Gap size dependence of the dielectric strength in nano vacuum gaps

Abstract

We study the dielectric strength of vacuum gaps of under 100 nm. We find their dielectric strengths to have a power law dependence on the gap size. We apply this power law to find that the dielectric strength of a vacuum gap of 10 nm between two tungsten electrodes is 6.5 V/nm. The dielectric strength can be used to compute the maximum energy density, charge density, and power density. For tungsten, the maximum volumetric energy density is 190 MJ/m3. Nano vacuum gaps can discharge in 10 nanoseconds, giving a maximum gravitometric power density of 1012 W/kg. While the external discharge time is a few nanoseconds, the self-discharge time can be hours or days. The specific capacitance of a vacuum gap of size d is C = e0/ d2. If d = 10nm then C = 8.85×104 F/m3.