Work function

From Free net encyclopedia

The work function is the minimum energy (usually measured in electron volts) needed to remove an electron from the Fermi level in a metal to a point at infinite distance away outside the surface. The work function is generally about half the ionization energy of a free atom of the metal.

1 Example
2 Photoelectric work function
3 Thermionic work function
4 Applications
5 See also
6 External links

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Example

For example, Caesium has ionization energy 3.9 eV and work function 1.9 eV.

<math> W = -E_{tot}(N+1) + \{E_{tot}(N) + V(\infty) \} = - {\partial E_{tot} \over {\partial N} } + V(\infty) = - \mu + V(\infty) </math>

<math> E_{tot}(N+1) - E_{tot}(N) = {\partial E_{tot} \over {\partial N} } = \mu </math>

<math> \epsilon_F = \, \mu </math>

Here V is vacuum level and F is Fermi level.

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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:

φ=hf_{0_,}

where h is Planck's constant and f_{0_{is the minimum (threshold) frequency of the photon required for photoelectric emission.}}

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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 example that of 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.

It 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 V. It is somewhat higher on dense crystal faces than open ones.

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Applications

In electronics the work function is important for design of the metal-semiconductor junction in Schottky diodes and for design of vacuum tubes. 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 example that of 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.

It 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.

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