Contact Modeling of an RF MEMS Switch

1
Contact Modeling of an RF MEMS Switch
Harsh Environment Robust MIcromechanical Technolo
gy

• Yan Du
• Advisors Prof. McGruer
• Prof. Adams
• Electrical and Computer Engineering
• Northeastern University

MicroFabrication Laboratory
2
Outline

• Introduction
• Existing contact theories with adhesion
• Microcontact (FEM model)
• Parameter study of separation modes
• Nanocontact (FEM model)
• Conclusions

3
A Single Asperity Contact
4
Application to Contact of Microswitch
MEMS Substrate
Designed by MicroAssembly Inc.
Package Substrate
Actuator
Ohmic Contact MEMS Switch
A SEM image of an Au contact bump taken by Lei
Chen.
5
Reliability Problem 1 Material Transfer During
Cycling
SEM micrograph of Au contact bump cycled at a
force of 200 µN for 106 cycles. (test station,
not a real switch)
Lei Chen, Ph.D. thesis (2007).
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Reliability Problem 2 Stiction
Change in adhesion in a hemispherical/flat
contact with cycling for Au contacts at 200 µN.
Lei Chen, Ph.D. thesis (2007).
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Outline

• Introduction
• Existing contact theories with adhesion
• Microcontact (FEM model)
• Parameter study of separation modes
• Nanocontact (FEM model)
• Conclusions

8
Pressure Distribution of Four Elastic Contact
Models
JKR
Hertz
JKR µ gt 3
Maugis
DMT
DMT µ lt 0.1
Maugis any µ
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Maugis Model Contact Radius vs. Applied Force
JKR
DMT
Adherence Force
Hertz
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Simple Analytical Model (SAM) for Plastic Contact
Fully-plastic deformation
Elasto-plastic deformation
S. Majumder, N. McGruer, and G.G. Adams,
Contact Resistance and Adhesion in a MEMS
Microswitch, 2003 STLE/ASME International Joint
Tribology Conference, paper 2003-Trib-270, 6
pages on CD-ROM.
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Maugis Pollock 3 Separation Modes
Ductile (Fd) mode Separates at
Brittle (Fm) mode Separates at
Brittle (Fb) mode Separates at
.
Ductile separation is more likely to occur at
small loads, high Youngs modulus, low hardness
and high adhesion energy.
Maugis, D., and Pollock, H.M., 1984, Surface
forces, deformation and adherence at metal
microcontacts, Acta Metall., 32 (9), pp.
1323-1334.
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Outline

• Introduction
• Existing contact theories with adhesion
• Microcontact (FEM model)
• Parameter study of separation modes
• Nanocontact (FEM model)
• Conclusions

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Related FEM Work
-- KE Curve-fits for the relations between
contact force, contact radius and
interference1 -- EKK Curve-fits for the
residual radius and residual interference2
1 Kogut, L., and Etsion, I., 2003, Adhesion in
elastic-plastic spherical microcontact, J. of
Coll. and Interf. Sci., 261, pp. 372-378. 2
Etsion, I, Kligerman, Y., and Kadin, Y., 2005,
Unloading of an elastic-plastic loaded spherical
contact, Int. J. Solids and Structures 42, pp.
3716-3729.
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Lennard-Jones Potential Between Two Parallel
Surfaces
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FEM Model For This Work

• Use L-J potential to alter surface deformation
  stress
• Finer mesh at the thin layer of the surface
• Consists of no more than 17,331 elements and
  31,681 nodes.

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Animation of von Misés Stresses during A
Load-Unload Cycle
?? - 0.6 J/m2 R - 4nm H - 3GPa E - 91GPa
Strain Hardening - 2
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Iteration Method
Curve-fit of separation
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Material Properties for Ru and Au
Case R(µm) E(GPa) ? H(GPa) Z0(nm) ??(J/m2) dc(nm) µ
Ru 4 410 0.3 10.25 0.169 1 1.70 1.6
Au 1 80 0.42 2 0.184 1 0.41 2.7
Three types of plasticity Macro Conventional
plasticity Micro Strain gradient
plasticity Nano Dislocation Dynamics
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Contact Radius vs. Interference(Small Loads)
Loading
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External Force vs. Interference(Small Loads)
Loading
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Contact Radius vs. Interference(Large Loads)
Loading
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External Force vs. Interference(Large Loads)
Loading
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Dimensionless Contact Radius vs. Dimensionless
Interference
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Dimensionless External Force vs. Dimensionless
Interference
This Work
(1.6,0.8)
(3.5,1.0)
(3.8,0.8)
(0.6, 2.2)
(4.4,0.7)
(0.6, 1.1)
(0.6, 0.9)
(0.6, 0.9)
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Profile of The Sphere Just Before Separation
Au
Ru
Neck
No Neck
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Ductile and Brittle Separation in Fracture
Mechanics
Ductile Au, Al, Cu, Pt Brittle glass,
polystyrene, concrete, ceramics, iron
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Rice Theory
For ductile separation
For Pure Mode I
For 10 Shear Mode
Au (fcc)
James R. Rice, Dislocation nucleation from a
crack tip an analysis based on the peierls
concept, J. Mech. Phys. Solids, 40 (2), pp.
239-271 (1992).
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Molecular Dynamics Model

• Boundary conditions
• The lower layer of the substrate and the upper
  layer of the top are fixed.
• The normal stresses on the side planes are zero.

Contains 13880 atoms.
Jun Song, and David J. Srolovitz, Adhesion
Effects in Mechanical Contact, Acta Materialia
54, 5305 (2006).
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Morphologies after Separation
Adhesion Energy (J/m2) (a)1.4 (b)1.2 (c)
1.0 (d) 0.9 (e)0.74 (f) 0.69 (g)
0.61 (h)0.53 (i) 0.39
III
II
I
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Outline

• Introduction
• Existing contact theories with adhesion
• Microcontact (FEM model)
• Parameter study of separation modes
• Nanocontact (FEM model)
• Conclusions

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Four Parameters
Final Loading Interference Critical Interference
Theoretical stress Hardness
E/sY
Rres
Adherence Force
Curve-fit from a FEM model
Tabor Parameter governing elastic
loading/unloading with adhesion
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Adherence Force of Brittle Separation
Derived from the combination of curve-fit results
of two FEM models (KE EKK) Applicable only
for brittle separation
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Influence of S
S varies from 0.6 2.9 E/sY 120 µ 1.60 df
/dc 30
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Influence of Interference
df /dc varies from 2.94 30 S 0.6 E/sY
120 µ 1.60
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Influence of Interference
df /dc varies from 2.94 30 S 1.2 E/sY
500 µ 1.60
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Influence of E/sY
E/sY varies from 120 500 S 1.2, µ 1.60, df
/dc 30
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Influence of µ
µ varies from 1.6 3.5 S 1.2, E/sY 120, df
/dc 30
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Outline

• Introduction
• Contact theories and applications
• Microcontact (FEM model)
• Parameter study of separation modes
• Nanocontact (FEM model)
• Conclusions

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Study on Multi-asperity Contact with Flat Bump
Gaussian Distribution
Sumit Majumder, Ph.D. Thesis (2003).
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FEM Model for Nanocontact
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Material Properties
Material R (nm) E (GPa) H (GPa) ? ?? (J/m2) Z0 (nm)
Au 3 91 3 0.32 0.3 -1.5 0.184 0.16-0.47
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Contour of von Misés Stresses
?? 0.4 J/m2 0.5 nm
?? 0.6 J/m2 0.5 nm
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Sutton-Chen Potential for Metals
lt001gt direction Au
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Outline

• Introduction
• Existing contact theories with adhesion
• Microcontact (FEM model)
• Parameter study of separation modes
• Nanocontact (FEM model)
• Conclusions

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Conclusions

• Give a rough understanding of the contact of real
  microswitches
• -- A FEM model which is applicable to a wide
  range of material properties is built to study
  the contact of microswitches for large loading
  this model is consistent with existing models
• 2. This is the first time that an FEM model has
  predicted ductile separation
• 3. Four parameters (µ, E/sY, df /dc,
  ) are identified which govern the effects of
  adhesion and plasticity during loading and
  unloading
• 4. Large adhesion energy, low hardness, and
  small loading level promote ductile separation.

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Future Work

• Use an appropriate potential for metals
• Implement nano plasticity theory
• Apply to nanocontacts obtain curve-fit
• Build a Multi-asperity Model by cascading the
  numerical results for microscopic level
• Help MEMS switches design to increase the
  reliability.

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Acknowledgement
This research has been supported by Northeastern
University, and DARPA under its HERMIT program
through research contract F33615-03-1-7002 and
under its ST Fundamentals program through
research contract HR0011-06-1-0051

• I would like to thank Prof. McGruer and
  Prof.Adams for their guidance and support
• I am grateful to Dean Zavracky for serving as my
  Ph.D. committee member
• Also I express my gratitude to the rest of
  faculty, staff, and colleagues in MFL group.

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Questions?
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Material Properties for Ru and Au
Material R (µm) E (GPa) H (GPa) ? ?? (J/m2) Z0 (nm)
Soft Au 4 91 0.2 0.32 2 0.184 6.77
Hard Au 4 91 2 0.32 2 0.184 6.77
High ?? Ru 4 450 15 0.32 2 0.4 1.07
Low ?? Ru 4 450 15 0.32 0.2 0.4 0.23
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Adherence Force vs. Applied Force of SAM
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ANSYS Solution Failure
MX
X-direction Stress