Roughness correction to the Casimir force beyond perturbation theory

Broer, Wijnand; Palasantzas, G.; Knoester, Jasper; Svetovoy, V. B.

doi:10.1209/0295-5075/95/30001

Cited by 39 publications

(58 citation statements)

References 28 publications

(64 reference statements)

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“…It has been shown 44,45 that the disagreement between the experiment 47 and the theory describing roughness perturbatively 48,49 can be resolved by taking into account rare high peaks on rough surfaces. These high peaks can be described by "extreme value statistics," as follows from a statistical analysis of Atomic Force Microscopy (AFM) topography data for gold films.…”

Section: Roughness Correction To the Electrostatic Forcementioning

confidence: 99%

“…These high peaks can be described by "extreme value statistics," as follows from a statistical analysis of Atomic Force Microscopy (AFM) topography data for gold films. 44,45,50 Indeed, recently there has been more awareness of the importance of extreme value statistics for the analysis of rough surfaces. 51 The Casimir force between rough surfaces can be written as…”

Section: Roughness Correction To the Electrostatic Forcementioning

confidence: 99%

“…The term F peaks (z) represents the contribution of high peaks, which is associated with the aforementioned extreme value statistics. It is important to note that F Cas (z) is singular at the distance upon contact 44,45,50 (z = d 0 ), which is the real minimum separation due to surface roughness. It is assumed that the contributions of high peaks are independent of each other, an approximation justified by the large horizontal distance between them.…”

Section: Roughness Correction To the Electrostatic Forcementioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2013

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Using the measured optical response and surface roughness topography as inputs, we perform realistic calculations of the combined effect of Casimir and electrostatic forces on the actuation dynamics of micro-electromechanical systems (MEMS). In contrast with the expectations, roughness can influence MEMS dynamics even at distances between bodies significantly larger than the rootmean-square roughness. This effect is associated with statistically rare high asperities that can be locally close to the point of contact. It is found that, even though surface roughness appears to have a detrimental effect on the availability of stable equilibria, it ensures that those equilibria can be reached more easily than in the case of flat surfaces. Hence our findings play a principal role for the stability of microdevices such as vibration sensors, switches, and other related MEM architectures operating at distances below 100 nm.

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Section: Roughness Correction To the Electrostatic Forcementioning

confidence: 99%

Section: Roughness Correction To the Electrostatic Forcementioning

confidence: 99%

Section: Roughness Correction To the Electrostatic Forcementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2013

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“…The free energy can be expressed by the Lifshitz formula 1 via the dielectric properties of the bodies. Note that roughness of the bodies can only increase the value of Γ and for small d 0 this effect can be significant 6,26,27 . If only the dispersion pressure contributes to the adhesion energy, Γ and P C have the same physical origin and, therefore, are related to each other as energy and force: Γ = P C d 0 /(α − 1).…”

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Global consequences of a local Casimir force: Adhered cantilever

Svetovoy

Melenev

Lokhanin

et al. 2017

Applied Physics Letters

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Although stiction is a cumbersome problem for microsystems, it stimulates investigations of surface adhesion. In fact, the shape of an adhered cantilever carries information of the adhesion energy that locks one end to the substrate. We demonstrate here that the system is also sensitive to the dispersion forces that are operative very close to the point of contact, but their contribution to the shape is maximum at about one third of the unadhered length. When the force exceeds a critical value the cantilever does not lose stability but it settles at smaller unadhered length, whose relation to adhesion energy is only slightly affected by the force. Our calculations suggest to use adhered cantilevers to measure the dispersion forces at short separations, where other methods suffer from jump-to-contact instability. Simultaneous measurement of the force and adhesion energy allows the separation of the dispersion contribution to the surface adhesion.The dispersion forces, a common name for the fluctuation-induced van der Waals (vdW) and Casimir forces 1,2 , become measurable with relative ease at separations less than 100nm3-6 since they have significant magnitude. However, even at these separations they are weak compared to background forces such as elastic, electrostatic, or capillary forces. Only at very small separations between bodies ∼ 1 nm do the dispersion forces dominate. The latter means that these forces play a crucial role only near or at the point of contact of two macroscopic bodies. Although it is natural to expect that these forces are not important far away from the point of contact as, for example, was formulated in the crack theory by Barenblatt 7 , there are physical situations where the finite range of the dispersion interaction plays a principal role.One example that was considered recently 8 demonstrated this effect for surface nanobubbles. These nanobubbles are gaseous domains trapped at the solidliquid interface 9,10 . They have the shape of a spherical cap with heights of ∼ 10 nm. The liquid and solid separated by a gaseous gap attract each other due to the dispersion interaction. The energy associated with this interaction at distances d ∼ 10 nm is estimated as ∼ 10 −5 J/m 2 that is much smaller than the surface tension of liquids γ ∼ 10 −2 J/m 2 . However, in the corners, where the gas-solid and gas-liquid interfaces are met, the energy is singular. The singularity is resolved due to balance of the attractive vdW and repulsive chemical interaction at distances ∼ 3Å11 . For a drop in gas or in another liquid the effect of the dispersion interaction is important only at the very corners 12 . However, for nanobubbles both the gas compressibility and a finite range of interaction influence significantly the global characteristics of the bubbles such as the aspect ratio or the contact angle Furthermore, the dispersion interaction close to the point of contact can influence the global characteristics of contacting bodies, which is a crucial issue in the fabrication and operation of micro/nano de...

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13.5 Dependence on surface roughness

Iannuzzi

Sedmik

2015

Physics of Solid Surfaces

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Roughness correction to the Casimir force beyond perturbation theory

Cited by 39 publications

References 28 publications

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

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

Global consequences of a local Casimir force: Adhered cantilever

13.5 Dependence on surface roughness

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