silicon wafer shaping: plastic vs. elastic...
TRANSCRIPT
1 Confidential Proprietary
Silicon wafer shaping:
plastic vs. elastic deformation
J. Šik1, R. Lenhard1, R. Hudec2,3
1ON Semiconductor Czech Republic
2Astronomical Institute of the Academy of Sciences of the Czech Republic
3Czech Technical University in Prague, Faculty of Electrical Engineering, Prague,
Czech Republic
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Silicon wafer shaping: plastic vs. elastic deformation
J. Šik, R. Lenhard, R. Hudec
Abstract:
Polished wafer from monocrystalline silicon available in semiconductor industry has thickness
homogeneity of tenths of micrometer and surface roughness of tenths of nanometer. The possible
utilization of silicon wafers for mirrors in astronomical x-ray optics is dependent on the possibility to
precisely shape them without surface deterioration. One of the proposed solutions is lightweight
optics based on self supporting wafers. We present comparison of two shaping methods: plastic
deformation and the use of thin layers with intrinsic stress. Advantages and disadvantages of both
methods are discussed.
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OUTLINE
• Motivation
• Silicon wafer
• Deformation of silicon wafer with thin layers
• Method summary
• Plastic deformation of crystalline silicon
• Method summary
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MOTIVATION
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SILICON WAFER
• Available in semiconductor industry
• Diameters 100 – 300 mm
• Thickness 300 – 900 m
• Thickness variation (TTV) ~ 0.1 m
• Flatness (Warp) ~ 1 m
• Crystallographic orientations (100) and (111)
• Material properties can be tuned with dopants (As, P, B, Sb, Oi)
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• Thermal expansion
• Intrinsic
- growth
- misfit
- phase transformation
• Extrinsic
- applied stress
- plastic deformation
extthtot int
ORIGIN of THIN FILM STRESS
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THIN FILM
SUBSTRATE
Compressive stress in layer
sf
Due to mismatch of thermal expansion coefficient between substrate ( ) and film ( ),
after temperature ramp down a strain ( ) is built in.s f
th
DEPOSITION TEMPERATURE ROOM TEMPERATUREdepT roomT
0th ))(( roomdepsfth TT
THERMAL STRAIN and STRESS
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Biaxial stress in thin film on thick substrate is related with strain:
thth
E
1
Young’s modulus; Silicon (100) – 1.3·1011 N/m2
Poisson’s ratio; Silicon (100) – 0.28
E
Material[1/°C]
Silicon 2,6·10-6
Polysilicon 2,8·10-6
Thermal SiO2 0,35·10-6
PECVD SiO2 2,3·10-6
LPCVD Si3N4 1,6·10-6
Aluminum 25·10-6
Tungsten 4,3·10-6
THERMAL STRAIN and STRESS
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THIN LAYER
w
Young’s modulus ; Silicon (100) – 1.3·1011 N/m2
Poisson’s ratio; Silicon (100) – 0.28
Wafer thickness
Radius of curvature after film depo
Radius of curvature before film depo
WAFER
COMPRESSIVE STRESS in layer
R
Thin film with residual stress on the
top of silicon wafer deform wafer
according stress value and stress type
[S.Timoshenko, J. Opt. Soc. Am., 11, 233 (1925) ]
(compressive or tensile)
Therefore the warp is proportional to the
residual stress and film thickness and
inversely proportional to the wafer
thickness squared.
TENSILE STRESS in layerTHIN LAYER
WAFER
f
st
E
0
2 11
)1(6 RRt
tE
f
sf
R
0R
INTRINSIC THIN FILM STRESS
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Example of residual stress in different depo and thermal growth layers are in tables.
Values are just indicative as the intrinsic stress may vary with the process conditions.
LayerStress[N/m2]
PE TEOS low stress 0,5·108
PECVD Si3N4 low stress 0,5·108
PECVD TEOS 1,8·108
Thermal SiO2 3·108
PECVD Si3N4 5·108
LPCVD Poly Si ~ 2·108 *)
Compressive stress
LayerStress
[N/m2]
LPCVD SiO2 3·108
LPCVD Si3N4 1·109
Tensile stress
*) at deposition temperature 615°C
THIN FILM STRESS VALUE
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BACK SIDE LAYER
After depo of poly-Si (THX 1436 nm at temperature 615°C) and for wafer thickness 507 m
the warp 110 m (R = 25.6 m) was achieved.
Wafer deformation map Warp profile perpendicular to
the facet
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Circular 150 mm wafer, thickness 378 m, warp 181 m was squared to □ 100 mm.
Squared wafer keeps axially symmetrical shape.
WAFER SHAPE
-60 -40 -20 0 20 40 60
0
20
40
60
80
100
120
140
160
1
2
3
4
4
3
2
1
D
evia
tio
n (m
)
Position (mm)
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-60 -40 -20 0 20 40 60
0
20
40
60
80
100
120
140
160
180
measured data
spherical R=11.7m
De
via
tio
n (m
)
Position (mm)
Squared wafer has spherical shape. Deviation from ideal sphere is within 1 m.
WAFER SHAPE
-60 -40 -20 0 20 40 60
-1
0
1
deviation from sphere
De
via
tio
n (m
)
Position (mm)
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WAFER THICKNESS INFLUENCE
• For any layer stack we can calculate the wafer thickness to achieve expected radius of curvature.
• In example picture the wafer thickness of 195 m would be needed for R ~ 2 m.
• That thin wafer is sensitive for handling and also it is affected by gravity sag.
0,0
1,0
2,0
3,0
4,0
5,0
6,0
7,0
100 150 200 250 300 350 400
Wafer THX [um]
R [
m]
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Technology is available in semiconductor industry
Layers with intrinsic stress uniformly shape silicon wafer w/o deterioration of high
quality of the polished front side.
Multilayer stack can be designed to decrease the radius of wafer curvature to R ~ 2 m.
For other than spherical shape a lateral stress pattern needs to be modified with
photolithography process.
Achieve radius of wafer curvature R < 2 m is difficult.
Material properties (thermal expansion, durability, ..) of layers influence the shape of
mirrors
SUMMARY: THIN FILMS WITH INTERNAL STRESS
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kT
QK exp5,10
0.25 eV for crystallographic plane (100)
k... Boltzman constant
T... wafer temperature [K]
In crystalline silicon (at temperatures <800-900°C) after the Hooke's law region follows the brittle
rupture.
At temperatures >800-900°C is plastic deformation via dislocations and slips possible,
i.e., crystalline segments will shift to each other in order to decrease stress in material. After cooling
wafer will hold formed shape, but shifted segments will form surface steps.
Plastic deformation of silicon wafer is dependent on the critical stress (K) for dislocation formation.
Experimental dependence on the temperature can be expressed as:
PLASTIC DEFORMATION
OF MONOCRYSTALLINE SILICON
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2,45 nm
SURFACE STEPS AFTER PLASTIC DEFORMATION
(AFM)
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SLIPS ON THE SILICON SURFACE
(OPTICAL MICROSCOPY)
4 mm 2 mm 1mm
Silicon wafer edge
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SLIPS ON THE SILICON SURFACE (PROFILOMETER)
90 nm
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SUMMARY: PLASTIC DEFORMATION
Shaped wafer is without intrinsic stress
Radius of wafer curvature R < 2 m is possible
Clean technology has to be developed (surface contamination)
Surface steps and slips are present due to crystallographic arrangement of atoms