Diode constant for parallel-plane vacuum diode

The current-voltage characteristic of a vacuum diode is described by the \(3/2\)-power law (see Current from voltage and diode constant in vacuum diode). The diode constant in this law depends only on the relative position, shape and size of the electrodes of the vacuum diode. The vacuum diode may have different electrode geometries. Here we are talking about a vacuum diode with parallel-plane electrodes.

Notation:

  1. \(\varepsilon_0\) (epsilon_0) is vacuum_permittivity.

  2. \(e\) (e) is elementary_charge.

  3. \(m_\text{e}\) (m_e) is electron_rest_mass.

Links:

  1. Wikipedia, derivable from first formula.

diode_constant

diode_constant.

Symbol:

g

Latex:

\(g\)

Dimension:

current/voltage**(3/2)

electrode_area

area of an electrode.

Symbol:

A

Latex:

\(A\)

Dimension:

area

electrode_distance

euclidean_distance between electrodes.

Symbol:

d

Latex:

\(d\)

Dimension:

length

law

g = 4 * epsilon_0 / 9 * sqrt(2 * e / m_e) * A / d^2

Latex:
\[g = \frac{4 \varepsilon_0}{9} \sqrt{\frac{2 e}{m_\text{e}}} \frac{A}{d^{2}}\]