Information about Work Function
The work function is the minimum energy (usually measured in electron volts) needed to remove an electron from a solid to a point immediately outside the solid surface (or energy needed to move an electron from the Fermi energy level into vacuum). Here "immediately" means that the final electron position is far from the surface on the atomic scale but still close to the solid on the macroscopic scale. The work function is an important property of metals. The magnitude of the work function is usually about a half of the ionization energy of a free atom of the metal.
yet the two quantities are not exactly the same. This is due to the surface effect of a real-world solid: a real-world solid is not infinitely extended with electrons and ions repeatedly filling every primitive cell over all Bravais lattice sites. Neither can one simply take a set of Bravais lattice sites 
inside the geometrical region V which the solid occupies and then fill undistorted charge distribution basis into all primitive cells of . Indeed, the charge distribution in those cells near the surface will be distorted significantly from that in a cell of an ideal infinite solid, resulting in an effective surface dipole distribution, or, sometimes both a surface dipole distribution and a surface charge distribution.
It can be proven that if we define work function as the minimum energy needed to remove an electron to a point immediately out of the solid, the effect of the surface charge distribution can be neglected, leaving only the surface dipole distribution. Let the potential energy difference across the surface due to effective surface dipole be
. And let be the Fermi energy calculated for the finite solid without considering surface distortion effect, when taking the convention that the potential at 
is zero. Then, the correct formula for work function is:
Where is negative, which means that electrons are bound in the solid.
Photoelectric work function is
Thermionic emission requires a filament heating current (if), to maintain a temperature of 2000-2700 K. A saturation state of the filament current is reached, where a minor change in the filament current does not affect the beam current. The electron gun is then operated with the filament current very near the potential to overcome the work function (W)(Goldstein, 2003) The thermionic work function depends on the orientation of the crystal and will tend to be smaller for metals with an open lattice, larger for metals in which the atoms are closely packed. The range is about 1.5–6 eV. It is somewhat higher on dense crystal faces than open ones.
Methods of the first group employ electron emission from the sample induced by photon absorption (photoemission), by high temperature (thermionic emission), due to an electric field (field emission), or using electron tunnelling.
All 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).
lower than 100 eV it is able to extract only valence electrons. Due to limitations of the escape depth of electrons in solids UPS is very surface sensitive, as the information depth is in the range of 2 – 3 monolayers. At the same time the measurement principle restricts PES to be used in UHV conditions. The resulting spectrum reflects the electronic structure of the sample providing information on the density of states, the occupation of states, and the work function.
of the electrons collected by the sample depends on the work function 
of the sample and is given by the Richardson–Dushman equation 
where 
, the Richardson constant, is a specific material constant. The current density increases rapidly with temperature and decreases exponentially with the work function. Changes of the work function can be easily determined by applying a retarding potential 
between the sample and the electron emitter; is replaced by 
in above equation. The difference in the retarding potential measured at constant current is equivalent to the work function change, assuming that the work function and the temperature of the emitter is constant.
One can use the Richardson–Dushman equation directly to determine the work function by temperature variation of the sample, as well. Rearranging the equation yields
. The line produced by plotting 
vs. 
will have a slope of 
allowing to determine the work function of the sample.
Work Function and Surface Effect
Work function W of a metal is closely related to its Fermi energy level yet the two quantities are not exactly the same. This is due to the surface effect of a real-world solid: a real-world solid is not infinitely extended with electrons and ions repeatedly filling every primitive cell over all Bravais lattice sites. Neither can one simply take a set of Bravais lattice sites inside the geometrical region V which the solid occupies and then fill undistorted charge distribution basis into all primitive cells of . Indeed, the charge distribution in those cells near the surface will be distorted significantly from that in a cell of an ideal infinite solid, resulting in an effective surface dipole distribution, or, sometimes both a surface dipole distribution and a surface charge distribution.
It can be proven that if we define work function as the minimum energy needed to remove an electron to a point immediately out of the solid, the effect of the surface charge distribution can be neglected, leaving only the surface dipole distribution. Let the potential energy difference across the surface due to effective surface dipole be
. And let be the Fermi energy calculated for the finite solid without considering surface distortion effect, when taking the convention that the potential at is zero. Then, the correct formula for work function is:
Where
is negative, which means that electrons are bound in the solid.
Example
For example, Caesium has ionization energy 3.9 eV and work function 1.9 eV.Photoelectric work function
The work function is the minimum energy that must be given to an electron to liberate it from the surface of a particular metal. In the photoelectric effect if a photon with an energy greater than the work function is incident on a metal photoelectric emission occurs. Any excess energy is given to the electron as kinetic energy.Photoelectric work function is
,
Thermionic work function
The work function is also important in the theory of thermionic emission. Here the electron gains its energy from heat rather than photons. In this case, as for an electron escaping from the heated negatively-charged filament of a vacuum tube, the work function may be called the thermionic work function. Tungsten is a very common metal for vacuum tube elements, with a work function of approximately 4.5 eV.Thermionic emission requires a filament heating current (if), to maintain a temperature of 2000-2700 K. A saturation state of the filament current is reached, where a minor change in the filament current does not affect the beam current. The electron gun is then operated with the filament current very near the potential to overcome the work function (W)(Goldstein, 2003) The thermionic work function depends on the orientation of the crystal and will tend to be smaller for metals with an open lattice, larger for metals in which the atoms are closely packed. The range is about 1.5–6 eV. It is somewhat higher on dense crystal faces than open ones.
Applications
In electronics the work function is important for design of the metal-semiconductor junction in Schottky diodes and for design of vacuum tubes.Measurement
Many techniques have been developed based on different physical effects to measure the electronic work function of a sample. One may distinguish between two groups of experimental methods for work function measurements: absolute and relative.Methods of the first group employ electron emission from the sample induced by photon absorption (photoemission), by high temperature (thermionic emission), due to an electric field (field emission), or using electron tunnelling.
All 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).
Methods Based on Photoemission
Photoelectron emission spectroscopy (PES) is the general term for spectroscopic techniques based on the outer photoelectric effect. In the case of Ultraviolet Photoelectron Spectroscopy (UPS), the surface of a solid sample is irradiated with ultraviolet (UV) light and the kinetic energy of the emitted electrons is analysed. As UV light is electromagnetic radiation with an energy lower than 100 eV it is able to extract only valence electrons. Due to limitations of the escape depth of electrons in solids UPS is very surface sensitive, as the information depth is in the range of 2 – 3 monolayers. At the same time the measurement principle restricts PES to be used in UHV conditions. The resulting spectrum reflects the electronic structure of the sample providing information on the density of states, the occupation of states, and the work function.
Methods Based on Thermionic Emission
The retarding diode method is one of the simplest and oldest method of measuring work functions. It is based on the thermionic emission of electrons from an emitter. The current density of the electrons collected by the sample depends on the work function of the sample and is given by the Richardson–Dushman equation where , the Richardson constant, is a specific material constant. The current density increases rapidly with temperature and decreases exponentially with the work function. Changes of the work function can be easily determined by applying a retarding potential between the sample and the electron emitter; is replaced by in above equation. The difference in the retarding potential measured at constant current is equivalent to the work function change, assuming that the work function and the temperature of the emitter is constant.
One can use the Richardson–Dushman equation directly to determine the work function by temperature variation of the sample, as well. Rearranging the equation yields
. The line produced by plotting vs. will have a slope of allowing to determine the work function of the sample.
See also
- Electron affinity. See NEA cathode for an application to condensed matter.
References
As a book:- Solid State Physics, by Ashcroft and Mermin. Thomson Learning, Inc, 1976
- Goldstein, Newbury, et al, 2003. Scanning Electron Microscopy and X-Ray Microanalysis. Springer, New York.
- Herbert B. Michaelson, "The work function of the elements and its periodicity". J. Appl. Phys. 48, 4729 (1977)
External links
*Some of the work functions listed on these sites do not agree!*- Work functions of common metals
- Work functions of various metals for the photoelectric effect
- Contains some work functions for metals and the corresponding heat required to eject them by thermionic emission
energy (from the Greek ενεργός, energos, "active, working")[1] is a scalar physical quantity that is a property of objects and systems of objects which is conserved by nature.
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The electronvolt (symbol eV) is a unit of energy. In theoretical physics, where distinctions between mass and energy are not concrete, it is often used also as a unit of mass (AAAS Science journal, 2006).
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Electron
Theoretical estimates of the electron density for the first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density
Composition: Elementary particle
Family: Fermion
Group: Lepton
Generation: First
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Theoretical estimates of the electron density for the first few hydrogen atom electron orbitals shown as cross-sections with color-coded probability density
Composition: Elementary particle
Family: Fermion
Group: Lepton
Generation: First
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The ionization potential, ionization energy or EI of an atom or molecule is the energy required to remove one mole of electrons from one mole of isolated gaseous atoms or ions.
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The Fermi energy is a concept in quantum mechanics referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature. This article requires a basic knowledge of quantum mechanics.
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primitive cell, is a minimum cell corresponding to a single lattice point of a structure with translational symmetry in 2D, 3D, or other dimensions. A lattice can be characterized by the geometry of its primitive cell.
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In geometry and crystallography, a Bravais lattice, named after Auguste Bravais, is an infinite set of points generated by a set of discrete translation operations. A crystal is made up of one or more atoms (the basis) which is repeated at each lattice point.
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The Fermi energy is a concept in quantum mechanics referring to the energy of the highest occupied quantum state in a system of fermions at absolute zero temperature. This article requires a basic knowledge of quantum mechanics.
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Caesium (also spelled cesium, IPA: /ˈsiːziəm/) is a chemical element in the periodic table that has the symbol Cs and atomic number 55.
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photoelectric effect is a quantum electronic phenomenon in which electrons are emitted from matter after the absorption of energy from electromagnetic radiation such as x-rays or visible light.
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Photon
Photons emitted in a coherent beam from a laser
Composition: Elementary particle
Family: Boson
Group: Gauge boson
Interaction: Electromagnetic
Theorized: Albert Einstein (1905–17)
Symbol: or
Mass: 0[1]
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Photons emitted in a coherent beam from a laser
Composition: Elementary particle
Family: Boson
Group: Gauge boson
Interaction: Electromagnetic
Theorized: Albert Einstein (1905–17)
Symbol: or
Mass: 0[1]
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photoelectric effect is a quantum electronic phenomenon in which electrons are emitted from matter after the absorption of energy from electromagnetic radiation such as x-rays or visible light.
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Planck constant (denoted ) is a physical constant that is used to describe the sizes of quanta. It plays a central role in the theory of quantum mechanics, and is named after Max Planck, one of the founders of quantum theory.
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Thermionic emission (archaically known as the Edison effect) is the flow of charged particles called thermions from a charged metal or a charged metal oxide surface, caused by thermal vibrational energy overcoming the electrostatic forces holding electrons to the
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vacuum tube, electron tube (inside North America), thermionic valve, or just valve (elsewhere); is a device used to amplify, switch, otherwise modify, or create an electrical signal by controlling the movement of electrons in a low-pressure space, often not
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6, 5, 4, 3, 2, 1, 0, −1
(mildly acidic oxide)
Electronegativity 2.36 (scale Pauling)
Ionization energies 1st: 770 kJ/mol
2nd: 1700 kJ/mol
Atomic radius 135 pm
Atomic radius (calc.
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(mildly acidic oxide)
Electronegativity 2.36 (scale Pauling)
Ionization energies 1st: 770 kJ/mol
2nd: 1700 kJ/mol
Atomic radius 135 pm
Atomic radius (calc.
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Electronics is the study of the flow of charge through various materials and devices such as, semiconductors, resistors, inductors, capacitors, nano-structures, and vacuum tubes. All applications of electronics involve the transmission of power and possibly information.
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The Schottky diode (named after German physicist Walter H. Schottky; also known as hot carrier diode) is a semiconductor diode with a low forward voltage drop and a very fast switching action.
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vacuum tube, electron tube (inside North America), thermionic valve, or just valve (elsewhere); is a device used to amplify, switch, otherwise modify, or create an electrical signal by controlling the movement of electrons in a low-pressure space, often not
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Field emission, also known as Fowler-Nordheim tunneling, is a form of quantum tunneling in which electrons pass through a barrier in the presence of a high electric field.
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Kelvin probe force microscopy (KPFM), also known as surface potential microscopy, is a noncontact variant of atomic force microscopy (AFM) that was invented in 1991. With KPFM, the work function of surfaces can be observed at atomic or molecular scales.
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Ultraviolet (UV) light is electromagnetic radiation with a wavelength shorter than that of visible light, but longer than soft X-rays. It is so named because the spectrum starts with wavelengths slightly shorter than the wavelengths humans identify as the color violet
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kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity.
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Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. These components oscillate at right angles to each other and to the direction of propagation, and are in phase with each other.
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In chemistry, valence electrons are the electrons contained in the outermost, or valence, electron shell of an atom. Valence electrons are important in determining how an element reacts chemically with other elements: The fewer valence electrons an atom holds, the less
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UHV could refer to:
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- University of Houston–Victoria
- Ultra high vacuum
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