Analysis of the planar field-emission diode

Field emission in a plane-parallel electrode geometry at energies up to the relativistic regime is considered with the inclusion of finite velocity of electron emission from the cathode surface. The effect of this velocity is subsequently shown to be negligible. A technique is developed for evaluating the anode current/voltage/electrode-spacing characteristics for any cathode material, from which the electrical impedance of the diode can be calculated. The completely space-charge-limited case is of particular interest, and a criterion is established that imposes an upper limit on the cathode workfunction in order that a particular diode should be at least 90% space-charge-limited. Fulfilment of this criterion implies that the diode current and impedance are determined, to 5% accuracy, solely by the anode voltage, electrode spacing and cathode area. Consideration is also given to the transition from the field-emission discharge to the vacuum arc and another criterion imposed on the cathode material in order that this transition should not occur. Finally the bearing of this analysis on field emission in nonplanar geometries is considered.