Two dimensional Child-Langmuir law for a sharp field emitter

Summary form only given, as follows. 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 [1] to Child-Langmuir (CL) law [2] 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.