Space charge limited current with distributed velocity of initial electrons in planar diode

Abstract

The research on the space-charge limited current is of great importance for developing insight into the high current diodes. The Child-Langmuir law presents one-dimensional (1D) space-charge limited current density by considering a full electrostatic solution. Jaffe investigated the 1D space-charge limited current density modified by the uniform initial velocity of electrons emitted from the cathode by using the equation of motion for the individual electron. Luginsland et al. presented the two-dimensional (2D) space-charge limited current density by using the particle-in-cell (PIC) codes neglecting initial velocity distribution of the emitted electrons. In this Letter, the effects of initial electrons with the uniform energy distribution and thermal equilibrium distribution on the space charge limited current density are studied by using the full electromagnetic PIC method; the 2D modification factors to the space charge limited current density for the two cases are presented and discussed.