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)