User:Luke.A.Johnson

Child-Langmuir Law


Also known as Child's Law or the Three-Halves Power Law, Child's Law states that the space charge-limited current (SCLC) in a plane-parallel diode varies directly as the three-halves power of the anode voltage $${V_a}$$ and inversely as the square of the distance $$d$$ separating the cathode and the anode. That is,


 * $$I_a=JS=2.33\times10^{-6}\frac{S\nu{V_a}^{3/2}}{d^2}$$.

Where $$I_a$$ is the anode current, $$J$$ the current density, and $$S$$ the area. This assumes the following:
 * 1) The electrodes are planar, parallel, equipotential surfaces of infinite dimensions.
 * 2) The electrons have zero velocity at the cathode surface.
 * 3) In the interelectrode region, only electrons are present.
 * 4) The current is space-charge limited.
 * 5) The anode voltage remains constant for a sufficiently long time so that the anode current is steady.

Extension of Child's Law
By dropping the assumption that the electrode surface is infinite, ...