n.a.inogamov, v.v.zhakhovskii, v.a.khokhlov, v.v.shepelev ... fileand dielectrics : multi-photon...
TRANSCRIPT
![Page 1: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/1.jpg)
N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev,Yu.V.Petrov, S.I.Anisimov, M.B.Agranat, S.I.Ashitkov, P.S.Komarov,A.V.Ovchinnikov, D.S.Sitnikov, V.E.Fortov, A.Ya.Faenov, I.Y.Skobelev, T.A. Pikuz
* L.D. Landau Institute for Theoretical Physics, RAS* Joint Institute for High Temperatures, RAS* University of South Florida, Tampa, USA* Kansai Photon Science Institute, Japan Atomic Energy Agency, Kyoto, Japan* Institute for Computer Aided Design, RAS* The Graduate School for the Creation of New Photonics Industries, Shizuoka, Japan
![Page 2: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/2.jpg)
Toolbox: Ultrashort IR, viz. lasers hυ~1eV, pulse duration τL from few cyclesFs-ps XUV – X-ray lasers hυ~0.1-10 keV :1) Transient-collisional scheme2) High order harmonic generation by fs IR, viz. laser3) X-ray free electron laser, XFEL
Applications:Surface micromachining, Nano-particle synthesis, Mass-spectrometry, etc
![Page 3: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/3.jpg)
Toolbox: Ultrashort IR, viz. lasers hυ~1eV, pulse duration τL from few cyclesFs-ps XUV – X-ray lasers hυ~0.1-10 keV :1) Transient-collisional scheme2) High order harmonic generation by fs IR, viz. laser3) X-ray free electron laser, XFEL
Applications:Surface micromachining, Nano-particle synthesis, Mass-spectrometry, etc
Fundamental Problems:
(1) Electron-ion non-equilibrium states with highly excited electron subsystem, two-temperature warm dense matter(2T WDM)
(2) Metastable decay, foaming, nanostructuring
![Page 4: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/4.jpg)
Two-temperature WDMAbsorption : hυ electrons (IR,viz. v. X-ray)Electron-electron relaxationElectron-ion relaxationMetastable decayHydrodynamics :Expansion,Transition to metastable state,Nucleation (in solid state v. in liquid state)
time axis
Sequence of stagesAbsorption of photons
e-ee-i
hydrodynamicsPe dominates
1T P =one-tempr.pressure
NucleationSolid
Liquid
![Page 5: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/5.jpg)
IR, viz. versus XUV-X-rayIR, viz. lasers have photons with energies hυ ~ energy of the valence bands, while the X-ray quanta ionizes the internal shellsMetalsSemiconductors and dielectrics :Multi-photon ion-nTunnel ionizationKeldysh expressionElectron impact ionization and avalanche
EFIR, viz.
X-ray
Δ
![Page 6: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/6.jpg)
X-ray photons knock out electrons from the deep levels making holes in the internal shellsAppearance of deep holes triggers the Auger processes While appearance of energetic electrons starts impact ionization
This picture is drawn for substances with the gap. Similar scheme is applicable to metals. In metals energetic electrons finally transfer their energy to conductivity electrons
X-rayion-n
Auger +impaction-n
Forbidden gap
(3/2) k Te
![Page 7: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/7.jpg)
(1) Impact ionization starts immediately with the pulse = we have not wait when ionized electrons accumulate enough energy by inverse Bremsstrahlung to overcome the gap (no significant inverse Bremsstrahlungabsorption), (2) no avalanche, (3) energy conservation
X-rayion-n
Auger +impaction-n
Forbidden gap
(3/2) k Te
Auger
ui1
ui2
EFIR, viz.
X-ray
Δ
![Page 8: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/8.jpg)
Attenuation depth varies in a wide range with hυ. Photon energy of the Ag X-ray laser is between the L-edges for Al and Si. Therefore the attenuation depths for Al (37 nm) and Si (590 nm) are very different.Taken from Henke
![Page 9: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/9.jpg)
We exclude short stage when electrons are non-Maxwellian. The equations are written for electron and ion subsystems which may be described by average concentration of free electrons and two temperatures Te and Ti.
X-rayion-n
Auger +inpaction-n
Forbidden gap
(3/2) k Te
time axis
Sequence of stagesAbsorption of photons
e-ee-i
hydrodynamicsPe dominates
1T P =one-tempr.pressure
NucleationSolid
Liquid
Energy conservation!
Equations are written in Lagrangian coordinate xo
Esume= ne ui2 + Ee, Ee = (3/2) kB Te
![Page 10: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/10.jpg)
We have considered ablation of LiF dielectrics by X-ray laser with 89.3 eV photons and short pulse duration 7 psElectron and phonon thermal conductivity and ambipolardiffusion may be neglected for our time interval <100 psPotential energy of holes ui2 was taken ~ ∆ - width of the gapElectron impact frequency υimp was taken from [Biberman, Vorobyev, Yakubov, 1987; Sobelman, Vainshtein, Yukov,2007]Esum
e=ne ui2+Ee. dotEei=A Ee , A~ 3*1011 s-1
The coefficient of three-body recombination k3 was calculated from condition of detailed equilibrium
![Page 11: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/11.jpg)
For dielectrics thermal conduction and diffusion are small – we can neglect them at our time scale. The averaged equations are
![Page 12: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/12.jpg)
Pulse duration 7 ps, Fabs = 10 mJ/cm2, hυ=89.3 eV
-20 0 20 40 60 80time, ps
0
0.4
0.8
1.2
1.6ne / nat, % 1: ui2=14 eV, Aei=2*1011
2: ui2=14 eV, Aei=9*1011
3: ui2=25 eV, Aei=2*1011
4: Laser source Q(t) [a.u.]
1
2
3
4
-20 0 20 40 60 80time, ps
0
0.5
1
1.5
2
2.5Te , eV
1: ui2=14 eV, Aei=2*1011
2: ui2=14 eV, Aei=9*1011
3: ui2=25 eV, Aei=2*1011
4: Laser source Q(t) [a.u.]
1
2
3
4
Att. depth LiF=28 nm
![Page 13: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/13.jpg)
Simulations show that temperature and pressure rise approximately follows X-ray laser pulse
-20 0 20 40 60 80time, ps
0.2
0.4
0.6
0.8
1Tat , kK
1
23
Room temperature
0 20 40
time, ps0
2
4
6
P, Pat, Pe [ GPa ]
ΔE = 14 eV, Aei = 2*1011 s-1
(1) Pe
(2) Pat
(3) P = Pe + Pat
1
23
![Page 14: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/14.jpg)
To describe spatial profiles we solve equations
We neglect heat conductivity, write Ee except Esume=ne ui2+Ee,
and write e-i exchange dotEea asA1*(Te-Ti) = A1*Te = A*Ee, as Ee = (3/2) k Te, EF is small
-20 0 20 40 60 80time, ps
0
0.4
0.8
1.2
1.6ne / nat, % 1: ui2=14 eV, Aei=2*1011
2: ui2=14 eV, Aei=9*1011
3: ui2=25 eV, Aei=2*1011
4: Laser source Q(t) [a.u.]
1
2
3
4
-20 0 20 40 60time, ps
0
0.5
1
1.5
2
2.5Te , eV
1: ui2=14 eV, 2: ui2=14 eV, 3: ui2=25 eV, 4: Laser sourc
1
2
3
4
![Page 15: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/15.jpg)
To have significant mechanical effect the large pressures are necessaryMaximum pressure is defined by energy absorbed during acoustic response time ts= dT / cs ~ 10 ps
Therefore short pulses are more effective in creation of high pressures
![Page 16: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/16.jpg)
Examples with two-temperature hydrodynamic simulation and one-temperature molecular-dynamics (MD) simulationWe have used power density dotEea calculated by 2T code as input for MD simulation
0 100 200x, nm
-0.8
-0.4
0
0.4
0.8
1.2Pe, P, GPa t = 20 ps, A = 2*1011 s-1
P = Pe + PiPe
τL = 7 ps, F = 10 mJ/cm2, dT = 28 nmTensile
stress
P
Pe
0 50 100 150 200x, nm
-2
-1
0
1
2
p, G
Pa
τL = 7 ps, F = 17 mJ/cm2
t = 5 pst = 10 pst = 20 ps
![Page 17: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/17.jpg)
Temperature field is “frozen” and does not change significantly at acoustic time scale when acoustic wave travels out from laser energy absorption layer
0 50 100 150 200x, nm
-2
-1
0
1
2
p, G
Pa
τL = 7 ps, F = 17 mJ/cm2
t = 5 pst = 10 pst = 20 ps
0 50 100 150 200x, nm
0
200
400
600
800
T, K
τL = 7 ps, F = 17 mJ/cm2
t = 5 pst = 10 pst = 20 ps
![Page 18: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/18.jpg)
Above we have considered:Absorption of X-ray photonsThermalization of electron subsystemTwo-temperature equations describing electron-ion temperature relaxation and hydrodynamic motionNow we can conclude :
0 100 200x, nm
-0.8
-0.4
0
0.4
0.8
1.2Pe, P, GPa t = 20 ps, A = 2*1011 s-1
P = Pe + PiPe
τL = 7 ps, F = 10 mJ/cm2, dT = 28 nmTensile
stress
P
Pe
The amplitude of the tensile stress 8-10 kbar is enough to trigger the spallative ablationMaterial strength for PMMA = 8 kbar, Krasyuk, Vovchenko et al., 2009
![Page 19: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/19.jpg)
X‐ray laser
LiF detectorAg target
Spherical mirrorf = 525 mm
XZ stage
Filter
Images of X‐ray laser spots at different Z positions:
E’XRL = 170 nJ
ΔZ
ΔZ
ΔX
ΔX
LiF detector X‐ray lasera)
c)
b)
‐ 1 0 + 2 + 3+ 1‐ 2‐ 3 Z , mm
+ 4
Fig. 1
Experiments with Experiments with spallativespallative ablationablationby Xby X--ray laserray laser
![Page 20: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/20.jpg)
0 20 40 600
20
40
60
80
Dep
th, n
m
M icrons
0 10 20 30 400
20
40
60
80
Dep
th, n
m
Microns
AFM image of focal spot after irradiation by full (10.2 mJ/cm2) XRL energy
~ 55 nm
~ 55 nm
Fig. 2
![Page 21: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/21.jpg)
AFM image trace
50 um x 50 um
3 laser shots E = 5 mJ/cm2, 8.5x108 W/cm2
50 um x 50 um
300 um x 300 um300 um x 300 um
25 um x 25 um
0 5 10 15 20 25
60
80
100
120
Dep
th, n
m
Microns
50 nm
1 laser shots E = 5 mJ/cm2, 8.5x108 W/cm2
Fig. 3
AFM imageVisible imageVisible image
Luminescent image Luminescent image
![Page 22: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/22.jpg)
Pico-second XRL ablation shows drastic decrease of ablation threshold of energy fluency
Abl
atio
n th
resh
old
(J/c
m2 )
Faenov, Inogamov, Zhakhovskii et al. Appl. Phys. Lett., 94, 231107 (2009)
0.001
0.01
0.1
1
10
4 6 8
12 4 6 8
102 4 6 8
1002
1053nm2ns pulse1ps
0.4ps pulse 46.9nm XRL1.7ns (Italy)
13.9nm XRL7ps pulse (JAEA)
Photon energy of pump light (eV)
![Page 23: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/23.jpg)
Short laser pulse creates stretching and tensile stressLaser may be or optical, or –as was shown above-the X-ray laserP<0 is the reason for nucleation-foaming-nanostructure formationFor optical lasers this has been shown previouslyNow we extend this to the case of X-rays
time axis
Sequence of stagesAbsorption of photons
e-e
e-i
hydrodynamicsPe dominates
1T P =one-tempr.pressure
NucleationSolid
Liquid
Laser-acoustics-nucleation-foaming-nanostructuring : this is development in time
![Page 24: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/24.jpg)
To produce foaming and nanostructures melting is necessary. This is the first conditionThe second condition is: to produce nanostructures we have to be near the ablation threshold, because motion should be slow down significantly to allow to weak surface tension forces to create nanostructuresTwo-temperature hydrodynamic and molecular-dynamics simulations show that at the ablation threshold LiF nucleates in solid stateWe can rise fluence and melt LiF but then the second condition will be violated
![Page 25: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/25.jpg)
As was said above to produce surface nanostructures it is necessary to have (condition 2) near threshold spallative ablation in (condition 1) molten materialOur estimates show that Al is good candidate for this. It has small attenuation depth (37 nm, Henke) for our Ag X-ray laser 89.3 eVAnd strong solid state as was shown in our previous simulation s. Therefore for Al : the condition (1) Fm<Fabl is fulfilled
![Page 26: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/26.jpg)
Our MD simulations and experiment done by Vorobyev and Guo, 2007
![Page 27: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/27.jpg)
![Page 28: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/28.jpg)
![Page 29: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/29.jpg)
Long pulse lasers, Krasyuk, Fortov et al., 2002; Eliezer et al., 2002; Krasyuk, Vovchenko et al., 2009Here short pulses, tauL = 40-200 fs
Glass Al film Laser
Glass Al film
X(t)
![Page 30: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/30.jpg)
Non-trivial pressure wave: two-temperature relaxation, fast melting, rarefaction, expansion of molten layer supporting pressure
![Page 31: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/31.jpg)
![Page 32: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/32.jpg)
![Page 33: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/33.jpg)
![Page 34: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/34.jpg)
![Page 35: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/35.jpg)
![Page 36: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/36.jpg)
![Page 37: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/37.jpg)
![Page 38: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/38.jpg)
Short X-ray pulse produces tensile stress (theory)
Experiments show that X-ray ablation with low threshold exists
Then X-ray laser may produce spallativeablation as it is now well known for optical short pulse lasers
Near ablation threshold this may (if the X-ray Fm < Fabl) cause nanostructuring
0 100 200x, nm
-0.8
-0.4
0
0.4
0.8
1.2Pe, P, GPa t = 20 ps, A = 2*1011 s-1
P = Pe + PiPe
τL = 7 ps, F = 10 mJ/cm2, dT = 28 nmTensile
stress
P
Pe
0 5 10 15 20 25
60
80
100
120
Dep
th, n
m
Microns
50 nm
![Page 39: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/39.jpg)
![Page 40: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/40.jpg)
EoS is necessary to simulate energy absorption (heating) together with dynamicsWe compare EoS for LiF and Al from the cite ..\rusbankcreated by Khishchenko, Lomonosov, Levashov, Fortov, et al.In our form of presentation of equations only Pat and Eat are usedPat = G*Eat and Pat(rho, T=0) are similar for LiF and Al (G=Grueneisen parameter)
0.8 1 1.2 1.4V/V0
-20
0
20
40
P [G
Pa]
Material Strengthsof Al and LiF
Al from Rose EoSLiF from wide-range EoS
P = 0
LiF
LiF strength
The range of strengthsfor crystal or liquid Alat high strain rate (dot V/V)• Therefore we use EOS fo Al
to simulate LiF• The only open question
concerns the material strength for LiF
• LiF is brittle material –its strength should be small in comparison with metals
![Page 41: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/41.jpg)
![Page 42: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/42.jpg)
![Page 43: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/43.jpg)
![Page 44: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/44.jpg)
![Page 45: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/45.jpg)
![Page 46: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/46.jpg)
(1) Temperature rise – it should be fast! How fast? Faster than sonic relaxation(2) Pressure rise(3) Acoustic relaxation: decomposition into waves wave reflection from vacuum boundary of a plane target reflection creates negative pressures (tensile stress)(4) Strength of material: ability to resist to stretching and tensile stress. Limiting strength. Sharp ablation threshold
![Page 47: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/47.jpg)
Thickness of the layer heated by laser is dTSonic relaxation time is ts = dT / csFast means that duration of laser pulse tauL is smaller than ts
T, p
x = 0
dT
Q
![Page 48: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/48.jpg)
Acoustic decomposition: solutions of the wave equation dttP – c2dxxP=0 : P=P+(x+c*t)+P_(x-c*t)Reflection from boundary with vacuum: therefore there are three waves: left, right, and reflected
rightleft
reflected
p
x = 0
P > 0
P < 0
x = 0
pr+l
-ptens
P > 0
P < 0
![Page 49: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/49.jpg)
Ptensile|limiting. This is why there is a sharp threshold Fabl for spallative ablationRupture takes place at a finite depth under vacuum boundary, therefore a finite piece of removed (=ablated) material appears
x = 0F1
F2 > F1
Ptens|lim
P > 0
P < 0
x = 0
F > Fabl
Ptens|lim
dcrat
xP = 0 P > 0
P < 0
![Page 50: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/50.jpg)
Introduction of spallative ablation (Inogamov et al., 1999) solves the puzzle of Newton rings observed in pump-probe experiments at all metals and semiconductors (universality of this phenomenon), Sokolowski-Tintev, von der Linde, et al., 1998Owing to this mechanism combination of two-temperature physics together with thermodynamic properties of condensed material becomes importantThe mechanism explains existence of sharp ablation thresholdThe laser plume has unusual shape with flying cupola around liquid-vapor mixture. Cupola remains in condensed state. Therefore density profile in the plume is non-monotonous Near threshold irradiation forms nanorelief at surface
![Page 51: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/51.jpg)
Our case is: 90 eV photons, tauL = 7 ps, Fluence = 5 – 10 mJ/cm2
Absorption, attenuation length in LiF is 28 nmPhotoionization, primary ions are single charged (Z=1) Li 1s2s, F 1s2 2s 2p5. Z mainly =1 because ion concentration is low (~ 1%)
Auger
ui1
ui2• Auger
recombination from primary ions to Z=1 ions with a hole at external electronic shell
![Page 52: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/52.jpg)
Auger
ui1
ui2
• Ions gradually disappear as result of cooling of initially hot electron subsystem due to energy transfer to cold atoms
• Q/ui2 is a X-ray source of free electrons, nuimp =<v*sigma>nat is a frequency of ionization by an electron impact, kapparec is a coefficient of three body recombination
• Ees is total energy of electron subsystem, it is a sum of potential
and thermal energies• dot Eea is an energy exchange rate between atomic and electron
subsystems. This is the only term taking away energy of electron subsystem – radiation loses are small at our time scale
![Page 53: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/53.jpg)
Increase and decrease of free electron population: influence of ionic potential ui2 is rather small, while influence of the coefficient A in dot_Eea=A*Ee is rather significant. The rate dot_Eea is connected with almost elastic collisions of the conductivity band electrons with atomsThis is solution of ODE for {ne, Te} neglecting acoustic effects
![Page 54: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/54.jpg)
System of hydrodynamic equations: two thermal eqs. for Eeand Eat and eq. for momentumWe neglect here equation for neCorresponding space homogeneous eq. isWe call this eq. {Ee}It has main terms: X-ray heating Q and e a cooling
![Page 55: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/55.jpg)
The worst case with small A and therefore slow e-aenergy transfer is shown. Conclusion from this comparison is: the {Ee} approach may be used for estimates of pressure amplitudes
![Page 56: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/56.jpg)
Measured ablation threshold is surprisingly low! Only 10 mJ/cm2. To understand that this is indeed unexpected it is enough to compare this threshold with typical thresholds of several thousands mJ/cm2 for dielectrics for IR-vis. lasers (fs-ns duration) and with 100 mJ/cm2
threshold for X-ray 1.7 ns laser duration is important (our XRL has tauL = 7 ps)The crater depth is approximately 50 nm
![Page 57: N.A.Inogamov, V.V.Zhakhovskii, V.A.Khokhlov, V.V.Shepelev ... fileand dielectrics : Multi-photon ion-n ... applicable to metals. In metals energetic electrons finally transfer their](https://reader030.vdocuments.mx/reader030/viewer/2022040220/5e1f3521a1ce3a69a817ae79/html5/thumbnails/57.jpg)
Experimentally very low ablation threshold has been foundTheory explains this as transition from evaporative to spallativeablation