Kelvin probe force microscopy of metallic surfaces used in Casimir force measurements

Abstract

Kelvin probe force microscopy at normal pressure was performed by two different groups on the same Au-coated planar sample used to measure the Casimir interaction in a sphere-plane geometry. The obtained voltage distribution was used to calculate the separation dependence of the electrostatic pressure Pres(D) in the configuration of the Casimir experiments. In the calculation it was assumed that the potential distribution in the sphere has the same statistical properties as the measured one, and that there are no correlation effects on the potential distributions due to the presence of the other surface. The result of this calculation, using the currently available knowledge, is that Pres(D) does not explain the magnitude or the separation dependence of the difference ∆P (D) between the measured Casimir pressure and the one calculated using a Drude model for the electromagnetic response of Au. We discuss in the conclusions the points which have to be checked out by future work, including the influence of pressure and a more accurate determination of the patch distribution, in order to confirm these results.

The effect of patch potentials in Casimir force measurements determined by heterodyne Kelvin probe force microscopy

“…Here we show that the plasma-Drude pressure difference falls within the range of pressures generated by patch potentials on several gold surfaces, as measured by HAM-KPFM, which differs from an earlier result using AM-KPFM [20]. Furthermore, we demonstrate an improved spatial resolution when using HAM-KPFM instead of AM-KPFM on the same area.…”

“…The AFM scan of a sputtered gold surface (250 nm) has topographical peaks at both high and low potentials (a) (total topographic range is 5.7 nm over the scanned area). The cross correlation between surface potential and topography falls below the limit used in [20] (thick lines at top and bottom) and takes on both positive and negative values depending on the sample and scan (b).…”

“…While noting that a correlation between potential and topography does not imply a topographical artifact in the potential, nor does its absence imply the absence of a topographical artifact, it is a useful way to compare our measurements to [20], which designated 0.5 as a maximum acceptable topographical-potential correlation. We found that the topography-potential correlation in our measurements varied significantly from scan to scan, but remained below 0.5 for all.…”

“…Recently, Kelvin probe techniques have been used to measure the SP of gold in Casimir force experiments [19,20]. The measurement of the SP on a gold-coated silicon nitride membrane in situ with a modification of frequency modulated (FM) KPFM is reported in [19].…”

“…The measurement, however, was limited in spatial resolution by size of the probe (4 mm), and was not able to resolve the smallest patches. Another recent experiment [20] measured the SP on a gold plate in a nitrogen environment, which had been used previously in vacuum-based Casimir force measurements [21,22], and estimated the sphere/plate equivalent electrostatic pressure assuming both surfaces were covered with the measured potential. The estimated pressure was over an order of magnitude less than the discrepancy between the measured pressure and the pressure calculated by the Drude model.…”