Child's Law
Also known as the Child-Langmuir 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 and inversely as the square of the distance separating the cathode and the anode. That is,
- .
Where is the anode current, the current density, and the anode surface inner area. This assumes the following:
- The electrodes are planar, parallel, equipotential surfaces of infinite dimensions.
- Electrons travel ballistically between electrodes (i.e., no scattering).
- The electrons have zero velocity at the cathode surface.
- In the interelectrode region, only electrons are present.
- The current is space-charge limited.
- The anode voltage remains constant for a sufficiently long time so that the anode current is steady.
The assumption of no scattering (ballistic transport) is what makes the predictions of Child-Langmuir Law different from those of Mott-Gurney Law. The latter assumes steady-state drift transport and therefore strong scattering.
Read more about this topic: Space Charge
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