Electron emission: From the Fowler–Nordheim relation to the Child–Langmuir law

Universal voltage-current characteristics are presented for a planar diode, showing the general transition from the Fowler–Nordheim relation to the Child–Langmuir law. These curves are normalized to the intrinsic scales that are constructed from the Fowler–Nordheim coefficients A, B. They provide an immediate assessment of the importance of the space charge effects, once the gap voltage, gap spacing, and the Fowler–Nordheim coefficients are specified. An example in the parameter regime of vacuum microelectronics is presented.