# Schottky equation

 The articles space charge , space charge law and Schottky equation overlap thematically. Help me to better differentiate or merge the articles (→  instructions ) . To do this, take part in the relevant redundancy discussion . Please remove this module only after the redundancy has been completely processed and do not forget to include the relevant entry on the redundancy discussion page{{ Done | 1 = ~~~~}}to mark. 141.34.3.113 17:42, Oct 25, 2013 (CEST)

The Schottky equation (also known as Langmuir-Schottky space charge law or Schottky-Langmuir space charge law , after Walter Schottky and Irving Langmuir ) describes the dependence of the electrical current density on the anode voltage in an electron tube .

The related relationship between the electrical current through the connections of an electron tube and the voltage across them is described by the law of space charge .

The equation states that with an ideal space charge cloud in an electron tube, the current density increases with the 1.5th  power of the anode voltage : ${\ displaystyle J}$${\ displaystyle \ Delta U}$

${\ displaystyle J = {\ frac {4} {9}} \ varepsilon _ {0} {\ sqrt {\ frac {2e} {m _ {\ mathrm {e}}}}} \ cdot {\ frac {(U_ {\ mathrm {A}} -U _ {\ mathrm {K}}) ^ {\ frac {3} {2}}} {l ^ {2}}}}$

With

• the electric field constant ${\ displaystyle \ varepsilon _ {0}}$
• the elementary charge ${\ displaystyle e}$
• the electron mass ${\ displaystyle m _ {\ mathrm {e}}}$
• the electrical voltage at the anode${\ displaystyle U _ {\ mathrm {A}}}$
• the electrical voltage at the cathode${\ displaystyle U _ {\ mathrm {K}}}$
• the distance between anode and cathode.${\ displaystyle l}$

This relationship is only valid until the saturation current density is reached, which results from the Richardson equation .

## Individual evidence

1. Peter Schaaf: The physical internship . Universitätsverlag Göttingen, 2006, ISBN 3-938616-43-1 , p. 150 f . ( limited preview in Google Book search).