MEMS 487. Class 04, Feb. 13, K.J. Hemker

Transcription

1 MEMS 487 Class 04, Feb. 13, 2003

2 Materials Come As:!Amorphous Glasses, polymers, some metal alloys Processing can result in amorphous structures! Crystalline Single crystals Textured crystals Polycrystalline

3 Cubic Crystals Body Centered Cubic BCC Silicon Interlaced FCC Face Centered Cubic FCC

4 BCC Atomic Planes: {001} 4-fold

5 BCC Atomic Planes: {011} 2-fold

6 BCC Atomic Planes: {111} 3-fold

7 FCC Atomic Planes: {001} 4-fold

8 FCC Atomic Planes: {011} 2-fold

9 FCC Atomic Planes: {111} 3-fold

10 Atomic Planes in Si: {001} 4-fold

11 Atomic Planes in Si: {011} 2-fold

12 Atomic Planes in Si: {111} 3-fold

13 Useful crystallography web sites note: Si is the same structure as diamond, gold is FCC and Fe is BCC EMS On Line at

14 Crystallographic directions : [101] [001] [111] [011] <100> cube edges <011> face diagonals [010] <111> cube diagonals [100] [110]

15 Silicon wafers: {100} [001] [0-1-1] [00-1] [001] [010] [010 {100} Primary flat <110> ±3 Primary flat <110> ±3 [0-10] [011] [010] [0-11] [00-1] [01-1]

16 Isotropic Elasticity All directions the same polycrystalline σ = E ε τ = G γ p = -K ν = ε yy / ε xx σ yy = λ ε xx 5 constants only 2 independent Lamé Coefficient (λ) ε xx σ yy

17 Anisotropic elasticity (stiffness) σ i =C ij ε j σ xx C 11 C 12 C 13 C 14 C 15 C 16 ε xx σ yy C 21 C 22 C 23 C 24 C 25 C 26 ε yy σ zz = C 31 C 32 C C C 35 C 36 ε zz σ yz C 41 C 42 C 43 C 44 C 45 C 46 ε yz σ xz C 51 C 52 C 53 C 54 C 55 C 56 ε xz σ xy C 61 C 62 C 63 C 64 C 65 C 66 ε xy

18 Compliance ε i =S ij σ j ε xx S 11 S 12 S 13 S 14 S 15 S 16 σ xx ε yy S 21 S 22 S 23 S 24 S 25 S 26 σ yy ε zz = S 31 S 32 S 33 S 34 S 35 S 36 σ zz ε yz S 41 S 42 S 43 S 44 S 45 S 46 σ yz ε xz S 51 S 52 S 53 S 54 S 55 S 56 σ xz ε xy S 61 S 62 S 63 S 64 S 65 S 66 σ xy

19 C ij and S ij for Cubic Crystals C 11 C 12 C 12 C 12 C 11 C 12 C ij = C 12 C 12 C 11 C C 44 C 44 C 11, C 12, C 44

20 1-Dimensional Loading E [100], E [110], and E [111] E [100] = 1 s 11 E [110] = 2 [s 11 + s 12 + s 44 /2] E [111] = 3 [s s 12 + s 44 ]

21 Relations : c 11 = s 11 + s 12 (s 11 -s 12 ) (s s 12 ) s 11 = c 11 + c 12 (c 11 -c 12 ) (c c 12 ) c 12 = -s 12 (s 11 -s 12 ) (s s 12 ) s 12 = -c 12 (c 11 -c 12 ) (c c 12 ) c 44 = 1 s 44 s 44 = 1 c 44

22 Example of Anisotropic Elasticity:! To be addressed in homework problem. Assume that for Si C 11 = 166 GPa C 12 = 64 GPa C 44 = 80 GPa Calculate Young s modulus (E) along <100>, <110> and <111>

23 Elasticity of Textured Films: 1. Consider a textured thin film [001] 2. Calculate E from Sij's β' β α' (011) α 3. Estimate Voight and Reuss bounds for E 1000 EVoight = Σ ViEi i=1 EReuss = Σ ( V i Ε ) i i=1

24 LIGA-Ni texture model 450 Young's modulus (GPa) <111>, 303 GPa <011>, 232 GPa <001>, 136 GPa (011) (111) (001) 232 GPa <001> out-of-plane No in-plane texture Isotropic E E (001) = 177 GPa E measured = 180 GPa Angle (degree) J OHNS HOPKINS ENGI NEERI NG

25 Headlines about elasticity:![c ij ] s will not change at micro-scale.! What out for texture effects.!single-crystalline materials require anisotropic elasticity.

26 Mechanical Strength:! Ductile Materials (Metals, hi T Si) Deform plastically or yield! Brittle Materials (Ceramics, Glass, RT Si) Fracture

27 Yield Strength:! Dislocations lead to plastic deformation

28 Atomic description of plasticity:

29 Yield Strength:! Dislocations lead to plastic deformation! Slow down dislocations = strengthening lattice solute atoms precipitates grain boundaries Note: MEMS is a young field many people still use pure materials.

30 Fracture Strength: σ f

31 Stress Magnification: σ Inglis h ρ 2c σ σ max σ ο σ max = σ (1+2c / h) for an ellipse: ρ = h 2 / c σ max = 2σ (c / ρ) 1/2 lim ρ >0 (ρ) =a o σ max = 2σ (10-2 / ) 1/2 σ σ max = 20,000 σ!!!!!

32 Basis for Fracture Mechanics σ (π c ) 1/2 = K c Geometry and loading Material Parameter Stress Intensity Factor Fracture Toughness

33 Key to Fracture Mechanics 1. Determine K c - measure on specimens of known geometry 2. Calculate K - from current geometry and loading 3. Compare K with Kc -K < K c is OK -K > K c will fracture

34 Typical Values for K IC Silicon

35 Micro Comparison of structural members: beams Macro steel polysilicon

36 Micro Comparison of structural members: turbines Macro GE 90 Jet Engine : silicon -> SiC Ni superalloys

37 Micro Comparison of structural members: gears Macro Steel, Ti polysilcion

38 Design views:!mems view: Silicon a wonderful structural material!macro view: Silicon too brittle and too expensive Who is right?

39 When will Si fracture?!macro world defects ~ 1 mm σ f = K Ic /(πc) 1/2 = 0.9 MPa m 1/2 / (π 10-3 m) 1/2 = 16 MPa!MEMS world defects ~1 µm σ f =K Ic /(πc) 1/2 = 0.9 MPa m 1/2 / (π 10-6 m) 1/2 = 508 MPa

40 How much will Si cost? Total Cost = C material + C manufacture + C disposal! Macro world C steel = $0.20/lb x tons + $ C Si = $4.00/lb x tons + $$$!MEMS world C steel = $0.20/lb x grams + $$$$ C Si = $4.00/lb x tons + $$$

41 Farmer s view on polysilcion:!cost: Tolerable, should get better, key is batch processing.! Mechanical performance: Ok for low T applications where components are over-sized and flaws are controlled.