h diffusion in cu: bonding

1

H Diffusion in Cu: Bonding

0 100 200 300 400 500 600 7000

300

600

900

1200

2020 20

1040 1040

800

1040_H2

Time (minutes)

T

(°C

)

2

H Diffusion in Cu: Bonding

• Second Fick’s law

Diffusion in a plane sheet

H2H2 H2

3

H Diffusion in Cu: Second Fick’s law

semi-infinite material 1-D concentration profile

x

2

2

x

CD

t

C

Dt

xerf

CC

CC

s

x

21

0

0

H2

4

H Diffusion in Cu: Second Fick’s lawo Solubility :

o Diffusion :

PapHKT

pHxH 5^10*1,13567702426

77.4log2

1log 22

RTD

37320exp10*34.8 3

5

H Diffusion in Cu: Bonding plateau

0.0 0.5 1.0 1.50.00000

0.00005

0.00010

0.00015

C (

x)

x

1000 2000 3000 4000 5000

0.00000

0.00002

0.00004

0.00006

0.00008

Cx

t (s)

0.000119 wt%

C0 =0

1.2 ppm

6

0.0 0.5 1.0 1.51000

2000

3000

4000

5000

0.00000

0.00005

0.00010

0.00015

t (s)

Cx

x (cm)

H Diffusion in Cu: Bonding

7

H Diffusion in Cu: Diffusion in a plane sheet

n = 1,2,3,4Cs equal and constant at the

surfaces

H2 H2

02

22

0

0

2

)12(cos

4)12(exp

12

)1(41

n

n

s l

xn

l

tnD

nCC

CC

8

H Diffusion in Cu: Bonding plateau

C0 =0

0.0 0.5 1.0

0.0001196

0.0001198

0.0001200

0.0001202

0.0001204C

x (w

t%)

x (cm)

9

H Diffusion in Cu: Bonding ramp down

• 1040 – 800 °C • 4 °C/min• C0(T) = C(T - 4°C)

4°C

60 s

10

H Diffusion in Cu: Bonding ramp down

C(800 °C) = 4.63234E-05 % wt (0.46 ppm)

0.0 0.5 1.00.000105

0.000110

0.000115

0.000120

C(x

)

x (cm)

1036 ° C 1032 ° C 1028 ° C 1024 ° C 1020 ° C 1016 ° C 1012 ° C 1008 ° C 1004 ° C

11

H Diffusion in Cu: thermal treatment after bonding• 10 d, @ 650 °C• C0=C(x) @ 800 °C

• Cs= CH2 in the oven (10^-8 mBar)

0.0 0.5 1.00.0000000

0.0000002

0.0000004

0.0000006

C(x

)

x (cm)

12

H Diffusion in Cu: thermal treatment after bonding

0.0 0.5 1.01.00E-009

1.20E-009

1.40E-009

1.60E-009

1.80E-009

2.00E-009

C(x

)

x (cm)

13

Next steps search for thermodynamics data

@ room temperature check the ramp down to 20°C calculate the effective content of

H in Cu

14

Solubility of H in Cu

H2

2HH

)][ln(ln 22

022

02 HHHHH sRTPRT

202 ln2ln HHH RTsRT

solsolHH STHG 02

2

ln

22ln 2

s

R

Si

RT

H iH

2

ln

2

ln

2ln 2

2

sP

RT

H HiH

Sieverts`s Law

Hp Ideal Gas

15

Solubility of H in Cu

Cu is an endothermic material

TpHxH

242677.4log

2

1log 2

2

ln

2

ln

2ln 2

2

sP

RT

H HiH

HMHHM x 22

16

Solubility of H in Cu

log

XH

2

1/T

LogX

H2

LogP