Contact Properties of a Microelectromechanical(MEMS) switch with gold-on-gold contacts

Sumit MajumderECE, Northeastern University

MEMS switches - background

• Advantages– size, flexible configuration, integration capability– zero steady-state power consumption– low leakage, high isolation compared to FET switches

• Applications– Pin diode replacement in RF applications (no steady-state power,

easy scalability to multi-pole, multi-throw configurations)– Reed relay replacement in various applications (ultrasound, ATE)

MEMS switches - actuation mechanisms

• Electrostatic Vs electromagnetic– Electrostatic switches are easier to build, smaller and faster, do not

draw steady-state power– Electromagnetic switches have higher actuation force (more

reliable contact), easier to build 4-terminal relay

Why study contact adhesion?

x(V)V

2

2

)(2 VxAVF ε

=

• A = 0.005-0.05 mm2, x(V) = 0.5-1 µm, V less than 100 V• Total actuator force typically ~ 1 mN• Contact force 100 µN - 1 mN, restoring force 100 µN - 1

mN

Why study contact adhesion?

• To obtain low and stable contact resistance, require a minimum clean, metallic contact area => – minimum contact force– minimum restoring force to overcome contact adhesion

• Actuator force 1 order higher in MEMS electromagnetic relays, 2 orders higher in reed relays

• Much more difficult to meet contact force and restoring force constraints

• Objective of this thesis: increase our understanding of adhesion in electrostatically actuated microswitch contacts

Evolution of measured characteristics

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ohm

s)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ohm

s)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

10 cyclesInitial

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ohm

s)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ohm

s)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1000 cycles 10000 cycles

Outline

• Introduction to Northeastern University switch• Related work• Modeling of contact surface with asperities (Greenwood &

Williamson)• Deformation model for single asperity

– loading without adhesion– loading with adhesion– unloading and separation

• Multi-asperity contact model• Contact resistance model• Measurements and discussion• Conclusions

Northeastern University microswitch

• Predecessor: Zavracky & Morrison, Foxboro (1984).• Devices used in this work fabricated in Microfabrication

Laboratory (MFL) at NU in 1999.• Since 1999, further development and commercialization at

Analog Devices and Radant MEMS.• Fabricated using all-metal surface micromachining process

developed at NU.

Northeastern University microswitch

100 µm

Drain Source

Gate

Contact Detail

Beam S

G

DSOURCEGATE

SOURCEGATEDRAIN

DRAIN

S

G

DSOURCEGATE

SOURCEGATEDRAIN

S

G

DSOURCEGATEDRAIN

• Gold cantilever beam, sputtered gold contacts.

• Threshold voltage 65-70 V. Restoring force 70 µN per contact.

• Actuation voltage 90-120 V => contact force 70-180 µN per contact.

• Operated in dry nitrogen.• Contact resistance initially 0.5-1 Ω, after

103-104 cycles 0.1-0.2 Ω.• Lifetime ~106 cycles with 10 mA per

contact, limited by permanent stuck-closed failures.

Northeastern University microswitch with gold-gold contacts

SOURCEGATEDRAIN SOURCEGATEDRAIN

75

15

Φ=2

20

35

0.3 0.66

Related work• MEMS switch contacts:

– Majumder et al. (1997,1998,2001)– Hyman et al. (1998) thermal model– Yan et al.(2001) thermal model– Kruglick (1999), Lafontan (2001) simple contact models from

device perspective

• AFM-based work in MEMS switch force range– Beale and Pease (1992)– Schimkat (1998), Bromley et al. (2001)

• MEMS switches– First switch Petersen (1979). Many switches since 1995 (majority

electrostatic, some electromagnetic and thermal)

• Large body of work on contact mechanics and adhesion (cited while developing models)

Outline

• Introduction to Northeastern University switch• Related work• Modeling of contact surface with asperities (Greenwood &

Williamson)• Deformation model for single asperity

– loading without adhesion– loading with adhesion– unloading and separation

• Multi-asperity contact model• Contact resistance model• Measurements and discussion• Conclusions

Model of contact surface

• Contact bump surface much rougher than drain surface - drain assumed to be a smooth surface.

• Greenwood and Williamson (1966) -surface represented by asperities of known shape and varying heights

• n asperities of radius R, heights z1,z2,...

• Deformation of asperities under load => contact spots are formed.

• Asperities assumed to deform independently, total contact force

d z1

z2

z3

z4

a1

a2

∑=n

FF=i

i1

GW (asperity-based) model versus fractal model

• Real surfaces have roughness at different length scales, GW model represents roughness at a single length scale (represented by asperity radius)

• Fractal-based contact models capture roughness at different length-scales (Bhushan and Majumdar (1990)) , but:– more complicated than GW model– requires more accurate surface profile than GW model– published models do not include adhesion

Selecting parameter values for GW model• Surface described by

– Radius of curvature (R)– Number of asperities (n)– distribution of heights - Gaussian

distribution => standard deviation σ

• SEM of drain shows 10-50 distinct spots, ~10 nm size. R=0.01 µm too small for this spot size. Assume R=0.1 µm, later vary R between 0.1 - 1 µm.

• Distribution of heights: assume 100 asperities, σ=0.1 µm (few contact spots) and σ=0.01 µm (10’s of contact spots). Later vary σ between 0.003 µm and 0.1 µm.

d z1

z2

z3

z4

a1

a2

Mechanical properties

• Nanoindentation measurements at Hysitron, MN• Elastic modulus E=91 GPa• Hardness H=2.2 GPa• Poisson’s ratio ν=0.5 (assumed; reported as 0.44 for bulk

gold)

Outline

• Introduction to Northeastern University switch• Related work• Modeling of contact surface with asperities (Greenwood &

Williamson)• Deformation model for single asperity

– loading without adhesion– loading with adhesion– unloading and separation

• Multi-asperity contact model• Contact resistance model• Measurements and discussion• Conclusions

Single asperity without adhesion - elastic/perfectly plastic

• Effective elastic modulus• Elastic deformation (Hertz): contact radius a

and vertical deformation α• Plastic deformation: a and α

α modified to obtain geometric continuity with elastic model (Chang, Etsion and Bogy (1988))

• Elastic to perfectly plastic transition

)11(431

2

22

1

21

EEKνν −

+−

=

3/1)(KFRa =

R

F=0 F=F1

HaF

=2π

ERYa p 11=

Ra2

=α

Ra2

2

=α

)2(αα

α pRa −=

Single asperity without adhesion - elasto-plastic model

• Physically realistic transition from elastic to perfectly plastic

• Elastic (Hertz)

• Fully plastic

• Elastic to elastoplastic - from von Mises yield criterion

• Elastoplastic to fully plastic• Semi-empirical formula in

elastoplastic (Studman (1976), modified after Maugis and Pollock (1984))

Ra2

=α3/1)(KFRa =

HaF

=2π

.1.12 YaF

=π

ERYaa p 60≈=

)9.3

ln7.01.1(2 YREaY

aF

+=π

Single asperity without adhesion - contact force-contact radius

Force (N)10-8 10-7 10-6 10-5 10-4

Con

tact

radi

us (m

)

10-9

10-8

10-7

elastic-fully plastic model, elastic elastic-fully plastic model, plasticmodified Studman model, elasticmodified Studman model, elasto-plasticmodified Studman model, plastic

• R=0.1 µm• Elastic to perfectly plastic: F=0.55 µN, a=8.9 nm • Elastic to elasto-plastic: F=0.025 µN, a=3.1 nm, elasto-

plastic to perfectly plastic F=16 µN, a=49 nm

Outline

• Introduction to Northeastern University switch• Related work• Modeling of contact surface with asperities (Greenwood &

Williamson)• Deformation model for single asperity

– loading without adhesion– loading with adhesion– unloading and separation

• Multi-asperity contact model• Contact resistance model• Measurements and discussion• Conclusions

Single asperity model with adhesion

• Physical origins of contact adhesion• Elastic contact models with adhesion

– JKR– DMT

• Elasto-plastic and perfectly plastic models with adhesion• Unloading and separation of contact surfaces; adherence

force

Physical origins of adhesion

• Various surface forces act between two surfaces in contact or proximity - van der Waals, ionic, covalent, metallic.

• Interaction characterized by a potential U(z).• When surfaces are in contact, U(z) reaches a (negative)

minimum. Defined as adhesion energy w (energy required to separate unit areas of two surfaces in contact).

• A surface is characterized by surface energy ν (energy required to create unit area of the surface). w=2ν for two identical surfaces

Van der Waals vs metallic bonds

⎥⎦⎤

⎢⎣⎡ −−= 8020

20

)(41)(

12)(

zZ

zZ

ZAzUπ

• van der Waals forces – long-range (several nm)– w~50 mJ/m2

• Metallic bonds– short range (characteristic length ~ 0.5 A0)– w=2-2.5 J/m2 for gold

• Metallic bonds can be screened by adsorbed molecules, films.

Lennard-Jones

( ) *

)1( *0

* zezUzU ββ −+−=

Ferrante et al. (1982)

Adhesion and elastic stresses are part of the same continuum

z*-2 0 2 4 6 8 10 12

σ /σ th

-0.5

0.0

0.5

1.0

1.5

z*-4 -2 0 2 4 6 8 10 12 14

U/U

0

-0.5

0.0

0.5

1.0

1.5

• Equilibrium at z*=0. Stress-strain is linear only when z*~0.• Compressive stress when z*<0• Tensile stress/adhesion when z*>0

Adhesive elastic contact and fracture mechanics• Elastic loading and unloading of sphere-

flat contact is analogous to retreat and advance of a crack (“external circular crack”)

• Crack advances by creating new surface area - requires energy wdA.

• Crack advances if -dUE>wdA.• In equilibrium• Contact area under load, and contact

adherence force can be calculated by invoking this equilibrium

crack

( ) wAUG E =∂∂−= δ/

Single asperity with adhesion - JKR model σ

ra

Hertz model Compressive Force F1 > F

σ

ra

∞

Flat punch model Force F -F1Boussinesq (1885)Sneddon (1946)

σ

ra

∞

JKR model Force FJohnson, Kendall and Roberts (1971)

Physically unrealistic solution at contact boundary, due to flat-punch model assumption of abrupt contact boundary

Single asperity with adhesion - JKR model ( )2

3

363 wRwRFwRFRKa πππ +±+=• Contact radius a:

• Vertical deformation α:

• Contact adherence force is the tensile force at which the equilibrium G=w becomes unstable

Kaw

Ra

382 πα −=

wRFadh π23

−=3./12

min 23

⎟⎟⎠

⎞⎜⎜⎝

⎛=

KwRa π

Single asperity with adhesion - DMT model

• Derjaguin, Muller and Toporov (1975).• Adhesion forces assumed to exist in a ring surrounding the

contact spot, but does not change Hertz solution for deformed surface profiles, stress within contact spot. Solution is not self-consistent.

• Contact adherence force: wRFadh π2−=

Validity of JKR and DMT models

DMTJKR3/1

2

2

2 ⎟⎟⎠

⎞⎜⎜⎝

⎛≈

KRwh• Height of “neck” in JKR model at small loads:

• Characteristic length for adhesive forces λ~0.5 A0

• R=0.1-1 µm, w=2.5 J/m2, K=81 GPa => h>> λ• Therefore forces outside contact spot can be

neglected => JKR is valid.

Single asperity with adhesion - elasto-plastic / plastic models • Roy Chowdhury and Pollock (1981),

Maugis (1984)• Adhesion forces assumed to exist in a ring

surrounding the contact spot, but does not change adhesionless (elasto-plastic/perfectly plastic) solution for deformed surface profiles, stress within contact spot. Solution is not self-consistent.

• Contact radius in elasto-plastic regime:

• Contact radius in plastic regime:

• Vertical deformation modified to obtain geometric continuity with JKR model

RwpaF m ππ 22 −=

)9.3

ln7.01.1(YR

EaYpm +=

RwHaF ππ 22 −=

Kwa

Ra ee

38

21

22

2 παα −+=

Single asperity with adhesion - contact force-contact radius

Force (N)

10-9 10-8 10-7 10-6 10-5 10-4

Con

tact

radi

us (m

)

10-9

10-8

10-7 No adhesion, elasticNo adhesion, elasto-plasticNo adhesion, fully plasticw=2.5 J/m2, elasto-plasticw=2.5 J/m2, fully plastic

Outline

• Introduction to Northeastern University switch• Related work• Modeling of contact surface with asperities (Greenwood &

Williamson)• Deformation model for single asperity

– loading without adhesion– loading with adhesion– unloading and separation

• Multi-asperity contact model• Contact resistance model• Measurements and discussion• Conclusions

Single asperity with adhesion - recovered asperity radius after elasto-plastic / plastic deformation

• Elasto-plastic/plastic deformation after loading to Ff (no adhesion): flattening of asperity (radius R to R1), concavity in drain radius=-R2.

• Equivalent to contact between flat and sphere of radius Reff,

21

111RRReff

−=

• Re-loading the contact to Ff forms contact spot of same radius af as given by earlier plastic loading:

f

feff F

KaR

3

=

• Elasto-plastic/plastic deformation with adhesion: Reff, is assumed to be the same as in the absence of adhesion (Johnson (1977)).

m

f

mf

feff p

KapaKa

Rππ

== 2

3

HKa

HaKa

R f

f

feff ππ

== 2

3

Single asperity with adhesion - recovered asperity radius after elasto-plastic / plastic deformation

Contact Force (N)

10-8 10-7 10-6 10-5 10-4

Asp

erity

radi

us (m

icro

n)

0.0

0.2

0.4

0.6

0.8

1.0No adhesion, elasticNo adhesion, elasto-plasticNo adhesion, fully plasticw=2.5 J/m2, elasto-plasticw=2.5 J/m2, fully plastic

Unloading and separation of single asperity

• Elastic loading: unloadinaccording to JKR model. Equilibrium becomes unstable at

wRFadh π23

−=3./12

min 23

⎟⎟⎠

⎞⎜⎜⎝

⎛=

KwRa π

• Elasto-plastic loading:– Initial unloading follows elastic unloading of a flat punch with

constant contact radius

f

ff Ka

FF2

)(3 −=−αα

– Followed by one of three possible modes.

Unloading and separation of single asperity

2)(6

mf pH

Kwa+

<π

223

HKwa f π

<

• Ductile (Fd) mode: axial stress becomes tensile and equal to H - (yield point) plastic yield followed by cohesive separation

• Brittle (Fm) mode: contact force F is such that JKR equilibrium point is reached, and a<amin - unstable equilibrium - adhesive separation.

• Brittle (Fb) mode: contact force F is such that JKR equilibrium point is reached, and a>amin - elastic (JKR) unloading until F=Fadh and a=amin - adhesive separation.

22 23

)(6

mf

m pKwa

pHKw

ππ<<

+

223

mf p

Kwaπ

>

223

HKwa f π

>

Unloading and separation of single asperity

• If contact interface is metallic it becomes indistinguishable from the bulk.

• Even if the contact separation is predicted to be brittle, the contacts may not separate along the interface (material transfer).

Unloading and separation of single asperity

Contact force (N)

10-9 10-8 10-7 10-6 10-5 10-4

Adh

eren

ce F

orce

(N)

10-6

10-5

10-4

Ductile separationBrittle separation (Fm mode)Brittle separation (Fb mode)

Contact Force (µN)

-6 -4 -2 0 2 4 6

Con

tact

radi

us (n

m)

1416182022242628303234

LoadUnload from Ff=4 µN, brittle separationUnload from Ff=1.9 µN, brittle separationUnload from Ff=0.7 µN, ductile separation

Outline

• Introduction to Northeastern University switch• Related work• Modeling of contact surface with asperities (Greenwood &

Williamson)• Deformation model for single asperity

– loading without adhesion– loading with adhesion– unloading and separation

• Multi-asperity contact model• Contact resistance model• Measurements and discussion• Conclusions

Multiple asperity model

d z1

z2

z3

z4

a1

a2

• N asperities, heights z1 > z2 > … > zN

• First n asperities in contact, zn > d > zn+1.• For each contacting asperity i,vertical

deformation:

.dzii −=α

• Using elastic (JKR), elasto-plastic or plastic model, determine Fi(αi) and ai(αi).

• Total contact force ∑=

=n

iiFF

1

Multiple asperity model-loading

Contact Force (N)

10-7 10-6 10-5 10-4 10-3

Aspe

ritie

s in

con

tact

0

20

40

60

80

100All asperities in contactElasto-plastic asperitiesPlastic asperities

Contact Force (N)

10-6 10-5 10-4 10-3

Con

tact

spo

t rad

ius

(m)

10-9

10-8

10-7

10-6

Asperity 1Asperity 2Asperity 5Asperity 10Asperity 50

σ=0.01 µm

Contact Force (N)

10-7 10-6 10-5 10-4 10-3

Asp

eriti

es in

con

tact

0

5

10

15

20All asperities in contactElasto-plastic asperitiesPlastic asperities

Contact Force (N)

10-6 10-5 10-4 10-3

Con

tact

spo

t rad

ius

(m)

10-9

10-8

10-7

10-6

Asperity 1Asperity 2Asperity 5Asperity 10

σ=0.1 µm

Multiple asperity model-unloading

Contact Force (µN)

-100 -50 0 50 100 150 200

Num

ber o

f asp

eriti

es

0

10

20

30

40

50Total asperitiesDuctile separationBrittle (Fm) separationBrittle (Fb) separation

Contact Force (µN)

Contact Force (µN)

-40 -20 0 20 40 60 80 100

Num

ber o

f asp

eriti

es

0

5

10

15

20

25Total asperitiesDuctile separationBrittle (Fm) separationBrittle (Fb) separation

-100 -50 0 50 100 150 200

Num

ber o

f asp

eriti

es

0

2

4

6

8

10

σ=0.01 µm

Contact Force (µN)

-40 -20 0 20 40 60 80 100

Num

ber o

f asp

eriti

es

0

2

4

6

8

10σ=0.1 µm

Outline

• Introduction to Northeastern University switch• Related work• Modeling of contact surface with asperities (Greenwood &

Williamson)• Deformation model for single asperity

– loading without adhesion– loading with adhesion– unloading and separation

• Multi-asperity contact model• Contact resistance model• Measurements and discussion• Conclusions

Contact resistance - single contact spot

Sharvin resistance (contact radius < electron mean free path length)

ρ = resistivity r = radius of contact spotle = electron mean free path length0.69<ν<1 (interpolation factor: Wexler)

Rlr r

e= +43 22

ρπ

νρ

Constriction resistance (contact radius > electron mean free path length) (Maxwell)

Measured ρ = 6.75x10-8 Ω-m (drain) 3.85x10-8 Ω-m (beam). Used average.

Contact resistance - multiple contact spots

• Lower bound: contact spots are far apart, conduct independently

• Upper bound: spots are merged into a single large spot

∑=i

iconlbcon RR ,, /1/1

∑= 2ieff aa

effeffe

eff

eubcon a

ala

lR2

)/(34

2,ρυ

πρ

+=

Contact resistance model - with and without adhesion

Contact Force (N)

10-7 10-6 10-5 10-4 10-3

Con

tact

Res

ista

nce

(Ω)

0.0

0.5

1.0

1.5

2.0

2.5

3.0w=2.5J/m2,lower boundw=2.5J/m2,upper boundno adhesion, lower boundno adhesion, upper bound

• N=100, R=0.1µm and σ=0.01 µm

Contact resistance model - load and unload characteristics

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper bound

Contact Force (µN)

-100 0 100 200

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper bound

• N=100, R=0.1µm and σ=0.01 µm

Contact resistance model - effect of σ and R on number of contacting asperities

σ (µm)

0.001 0.01 0.1

Asp

eriti

es

0

10

20

30

40

50

R=0.1 µm R=0.3 µmR=1 µm

R (µm)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Asp

eriti

es

0

10

20

30

40

50

σ=0.003 µm σ=0.01 µm σ=0.1 µm

Contact resistance model - effect of σ and R on contact adherence force

σ (µm)

0.001 0.01 0.1

Adhe

renc

e fo

rce

(µN

)

-100

-80

-60

-40

-20

0

R=0.1 µm R=0.3 µm R=1 µm

R (µm)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Adhe

renc

e fo

rce

(µN

)

-80

-70

-60

-50

-40

-30

-20

-10

σ=0.003 µm σ=0.01 µm σ=0.1 µm

Contact resistance model - effect of σ and R on contact resistance bounds

σ (µm)

0.001 0.01 0.1

Con

tact

resi

stan

ce (Ω

)

0.0

0.1

0.2

0.3

0.4

R=0.1 µm, upper boundR=0.1 µm, lower bound R=0.3 µm, upper bound R=0.3 µm, lower boundR=1 µm, upper boundR=1 µm, lower bound

R (µm)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Res

ista

nce

(Ω)

0.0

0.1

0.2

0.3

0.4σ=0.003 µm, upper boundσ=0.003 µm, lower boundσ=0.01 µm, upper boundσ=0.01 µm, lower boundσ=0.1 µm, upper boundσ=0.1 µm, lower bound

Effect of σ on sensitivity of resistance to force while loading

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper bound

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper bound

N=100, R=0.1µm and σ=0.03 µmN=100, R=0.1µm and σ=0.1 µm

Effect of R on sensitivity of resistance to force while loading

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper bound

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper bound

N=100, R=0.1µm and σ=0.01 µmN=100, R=1µm and σ=0.01 µm

Model of film-covered surface

• Asperities with load < Fth have zero surface energy, are electrically non-conductive

N=100, R=0.1µm and σ=0.01 µm

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper bound

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper bound

Fth = 0Fth = 5 µN

Outline

• Introduction to Northeastern University switch• Related work• Modeling of contact surface with asperities (Greenwood &

Williamson)• Deformation model for single asperity

– loading without adhesion– loading with adhesion– unloading and separation

• Multi-asperity contact model• Contact resistance model• Measurements and discussion• Conclusions

Measurement of contact resistance

V

Contact bump

Drain 1

Drain 2

Source 1

Source 2

Actuation Voltage (V)0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ohm

s)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Translating actuation voltage into contact force

Actuation Voltage (V)0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ohm

s)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

FE

Contact ForceR1

M

Gate

Actuation Voltage (V)0 20 40 60 80 100 120 140

Con

tact

For

ce (µ

N)

-200

-100

0

100

200

300

400

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ohm

s)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Evolution of measured characteristics

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ohm

s)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ohm

s)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

10 cyclesInitial

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ohm

s)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ohm

s)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1000 cycles 10000 cycles

Can measured evolution be explained by change in σ?

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper boundMeasured after 10000 cycles

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper boundMeasured after 1000 cycles

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper boundMeasured after 10 cycles

R=0.1µm, σ=0.1 µm, meas. 10 cycles

R=0.1µm, σ=0.01 µm, meas. 1000 cycles

R=0.1µm, σ=0.003 µm, meas. 104 cycles

Does the surface film model explain measured evolution?σ=0.003 µm, Fth = 3 µN meas. initial

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper boundMeasured after 1000 cycles

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper boundMeasured - initial

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ω)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4 Load, lower boundLoad, upper boundUnload, lower boundUnload, upper boundMeasured after 10000 cycles

σ=0.003 µm, Fth = 1 µN meas. 1000 cycles

σ=0.003 µm, Fth = 0 meas. 10000 cycles

Evolution towards flat punch geometry?

• Contact resistance load-half cycle extremely force-insensitive after a high number of cycles, similar to unload-half cycle

• Suggests asperities may tend towards a flat punch-like geometry (very flat tops), and deformation becomes completely elastic.

• Completely force-insensitive contact while loading and unloading, all asperities separate simultaneously

Sample calculation for a simple flat-punch model:

• assume n contacting asperities, cylinders of equal heights and radii• total contact area under 70 µN ~ 3x10-14 m2 (assuming plastic

deformation), effective spot radius aeff= 10-7m, each spot • Total contact adherence force =

naa eff /=

Kwan eff34/1 6π or Haeff

2π

Contact Force (µN)

-80 -60 -40 -20 0 20 40 60 80 100

Con

tact

Res

ista

nce

(Ohm

s)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

10000 cycles• Fadh=-86 µN• n=10=> contact resistance 0.2 Ω - 0.06 Ω• n=50=> contact resistance 0.2 Ω - 0.03 Ω

Conclusions• Initial contact not completely metallic (measured contact

resistance too high)• Metal-to-metal contact is obtained after cycling (typically

100-1000 cycles)– measured contact resistance – measured contact adherence– evidence of material transfer

• Model predicts some plastic deformation of asperities even at very small loads.

• With a large number of contact spots (20-50) - ductile separation of asperities likely, makes material transfer more likely.

• Asperities unload like flat punches - explains force-insensitive contact resistance while unloading

Conclusions - changes with cycling

• With cycling, measured contact resistance decreases, contact adherence increases, load half-cycle of characteristic becomes force-insensitive

• Decrease in contact resistance: removal of surface film, decrease in surface roughness.

• Increase in contact adherence: removal of surface film, decrease in surface roughness, blunting of asperities.

• Force-insensitive contact resistance while loading: blunting of asperities.

Conclusions - mechanisms of contact surface evolution

• Surface film removed by repeated contact, possibly plastic deformation and material transfer. Increasing metallic contact area may accelerate process further.

• Blunting of asperities by repeated contact, removal of surface film (surface forces cause “necking” of asperity), ductile separation?

• Decrease of surface roughness: ductile separation could cause material to be transferred from asperity to flat.

• Other mechanisms that can cause surface changes with time/cycling: electromigration, visco-elasticity /creep.

Conclusions - device design

• Central goal: obtain low and stable contact resistance and a favorable balance between restoring force and contact adherence force.

• To obtain better device performance:– change actuator design to obtain greater actuator force at a given

voltage; – changes choice or deposition methods of the contact materials, or

treatment of the contact surface, to reduce the contact adherence force.

Conclusions - device design

• Actuator design: – force can be increased by increasing area, reducing gap, making

beam more rigid in closed position– trade-off with beam-gate capacitance, switching speed,

manufacturability

• Contact material/surface– contact surface should be clean and inert => low and stable contact

resistance with small contact force. (gold)– minimize material transfer for stable contact resistance - hard metal

(Pt group) (mate hard metal with soft metal?)– surface should have low surface energy; some Pt group metals

form conducting oxide, but cleanliness hard to control, form frictional polymer.

Acknowledgments

• Prof. McGruer & Prof. Adams• Prof. Zavracky• Professors, staff and students at MFL: Rick Morrison,

Weilin Hu, Keith Warner, Greg Jenkins, Michael Miller, Xiaomin Yan, Prof. Hopwood.

• Analog Devices and Radant MEMS.