INTRODUCTION
1
C. Giannetti 1 *, B. Revaz 2 , F. Banfi 2 , M. Montagnese 5 , G. Ferrini 1 , P. Vavassori 3 , V. Metlushko 4 and F. Parmigiani 5,6 1 Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, I-25121 Brescia, Italy 2 Department of Condensed Matter Physics, University of Genève, Switzerland 3 Dipartimento di Fisica, Università di Ferrara, Italy 4 Department of Electrical and Computer Engineering, University of Illinois at Chicago, IL 5 Dipartimento di Fisica, Università degli Studi di Trieste, Italy 6 Elettra Sincrotrone Trieste, I-34012 Basovizza, Trieste, Italy *email: c.giannetti @ dmf.unicatt.it , webpage: http://www.dmf.unicatt.it/elphos/ Elastic and thermodynamic properties of nano-structured arrays impulsively excited by femtosecond laser pulses INTRODUCTION The possibility to prepare macroscopic areas of ordered arrays of metallic nano-objects on different substrates led intensive efforts toward the use of these structures as potential transducers and sources of coherent acoustic excitations in the GHz and THz range. Time-resolved reflectivity experiments have been performed on gratings of metallic nanometric stripes (2-d confined) on transparent (SiO 2 ) or semitransparent (Si) substrates, evidencing oscillations in the GHz range [1–4]. However, the attribution of the measured modulations to one-dimensional SAWs, induced in the substrate, or to the oscillation modes of the single nano-objects has been a debated question. Less data are available on the mechanical properties of 3-d confined nanoparticles, as a consequence of the difficulties in measuring and modeling the elastic and thermodynamic properties of these systems. TIME-RESOLVED MEASUREMENTS OF THE DIFFRACTED PATTERN [1] H. Lin et al., J. Appl. Phys. 73, 37 (1993). [2] B. Bonello et al., J. Acoust. Soc. Am. 110, 1943 (2001). [3] G. Antonelli et al., J. Appl. Phys. 91, 3261 (2002). [4] D. Hurley et al., Phys. Rev.B 66, 153301 (2002). [5] R.G. Pratt et al., Appl. Phys. Lett. 15, 403 (1969). OUR APPROACH We developed a dedicated time-resolved optical technique, in order to investigate the mechanical and thermodynamic properties of square arrays of permalloy (Fe 20 Ni 80 ) nano Exploiting the periodicity of the system, we have measured the relaxation dynamics of the intensity of the first-order diffracted beam, after the excitation by sub-ps laser the samples, we demonstrate that: 1)Collective modes, i.e. two-dimensional surface acoustic waves (SAW), are excited in the silicon 2)The nano-objects interact with the silicon surface renormalizing the SAW velocity. This result suggests the possible opening of a phononic band-gap FUTURE: • Brillouin scattering measurements to evidence the opening of the gap in the two-dimensional surface phononic crystal • Decoupling of the thermodynamic and mechanical dynamics CALORIMETRY ON NANOPARTICLES • Applications to sub-wavelength optics TWO-DIMENSIONAL SURFACE ACOUSTIC WAVES We measured the frequencies and damping of the two- dimensional surface acoustic waves as a function of the array wavevector and disk diameter . This technique strongly increases the sensitivity to the periodicity of the system, allowing to follow the mechanical and thermodynamic relaxation dynamics of the system with high accuracy. The pump-induced variation of the geometrical radius of the disks (δa(t)/a) induces a variation both of the reflected and diffracted intensities. a t a a t a R R a D R R R I I Si Py Si Si Py refl refl ) ( 28 . 0 ) ( ) ( ) ( 2 2 2 a t a a t a R R Ga J Ga J G I I Si Py D D ) ( 5 . 2 ) ( ) ( ) ( ) ( 2 1 0 1 1 By measuring the variation of the diffracted beam: THE S/N RATIO IS INCREASED BY A FACTOR ≈9 D G 2 2000 1600 1200 800 array period (nm ) 400 350 300 250 200 150 oscillation period (ps) v SAW =4850±75 m /s 10 7 10 8 10 9 10 10 a 2 · (µm 4 ·ps) 5 6 7 8 9 1000 2 3 4 5 array period (nm ) 1 10 100 1000 (ns) n=4 n=2.5 1 st o rder diffraction A F M im age PEM 10 s p u m p b eam crossed p ola rizers p ro b e beam U N IT CELL 2 a D=4 a z r 0 Z d h 2.5 2.0 1.5 1.0 0.5 I 1D /I 1D x 10 -5 3000 2000 1000 0 delay (ps) 1/ =950±30 ps 2=134.8±0.1 ps 2.5 2.0 1.5 1.0 0.5 I 1D /I 1D x 10 -5 1/ =1690±60 ps 2 =175±0.1 ps 2.5 2.0 1.5 1.0 0.5 I 1D /I 1D x 10 -5 1/ =3980±300 ps 2 =211.2±0.1 ps 2.5 2.0 1.5 1.0 0.5 I 1D /I 1D x 10 -5 1/ =17000±5500 ps 2 =409.4±0.3 ps CHANGING THE PERIODICITY D=2018±30 nm 2a=990 ±10 nm h=31±1 nm D=1020±50 nm 2a=470 ±10 nm h=21±2 nm D=810±10 nm 2a=380 ±20 nm h=33±5 nm D=610±3 nm 2a=320 ±10 nm h=60±20 nm 2 4 2 2 2 0 4 1 a D a h u D z Dispersion relation of the 2D SAW excited at the center of the Brillouin zone. SURFACE WAVE VELOCITIES V SAW =4900 m/s @ Si(100) [5] V SAW =5100 m/s @ Si(110) [5] The damping , due to energy radiation of SAWs to bulk modes , is proportional to G 4 [1]. SAW damping SAW dispersion CHANGING THE DISK RADIUS Initial transverse displacement u z0 h -1 3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 I 1D /I 1D x10 -5 3000 2500 2000 1500 1000 500 0 delay (ps) frequency shift 2a=395 ±7 nm 2a=785 ±7 nm 2a=320 ±10 nm D=1000 nm h=50 nm Only a slight dependence of the SAWs frequency on the disk diameters is detected: 1. Oscillation frequencies are mainly determined by the wavevector 2. Strong coupling between the metallic disks and the substrate Constant periodicities and thicknesses -1.6 -1.2 -0.8 -0.4 0.0 V/V)·D /h 0.5 0.4 0.3 0.2 0.1 filling factor 1st order perturbation theory predicts a frequency-shift due to the mechanical loading: D h r s SAW SAW v v r S : reflection coeff. =a 2 /D 2 filling factor Failure of the 1st order perturbative approach at large filling factors TIME-FREQUENCY ANALYSIS 2.0 1.5 1.0 0.5 0.0 I 1D /I 1D x 10 -5 3000 2500 2000 1500 1000 500 0 delay (ps) F ourier T ransform (arb.units 16 12 8 4 0 SAW frequency (G H z) time-domain dynamics frequency analysis Si(110) Si(100) G 1 G 2 SAW 2 Detection of the diagonal collective mode: 2 / SAW =1.386±0.004 influence of the substrate anisotropy 400 300 200 100 0 period (ps) 400 300 200 100 0 period (ps) 3000 2000 1000 0 delay (ps) WAVELET D=1005±6 nm 2a=785±7 nm h=51±2 nm ' ' ) ' ( ) , ( dt s t t t x t s W 2 0 2 1 4 1 ) ( e e s i data 3-frequency fit excitation 2 - SAW beating highly damped 3 2.0 1.5 1.0 0.5 0.0 I 1D /I 1D x 10 -5 3000 2000 1000 0 delay (ps) eigenmodes calculation Convolution with the wavelet C-Morlet wavelet t t e e t t sin cos : heat-exchange time : 1/- : ( 0 2 - 2 ) 1/2 SAW t sin modes 2 3 =8.56 GHz Periodic conditions on displacement, strain and stress Mode 1 Mode 3 Mode 2 Mode 4 1 µm 4.19 GHz 3.78 GHz 4.52 GHz 5.80 GHz 0.5 1.5 2.5 3.5 4.5 5.5 6.5 0 100 200 300 400 500 disk radius (nm ) frequency (G H z) m ode 1 m ode 2 m ode 3 data eigenmodes dependence on the disk radius Single disk modes Possible opening of a gap TWO-DIMENSIONAL SURFACE PHONONIC CRYSTAL Symmetric mode Form-factor modulation at Asymmetric mode Form-factor modulation at 2 Asymmetric mode Form-factor modulation at 2 Asymmetric mode Form-factor modulation at 2 The highly damped 3 frequency is close to the double of the asymmetric mode 2 frequency at the bottom of the band-gap Diffracted intensity variation Reflected intensity variation
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h. CHANGING THE PERIODICITY. D=2018 ±30 nm 2 a =990 ±10 nm h=31±1 nm. D=1020 ±50 nm 2 a =470 ±10 nm h=21±2 nm. 2 a =320 ±10 nm. 2 a =395 ±7 nm. D=810 ±10 nm 2 a =380 ±20 nm h=33±5 nm. 2 a =785 ±7 nm. D=1000 nm h=50 nm. D=610 ±3 nm 2 a =320 ±10 nm h=60±20 nm. - PowerPoint PPT Presentation
Transcript of INTRODUCTION
C. Giannetti1 *, B. Revaz2, F. Banfi2, M. Montagnese5, G. Ferrini1, P. Vavassori3, V. Metlushko4 and F.
Parmigiani5,6
1Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, I-25121 Brescia, Italy2Department of Condensed Matter Physics, University of Genève, Switzerland
3Dipartimento di Fisica, Università di Ferrara, Italy4Department of Electrical and Computer Engineering, University of Illinois at Chicago, IL
5Dipartimento di Fisica, Università degli Studi di Trieste, Italy6Elettra Sincrotrone Trieste, I-34012 Basovizza, Trieste, Italy
*email: [email protected], webpage: http://www.dmf.unicatt.it/elphos/
Elastic and thermodynamic properties of nano-structured arrays impulsively excited by femtosecond laser pulses
INTRODUCTION
The possibility to prepare macroscopic areas of ordered arrays of metallic nano-objects on different substrates led intensive efforts toward the use of these structures as potential transducers and sources of coherent acoustic excitations in the GHz and THz range.
Time-resolved reflectivity experiments have been performed on gratings of metallic nanometric stripes (2-d confined) on transparent (SiO2) or semitransparent (Si) substrates, evidencing oscillations in the GHz range [1–4]. However, the attribution of the measured modulations to one-dimensional SAWs, induced in the substrate, or to the oscillation modes of the single nano-objects has been a debated question.
Less data are available on the mechanical properties of 3-d confined nanoparticles, as a consequence of the difficulties in measuring and modeling the elastic and thermodynamic properties of these systems.
TIME-RESOLVED MEASUREMENTS OF THE DIFFRACTED PATTERN
[1] H. Lin et al., J. Appl. Phys. 73, 37 (1993).[2] B. Bonello et al., J. Acoust. Soc. Am. 110, 1943 (2001).[3] G. Antonelli et al., J. Appl. Phys. 91, 3261 (2002).[4] D. Hurley et al., Phys. Rev.B 66, 153301 (2002).[5] R.G. Pratt et al., Appl. Phys. Lett. 15, 403 (1969).
OUR APPROACH
We developed a dedicated time-resolved optical technique, in order to investigate the mechanical and thermodynamic properties of square arrays of permalloy (Fe 20Ni80) nano-disks deposited on a Si(100) surface. Exploiting the periodicity of the system, we have measured the relaxation dynamics of the intensity of the first-order diffracted beam, after the excitation by sub-ps laser pulses. By changing the parameters of the samples, we demonstrate that:
1) Collective modes, i.e. two-dimensional surface acoustic waves (SAW), are excited in the silicon2) The nano-objects interact with the silicon surface renormalizing the SAW velocity. This result suggests the possible opening of a phononic band-gap
FUTURE: • Brillouin scattering measurements to evidence the opening of the gap in the two-dimensional surface phononic crystal• Decoupling of the thermodynamic and mechanical dynamics CALORIMETRY ON NANOPARTICLES• Applications to sub-wavelength optics
TWO-DIMENSIONAL SURFACE ACOUSTIC WAVES
We measured the frequencies and damping of the two-dimensional surface acoustic waves as a function of the array wavevector and disk diameter.
This technique strongly increases the sensitivity to the periodicity of the system, allowing to follow the mechanical and thermodynamic relaxation dynamics of the system with high accuracy.The pump-induced variation of the geometrical radius of the disks (δa(t)/a) induces a variation both of the reflected and diffracted intensities.
a
ta
a
ta
RRaDR
RR
I
I
SiPySi
SiPy
refl
refl )(28.0
)(
)(
)(222
a
ta
a
taRR
GaJ
GaJG
I
ISiPy
D
D )(5.2
)()(
)(
)(2
1
0
1
1
By measuring the variation of the diffracted beam:
THE S/N RATIO IS INCREASED BY A FACTOR ≈9
DG
2
2000
1600
1200
800
arra
y pe
riod
(nm
)
400350300250200150oscillation period (ps)
vSAW=4850±75 m/s
107
108
109
1010
a2·
(µ
m4·p
s)
5 6 7 8 91000
2 3 4 5
array period (nm)
1
10
100
1000
(n
s)
n=4
n=2.5
1st order d iffraction
AFM im age
PEM
10 s
pum p beam
crossedpolarizers
probe beam
UNIT CELL2a
D =4az
r0Zdh
2.5
2.0
1.5
1.0
0.5
I 1
D/I 1
D x
10-5
3000200010000delay (ps)
1/=950±30 ps
2=134.8±0.1 ps
2.5
2.0
1.5
1.0
0.5
I 1
D/I 1
D x
10-5
1/=1690±60 ps
2=175±0.1 ps
2.5
2.0
1.5
1.0
0.5
I 1
D/I 1
D x
10-5
1/=3980±300 ps
2=211.2±0.1 ps
2.5
2.0
1.5
1.0
0.5
I 1
D/I 1
D x
10-5
1/=17000±5500 ps
2=409.4±0.3 ps
CHANGING THE PERIODICITY
D=2018±30 nm2a=990 ±10 nmh=31±1 nm
D=1020±50 nm2a=470 ±10 nmh=21±2 nm
D=810±10 nm2a=380 ±20 nmh=33±5 nm
D=610±3 nm2a=320 ±10 nmh=60±20 nm
2
4
2220
41
a
D
ahu
D
z
Dispersion relation of the 2D SAW excited at the center of the Brillouin zone.
SURFACE WAVE VELOCITIESVSAW=4900 m/s @ Si(100) [5]VSAW=5100 m/s @ Si(110) [5]
The damping , due to energy radiation of SAWs to bulk modes, is proportional to G4 [1].
SAW damping
SAW dispersion
CHANGING THE DISK RADIUS
Initial transverse displacement uz0 h-1
3.0
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
I 1
D/I 1
D x
10-5
300025002000150010005000delay (ps)
frequency shift
2a=395 ±7 nm
2a=785 ±7 nm
2a=320 ±10 nm
D=1000 nmh=50 nm
Only a slight dependence of the SAWs frequency on the disk diameters is detected:
1. Oscillation frequencies are mainly determined by the wavevector2. Strong coupling between the metallic disks and the substrate
Constant periodicities and thicknesses
-1.6
-1.2
-0.8
-0.4
0.0
V
/V)·
D/h
0.50.40.30.20.1filling factor
1st order perturbation theory predicts a frequency-shift due to the mechanical loading:
D
hrs
SAW
SAW v
v rS: reflection coeff.=a2/D2 filling factor
Failure of the 1st order perturbative approach at large
filling factors
TIME-FREQUENCY ANALYSIS
2.0
1.5
1.0
0.5
0.0
I 1
D/I 1
D x
10-5
300025002000150010005000delay (ps)
Fo
uri
er
Tra
nsf
orm
(a
rb.
un
its)
1612840SAW frequency (GHz)
time-domain dynamics frequency analysis
Si(110)
Si(100
)
G1
G2
SAW
2
Detection of the diagonal collective mode:
2/SAW=1.386±0.004influence of the
substrate anisotropy
400
300
200
100
0
pe
riod
(p
s)
400
300
200
100
0
pe
riod
(p
s)
3000200010000delay (ps)
WAVELET
D=1005±6 nm2a=785±7 nmh=51±2 nm
''
)'(),( dts
tttxtsW
202
1
4
1
)( ees i
data
3-frequency fit
excitation
2-SAW beatinghighly damped 3
2.0
1.5
1.0
0.5
0.0
I1D/I 1
D x
10-5
3000200010000delay (ps)
eigenmodes calculation
Convolution with the wavelet
C-Morlet wavelet
ttee tt
sincos
: heat-exchange time: 1/-: (0
2-2)1/2
SAW
t
sin modes
2
3=8.56 GHz Periodic conditions on displacement, strain and stress
Mode 1
Mode 3
Mode 2
Mode 4
1 µm
4.19 GHz 3.78 GHz
4.52 GHz 5.80 GHz 0.5
1.5
2.5
3.5
4.5
5.5
6.5
0 100 200 300 400 500
disk radius (nm)
freq
uen
cy (
GH
z)
mode 1mode 2
mode 3
data
eigenmodes dependence on the disk radius
Single disk modes
Possible opening of a gap TWO-DIMENSIONAL SURFACE
PHONONIC CRYSTAL
Symmetric mode Form-factor modulation at
Asymmetric mode Form-factor modulation at 2
Asymmetric mode Form-factor modulation at 2
Asymmetric mode Form-factor modulation at 2
The highly damped 3 frequency is close to the
double of the asymmetric mode 2 frequency at the bottom of the band-gap
Diffracted intensity variation
Reflected intensity variation
