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Tas t sonnenberg h jansen r legtenberg and m

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Unformatted text preview: icon [22] or operation. Examples of this compounds [12] show a strong dependence of the static rubbing surfaces [15] and charge accu friction coefficient on relative humidity. In macrotribology of electrostatic operated micromoto it is well known that adhesion of solids can strongly stiction is not expected due to thes depend on relative humidity [13]. This is caused by non-equilibrium charging will relax i capillary Selected Stiction that wet or have a small condensation. Liquids References contact angle on surfaces will spontaneously condense into 2.4. Van der Waals forces cracks, pores, and into small gaps surrounding the points of contact between the contacting surfaces. At equilibrium The van der Waals dispersion forces b the meniscus curvature is equal to the Kelvin radius [10]: N. Tas, T. Sonnenberg, H. Jansen, R. Legtenberg, and M. Elwenspoek, caused by mutual electric interaction “Stiction in Surface Micromachining”, lJournal of Micromechanics and in the two bodies. Dispersion force γ aV over orientation and induction force rK = (5) Microengineering, vol. 6, 1996, pp.T385-397 s ) R log(p /p polar molecules [24]. The interaction due to van der Waals interaction betw C. H. Mastrangelo, and C. H. Hsu, “Mechanicalvapor pressure and where V is the molar volume, p is the stability and adhesion of microstructures under capillary forces—part I: basic theory”, Journal of in the non-retarded regime (d < 20 n ps is the saturation vapor pressure. At room temperature, Microelectromechanical 0.54 nm vol. water [10]. 33-43 meniscus γl a V /(R T ) = Systems, for 2, 1993, pp. The A Evd W = − curvature strongly depends on the relative vapor pressure 12π d W. Merlijn/van For a relative Puers, and I.50%Wolf, “Alog(p/ps ) Model to p ps . Spengen, R. humidity of De we find Physical = where A is the Hamaker constant a Predict Stiction in MEMS”, Journal of At 100% relative and −0.69 and rk = −0.8 nm. Micromechanics humidity, between the surfaces. For most so Microengineering, vol. 12, 2002, ∞ which means that a water film pp. 702-713 log(p /ps ) = 0 and rk = Hamaker constant lies in the range can grow all over the surface. The amount of condensed For surfaces in contact a cut-off d liquid in thermodynamic equilibrium is determined by both slightly smaller than the interatomic the Kelvin radius and the contact angle. The meniscus used to calculate the adhesion energ curvatures are equal to the Kelvin radius and the contact cut-off distance of d0 = 0.165 nm an angles satisfy Young’s equation (figure 5). calculated by the Lifshitz theory, a go Capillary condensation can lead to a large increase in experimental values and adhesion en the RCA of solids by means of liquid bridging. It can, equation (6) is found for non-hyd therefore, drastically increase the adhesion of those solids 36 metallic solids and liquids [10]. Equ that due to their roughness show a low adhesion in a dry can be used to predict the adhesio environment [13]. Models for the adhesion force due to hydrophobic silicon surface. Howeve capillary condensed liquid have been developed in hardstrongly depends on the surface term disk tribology [14–16]. not exactly known. For pure silicon...
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