The transition from thermionic to space charge limited emission for needle-like surfaces—A particle-in-cell simulation study

Abstract

We perform particle-in-cell simulations of thermionic emission from hemi-ellipsoidal shaped needle emitters. The Schottky corrected Richardson–Dushman equation is used to compute the emitted current from the curved emitter surface. It is shown that the transmitted thermionic current increases with cathode temperature before eventually settling to the enhanced space charge limited (SCL) current. It is further shown that the critical temperature at which transition to the saturation region occurs increases with the height of the emitter, leading to a softening in the transition. This may be attributed to the non-uniformity in the cathode work function as in planar diodes. The SCL current is found to increase linearly with the electrostatic apex field enhancement factor as predicted recently [Singh et al., Phys. Plasmas 27, 104501 (2020)].