thermal stress analysis of the extreme ultraviolet multi...

1

October 24, 2016

Thermal stress analysis of the extreme ultraviolet multi-stack pellicle

with high emissivity coating by finite element method

Eun-Sang Park, Min-Ha Kim, Sollee Hwang, and Hye-Keun Oh*

Hanyang University

2

Contents

• Introduction

• FEM simulation of the EUV pellicle

• Optimization of the EUV pellicle structure

• Additional considerations

• Conclusion

3

Introduction

How can we extend the lifetime of the EUV pellicle?

Effective cooling

Low heat absorption

Low thermal stress

4

Introduction

Heat absorption to the pellicle

EUV source power (W)

High absorption at the

EUV wavelength

Low k and n~1 material is preferred.

5

Introduction

Cooling of the EUV pellicle

Radiation

Conduction

Convection

Ineffective at thin film

Negligible under high vacuum

chamber environmentHigh emissivity coating is needed.

6

Introduction

Thermal stress of the EUV pellicle

Single film thermal stress

equation (for edge clamped case)

σ =1

2· E · α · ΔT

Core layer

Coating layer

Coating layer

Optically & thermally optimized

EUV pellicle is needed.

7

FEM simulation of the EUV pellicle

Design & concept

8


FEM simulation for thermal stress calculation

Heat

Heat

Single layer pellicle

Multi layer pellicle

Discretization (mesh)

Discretization (mesh)

Boundary

condition

Boundary

condition

9


Material properties

Ru SiN SiO2 Si p-Si Graphene B4C

Index of reflection

(@EUV wavelength)0.8864 0.9731 0.9780 0.9990 0.9929 0.9616 0.9638

Extinction coefficient

(@EUV wavelength)0.017 0.0093 0.011 0.0018 0.0021 0.0069 0.0051

Density

(g/cm3)12.41 3.31 2.65 2.329 2.328 2.200 2.550

Young's modulus

(GPa)454 410 66.3 188 169 1050 472

Poisson's ratio 0.25 0.14 0.19 0.28 0.22 0.186 0.21

Specific heat (J/g∙K) 0.238 0.750 0.730 0.712 0.753 0.70 1.288

C.T.E (10−𝟔/K) 11.1 4 0.55 2.6 2.9 -7.0 5.0

Thermal conductivity (W/m∙K) 120 30 1.5 149 125 3000 42

10


Thickness dependent emissivity

Ref) P. J. van Zwol, D.F. Vles, W.P. Voorthuijzen, M. Péter, H. Vermeulen, W.J. van der Zande J. M. Sturm. R.W.E. van de Kruijs, and

F. Bijkerk, J. Appl. Phy., 118.21 213107 (2013).

SiN thickness

(nm)Emissivity

25 0.0048

100 0.005

Ru thickness

(nm)Emissivity

25 0.14

100 0.069

0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.1

0.2

0.3

0.4

0.5

Em

issi

vit

y

Ru thickness (nm)

Ru thickness below 20 nm

Bulk Ru thickness

11


Analytic thermal differential equation for single layer EUV pellicle

Ref) Lee, H. C., Kim, E. J., Kim, J. W., & Oh, H. K. (2012). Temperature behavior of pellicles in extreme ultraviolet lithography

Journal of the Korean Physical Society, 61(7), 1093-1096 (2012).

EUV Source power (W) 250 EUV scan slit area (mm2) 110 × 6

Exposure time (ms) 10 Incident power on the pellicle (W/cm2) 5

Cooling time (ms) 90 Beam pass Single pass

m : mass (kg)

c : specific heat (J/kg∙K)

A : absorption ratio

ε : emissivity

S : radiation area (cm2)

Ts : surface temperature (K)

Tmax : maximum temp. (K)

Tp : temperature for

analytic expression (K)

σ : Boltzmann constant (J/K)

12


FEM matches analytic solution

13


FEM simulation matches the experiment

MaterialThickness

(nm)Emissivity

Maximum

temperature (℃)

Coating - - -

1661Core SiN 22 0.0093

Coating - - -

MaterialThickness

(nm)Emissivity

Maximum

temperature (℃)

Coating Ru 1.25 0.24

532Core SiN 22 -

Coating Ru 1.25 0.24

Ref) ASML, A pellicle solution for EUV, P. Janssen 2015 EUV symp.

14


FEM simulation matches experiment

0.0 0.1 0.2 0.3 0.4 0.5

400

600

800

1000

1200

1400

1600

1800

Tem

per

atu

re (

oC

)membrane emissivity

FEM (ANSYS)

Experiment (Zwol et al)

Silicon nitride melting temperature ~ 1900 °C

Ref) P. J. van Zwol, D.F. Vles, W.P. Voorthuijzen, M. Péter, H. Vermeulen, W.J. van der

Zande J. M. Sturm. R.W.E. van de Kruijs, and F. Bijkerk, J. Appl. Phy., 118.21 213107 (2013).

15


Temperature and Thermal Stress change with coating thickness

0 10 20 30 40 50 60 70 80 90 100

300

600

900

1200

1500

1800

2100

Tem

per

atu

re (

K)

Time (ms)

Single SiNx

Ru 0.5 nm

Ru 0.75 nm

Ru 1 nm

Ru 1.5 nm

Ru 2 nm

Ru 3 nm

PECVD Silicon Nitride tensile fracture strength 2.4 GPa

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0

200

400

600

800

1000

Thermal stress (MPa)

Temperature (K)

Ru coating thickness (nm)T

her

mal

stre

ss (

MP

a)

600

800

1000

1200

1400

1600

1800

2000

Tem

per

atu

re (

K)

16

Progress on reported EUV pellicles

2014

SPIE

Optimization of the EUV pellicle structure

c-Si 50 nm SiN 4 nm

p-Si 50 nm

SiN 4 nm

SiN 4 nm

p-Si 50 nm

SiN 4 nm

Ru 3 nm

B4C 4 nm

c-Si 40 nm

B4C 4 nm

Thermal

stress (MPa)138 999.8 40.7 81.0 385 32.8

Single pass

transmission (%)92 85 81 90 84 76

SiN 20 nm

c-Si pellicle IBM

ASML

(prototype)

ASML

(experiment) SAMSUNG

2016

SPIE

2015

Symposium

2015

Symposium

Ru 2 nm

SiN 25 nm

Ru 2 nm

ASML

(experiment)

2015 van Zwol, P. J., et al.

"Emissivity of

freestanding membranes

with thin metal

coatings." Journal of

Applied Physics 118.21

(2015): 213107.

17


Transmission and thermal stress trade-off

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0

200

400

600

800

1000

Thermal stress (MPa)

Transmission(%)

Ru coating thickness (nm)

Th

erm

al

stre

ss (

MP

a)

73

74

75

76

77

78

79

80

81

Sin

gle

pass

tra

nsm

issi

on

(%

) SiN 25 nm

Ru 3 nm

Ru 3 nm

SiN 25 nm

~ 81 % transmission ~ 73 % transmission

~ 900 MPa thermal stress ~ 30 MPa thermal stress

The coating layer induces thermal and optical trade-off.

The SiN core is suggested for considering Ru closed

surface (at least 1 nm Ru coating preferred)

The high transmission ~ 90 % core is needed

SiO2 has also good Ru surface coverage

Ref) Ribera, R. Coloma, et al. "In vacuo growth studies of Ru thin films on Si, SiN, and SiO2 by

high-sensitivity low energy ion scattering." Journal of applied physics 120.6 (2016): 065303.

18


3 layer EUV pellicle with Ru 1 nm coating

Coating

Coating

Core

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 1

1.47 1058 44 82.5Core Graphene 25

Coating Ru 1

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 1

1.83 1109 191 78.0Core SiN 25

Coating Ru 1

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 1

0.6 863 130 92.9Core p-Si 25

Coating Ru 1

19


3 layer EUV pellicle with B4C 4 nm coating

0 10 20 30 40 50 60 70 80 90 100

400

600

800

1000

1200

1400

1600

Tem

per

atu

re (

K)

Time (ms)

SiN coating

B4C coating

Maximum thermal

stress (MPa)

Single pass

transmission (%)

SiN coating 559 89

B4C coating 81 90

20


MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating B4C 4

1.52 726 43.8 81.8Core Graphene 25

Coating B4C 4

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 4

2.07 781 43.8 78.0Core Graphene 25

Coating Ru 4

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating B4C 4

0.70 802 29.1 91.7Core p-Si 25

Coating B4C 4

3 layer EUV pellicle with 4 nm coating

Coating

Coating

Core

21


Coating

Coating

Core

5 layer EUV pellicle with 1 nm coating and with SiN core

Capping

Capping

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 1

1.96 1032 106 76.4Capping SiO2 1

Core SiN 25

Capping SiO2 1

Coating Ru 1

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 1

1.94 1036 108 76.7Core SiN 27

Coating Ru 1

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 1

1.92 984 139 77.0Capping Graphene 1

Core SiN 25

Capping Graphene 1

Coating Ru 1

22


Coating

Coating

Core

5 layer EUV pellicle with 1 nm coating and with graphene core

Capping

Capping

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 1

1.60 987 84.1 80.8Capping SiO2 1

Core Graphene 25

Capping SiO2 1

Coating Ru 1

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 1

1.55 780 79.9 81.5Core Graphene 27

Coating Ru 1

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 1

1.58 969 85.6 81.1Capping SiN 1

Core Graphene 25

Capping SiN 1

Coating Ru 1

23


Coating

Coating

Core

5 layer EUV pellicle with Si core

Capping

Capping

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 1

0.76 795 68.1 91.0Capping SiO2 1

Core Si 25

Capping SiO2 1

Coating Ru 1

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 1

0.62 832 72.6 92.6Core Si 27

Coating Ru 1

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 1

0.68 777 71.3 92.0Capping SiO2 0.5

Core Si 25

Capping SiO2 0.5

Coating Ru 1

24


Coating

Coating

Core

5 layer EUV pellicle with Si core

Capping

Capping

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 2

0.91 610 32.6 89.1Capping SiO2 0.5

Core Si 25

Capping SiO2 0.5

Coating Ru 2

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 3

1.14 620 32.59 86.3Capping SiO2 0.5

Core Si 25

Capping SiO2 0.5

Coating Ru 3

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 1.5

0.80 696 31.4 90.5Capping SiO2 0.5

Core Si 25

Capping SiO2 0.5

Coating Ru 1.5

25


Consideration of Ru coverage for minimum coating thickness

Ref) Ribera, R. Coloma, et al. "In vacuo growth

studies of Ru thin films on Si, SiN, and SiO2 by

high-sensitivity low energy ion scattering."

Journal of applied physics 120.6 (2016): 065303.

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 3.2

0.76 625 32.6 85.9Capping SiN 0.5

Core Si 25

Capping SiN 0.5

Coating Ru 3.2

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 2

0.91 610 32.6 89.1Capping SiO2 0.5

Core Si 25

Capping SiO2 0.5

Coating Ru 2

MaterialThickness

(nm)

Absorbed heat

(W/cm2)

Maximum

temperature (K)

Maximum

stress (MPa)

Single pass

transmission (%)

Coating Ru 4.7

1.43 711 33.0 82.2Core Si 25

Coating Ru 4.7

26


Optimized pellicle candidates for EUVL

MaterialThickness

(nm)

Maximum

stress (MPa)

Single pass

transmission (%)

B4C 4

43.8 81.8Graphene 25

B4C 4

MaterialThickness

(nm)

Maximum

stress (MPa)

Single pass

transmission (%)

B4C 4

29.1 91.7p-Si 25

B4C 4

MaterialThickness

(nm)

Maximum

stress (MPa)

Single pass

transmission (%)

Ru 2

32.6 89.1SiO2 0.5

Si 25

SiO2 0.5

Ru 2

0 10 20 30 40 50 60 70 80 90 100

300

400

500

600

700

800

900

1000

Tem

per

atu

re (

K)

Time (ms)

Si core with Ru

p-Si core with B4C

Graphene core with B4C

27


EUV pellicle simulation discussion

Ref) Lee, Changgu, et al. "Measurement of the elastic properties and intrinsic

strength of monolayer graphene." science 321.5887 (2008): 385-388.

ASML

(prototype)

ASML

(experiment)

28

Progress on reported EUV pellicles

2014

SPIE


c-Si 50 nm

SiN 4 nm

p-Si 50 nm

SiN 4 nm

SiN 4 nm

p-Si 50 nm

SiN 4 nm

Ru 3 nm

B4C 4 nm

c-Si 40 nm

B4C 4 nm

Thermal

stress (MPa) 138 999.8 40.7 81.0 385 32.8

Single pass

transmission (%) 92 85 81 90 84 76

SiN 20 nm

c-Si pellicle IBMSAMSUNG

2016

SPIE

2015

Symposium

2015

Symposium

Ru 2 nm

SiN 25 nm

Ru 2 nm

ASML

(experiment)

2015 van Zwol, P. J., et al.

"Emissivity of freestanding

membranes with thin metal

coatings." Journal of

Applied Physics 118.21

(2015): 213107.

32.6 43.8 29.1

89 82 92

B4C 4 nm

Graphene 25 nm

B4C 4 nm

B4C 4 nm

p-Si 25 nm

B4C 4 nm

Ru 2 nm

SiO2 0.5 nm

c-Si 25 nm

SiO2 0.5 nm

Ru 2 nm

Ref) P. J. van Zwol, D.F. Vles, W.P. Voorthuijzen, M. Péter, H. Vermeulen, W.J. van der

Zande J. M. Sturm. R.W.E. van de Kruijs, and F. Bijkerk, J. Appl. Phy., 118.21 213107 (2013).

29

Additional considerations

Gravitational stress of the EUV pellicle

REF) Park, E. S., Shamsi, Z. H., Kim, J. W., Kim, D. G., Park,

J. G., Ahn, J. H., & Oh, H. K. (2015). Mechanical deflection of

a free-standing pellicle for extreme ultraviolet lithography.

Microelectronic Engineering, 143, 81-85.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0

200

400

600

800

1000

Thermal stress

Mechanical stress

Ru thickness (nm)

Th

erm

al

stre

ss (

MP

a)

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

Mec

han

ica

l st

ress

(M

Pa)

0.0 0.1 0.2 0.3 0.4 0.5

400

600

800

1000

1200

1400

1600

1800

Temperature

Deflection

membrane emissivity

Tem

pera

ture (

oC

)

58

60

62

64

66

68

70

Defl

ecti

on

(

m)

w03≈

qa4

5π6

2048 in Eihi

1−νi2

Multi-stack deflection equation

30


Gravitational stress and deflection of the EUV pellicle

MaterialThickness

(nm)

Thermal stress

(MPa)

Mechanical stress

(MPa)

Deflection

(𝝁𝒎)

Single pass

transmission (%)

B4C 4

43.8 0.26 40.1 81.8Graphene 25

B4C 4

MaterialThickness

(nm)

Thermal stress

(MPa)

Mechanical stress

(MPa)

Deflection

(𝝁𝒎)

Single pass

transmission (%)

Ru 2

32.6 0.9 76.6 89.1

SiO2 0.5

Si 25

SiO2 0.5

Ru 2

MaterialThickness

(nm)

Thermal stress

(MPa)

Mechanical stress

(MPa)

Deflection

(𝝁𝒎)

Single pass

transmission (%)

B4C 4

29.1 0.63 62.7 91.7p-Si 25

B4C 4

EUV pellicle deflection

31

Residual stress equation for multi-layer thin film

Ref) C. H. Hway et al., “Modeling of Elastic Deformation of Multilayers Due to

Residual Stress and External Bending”, Journal of Applied Physics 91, 9652, (2002)

z=𝒉𝒏

z=𝒉𝟏

z=𝒉𝒏−𝟏

z= -𝐭𝐬

Substrate

layer 1

𝐭𝐬

layer n

𝐭𝟏

𝐭𝒊

𝐭𝒏

layer i 𝐭𝒊

𝛔𝐢 = 𝐄𝒊 𝛂𝐬 − 𝛂𝐢 + 𝟒

𝐣=𝟏

𝐧𝐄𝐣𝐭𝐣 𝛂𝐣 − 𝛂𝐬

𝐄𝐬𝐭𝐬∆𝐓

𝛔𝐟 =𝟏

𝒕𝒇 𝟎

𝒕𝒇

𝝈𝒇𝒅𝒛


𝑬𝒊 : Young’s modulus of layer i of film (Pa)

𝑬𝒔 : Young’s modulus of substrate (Pa)

𝒕𝒊 : Thickness of layer i of film (nm)

𝒕𝒔 : Thickness of substrate (μm)

𝜶𝒇 : Thermal expansion coefficient of layer i of film (μm/K)

𝜶𝒔 : Thermal expansion coefficient of substrate (μm/K)

∆𝐓 : Deposition temperature (K)

32

Calculated residual stress of EUV pellicle

MaterialThickness

(nm)

Thermal expansion

coefficient(μm/K)

Substrate

material

Thickness

(mm)

Maximum stress

(MPa)

Residual stress

(MPa)

Single pass

transmission (%)

Deposition

Temperature(℃)

B4C 4 5.0 Si0.7 43.8

-248081.8 300 ℃Graphene 25 -7.0

Si𝐎𝟐 -2570B4C 4 5.0

MaterialThickness

(nm)

Thermal expansion

coefficient(μm/K)

Substrate

material

Thickness

(mm)

Maximum stress

(MPa)

Residual stress

(MPa)

Single pass

transmission (%)

Deposition

Temperature(℃)

Ru 2 11.1

Si

0.7 43.8

-5.74e8

89.1 820 ℃

SiO2 0.5 0.75

Si 25 2.6

Si𝐎𝟐 -5.73e8SiO2 0.5 0.75

Ru 2 11.1

Reference temperature : 25 ℃


MaterialThickness

(nm)

Thermal expansion

coefficient(μm/K)

Substrate

material

Thickness

(mm)

Maximum stress

(MPa)

Residual stress

(MPa)

Single pass

transmission (%)

Deposition

Temperature(℃)

B4C 4 5.0Si

0.7 29.1315

91.7 820 ℃p-Si 25 2.9

Si𝐎𝟐 769B4C 4 5.0

33

Conclusion

Thermal stress could be induced by EUV exposure and it would decrease the pellicle

lifetime. Thus, the multi-stack structure with lower thermal stress is needed.

The reported pellicle shows relatively high thermal stress or low transmission.

Therefore, high emissivity coating with transparent core material is preferred.

Some of new EUV pellicles with higher transmission and lower thermal stress are

suggested, so that the extension of the lifetime is possible.

Additional considerations (surface coverage, structural analysis, and residual stress

etc.) should be also analyzed to extend the pellicle lifetime.

thermal stress analysis of the extreme ultraviolet multi...

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