Roughness corrections to the Casimir force: The importance of local surface slope

Zwol, P. J. van; Palasantzas, G.; Hosson, J.Th.M. De

doi:10.1063/1.2795795

Cited by 19 publications

(27 citation statements)

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“…The correlation lengths for the first three samples corresponding to the lateral feature sizes were reported before. 28 It should be noted that for sample 4 ͑120 nm Au/ Si͒ the correlation length is larger than those for the other three films on Si. It can result from differences in the evaporation process or due to different adhesive layers.…”

Section: Methodsmentioning

confidence: 97%

Optical properties of gold films and the Casimir force

et al. 2008

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Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Precise optical properties of metals are very important for accurate prediction of the Casimir force acting between two metallic plates. Therefore we measured ellipsometrically the optical responses of Au films in a wide range of wavelengths from 0.14 to 33 m. The films at various thicknesses were deposited at different conditions on silicon or mica substrates. Considerable variation of the frequency dependent dielectric function from sample to sample was found. Detailed analysis of the dielectric functions was performed to check the Kramers-Kronig consistency, and extract the Drude parameters of the films. It was found that the plasma frequency varies in the range from 6.8 to 8.4 eV. It is suggested that this variation is related with the film density. X-ray reflectivity measurements support qualitatively this conclusion. The Casimir force is evaluated for the dielectric functions corresponding to our samples, and for that typically used in the precise prediction of the force. The force for our films was found to be 5%-14% smaller at a distance of 100 nm between the plates. Noise in the optical data is responsible for the force variation within 1%. It is concluded that prediction of the Casimir force between metals with a precision better than 10% must be based on the material optical response measured from visible to mid-infrared range.

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Section: Methodsmentioning

confidence: 97%

Optical properties of gold films and the Casimir force

et al. 2008

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“…46,47 Lateral effects may provide corrections of 5% or more at separations less than 200 nm. 48 Roughness may be accounted for by taking the probability distribution of the height of each surface. Conceptually, the surface is divided into infinitesimal unit areas, with the height of the unit surface placed at z 1 for the first surface and z 2 for the second.…”

Section: Modelling Roughnessmentioning

confidence: 99%

Surface forces: Surface roughness in theory and experiment

Parsons

Walsh

Craig

2014

The Journal of Chemical Physics

119

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A method of incorporating surface roughness into theoretical calculations of surface forces is presented. The model contains two chief elements. First, surface roughness is represented as a probability distribution of surface heights around an average surface height. A roughness-averaged force is determined by taking an average of the classic flat-surface force, weighing all possible separation distances against the probability distributions of surface heights. Second the model adds a repulsive contact force due to the elastic contact of asperities. We derive a simple analytic expression for the contact force. The general impact of roughness is to amplify the long range behaviour of noncontact (DLVO) forces. The impact of the elastic contact force is to provide a repulsive wall which is felt at a separation between surfaces that scales with the root-mean-square (RMS) roughness of the surfaces. The model therefore provides a means of distinguishing between "true zero," where the separation between the average centres of each surface is zero, and "apparent zero," defined by the onset of the repulsive contact wall. A normal distribution may be assumed for the surface probability distribution, characterised by the RMS roughness measured by atomic force microscopy (AFM). Alternatively the probability distribution may be defined by the histogram of heights measured by AFM. Both methods of treating surface roughness are compared against the classic smooth surface calculation and experimental AFM measurement.

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“…For stochastic roughness all perturbative calculations [6,9,12] show an increase in magnitude of the Casimir energy and force with decreasing correlation length ℓ, approaching the PFA for ℓ ≫ a [14]. For a massless scalar field this trend is shown by the dashed curves in fig.…”

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confidence: 86%

“…When Casimir forces were accurately measured with atomic force microscope techniques [7] at plate separations of only a few hundred nanometers, corrections caused by the roughness of the plates could no longer be ignored. They are even more important at the small separations and higher accuracy of more recent experiments [8,9]. An increasing amount of experimental [8,9] and theoretical [9][10][11][12][13][14][15] effort has since been devoted to understanding roughness effects.…”

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confidence: 99%

“…They are even more important at the small separations and higher accuracy of more recent experiments [8,9]. An increasing amount of experimental [8,9] and theoretical [9][10][11][12][13][14][15] effort has since been devoted to understanding roughness effects. Currently the only rigorous non-perturbative approach is the proximity force approximation(PFA) (and some recent modifications thereof [15]).…”

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Field theoretic approach to roughness corrections

Schaden

2012

Phys. Rev. D

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We develop a systematic field theoretic description for the roughness correction to the Casimir free energy of parallel plates. Roughness is modeled by specifying a generating functional for correlation functions of the height profile, the two-point correlation function being characterized by the variance, σ 2 , and correlation length, ℓ, of the profile. We obtain the partition function of a massless scalar quantum field interacting with the height profile of the surface via a δ-function potential. The partition function of this model also is given by a holographic reduction to three coupled scalar fields on a two-dimensional plane. The original three-dimensional space with a flat parallel plate at a distance a from the rough plate is encoded in the non-local propagators of the surface fields on its boundary. Feynman rules for this equivalent 2 + 1-dimensional model are derived and its counter terms constructed. The two-loop contribution to the free energy of this model gives the leading roughness correction. The absolute separation, a eff , to a rough plate is measured to an equivalent plane that is displaced a distance ρ ∝ σ 2 /ℓ from the mean of its profile. This definition of the separation eliminates corrections to the free energy of order 1/a 4 eff and results in a unitary model. We derive an effective low-energy theory in the limit ℓ ≪ a. It gives the scattering matrix and equivalent planar surface of a very rough plate in terms of the single length scale ρ. The Casimir force on a rough plate is found to always weaken with decreasing correlation length ℓ. The two-loop approximation to the free energy interpolates between the free energy of the effective low-energy model and that of the proximity force approximation -the force on a very rough Dirichlet plate with σ 0.5ℓ being weaker than on a flat plate at any separation.

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Roughness corrections to the Casimir force: The importance of local surface slope

Cited by 19 publications

References 32 publications

Optical properties of gold films and the Casimir force

Optical properties of gold films and the Casimir force

Surface forces: Surface roughness in theory and experiment

Field theoretic approach to roughness corrections

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