Mechanics of thin film on wafer
R91943100
詹孫戎
Project Title
Mechanics of thin film on wafer
 Basic mechanics
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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
P

A
Project Title
Source:Mechanics of materials
by R.C.Hibbeler
Axial strain
 Strainε (dimensionless)：
 Deformation changes in length
 Average elongation／Original length
 avg 

L0
 Yong’s modulus E (N/m2；Pa)：
E
Project Title


E (GPa)
Si
190
SiO2
73
Diamond
1035
Poisson’s ratio
 Poisson’s ratio ν：
 Transverse strain／Longitudinal strain
 lat
 
 long
 ν= 0.5 → volume conserved
 long 
 lat

L
'

r
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

V
A
 Shear strain γ (rad)
 Shear modulus G (N/m2；Pa)：

G

Source:Mechanics of materials
by R.C.Hibbeler
Project Title
Stress-strain
 Low stress
 Elastic
 stress／strain = constant
 σy = yield stress
Material
Yield Strength(Mpa)
Al
170
Steel
2,100
W
4,000
Si
7,000
Quartz
8,400
Diamond
53,000
 Ultimate stress – material break
 Si (brittle) ；ultimate stress ~ yield stree
Project Title
Source:UC Berkeley EE143,Lec 25
Thermal strain
 1εth = ∫[αf(T) – αs(T)] dT ≒ (αf – 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
－
73
0.17
0.4×10-6
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
410(stiff!)
0.28
4.3×10-6
varies
3.2
0.42
20~70 ×10-6(very high!)
tensile
silica
Films
tungsten(W)
polyimide
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

1
f A fB
Ey

EA

EB
 Material with small E takes larger strain
Source:UC Berkeley EE143,Lec 25
Project Title
Substrate warpage
 Radius of curvature of warpage
 Stoney’s equation
Es  t s
r
(1  s )   f  t f
2




ts：substrate thickness
tf：film thickness
Es：Young’s modulus of substrate
υs：Posson’s ratio of subsrate
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
E


1 
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：
d f  ds
 top 
2R
 df：film thickness
 ds：substrate thickness
Source:Z.Sue,E.Y.Ma,H.Gleskova,
and S.Wagner,
Appl.Phys.Lett.74,1177(1999)
 Circuit sandwiched between substrate and encapsulation layer
 Circuit in the neutral surface if Ys d s 2  Ye de 2
Project Title
Mechanics of film-on-foil electronics
 Film and substrate have different Young’s moduli

 d f  d s  1  2   2

 top  
 2 R  (1   )(1   )
 η = df／ds
 χ = Yf／Ys
 Two kids of substrate
 Steel： Yf／Ys ≒100
 Plastic： Yf／Ys ≒1
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
Project Title
Source:H.Gleskova,S.Wagner,and Z.Sue,Appl.Phys.Lett.75,3011(1999)
Failure resistance of amorphous silicon transistors
 TFT bent to a radius R

 1 1  d s  d f 1  d f 2  (12  2 2 )  2( 1  12  2 )  1
 surface    
2
 (1  2 ) 2  (1  2 )(1   )  1
 R R0 
 χ= Yf／Ys；η1= df1／ds； η2= df2／ds
 Yf≒200GPa；Ys≒5GPa
 TFT
 Compressed by at least 2% without failing
 Tensile 0.5%
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)
Project Title