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Adhesion and contact modeling and experiments in microelectromechanical systems including roughness effects

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Abstract

The intermolecular adhesive forces in microelectromechanical systems (MEMS) applications are very significant and can hinder normal operation of sensors and actuators as well as micro-engines where catastrophic adhesion and high friction could be promoted. It has been experimentally shown that surface texturing (roughening) decreases the effect of these forces. In this paper, a model that predicts the effects of roughness, on the adhesion and contact forces in MEMS interfaces is presented. The three key parameters used to characterize the roughness, the asymmetry and the flatness of a surface topography are the root-mean-square roughness (RMS), skewness and kurtosis, respectively. It is predicted that surfaces with high RMS, high kurtosis and positive skewness exhibit lower adhesion and are thus less prone to collapsing when they come into contact or near contact. Moreover, polysilicon films with different levels of roughness, asymmetry and peakiness (sharpness) were fabricated. Experiments were conducted to evaluate the adhesive pull-off forces associated with these films. The roughness characteristics of these films were also used in the model to predict the adhesive pull-off forces. Good agreement was obtained between the theoretical and experimental results. Such a model could be used to determine the critical characteristics of a microstructure prior to fabrication to prevent adhesion and lower friction in terms of surface roughness, mechanical properties and environment.

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Abbreviations

A :

real area of contact, (A* = A/A n)

A n :

nominal contact area

d :

mean separation, (d* = d/σ)

E :

composite elastic modulus for the two contacting surfaces \( E = {\left[ {{\left( {{1 - \nu ^{2}_{1} } \mathord{\left/ {\vphantom {{1 - \nu ^{2}_{1} } {E_{1} }}} \right. \kern-\nulldelimiterspace} {E_{1} }} \right)} + {\left( {{1 - \nu ^{2}_{2} } \mathord{\left/ {\vphantom {{1 - \nu ^{2}_{2} } {E_{2} }}} \right. \kern-\nulldelimiterspace} {E_{2} }} \right)}} \right]}^{{ - 1}} \)

F :

external normal force, (F* = F/(A n E))

F e :

electrostatic force

F c :

capillary force

F s :

total adhesion force, (F s* = F s/(A n E))

F sbl :

total adhesion force in the case of lubricated contact, (F sbl* = F sbl/(A n E))

H :

hardness of softer material

K :

maximum contact pressure factor: K = 0.454 + 0.41ν

N :

number of contacting asperities, (N* = N/(ηA n))

P :

contact load, (P*/(A n E)

p :

attractive pressure outside the contact region in the Lennard–Jones surface potential

r :

radial coordinate of asperity contact region

R :

average radius of curvature of asperities

r 1 :

radius at the intersection of lubricant layers

R k :

kurtosis of surface heights

R q :

standard deviation of surface heights

R Sk :

skewness of surface heights

s :

convenient transformation, (r 2−r 21 )1/2, (s* = s/σ)

t :

lubricant layer thickness, (t* = t/σ)

z :

asperity height, (z* = z/σ)

Z :

separation of the two surfaces outside the contact area in the Lennard–Jones surface potential

Z o :

minimum distance between two asperities in the Lennard–Jones surface potential

β:

roughness parameter, ηRσ

ε:

equilibrium spacing parameter in the Lennard–Jones potential

η:

area density of asperities

ν:

Poisson’s ratio of the softer material

ϕ*:

distribution function of the normalized asperity heights

σ:

standard deviation of asperity heights

σ K :

kurtosis of asperity heights

σSk :

skewness of asperity heights

Ψ:

GW plasticity index

ω:

local interference, ω = z − d, (ω* = ω/σ)

ωc :

critical interference at the interception of plastic deformation, (ωc* = ω c /σ)

Δγ:

surface energy

*:

dimensionless quantity

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Acknowledgments

This research was supported in part by the National Science Foundation under grant number CAREER CMS-0239232. The AFM measurements were performed by Dr. Allison Y. Suh of the Microtrobodynamics Laboratory at the University of Illinois. The surface characterization of the samples was performed at the Center for Microanalysis of Materials at the University of Illinois, which is supported by the U.S. Department of Energy under grant DEFG02-96-ER45439. The authors gratefully acknowledge these supports.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    N. Tayebi

  2. Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA

    A. A. Polycarpou

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  1. N. Tayebi
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Correspondence to A. A. Polycarpou.

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Tayebi, N., Polycarpou, A.A. Adhesion and contact modeling and experiments in microelectromechanical systems including roughness effects. Microsyst Technol 12, 854–869 (2006). https://doi.org/10.1007/s00542-006-0169-0

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