Space-charge-limited Current in the Quantum Regime by Solving the Schroedinger-Poisson Equation

M.-C. Lin
NanoScience Simulation Laboratory, Department of Physics, Fu Jen Catholic University, Taipei County, Taiwan

The Child-Langmuir law gives the maximum electron current, known as the space-charge-limited current, which arises because the space charge in the diode presents a potential barrier to the incident electrons.

While there are modifications due to geometrical and relativistic effects, the limited current remains a fundamental quantity characterizing the beam-gap interaction. In the research of vacuum electronics on a scale down to a few or tens of nanometers, i.e., the nano-scale, the quantum effects should be considered and cannot be neglected. In a previous work by Lau et al., they extended the classical work of Child and Langmuir to the quantum regime by considering a parallel, planar gap.