Project Title

Mechanics of thin film on wafer

R91943100

詹孫戎

Project Title

Mechanics of thin film on wafer

Basic mechanics Axial stress ， strainPoisson’s ratio Poisson’s ratio Shear stress ， strain ， modulus Stress-strain Thermal strain Mechanical properties of microelectronic material Effective Young’s modulus of composite layers Substrate warpage Biaxial stress in thin film on thick substrate

Mechanics of film-on-foil electronics Failure resistance of amorphous silicon transistors Mobility in thin-film under compressive strain Reference

Project Title

Axial stress

Load P (Newton) ： Internal resultant normal force

Area A (m2) ： Cross-section area of the bar

Stressσ (N/m2 ； Pa) ： Average normal stress at any point on the cross-sectional area σ ＞ 0 tensile σ ＜ 0 compressive

A

P

Source:Mechanics of materials

by R.C.Hibbeler

Project Title

Axial strain

Strainε (dimensionless) ： Deformation changes in length Average elongation ／ Original length

Yong’s modulus E (N/m2 ； Pa) ：

0Lavg

E E (GPa)

Si 190

SiO2 73

Diamond 1035

Project Title

Poisson’s ratio

Poisson’s ratio ν ： Transverse strain ／ Longitudinal strain

ν= 0.5 → volume conserved

long

lat

r

L

lat

long

'

Source:Mechanics of materials

by R.C.Hibbeler

Project Title

Shear stress ， strain ， modulus

Shear stress τ (N/m2 ； Pa) ： V (Newton) ； internal result shear force A (m2) ： area at the section

Shear strain γ (rad)

Shear modulus G (N/m2 ； Pa) ：

A

V

G

Source:Mechanics of materials

by R.C.Hibbeler

Project Title

Stress-strain

Low stress Elastic stress ／ strain = constant

σy = yield stress

Ultimate stress – material break Si (brittle) ； ultimate stress ~ yield stree

Material Yield Strength(Mpa)

Al 170

Steel 2,100

W 4,000

Si 7,000

Quartz 8,400

Diamond 53,000

Source:UC Berkeley EE143,Lec 25

Project Title

Thermal strain

1εth = ∫[αf(T) – αs(T)] dT (α≒ f – αs)(TDep – Troom)

Source:UC Berkeley EE143,Lec 25

Project Title

Mechanical properties of microelectronic material

E(Gpa) ν α(1 ／℃ ) σo(residual stress)

Substrate －silicon 190 0.23 2.6×10-6 －alumina ~415 － 8.7×10-6 －silica 73 0.17 0.4×10-6

Films

polysilicon 160 0.23 2.8×10-6 varies

thermal SiO2 70 0.20 0.35×10-6 compressive

PECVD SiO2 － － 2.3×10-6 －LPCVD Si3N4 270 0.27 1.6×10-6 tensile

aluminum 70 0.35 25×10-6(high!) varies

tungsten(W) 410(stiff!) 0.28 4.3×10-6 varies

polyimide 3.2 0.42 20~70 ×10-6(very high!) tensile

Project Title

Effective Young’s modulus of composite layers

Stressing along x-direction All layers takes the same strain Ex = fAEA + fBEB

Material with lager E takes larger stress

Stressing along y-direction All layers takes the same stress

Material with small E takes larger strain

B

B

A

A

y E

f

E

f

E

1

Source:UC Berkeley EE143,Lec 25

Project Title

Substrate warpage

Radius of curvature of warpage Stoney’s equation

ts ： substrate thickness

tf ： film thickness

Es ： Young’s modulus of substrate

υs ： Posson’s ratio of subsrate

ffs

ss

t

tEr

)1(

2

Source:UC Berkeley EE143,Lec 25

Project Title

Biaxial stress in thin film on thick substrate

σz = 0 No stress direction normal to substrate

Assume isotropic film εx = εy = ε → σx = σy = σ

1

E

Source:UC Berkeley EE143,Lec 25

Project Title

Mechanics of film-on-foil electronics

When sheet is bent Top surface in tension Bottom surface in compression Neutral surface ： one surface inside

the sheet has no strain Strain in top surface ：

df ： film thickness

ds ： substrate thickness

Circuit sandwiched between substrate and encapsulation layer Circuit in the neutral surface if

R

dd sftop 2

22eess dYdY

Source:Z.Sue,E.Y.Ma,H.Gleskova,

and S.Wagner,

Appl.Phys.Lett.74,1177(1999)

Project Title

Mechanics of film-on-foil electronics

Film and substrate have different Young’s moduli

η = df ／ ds

χ = Yf ／ Ys

Two kids of substrate Steel ： Yf ／ Ys 100≒

Plastic ： Yf ／ Ys 1≒

)1)(1(

21

2

2

R

dd sftop

Source:Z.Sue,E.Y.Ma,H.Gleskova,

and S.Wagner,Appl.Phys.Lett.74,1177(1999)

Project Title

Failure resistance of amorphous silicon transistors

a-Si:H TFTs 51-μm-thick polyimide Both side coated 0.5-μm-thick SiNx

100-nm-thick Ti ／ Cr layer electrode 360nm gate SiNx

100nm undoped a-Si:H 180nm passivating SiNx

50nm (n+) a-Si:H 100nm Al for source-drain contact

Compliant substrate Without SiNx back layer

Stiff substrate With SiNx back layer

Source:H.Gleskova,S.Wagner,and Z.Sue,Appl.Phys.Lett.75,3011(1999)

Project Title

Failure resistance of amorphous silicon transistors

TFT bent to a radius R

χ= Yf ／ Ys ； η1= df1 ／ ds ； η2= df2 ／ ds

Yf 200GPa≒ ； Ys 5GPa≒

TFT Compressed by at least 2% without failing Tensile 0.5%

1)1)(()(

1)(2)(

2

11

212

21

22112

22

121

0

ffs

surface

ddd

RR

Source:H.Gleskova,S.Wagner,and Z.Sue,

Appl.Phys.Lett.75,3011(1999)

Project Title

Failure resistance of amorphous silicon transistors

Source:H.Gleskova,S.Wagner,and Z.Sue,Appl.Phys.Lett.75,3011(1999)

Project Title

Mobility in thin-film under compressive strain

Electronic mobility in amorphous silicon thin-film transistor under compressive strain

Source:H.Gleskova,S.Wagner ,Appl.Phys.Lett.79,3347(2001)

Project Title

Reference

UC Berkeley EE143,Lec 25 Mechanics of materials by R.C.Hibbeler Z.Sue,E.Y.Ma,H.Gleskova,and

S.Wagner,Appl.Phys.Lett.74,1177(1999) H.Gleskova,S.Wagner,and Z.Sue,Appl.Phys.Lett.75,3011(1999) H.Gleskova,S.Wagner ,Appl.Phys.Lett.79,3347(2001)