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Femtosecond ablation: theory and experiment
Petrov Yu.V.(1), Inogamov N.A.(1), Khokhlov V.A.(1), Anisimov S.I.(1),
Ashitkov S.I.(2), Zhakhovskii V.V.(2,3), Agranat M.B.(2), Fortov V.E.(2),
Shepelev V.V.(4), Komarov V.P.(2)
(1) Landau Institute for Theoretical Physics, RAS, Chernogolovka, Russia
(2) Joint Institute for High Temperatures, RAS, Moscow, Russia
(3) Institute of Laser Engineering, Osaka University, Osaka, Japan
(4) Institute for Computer Aided Design, RAS, Moscow, Russia
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
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Non-equilibrium processes :
(1) Pump absorption and electron-electron relaxation
(2) Electron-ion thermal relaxation
(3) Heating of ion subsystem and melting – subsonic
surface melting, supersonic volume melting, thermal
and mechanical interaction of melt and crystal through
a melting front
• (4a) Acoustic release of the fast thermal pressure rise
– physics of negative pressure at nanoscales,
nucleation
• (4b) Foaming
• (5) Fast solidification and recrystallization: frozen
closed bubbles, frozen foam, bubbles frozen during
their break out, frozen nanojets
I. Femtosecond laser irradiation creates the unique state of
matter
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 eV
Unique state of metals under the action of femtosecond laser
irradiation. Dependence of a melting temperature of a simple
metal on the electron temperature
Reduced lattice constant
a  0.6; 1.2; 1.6; 2.0
a  aZ 1/ 3
Melting temperatu re
Tm (Te , v)  Z 7 / 3 Tm (Te , v) 
Z 7 / 3 Tm ( Z 4 / 3Te , Zv)
The only state suitable to investigate dependence of a
melting on the electron temperatures
Femtosecond laser irradiation creates unique conditions
for phase transition processes
Specific features of melting under the action of
femtosecond lase irradiation
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(1) Slow subsonic melting from the free surface with well defined melting front
(2) Near equilibrium (this means slow) volume isochoric melting : homogeneous
nucleation
(3) Non-equilibrium (fast) volume melting

The particular regime of melting is defined by the rate of heating ( Ti ) and the
degree of overheating of lattice [T - Tm(p) ] / Tm(p)
The peculiarity of melting after action of ultrashort laser pulse: this is a melting in
the 2T state. Shift of conduction electrons up at the energy axis influences
interatomic interaction potential, elastic properties of crystal and therefore can
influence melting, especially in noble and transition metals.

In our case of supersonic electron heat conduction wave there are: high Ti and
large degrees of overheating (>0.3). In this case the regime (3) takes place during
the electron-ion temperature equilibration stage. After that there is gradual
transition to the regime (1). Our case corresponds to significant exceeds above the
melting threshold
Electron heat propagation at the 2T stage is supersonic as result of high electron
velocities (Fermi velocity) in comparison with low ionic velocities (cs – speed of
sound)
R / Ro : Reflectivity of prob fsLP normalized to Reflectivity before Pump
DETERMINING INTRINSIC PARAMETERS OF METALS.
AL, ELECTRON-ELECTRON INTERACTION.
USE OF REFLECTIVITY
alpha = 30, b = 3.5
Al, Fabs = 65 mJ / cm2, Finc = 0.75 J / cm2
1
0.96
0.92
The black curve with markers=experiment
The blue curve = 2Tgd with b=0
The red curve = 2Tgd with b=3.5
where nu = nuei + nuee
nuee = b*(EF/hbar)(Te/TF)2
0.88
0.84
0
2
4
t, ps
6
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
between the current phase and the phase before pump
Psi, nm - phase difference
6
Al, Fabs = 65 mJ / cm2, Finc = 0.75 J / cm2
alpha = 30*1017 (erg/s)/(cm3 K)
4

Melting kinetics is described accurately:
because 2Tgd dependence agrees well
with experiment
expansion
bopt=3.5, meff=1.2
crater
2
bopt=0, meff = 1.6
experiment
0
0
2
4
t, ps
6
DETERMINING INTRINSIC PARAMETERS OF METALS.
Dielectric permittivity
•
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
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  .
 Drude is defined by Z and  :

 p2
 p2 
 Drude  1  2 2  i 2 2
 
  
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Z=3 (this value defines a frequency of plasma oscillations  p ): 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  Drude 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  ei may influence  Drude .
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
 ei weakly depends on Te
 ei /  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
Evolution of Optical Parameters after the Pump Impact
• Changes in the reflectivity and the phase of reflected
probe light after the pump action, Au
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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 :   1eV
The probe operates at the second
  2eV
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 
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)
• Change in 1  Re 
at the early stage. They
are initiated by the
pump action
• Relative values of  1
are shown –
normalization to the
R.T. values
corresponding to the
state before the pump
1  Re 
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)
RT
EF
probe
2 eV
6s
5d
E
2T, Te ~ 5-10 eV
EF
probe
2 eV
6s
5d
E
Exitation of 5d-electrons into 6s-6p-bands
• Equation for the chemical potential
2  mkTe 
z  zs  zd  2
 n   
3

1  exp(
  1
)
kTe
0     gkT ln
 2
1  exp(
)
  1
exp  x 
kTe
kTe 

x dx
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
Exitation of 5d-electrons into 6s-6p-bands
Y axis (kJ/mol)
100
50
0
-0.4
-0.2
0
0.2
0.4
0.6
X axis (kJ/mol)
• Increase of the number of
electrons in 6s-p bands
Number of electrons in 6s + 6p zones
5
4
Au
3
2
1
0
2
4
6
Te, eV
8
10
Band structure, plasma frequency and electron
collision frequency
• Describing the experimental data on a phase shift and raflectivity
• Z=Ne6s ~ (2-4) для Te ~ (5-10) eV
( /  )
1.2  21( 0 /  )  1, 10  21Z
 i
2
1  ( /  )
21Z
 9  1  21  11,  14.5  1 
 r
2
1  ( /  )
Z ~3
( /  ) ~ 2  3
RT
Probe :   3 1015 (2eV),
EF
probe
2 eV
21  ( pl /  ) 2 at Z 0  1, meff  1
6s
5d
E
2T, Te ~ 5-10 eV
EF
probe
2 eV
6s
5d
E
Dielectric permittivity of Au
   s   d , calculations show that d term is
small in comparison with the s term at the
considered range 0<Te<10 eV
• At small Te it is due to the small number of holes
N h = 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] N h ~ 1 , but the
electron-ion collision frequency for the d electrons
is high – again  d is small
•
2T dielectric permittivity of Au : Z and
collision frequencies for
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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
Femtosecond laser irradiation results in specific forms of ablation
Two-temperature hydrodynamics approach
u
p
 0
t
x
   Te 
u  0
0
0  ( Ee /  )

 0  0 0   pe 0   (Te  Ti ) 
Q
t
x   x 
x


0
0

(
E
/

)

u

i
0
 pi 0 
 (Te  Ti )
t
x

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.
 , g / cm3
p, GPa
F (t )  F0 exp( t 2 /  2 )
v, km / s
F (t )  F0 exp( t 2 /  2 )
x, nm
T , K
  100 fs
Target parameters at instant t=0, corresponding to the
fluence maximum
Target parameters immediately at the end of laser pulse
(t=0.3ps)
Parameters of a target at the instant of the equalization of
electron and ion temperatures Te=Ti
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.
Embedded atom potential for aluminum
U i   V (rij )  F (ni )
j i
ni   nrik 
k i
x  a1r 2 , xc  a1rc2 ,
V (r )  (1 / x  a2 )( x  xc ) (( x  xc )  (a3 x) )
10
6
6
F (n)  b1n(b2  (b3  n) ) /(1  b4 n)
2
n(r )  c1 (r  r ) /(1  (c2 r ) )
2
rc  0.6875 nm
2 2
c
2 3
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
Gaussian fluence F(r)
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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
Fa
Fc
Fm
thermomechanical
ablation threshold
cavitation threshold
melting threshold
evaporation
rim
debris
crater
frozen bubbles
surface profile long after irradiation
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 meltingsolidification front
Molecular dynamics simulation of the ablation pattern
above the ablation threshold. Formation of the spalled
cupola
y
Fm
Fa
M
A
Fev
Fcrit
Fc c
(a)
E
crit
1
z
v
z
1
iv iii
ii i
2
0
2
E
A M
E
Cr
Cr
M
Time dependence of the spalled layer pattern
cS t / dT = 0.72
0
A M
0'
(b)
(c)
Formation of the spalled cupola under the action
of laser pulse with spatial Gaussian fluence
profile
2.1
Ablation pattern for different intstants
3.7
Experimental results on aluminum.
Comparison with the theoretical calculation
2
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 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.
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
0.1ps pump
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.
Another important object is thin metal films.
Intrinsic characteristics of a metal such as the rate of energy
exchange between electrons and ions, electron thermal
conductivity effectively influence onto the acoustic
phenomena within the metal foil and onto the results of optical
diagnostics of frontal and rear side boundaries of a foil
Nonequilibrium processes in a metal foil. Observation by the frontal and rear side
probe reflection
Five stages of nonequilibrium processes under the action of
femtosecond laser pulse onto the thin metal foil.
(1) t ~ 0.2 ps
refl. ~ 90 %
Te
probe
pump fsLP
Ti
~ 1 m
probe
~20 nm
•
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pi - pressure
probe
probe
T i =T e
~100 nm
v ~ 1 km/s
probe
~50 nm
~0.5 km/s
probe
(3) t ~ 20 ps
nucleation
•
(2) t ~ 3 ps
v
cavitation
•
Absorbtion of laser irrradiation by electrons, heating of
electrons, difference between electron and ion temperatures
(2T-model, Anisimov et al, 1974)
Electron-ion thermal relaxation, equalization of electron and
ion tmperatures, formation of a heated layer of a target and
a high pressure profile
Acoustic destroy of a pressure profile - creation of “z”-wave
as a superposition of the compression (p>0) and rarefaction
(p<0) waves. Onset of cavitation in a streched melt.
Formation of a shock wave with p<0
Growth of cavitation bubbles because of their stretching and
merger. Motion of z-wave towards the rear side of a foil.
Exposure of z-wave onto a rear side of foil. Spallation and
generation of two shock waves with p<0, propagating out of
the destruction zone. Formation of the nanorelief on the
frontal side of foil at the bottom of a crater. Nanorelief
freezing.
p>0
probe
p<0
melting front
(4) t ~ 70 ps
probe
p<0
~100 nm
(5) t ~ 120 ps
~0.2 km/s
probe
Sf
p>0
Se
~100 nm
ablated layer
•
~50 nm
~0.2 km/s
S
solidification
front
S
probe
p<0
spalled
layer
The main processes in thin metal foil induced by femtosecond laser pulse (pump fsLP)
and measured by two backscattered probe pulses (from frontal and rear surfaces). The diagram
is based on our MD simulation12 of Aluminum foil under fsLP with absorbed fluence F =
0.15 J/cm2.
Femtosecond laser irradiation leads to the formation of
nanorelief on a target surface
Conductive Cooling and Freezing of Bubbles
• Example of beginning of cooling. MD simulation of the wide-sized Al foil
183×243×21 nm3 (55×10**6 atoms) heated up to To = 3.9 kK with dT =
18.6 nm (below ablation threshold). Density maps of cavitation zone shown
at t=154 ps, when tension of the binding foam stops the expansion of
bubbles at diameters ~30 nm. Molten surface layer with three times
shrunken bubbles will finally be frozen at ~500 ps. The cooling rate is
~10**12 K/s.
Nanorelief: Development in Time
• llMD simulation of ablation of the wide-sized Al foil 122x14 nm2
heated up to T0 = 3.9 kK with dT = 18.6 nm. Density maps of
cavitation zone formed at 11.5 ps, stretching of the binding foam
before its breakup (38.4 ps), and detachment of ablated runaway
layer (153.5 ps) from the front side.
In the case of essential exceeding of the ablation threshold
two-phase foam has a wide range and consists of large number
of bubbles.
Foam breakup takes place in the central part of the foam.
Close to the spalled layer part of the foam joints to it.
Central part of the foam forms a vapor-droplet ejecta
Close to the crater bottom part of the foam creates or freezen
bubbles in a crater or freezem nonregular nanostructures in
its surface
Widening of the Foam Region, Break-out of the Foam, Slow
Motions of the Foam Remnants near the Bottom of the Crater,
Freezing of These Remnants, Formation of Solidified
Nanojets (Left Picture from Vorobyev, Guo, 2007)