Much work has been done in the approximation of the stress state of microelectronic interconnects on chips. The thermally induced stresses in passivated interconnects are of interest as they are used as input in interconnect reliability failure models (stress-driven void growth, electromigration-driven void growth). The classical continuum mechanics and physics typically used is, however, intrinsically size independent. This is in contradiction to the physical fact that at the size scale of a few nanometers, the elastic state is size dependent and a departure from classical mechanics is expected. In this work, we address the various physical causes (and the affiliated mathematical modeling) of the size dependency of mechanical stresses in nanointerconnects. In essence, we present scaling laws for mechanical stresses valid for nanosized interconnects.

1.
A.
Wikstrom
,
P.
Gudmundson
, and
S.
Suresh
,
J. Appl. Phys.
86
,
6088
(
1999
).
2.
A.
Gouldstone
,
Y.-L.
Shen
,
S.
Suresh
, and
C. V.
Thompson
,
J. Mater. Res.
13
,
1956
(
1998
).
3.
A. I.
Sauter
and
W. D.
Nix
,
IEEE Trans. Compon., Hybrids, Manuf. Technol.
15
,
594
(
1992
).
4.
M. A.
Korhonen
,
R. D.
Black
, and
C.-Y.
Li
,
J. Appl. Phys.
69
,
1748
(
1991
).
5.
H.
Niwa
,
H.
Yagi
,
H.
Tsuchikawa
, and
M.
Kato
,
J. Appl. Phys.
68
,
328
(
1990
).
6.
P.
Sharma
,
H.
Ardebili
, and
J.
Loman
,
Appl. Phys. Lett.
79
,
1706
(
2001
).
7.
C. H.
Hsueh
,
J. Appl. Phys.
92
,
144
(
2002
).
8.
D. N.
Bhate
,
A.
Kumar
, and
A. F.
Bower
,
J. Appl. Phys.
87
,
1712
(
2000
).
9.
Materials Reliability in Microelectronics IV, edited by P. Borgensen et al. (Materials Research Society, Pittsburgh, PA, 1994).
10.
ITRS (International Technical Roadmap for Semiconductors) roadmap for interconnect technology, 2001.
11.
Quantum Dots and Nanowires, edited by S. Bandyopadhyay and H. S. Nalwa (American Scientific Publishers, Stevenson Ranch, CA, 2003).
12.
J. D.
Meindl
,
Comput. Sci. Eng.
5
,
20
(
2003
).
13.
A. E.
Kaloyeros
,
E. T.
Elsenbraun
,
J.
Welch
, and
R. E.
Geer
,
Semicond. Int.
26
,
56
(
2003
).
14.
X.
Pang
,
A. M.
Kriman
, and
G. H.
Bernstein
,
J. Electrochem. Soc.
149
,
G103
(
2002
).
15.
M.
Kato
,
H.
Niwa
,
H.
Yagi
, and
H.
Tsuchikawa
,
J. Appl. Phys.
68
,
334
(
1990
).
16.
J. D.
Eshelby
,
Proc. R. Soc. London, Ser. A
241
,
376
(
1957
).
17.
M. E.
Gurtin
,
J.
Weissmuller
, and
F.
Larche
,
Philos. Mag. A
78
,
1093
(
1998
).
18.
M. E.
Gurtin
and
A. I.
Murdoch
,
Arch. Ration. Mech. Anal.
59
,
389
(
1975
).
19.
M. E.
Gurtin
and
A. I.
Murdoch
,
Int. J. Solids Struct.
14
,
431
(
1978
).
20.
H.
Ibach
,
Surf. Sci. Rep.
29
,
193
(
1997
).
21.
P. Sharma and S. Ganti (unpublished).
22.
J. A. Krumhansl, in Mechanics of Generalized Continua, edited by E. Kroner (Springer-Verlag, Berlin, 1968), p. 298.
23.
I. A.
Kunin
,
Prikl. Mat. Mekh.
30
,
542
(
1966
).
24.
A. C.
Eringen
and
D. G. B.
Edelen
,
Int. J. Eng. Sci.
10
,
233
(
1972
).
25.
I. A. Kunin, Elastic Media with Microstructure I (Springer-Verlag, Berlin, 1982).
26.
I. A. Kunin, Elastic Media with Microstructure II (Springer-Verlag, Berlin, 1983).
27.
A. C. Eringen, Nonlocal Continuum Field Theories (Springer-Verlag, New York, 2002).
28.
A. C. E.
Reid
and
R. J.
Gooding
,
Phys. Rev. B
46
,
6045
(
1992
).
29.
P. Sharma and S. Ganti, Philos. Mag. Lett. (to be published).
30.
G.
Cui
,
M.
Lane
,
K.
Vijayamohanan
, and
G.
Ramanath
,
Mater. Res. Soc. Symp. Proc.
695
,
329
(
2002
).
31.
S. Ganti, P. Sharma, and N. Bhate (unpublished).
32.
R. E.
Miller
and
V. B.
Shenoy
,
Nanotechnology
11
,
139
(
2000
).
33.
H. F.
Tiersten
,
J. Appl. Phys.
40
,
770
(
1969
).
34.
P. R.
Vyas
,
C. V.
Pandya
,
T. C.
Pandya
, and
V. B.
Gohel
,
Pramana, J. Phys.
56
,
559
(
2001
).
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