Contact Properties of a Microelectromechanical (MEMS) switch with gold-on-gold contacts. Sumit Majumder ECE, Northeastern University

Transcription

1 Contact Properties of a Microelectromechanical (MEMS) switch with gold-on-gold contacts Sumit Majumder ECE, Northeastern University

2 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)

3 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

4 Why study contact adhesion? F = εav x( V ) x(v) V A = mm, x(v) = µm, V less than 100 V Total actuator force typically ~ 1 mn Contact force 100 µn - 1 mn, restoring force 100 µn - 1 mn

5 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, 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

6 Evolution of measured characteristics Contact Resistance (Ohms) Initial Contact Resistance (Ohms) cycles Contact Force (µn) Contact Force (µn) Contact Resistance (Ohms) Contact Resistance (Ohms) cycles cycles Contact Force (µn) Contact Force (µn)

7 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

8 Northeastern University microswitch Predecessor: Zavracky & Morrison, Foxboro (1984). Devices used in this work fabricated in Microfabrication Laboratory (MFL) at NU in Since 1999, further development and commercialization at Analog Devices and Radant MEMS. Fabricated using all-metal surface micromachining process developed at NU.

9 Northeastern University microswitch Contact Detail Gate G Drain Beam Source S DRAIN GATE SOURCE D 100 µm DRAIN GATE SOURCE Gold cantilever beam, sputtered gold contacts.

10 Northeastern University microswitch with gold-gold contacts Φ= Threshold voltage V. Restoring force 70 µn per contact. Actuation voltage V => contact force µn per contact. Operated in dry nitrogen DRAIN GATE 6 SOURCE Contact resistance initially Ω, after cycles Ω. Lifetime ~10 6 cycles with 10 ma per contact, limited by permanent stuck-closed failures.

11 MEMS switch contacts: Related work Majumder et al. (1997,1998,001) Hyman et al. (1998) thermal model Yan et al.(001) thermal model Kruglick (1999), Lafontan (001) simple contact models from device perspective AFM-based work in MEMS switch force range Beale and Pease (199) Schimkat (1998), Bromley et al. (001) 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)

12 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

13 Model of contact surface d z 4 z z 3 z 1 a 1 a 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 z 1,z,... Deformation of asperities under load => contact spots are formed. Asperities assumed to deform independently, total contact force F n = i= 1 F i

14 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

15 Selecting parameter values for GW model d z 4 z z 3 z 1 a 1 a Surface described by Radius of curvature (R) Number of asperities (n) distribution of heights - Gaussian distribution => standard deviation σ SEM of drain shows distinct spots, ~10 nm size. R=0.01 µm too small for this spot size. Assume R=0.1 µm, later vary R between 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 µm and 0.1 µm.

16 Mechanical properties Nanoindentation measurements at Hysitron, MN Elastic modulus E=91 GPa Hardness H=. GPa Poisson s ratio ν=0.5 (assumed; reported as 0.44 for bulk gold)

17 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

18 Single asperity without adhesion - elastic/perfectly plastic R F=0 F=F 1 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 1 K = 3 1 ν1 1 ν ( + ) 4 E E 1 FR 1/3 a = ( ) K F = πa a = H RY a p = 11 E α = α = α p Rα( ) α a R a R

19 Single asperity without adhesion - elasto-plastic model Physically realistic transition from elastic to perfectly plastic Elastic (Hertz) FR 1/3 a = ( ) K α = a R Fully plastic F = πa H 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)) F 1.1Y. = πa a = a p 60 F πa RY E = Y ( ln Ea ) 3.9YR

20 Single asperity without adhesion - contact force-contact radius 10-7 Contact radius (m) 10-8 elastic-fully plastic model, elastic elastic-fully plastic model, plastic modified Studman model, elastic modified Studman model, elasto-plastic modified Studman model, plastic R=0.1 µm Force (N) Elastic to perfectly plastic: F=0.55 µn, a=8.9 nm Elastic to elasto-plastic: F=0.05 µn, a=3.1 nm, elastoplastic to perfectly plastic F=16 µn, a=49 nm

21 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

22 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

23 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=ν for two identical surfaces

24 Van der Waals vs metallic bonds van der Waals forces long-range (several nm) w~50 mj/m A U ( z) = 1πZ 0 Z ( z Lennard-Jones 0 ) 1 4 Z ( z 0 ) 8 Metallic bonds short range (characteristic length ~ 0.5 A 0 ) w=-.5 J/m for gold U ( z ) = U (1 + βz ) e * * βz 0 Ferrante et al. (198) * Metallic bonds can be screened by adsorbed molecules, films.

25 Adhesion and elastic stresses are part of the same continuum U/U σ/σ th z* z* Equilibrium at z*=0. Stress-strain is linear only when z*~0. Compressive stress when z*<0 Tensile stress/adhesion when z*>0

26 Adhesive elastic contact and fracture mechanics Elastic loading and unloading of sphereflat 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 -du E >wda. In equilibrium Contact area under load, and contact adherence force can be calculated by invoking this equilibrium ( U / A) w G E = = δ crack

27 Single asperity with adhesion - JKR model σ σ Hertz model Compressive Force F 1 > F a r Flat punch model Force F -F 1 Boussinesq (1885) Sneddon (1946) a r σ JKR model Force F Johnson, Kendall and Roberts (1971) a r Physically unrealistic solution at contact boundary, due to flat-punch model assumption of abrupt contact boundary

28 Single asperity with adhesion - JKR model Contact radius a: 3 a K = R ( 3π ) F + 3π wr ± 6πwRF + wr Vertical deformation α: α = a R 8πaw 3K Contact adherence force is the tensile force at which the equilibrium G=w becomes unstable 3 F adh = πwr 3 πwr amin = K 1/.3

29 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: = πwr F adh

30 Validity of JKR and DMT models JKR DMT Height of neck in JKR model at small loads: Characteristic length for adhesive forces λ~0.5 A 0 R=0.1-1 µm, w=.5 J/m, K=81 GPa => h>> λ Therefore forces outside contact spot can be neglected => JKR is valid. h 1/3 Rw K

31 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: F = πa pm πrw Ea p m = Y ( ln ) 3.9YR Contact radius in plastic regime: F = πa H πrw Vertical deformation modified to obtain geometric continuity with JKR model a α = R αe + 1 8πa ew 3K

32 Single asperity with adhesion - contact force-contact radius Contact radius (m) 10-7 No adhesion, elastic No adhesion, elasto-plastic No adhesion, fully plastic w=.5 J/m, elasto-plastic w=.5 J/m, fully plastic Force (N)

33 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

34 Single asperity with adhesion - recovered asperity radius after elasto-plastic / plastic deformation Elasto-plastic/plastic deformation after loading to F f (no adhesion): flattening of asperity (radius R to R 1 ), concavity in drain radius=-r. Equivalent to contact between flat and sphere of radius R eff, 1 R eff 1 = R 1 1 R Re-loading the contact to F f forms contact spot of same radius a f as given by earlier plastic loading: R eff = Ka F f 3 f Elasto-plastic/plastic deformation with adhesion: R eff, is assumed to be the same as in the absence of adhesion (Johnson (1977)). R eff a 3 f = πa f K p m = a f πp K m R eff a 3 f = πa f K H = a f K πh

35 Single asperity with adhesion - recovered asperity radius after elasto-plastic / plastic deformation Asperity radius (micron) No adhesion, elastic No adhesion, elasto-plastic No adhesion, fully plastic w=.5 J/m, elasto-plastic w=.5 J/m, fully plastic Contact Force (N)

36 Unloading and separation of single asperity Elastic loading: unloadinaccording to JKR model. Equilibrium becomes unstable at 3 F adh = πwr a min Elasto-plastic loading: 3 πwr = K Initial unloading follows elastic unloading of a flat punch with constant contact radius α α f 3( F Ff ) = Ka f 1/.3 Followed by one of three possible modes.

37 Unloading and separation of single asperity Ductile (F d ) mode: axial stress becomes tensile and equal to H - (yield point) plastic yield followed by cohesive separation a f a f 6Kw < π ( H + p 3Kw < πh m ) Brittle (F m ) mode: contact force F is such that JKR equilibrium point is reached, and a<a min - unstable equilibrium - adhesive separation. Brittle (F b ) mode: contact force F is such that JKR equilibrium point is reached, and a>a min - elastic (JKR) unloading until F=F adh and a=a min - adhesive separation. 6Kw π ( H + p a f a f m ) 3Kw > πp m 3Kw > πh < a f < 3Kw πp m

38 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).

39 Unloading and separation of single asperity 10-4 Adherence Force (N) Ductile separation Brittle separation (F m mode) Brittle separation (F b mode) Contact force (N) Contact radius (nm) Load Unload from Ff=4 µn, brittle separation Unload from Ff=1.9 µn, brittle separation Unload from Ff=0.7 µn, ductile separation Contact Force (µn)

40 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

41 Multiple asperity model N asperities, heights z 1 > z > > z N First n asperities in contact, z n > d > z n+1. For each contacting asperity i,vertical deformation: α i = z i d. d z 4 z z 3 z 1 a 1 a Using elastic (JKR), elasto-plastic or plastic model, determine F i (α i ) and a i (α i ). n Total contact force F = F i i= 1

42 Asperities in contact Multiple asperity model-loading All asperities in contact Elasto-plastic asperities Plastic asperities Contact spot radius (m) 10-6 Asperity 1 Asperity Asperity Asperity 10 Asperity Contact Force (N) 10-9 σ=0.01 µm Contact Force (N) Asperities in contact All asperities in contact Elasto-plastic asperities Plastic asperities σ=0.1 µm Contact spot radius (m) 10-6 Asperity 1 Asperity Asperity 5 Asperity Contact Force (N) Contact Force (N)

43 Multiple asperity model-unloading Number of asperities Total asperities Ductile separation Brittle (F m ) separation Brittle (F b ) separation Number of asperities Contact Force (µn) σ=0.01 µm Contact Force (µn) Number of asperities Total asperities Ductile separation Brittle (F m ) separation Brittle (F b ) separation σ=0.1 µm Number of asperities Contact Force (µn) Contact Force (µn)

44 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

45 Contact resistance - single contact spot R ρ Sharvin resistance (contact radius < electron mean free path length) 4 l = e + 3 r r π ν ρ Constriction resistance (contact radius > electron mean free path length) (Maxwell) ρ = resistivity r = radius of contact spot l e = electron mean free path length 0.69<ν<1 (interpolation factor: Wexler) Measured ρ = 6.75x10-8 Ω-m (drain) 3.85x10-8 Ω-m (beam). Used average.

46 Contact resistance - multiple contact spots Lower bound: contact spots are far apart, conduct independently 1/ R con, lb / Rcon, i i = 1 Upper bound: spots are merged into a single large spot a eff = a i R con, ub 4ρl = 3πa e eff + υ( l e / a eff ) ρ a eff

47 Contact resistance model - with and without adhesion Contact Resistance (Ω) w=.5j/m,lower bound w=.5j/m,upper bound no adhesion, lower bound no adhesion, upper bound Contact Force (N) N=100, R=0.1µm and σ=0.01 µm

48 Contact resistance model - load and unload characteristics Contact Resistance (Ω) 1.4 Load, lower bound Load, upper bound 1. Unload, lower bound Unload, upper bound Contact Resistance (Ω) 1.4 Load, lower bound 1. Load, upper bound Unload, lower bound 1.0 Unload, upper bound Contact Force (µn) Contact Force (µn) N=100, R=0.1µm and σ=0.01 µm

49 Contact resistance model - effect of σ and R on number of contacting asperities Asperities R=0.1 µm R=0.3 µm R=1 µm Asperities σ=0.003 µm σ=0.01 µm σ=0.1 µm σ (µm) R (µm)

50 Contact resistance model - effect of σ and R on contact adherence force Adherence force (µn) R=0.1 µm R=0.3 µm R=1 µm Adherence force (µn) σ=0.003 µm σ=0.01 µm σ=0.1 µm σ (µm) R (µm)

51 Contact resistance model - effect of σ and R on contact resistance bounds Contact resistance (Ω) R=0.1 µm, upper bound R=0.1 µm, lower bound R=0.3 µm, upper bound R=0.3 µm, lower bound R=1 µm, upper bound R=1 µm, lower bound Resistance (Ω) σ=0.003 µm, upper bound σ=0.003 µm, lower bound σ=0.01 µm, upper bound σ=0.01 µm, lower bound σ=0.1 µm, upper bound σ=0.1 µm, lower bound σ (µm) R (µm)

52 Effect of σ on sensitivity of resistance to force while loading Contact Resistance (Ω) 1.4 Load, lower bound Load, upper bound 1. Unload, lower bound Unload, upper bound Contact Resistance (Ω) 1.4 Load, lower bound 1. Load, upper bound Unload, lower bound 1.0 Unload, upper bound Contact Force (µn) Contact Force (µn) N=100, R=0.1µm and σ=0.1 µm N=100, R=0.1µm and σ=0.03 µm

53 Effect of R on sensitivity of resistance to force while loading Contact Resistance (Ω) 1.4 Load, lower bound Load, upper bound 1. Unload, lower bound Unload, upper bound Contact Resistance (Ω) 1.4 Load, lower bound Load, upper bound 1. Unload, lower bound Unload, upper bound Contact Force (µn) Contact Force (µn) N=100, R=1µm and σ=0.01 µm N=100, R=0.1µm and σ=0.01 µm

54 Model of film-covered surface Asperities with load < F th have zero surface energy, are electrically non-conductive N=100, R=0.1µm and σ=0.01 µm Contact Resistance (Ω) 1.4 Load, lower bound Load, upper bound 1. Unload, lower bound Unload, upper bound Contact Resistance (Ω) 1.4 Load, lower bound Load, upper bound 1. Unload, lower bound Unload, upper bound Contact Force (µn) Contact Force (µn) F th = 5 µn F th = 0

55 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

56 Measurement of contact resistance Contact bump Source V Drain 1 Drain Source Contact Resistance (Ohms) Actuation Voltage (V)

57 Translating actuation voltage into contact force 1.4 Contact Resistance (Ohms) M R 1 F E Gate Contact Force Actuation Voltage (V) Contact Resistance (Ohms) Contact Force (µn) Contact Force (µn) Actuation Voltage (V)

58 Evolution of measured characteristics Contact Resistance (Ohms) Initial Contact Resistance (Ohms) cycles Contact Force (µn) Contact Force (µn) Contact Resistance (Ohms) Contact Resistance (Ohms) cycles cycles Contact Force (µn) Contact Force (µn)

59 Can measured evolution be explained by change in σ? R=0.1µm, σ=0.1 µm, meas. 10 cycles Contact Resistance (Ω) Contact Resistance (Ω) 1.4 Load, lower bound Load, upper bound 1. Unload, lower bound Unload, upper bound 1.0 Measured after 10 cycles Load, lower bound 1. Load, upper bound Unload, lower bound 1.0 Unload, upper bound Measured after cycles Contact Force (µn) R=0.1µm, σ=0.003 µm, meas cycles R=0.1µm, σ=0.01 µm, meas cycles Contact Resistance (Ω) 1.4 Load, lower bound Load, upper bound 1. Unload, lower bound Unload, upper bound 1.0 Measured after 1000 cycles Contact Force (µn) Contact Force (µn)

60 Does the surface film model explain measured evolution? σ=0.003 µm, F th = 3 µn meas. initial Contact Resistance (Ω) 1.4 Load, lower bound Load, upper bound 1. Unload, lower bound Unload, upper bound 1.0 Measured - initial Contact Force (µn) σ=0.003 µm, F th = 0 meas cycles Contact Resistance (Ω) 1.4 Load, lower bound 1. Load, upper bound Unload, lower bound 1.0 Unload, upper bound Measured after cycles σ=0.003 µm, F th = 1 µn meas cycles Contact Resistance (Ω) 1.4 Load, lower bound Load, upper bound 1. Unload, lower bound Unload, upper bound 1.0 Measured after 1000 cycles Contact Force (µn) Contact Force (µn)

61 Evolution towards flat punch geometry? Contact resistance load-half cycle extremely forceinsensitive 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

62 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 m (assuming plastic deformation), effective spot radius a eff = 10-7 m, each spot a = aeff / Total contact adherence force = n n 1/ 4 3 6πa Kw or π H eff a eff 1.4 F adh =-86 µn n=10=> contact resistance 0. Ω Ω n=50=> contact resistance 0. Ω Ω Contact Resistance (Ohms) cycles Contact Force (µn)

63 Conclusions Initial contact not completely metallic (measured contact resistance too high) Metal-to-metal contact is obtained after cycling (typically 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 (0-50) - ductile separation of asperities likely, makes material transfer more likely. Asperities unload like flat punches - explains forceinsensitive contact resistance while unloading

64 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.

65 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.

66 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.

67 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.

68 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.