Rapid Communications
1
6,17
cores.
This might be achieved either by an excess of
must be some additional factors contributing to the drop
in permittivity. One such factor could be a dependence of
the Ba/Sr ratio in the grain interiors on the overall Ti/
(Ba + Sr) ratio in the film; more precise measurements
of the Sr content (i.e., Ti/Sr ratio) in the grain interiors
are necessary to clarify this issue.
Ti ions or by oxygen vacancies present at concentrations
1
6
higher than those of the Ba/Sr vacancies; in both
cases an increased Ti/O ratio at the grain boundary core
is expected. Surprisingly, measurements of the Ti/O ratio
by Stemmer et al. for a 50.7% film performed at much
higher spatial resolution (a probe size of less than 0.4 nm
has been quoted), did not reveal any visible change in
Ti/O ratio at the grain boundaries. At present, there is no
explanation for this discrepancy.
These results demonstrate that the BST films with Ti
contents ranging from 50.7% to 53.4% consist of at least
two phases with distinct chemical composition: grain in-
teriors and grain boundaries. Assuming a hexagonal
prism shape for grains with an average diameter of
22
11
ACKNOWLEDGMENTS
The specimens for this study were kindly provided by
P.C. van Buskirk, S. Bilodeau, and R. Carl of Advanced
Technology Materials, Inc. The discussions with S.K.
Streiffer (Argonne National Laboratory) are acknowl-
edged. The use of brand or trade names does not imply
endorsement of the product by NIST.
1
5 nm, the volume fraction of grain boundaries with a
18
thickness t ס
1 nm is estimated to be 18%. The grain
boundaries in the present films are connected mostly in
parallel to the grain interiors, and therefore their effect
on the dielectric constant is expected to be roughly pro-
portional to the volume fraction. Because the grain size is
independent of the average composition, the grain
boundaries alone cannot account for the strong compo-
sitional dependence of dielectric constant, even though
the thickness of the space charge regions can vary with
changes in the overall Ti/(Ba + Sr) ratio. As the Ti/
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4
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1
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eff
1
(
2
(⑀ + ⑀ ) [⑀ ס
f ⑀ + (1 − f )⑀
eff
p
s
p
a a
a
c
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−1
−1
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s a a a c a c
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line phases, respectively, and f is a volume fraction of
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p
s
1
1
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19,20
1
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15
and a volume fraction of 5% would reduce the effective
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10
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0, 733 (1992).
dielectric constant from ס
280 for the 50.7% speci-
men (no amorphous phase) to ⑀ ס
208 for the 53.4%
specimen. This value is still significantly larger than the
2
1
21. H. Funakubo, Y. Takeshima, D. Nagano, K. Shinozaki, and
10
ס
160 measured for the 53.4% specimen; thus, there
N. Mizutani, J. Mater. Res. 13, 3512 (1998).
⑀
1
436
J. Mater. Res., Vol. 15, No. 7, Jul 2000
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