# Work function

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

[itex] W = -E_{tot}(N+1) + \{E_{tot}(N) + V(\infty) \} = - {\partial E_{tot} \over {\partial N} } + V(\infty) = - \mu + V(\infty) [itex]

[itex] E_{tot}(N+1) - E_{tot}(N) = {\partial E_{tot} \over {\partial N} } = \mu [itex]

[itex] \epsilon_F = \, \mu [itex]

Here V is vacuum level and F is Fermi level.

 Contents

## Photoelectric work function

In photoelectric emission, the electron gains the kinetic energy needed to escape from photons, such an electron is called a photoelectron and the emission is called the photoelectric effect.

Photoelectric work function: φ=hf0,

where h is Planck's constant and f0 is the critical frequency required for photoelectric emission.

## 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.

## Applications

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

• free energy for the Helmholtz free energy equation, which is the thermodynamic work, note that this work is not related to electron emission and is thus not directly related to the work function.
• Electron affinity

• Art and Cultures
• Countries of the World (http://www.academickids.com/encyclopedia/index.php/Countries)
• Space and Astronomy