Topic Name: Important Milestone on the Way to the Setup of a New Standard for Capacitance using a Single-Electron Pump
Research persons: PTB Scientists
Location: Physikalisch-Technische Bundesanstalt (PTB), Germany
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
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.
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