Micro-Raman spectroscopy is used to determine the multiaxial stress state in silicon wafers using a strategy proposed by Narayanan, et al. (J. Appl. Phys. 82, 2595–2602 (1997)) Previously, this strategy was validated when silicon was subjected to uniaxial stress in the laboratory frame (Harris, et al. J. Appl. Phys. 96, 7195–7201 (2004)). In the present work, silicon wafers have been analyzed that were subjected to biaxial stress states in the laboratory frame. The predicted curves for the initially degenerate F2g peaks were found to fall within the variability of the measured curves. Stress ratios were found to be predictable. Stress magnitudes were also found to be predictable, but are subject to uncertainty greater than 25%. To perform these tests, an apparatus has been developed which can provide controlled ratios of biaxial stress in a simple and compact test geometry. This fixture was used under a microscope, enabling in situ measurement of biaxial stress states.

1.
Wang
,
Q. G.
,
Caceres
,
C. H.
, and
Griffiths
,
J. R.
, 2003, “
Damage by Eutectic Particle Cracking in Aluminum Casting Alloys A356/357
,”
Metall. Mater. Trans. A
1073-5623,
34
(
12
), pp.
2901
2912
.
2.
Clyne
,
T.
, 1989, “
A Simple Development of the Shear Lag Theory Appropriate for Composites With a Relatively Small Modulus Mismatch
,”
Mater. Sci. Eng., A
0921-5093,
122
(
183
), pp.
183
192
.
3.
Eshelby
,
J. D.
, 1957, “
The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problem
,”
Proc. R. Soc. London, Ser. A
1364-5021,
241
(
376
), pp.
376
396
.
4.
Mori
,
T.
, and
Tanaka
,
K.
, 1973, “
Average Stress in Matrix and Average Elastic Energy of Materials with Misfitting Inclusions
,”
Acta Metall.
0001-6160,
21
(
5
), pp.
571
574
.
5.
Harris
,
S. J.
,
ONeill
,
A. E.
,
Gustafson
,
P. A.
,
Boileau
,
J.
,
Yang
,
W.
,
Weber
,
W. H.
,
Majumdar
,
B.
, and
Ghosh
,
S.
, 2004, “
Measurement of the State of Stress in Silicon with Micro-Raman Spectroscopy
,”
J. Appl. Phys.
0021-8979,
96
(
12
), pp.
7195
7201
.
6.
DeWolf
,
I.
,
Ignat
,
M.
,
Pozza
,
G.
,
Maniguet
,
L.
, and
Maes
,
H. E.
, 1999, “
Analysis of Local Mechanical Stresses In and Near Tungsten Lines on Silicon Substrate
,”
J. Appl. Phys.
0021-8979,
85
(
9
), pp.
6477
.
7.
DeWolf
,
I.
, 1996, “
Micro-Raman Spectroscopy to Study Local Mechanical Stress in Silicon Integrated Circuits
,”
Semicond. Sci. Technol.
0268-1242,
11
(
2
), pp.
139
154
.
8.
DeWolf
,
I.
,
Maes
,
H. E.
, and
Jones
,
S. K.
, 1996, “
Stress Measurements in Silicon Devices through Raman Spectroscopy: Bridging the Gap Between Theory and Experiment
,”
J. Appl. Phys.
0021-8979,
79
(
9
), p.
7148
.
9.
DeWolf
,
I.
,
Pozzat
,
G.
,
Pinardi
,
K.
,
Howard
,
D. J.
,
Ignat
,
M.
,
Jain
,
S. C.
, and
Maes
,
H. E.
, 1996, “
Experimental Validation of Mechanical Stress Models by Micro-Raman Spectroscopy
,”
Microelectron. Reliab.
0026-2714,
36
(
11-12
), pp.
1751
1754
.
10.
Ajito
,
K.
,
Sukamto
,
J. P. H.
,
Nagahara
,
L. A.
,
Hashimoto
,
K.
, and
Fujishima
,
A.
, 1995, “
Strain Imaging Analysis of Si Using Raman Microscopy
,”
13
, pp.
1234
1238
, AVS, May 1995.
11.
Anastassakis
,
E.
, and
Liarokapis
,
E.
, 1987, “
Polycrystalline Si Under Strain: Elastic and Lattice-Dynamical Considerations
,”
J. Appl. Phys.
0021-8979,
62
(
8
), pp.
3346
3352
.
12.
Anastassakis
,
E.
,
Pinczuk
,
A.
,
Burstein
,
E.
,
Pollak
,
F. H.
, and
Cardona
,
M.
, 1970, “
Effect of Static Uniaxial Stress on the Raman Spectrum of Silicon
,”
Solid State Commun.
0038-1098,
8
(
2
), pp.
133
138
.
13.
Englert
,
Th.
,
Abstreiter
,
G.
, and
Pontcharra
,
J.
, 1980, “
Determination of Existing Stress in Silicon Films on Sapphire Substrate Using Raman Spectroscopy
,”
Solid-State Electron.
0038-1101,
23
(
1
), pp.
31
33
.
14.
Kobayashi
,
K.
,
Inoue
,
Y.
,
Nishimura
,
T.
,
Hirayama
,
M.
,
Akasaka
,
Y.
,
Kato
,
T.
, and
Ibuki
,
S.
, 1990, “
Local-Oxidation-Induced Stress Measured by Raman Microprobe Spectroscopy
,”
J. Electrochem. Soc.
0013-4651,
137
(
6
), pp.
1987
1989
.
15.
Narayanan
,
S.
,
Kalidindi
,
S. R.
, and
Schadler
,
L. S.
, 1997, “
Determination of Unknown Stress States in Silicon Wafers Using Microlaser Raman Spectroscopy
,”
J. Appl. Phys.
0021-8979,
82
(
5
), pp.
2595
2602
.
16.
Brockenbrough
,
J. R.
, and
Zok
,
F. W.
, 1995, “
Role of Particle Cracking in Flow and Fracture of Metal Matrix Composites
,”
Acta Metall. Mater.
0956-7151,
43
(
1
), pp.
11
20
.
17.
Anastassakis
,
E. M.
, 1980,
Dynamic Properties of Solids
,
North-Holland
, Amsterdam.
18.
Loudon
,
R.
, 1964, “
Raman Effect in Crystals
,”
Adv. Phys.
0001-8732,
13
(
52
), pp.
423
430
.
19.
Loechelt
,
G. H.
,
Cave
,
N. G.
, and
Menendez
,
J.
, 1999, “
Polarized Off-Axis Raman Spectroscopy: A Technique for Measuring Stress Tensors in Semiconductors
,”
J. Appl. Phys.
0021-8979,
86
(
11
), pp.
6164
6180
.
20.
Anastassakis
,
E.
,
Cantarero
,
A.
, and
Cardona
,
M.
, 1990, “
Piezo-Raman Measurements and Anharmonic Parameters in Silicon and Diamond
,”
Phys. Rev. B
0163-1829,
41
(
11
), pp.
7529
7535
.
21.
Ugural
,
A. C.
, 1981,
Stresses in Plates and Shells
,
McGraw-Hill
, New York.
22.
Timoshenko
,
S.
, and
Woinowsky-Krieger
,
S.
, 1959,
Theory of Plates and Shells
,
McGraw-Hill
, New York.
23.
Blum
,
J.
, and
Roseblatt
,
J.
, 1972,
Probability and Statistics
,
Saunders
, Philadelphia, PA.
24.
Chandrasekhar
,
M.
,
Renucci
,
J.
, and
Cardona
,
M.
, 1978, “
Effects of Interband Excitations on Raman Phonons in Heavily Doped N‐Si
,”
Phys. Rev. B
0556-2805,
17
, pp.
1623
1633
.
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