Child–Langmuir Space-Charge Diode

The Child–Langmuir law describes the space-charge-limited current in a planar vacuum diode. Unlike a semiconductor Shockley junction where current follows an exponential relation, a vacuum diode with plentiful electron emission from a cold cathode has its current limited by the electrostatic repulsion of the electrons already in the gap.

Experiment with voltage, gap size, and position

Open the Child–Langmuir Space-Charge Diode module. Interact with the controls to see how space charge affects potential curvature and current density scaling.

1. Set Voltage V to 100, Gap millimeters to 2, and Position over gap to 0.5. Verify the current density is 583.4879842199841 A/m² and the potential is 39.68502629920499 V.
2. Set Voltage V to 1000. Notice the current density increases to 18451.510174755356 A/m² and the potential is 396.8502629920499 V.
3. Set Voltage V to 100, Gap millimeters to 1, and Position over gap to 0.5. Verify the current density is 2333.9519368799365 A/m². The smaller gap increases the field and thus the current.
4. Set Gap millimeters back to 2, and change Position over gap to 0. Observe the charge density becomes "Unavailable" as it diverges at the cathode.
5. Set Position over gap to 1. Verify the potential is exactly 100 V, the anode voltage.