In physics, a Coulomb blockade, named after Charles-Augustin de Coulomb, is the increased resistance at small bias voltages of an electronic device comprising at least one low-capacitance tunnel junction. Charles Augustin de Coulomb (born June 14, 1736, Angoulême, France - died August 23, 1806, Paris) was a French physicist. ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... In electronics, voltage bias (sometimes simply called bias) is a steady-state voltage It is used to activate the active component like transistor transistor, coil or other source of load. ... Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ... A tunnel junction is, in its simplest form, a thin insulating barrier between two conducting electrodes. ...

A tunnel junction is, in its simplest form, a thin insulating barrier between two conducting electrodes. If the electrodes are superconducting, Cooper pairs with a charge of two elementary charges carry the current. In the case that the electrodes are normalconducting, i.e. neither superconducting nor semiconducting, electrons with a charge of one elementary charge carry the current. The following reasoning is for the case of tunnel junctions with an insulating barrier between two normalconducting electrodes (NIN junctions). An electrode is an electrical conductor used to make contact with a metallic part of a circuit (e. ... A magnet levitating above a high-temperature superconductor, cooled with liquid nitrogen. ... A Cooper pair is the name given to electrons that are bound together in a certain manner first described by Leon Cooper. ... In physics, a charge may refer to one of many different quantities, such as the electric charge in electromagnetism or the color charge in quantum chromodynamics. ... The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ... A magnet levitating above a high-temperature superconductor, cooled with liquid nitrogen. ... A semiconductor is a fuckin solid whose electrical conductivity is in between that of a metal and that of an insulator, and can be controlled over a wide range, either permanently or dynamically. ... e- redirects here. ... The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ...

Schematic representation of an electron tunnelling through a barrier

According to the laws of classical electrodynamics, no current can flow through an insulating barrier. According to the laws of quantum mechanics, however, there is a nonvanishing (larger than zero) probability for an electron on one side of the barrier to reach the other side (see quantum tunnelling). When a bias voltage is applied, this means that there will be a current flow. In first-order approximation, that is, neglecting additional effects, the tunnelling current will be proportional to the bias voltage. In electrical terms, the tunnel junction behaves as a resistor with a constant resistance, also known as an ohmic resistor. The resistance depends exponentially on the barrier thickness. Typical barrier thicknesses are on the order of one to several nanometers. Image File history File links Download high resolution version (915x650, 23 KB) Summary Schematic representation of an electron (e, right) tunnelling through a barrier of height (vertical dimension is energy) e*V_b and thickness (horizontal dimension is spatial) d_b. ... Image File history File links Download high resolution version (915x650, 23 KB) Summary Schematic representation of an electron (e, right) tunnelling through a barrier of height (vertical dimension is energy) e*V_b and thickness (horizontal dimension is spatial) d_b. ... Classical electromagnetism is a theory of electromagnetism that was developed over the course of the 19th century, most prominently by James Clerk Maxwell. ... Fig. ... Probability is the likelihood that something is the case or will happen. ... Quantum tunnelling (or tunneling) is the quantum-mechanical effect of transitioning through a classically-forbidden energy state. ... In electronics, voltage bias (sometimes simply called bias) is a steady-state voltage inserted in series with an element of an electronic device like a transistor, coil or other source of load. ... Often in science, engineering, or other quantitative disciplines, it is necessary to make approximations with various degrees of precision. ... Resistor symbols (non-European) Resistor symbols (Europe, IEC) Axial-lead resistors on tape. ... A voltage source, V, drives an electric current, I , through resistor, R, the three quantities obeying Ohms law: V = IR Ohms law states that, in an electrical circuit, the current passing through a conductor between two points is proportional to the potential difference (i. ... The exponential function is one of the most important functions in mathematics. ... A nanometre (American spelling: nanometer) is 1. ...

An arrangement of two conductors with an insulating layer in between not only has a resistance, but also a finite capacitance. The insulator is also called dielectric in this context, the tunnel junction behaves as a capacitor. Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ... A dielectric, or electrical insulator, is a substance that is highly resistant to electric current. ... See Capacitor (component) for a discussion of specific types. ...

Due to the discreteness of electrical charge, current flow through a tunnel junction is a series of events in which exactly one electron passes (tunnels) through the tunnel barrier (we neglect events in which two electrons tunnel simultaneously). The tunnel junction capacitor is charged with one elementary charge by the tunnelling electron, causing a voltage buildup U = e / C, where e is the elementary charge of 1.6×10^-19 coulomb and C the capacitance of the junction. If the capacitance is very small, the voltage buildup can be large enough to prevent another electron from tunnelling. The electrical current is then suppressed at low bias voltages and the resistance of the device is no longer constant. The increase of the differential resistance around zero bias is called the Coulomb blockade. International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ... The coulomb (symbol: C) is the SI unit of electric charge. ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ...

In order for the Coulomb blockade to be observable, the temperature has to be low enough so that the characteristic charging energy (the energy that is required to charge the junction with one elementary charge) is larger than the thermal energy of the charge carriers. For capacitances below 1 femtofarad (10^-15 farad), this implies that the temperature has to be below about 1 kelvin. This temperature range is routinely reached for example by dilution refrigerators. The farad (symbol: F) is the SI unit of capacitance. ... Examples of various types of capacitors. ... The kelvin (symbol: K) is a unit increment of temperature and is one of the seven SI base units. ... A dilution refrigerator is a cryogenic device first proposed by Heinz London. ...

To make a tunnel junction in plate condenser geometry with a capacitance 1 femtofarad, using an oxide layer of electric permeability 10 and thickness one nanometer, one has to create electrodes with dimensions of approximately 100 by 100 nanometers. This range of dimensions is routinely reached for example by electron beam lithography and appropriate pattern transfer technologies, like the Niemeyer-Dolan technique, also known as shadow evaporation technology. Permeability has several meanings: In electromagnetism, permeability is the degree of magnetisation of a material in response to a magnetic field. ... A nanometre (American spelling: nanometer) is 1. ... // Conventional electron-beam lithography The practice of using a beam of electrons to generate patterns on a surface is known as Electron beam lithography. ... Niemeyer-Dolan technique for the fabrication of single electron transistors The Niemeyer-Dolan technique, also called Dolan technique or shadow evaporation technique (the term preferred by its inventor, J. Niemeyer), is a lithographic method to create nanometer-sized overlapping structures comprised of two or more materials. ...

Another problem for the observation of the Coulomb blockade is the relatively large capacitance of the leads that connect the tunnel junction to the measurement electronics.

Single electron transistor

Schematic of a single electron transistor

Energylevels of source, island and drain (from left to right) in a single electron transistor for both the blocking state (upper part) and the transmitting state (lower part).

Single electron transistor with niobium leads and aluminium island

The simplest device in which the effect of Coulomb blockade can be observed is the so-called single electron transistor. It consists of two tunnel junctions sharing one common electrode with a low self-capacitance, known as the island. The electrical potential of the island can be tuned by a third electrode (the gate), capacitively coupled to the island. Image File history File links Set_schematic. ... Image File history File links Set_schematic. ... Image File history File links Single_electron_transistor. ... Image File history File links Single_electron_transistor. ... Image File history File links Download high resolution version (1917x958, 301 KB) Summary Single electron transistor with niobium leads and aluminium island. ... Image File history File links Download high resolution version (1917x958, 301 KB) Summary Single electron transistor with niobium leads and aluminium island. ... General Name, Symbol, Number niobium, Nb, 41 Chemical series transition metals Group, Period, Block 5, 5, d Appearance gray metallic Standard atomic weight 92. ... General Name, Symbol, Number aluminium, Al, 13 Chemical series poor metals Group, Period, Block 13, 3, p Appearance silvery Standard atomic weight 26. ... Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ...

In the blocking state no accessible energy levels are within tunneling range of the electron (red) on the source contact. All energy levels on the island electrode with lower energies are occupied.

When a positive voltage is applied to the gate electrode the energy levels of the island electrode are lowered. The electron (green 1.) can tunnel onto the island (2.), occupying a previously vacant energy level. From there it can tunnel onto the drain electrode (3.) where it inelastically scatters and reaches the drain electrode Fermi level (4.).

The energy levels of the island electrode are evenly spaced with a separation of ΔE. ΔE is the energy needed to each subsequent electron to the island, which acts as a self-capacitance C. The lower C the bigger ΔE gets. It is crucial for ΔE to be larger than the energy of thermal fluctuations k_BT, otherwise an electron from the source electrode can always be thermally excited onto an unoccupied level of the island electrode, and no blocking can be observed.

Coulomb Blockade Thermometer

A typical Coulomb Blockade Thermometer (CBT) is made from an array of metallic islands, connected to each other through a thin insulating layer. A tunnel junction forms between the islands, and as voltage is applied, electrons may tunnel across this junction. The tunneling rates and hence the condutance vary according to the charging energy of the islands as well as the thermal energy of the system.

Coulomb Blockade Thermometer is a primary thermometer based on electric conductance characteristics of tunnel junction arrays. The parameter V_½=5.439Nk_BT/e, the full width at half minimum of the measured differential conductance dip over an array of N junctions together with the physical constants provide the absolute temperature. It has been suggested that List of temperature sensors be merged into this article or section. ... In science, a physical constant is a physical quantity whose numerical value does not change. ...

Literature

• T. Henning, Charging effects in niobium nanostructures, PhD thesis, Mikroelektronik och Nanovetenskap, Chalmers Tekniska Högskola AB och Göteborgs Universitet, Göteborg/Sweden, 1999. Full text available online [1] as www.arxiv.org e-print cond-mat/9901308.

• D.V. Averin and K.K Likharev Mesoscopic Phenomena in Solids, edited by B.L. Altshuler, P.A. Lee, and R.A. Webb (Elsevier, Amsterdam, 1991)

• J. P. Pekola, K. P. Hirvi, J. P. Kauppinen, and M. A. Paalanen, Thermometry by Arrays of Tunnel Junctions, Phys. Rev. Lett. 73, 2903 (1994).

External links

• NACARDIO - European Commission FP6 Programme