# How to calculate the work function of a semiconductor

## Work function

The Work function (or Release work, Replacement work) is the work, i.e. the minimum energy that must be expended to release an electron from an uncharged solid. As a rule, the work function is specified in electron volts. The work function is important, among other things, in the external photoelectric effect, in which electrons are "knocked out" by light.

### Description and measurement

material Exit work in eV
Rb 2,13
Cs 1,7 … 2,14
K 2,25
N / A 2,28
Ba 1,8 … 2,52
Al 4,0 … 4,20
Zn 4,34
Pt 5,32 … 5,66
Ta 4,19
Mon 4,16 … 4,2
Cu 4,3 … 4,5
Ag 4,05 … 4,6
W. 4,54 … 4,6
Au 4,8 … 5,4
Ti 4,33[3]
Li 2,2
Ni 5,0
LaB6 2,4 … 2,7
BaO + SrO 1,0

The work function must be distinguished from the electron binding energy, which is comparable to the ionization energy of an atom or molecule. The electron binding energy is different for electrons of the different electron shells: If you want to release an electron from a deeper (energetically lower) shell, more energy has to be applied. The ionization energy only refers to the minimum energy that has to be applied to detach a certain electron from its bond. In contrast to this, the work function is the generally minimum energy for the exit of an electron, i.e. the energy when an electron is extracted from the Fermi level.

The work function is therefore dependent on the chemical potential of the type of solid (substance) from which electrons are released. It is relatively small for alkali metals like rubidium (2.13 eV), cesium (2.14 eV), potassium (2.25 eV) or sodium (2.28 eV), while it is for metals like aluminum (4.20 eV) ), Zinc (4.34 eV) or platinum (5.66 eV) is significantly higher.[4]

UV-poor daylight or UV-free incandescent light consists of photons with a maximum energy of 3 eV and can release electrons from cesium, while zinc requires the more energetic ultraviolet. The released electrons have a certain kinetic energy:

\$ \! \, W _ {\ mathrm {light}} = W _ {\ mathrm {kin}} + W_ \ mathrm {A} \$.

The measurement of the work function with the help of the photo effect is mostly realized by measuring the kinetic energy of the released electrons. This results from the difference between the energy introduced (usually the energy of the incident photon) and the work function. If you have measured the kinetic energy of the electrons (with the help of an electron spectrometer) and the wavelength used is known through filters or laser properties, you can calculate the work function as the difference:

\$ \! \, W _ {\ mathrm {A}} = E _ {\ mathrm {photon}} - E _ {\ mathrm {electron (max)}} \$

The opposing field method is also a simple measurement option.

Different work functions of two metals lead to a contact potential, which can therefore be used to measure relative work functions. The measurement using a Kelvin probe, also known as a Kelvin transducer, is important.

### application

An electron tube uses heated metals as an electron source. First tungsten with a work function of 4.5 eV was used, then tungsten with a one-atom thick thorium layer with 2.6 eV. A thin barium layer on tungsten gave 1.7 eV and the combination of tungsten, barium oxide and outer barium layer called the oxide cathode gave 1.1 eV to 1.0 eV. Due to the reduced work function, the cathode temperature could be reduced from 2400 ° C for tungsten to 700 ° C for oxide cathodes.[5]