Ultrafast Phenomena in Condensed Ma3er : basics Prof. P.Ruello Ins;tut des Molécules et Matériaux du Mans, UMR 6283 CNRS-Université du Maine.

(1)

Ultrafast Phenomena in Condensed Ma3er : basics Prof. P.Ruello

Ins;tut des Molécules et Matériaux du Mans, UMR 6283 CNRS-Université du Maine.

h ν

pump probe

phonons

1

Pascal.ruello@univ-lemans.fr

(2)

Ultrafast Phenomena in Condensed Matter

Enseignant : P. Ruello (IMMM) Chargé de TD : P. Ruello (IMMM)

Nombre d’heures : 10h cours/10h TD/5h TP Nombre ECTS : 3

Langue d’enseignement : English

Prérequis : Solid State Physics, Quantum Mechanics, Electrodynamics.

Evaluation : 2 examinations

In this lecture we introduce the fascinating world of ultrafast phenomena in condensed matter where the motion of electrons and atoms can be somehow viewed in the time domain. After a general introduction and some reminder about fundamentals of optics and electrodynamics, we will discuss the experimental setup permitting such studies (femtosecond lasers). We will then present the general electron-electron and electron- phonon collision processes. In particular, we will see how it is possible to measure the electron-phonon coupling involving, relaxation of electron and phonon with recent time- resolved optical setup.

-1 Introduction on the ultrafast physics in condensed matter : history, goals, applications : -2 Light-matter interaction at equilibrium :

- Classical electrodynamics : reminder on Maxwell equations and the classical dielectric response in a metal and in an insulator.

- Quantum electrodynamics : description of the dielectric constant within the time- dependent Shrödinger equation.

-3 Introduction on experimental time-resolved studies :

- principle of a pump-probe method : detectors bandwidth, stroboscopic regime of measurement, lock-in amplifier detection, basics of ultrafast laser technology -4 Properties of electron and phonons at the thermodynamic equilibrium

- reminder on the Sommerfel model, the band theory of electron and the classical lattice dynamics (phonons)

- quantum origin of the electron-electron and electron-phonon coupling (deformation potential, Fröhlich interaction)

-5 Properties of non-equilibrium photoexcited carriers - Two-Temperatures Model for metals

- Boltzman equation applied to photoexcited semiconductors -6 Optical and acoustic phonons ultrafast photogeneration processes

- Optical phonons : stimulated Raman process, displacive excitation (deformation potential).

- Acoustic phonon : deformation potential, thermoelasticity

-7 Applications of picosecond acoustics : evaluation of elasticity at the nanoscale of

nanostructures (echography of nanostructures by laser optoacoustics, example coming from the industry and labs).

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3

Ultrafast Phenomena in Condensed Matter

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19#

# Fig$1.12!Time!Scale!VS!Physical!Process.!

During# a# PIPT# in# solid# state,# a# superposition# of# different# physical# process# at# different# time#

scales# might# happen.# Several# degrees# of# freedom# inside# the# material# are# involved# during# the#

emergence#of# new# macroscopic# order.# Electrons# which#drive# the# system# to# new# order# have# typical#

motion#around#fs#time#scale.#The#red#line#denotes#the#temporal#limit#of#the#results#I#will#present#in#

this#manuscript.#

All#the#couplings#in#systems#previously#presented#involve#electronic#and#structural#dynamics#

that#may#be#ultrafast.#In#order#to#increase#material#control,#determining#the#potential#energy#surface#

of# excited# state# is# the# goal# of# ultrafast# studies# to# increase# the# understanding# on# light# triggered#

transitions.#Indeed,#PES#determines#which#kind#of#new#phase#is#reached#after#the#excitation.#So#tools#

are#needed#with#time#resolution#high#enough#to#follow#in#real#time#all#these#dynamics.##

Figure with the courtesy of R. Bertoni

laser

Ultrafast

Phenomena

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Light and telecommunica;on

Light velocity c=3.10

⁸

m/s

- Necessity of control of light : propagation, source, etc

- New emerging technologies based on the manipulation of the matter with light (photonic fast communication, photoinduced phase transition for memory, etc … )

Fermi velocity V=10

⁶

m/s

~1900-1960

Theroy of electrons in solids

~1950-1960

-  Semiconductor industry development

-  Laser theory and first experiments

~1980

-  Optical fiber

-  III-V semiconductors physics

~2000

-  Photonic crystal -  Photonic fiber -  Plasmonics -  Spintronics,

Sound speed in air

V=340 m/s

Hertzian antenna (telegraphy)

Transistor and day-to-day life electronics (kHz-MHz)

Advanced electronics and beginning of photonics GHz

THz

technologies ?

(6)

Photonics and materials

Guiding light

Bragg (2dsin(θ)=λ)

Optical fiber and photonic crystals

v

_g

= ∂ ω

∂ k

Group velocity

ω

k

vide

Inside the photonic crystal

à light transport = less Joule eﬀet than for electron transport

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Informa;on : wri;ng and reading as fast as possible

Today : GHz, Tomorrow 1 THz

à  Transistor (saturation state as bit 0-1)

à  Magnetic memory (RAM, DRAM, SDRAM,

…)

à  Cr

₂

O

₃

, Fe

₂

O

₃

,

à  GMR, CMR (magnetoristance) LaSrMnO3

à  Phase change memory (PCM) :

amoprhous to crystalline phase transition as wa way to creat a bit (0-1).

à  Rewritable CD-DVD

2 states (O –

1 bit)

(8)

Phase change memories (GeTe, GeSbTe, etc)

Laser

writing ^Laser« reading »

(9)

Ecrire et lire avec la lumière (CD, DVD

réinscrip;ble du future)

(10)

Photovoltaics

•  Light energy received per day > total consumption

•  How can we harvest this energy ?

•  How can we store it ?

How does a cell

work ?

(11)

-  Electric energy harvesting is efficient if

à  the electron-phonon collision is reduced (non-raditaive recombination)

à  The carriers radiative recombination is reduced

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Photovoltaics : ;meline

~1839-1905

Effet photoélectrique -  Becquerel

-  Hertz - Einstein

~1970

Première génération de cellule

photovoltaique Semiconcteurs

~1980

2nd génération

2000

Cellule de Graetzel

E = h υ

2017

Perovskite hybrides

(13)

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Ultrafast phenomena : interplay

between technologies challenges and real fundamental knowledge

•  For advanced telecommuncia;on, for storage technologies, for photovoltaïcs, it is important to understand the light-ma3er interac;on

including the ultrafast processes.

•  Ultrafast processes = ul;mate process

involving charge excita;on, charge transport,

electron-phonon coupling

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Electron-phonon interac;on : Drude model

•  Characteris;c ;me of electron-phonon coupling

σ = ne

²

τ m

^*

For a metal

σ ≈ 10

⁸

S / m n ≈ 10

²⁸

m

⁻³

m

^*

≈ 0.5m

₀

τ ≈ 100 fs = 0.1.10

⁻¹²

s = 0.1ps

electron ca;on

m v(t + τ ⁾ − v(t )

τ ⁼ ^eE ^v(t ⁺ τ ⁾ = eE τ

m = µ ^E

τ Time between two electron-phonon shocks

σ = ne µ = ne

²

τ

m

15

h3p://en.wikipedia.org/wiki/Drude_model

(16)

Ultrafast phenomena

Observa;on in the ;me domain of the dynamics (mo;on, relaxa;on, …) of degrees of freedom of a solid : -  Electron

-  Phonon -  Spin

àin par;cular observa;on of vibra;ons of nanomaterials (par;cle, thin ﬁlm, …)

Control of these degrees of freedom by light (coherent control) :

ULTRAFAST LIGHT ACTUATOR

Ultrafast phenomena = ultrashort space scale (nanophysics) :

- Inves;ga;on of electron and phonon propaga;on at nanoscale

16

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GHz-THz Coherent acous;c phonon sources : for what ? -  - Controlling the lahce mo;on, lahce strain with light -  - New optomechanics devices

-  - Light-control of ultrafast mechanical actuator

NEMS :

Nano Electro Mechanical Systems : 10-100nm

Characteris;c frequencies of mechanical vibra;ons :

f ≈ V

d = 50 − 500GHz

(Tanglab, Yale)

Domain of Ultrafast acous;cs Picosecond acous;cs

Necessity to understand and to control the conversion of light energy into

mechanical energy : photogenera;on processes of acous;c phonons

Ultrafast acous;cs

17

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18

Ultrafast lattice dynamics

Photogenera;on of coherent op;cal phonons (case of bismuth, Melnikov et al)

2018 A.A. Melnikov et al. / Physics Letters A 375 (2011) 2017–2022

One straightforward way to check the validity of the general- ized Raman model is to measure the initial phase of oscillations in the photoinduced response. However, this approach has at least two disadvantages. The first is that for a number of semimetals (Te, Bi, and Sb) DECP and RM give nearly identical predictions for the initial phase of fully symmetric phonon modes [11]. The second results from the diﬃculty in a precise phase determination. The latter procedure deals with a signal at the moment of the pump and probe pulses overlap and thus it is usually ambiguous.

In the present study an alternative approach is used. We have measured the dependence of coherent phonon amplitude of fully symmetric A1g and doubly degenerateEg phonon modes in bismuth on excitation wavelength in visible and near infrared ranges.

According to the unified Raman model, the coherent phonon am- plitudes should be proportional to the corresponding Raman cross sections. Moreover, at any given wavelength the relative intensi- ties of excited phonon modes obtained from the frequency- and time-domain data should be identical. Yet, a comparison of our pump-probe results with spontaneous Raman measurements ob- viously contradicts the predictions of the unified Raman theory, showing that DECP cannot be reduced to RM.

2. Experimental details

In our experiments all measurements were done at room temperature with a typical ultrafast pump-probe setup. Amplified pulses of a Ti:Sapphire laser operating at λ=800 nm were di- vided into two parts. The first was attenuated to be used to probe the sample — a single crystal of bismuth oriented in such a way that its surface was perpendicular to the trigonal axis. The second part of the beam was used to seed a parametric amplifier to provide pump pulses of 70 fs duration with a tunable central wavelength. The pump and probe beams were incident nearly perpendicular to the surface of the crystal. We detected a component of the probe beam reflected from the crystal and polarized parallel to the pump polarization, while the probe pulses were polarized at 45^◦ relative to the pump. Energy of this component was measured with opened and closed pump beam and the relative change in reflectivity"R/R0was recorded at a given time delay between the pump and probe pulses. The size of the probe beam spot was about 50 µm in all experiments. The size of the pump beam had a minimum value of about 120 µm for 400 nm pulses and increased at longer pump wavelengths (e.g. for 1300 nm the spot size was as large as 400 µm).

3. Results

Fig. 1 shows the transient reflectivity obtained with pump wavelengths ofλ=400 andλ=1300 nm. Ultrafast excitation at t=0 is followed by a monotonic decay on which pronounced oscillations are superimposed. Since the dominant oscillation frequency almost matches that of A1g phonon mode, these oscillations are the result of fully symmetricA1gcoherent atomic motion induced by the laser pulse. It should be emphasized that we did not define zero time delay and therefore, the initial phase of coherent oscillations remains unknown. Nevertheless, in the previous time-domain studies[8,12]the phase ofA1gmode was measured for 600 and 800 nm excitation wavelengths and we use this result here, assuming A1goscillations to be cosine ones, at least in the visible excitation range.

Taking into account the above, the transient reflectivity excited by theλ=400 nm pump pulses can be well fitted at positive time delays by the sum of a damped cosine with varying frequency and a monotonic term:

! "

Fig. 1.(a) Transient reflectivity of bismuth excited atλ=400 nm as a function of time delay. The inset shows normalized Fourier spectrum for the oscillatory part of the signal. (b) The same curves for the case ofλ=1300 nm excitation. Note that in the inset apart from theA1gmode, theEgmode is clearly visible.

where A(A1g)is the amplitude and γ1 is the decay rate of coherent A1g oscillations. The exact form ofB(t)term is of no im- portance in the present study; however, we note that the term has a multi-exponential character. The temporal dependence of frequencyν1reflects the effect of so-called frequency or bond soft- ening[13]. Briefly, the instantaneous frequency of A1g coherent phonons in bismuth is not constant due to the presence of excited charge carriers. Its decrease is the most appreciable during few initial cycles of vibrations and then the frequency gradually re- turns to the unperturbed value of 2.93 THz. It is reasonable in our case to treat the relaxation of the frequency shift as exponential with decay time of∼1 ps, while the minimal value ofν1attained near zero time delay is∼2.8 THz. The photoinduced response de- scribed by Eq.(1)is typical for bismuth and it has been observed in numerous previous experiments[8,12,13].

As far as the photoinduced response measured with 1300 nm pump pulses is concerned, it shows a considerable deviation from that excited by the shorter wavelength pulses, especially during the first few picoseconds. Its Fourier spectrum shown in the inset indicates that the main difference is due to the presence of strongly damped oscillations at ∼².1 THz, which can be natu- rally ascribed to the coherent phonons of Eg symmetry[14,15].

By including Eg oscillations into analysis it is possible to fit the measured decay traces. The additional term is a damped harmonic oscillatory function at frequency of 2.1 THz and the only param- eter to be addressed specially is its phase. As it has been already noted, we did not measure the absolute initial phase, and in the case of A1gmode just relied on the data available. For Egmode in bismuth the coherent oscillations reported to have sine-like pat- tern, with the initial phase being independent on temperature[16].

In our measurements, due to significant difference of A1g andEg frequencies therelativephase may be defined with a satisfactory precision. Therefore, we represented the overall time resolved signal in the following form:

"R/R0=^A(A1g)exp(−γ₁t)cos!ν₁(t)t"

L T

L 10¹⁸cm ³

a=b=c= 4.746 , =⇥=⇤= 57.23^⇥

A1g

2.92T Hz 342f s

Eg

2.22T Hz 450f s

100f s

2.7 6.7mJ/cm²

1 20mJ/cm²

30mJ/cm²

Photogenera;on of coherent op;cal phonons (shear displacement in graphene, Bosche3o et al )

sonde = 800nm

pompe= 400nm

40⇥ 4 µm Fsonde= 0.5mJ/cm² Fpompe = 1mJ/cm²

s p

A B

A B A

A B

(A B)

S = 0.3µV S= 1V

S

S = 3⇥10 ⁷ 10 ⁸

⇥₀

⌅⌅

⌅⇤

⌅⌅

⌅⇥

d²x₁(t)

dt² +⇥²₀[x1(t) x2(t)] = 0

d²x_n(t)

dt² +⇥₀²[xn(t) x_n ₁(t)] +⇥²₀[xn(t) x_n+1(t)] = 0

d²x_N(t)

dt² +⇥²₀[x_N(t) x_N ₁(t)] = 0

N n n

(19)

Ultrafast acoustics : nano-echography of materials

Thomsen et al, PRB 1986

As

₂

Te

₃

/ Al

₂

O

₃

1st echo 2nd

echo Optical pump-probe experiment : how does it

work ?

substrate film

Photogenerated acoustic phonons

Probe beam (200fs)

Pump beam (200fs)

1

Nanoscale Noncontact Subsurface

2

Investigations of Mechanical and

3

Optical Properties of Nanoporous

4

Low-k Material Thin Film

5 Alexey M. Lomonosov,^{†,^}Adil Ayouch,^†Pascal Ruello,^†,* Gwenaelle Vaudel,^†Mikhail R. Baklanov,^‡

6 Patrick Verdonck,^‡ Larry Zhao,^§and Vitalyi E. Gusev^†,*

7 ^†Laboratoire de Physique de l'Etat Condensé, UMR 6087 CNRS!Université du Maine, Le Mans, France,^‡IMEC, Kapeldreef 75, B-3001 Leuven, Belgium, and

8 ^§GLOBALFOUNDRIES assignee at IMEC, Kapeldreef 75, B-3001 Leuven, Belgium ^{^}On leave from Institute of General Physics, Russian Academy of Sciences,

9 Moscow, Russia.

1011

S

patial in-depth nonuniformity of thin

12 solid ﬁlms is becoming a critical factor

13 with the aggressive down-scaling of

14 their thickness. The most crucial reason for

15 the nonuniformity is related to the diﬀerent

16 mechanisms of chemical reactions occur-

17 ring in the bulk and at interfaces and to the

18 increasing surface/volume ratio. Many dif-

19 ferent examples demonstrate this state-

20 ment. For instance, the Young modulus

21 of polycrystalline diamond ﬁlms grown by

22 microwave-³ or e-beam-assisted⁴ chemical

23 vapor deposition continuously varies from

24 the nucleation side to the growth side. The

25 variation in theﬁlm texture with the increas-

26 ing ﬁlm thickness is considered a common

27 phenomenon for ﬁlm growth in general.⁵

28 The variations of the material properties

29 inside the ﬁlm can take place at the scales

30 from a few nanometers to hundreds of

31 nanometers.³^!⁵Inhomogeneity of thinﬁlms

32 can also be caused by their postdeposition

33 processing such as radiation-assisted curing

34 used in the fabrication of low dielectric con-

35 stant (low-k)ﬁlms for modern microelectro-

36 nic devices.⁶^!¹⁰In addition, inhomogeneity

37 can be introduced intentionally for the pro-

38 duction of multilayered optical antireﬂec-

39 tive and highly reﬂective coatings.¹¹ For

40 these UV optics the individual layers, consti-

41 tuting the coating, are of nanoscale thickness.

42 Several techniques allow inspection of

43 the physical and chemical properties of

44 solids with a nanometric resolution. Scan-

45 ning probe microscopy (SPM¹²) is routinely

46 employed, but it is limited to surface investi-

47 gation. When subsurface information is re-

48 quired, invasive treatments are usually needed.

49 Typically, sub-nanometer resolution images

50

51

52

53

54 55 56 57585960616263646566 676869707172

of the microstructure are obtained after sample microtoming (cross section image 73

with transmission electron microscopies¹³). 74

In-depth chemical and physical analysis can 75

also be performed by slicing the material 76

and analyzing either the removed matter 77

(secondary ion mass spectroscopy¹⁴) or 78

the newly created surface (ion-sputtering- 79

assisted X-ray and ultraviolet photoemission 80

* Address correspondence to vitali.goussev@univ-lemans.fr;

pascal.ruello@univ-lemans.fr.

Received for review November 1, 2011 and accepted January 1, 2012.

Published online 10.1021/nn204210u ABSTRACT

Revealing defects and inhomogeneities of physical and chemical properties beneath a surface or an interface with in-depth nanometric resolution plays a pivotal role for a high degree of reliability in nanomanufacturing processes and in materials science more generally.^1,2Nanoscale noncontact depth profiling of mechanical and optical properties of transparent sub-micrometric low-kmaterial film exhibiting inhomogeneities is here achieved by picosecond acoustics interferometry. On the basis of the optical detection in the time domain of the propagation of a picosecond acoustic pulse through the Brillouin process, the depth profile of acoustical velocity and optical refractive index are measured simultaneously with spatial resolution of tens of nanometers. Furthermore, measuring the magnitude of this Brillouin signal provides an original method for depth profiling of photoelastic moduli. This development of a new opto-acoustical nanometrology paves the way for in-depth inspection and for subsurface nanoscale imaging of inorganic- and organic-based materials.

KEYWORDS: picosecond laser ultrasonics . nanoacoustics . acousto-optics . depth profiling . transparentfilms . low-permittivityfilms

ARTICLE

ACS Nano | 3b2 | ver.9 | 4/1/012 | 20:2 | Msc: nn-2011-04210u | TEID: deb00 | BATID: 00000 | Pages: 5.39

LOMONOSOVET AL. VOL. XXX ^’ NO. XX ^’ 000–000 ^’ XXXX

www.acsnano.org A

CXXXX American Chemical Society

1

Nanoscale Noncontact Subsurface

2

Investigations of Mechanical and

3

Optical Properties of Nanoporous

4

Low-k Material Thin Film

5 Alexey M. Lomonosov,^{†,^} Adil Ayouch,^† Pascal Ruello,^†,* Gwenaelle Vaudel,^† Mikhail R. Baklanov,^‡

6 Patrick Verdonck,^‡ Larry Zhao,^§ and Vitalyi E. Gusev^†,*

7 ^†Laboratoire de Physique de l'Etat Condensé, UMR 6087 CNRS!Université du Maine, Le Mans, France, ^‡IMEC, Kapeldreef 75, B-3001 Leuven, Belgium, and

8 ^§GLOBALFOUNDRIES assignee at IMEC, Kapeldreef 75, B-3001 Leuven, Belgium ^{^}On leave from Institute of General Physics, Russian Academy of Sciences,

9 Moscow, Russia.

1011

S patial in-depth nonuniformity of thin

12

solid

ﬁ

lms is becoming a critical factor

13

with the aggressive down-scaling of

14

their thickness. The most crucial reason for

15

the nonuniformity is related to the di

ﬀ

erent

16

mechanisms of chemical reactions occur-

17

ring in the bulk and at interfaces and to the

18

increasing surface/volume ratio. Many dif-

19

ferent examples demonstrate this state-

20

ment. For instance, the Young modulus

21

of polycrystalline diamond

ﬁ

lms grown by

22

microwave-

³

or e-beam-assisted

⁴

chemical

23

vapor deposition continuously varies from

24

the nucleation side to the growth side. The

25

variation in the

ﬁ

lm texture with the increas-

26

ing

ﬁ

lm thickness is considered a common

27

phenomenon for

ﬁ

lm growth in general.

⁵

28

The variations of the material properties

29

inside the

ﬁ

lm can take place at the scales

30

from a few nanometers to hundreds of

31

nanometers.

³^!⁵

Inhomogeneity of thin

ﬁ

lms

32

can also be caused by their postdeposition

33

processing such as radiation-assisted curing

34

used in the fabrication of low dielectric con-

35

stant (low-k)

ﬁ

lms for modern microelectro-

36

nic devices.

⁶^!¹⁰

In addition, inhomogeneity

37

can be introduced intentionally for the pro-

38

duction of multilayered optical antire

ﬂ

ec-

39

tive and highly re

ﬂ

ective coatings.

¹¹

For

40

these UV optics the individual layers, consti-

41

tuting the coating, are of nanoscale thickness.

42

Several techniques allow inspection of

43

the physical and chemical properties of

44

solids with a nanometric resolution. Scan-

45

ning probe microscopy (SPM

¹²

) is routinely

46

employed, but it is limited to surface investi-

47

gation. When subsurface information is re-

48

quired, invasive treatments are usually needed.

49

Typically, sub-nanometer resolution images

50

51

52

53

54 55 56 57585960616263646566 676869707172

of the microstructure are obtained after sample microtoming (cross section image

73

with transmission electron microscopies

¹³

).

74

In-depth chemical and physical analysis can

75

also be performed by slicing the material

76

and analyzing either the removed matter

77

(secondary ion mass spectroscopy

¹⁴

) or

78

the newly created surface (ion-sputtering-

79

assisted X-ray and ultraviolet photoemission

80

* Address correspondence to vitali.goussev@univ-lemans.fr;

pascal.ruello@univ-lemans.fr.

Received for review November 1, 2011 and accepted January 1, 2012.

Published online 10.1021/nn204210u

ABSTRACT

Revealing defects and inhomogeneities of physical and chemical properties beneath a surface or an interface with in-depth nanometric resolution plays a pivotal role for a high degree of reliability in nanomanufacturing processes and in materials science more generally.^1,² Nanoscale noncontact depth profiling of mechanical and optical properties of transparent sub-micrometric low-kmaterial film exhibiting inhomogeneities is here achieved by picosecond acoustics interferometry. On the basis of the optical detection in the time domain of the propagation of a picosecond acoustic pulse through the Brillouin process, the depth profile of acoustical velocity and optical refractive index are measured simultaneously with spatial resolution of tens of nanometers. Furthermore, measuring the magnitude of this Brillouin signal provides an original method for depth profiling of photoelastic moduli. This development of a new opto-acoustical nanometrology paves the way for in-depth inspection and for subsurface nanoscale imaging of inorganic- and organic-based materials.

KEYWORDS: picosecond laser ultrasonics . nanoacoustics . acousto-optics . depth profiling . transparent films . low-permittivity films

ARTICLE

ACS Nano | 3b2 | ver.9 | 4/1/012 | 20:2 | Msc: nn-2011-04210u | TEID: deb00 | BATID: 00000 | Pages: 5.39

LOMONOSOV ET AL. VOL. XXX ^’ NO. XX ^’ 000–000 ^’ XXXX

www.acsnano.org

A

CXXXX American Chemical Society

Lomonosov et al, 2012

T h e o p e n – a c c e s s j o u r n a l f o r p h y s i c s

New Journal of Physics

Coherent acoustic oscillations of nanoscale Au triangles and pyramids: influence of size and substrate

R Taubert, F Hudert, A Bartels, F Merkt, A Habenicht, P Leiderer and T Dekorsy¹

Department of Physics and Center of Applied Photonics, Universität Konstanz, D-78457 Konstanz, Germany E-mail:thomas.dekorsy@uni-konstanz.de New Journal of Physics9(2007) 376 Received 24 July 2007 Published 19 October 2007 Online athttp://www.njp.org/

doi:10.1088/1367-2630/9/10/376

Abstract. We investigate the impulsively excited acoustic dynamics of nanoscale Au triangles of different sizes and thicknesses on silicon and glass substrates. We employ high-speed asynchronous optical sampling in order to study the damping of the acoustic vibrations with high sensitivity in the time domain. From the observed damping dynamics we deduce the reflection coefficient of acoustic energy from the gold–substrate interface. The observed damping times of coherent acoustic vibrations are found to be significantly longer than expected from the acoustic impedance mismatch for an ideal gold–

substrate interface, hence pointing towards a reduced coupling strength. The strength of the coupling can be determined quantitatively. For Au triangles with large lateral size-to-thickness ratio, i.e. a small aspect ratio, the acoustic dynamics is dominated by a thickness oscillation similar to that of a closed film.

For triangles with large aspect ratio the coherent acoustic excitation consists of a superposition of different three-dimensional modes which exhibit different damping times.

1Author to whom any correspondence should be addressed.

New Journal of Physics9(2007) 376 PII: S1367-2630(07)55896-9

1367-2630/07/010376+08$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft

Confined coherent acoustic modes in tubular nanoporous alumina film probed by picosecond acoustics methods 4

!""#$%

!^"%

&'"%

(%

)*%

+%!%

,%

%

-%

&%

.-% /0123%

Figure 1. (color online) View of the surface of the unidirectionally oriented tubular nanoporous film. Insert : scheme of the pump-probe experiment. The probe beams reflected by the surface (1), interface (3) and moving acoustic front (2) are indicated by arrows. The coherent acoustic phonons are initially photogenerated after the interaction of the pump beam with the aluminum substrate.

2. Experimental methods

2.1. Tubular nanoporous samples

The fabrication of the tubular nanoporous material follows the well known anodization electrolytic process whose description and experimental details can be found in the literature [10, 13, 24, 48]. The typical nanostructure studied in this work is shown on the SEM picture in Fig. 1. The mean wall thickness of the tubular porous film is between 20 and 30 nm, and a wall height is around H 360 nm. A dense thin alumina layer (h 60 nm) is present at the interface between the nanoporous alumina film and the aluminum substrate. A sketch of the pump-probe experiment is shown in insert.

2.2. Pump-probe experiments

The pump probe technique used here consists in the optical excitation of the system by a femtosecond laser and the detection of the corresponding transient optical reflectivity using the second laser beam called probe beam. The setup employed follows the classical scheme of picosecond acoustics [30, 31, 32, 49]. In the particular case of our studies, considering the fact that within the optical wavelength range of the laser excitation the tubular nanoporous material is transparent, the pump beam deposits its energy when it interacts with the aluminum opaque substrate as it is indicated by the arrow in insert of Fig. 1. Due to an ultrafast laser-induced heating of the metallic substrate a thermoelastic stress gives rise to a picosecond acoustic pulses which propagate both within the semi-infinite substrate and within the nanoporous film. The probe beam is delayed in time relative to the pump beam by using a motorized mechanical optical mirror which permits transformation of a variation of the optical path in a time delay. The propagating laser-generated acoustic strain field leads to modifications of the refractive index and also induces displacements of surfaces and interfaces which

Mechri et al, NJP 2012

Confined coherent acoustic modes in tubular nanoporous alumina film probed by picosecond acoustics methods8

!

"#$!

"%$!

!

0 20 40 60 80 100 120

0 0.2 0.4 0.6 0.8 1

Frequency (GHz)

Spectral density (a.u.)

"#$!

"#%!

"#&!

"#'!

"#(!

"#$%!

!

"#$!

%&'! %&(!

%&)! %&*!

%&+!

%&,! %&-!

!

0 20 40 60 80 100 120

0 0.2 0.4 0.6 0.8 1

Frequenc y (GHz )

Spectral density (a.u.)

"#$!

"#%!

"#&!

"#'!

"#(!

"#$%!

".$!

"&$!

Figure 3. (color online) (a) Time derivative of the transient reflectivity signal over a large time scale (probe wavelength⇥= 750 nm, external incidence angle 0=21 ). The baseline has been removed for the clarity of presentation of the vibratory component.

For t < 200 ps, the Brillouin frequency (around 17 GHz) is the main components.

At longer time scale several additional components are detected. (b) zoom on the time scale 400 1200 ps. The dashed line depicts to the first acoustic vibration eigenmode of the nanoporous film (c) Fast Fourier Transform (FFT) of the signal shown in Fig. 3. The modes at 48 GHz and 76 GHz are magnified by a ratio of 2. nis the eigenmode number. (insert) FFT obtained for different detection configurations.

Red curve : ⇥= 750 nm, 0=41 , blue curve : ⇥= 400 nm, 0=73 . The FFT plots were normalized in magnitude to the maximum peak for clarity.

reflectivity signal to periodic jumps in magnitude [31, 42, 52, 41, 53, 54]. These jumps are well observed att⇥76±5 ps in Figs. 2(a), 2(b) which is half the time of the detection

Nanoscale depth proﬁling of elas;ccity Life;me of conﬁned acous;c eigenmodes

Brown University, HJ Maris

19

(20)

Generation and detection of Nanoparticles resonances

0$

75F

>$(;

$

1$

!)A;!=!!$I

&

The resonance frequency f of the nanoparticle

provides the opportuniy to determine the sound speed (f=Vs/2D, D=diameter of the nanoparticle)

Diameter D=

7nm

Time (s)

Laser

(21)

21

The Story of Picosecond Ultrasonics

Christopher Morath, Ph.D.

1

From “Lab”… …to “Fab”

Rudolph MetaPULSE™

(22)

Key success factors for MetaPULSE

6

Ultrafast Laser Technology Rapid Advances 1980’s – 90’s

Picosecond Ultrasonics Research & Applications

Semiconductor Industry Rapid Growth 1970’s – 90’s

Rob Stoner

More than breakthrough technology was

necessary!

(23)

23

Ultrafast Phenomena in Condensed Matter

(24)

2-1 - Classical electrodynamics : reminder on

Maxwell equa;ons and on the classical dielectric

response

(25)

2-1 Maxwell equa;ons

25

-  Propaga;on of light in the ma3er, deﬁni;on of the refrac;ve index

Light penetra;on

K

²

= !

²

(µ

₀

✏ + iµ

₀

! ) = !

²

µ

₀

✏

₀

(✏

_r

+ i

!✏

₀

) That can be rewritten with :

!

²

= K

²

⇥ 1

µ

₀

✏

₀

(✏

_r

+ i

!✏

₀

)

¹

= K

²

⇥ c

²

˜ n

²

Where ˜ n = q

✏

_r

+

_!✏ⁱ

0

= n + i We can notice here that the light speed in slowed down by the amount ˜ n.

The electric field becomes then (for an isotropic medium) :

E ~ = E ~

₀

e

ⁱ⁽^K.~^~ ^r ^!t)

= E ~

₀

e

ⁱ⁽^K^~⁰^.~^rⁿ^˜ ^!t)

= E ~

₀

e

ⁱ⁽^K^~⁰^.~^rn ^!t)

e

⁽^K^~⁰^.~^r)

with K

₀

= !/c =

^2⇡

(K

₀

the wave vector in the vacuum, the wavelength of the light in the vacuum). If we consider the case of one 1D system we have :

E ~ = E ~

₀

e

^i(K⁰^.xn ^!t)

e

^(K⁰^.x)

The light intensity is proportional to E ~

^⇤

E ~ , so we can rewrite the expression of the intensity in the matter as :

I = E

₀²

e

^(2K⁰^)^⇥^x

The quantity ⇠ = (2K

₀

)

¹

=

_4⇡

is called the ”skin depth” and corresponds to the characteristic length over which the light penetrates in the matter. For a metal  ⇠ 2 (a value of 1 or 4 can be found depending on the incident wavelength ), so that ⇠ ⇠ 20nm at a wavelength of = 500nm.

II. HOW MUCH LIGHT IS ABSORBED IN THE MATTER ?

In this section we describe the Joule e↵ect (loss) associated to the interaction of the EW waves and the matter.

3 Figure 2.1

(26)

26 I. REFRACTIVE INDEX AND SKIN DEPTH

The Maxwell equations are :

div(E~) = ⇢

✏ rot~ E~ = @ ~B

@t rot~ B~ = µ0~j+✏µ0

@ ~E

@t div(B) = 0~

Considering that rot(~ rot~ E~) = ~ ~E +grad(div(~ E~)) and that no net charge exist in the matter (⇢ = 0), we arrive to:

rot(~ rot~ E~) = ~ ~E = @ ~rotB~

@t

= µ0

@~j

@t ✏µ0

@²E~

@t²

(1) We arrive to the following wave equation :

~ ~E ✏µ₀@²E~

@t² = µ₀@~j

@t For a 1D transport (along x direction), we have :

@²E~

@x² 1 v²

@²E~

@t² = µ0

@~j

@t

where the wave velocity is v = c/˜n, the refractive index ˜n = p✏r with c = 1/p✏0µ0 and

✏ = ✏0✏r.

We assume in the following that the electromagnetic waves propagate in an isotropic medium and along the x direction. so the electric field has the following formE~ = E~0e^K.~^~ ^r ^!t. K is the wave vector. We consider the linear response of a solid with~j = E~ where is the conductivity of the material. When we inject the expression of the electric field in the wave equation, we arrive to the following dispersion curve :

Propaga;on of light in the ma3er

(27)

27

I. REFRACTIVE INDEX AND SKIN DEPTH The Maxwell equations are :

div(E~) = ⇢

✏ rot~ E~ = @ ~B

@t

rot~ B~ = µ₀~j +✏µ₀@ ~E

@t div(B) = 0~

Considering that rot(~ rot~ E~) = ~ ~E + grad(div(~ E~)) and that no net charge exist in the matter (⇢ = 0), we arrive to:

rot(~ rot~ E~) = ~ ~E = @ ~rotB~

@t

= µ0

@~j

@t ✏µ0

@²E~

@t²

(1) We arrive to the following wave equation :

~ ~E ✏µ₀@²E~

@t² = µ₀@~j

@t For a 1D transport (along x direction), we have :

@²E~

@x²

1 v²

@²E~

@t² = µ0

@~j

@t

where the wave velocity is v = c/˜n, the refractive index ˜n = p✏_r with c = 1/p✏₀µ₀ and

✏ = ✏0✏r.

We assume in the following that the electromagnetic waves propagate in an isotropic medium and along the x direction. So the electric field has the following form E~ = E~₀e^K.x ^!t. K is the wave vector. We can consider that E~ is along the z axis. We consider the linear response of a solid with ~j = E~ where is the conductivity of the material. When we inject the expression of the electric field in the wave equation, we arrive to the following dispersion curve :

2

(28)

28

K² = !²(µ0✏+ iµ0

! ) = !²µ0✏0(✏r + i

!✏0

) That can be rewritten with :

!² = K² ⇥ 1 µ0✏0

(✏r + i

!✏0

) ¹ = K² ⇥ c²

˜ n² Where ˜n = q

✏r + _!✏ⁱ

0 = n + i We can notice here that the light speed in slowed down by the amount ˜n.

The electric field becomes then (for an isotropic medium) :

E~ = E~0eⁱ⁽^K.~^~ ^r ^!t) = E~0eⁱ⁽^K^~⁰^.~^rⁿ^˜ ^!t) = E~0eⁱ⁽^K^~⁰^.~^rn ^!t)e ⁽^K^~⁰^.~^r)

with K0 = !/c = ^2⇡ (K0 the wave vector in the vacuum, the wavelength of the light in the vacuum). If we consider the case of one 1D system we have :

E~ = E~0e^i(K⁰^.xn ^!t)e ^(K⁰^.x)

The light intensity is proportional toE~^⇤E~, so we can rewrite the expression of the intensity in the matter as :

I = E₀²e ^(2K⁰^)^⇥^x

The quantity ⇠ = (2K0) ¹ = _4⇡ is called the ”skin depth” and corresponds to the characteristic length over which the light penetrates in the matter. For a metal  ⇠ 2 (a value of 1 or 4 can be found depending on the incident wavelength ), so that ⇠ ⇠ 20nm at a wavelength of = 500nm.

II. HOW MUCH LIGHT IS ABSORBED IN THE MATTER ?

In this section we describe the Joule e↵ect (loss) associated to the interaction of the EW waves and the matter.

3

Ultrafast Phenomena in Condensed Ma3er : basics Prof. P.Ruello Ins;tut des Molécules et Matériaux du Mans, UMR 6283 CNRS-Université du Maine.

Ultrafast Phenomena in Condensed Ma3er : basics Prof. P.Ruello

Ins;tut des Molécules et Matériaux du Mans, UMR 6283 CNRS-Université du Maine.

h ν

phonons

Pascal.ruello@univ-lemans.fr

Ultrafast Phenomena in Condensed Matter

Ultrafast Phenomena in Condensed Matter

laser

Ultrafast

Phenomena

Light and telecommunica;on

Light velocity c=3.10

m/s

- Necessity of control of light : propagation, source, etc

- New emerging technologies based on the manipulation of the matter with light (photonic fast communication, photoinduced phase transition for memory, etc … )

Fermi velocity V=10

m/s

~1900-1960

~1950-1960

~1980

~2000

Sound speed in air

V=340 m/s

Photonics and materials

Guiding light

Bragg (2dsin(θ)=λ)

Optical fiber and photonic crystals

v

= ∂ ω

∂ k

ω

k

vide

à light transport = less Joule eﬀet than for electron transport

Informa;on : wri;ng and reading as fast as possible

Today : GHz, Tomorrow 1 THz

à Transistor (saturation state as bit 0-1)

à Magnetic memory (RAM, DRAM, SDRAM,

…)

à Cr

O

, Fe

O

,

à GMR, CMR (magnetoristance) LaSrMnO3

à Phase change memory (PCM) :

amoprhous to crystalline phase transition as wa way to creat a bit (0-1).

à Rewritable CD-DVD

2 states (O –

1 bit)

Phase change memories (GeTe, GeSbTe, etc)

Ecrire et lire avec la lumière (CD, DVD

réinscrip;ble du future)

Photovoltaics

• Light energy received per day > total consumption

• How can we harvest this energy ?

• How can we store it ?

How does a cell

work ?

- Electric energy harvesting is efficient if

à the electron-phonon collision is reduced (non-raditaive recombination)

à The carriers radiative recombination is reduced

Photovoltaics : ;meline

~1839-1905

~1970

~1980

2000

E = h υ

2017

Ultrafast phenomena : interplay

between technologies challenges and real fundamental knowledge

• For advanced telecommuncia;on, for storage technologies, for photovoltaïcs, it is important to understand the light-ma3er interac;on

including the ultrafast processes.

• Ultrafast processes = ul;mate process

involving charge excita;on, charge transport,

electron-phonon coupling

Electron-phonon interac;on : Drude model

• Characteris;c ;me of electron-phonon coupling

σ = ne

à  Transistor (saturation state as bit 0-1)

à  Magnetic memory (RAM, DRAM, SDRAM,

à  Cr

à  GMR, CMR (magnetoristance) LaSrMnO3

à  Phase change memory (PCM) :

à  Rewritable CD-DVD

•  Light energy received per day > total consumption

•  How can we harvest this energy ?

•  How can we store it ?

-  Electric energy harvesting is efficient if

à  the electron-phonon collision is reduced (non-raditaive recombination)

à  The carriers radiative recombination is reduced

•  For advanced telecommuncia;on, for storage technologies, for photovoltaïcs, it is important to understand the light-ma3er interac;on

•  Ultrafast processes = ul;mate process

•  Characteris;c ;me of electron-phonon coupling

m v(t + τ ⁾ − v(t )

τ ⁼ ^eE ^v(t ⁺ τ ⁾ = eE τ

m = µ ^E

Observa;on in the ;me domain of the dynamics (mo;on, relaxa;on, …) of degrees of freedom of a solid : -  Electron

-  Phonon -  Spin

GHz-THz Coherent acous;c phonon sources : for what ? -  - Controlling the lahce mo;on, lahce strain with light -  - New optomechanics devices

-  - Light-control of ultrafast mechanical actuator