Analysis of space-charge effects on electron emission typically makes some assumption of continuity and smoothness, whether this is continuity of charge as in the classical derivation of the Child–Langmuir current or the mean-field approximation used in particle-in-cell simulations. However, when studying the physics of electron emission and propagation at the mesoscale, it becomes necessary to consider the discrete nature of electronic charge to account for the space-charge effect of each individual point charge. In this paper, we give an extensive analysis of some previous work on the distribution of electrons under space-charge limited conditions Gunnarsson et al., IEEE Trans. Electron Devices 68, 342 (2021). We examine the spacing of electrons as they are emitted from a planar surface. We present simplified models for analysis of such conditions to derive scaling laws for emission and compare them to computer simulations.
Jónsson et al. (Sun,) studied this question.
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