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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

2 • Confidential Proprietary

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.


OUTLINE

• Motivation

• Silicon wafer

• Deformation of silicon wafer with thin layers

• Method summary

• Plastic deformation of crystalline silicon

• Method summary


MOTIVATION


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)


• Thermal expansion

• Intrinsic

- growth

- misfit

- phase transformation

• Extrinsic

- applied stress

- plastic deformation

extthtot int

ORIGIN of THIN FILM STRESS


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


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


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


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


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


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)


-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)


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]


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


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


2,45 nm

SURFACE STEPS AFTER PLASTIC DEFORMATION

(AFM)


SLIPS ON THE SILICON SURFACE

(OPTICAL MICROSCOPY)

4 mm 2 mm 1mm

Silicon wafer edge


SLIPS ON THE SILICON SURFACE (PROFILOMETER)

90 nm


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