Nano-Ultrasonics and Nano-Acoustics

139 Pages·2008·6.7 MB·English

Nano-Ultrasonics and Nano-Acoustics
Chi-Kuang Sun
Graduate Institute of Electro-Optical Engineering, Department of
Electrical Engineering, and Center for Genomic Medicine
National Taiwan University
&
Research Center for Applied Science, Acadia Sinica
Taipei, TAIWAN
Medical Ultrasonics
Resolution limited by Acoustic Wavelength
50MHz, 50-500 μm
Acoustic Controlled Electronic Devices by using
SAWs (Surface Acoustic Waves)
Frequency
~ 1GHz
Wavelength
Several μm
C. L. Foden, et al., Phys. Rev. A 62, 011803 (R), 2000.
Acousto-electric Effect: SAW (GHz, μm)
(cid:198) 2D, Slow response time, Micron scale resolution
Nanoultrasonics
3D imaging with nano resolution
(cid:132)
THz electronic control with high spatial accuracy
(cid:132)
(down to a nano scale)
Require
(cid:132)
(Coherent) acoustic wave with a nano wavelength
(cid:132)
Generation
(cid:132)
Detection
(cid:132)
Synthesization
(cid:132)
Propagation control
(cid:132)
Based on piezoelectric semiconductor
(cid:132)
Subjects of this lecture
Acoustics 101.
(cid:132)
Previous non-piezoelectric works.
(cid:132)
Generation and detection of coherent acoustic phonons
(cid:132)
(nanoacoustic waves) in piezoelectric multilayers and a
single layer
Manipulation and optical coherent control of the
(cid:132)
nanoacoustic waves
Study of the nanoacoustic superlattice (phononic bandgap
(cid:132)
crystal), nanoacoustic cavity, and the supersonic paradox.
Nanoultrasonics.
(cid:132)
THz electronic control using nano-acoustic waves.
(cid:132)
Nano-acoustic waveguiding.
(cid:132)
Confined acoustic vibrations in nanoparticles.
(cid:132)
Subject 1
Acoustics 101.
(cid:132)
Previous non-piezoelectric works.
(cid:132)
Generation and detection of coherent acoustic phonons
(cid:132)
(nanoacoustic waves) in piezoelectric multilayers and single
layer.
Manipulation and optical coherent control of the
(cid:132)
nanoacoustic waves
Study of the nanoacoustic superlattice (phononic bandgap
(cid:132)
crystal), nanoacoustic cavity, and the supersonic paradox.
Nanoultrasonics.
(cid:132)
THz electronic control using nano-acoustic waves.
(cid:132)
Nano-acoustic waveguiding.
(cid:132)
Confined acoustic vibrations in nanoparticles.
(cid:132)
⎡⎡XX ⎤⎤
xx
⎢⎢ ⎥⎥
YY
⎢⎢ yy ⎥⎥
⎢⎢ZZ ⎥⎥ Longitudinal Acoustic Wave
zz
⎢⎢ ⎥⎥
YY
⎢⎢ zz ⎥⎥
⎢⎢ZZ ⎥⎥
⎢⎢ xx ⎥⎥ ∂u
⎢⎣⎢⎣XXyy⎥⎦⎥⎦
S =
Strain (no unit): ; u: displacement;
(cid:132)
∂z
應力
Stress (force/area): T = CS; C: elastic constant (area/force);
(cid:132)
應變
X
x
X ⎡X ⎤ ⎡c c c c c c ⎤ ⎡e ⎤
y x 11 12 13 14 15 16 xx
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
Y c c c c c c e
⎢ y ⎥ ⎢ 21 22 23 24 25 26 ⎥ ⎢ yy ⎥
⎢ Z ⎥ ⎢c c c c c c ⎥ ⎢e ⎥
z 31 32 33 34 35 36 zz
⎢ ⎥ = ⎢ ⎥ ⎢ ⎥
Y c c c c c c e
⎢ ⎥ ⎢ ⎥ ⎢ ⎥
z 41 42 43 44 45 46 yz
⎢ Z ⎥ ⎢c c c c c c ⎥ ⎢e ⎥
⎢ x ⎥ ⎢ 51 52 53 54 55 56 ⎥ ⎢ zx ⎥
⎢⎣X ⎥⎦ ⎢⎣c c c c c c ⎥⎦ ⎢⎣e ⎥⎦
y 61 62 63 64 65 66 xy
T = C S
Wave Equation of Stress T
∂T
(1) = F = ρ u(cid:5) (cid:5) = ρ v (cid:5) v : velocity; ρ : density of mass;
mo mo mo
∂z
∂v ∂S
(2) “Conservation of mass”
=
∂z ∂t
∂v ∂ ⎛ ∂u ⎞ ∂ ⎛ ∂u ⎞ ∂S
= = =
⎜ ⎟ ⎜ ⎟
∂z ∂z ⎝ ∂t ⎠ ∂t ⎝ ∂z ⎠ ∂t
From (1) and (2), we have wave eq. of T
∂ 2T ∂ ⎛ ∂ 2u ⎞ ∂ 2S ρ ∂ 2T
= ρ = ρ = mo
⎜ ⎟
∂z2 mo ∂z ∂t2 mo ∂t2 C ∂t2
⎝ ⎠
Assume
j(ωt±β z)
T ∝ e a
We have
ρ ω C
β =ω m0 = V =
, 聲速
a c V a ρ
a m0
Energy Density
Elastic energy density
(cid:132)
1 1 1
2 2
W = T S = CS = T
c
2 2 2C
Kinetic energy density
(cid:132)
1
2
W = ρ v
v m0
2
Considering the wave propagating in the forward direction :
∂ u ∂ u ∂ z V
v = = = SV = a T
a
∂ t ∂ z ∂ t C
V 2 1
ρ vv∗ = ρ a TT ∗ = TT ∗ C
V =
m0 m0 C 2 C a ρ
m0
∴ W = W
c v
Acoustic Impedance
E
T
y
Z ≡ ⇔ Z =
a EM
v H
x
Note when the propagation direction is reversed, the acoustic
•
impedance is different in sign.
Consider forward propagation
•
T C
Z = − F = = ρ C = V ρ ≡ Z
F m0 a m0 0
v V
F a
Reflection of acoustic waves from interface
Z − Z
Γ = 02 01 − − − − → z
Z + Z
02 01
medium 1 medium 2