work function

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Work function Work function Escape work , on Solid state physics It is defined as the minimum energy required to move an electron from the interior of a solid to the surface of an object. Generally, the work function refers to the work function of metal. The definition of work function is seldom used for non-metallic solids, but expressed by contact potential.

Chinese name: work function
Foreign name: work function

expression: J=ATe
Applied discipline: electronics

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Work function The number is usually about free metal atoms ionization energy One half of. The work function of metal is expressed as an initial energy equal to Fermi energy The smallest amount of energy required for electrons to escape into vacuum from the metal. The size of the work function indicates the strength of the electron's binding in the metal. The larger the work function, the more difficult it is for the electron to leave the metal. The work function of metal is about several Electron volt 。 The work function of cesium is the lowest, 2.14 ev; Platinum is the highest, 5.65 ev. The value of the work function is related to the surface condition Atomic number The work function also presents Periodic change 。 In semiconductors, conduction band Bottom and Price band The top is generally lower than the minimum electron escape energy of metal. To make electrons escape from semiconductors, they must also be given corresponding energy. Unlike metals, the work function sum of semiconductors Doping concentration of

It can be simply understood as the ability of an object to possess or capture electrons.^[1]

Metal related

Company: Electron volt ,eV

Metal	work function	Metal	work function	Metal	work function	Metal	work function	Metal	work function	Metal	work function
Ag	four point two six	Al	four point two eight	As	three point seven five	Au	five point one	B	four point four five	Ba	two point seven
Be	four point nine eight	Bi	four point two two	C	five	Ca	two point eight seven	Cd	four point two two	Ce	two point nine
Co	five	Cr	four point five	Cs	two point one four	Cu	four point six five	Eu	two point five	Fe	four point five
Ga	four point two	Ge	three point one	Hf	three point nine	Hg	four point four nine	In	four point one two	Ir	five point two seven
K	two point three	La	three point five	Li	two point nine	Lu	three point three	Mg	three point six six	Mn	four point one
Mo	four point six	Na	two point seven five	Nb	four point three	Nd	three point two	Ni	five point one five	Os	four point eight three
Pb	four point two five	Pt	five point six five	Rb	two point one six	Re	four point nine six	Rh	four point nine eight	Ru	four point seven one
Sb	four point five five	Sc	three point five	Se	five point nine	Si	four point eight five	Sm	two point seven	Sn	four point four two
Sr	two point five nine	Ta	four point two five	Tb	three	Te	four point nine five	Th	three point four	Ti	four point three three
Tl	three point eight four	U	three point six three	V	four point three	W	four point five five	Y	three point one	Zn	four point three three

effect

Metal Work function of W With its Fermi energy Class is closely related but not equal. that is because real world The solids in have surface effect : Real world solids are not the infinite extension of electrons and ions that repeatedly fill every one of the entire Braffie lattice Protocell 。 No one can only be located in a series of Bragg points occupied by solid and full of non distortion charge distribution Geometric region from base to all primitive cells V 。 Indeed, the charge distribution near the surface in those cells will be significantly distorted compared with the ideal infinite solid, resulting in an effective surface dipole Distribution, or, sometimes, there are both surface dipole distribution and surface charge distribution.

It can be proved that if we define the work function as immediately The minimum energy required to move out to a point, but the effect of surface charge distribution can be ignored, leaving only the surface dipole distribution. If the effective surface dipole that brings the potential energy difference between the two ends of the surface is defined as. And it is defined as Fermi energy , when conventionally located potential is zero. Then, the correct work function formula is:

Where is negative, indicating that electrons are enriched in solids.

Photoelectric work function

The work function is the minimum energy that must be given to release electrons from a metal. stay photoelectric effect If a photon with energy greater than the work function is irradiated on the metal, then Photoemission Will occur. Any excess energy will be given to the electron in the form of kinetic energy.

The photoelectric work function is

φ = hf 0, where h is Planck constant F0 is the minimum (threshold) frequency that can generate photoemission photons. When an electron gains energy, it takes " Quantum transition "To jump to another energy level. This process is called electron excitation, and the higher energy level is called " excited state " Low energy level It is called " ground state 」。

Thermal work function

Work function in Thermal emission It is equally important in theory. Here electrons derive energy from heat rather than photons. In this case, the electrons are filled from heating negative electricity Of Vacuum tube filament In the case of escape, the work function can be called the thermal work function. Tungsten is common in vacuum tubes metallic element Its work function is about 4.5eV.

The filament heating current (if) is required for thermal emission to maintain the temperature of 2000-2700K. Once reached Filament current The small change of filament current will no longer affect electron beam electric current. electron gun The filament current provided is very close to the potential required to overcome the work function (W) (Goldstein, 2003). The thermal function depends on Crystal orientation And it tends to be smaller for metals with open lattice, and larger for metals with closely packed atoms. The range is approximately 1.5 – 6 eV. Dense to some extent Crystal plane Higher than open lattice metals.

application

Work Function Pair Design in Electronics Schottky diode or light-emitting diode Medium metal semiconductor junction and Vacuum tube Very important

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Many are based on different Physical effects The technique of measuring the electrical work function of a sample has been developed. Two types of test methods for work function measurement can be distinguished: Absolute measurement and Relative measurement 。

The first method uses samples from light absorption ( Light emission ）Raised electron emission , through high temperature（ Thermal emission ）, or electric field（ Field emission ）, and the use of electron tunneling effects.

All Relative measuring method The contact between the sample and the reference electrode is used Potential difference 。 Experimentally, we use diode Cathode current or sample and object of reference Is caused by the artificially changed capacitance between the two Displacement current And other methods (Kelvin probe, Kelvin force microscope).

Light emission

Photoemission spectroscopy (PES) is based on External photoelectric effect Spectroscopic technical terms of the. about ultraviolet Electron spectroscopy（ UPS ）, the surface of the solid sample is treated with UV（ UV ) Photoexcitation Then the kinetic energy of the emitted electrons is analyzed. Because ultraviolet light is energy h ν below 100eV electromagnetic radiation , it can only catch bid electrons. Because the escape depth of electrons in solids is limited by ultraviolet light Electronic spectrum It is very sensitive to the surface, because the information depth ranges from 2 to 3 single layers. meanwhile measuring principle Limited photoelectric Emission spectroscopy Used in UHV situations. The obtained spectrum is provided by Density of states The electronic structure of the sample is reflected by the information of occupation state, work function, etc.

Thermal emission

Delay diode method is one of the simplest and oldest methods for measuring work function. It is derived from the transmitter electronics Thermal emission 。 Electrons collected from the sample current density J It depends on the work function φ of the sample and can be calculated by Richardson – Dushman equation J = ATe Calculation, where A Richardson constant is the specific material constant. The current density increases rapidly with temperature and decreases exponentially with work function. The work function can be changed simply by applying a Postponement potential V To decide; In the above equation, φ is e (Φ + V ）Replace. stay Constant current The delay potential difference measured below is equal to the change of work function, assuming that the work function and temperature of the transmitter remain unchanged.

The Richardson – Dushman equation can also be used to directly determine the work function by changing the temperature of the sample. Rewrite equation ln ( J / T ) = ln ( A ) − φ kT 。 describe ln ( J / T ）And 1/ T Slope of the obtained curve − φ/ k It is allowed to determine the work function of the sample.

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