Two dimensional Child-Langmuir law for a sharp field emitter

Summary form only given. Space-Charge-Limited (SCL) electron flow describes the maximum current density allowed for electron transport across a planar gap. It has been an active research in the development of Non-neutral plasma physics, high current diodes, high power microwave sources, vacuum microelectronics, and sheath physics in plasma processing. Although the transition from field emission or Fowler-Nordheim (FN) law to Child-Langmuir (CL) law has been studied before, the models do not include the effect of the emitter sharpness. In this paper, we are interested to develop a protrusive CL law to account for the sharpness of emitter. In this paper, a protrusive model of the Child-Langmuir (CL) law is proposed for non-uniform electron field emission from a sharp tip of either Lorentzian or hyberboloid shape. The model is expressed as JPCL = μx Jcl at a large electric field higher than a critical value of Ec and Jcl is the 1D classical CL law. Here, the enhancement factor depends only on the calculate fiddle enhancement factor (β), independent of work work function and gap spacing. In particular, μ increases with β and it converges to a constant at β>;>;1 for a very sharp tip with small emission area. The calculations are compared with particle-in-cell simulation for a circular patch with arbitrary emission area.