The electrical resistance of vacuum

Abstract

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.

The thermodynamical foundation of electronic conduction in solids

“…The thermalisation-to-scattering time ratio is typically 10 4 [28,34,35] so that thermalisation proceeds at a fast rate anyway. Only in specially designed conductors where τ and the mean free path v g τ are very long [36], or in vacuum [37], can ballistic electron transport be observed: thermalisation is then prevented and Ohm's local law is observed not to be valid. In restating Drude's original calculation of mobility, we have remarked that, just as it makes no room for the thermalisation of the conduction electrons, it does not account for the Joule-Lenz heating effect either.…”

“…La thermalisation est donc malgré tout rapide. Mais dans des conducteurs conçus pour que τ et le libre parcours moyen v g τ soient très longs [36], ou dans le vide où τ est infini [37], un transport balistique d'électrons est possible : la thermalisation est alors entravée et on observe que la loi d'Ohm locale n'est pas valide.…”

Analysing the pressure effect on the contact resistance of electrical connections

“…Figure 3 schematizes the experimental setup. The Joule's law entails a heat production proportional to the product of the square of the electric current by the resistance [19], so the measurement of the resistance must be done by applying a current whose value is low enough to produce a negligible temperature rise of the analyzed sample, but high enough to do not compromise the accuracy in the measurements.…”