1. 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

2. 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

3. 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

4. I. Femtosecond laser irradiation creates the unique state of matter

5. 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

6. Unique state of metals under the action of femtosecond laser irradiation. Dependence of a melting temperature of a simple metal on the electron temperature The only state suitable to investigate dependence of a melting on the electron temperatures

7. Femtosecond laser irradiation creates unique conditions for phase transition processes

8. Specific features of melting under the action of femtosecond lase irradiation (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 ( ) 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 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)

9. DETERMINING INTRINSIC PARAMETERS OF METALS. AL, ELECTRON-ELECTRON INTERACTION. USE OF REFLECTIVITY

10. 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 expansion crater

11. 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

12. Evolution of Optical Parameters after the Pump Impact Changes in the reflectivity and the phase of reflected probe light after the pump action, Au 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

13. 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 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

14. 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)

15. Exitation of 5d-electrons into 6s-6p-bands Equation for the chemical potential 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

16. Exitation of 5d-electrons into 6s-6p-bands Increase of the number of electrons in 6s-p bands

17. Band structure, plasma frequency and electron collision frequency Describing the experimental data on a phase shift and raflectivity Z=N e6s ~ (2-4) для T e ~ (5-10) eV

18. 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

19. 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

20. Femtosecond laser irradiation results in specific forms of ablation

21. Two-temperature hydrodynamics approach 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

22. Initial state of a crystal for two-temperature hydrodynamics. Pulse has a gaussian temporal form.

23. Target parameters at instant t=0, corresponding to the fluence maximum

24. Target parameters immediately at the end of laser pulse (t=0.3ps)

25. Parameters of a target at the instant of the equalization of electron and ion temperatures T e =T i

26. 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.

27. Embedded atom potential for aluminum 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

28. 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

29. 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

30. Molecular dynamics simulation of the ablation pattern above the ablation threshold. Formation of the spalled cupola c S t / d T = 0.72 2.13.7 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

31. Microinterferometer monitoring of the ablating target surface

32. 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

33. 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.

34. 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.

35. Мolecular dynamics simulation of the laser ablation of bulk aluminum The wide Al target with cross section L y x L z =122x14 nm 2 heated up to the T 0 (0)=5 kK at the small heated depth d T =18.6 nm. The total simulation time is 153.5 ps. 0.1ps pump

36. 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

37. 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. 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. 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 simulation 12 of Aluminum foil under fsLP with absorbed fluence F = 0.15 J/cm 2.

38. Femtosecond laser irradiation leads to the formation of nanorelief on a target surface

39. 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.

40. 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.

41. 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

42. 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)