An analytical model of electromigration and stress affected kinetics of a chemical reaction is investigated based on the notion of the chemical affinity tensor within the small strain approximation. Effects of stresses are accounted for through their influence on the chemical affinity tensor on which the reaction front velocity depends. Electromigration is considered as an additional summand in the total flux of the diffusive constituents. The Mean-Time-To-Failure (MTTF) is estimated based on Black's equation. Then the critical thickness of the IMC layer is calculated and a dimensionless parameter, which characterizes the accumulation of vacancies due to electromigration enhanced diffusion is proposed.

1.
S.
Cheng
,
C.-M.
Huang
, and
M.
Pecht
,
Microelectronics Reliability
75
,
0026
2714
(
2017
)
2.
F.
Mohd
,
C.
Basaran
, and
Y.-S.
Lai
,
Advanced Packaging, IEEE Transactions on
32
,
627
635
(
2009
).
3.
B.
Chao
,
S.-H.
Chae
,
X.
Zhang
,
K.
Lu
,
M.
Ding
,
J.
Im
, and
P.
Ho
,
Journal of Applied Physics
100
,
084909
084909
(
2006
).
4.
A.
Smigelskas
and
E.
Kirkendall
,
Trans. AIME
27
,
130
142
(
1947
).
5.
B.
Chao
,
X.
Zhang
,
S.-H.
Chae
, and
P.
Ho
,
Microelectronics Reliability
49
,
253
263
(
2009
).
6.
J.-Y.
Park
,
T.
Lee
,
W.
Seo
,
S.
Yoo
, and
Y.-H.
Kim
,
Journal of Materials Science: Materials in Electronics
30
,
7645
7653
(
2019
).
7.
A.
Paul
, “
The Kirkendall effect in solid state diffusion
”, Ph.D. thesis,
Department of Chemical Engineering and Chemistry
(
2004
).
8.
B.
Chao
,
S.-H.
Chae
,
X.
Zhang
,
K.
Lu
,
J.
Im
, and
P.
Ho
,
Acta Materialia
55
,
2805
2814
(
2007
).
9.
G.
Ross
,
V.
Vuorinen
, and
M.
Paulasto-Kröckel
,
Journal of Alloys and Compounds
677
,
0925
8388
(
2016
).
10.
T.
Laurila
,
A.
Paul
,
V.
Vuorinen
, and
S.
Divinski
,
Thermodynamics, Diffusion And The Kirkendall Effect In Solids,
(
Springer Berlin Heidelberg
,
Berlin, Heidelberg
,
2014
).
11.
K.
Zeng
,
R.
Stierman
,
T.-C.
Chiu
,
D.
Edwards
,
K.
Ano
, and
K. N.
Tu
,
Journal of Applied Physics
97
(
2005
).
12.
J.
Kim
,
J.
Yu
, and
S.
Kim
,
Acta Materialia - ACTA MATER
57
,
5001
5012
(
2009
).
13.
L.
Xu
,
J. H. L.
Pang
, and
F.
Che
,
Journal of Electronic Materials
37
,
880
886
(
2008
).
14.
A. B.
Freidin
and
E. N.
Vilchevskaya
, in
Encyclopedia of Continuum Mechanics
, edited by
H.
Altenbach
and
A.
Öchsner
(
Springer Berlin Heidelberg
,
Berlin, Heidelberg
,
2019
) pp.
1
17
.
15.
A.
Freidin
,
E.
Vilchevskaya
, and
I.
Korolev
,
International Journal of Engineering Science
83
,
57
75
(
2014
).
16.
A.
Morozov
,
S.
Khakalo
,
V.
Balobanov
,
A.
Freidin
,
W.
Müller
, and
J.
Niiranen
,
Technische Mechanik
38
,
73
90
(
2018
).
17.
M.
Poluektov
,
A.
Freidin
, and
Ł.
Figiel
,
International Journal of Engineering Science
128
,
44
62
(
2018
).
18.
A.
Morozov
,
A. B.
Freidin
,
V. A.
Klinkov
,
A. V.
Semencha
,
W. H.
Müller
, and
T.
Hauck
,
Journal of Electronic Materials
49
,
7194
7210
(
2020
).
19.
A.
Morozov
,
A.
Freidin
,
W. H.
Müller
,
A.
Semencha
, and
M.
Tribunskiy
, in
20th International Conference on Thermal, Mechanical and Multi-Physics Simulation and Experiments in Microelectronics and Microsystems– 2019 (EuroSimE),
pp.
1
8
.
20.
P.
Glansdorff
,
I.
Prigogine
, and
R. N.
Hill
,
American Journal of Physics
41
,
147
148
(
1973
)
21.
A.
Freidin
, “
Chemical affinity tensor and stress-assist chemical reactions front propagation in solids
,”
ASME 2013 International Mechanical Engineering Congress and Exposition
, p.
V009T10A102
.
22.
K. N.
Tu
, “Fundamentals of electromigration,” in
Springer Series in Materials Science
,
Springer Series in Materials Science
(
Springer Verlag
,
2007
) pp.
211
243
.
23.
C.
Chen
,
H.
Tong
, and
K.
Tu
,
Annual Review of Materials Research
40
,
531
555
(
2010
).
24.
J. R.
Black
,
IEEE Transactions on Electron Devices
16
,
338
347
(
1969
).
This content is only available via PDF.
You do not currently have access to this content.