The electrical resistance of vacuum

This paper deals with the physics of electrical conduction in vacuum between two parallel conducting planes (planar vacuum diode). After reviewing known features of conduction in the high-voltage range, we turn to the low-voltage range. An ohmic current–voltage characteristic is calculated in the case of identical cathodic and anodic electrodes, whence an electrical resistance of the vacuum gap can be defined. The inverse resistance involves the elemental conductance 2e 2/h and the number of conductance channels between the two electrodes. The channels are thermally populated from the electrodes and the population is analytically calculable from the Poisson equation of electrostatics and the Boltzmann law of thermal equilibrium. The observed resistance of a real vacuum diode (Mullard's EB 91) is accounted for without adjusting parameters. The paper also examines the link-up between Joule's law, involving dissipation, and Ohm's law, with vacuum being contrasted with a material conducting medium; the origin of dissipation in vacuum is understood. Quantum and statistical physics are kept at the undergraduate level. Finally, the results obtained for the vacuum diode shed light upon the quantized conductance of nanoscale semiconductor wires, a topic usually handled only in graduate courses. (paper)