h diffusion in cu: bonding
DESCRIPTION
H Diffusion in Cu: Bonding. H Diffusion in Cu: Bonding. Second Fick’s law. Diffusion in a plane sheet. H 2. H2. H2. H Diffusion in Cu: Second Fick’s law. semi-infinite material 1-D concentration profile. H 2. x. H Diffusion in Cu: Second Fick’s law. Solubility : - PowerPoint PPT PresentationTRANSCRIPT
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