Laser-induced transient grating measurements and ultrafast optical pump-probe imaging of surface acoustic waves near a linear boundary between copper and silica films on a silicon substrate indicate the presence of a boundary-localized mode with a phase velocity slightly below the Rayleigh wave velocity on the copper film. We analyze in detail the dispersion of this localized mode in comparison with that of the Rayleigh waves in the surrounding materials. The existence of the localized mode is ascribed to the nonuniformity of the copper film thickness near its edge resulting from polishing during fabrication.

1.
A.
Neubrand
and
P.
Hess
,
J. Appl. Phys.
71
,
227
(
1992
).
2.
J. A.
Rogers
,
A. A.
Maznev
,
M. J.
Banet
, and
K. A.
Nelson
,
Annu. Rev. Mater. Sci.
30
,
117
(
2000
).
3.
D. M.
Profunser
,
O.
Matsuda
, and
O. B.
Wright
,
Phys. Rev. Lett.
97
,
055502
(
2006
).
4.
C.
Giannetti
,
B.
Revaz
,
F.
Banfi
,
M.
Montagnese
,
G.
Ferrini
,
F.
Cilento
,
S.
Maccalli
,
P.
Vavassori
,
G.
Oliviero
,
E.
Bontempi
,
L. E.
Depero
,
V.
Metlushko
, and
F.
Parmigiani
,
Phys. Rev. B
76
,
125413
(
2007
).
5.
J. -F.
Robillard
,
A.
Devos
,
I.
Roch-Jeune
, and
P. A.
Mante
,
Phys. Rev. B
78
,
064302
(
2008
).
7.
C.
Diebold
and
R.
Stoner
,
Handbook of Silicon Semiconductor Metrology
, edited by
A. C.
Diebold
(
Dekker
,
New York
,
2001
), p.
197
.
8.
M.
Gostein
,
M.
Banet
,
M.
Joffe
,
A. A.
Maznev
,
R.
Sacco
,
J.
Rogers
, and
K. A.
Nelson
,
Handbook of Silicon Semiconductor Metrology
, edited by
A. C.
Diebold
(
Dekker
,
New York
,
2001
), p.
167
.
9.
P.
Malischewsky
,
Surface Waves and Discontinuities
(
Elsevier
,
Amsterdam
,
1987
).
10.
D. H.
Hurley
,
O. B.
Wright
,
O.
Matsuda
,
T.
Suzuki
,
S.
Tamura
, and
Y.
Sugawara
,
Phys. Rev. B
73
,
125403
(
2006
).
11.
B. A.
Auld
,
Acoustic Fields and Waves in Solids
, 2nd ed. (
Krieger
,
Malabar
,
1990
), Vol.
II
.
12.
G. W.
Farnell
and
E. L.
Adler
, in
Physical Acoustics, Principles and Methods
, edited by
W. P.
Mason
and
R. N.
Thurston
(
Academic
,
New York
,
1972
), Vol.
9
, p.
35
.
13.
R. O.
Claus
and
C. H.
Palmer
,
Appl. Phys. Lett.
31
,
547
(
1977
).
14.
O. A.
Godin
and
D. M. F.
Chapman
,
J. Acoust. Soc. Am.
110
,
1890
(
2001
).
16.
R.
Rosenberg
,
D. C.
Edelstein
,
C. -K.
Hu
, and
K. P.
Rodbell
,
Annu. Rev. Mater. Sci.
30
,
229
(
2000
).
17.
A. A.
Maznev
,
A.
Mazurenko
,
L.
Zhuoyun
, and
M.
Gostein
,
Rev. Sci. Instrum.
74
,
667
(
2003
).
18.
T.
Tachizaki
,
T.
Muroya
,
O.
Matsuda
,
Y.
Sugawara
,
D. H.
Hurley
, and
O. B.
Wright
,
Rev. Sci. Instrum.
77
,
043713
(
2006
).
19.
The following values of density and elastic constants of the constituent materials were used in the calculations: Cu:ρ=8930kg/m3, E=128.7GPa, ν=0.344; Ta:ρ=16654kg/m3, E=184.2GPa, ν=0.342; SiN:ρ=2650kg/m3, E=171.7GPa, ν=0.161; SiO2:ρ=2200kg/m3, E=71.3GPa, ν=0.164; Si:ρ=2330kg/m3, C11=165.7GPa, C12=63.7GPa, C44=79.6GPa. Thin film materials were modeled as elastically isotropic and their elastic properties are listed above in terms of the Young’s modulus E and the Poisson’s ratio ν, whereas for the single crystal silicon substrate three independent terms of the elastic constant tensor are listed.
20.
See EPAPS supplementary material at http://dx.doi.org/10.1063/1.3298472 for details on the animation.
21.
D. M.
Profunser
,
E.
Muramoto
,
O.
Matsuda
,
O. B.
Wright
, and
U.
Lang
,
Phys. Rev. B
80
,
014301
(
2009
).
22.
A. A.
Oliner
, in
Acoustic Surface Waves
, edited by
A. A.
Oliner
(
Springer Verlag
,
Berlin
,
1978
), p.
187
.

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