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 *V _{a}* and inversely as the square of the distance

*d*separating the cathode and the anode.

Where *I _{a}* is the anode current,

*J*the current density, and

*S*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.
Wikipedia, Space Charge

See Also

**Inverse Square Law**
**Laser Cluster Interactions**
**Law of Atomic Dissociation**
**Law of Atomic Pitch**
**Law of Oscillating Atomic Substances**
**Law of Pitch of Atomic Oscillation**
**Law of Variation of Atomic Oscillation by Electricity**
**Law of Variation of Atomic Oscillation by Sono-thermism**
**Law of Variation of Atomic Oscillation by Temperature**
**Law of Variation of Atomic Pitch by Electricity and Magnetism**
**Law of Variation of Atomic Pitch by Rad-energy**
**Law of Variation of Atomic Pitch by Temperature**
**Law of Variation of Pitch of Atomic Oscillation by Pressure**
**Models of Laser Cluster Interactions**
**Space Charge**
**Square Law**