantum Hall effect) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields.
The quantization of the Hall conductance has the important property of being incredibly precise. Actual measurements of the Hall conductance have been found to be integer or fractional multiples of e2 / h to nearly one part in a billion. This phenomenon, referred to as "exact quantization", has been shown to be a subtle manifestation of the principle of gauge invariance. It has allowed for the definition of a new practical standard for electrical resistance: the resistance unit h / e2, roughly equal to 25812.8 ohms, is referred to as the von Klitzing constant RK (after Klaus von Klitzing, the discoverer of exact quantization) and since 1990, a fixed conventional value RK-90 is used in resistance calibrations worldwide. The quantum Hall effect also provides an extremely precise independent determination of the fine structure constant, a quantity of fundamental importance in quantum electrodynamics.
The integers that appear in the Hall effect are examples of topological quantum numbers. They are known in mathematics as the first Chern numbers and are closely related to Berry's phase. A striking model of much interest in this context is the Azbel-Harper-Hofstadter model whose quantum phase diagram is the Hofstadter's butterfly shown in the figure. The vertical axis is the strength of the magnetic field and the horizontal axis is the chemical potential, which fixes the electron density. The colors represent the integer Hall conductances. Warm colors represent positive integers and cold colors negative integers. The phase diagram is fractal and has structure on all scales.

About Physikalisch-Technische Bundesanstalt (PTB)
The Physikalisch-Technische Bundesanstalt (PTB) is based in Braunschweig and Berlin. It is the national institute for natural and engineering sciences and the highest technical authority for metrology and physical safety engineering in Germany.
Part of its brief is the accurate measurement of time. It is responsible for the German atomic clock DCF77.
They are also responsible for the certification of voting machines for the German federal and European elections.
The PTB was originally founded in 1887 as the Physikalisch-Technische Reichsanstalt (PTR) – 'the Reich Physical and Technical Institute'. The goal of the organization was supervising and directing calibration and establishing metrological standards. Research areas included spectroscopy, photometry, electrical engineering, and cryogenics. Werner von Siemens was instrumental in its establishment. Until 1934, the PTR was under the Reichsinnenministerium – the Reich Interior Ministry - and then under Reichserziehungsministerium – the Reich Education Ministry.
The Institute’s board of directors included Heinrich Konen and Walther Nernst circa 1930, Albert Einstein (1917 – 1933), Ludwig Prandtl, and Max Planck, as well as representative from Siemens AG, Krupp, and Zeiss. Its presidents were:
Hermann von Helmholtz (1887 – 1892)
Friedrich Kohlrausch (1892 – 1905)
Walther Nernst (1922 – 1924)
Friedrich Paschen (1924 – 1933)
Johannes Stark (1933 – 1939)
Abraham Esau (1939 – 1945).
Max von Laue was the physics advisor 1925 – December 1933.
The Institute had 292 employees 1932 and 443 in 1937. By 1942 there were over 500. After 1945, the Institute was renamed to the Physikalisch-Technische Bundesanstalt – the Federal Physical and Technical Institute.

In figure 1, The single-electron pump in our experiment (pictured above left) consists of a series of five ultra-circuit tunnel metallic contacts. This tunnel contact chain is the right to a metallic "island" electrode with a small overall capacitance C = Σ 20 fF.

With a rapid sequence of voltage pulses to the gate electrode of the pump (V1-4, the bottom of the image) is within 0.25 μ of an electron by the chain on the island pumped. The surplus electrons have a potential effect modification by about 8 μ V, which connected with the capacitive single-electron transistor (right) is demonstrated. After a waiting period, the tw surplus electron by creating a counter-voltage sequence back from the island.

In demonstrating "shuttle" operation, the successive loading and unloading of the island with one or more electrons periodically repeated. In the "off mode", the gate voltages at the single electron pump is not modulated. In the ideal case, the charge state of the island then constant, as the tunnel processes by Coulomb blockade effects are suppressed.

In figure 2, Measurements of the output signal of the single-electron transistor, converted to the electric potential of the island.
Image (a) shows the timing of the signal in the "off mode" of the single-electron pump: Apart from the noise of the single electron detector is the signal temporarily over several seconds. Adverse tunnel processes of individual electrons tunnel through the contact chain of individual electron pump cause erratic fluctuations and quantized potential of the island. The change in the island to charge an electron corresponds to a voltage change from 8 μ V. The mean time interval between these undesirable "Fehlereignissen" on the island was here 40 s.

Image (b) shows the timing signal during the course of shuttle operations, "where cargo packages from one to five electrons in the cycle of tw = 1 s and forth hergepumpt. The curves are vertically displaced. We see that the detected potential changes to the second cycle of loading and unloading the island follow, and that the signal amplitude of the number of surplus electrons on the island of proportion.