Schottky equation

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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).