An upper bound to the frequency dependence of the cryogenic vacuum-gap capacitor

Abstract

In attempting to develop a capacitance standard based on the charge of the electron, one question which has been open for many years is the frequency dependence of the vacuum-gap cryogenic capacitor; the crucial difficulty has been: How do we measure frequency dependence down to 0.01 Hz? In this paper, we succeed in putting an upper bound on the frequency dependence, from 0.01 Hz to 1 kHz, of about 2 × 10 −7. We do this by considering a model for the dispersion in the surface insulating films on the surface of the Cu electrodes; the crucial prediction of this model is that the dispersion falls to very low values at low temperatures. By measuring the frequency dependence over a restricted range of frequencies, we have verified this prediction, and thus provide adequate support to conclude that the model is correct. We also point out that, independent of the capacitance standard, this cryogenic capacitor provides a frequency-independent standard for measurements in fields such as the low-temperature dynamics of amorphous materials.

Single-electron current sources: Toward a refined definition of the ampere

“…A major weakness of the ECCS is that it calibrates C cryo at ∼ 0.01 Hz, but commercial capacitance bridges that are used to compare C cryo to the calculable capacitor (and also ac QHR) operate at ∼ 1000 Hz. Zimmerman et al (2006) presents a model for the dielectric dispersion of insulating films at the surface of the electrodes of the capacitor. They fit this model to measurements of the frequency dependence and its temperature dependence in the range 100-3000 Hz and 4-300 K. The frequency dependence decreases at low temperatures.…”

Electron Counting Capacitance Standard with an improved five-junctionR-pump

“…A conservative estimate based on [27] shows that the larger distance between the capacitor electrodes (5 mm for the PTB design vs. 50 µm for the NIST design) makes the uncertainty due to this frequency dependence smaller than two parts in 10 8 [9].…”

Recent progress in the setup of the electron counting capacitance standard at PTB

“…Typically, a standard deviation of the mean C value of < 10 -7 pF was observed (type A only) in measurements of 1 h duration. Applying a model for the frequency dependence of the cold capacitance between f = 10 mHz -1 kHz [7], we estimated a very small dependence of δC(f)/C < 5⋅10 -8 for our cryocap design.…”