Properties Of Materials

BiS 271

Spring, 2006

Biomechanics and Materials

V. Material Properties V.1 Properties of Materials

Prof. Young-Ho CHO Department of BioSystems, KAIST http://biosys.kaist.ac.kr Phn: +82-42-869-8699

E-mail: [email protected]

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

http://mems.kaist.ac.kr

Spring 2006, KAIST

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

[Note] Analysis of mechanical deformation

V.1.1 Mechanical Properties

How strong is it? Under what sort of deformation?

(1) Young’s Modulus (2) Mechanical Strength (yield, ultimate, fracture)

Tension

(3) Poisson’s Ratio

Compression

(4) Residual Stress (thermal, intrinsic) (5) Hardness

Torsion Shear

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

[Review] Stress-Strain Curve

[Review] Tensile Test

σu σy

• Specimen is “pulled” in tension at a constant rate • Load (F) necessary to produce a given elongation (ΔL) is monitored • Load vs elongation curve • Converted to stress-strain curve

Prof. Young-Ho Cho

BiS271: Biomechanics & Materials

Spring 2006, KAIST

(1) Young’s modulus

σf

σe

σ e : Elastic Limit σ y : Yield Strength σ u : Ultimate Strength σ f : Fracture Toughness

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

[Note] Resonant Test Method for Young’s Modulus The test structure is driven in the parallel direction to the silicon substrate by the electrostatic force. From the measured natural frequency of the test structure, Young’s modulus can be estimated.

σy

beam

Young’s modulus = modulus of elasticity σe

Measure the dimension of the test structure and the natural frequency

Hooke’s Law:

σ ( stress ) = Eε ( strain) σ Young ' s modulus, E = ε

truss

2 π 2 f n2 mL 3 E = tw 3

plate

1 12 mb where m = m p + mt + 4 35 [KAIST]

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

[Note] Blister Test for Young’s modulus and residual stress Pressurizing or blistering a diaphragm with pressure-deflection measurements Measurement of residual tensile stress and Young’s modulus. cylinder

Yield Strength: Strength when a definite amount of plastic strain has occurred (0.2%)

TP7658 polymer [Al Technology Inc.]

micrometer

(2) Yield Strength

Norm alized Displacem ent vs. Pressure 4500000

tube knob Dial pressure gauge microscope 3 σtd ⎡ E ⎤ td p = C1 2 + C2 ⎢ 4 a ⎣1 − ν ⎥⎦ a BiS271: Biomechanics & Materials

Normalized Pressure

4000000

specimen

3500000 3000000

Yield strength

2500000 2000000

E = 0.198 GPa

1500000

σ = 1.45 MPa

1000000 -0.002

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

Normalized Displacement

[KAIST]

• Young Modulus : 0.198GPa • Residual Stress : 1.45MPa Prof. Young-Ho Cho

Spring 2006, KAIST

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

[Note] Fracture Toughness

(3) Ultimate and Fracture Strength

*Energy required to fail → area under stress-strain curve. Ultimate Strength: Maximum stress

Fracture Toughness: Stress at Fracture

smaller toughness (ceramics)

Engineering tensile stress, σ

larg er toughness (metals, PMCs) smaller toughnessunreinforced polymers

Engineering tensile strain,

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

ε

Spring 2006, KAIST

[Note] Blade Test for Fracture Toughness

[Note] Pull Test for ultimate strength

Inserting blade

Pre-inserted blade Silicon

δb

Pyrex #7740 glass Silicon wafer

a

Bonded area

H Crack propagation length 10mm

3h 2δ 2 G= 4 b 3 c1a (1 + γη ) [Nagoya Univ.]

[KAIST]

[UCLA] Prof. Young-Ho Cho

BiS271: Biomechanics & Materials

Spring 2006, KAIST

[Note] Ductility

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

(4) Poisson’s Ratio, υ

A

Isotropic material

F L

Ductility: degree of plastic deformation at fracture ⎛ A − AF % Reduction in Area = ⎜⎜ 0 ⎝ A0

⎛ L f − L0 ⎞ ⎟⎟ × 100 % EL = ⎜⎜ ⎝ Lo ⎠

υ=−

εy εx =− εz εz

⎞ ⎟⎟ ×100 ⎠

Spring 2006, KAIST

to extension caused by tensile stress strain curve • υ = 0.26 to 0.35 for common metal alloys

⎛ L f − L0 ⎞ ⎟⎟ × 100 % Elongation = ⎜⎜ ⎝ L0 ⎠

Prof. Young-Ho Cho

• Elastic strain in compression perpendicular • Cannot be directly obtained from stress-

• υ < 0.25 for ceramics • υ has a maximum value of 0.50 (no volume

Brittle Materials have a fracture strain of less than approx. 5%

BiS271: Biomechanics & Materials

Pyrex glass

h

change)

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

[Example]

A cylindrical rod is made of steel having poisson’s ratio,0.3, is deformed under tensile loading. The initial length of the rod is 4m, and its original diameter is 1m. When the elongation is 0.1m, calculate the change in diameter of given rod.

ε radial = −υε longit

L=4m Tensile load

d=1m

(5) Hardness 1) Hardness - Material’s resistance to localized plastic deformation - Test tools: Rockwell, Brinell, Knoop, Vickers 2) Hardness vs. Tensile Strength

ε radial = −0.3 × 0.1 = −0.03 Δd = d × ε radial = 1× (−0.03) = −0.03m

For metals, su = 3.45 HB [MPa] or 500 HB [psi] 3) Assumptions for material dimension and loading conditions: (e.g.) material thickness > 10 X indentation depth

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

(6) Residual Stress • Residual Stress :

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

1) Thermal residual stress Origin - thermal expansion coefficient mismatch ε=0 αf αf

σ r = σ rt + σ ri Thermal stress

αs

Intrinsic stress

T = Td

ε rt = (α f − α s )(Td − Tr )

εrt

αs T = Tr αf > αs → εrt > 0 : tensile αf < αs → εrt < 0 : compressible

(ex) Poly silicon on (100) Silicon wafer αf = 2.8x10-6 /K, αs = 3.2x10-6 /K, Td = 625°C & Tr = 25°C → εrt = -2.4x10-4 BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

2) Intrinsic residual stress

3) Residual Stress Control

Origin – many !! ƒ

Doping (+, -) ~ ionic radius effect in substitutional site

Si B Si ƒ

σri > 0 (tensile)

Si

P

Si

σri < 0 (compressive)

Atomic peening (-)

(ex) Boron doping in Poly-Silicon

ƒ Material composition ƒ Process conditions

densified compressive film in ion bombardment by atoms

ƒ ƒ ƒ ƒ ƒ

ƒ Compensate dopant strain

Void (+)

(ex) Sputtering ~ gas pressure, substrate bias

Gas entrapment (-)

PECVD

~ everything affects residual stress

Shrinkage during cure (+)

LPCVD

~ temperature

Grain boundaries (complex, poorly understood) Etc. Prof. Young-Ho Cho

BiS271: Biomechanics & Materials

Spring 2006, KAIST

[Note] Disk or Curvature Method for residual Stress Disk method is based on a measurement of the deflection in the center of the disk substrate before and after processing.

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

[Note] Beam Buckling Method for Residual Stress The test structure, composed of a series of clamped-clamped beams, is used to measure the compressive residual stress. When a clamped-clamped beam is buckled, the compressive residual stress can be estimated.

Assumption Euler’s formula for elastic instability : no internal moments from gradients in residual stress

• Substrates ; thin, transversely isotropic, no bow • Film ; thin, uniform, constant stress • System ; uniform temperature, mechanically free

σ =

1 E T R 6 (1 − ν ) t

Thin Film

substrate BiS271: Biomechanics & Materials

When the critical load clamped beam for buckling is

2

Pcr = E

4π 2 I 2 Lc

Then, the residual stress is

-

σ = E

+

[KAIST] Prof. Young-Ho Cho

Spring 2006, KAIST

4π 2 1 A L 2c

BiS271: Biomechanics & Materials

[KAIST] Prof. Young-Ho Cho

Spring 2006, KAIST

[Note] Gauge Needle Method for Residual Stress

The test structure measures strain by interconnecting two opposed beams such that third beam to rotate as a gauge needle. The rotation of a gauge needle quantifies the residual strain.

The narrow beams amplify and transform deformations caused by residual stress into opposing displacement of the apices, where vernier scales are positioned to quantify the deformation.

Type B ; uniform response over the widest range of stress

FEM Analysis determines correction factor C f

σ = EC f

[Note] Bent-Beam Strain Gauge Method for Residual Stress

yY ( LA + LB )( LC + 0.5Y )

y L / 2 = 2(

σ=

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

V.1.2 Electrical Properties

tan θ A kL )(tan ) where k = k 4

E⎛ FL ⎞ ⎜ ΔL′ + ⎟ L⎝ 2 Ewt ⎠

F / EI

where L′ = −

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1 L / 2 ∂y 2 ( ) dx 2 ∫0 ∂x

Prof. Young-Ho Cho

Spring 2006, KAIST

(0) Electrical Quantities 1) Charge(q) : Coulomb[C] ≡ 1A⋅s - 1C = charge of 6.24×1018 electrons = charge transfer of 1 A⋅sec - Charge of single electron = 1.602 × 10-19 C

(0) Electrical Quantities (1) Resistance

2) Current(i) : Ampere[A] ≡ 1C/s

(2) Capacitance

3) Voltage(v) : volt[V] ≡ 1W/A - energy/charge or power/current

(3) Inductance

4) Electric field strength(E) : [V/m] ≡ N/C

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

[Note] Electrical Elements and Properties Resistance

Inductance

I

Capacitance

I

V

R

(1) Resistance Resistance

I

V

L

V

R=

ρL A

1

C

ρ (resistivity) L [Henry]

R [Ohm]

V =L

V = RI V I= R

I =C

dV dt

1 I = ∫ Vdt L

V=

ER = ∫0 VIdt = RI 2T

ER = ∫0 VIdt 1 = LI 2 2

ER = ∫0 VIdt 1 = CV 2 2

Dissipation

Storage (K.E.)

Storage (P.E.)

T

T

T

Prof. Young-Ho Cho

BiS271: Biomechanics & Materials

1 Idt C∫

Spring 2006, KAIST

ΔA Δd ΔL =2 = −2ν A d L

π d2 4

3

ΔL ⎞ ⎛ Δd = −ν ⎜Q ⎟ d L ⎠ ⎝

F [Farad]

dI dt

For a wire of diameter, d : A =

L

A

3 → 2

ΔR ΔL ΔA Δρ = − + R L A ρ

2

ΔR ΔL Δρ = (1 + 2ν ) + R L ρ 4 Dimensional Effect (Strain gauge) Prof. Young-Ho Cho

BiS271: Biomechanics & Materials

Piezoresistive Effect (Semiconductor gauge) Spring 2006, KAIST

(2) Capacitance • Piezoresistive effect comes from the effect of strain on the energy surface d

• Gauge factor (strain sensitivity)

(ΔR R ) = (1 + 2ν ) + (Δρ ρ ) G≡ (ΔL L ) (ΔL L )

Area : A where ν : Poisson's ratio

C =ε

[Note] • metal

:G=2~5

• p-Si

: G = 100 ~ 170

• n-Si

: G = -100 ~ -140

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

A A = ε 0ε r d d

ε = ε0 εr : permittivity [ F/m] ε0 = 8.85 pF/m εr = relative permittivity (dielectric constant)

Spring 2006, KAIST

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

V.1.3. Thermal Properties

(3) Inductance Inductors store energy in a magnetic field

(1) Heat Capacity & Specific Heat (2) Thermal Conductivity (3) Thermal Expansion (4) Temperature Coefficient of Resistance (5) Thermoelectric Effects

L = Inductance [V-s/A]

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

• As the material absorbs heat, its temperature rises • Quantitative: The energy required to increase the temperature of the material (J/mol·K)

p

energy input (J/mol) temperature change (K)

• Specific Heat, c: Heat capacity per unit mass (J/kg·K) Specific Heat (J/Kg-K)

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C c= m

Heat Capacity (J/mol-K) Mass (kg)

Prof. Young-Ho Cho

Spring 2006, KAIST

increasing c

dQ C= dT

Spring 2006, KAIST

[Note] Heat Capacity: Comparison

(1) Heat Capacity and Specific Heat

heat capacity (J/mol-K)

Prof. Young-Ho Cho

BiS271: Biomechanics & Materials

c p (J/kg-K) material at room T ? Polymers 1925 Polypropylene 1850 Polyethylene 1170 Polystyrene 1050 Teflon ? Ceramics Magnesia (MgO) 940 Alumina (Al 2 O 3 ) 775 Glass 840 ? Metals Aluminum Steel Tungsten Gold

BiS271: Biomechanics & Materials

c p : (J/kg-K) C p : (J/mol-K)

900 486 128 138

Prof. Young-Ho Cho

Spring 2006, KAIST

(2) Thermal Conductivity

(2) Thermal Conductivity

• General: The ability of a material to transfer heat. • Quantitative: temperature dT gradient q = −k heat flux dx (J/m2-s)

• Proportionality constant (k) that relates heat flow rate (dQ/dt) and temperature gradient (dT/dx) k=−

thermal conductivity (J/m-K-s)

1 dQ dx A dt dT

• Fourier’s Law is analogous to Fick’s Law T2 > T 1

T1 x1

x2

heat flux

q = −k

• Atomic view: Atomic vibrations in hotter region carry

7 KAIST Spring 2006,

Prof. Young-Ho Cho

1) Mechanism of Heat Transfer in Solids

• Heat transport by free electrons as they gain kinetic energy and migrate to low T areas (in Metals)

T2 > T 1

T1 x1

x2

heat flux

1 dQ A dt

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

2) Heat Transfer in Metals

• Heat transport by atomic vibrations as they move from high T to low T regions

• k = k a + ke

q=

• k in J/(s·m·K)

energy (vibrations) to cooler regions.

BiS271: Biomechanics & Materials

dT dx

A

• Free electrons are the main contributor to heat transport in high purity metals due to high velocities and lack of scattering • Alloying metals (solid solution) introduces scattering centers and the heat transfer reduces

e BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

4) Thermal Conductivity: Comparison

3) Heat Transfer in Ceramics

Material

k (W/m-K)

Energy Transfer

247 52 178 315

By vibration of atoms and motion of electrons

Magnesia (MgO) 38 Alumina (Al 2 O 3 ) 39 1.7 Soda-lime glass Silica (cryst. SiO 2 ) 1.4

By vibration of atoms

? Metals

Aluminum Steel Tungsten Gold

• They lack the free electrons of metals

? Ceramics

increasing k

• Phonon transport dominates and drops with rising temperature

? Polymers Polypropylene Polyethylene Polystyrene Teflon

Prof. Young-Ho Cho

BiS271: Biomechanics & Materials

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(3) Thermal Expansion

0.12 0.46-0.50 0.13 0.25

By vibration/ rotation of chain molecules

Selected values from Table 19.1, Callister 6e.

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

8 KAIST Spring 2006,

1) Atomic analysis

• Materials change size when heating. L final − L initial = α( Tfinal − Tinitial ) L initial

α= T init Linit T final

linear coefficient of thermal expansion (1/K)

Lfinal

1 ΔL L ΔT

• Bond strength determines α…the greater the bond energy, the smaller α • Generally

αceramics < αmetals < αpolymers

• Atomic view: Mean bond length increases with T.

increasing T

r(T 1 ) r(T 5 )

Bond energy

T5 T1

BiS271: Biomechanics & Materials

Bond length (r) bond energy vs bond length curve is 밶symmetric

Prof. Young-Ho Cho

Spring 2006, KAIST

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

2) Thermal expansion coefficient properties

3) Comparison α (10 -6 /K)

Material

α

• In general, thermal expansion coefficient increases with temperature increasing

• Can have negative α • Can have α near zero

Prof. Young-Ho Cho

BiS271: Biomechanics & Materials

Spring 2006, KAIST

where

E = hf = h

• Radiation : Energy transfer by electromagnetic wave phenomena Thermal radiation

10-8

10-6

10-2

101

102

104 λ[m]

Infrared(IR) UV Visible ray (0.39 μm ~ 0.78 μm)

X-ray

BiS271: Biomechanics & Materials

λ

[eV]

h : plank constant = 6.63x10-34 J·s = 4.135x10-5 eV·s f : wave frequency v : wave velocity λ : wave length

• Ep = eΦ (work function)

e

Elevel eΦ

Cosmic ray

v

• Energy band diagram 10-4

Spring 2006, KAIST

- Photon has no mass but energy

• Radiation (Thermal, Optical)

10-10

Prof. Young-Ho Cho

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(1) Light and its spectrum

10-12

• Q: Why does α generally decrease with increasing bond energy?

(2) Optical Energy

V.1.4. Optical Properties

• Spectrum

at room T ? Polymers 145-180 Polypropylene 106-198 Polyethylene 90-150 Polystyrene 126-216 Teflon ? Metals Aluminum 23.6 Steel 12 Tungsten 4.5 Gold 14.2 ? Ceramics Magnesia (MgO) 13.5 Alumina (Al 2 O 3 ) 7.6 Soda-lime glass 9 Silica (cryst. SiO 2 ) 0.4

Micro wave

Prof. Young-Ho Cho

Radio (RF)

Χ

Evacuum Econduction Ef

Egap

• E = Χ (electron affinity)

(forbidden band)

e

Evalance

e

Spring 2006, KAIST

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

v=0

Spring 2006, KAIST

V.1.5. Bio-chemical Properties

(3) Refraction

(1) Surface Energy

- index of refraction, n

n=

where

c v

c : light velocity v : wave velocity

Quantifies the disruption of chemical bonds when a surface is created

(4) Reflection - reflectivity, R where light

Ir R= Ii

Surface area ∝ Surface Energy Volume

Ir : intensity of reflected Ii : intensity of incident light

- Normal incident light

⎛ n2 − n1 ⎞ R=⎜ ⎟ ⎝ n2 + n1 ⎠

2

where

n1, n2 : indices of refraction

Prof. Young-Ho Cho

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V.1.5. Bio-chemical Properties

Hydrophilic θ < 90o

γ LG Gas θ

(2) Thermo-mechanical

Solid

Hydrophobic

γ SL = γ SG − γ LG cos θ

θ > 90

γ SL : Solid - Liquid Surface Tension γ SG : Solid - Gas Surface Tension γ LG : Liquid - Gas Surface Tension θ : Contact Angle

o

Mechanical

(3) Opto-mechanical (4) Chemo-electrical (5) Opto-electrical

γ SG

BiS271: Biomechanics & Materials

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(1) Electro-mechanical

ƒ Young’s Equation

Liquid

Prof. Young-Ho Cho

V.1.6. Material property interactions

(2) Contact Angle

γ SL

BiS271: Biomechanics & Materials

Electrical

Thermal

(6) Thermo-electrical (7) Thermo-chemical (8) Chemo-mechanical

Optical

Chemical

(9) Opto-chemical (10) Thermo-optical Prof. Young-Ho Cho

Spring 2006, KAIST

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

(1) Electro-mechanical: Piezo-electric

ƒ Electrical Charge induced by the external force F

ƒ Asymmetric charge distribution in the material structure

Q = dF = dσA = dεEA

• Voltage potential → Polarization of internal charge → Relative displacement of internal charges → Deformation (strain)

where, d is charge sensitivity coefficient (matrix) and E is Young’s Modulus of the material. ƒ Change in length per unit applied voltage

ƒ Piezoelectric material : Quartz, PZT (Lead Zirconate Titanate), Zinc Oxide, ZnO, Lithium Niobate

εε A 1 εε εε Δl C = ⋅ Δl = o r ⋅ ⋅ Δl = o r ⋅ Δl = o r ΔV ΔQ l dF ldσ dE Δl ε oε r = ≈ 1.23nm / V ΔV dE

ƒ Δl is independent of l, only depends on the voltage ΔV and material properties -> Stack for large Δl BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

(2) Thermo-mechanical

• Occurs due to: - uneven heating/cooling - mismatch in thermal expansion.

T room

ΔL

L room

T

compressive

σ keeps

ΔL = 0

σ(ΔT) = Eα(T0 – Tf)

Spring 2006, KAIST

Prof. Young-Ho Cho

ƒ A strongly focused laser beam has the ability to catch and hold particles (of dielectric material) in a size range from nm to µm.

Spring 2006, KAIST

d=10um

ƒ The basic principle behind optical tweezers is the momentum transfer associated with bending light ƒ The forces are in the order of 0.01 to 300pN. ƒ Possible to manipulate particles like atoms, molecules (even large) and small dielectric spheres

- Upon heating (Tf>T0), Compressive Stress (σ<0) - Upon heating (Tf0) BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

(3) Opto-mechanical: Optical tweezer

Thermal Stress

•For a constrained solid

BiS271: Biomechanics & Materials

BiS271: Biomechanics & Materials

V. Emiliani et.al., Optics Express, Vol.12(2004)

Prof. Young-Ho Cho

Spring 2006, KAIST

ƒ In the Rayleigh Regime (diameter of particle is very small compared to the wavelength, D « λ)

(4) Chemo-electrical: Electro-wetting ƒ ElectroWetting

ƒ Scattering force due to the radiation pressure on the particle 2

Fscat =

2 I o 128π 5r 6 ⎛⎜ n p − 1 ⎞⎟ nm 2 4 c 3λ ⎜⎝ n p + 2 ⎟⎠

I o : Intensity r : Radius of spherical particle

λ : Wave lenght of light n p : Refractive index of the particle nm : Refractive index of the medium

α : Polarizability of particle

ƒ Gradient force due to the Lorenz force acting on the dipole, induced by the electromagnetic field 2 2 3 nb nb r 3 ⎛⎜ np −1 ⎞⎟ 2 Fgrad = − α∇E = − ∇E2 2 2 ⎜⎝ np 2 + 2 ⎟⎠

Prof. Young-Ho Cho

BiS271: Biomechanics & Materials

Spring 2006, KAIST

γ SL = γ SG − γ LG cos θ

γ SL

θ

Prof. Young-Ho Cho

Spring 2006, KAIST

Prof. Young-Ho Cho

Spring 2006, KAIST

γ SL : Solid - Liquid Surface Tension γ SG : Solid - Gas Surface Tension γ LG : Liquid - Gas Surface Tension θ : Contact Angle

Gas

Liquid

BiS271: Biomechanics & Materials

External voltage applied. Charge density at EDL changes so that γSL and the contact angle decrease or increase.

Droplet Manipulation using Electro-Wetting (UCLA)

ƒ Young’s Equation γ LG

No external voltage applied. Charges are distributed at the electrode-electrolyte interface, building an EDL.

γ SG Solid

ƒ Lippmann-Young Equation cos θ = cos θ 0 + θ : Contact angle

1 1

γ LG 2

cV 2

c : Capacitance per unit area V : Applied voltage

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

BiS271: Biomechanics & Materials

(5) Opto-electrical Effects

(6) Thermo-electrical: TCR

1) Photoelectric (PE) 2) Photoconductive (PC) 3) Photovoltaic (PV) Ep(λ) → I(V)

Ep(λ) → R(I,V)

Ep > eΦ

Ep

Ep > Eg

Ep

I

R

Eo

e

Ep

I

n p or metal

Ic

Eb

Thermistor

R

Eo

p Ep

e

n

Ec

cathode

Eb

R(T ) = Ro(1 + αT + βT 2 + γT 3 +)

Ep > Eg

Ep

semiconductor

anode

-

Eg Ev

+

Ec Ef Ev

• nowadays, seldom used

• recombination nose • need bias (external source) → Exposure meter

2) Seebeck effect

3) Peltier effect

• Generation of a thermoelectric voltage due to a temperature difference between the junction of two dissimilar conducting materials

•Electrical E → Thermal E

A

VAB

Spring 2006, KAIST

4) Thomson effect

• Heat transfer due to electrical current heat generation/absorption rate

• Absorption or emission of heat due to carrier movement up or down a temperature gradient

B

T2

* ΔVAB = S AB ΔT

S*AB : Seebeck coeff. (0.2~80 µV/°C) BiS271: Biomechanics & Materials

cp[J/g-K] 0.7 0.9 0.39 1.0

Prof. Young-Ho Cho

BiS271: Biomechanics & Materials

Spring 2006, KAIST

[Note] • Joule heating : Thermal heat conduction (one way) • Seebeck effect, Peltier effect (two way)

[Note] • Seebeck effect = Peltier effect + Thomson effect

• Reverse of Seebeck effect T1

I

A

T2

T1

I

Heat absorption

B

Heat generation

[Note] T ↑ → carrier density ↑ → carrier diffusion ↑ T2

Q p = Π AB I = ( S1* − S 2* ) IT

qT = ∫ φ A IdT

ΠAB : Peltier coeff.

qT : heat/sec/voltage φA : Thomson coeff.

Q p : Amount of Heat Prof. Young-Ho Cho

A

T2

Qp T1 > T2 , V1 > V2

T1

k [W/cm-K] Si 1.48 Al 2.37 Cu 4.01 SiO2 0.014

• no recombination nose • no external source required → Solar cell

Prof. Young-Ho Cho

BiS271: Biomechanics & Materials

1) Temperature Coefficient of Resistance (TCR)

Ep(λ) → V

T1

Spring 2006, KAIST

VAB

QTA

Qp1 T1

[Applications]

B

T2

Qp2

QTB

1) Voltage, current, power temperature measurement in a wide frequency range (Hz ~ GHz) 2) Fluid flow, pressure, thermoconductivity measurement 3) Power generation (~mW) BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

(7) Thermo-chemical

(8) Chemo-mechanical

Surface tension driven fluid motion under temperature gradient

Polymer actuator Voltage-displacement Working principle

Temperature gradient

Polymer actuator shifting a coin

Surface energy gradient

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

BiS271: Biomechanics & Materials

(9) Others

Prof. Young-Ho Cho

Spring 2006, KAIST

References

Opto-chemical interactions Thermo-optical interactions [1] J.J. Wortman and R.A. Evans, “Young’s modulus, Shear modulus, and Poisson’s Ratio in Silicon and Germanium”, J. of Applied Phys., Vol.36, No.1, Jan. 1965, pp.153-156 [2] H. Guckel et al., “Mechanical Properties of Fine Grained Polysilicon : The Repeatability issue”. [3] M. Madou, Fundamentals of Microfabrication, CRC Press, 1997, pp.223-224. [4] Y. B. Gianchandani, “Bent-Beam Strain Sensors,” J. of MEMS, Vol. 5, No. 1(1996), pp.52-58. [5] K. Najafi, K. Suzuki, “A Novel Technique and Structure for the Measurement of Intrinsic Stress and Young’s Modulus of Thin Films,” Proc. IEEE MEMS Workshop, Salt Lake City, 1989, pp.96-97.

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST

BiS271: Biomechanics & Materials

Prof. Young-Ho Cho

Spring 2006, KAIST