SPALLATIVE ABLATION: FROM METALS TO DIELECTRICS
AND FROM INFRARED TO X-RAY LASERS
, Petrov Yu.V. , Khokhlov V.A. , ovN.A.Inogam , Anisimov S.I. 1111
,ii ZhakhovskV.V. ,Skobelev I.Yu. , Pikuz T.A. ,Fortov V.E. ,Faenov A.Ya. 22222
,M.Tanaka ,Nishikino M. ,Nishihara K.
,Kishimoto M. ,Kawachi T. ,Kato Y. ,Ishino M. ,Fukuda Y. ,Bulanov S.V.
333
333333
4Shepelev V.V.
Russia 142432, vkaChernogolo Sciences, ofAcademy Russian Physics, lTheoreticafor InstituteLandau 1
Russia 125412, Moscow Sciences, ofAcademy Russian es,TemperaturHigh for InstituteJoint 2
Japan 0215,-619 Kyoto Agency,Energy AtomicJapan Institute, SciencePhoton Kansai3
Russia 123056, Moscow , Sciences ofAcademy Russian Design, AidedComputer for Institute4
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Characteristics of a laser irradiation and a matter
metals with ginteractin eV 1~ energy photon n with theirradiatiolaser optical )1 L
torssemiconduc with ginteractin eV 1~ n irradiatiolaser optical 2) L
sdielectric with eV 1~ n irradiatiolaser optical ofn interactio 3) L
sdielectric and torssemiconduc metals,
onto actingn irradiatio rays-Xsoft or t ultraviole hard 4)
nm 250~Au for nm, 100~ AlFor
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as wellas eV) tensseveral to(up
emperatureelectron thigh very upon the spectraphonon a of dependence the
melting the toUp
layer. e within thexists metal a of state unique a At
Teq dtt
Unique state of metals under the action of femtosecond laser
irradiation. Phonon spectra of a metal with a hot electrons
within the Thomas-Fermi approach (simple metals)
The only state suitable to investigate the lattice
dynamics at electron temperatures up to several tens eV
) v,,(2
),v,(2
),v(
spectraPhonon
0.2parameter lattice Reduced
crystal bcc
3/13/4
,s
ZZTZZ
TZ
T
a
es
ese
kk
Unique state of metals under the action of femtosecond laser
irradiation. Dependence of a melting temperature of a simple
metal on the electron temperature
)v,(
)v,()v,(
re temperatuMelting
2.0 1.6; 1.2; ;6.0
constant lattice Reduced
crystal bcc
3/43/7
3/7
3/1
ZTZTZ
TTZTT
Zaa
a
em
emem
The only state suitable to investigate dependence of a
melting on the electron temperatures
0 2 4 6
t, ps
0.84
0.88
0.92
0.96
1
R /
Ro :
Re
fle
ctivity o
f pro
b f
sL
P n
orm
aliz
ed
to
Re
flectivity b
efo
re P
um
p
Al, Fabs = 65 mJ / cm2, Finc = 0.75 J / cm2
alpha = 30, b = 3.5
The black curve with markers=experiment
The blue curve = 2Tgd with b=0The red curve = 2Tgd with b=3.5
where nu = nuei + nuee
nuee = b*(EF/hbar)(Te/TF)2
DETERMINING INTRINSIC PARAMETERS OF METALS.
AL, INFLUENCE OF ELECTRON-ELECTRON INTERACTIONS
ONTO THE REFLECTIVITY
eeeie
F
eBFee
Tkb
2
Evolution of the phase shift of reflected light,
caused by the melting kinetics (Al)
• Phase shift with respect to the reflection from the cold aluminum state
• Calculations and experiments are in a good agreement
0 2 4 6
t, ps
0
2
4
6
P
si,
nm
- p
ha
se
diffe
ren
ce
be
twe
en
th
e c
urr
en
t p
ha
se
an
d th
e p
ha
se
befo
re p
um
p
Al, Fabs = 65 mJ / cm2, Finc = 0.75 J / cm2
alpha = 30*1017 (erg/s)/(cm3 K)
experiment
bopt=0, meff = 1.6
bopt=3.5, meff=1.2
Melting kinetics is described accurately:because 2Tgd dependence agrees wellwith experiment expansion
crater
Evolution of Optical Parameters after the Pump Impact
Au• Changes in the reflectivity and the phase of reflected
probe light after the pump action
eV1
• Gold
• The upper three curves are phases
• The bottom curves present the drop
in the normalized reflection
coefficient R/Ro
• Fabl is an ablation threshold
• Finc is incident fluence of the
chromium-forsterite laser
tau_L=100 fs, lambda=1240 nm (1
eV)
• The pump operates at the first
harmonics :
• The probe operates at the second
harmonics :
• The red rectangular presents
duration tau_L of the pump pulse
• It should be emphasized that
optical changes are fast :
compare duration tau_L and rise
time for R and
eV2
Exitation of 5d-electrons into 6s-6p-bands
0 2 4 6 8 10
Te, eV
1
2
3
4
5
Nu
mb
er
of e
lectr
on
s in
6s +
6p
zo
ne
s
Au
• Increase of the number of electrons in 6s-p bands
-0.4 -0.2 0 0.2 0.4 0.6
X axis (kJ/mol)
0
50
100
Y a
xis
(kJ/m
ol)
DETERMINING INTRINSIC PARAMETERS OF METALS.
Au
d
Tk
xBatis
eBe
dx
xx
xk
M
m
m
mnZ
s
0
2
0
2
2
1)(
12
.
dx
eexx
xk
M
m
m
mnZ
eBeB Tk
x
Tk
Batid
12
21
0
2
0
2
2
1
1
1
1
)(
12
.
(2007) Celli V. Zhigilei,L.V. Lin, Z.
101.2)eV2( ,106.1)eV1( 1717
K W/m10 α, 317
eV , Te
ACOUSTIC DECAY OF THE PRESSURIZED
BY THE LASER IRRADIATION TARGET LAYER
reflected) andleft (right, waves threeof composed is profile pressurecurrent The c)
wavereflected theproducesboundary aon Left wave b)
heatinglaser a todue layer sticcharacteri e within th pressure and re temperatua of Increase a) TdpT
Short pulse laser irradiation results in the spallative ablation
Two-temperature hydrodynamics approach
)()/(
)()/(
0
0
0
00
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0
0
ieii
ieeee
TTx
up
t
E
QTTx
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x
T
xt
E
x
p
t
u
Hydrodynamics equations describe:
Heating of ion subsystem via energy transfer from hot electrons to ions (term
with the coefficient )
Expansion of electron thermal wave into the bulk target (the -
term – electron heat conduction in the equation for the energy of electrons)
Expansion of a hot target matter
Initial state of a crystal for two-temperature hydrodynamics.
Pulse has a gaussian temporal form.
)/exp()( 22
0 tFtF
3/ , cmg GPap ,
skmv / , KT ,
nmx ,
fs
tFtF
100
)/exp()( 22
0
1. Two-temperature hydrodynamics provides adequate
initial conditions for further used molecular dynamics
simulation of laser ablation of metals.
2. Molecular dynamics simulation with many-body
potentials of metals is more adequate to describe the
ablation pattern late in a time when phase transitions
occur.
))(1/()()(
)1/())(()(
))()(())(/1()(
, ,
32
2
222
1
4
2
321
6
3
610
2
2
1
2
1
rcrrcrn
nbnbbnbnF
xaxxxxaxrV
raxrax
c
cc
cc
ik
iki
i
ij
iji
rnn
nFrVU )()(
Embedded atom potential for aluminum
The same potential will be used for AlF
nm 6875.0cr Is a cut0ff radius, other parameters are obtained from the
minimization procedure for a sum of deviations from the
experimental data at normal conditions and from the cold
stretching pressure evaluated by ABINIT density functional
code
Gaussian Focal Spot
and Final Morphology of Irradiated Area
• There are significant effects
connected with existence of foam
• The foam continues to decelerate
cupola after nucleation. In larger
objects this is impossible since
surface tension and existence of
foam are dynamically insignificant
against inertial force
• The foam is the reason for
appearance of the nanomodulations
at the surface of the cupola
• If solidification is fast enough
remnants of the foam remain frozen
around the crater and in the bottom of
the crater
thermomechanical
ablation threshold
cavitation threshold
melting threshold
evaporation
surface profile long after irradiation
Fa
Gaussian fluence F(r)
Fc
Fm
debris
crater
rim
frozen bubbles
Nucleation and Formation of a Foam
• Figure shows matter motion and its thermodynamic phase composition after action of Gaussian laser beam with maximum intensity at the middle vertical straight line.
• In metals and semiconductors nucleation under stretching takes place inside the molten layer (cavitation)
• Action of Gaussian in transverse plane laser beam creates nonhomogeneous heating – absorbed fluence depends on radius r from the beam axis. It results in the formation of thin liquid runaway layer (cupola) above the focal spot at a surface. Thickness of the cupola is a function of the local value Fabs(r) – it is thinner in the central region where Fabs is larger. There is a liquid-vapor foam under the cupola. Foam region becomes thicker near the central axis. The bottom of the future crater is located under the liquid layer, separated from the bulk matter by the melting-solidification front
Molecular dynamics simulation of the ablation pattern
above the ablation threshold. Formation of the spalled
cupola
cS t / dT = 0.72 2.1 3.7
y
AM
M
E
z
z
(a)
(b) (c)
crit
Cr
Cr
1
2
1
2
0 0'
0A A MME
ivv
E
Fm
Fa
Fev
Fcrit
Fc c
iii iii
Time dependence of the spalled layer pattern
Formation of the spalled cupola under the action
of laser pulse with spatial Gaussian fluence
profile
Ablation pattern for different intstants
Newton rings
Golden target. Pump light angle equals 45 degrees. The interval between the top
of parabolic cupola-shaped spallation plate and target surface equals 1800 nm.
Мolecular dynamics simulation of the laser
ablation of bulk aluminum
The wide Al target with cross section LyxLz=122x14 nm2 heated up to the T0(0)=5 kK at the small
heated depth dT =18.6 nm. The total simulation time is 153.5 ps.
0.1ps pump
torssemiconduc with ginteractin eV 1~ n irradiatiolaser Optical 2) L
metalsin that similar to depthscrater
and hresholdablation t fluence the torise giving place takestorssemiconducin ablation Spallative
metalsin asorder same theofstrength materialt significan a have and
hot t tooaren' torssemiconduc so electrons, exite torequied isenergy small a gap narrow the toDue
increasessharply eunit volumper energy laser absorbed and valuesmetallic to
dropsdepth absorbtion theelectrons, conduction ofdensity plasma critical a achievingWhen
processes. tunnelandphoton -multi
n, transitiointerbanddirect through band conduction to valencefrom electrons exitesn irradiatioLaser
Pictures of the Newtonring-like structure on sixdifferent materials:
1. silicon2. gallium arsenide3. aluminum4. gold5. magnesium6. mercury
K. Sokolowski-Tinten et al.Applied Surface Science 127–129 (1998) pp.755–760
Newton rings as a
manifestation of
spallative ablation
(1) (2)
(3)
(5)
(4)
(6)
sdielectric with eV 1~ n irradiatiolaser optical ofn Interactio 3) L
ablation spallative a toleading ,, torssemiconducin while
, thresholdbreakdown optical thesdielectricin sother word By the
expansion gas as looks state thisfromexpansion icalHydrodynam
strength. material small negligibly with statehot a into transfersDielectric
electrons. conduction of
density critical a achieve energy to large anessesary isit gap widea toDue
ablopt
ablopt
FF
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ereceimp
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AEEnnkCEdt
dTC
TnEEunEEQdt
dE
td
FQnn
u
Q
dt
dn
, cm106 , 6 ,
)2/3( , ,
)/exp( ,
3-22
2
223
2
Evolution of the parameters of a LiF matter within the heated layer Td
sdielectric and torssemiconduc metals,
onto actingn irradiatio rays-Xsoft or t ultraviole Hard 4)
eB
Fi
impec
Fi
impe
Fi
imp
Li
impec
Li
impe
Li
imp
Tk
en
en
/s][cm 18.0
)1/(107.0v ,v
/s][cm 5.1
)1/(1011v ,v
38
38
ELECTRON IMPACT IONIZATION FREQUENCIES
eV 14
THE THREE-BODY RECOMBINATION RATE
P)P( 15 , 18.0 1.6 , 1 :F
S)S( 1 , 5.1 ,12 , 0 :Li
1)(
, )(12
)(410
32
0
12
0
2/1
1
0
0
2/3
32/38
i
i
eB
i
i
Brec
QAl
QAl
AG
TkG
g
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l
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ELECTRON-ATOM ENERGY EXCHANGE RATE
1-11
216
s 10)2010(v3 with
Then
cm 10)147( nm 20.015.0
3v
frequency collision atom-electronv
collision onein
atom oelectron t from nsferredenergy tra average the32
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ceae
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e
Li
eB
Li
eeaa
nM
mAAEE
r
m
Tk
n
EM
mTk
M
m
nE
Evolution of the parameters of a LiF matter within the heated layer Td
;s102 eV, 25 :1 ;s109 eV, 14 :2 ;s102 eV, 14 :1
re temperatuatomic theof Increase (c)
cooling a-e thebecause decreases and
ionrecombinat and )( sourcelaser a ofaction the viaincreases emperatureElectron t (b)
ionrecombinat a todue isdecay andation photoioniz the todue is ofGrowth
. populationelectron free ofion Concentrat a)
1-11
2
1-11
2
1-11
2 AuAuAu
tQ
n
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e
nm28 ,ps 7 ,mJ/cm 10 3 TdF
TT
atatatea
at
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xt
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exp
TEMPORAL AND SPATIAL EVOLUTION OF THE PARAMETERS OF A MATTER
AT THE ACOUSTIC STAGE
3
CRYSTALLINE LITHIUM FLUORIDE
33
AlLiF
Molar mass 25.939 g/mol 26.981 g/mol
Density 2.635 g/cm 2.70 g/cm
Melting point 1118 K 931 К
Crystal structure NaCl-type fcc fcc
Isothermic compressibility-111 Pa 103.1 -111 Pa 103.1
EVOLUTION OF PRESSURE PROFILES IN LIF CRYSTAL CREATED BY
THE ABSORBTION OF XUV-PULSE.
Molecular dynamics simulation
CONCLUSION
1.Spallative (thermomechanical) ablation is the
universal mechanism of a matter removal from the
condensed targets by short laser irradiation equally
existing for metals, semiconductors and dielectrics
2. Spallative ablation for dielectrics takes place for
shorter light wavelength than in metals and
semiconducors
The interference pattern from Al target for a pump pulse fluence 0.96 J/cm .
The left figure was obtained by using Linnik microinterferometer at time delay
700 ps after pump. The right figure is a theoretical prediction based on Fresnel
formulae.
Experimental results on aluminum.
Comparison with the theoretical calculation
2
Experimental results on gold
and the comparison with the theory
The interference pattern from Au target for a pump pulse
fluence 2.86 J/cm2 (above the evaporation threshold). The
central part of cupola was destroyed. The right figure is a
theoretical prediction based on Fresnel formulae.
Femtosecond laser irradiation:
1.Creates unique state of matter when interacting
with metals and semiconductors
2. Originates in the specific forms of ablation of
these materials
3. Forms specific postablation structures in a
target
4. Provides the means of probing these
phenomena by itself
DETERMINING INTRINSIC PARAMETERS OF METALS.
Dielectric permittivity of Al
• At room temperature there is a significant contribution to from interband transitions between parallel bands (Palik, 1998; Miller, 1969)
• This contribution diminishes during melting (Miller,1969) and at a high electron collision frequency (Ashcroft, Sturm, 1971), thus the Drude term dominates in .
• is defined by Z and :
• Z=3 (this value defines a frequency of plasma oscillations ): there is no additional
excitations of electrons into s-band at our temperatures (Te is less than 10 eV)
• Important fact is: electron-electron collisions seems weakly contribute to even when crystalline lattice still exists after pump illumination. This means that in a rather hot electron gas the Umklapp contribution is weak
• Therefore only electron-ion collision frequency may influence .
• At early stage and even late in a time ion temperature Ti is limited by values less than 10 kK at our range of fluences Ti[kK] 2.5*(Fabs/65[mJ/cm2]), (Fabs)abl = 65 mJ/cm2, Fabs is absorbed fluence, (Fabs)abl is ablation threshold on absorbed fluence
• weakly depends on Te
• is less than 1 at the early stage, therefore there is no significant changes in
of Al at the early stage caused by the pump heating
22
2
22
2
1
pp
Drude i
Drude
p
ei Drude
ei /ei
Drude
Transformation of electron d-band of Au when the electron
temperature increases from the room temperature to the values
about 5 eV. Schematic presentation of the density of state.
Crystalline lattice remains cold up to the instants ~ 1 ps)
E
E
6s
6s
EF
EF
5d
5d
probe2 eV
probe2 eV
RT
2T, Te ~ 5-10 eV
Exitation of 5d-electrons into 6s-6p-bands
• Equation for the chemical potential
)exp(1
)exp(1
ln
1exp
2
2
1
0
3
2
e
e
e
e
kT
kTgkT
kTx
dxxmkT
nzdzsz
zs is a number of electrons in 6s-p-bands per atom
zd – the number of electrons in 6s-p-bands per atom
n is the atom density
g – the average density of state in 5d-band
Band structure, plasma frequency and electron
collision frequency
iZ
20
)/(1
)/(2110,1)/(212.1
r
Z
2)/(1
2115.14,112119
• Describing the experimental data on a phase shift and raflectivity
• Z=Ne6s ~ (2-4) для Te ~ (5-10) eV
1,1at)/(21
),eV2(103:Probe
0
2
15
effpl mZ
32~)/(
3~
Z
E
E
6s
6s
EF
EF
5d
5d
probe2 eV
probe2 eV
RT
2T, Te ~ 5-10 eV
Dielectric permittivity of Au
• , calculations show that d term is
small in comparison with the s term at the
considered range 0<Te<10 eV
• At small it is due to the small number of holes
= Z-1 in the d-band, ( Z is the number of
electrons per ion in 6s, 6p bands)
• At the elevated Te [3-6 eV] , but the
electron-ion collision frequency for the d electrons
is high – again is small
ds
eT
hN
1~hN
d
Comparison of the change of dielectric permittivity
of Al and Au with electron temperature growth
• Values of Te/TF are similar for Al and Au compared here but the 2T state remains hidden in Al (weak manifestation in eps) while the Te rise obviously manifests itself in case of gold (2T=Two-Temperature)
Re1
• Change in at the early stage. They are initiated by the pump action
• Relative values of are shown –normalization to the R.T. values corresponding to the state before the pump
1
Re1
pressure a of growths temporalacoustics and kinetics of Comparison (c)
pressure total the toonscontributi atomic and electronic of Comparison )b(
and sfor variou pressure Total (a) 2 Aui
LiF
2T dielectric permittivity of Au : Z and
collision frequencies for• Z grows with Te as a result of excitation of d-electrons
• Question about NU for epsilon:
• (1) es—ions
• (2) es—es (Umklapp)
• (3) es---ed
• NU for epsilon and NU for kappa
are different:
NUeps=1+2Umklapp+3, while
NUkappa=1+2all+3
• For Au in our conditions (1) is
rather important; (2,3) seems are
unimportant
• They explain fast changes in eps