Vacuum level

The vacuum level is the potential energy of a particle in a field that is in a vacuum . It must not be confused with vacuum energy , the energy of “empty space” in the complete absence of particles and fields.

Charged particles

In the electric field

For charged particles in an electric field , the vacuum level is equal to the product of the electric charge of the particle and the electrostatic potential of the field in a vacuum: ${\ displaystyle {\ vec {E}}}$ ${\ displaystyle E_ {pot, V} ({\ vec {r}})}$ ${\ displaystyle q}$ ${\ displaystyle \ phi _ {V} ({\ vec {r}})}$

{\ displaystyle E_ {pot, V} ({\ vec {r}}): = q \ cdot \ phi _ {V} ({\ vec {r}}).}

In the case of electrically conductive solids , e.g. B. metals , the vacuum level is also the difference between the work function and Fermi energy : ${\ displaystyle W_ {A}}$ ${\ displaystyle E_ {F}}$

{\ displaystyle E_ {pot, V} = W_ {A} -E_ {F}.}

The Fermi energy is usually determined by an electrical contact , which results in the vacuum level.

From this it follows that even without an external field between two interconnected conductive bodies that have different work functions, an electrical field is created (via spatial differences in the vacuum level and the electrostatic potential):

{\ displaystyle {\ begin {aligned} W_ {A} ({\ vec {r}}) & \ neq const. \\\ Rightarrow E_ {pot, V} ({\ vec {r}}) & \ neq const . \\\ Rightarrow \ phi _ {V} ({\ vec {r}}) & \ neq const. \\\ Rightarrow {\ vec {E}} & \ neq 0. \ end {aligned}}}

This phenomenon was previously described by the term contact voltage or contact potential.

Without an electric field

If, on the other hand, the room is free of electric fields:

{\ displaystyle {\ vec {E}} = 0,}

so the electrostatic potential and thus also the vacuum level is spatially constant:

{\ displaystyle {\ begin {aligned} \ Rightarrow \ phi _ {V} ({\ vec {r}}) & = \ phi _ {V} = const. \\\ Rightarrow E_ {pot, V} ({\ vec {r}}) & = E_ {pot, V} = const. \ end {aligned}}}

Atomic physics

In atomic physics , the vacuum level serves as a reference level for specifying the binding energy of the electrons ; this is therefore the minimum energy required to bring an electron from its bound state in an atom or molecule to the vacuum level (i.e. into the vacuum). If the electron receives more energy, it receives additional kinetic energy .

literature

Yu, PY, Cardona, M .: Fundamentals of Semiconductors , 1st edition, Springer 1996, ISBN 3-540-61461-3 , p. 426