Seemingly, contradictory results have been reported so far for electrostriction in anodic oxides. Furthermore, no definitive agreement could be obtained with theory. In this paper, in situ techniques are combined to elucidate electrostriction in anodic niobium oxide. The dependence of strain, internal stress, and dielectric constant on the electric field is measured by, respectively, spectroscopic ellipsometry, curvature, and impedance measurements. The through-thickness strain is tensile and proportional to the square of the electric field. The in-plane internal stress is compressive and proportional to the square of the electric field at low field values. The internal stress is predicted relatively well by the Maxwell stress because of the weak dependence of the dielectric constant on the volume change of the oxide. The dielectric constant decreases with the electric field, the dependence being quadratic. While the evolution of the strain and stress with the electric field can be ascribed to the dependence of the dielectric constant on strain, the dependence of the dielectric constant on the electric field contains an explicit strain and electric field dependence. A mechanism for the latter is proposed.

1.
R.
Pelrine
,
R.
Kornbluh
,
Q. B.
Pei
, and
J.
Joseph
,
Science
287
,
836
(
2000
).
2.
X.
Zhao
and
Z.
Suo
,
J. Appl. Phys.
104
,
123530
(
2008
).
3.
X.
Zhao
and
Z.
Suo
,
Phys. Rev. Lett.
104
,
178302
(
2010
).
4.
W. D.
Cornish
and
L.
Young
,
Proc. R. Soc. London, Ser. A
335
,
39
(
1973
).
5.
K. K.
Yee
and
L.
Young
,
Appl. Opt.
14
,
1316
(
1975
).
6.
J. L.
Ord
,
J. C.
Clayton
, and
K.
Brudzewski
,
J. Electrochem. Soc.
125
,
908
(
1978
).
7.
C. G.
Matthews
,
J. L.
Ord
, and
W. P.
Wang
,
J. Electrochem. Soc.
130
,
285
(
1983
).
8.
J. L.
Ord
and
W. P.
Wang
,
J. Electrochem. Soc.
130
,
1809
(
1983
).
9.
J. L.
Ord
,
J. Electrochem. Soc.
138
,
2934
(
1991
).
10.
D. A.
Vermilyea
,
J. Electrochem. Soc.
110
,
345
(
1963
).
11.
Q.
Van Overmeere
,
J.-F.
Vanhumbeeck
, and
J.
Proost
,
J. Electrochem. Soc.
157
,
C166
(
2010
).
12.
Q.
Van Overmeere
and
J.
Proost
,
Electrochim. Acta
56
,
10507
(
2011
).
13.
D. H.
Bradhurst
and
J. S. L.
Leach
,
J. Electrochem. Soc.
113
,
1245
(
1966
).
14.
N.
Wüthrich
,
Electrochim. Acta
25
,
819
(
1980
).
15.
J.-F.
Vanhumbeeck
and
J.
Proost
,
Electrochim. Acta
53
,
6165
(
2008
).
16.
D.
Barkey
and
J.
McHugh
,
J. Electrochem. Soc.
157
,
C388
(
2010
).
17.
J. E.
Houser
and
K. R.
Hebert
,
Nature Mater.
8
,
415
(
2009
).
18.
J.
Shieh
,
J. E.
Huber
,
N. A.
Fleck
, and
M. F.
Ashby
,
Prog. Mater. Sci.
46
,
461
(
2001
).
19.
S.
Blonkowski
,
Appl. Phys. Lett.
91
,
172903
(
2007
).
20.
21.
Y. M.
Shkel
and
D.
Klingenberg
,
J. Appl. Phys.
83
,
7834
(
1998
).
22.
L. B.
Freund
and
S.
Suresh
,
Thin Film Materials
(Cambridge,
Cambridge University Press
,
2003
).
23.
A.
Stratton
,
Electromagnetic Theory
(
McGraw-Hill
,
New York
,
1941
).
24.
Q.
Van Overmeere
,
J.-F.
Vanhumbeeck
, and
J.
Proost
,
Rev. Sci. Instrum.
81
,
045106
(
2010
).
25.
I.
Arsova
,
L.
Arsov
,
N.
Hebestreit
,
A.
Anders
, and
W.
Plieth
,
J. Solid State Electrochem
11
,
209
(
2007
).
26.
F.
La Mantia
,
M.
Santamaria
,
F.
Di Quarto
, and
H.
Habazaki
,
J. Electrochem. Soc.
157
,
C258
(
2010
).
27.
M. M.
Lohrengel
,
Mater. Sci. Eng. R
11
,
243
(
1993
).
28.
J. L.
Ord
,
J. Electrochem. Soc.
127
,
2682
(
1980
).
29.
L.
Young
and
F. G. R.
Zobel
,
J. Electrochem. Soc.
113
,
277
(
1966
).
30.
R. J.
Lederich
and
J. J.
Bellina
,
J. Opt. Soc. Am.
60
,
1697
(
1970
).
31.
S. N.
Dub
and
V. V.
Starikov
,
Funct. Mater.
14
,
347
(
2007
).
32.
R. N.
Viswanath
,
D.
Kramer
, and
J.
Weismüller
,
Electrochim. Acta
53
,
2757
(
2008
).
34.
H. Y.
Lee
,
Y.
Peng
, and
Y. M.
Shkel
,
J. Appl. Phys.
98
,
074104
(
2005
).
35.
Y.-M.
Li
and
L.
Young
J. Electrochem. Soc.
147
,
1344
(
2000
).
36.
F.
Di Franco
,
G.
Zampardi
,
M.
Santamaria
,
F.
Di Quarto
, and
H.
Habazaki
,
J. Electrochem. Soc.
159
,
C33
(
2012
).
37.
S.
Clima
,
G.
Pourtois
,
A.
Hardy
,
S.
Van Elshocht
,
M. K.
Van Bael
,
S.
De Gendt
,
D. J.
Wouters
,
M.
Heyns
and
J. A.
Kittl
,
J. Electrochem. Soc.
157
,
G20
(
2010
).
38.
P.
Delugas
,
V.
Fiorentini
, and
A.
Filippetti
,
Appl. Phys. Lett.
92
,
172903
(
2008
).
39.
P.
Delugas
,
V.
Fiorentini
,
A.
Filippetti
, and
G.
Pourtois
,
Phys. Rev. B
76
,
104112
(
2007
).
You do not currently have access to this content.