Work function

low-work-function
In solid-state physics, the work function (sometimes spelled workfunction) is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface.wikipedia
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Contact electrification

contact tensioncontact potentialcontact electricity
;Contact electrification: If two conducting surfaces are moved relative to each other, and there is potential difference in the space between them, then an electric current will be driven.
Although it was later found that these effects were caused by different physical processes - triboelectricity, the Volta effect, differing work functions of metals, and others - at the time they were all thought to be caused by a common 'contact electrification' process.

Field electron emission

field emissionfield emittersCold emission
Absolute methods employ electron emission from the sample induced by photon absorption (photoemission), by high temperature (thermionic emission), due to an electric field (field electron emission), or using electron tunnelling.
Field emission in pure metals occurs in high electric fields: the gradients are typically higher than 1 gigavolt per metre and strongly dependent upon the work function.

Hot cathode

thermionic cathodecathode poisoningfilament
Thermionic emission: In thermionic electron guns, the work function and temperature of the hot cathode are critical parameters in determining the amount of current that can be emitted. Tungsten, the common choice for vacuum tube filaments, can survive to high temperatures but its emission is somewhat limited due to its relatively high work function (approximately 4.5 eV). By coating the tungsten with a substance of lower work function (e.g., thorium or barium oxide), the emission can be greatly increased. This prolongs the lifetime of the filament by allowing operation at lower temperatures (for more information, see hot cathode).
This energy is called the work function of the metal.

Schottky barrier

SchottkySchottky contactSchottky (rectifying) contact
Band bending models in solid-state electronics: The behavior of a solid-state device is strongly dependent on the size of various Schottky barriers and band offsets in the junctions of differing materials, such as metals, semiconductors, and insulators. Some commonly used heuristic approaches to predict the band alignment between materials, such as Anderson's rule and the Schottky-Mott rule, are based on the thought experiment of two materials coming together in vacuum, such that the surfaces charge up and adjust their work functions to become equal just before contact. In reality these work function heuristics are inaccurate due to their neglect of numerous microscopic effects. However, they provide a convenient estimate until the true value can be determined by experiment.
To a first approximation, the barrier between a metal and a semiconductor is predicted by the Schottky-Mott rule to be proportional to the difference of the metal-vacuum work function and the semiconductor-vacuum electron affinity.

Kelvin probe force microscope

Kelvin ProbeForce-probe techniqueskelvin probe force microscopy
Relative methods make use of the contact potential difference between the sample and a reference electrode. Experimentally, either an anode current of a diode is used or the displacement current between the sample and reference, created by an artificial change in the capacitance between the two, is measured (the Kelvin Probe method, Kelvin probe force microscope).
With KPFM, the work function of surfaces can be observed at atomic or molecular scales.

Thermionic emission

thermionicthermionicsthermionic phenomenon
Thermionic emission: In thermionic electron guns, the work function and temperature of the hot cathode are critical parameters in determining the amount of current that can be emitted. Tungsten, the common choice for vacuum tube filaments, can survive to high temperatures but its emission is somewhat limited due to its relatively high work function (approximately 4.5 eV). By coating the tungsten with a substance of lower work function (e.g., thorium or barium oxide), the emission can be greatly increased. This prolongs the lifetime of the filament by allowing operation at lower temperatures (for more information, see hot cathode). Generally, these measurements involve fitting to Richardson's law, and so they must be carried out in a low temperature and low current regime where space charge effects are absent.
This occurs because the thermal energy given to the carrier overcomes the work function of the material.

Metal–semiconductor junction

metal-semiconductor junctionSchottky junctioncontact metallization
Band bending models in solid-state electronics: The behavior of a solid-state device is strongly dependent on the size of various Schottky barriers and band offsets in the junctions of differing materials, such as metals, semiconductors, and insulators. Some commonly used heuristic approaches to predict the band alignment between materials, such as Anderson's rule and the Schottky-Mott rule, are based on the thought experiment of two materials coming together in vacuum, such that the surfaces charge up and adjust their work functions to become equal just before contact. In reality these work function heuristics are inaccurate due to their neglect of numerous microscopic effects. However, they provide a convenient estimate until the true value can be determined by experiment.
The Schottky–Mott rule of Schottky barrier formation predicts the Schottky barrier height based on the vacuum work function of the metal relative to the vacuum electron affinity (or vacuum ionization energy) of the semiconductor:

Volta potential

contact potential differencecontact potentialcontact (Volta) potential
Relative methods make use of the contact potential difference between the sample and a reference electrode. Experimentally, either an anode current of a diode is used or the displacement current between the sample and reference, created by an artificial change in the capacitance between the two, is measured (the Kelvin Probe method, Kelvin probe force microscope).
The electric potential outside each material is controlled by its work function, and so dissimilar metals can show an electric potential difference even at equilibrium.

Photoelectric effect

photoelectricphotoelectronphotoemission
The photoelectric work function is the minimum photon energy required to liberate an electron from a substance, in the photoelectric effect.
In the photoemission process, if an electron within some material absorbs the energy of one photon and acquires more energy than the work function (the electron binding energy) of the material, it is ejected.

Fermi level

electron chemical potentialFermi ''levelFermi energy
is the Fermi level (electrochemical potential of electrons) inside the material.
The source of this vacuum potential variation is the variation in work function between the different conducting materials exposed to vacuum.

Band bending

band-bendingband-bending diagrambending of the band energies
Band bending models in solid-state electronics: The behavior of a solid-state device is strongly dependent on the size of various Schottky barriers and band offsets in the junctions of differing materials, such as metals, semiconductors, and insulators. Some commonly used heuristic approaches to predict the band alignment between materials, such as Anderson's rule and the Schottky-Mott rule, are based on the thought experiment of two materials coming together in vacuum, such that the surfaces charge up and adjust their work functions to become equal just before contact. In reality these work function heuristics are inaccurate due to their neglect of numerous microscopic effects. However, they provide a convenient estimate until the true value can be determined by experiment.
At the junction of a conductor and vacuum, the vacuum level (from vacuum electrostatic potential) is set by the material's work function and Fermi level. This also (usually) applies for the junction of a conductor to an insulator.

Electric current

currentcurrentselectrical current
If these electrons are absorbed by another, cooler material (called the collector) then a measurable electric current will be observed.
Thermionic emission occurs when the thermal energy exceeds the metal's work function, while field electron emission occurs when the electric field at the surface of the metal is high enough to cause tunneling, which results in the ejection of free electrons from the metal into the vacuum.

Space charge

Child-Langmuir charge (space charge)Child-Langmuir lawMott–Gurney law
Generally, these measurements involve fitting to Richardson's law, and so they must be carried out in a low temperature and low current regime where space charge effects are absent.
φ = work function of the cathode,

Thorium

Ththorium-232thoriated
Thermionic emission: In thermionic electron guns, the work function and temperature of the hot cathode are critical parameters in determining the amount of current that can be emitted. Tungsten, the common choice for vacuum tube filaments, can survive to high temperatures but its emission is somewhat limited due to its relatively high work function (approximately 4.5 eV). By coating the tungsten with a substance of lower work function (e.g., thorium or barium oxide), the emission can be greatly increased. This prolongs the lifetime of the filament by allowing operation at lower temperatures (for more information, see hot cathode).
A small addition of thorium to tungsten thermocathodes considerably reduces the work function of electrons; as a result, electrons are emitted at considerably lower temperatures.

Ruthenium

RuRu(NH 3 ) 6 3+ ruthenate
When replacing silicide gates with metal gates in MOSFETs, a key property of the metal is its work function.

Surface states

surface statelocalized stateShockley states
In reality, however, the energies of the bands near the surface are often pinned to the Fermi level, due to the influence of surface states.
The dipole perturbs the potential at the surface leading, for example, to a change of the metal work function.

Electron affinity

affinityelectron affinitiesaffine
This spacing is called the electron affinity (note that this has a different meaning than the electron affinity of chemistry); in silicon for example the electron affinity is 4.05 eV. If the electron affinity E EA and the surface's band-referenced Fermi level E F -E C are known, then the work function is given by
The electron affinity of a surface is closely related to, but distinct from, its work function.

Jellium

homogeneous electron gasuniform electron gasfree electron gas
One of the earliest successful models for metal work function trends was the jellium model, which allowed for oscillations in electronic density nearby the abrupt surface (these are similar to Friedel oscillations) as well as the tail of electron density extending outside the surface.
Semi-infinite jellium slabs are used to investigate surface properties such as work function and surface effects such as adsorption; near surfaces the electronic density varies in an oscillatory manner, decaying to a constant value in the bulk.

Solid-state physics

solid-statesolid statesolid-state physicist
In solid-state physics, the work function (sometimes spelled workfunction) is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface.

Work (thermodynamics)

workthermodynamic workpressure-volume work
In solid-state physics, the work function (sometimes spelled workfunction) is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface.

Electron

electronse − electron mass
In solid-state physics, the work function (sometimes spelled workfunction) is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface.

Vacuum

free spaceevacuatedhigh vacuum
In solid-state physics, the work function (sometimes spelled workfunction) is the minimum thermodynamic work (i.e., energy) needed to remove an electron from a solid to a point in the vacuum immediately outside the solid surface.

Electric potential

electrical potentialelectrostatic potentialpotential
is the electrostatic potential in the vacuum nearby the surface, and

Electrochemical potential

electrochemical driving forceelectrochemical potential differencepotential
is the Fermi level (electrochemical potential of electrons) inside the material.

Voltmeter

Digital voltmetervolt metervoltmeters
is the voltage of the material (as measured by a voltmeter, through an attached electrode), relative to an electrical ground that is defined as having zero Fermi level.