Roughness correction to the Casimir force at short separations: Contact distance and extreme value statistics

Abstract

So far there has been no reliable method to calculate the Casimir force at separations comparable to the root-mean square of the height fluctuations of the surfaces. Statistical analysis of rough gold samples has revealed the presence of peaks considerably higher than the root-mean-square roughness. These peaks redefine the minimum separation distance between the bodies and can be described by extreme value statistics. Here we show that the contribution of the high peaks to the Casimir force can be calculated with the proximity force approximation, while the contribution of asperities with normal height can be evaluated perturbatively. This method provides a reliable estimate of the Casimir force at short distances, and it solves the significant, so far unexplained discrepancy between measurements of the Casimir force between rough surfaces and the results of perturbation theory. Furthermore, we illustrate the importance of our results in a technologically relevant situation.

Surface forces: Surface roughness in theory and experiment

“…A sophisticated analysis of this situation has been performed using perturbation theory, but is complicated by the requirement that the second order roughness response function must be known. 44 A simpler method is to treat contact when l < 0 as elastic contact.…”

“…40 Other studies have introduced a statistical description of roughness into calculation of the van der Waals interaction. [41][42][43][44] Advanced statistical analysis of asperity contact has been performed 44,45 but requires detailed knowledge of the surface roughness, not routinely available, and not in combination with roughened noncontact forces. Our model of contact requires only a single asperity parameter (the thickness or curvature of asperities) to be determined, and can be described by explicit analytical formulae.…”

Derivation of the Lifshitz-Matsubara sum formula for the Casimir pressure between metallic plane mirrors

“…We do not treat the problems associated with experiments performed in the planesphere geometry and also disregard the discussion of possible systematic effects in the theory-experiment comparison. References can be found in [9,24] for general discussions, in [27,28] for experiments with magnetic mirrors, in [29] and [30] for systematic effects due to electrostatic patches and roughness respectively.…”

Significance of the Casimir force and surface roughness for actuation dynamics of MEMS

“…Advances made in the measurement and theoretical understanding of Casimir forces over the last 10 years allow today a more detailed study of MEMS made from real material surfaces. [44][45][46] Note that although electrostatic forces can be switched off if no potential is applied, Casimir forces will always be present and will influence the actuation dynamics.…”