We show that x-ray diffraction imaging (topography) and finite-element modelling can determine accurately the probability of propagation of individual cracks in brittle single crystal materials. The x-ray image of the crack provides a critical parameter for crack propagation which informs a predictive model, enabling us to identify critical defects that lead to catastrophic shattering of silicon wafers during high temperature thermal processing. Wafers fracture on cooling and finite element modelling shows that, during cooling, the tangential stress at the wafer edge is tensile and results in crack propagation. The predicted fracture geometry agrees extremely well with that observed experimentally.

1.
R. F.
Cook
,
J. Mater. Sci.
41
,
841
(
2006
).
2.
X. F.
Brun
and
S. N.
Melkote
,
Sol. Energy Mater. Sol. Cells
93
,
1238
(
2009
).
3.
A.
Ward
and
R. W.
Hendricks
,
J. Electron. Mater.
27
,
821
(
1998
).
4.
P.
Rupnowski
and
B.
Sopori
,
Int. J. Fract.
155
,
67
(
2009
).
5.
International SEMATECH Industry Economic Model, v8.1ss,
2004
.
6.
P. Y.
Chen
,
M. H.
Tsai
,
W. K.
Yeh
,
M. H.
Jing
, and
Y.
Chang
,
Jpn. J. Appl. Phys.
, Part 1
48
,
126503
(
2009
).
7.
P. Y.
Chen
,
M. H.
Tsai
,
W. K.
Yeh
,
M. S.
Jing
, and
Y.
Chang
.
Microelectron. Eng.
87
,
2065
(
2010
).
8.
D. K.
Bowen
and
B. K.
Tanner
,
X-ray Metrology in Semiconductor Wafer Manufacture
(
Taylor and Francis, CRC Press
,
Bocca Raton
,
2006
).
9.
B. K.
Tanner
,
J.
Wittge
,
D.
Allen
,
M. C.
Fossati
,
A. N.
Danilewsky
,
P.
McNally
,
J.
Garagorri
,
M. R.
Elizalde
, and
D.
Jacques
,
J. Appl. Cryst.
44
,
526
(
2011
).
10.
D. K.
Bowen
,
M.
Wormington
, and
P.
Feichtinger
,
J. Phys. D: Appl. Phys.
36
,
A17
(
2003
)
11.
T.
Jauss
,
A. N.
Danilewsky
,
J.
Wittge
,
A.
Cröll
,
J.
Garagorri
,
M. R.
Elizalde
,
D.
Allen
, and
P. J.
McNally
,
Cryst. Res. Technol
47
,
253
(
2012
).
12.
See supplementary material at http://dx.doi.org/10.1063/1.4738994 for details of experimental methods and finite element model.
13.
P. B.
Hirsch
,
A.
Howie
,
R. B.
Nicholson
,
D. W.
Pashley
, and
M. J.
Whelan
,
Electron Microscopy of Thin Crystals
(
Butterworths
,
London
,
1965
).
14.
A. A.
Griffith
.
Philos. Trans. R. Soc. London, Ser. A
221
,
163
(
1921
).
15.
J.
Garagorri
,
M. R.
Elizalde
,
M. C.
Fossati
,
D.
Jacques
, and
B. K.
Tanner
,
J. Appl. Phys.
111
,
094901
(
2012
).

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