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[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
nonequilibrium 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.T385397 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 nonretarded regime (d < 20 n
ps is the saturation vapor pressure. At room temperature,
Microelectromechanical 0.54 nm vol. water [10]. 3343 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. 702713
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 cutoff 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
cutoff 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 nonhyd
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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 Fall '07
 Podhorodeski
 Force, Moment Of Inertia, Stress, Surface tension, Van der Waals force, N. Dechev

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