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. 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. Work function is an important property of metal. The magnitude of work function is usually about a half of the ionization energy of a free atom of the metal.

Work Function and Surface Effect

Work function W of a metal is closely related to its Fermi energy level

\epsilon_F \;

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

\{R\} \;

inside the geometrical region V which the solid occupies and then fill undistorted charge distribution basis into every primitive cells of

\{R\} \;

. 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 proved 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 $W_S \;$ . And let $\epsilon_F \;$ be the Fermi energy calculated for the finite solid without considering surface distortion effect, when taking the convention that the potential at $r \rightarrow \infty \;$ is zero. Then, the correct formula for work function is:

$W = - \epsilon_F +W_S \;$

Where $\epsilon_F \;$ 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:

φ=hf_{0_,}

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

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 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-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.

Reference

Solid State Physics, by Ashcroft and Mermin. Thomson Learning, Inc, 1976

External links

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
Some work functions

Condensed matter physics | Chemistry

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