OSA's Digital Library

Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 26 — Dec. 26, 2005
  • pp: 10597–10607
« Show journal navigation

Plasma evolution during metal ablation with ultrashort laser pulses

J. König, S. Nolte, and A. Tünnermann  »View Author Affiliations


Optics Express, Vol. 13, Issue 26, pp. 10597-10607 (2005)
http://dx.doi.org/10.1364/OPEX.13.010597


View Full Text Article

Acrobat PDF (1059 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We report on time-resolved measurements of the plasma evolution during metal ablation with ultrashort laser pulses in the range from 200 fs to 3.3 ps. The plasma transmission exhibits two distinctive minima. Almost total attenuation is observed a few nanoseconds after the ablation pulse, while a second decrease of the transmission to approximately 50% is observed after about 150 ns. Images taken with a gated ICCD-camera confirm these data and allow determining the expansion velocity of the plasma plume. The attenuation in the first nanoseconds can be attributed to electrons and sublimated mass emitted from the target surface, while attenuation after several 10 ns is due to particles and droplets after a thermal boiling process. The possibility of a normal or an explosive boiling process, also called phase explosion, is discussed. Despite of the physical insight into the ablation process, these data provide valuable information for scaling the speed of ultrashort pulse laser materials processing in a fluence regime of several J/cm2 since they allow estimating the maximum usable pulse repetition rate.

© 2005 Optical Society of America

1. Introduction

Micro-machining using ultrashort laser pulses has attracted much interest in recent years, since it promises very precise and practically melting free processing of nearly all kinds of materials. Meanwhile the achieved processing quality meets industrial demands; however, processing speed is still far from an economical industrial use. Ultrashort pulse lasers with significantly higher average power and repetition rate than currently available will be required to overcome this limitation [1

1 . F. Dausinger , F. Lichter , and H. Lubatschowski , Femtosecond Technology for Technical and Medical Applications , ( Springer, Heidelberg , 2004 ) [CrossRef]

]. An upper limit for the highest repetition rate usable is given by the interaction of the generated plasma with succeeding laser pulses, since this will distort or shield the laser beam.

In addition, the ablation plasma is a field of interest on its own since the invention of lasers. As a consequence, ablation with laser radiation from cw to pulse durations in the nanosecond regime is discussed in various publications [2

2 . D. Bäuerle , Laser Processing and Chemistry , 3rd ed. ( Springer, Berlin-Heidelberg , 2000 )

]. In the past years the interest in the ablation characteristics of ultrashort laser pulses has grown. Although ablation thresholds and rates have been determined for different materials and experimental conditions, the time scales involved have been measured only in few studies [1

1 . F. Dausinger , F. Lichter , and H. Lubatschowski , Femtosecond Technology for Technical and Medical Applications , ( Springer, Heidelberg , 2004 ) [CrossRef]

, 3–8

3 . R. E. Russo , X. L. Mao , H. C. Liu , J. H. Yoo , and S. S. Mao , “ Time-resolved plasma diagnostics and mass removal during single-pulse laser ablation ,” Appl. Phys. A 69 , S887 – S894 ( 1999 ) [CrossRef]

]. Based on this ultrashort laser pulse ablation can be understood as a process over several orders of magnitude in time. In metals the initial absorption of the laser pulse happens on a femtosecond time scale by absorption of free electrons [2

2 . D. Bäuerle , Laser Processing and Chemistry , 3rd ed. ( Springer, Berlin-Heidelberg , 2000 )

]. During and after the absorption electrons are emitted from the target surface by photoelectric and thermionic effects as shown in experiments with pulse durations of a few tens of picoseconds [3

3 . R. E. Russo , X. L. Mao , H. C. Liu , J. H. Yoo , and S. S. Mao , “ Time-resolved plasma diagnostics and mass removal during single-pulse laser ablation ,” Appl. Phys. A 69 , S887 – S894 ( 1999 ) [CrossRef]

, 4

4 . S. S. Mao , X. Mao , R. Greif , and R. E. Russo , “ Initation of an early-stage plasma during picosecond laser ablation of solids ,” Appl. Phys. Lett. 77 , 2464 – 2466 ( 2000 ) [CrossRef]

]. After tens of picoseconds a plasma plume appears, consisting of electrons, and atomic and ionic mass [3

3 . R. E. Russo , X. L. Mao , H. C. Liu , J. H. Yoo , and S. S. Mao , “ Time-resolved plasma diagnostics and mass removal during single-pulse laser ablation ,” Appl. Phys. A 69 , S887 – S894 ( 1999 ) [CrossRef]

, 4

4 . S. S. Mao , X. Mao , R. Greif , and R. E. Russo , “ Initation of an early-stage plasma during picosecond laser ablation of solids ,” Appl. Phys. Lett. 77 , 2464 – 2466 ( 2000 ) [CrossRef]

]. In some experiments with pulse durations of several nanoseconds the ejection of clusters and larger particles is observed up to several hundred nanoseconds after the laser pulse. This delayed particle ejection is assumed to be phase explosion after homogenous nucleation [3

3 . R. E. Russo , X. L. Mao , H. C. Liu , J. H. Yoo , and S. S. Mao , “ Time-resolved plasma diagnostics and mass removal during single-pulse laser ablation ,” Appl. Phys. A 69 , S887 – S894 ( 1999 ) [CrossRef]

, 9

9 . R. Kelly and A. Miotello , “ Contribution of vaporization and boiling to thermal-spike sputtering by ions or laser pulses ,” Phys. Rev. E 60 , 2616 – 2625 ( 1999 ) [CrossRef]

, 10

10 . X. Xu and D. A. Willis , “ Non-Equilibrium Phase Change in Metal Induced by Nanosecond Pulsed Laser Irradiation ,” J. Heat Transfer 124 , 293 – 298 ( 2002 ) [CrossRef]

]. All this material is conglomerating in the atmosphere above the target surface and incident light will be absorbed, scattered and reflected by the different components.

The goal of this work is to determine the timescales of the ablation process for the micro-machining of metals with ultrashort laser pulses in the regime from 200 fs to 3.3 ps. The investigation of phase explosion for pulse durations in the femtosecond and picosecond regime is a special point of interest. Therefore, the plasma expansion is imaged with a fast gated ICCD-camera and light attenuation is measured in a pump-probe setup by the transmission of a fs-pulse train through the plasma. The experiments are carried out with different target materials and at different pulse energies and probe wavelengths. The experimental data is compared with theoretical estimations of plasma expansion and phase explosion after homogenous nucleation. These experiments allow to estimate a maximum repetition rate at which micro-machining can be realized without plasma attenuation effects.

2. Experimental realization

A schematic of the experimental setup for the time-resolved pump-probe measurements is shown in Fig. 1. The ablation pulse is generated by a commercial CPA-laser system (Spectra-Physics; “Spitfire”) with an energy up to 580 μJ at a wavelength of about 800 nm and a repetition rate of 1 kHz. The pulse energy is varied by a half-wave plate in combination with a polarizer, and single pulses are picked with a fast mechanical shutter. Pulse duration can be varied continuously from 200 fs to 3.3 ps without changing substantial beam parameters by adjusting the pulse compressor. These pulses are focused by an achromatic lens (f=100 mm) on the target surface, resulting in an ablation diameter between 35 μm and 60 μm depending on the pulse energy and focal plane.

The probe beam, which is parallel to the sample surface, is focused by an achromatic lens (f=20 mm) above the target surface, in the way that the beam waist is central with respect to the ablation spot position. A second lens (f=15 mm) after the sample collects the probe beam and directs it onto a photodiode (Femto, “PRX-500M-Si-DC”). The distance between the probe beam and the target surface (height) is adjusted that the photodiode signal observed without a target is twice the signal when the target is present.

Fig. 1. Schematic experimental diagram of time-resolved plasma attenuation measurements.

In case of measurements observing the first few nanoseconds of the ablation process a frequency-doubled part of the ablation pulse with 400 nm wavelength and 200 fs duration is used as the probe pulse. A defined time delay between ablation and probe pulse is changed by a variable delay line. For longer time scales up to the microsecond range this setup is impracticable. Thus, an ultrashort pulse laser oscillator with 75 MHz repetition rate, pulse duration of 200 fs and fundamental wavelength of 1050 nm is used as probe pulse source in this case. Although the ablation and probe pulses are not synchronized in this case, the high repetition rate allows a high resolution sampling of the transmission. This way, the whole ablation process can be observed using a single ablation pulse.

Different filter arrangements consisting of dielectric mirrors, color glass filters and metal interference filters are used to suppress the scattered light of the ablation laser pulse. For measurements of the influence of different probe wavelengths on the attenuation the second harmonic of the probe beam was generated and the filter arrangement in front of the photoreceiver was changed accordingly. The high variance in the raw data was reduced by background subtraction and referencing.

For space-resolved attenuation measurements the photoreceiver was replaced by a gated ICCD-camera (LaVision, “PicoStar TH7863”). In this case microscope objectives with numerical apertures of 0.69 and 0.85 have been used in order to image the plasma plume. Illumination was realized by the probe beam.

3. Processes involved in ultrashort pulse ablation of metals

The ablation of metals with intense ultrashort laser pulses involves a complex sequence of different processes over several orders of magnitude in time. In a first step the laser light is absorbed by free electrons due to inverse Bremsstrahlung in the skin layer lopt.

This is followed by a fast energy relaxation within the electron subsystem, thermal diffusion into the substrate and energy transfer to the lattice owing to electron-phonon coupling. In all practical cases these processes can be described by a one-dimensional two-temperature model, where the electrons and the lattice are described by their temperatures [11–13

11 . B.N. Chichkov , C. Momma , S. Nolte , F. von Alvensleben , and A. Tünnermann , “ Femtosecond, picosecond and nanosecond laser ablation of solids ,” Appl. Phys. A 63 , 109 – 115 ( 1996 ) [CrossRef]

].

After the energy transfer from the electrons to the lattice an equilibrium temperature is reached. Time evolution of the equilibrium temperature after relaxation can be described by the one-dimensional heat equation of uniform irradiation. The surface temperature Ts decreases in this case as Ts~f 1/2[2

2 . D. Bäuerle , Laser Processing and Chemistry , 3rd ed. ( Springer, Berlin-Heidelberg , 2000 )

].

Parallel to this temperature evolution several thermal and non-thermal ablation processes are starting and developing. As the first ablation process during the laser pulse photoelectric emission of electrons from the target surface can be expected. Under our experimental conditions the combined energy of 3–4 photons is necessary to overcome the work function of the metals used [4

4 . S. S. Mao , X. Mao , R. Greif , and R. E. Russo , “ Initation of an early-stage plasma during picosecond laser ablation of solids ,” Appl. Phys. Lett. 77 , 2464 – 2466 ( 2000 ) [CrossRef]

].

After the laser pulse thermionic emission of electrons from the surface becomes evident. The flux rate of this ablation process can by estimated by the Richardson law [4

4 . S. S. Mao , X. Mao , R. Greif , and R. E. Russo , “ Initation of an early-stage plasma during picosecond laser ablation of solids ,” Appl. Phys. Lett. 77 , 2464 – 2466 ( 2000 ) [CrossRef]

, 13

13 . S. I. Anisimov and B. S. Luk’yanchuk , “ Selected problems of laser ablation theory ,” Physics-Uspekhi 45 3 , 293 – 324 ( 2002 ) [CrossRef]

]. Atomic and ionic matter can be ablated at same timescale by sublimation from the surface or direct transition in the plasma state at higher laser energy densities [6

6 . K. Sokolowski-Tinten , J. Bialkowski , A. Cavalleri , M. Boing , H. Schüler , and D. von der Linde , “ Dynamics of femtosecond laser induced abaltion from solid surfaces ,” in High-Power Laser Ablation , C. R. Phipps , ed., Proc. SPIE 3343 , 46 – 57 ( 1998 ) [CrossRef]

].

At energy densities close to 1 J/cm2 i.e. below the threshold for plasma formation, and pulse durations up to 5 ps a rarefaction wave is observed [6

6 . K. Sokolowski-Tinten , J. Bialkowski , A. Cavalleri , M. Boing , H. Schüler , and D. von der Linde , “ Dynamics of femtosecond laser induced abaltion from solid surfaces ,” in High-Power Laser Ablation , C. R. Phipps , ed., Proc. SPIE 3343 , 46 – 57 ( 1998 ) [CrossRef]

]. In this case very high heating rates cause a rapid melting and the transition to an overcritical fluid near the thermodynamic critical temperature, so the material is in a non-equilibrium state of high pressure and high temperature [8

8 . B. Rethfeld , K. Sokolowski-Tinten , V. V. Temnov , S. I. Kudryashov , J. Bialkowski , A. Cavalleri , and D. von der Linde , “ Ablation dynamics of solids heated by femtosecond laser pulses ,” in Nonresonant Laser-Matter Interaction , M. N. Libenson , ed., Proc. SPIE 4423 , 186 – 196 ( 2001 ) [CrossRef]

]. The expansion starts with a rarefaction wave that proceeds from the surface into the material. After reflection at the unperturbed substrate the rarefaction wave travels towards the surrounding atmosphere. This results in a thin layer of high density, which is moving away from the target in front of a low density region. The low density region is assumed to be a liquid-gas mixture caused by homogenous nucleation within a few tens of picoseconds [7

7 . K. Sokolowski-Tinten , J. Bialkowski , M. Boing , A. Cavalleri , and D. von der Linde , “ Bulk phase explosion and surface boiling during short pulse laser ablation of semiconductors ,” in Quantum Electronics and Laser Science Conference ( OSA Technical Digest, Optical Society of America, Washington, DC , 1999 ) pp. 231 – 232

].

The same process of homogenous nucleation is used to interpret the emission of particles and droplets, which are observed several nanoseconds after application of nanosecond pulses [3

3 . R. E. Russo , X. L. Mao , H. C. Liu , J. H. Yoo , and S. S. Mao , “ Time-resolved plasma diagnostics and mass removal during single-pulse laser ablation ,” Appl. Phys. A 69 , S887 – S894 ( 1999 ) [CrossRef]

, 9

9 . R. Kelly and A. Miotello , “ Contribution of vaporization and boiling to thermal-spike sputtering by ions or laser pulses ,” Phys. Rev. E 60 , 2616 – 2625 ( 1999 ) [CrossRef]

, 10

10 . X. Xu and D. A. Willis , “ Non-Equilibrium Phase Change in Metal Induced by Nanosecond Pulsed Laser Irradiation ,” J. Heat Transfer 124 , 293 – 298 ( 2002 ) [CrossRef]

]. In this case the ablation is assumed to be due to phase explosion caused by homogenous nucleation in the superheated melt with a time lag τhn. In this time τhn vapor embryos grow to nuclei of critical size and the liquid breaks down into a liquid-gas mixture, which expands in an explosive way. The rate Jhn for the generation of bubbles with critical size is given by [10

10 . X. Xu and D. A. Willis , “ Non-Equilibrium Phase Change in Metal Induced by Nanosecond Pulsed Laser Irradiation ,” J. Heat Transfer 124 , 293 – 298 ( 2002 ) [CrossRef]

, 14

14 . V. P. Carey , Liquid-Vapor Phase-Change Phenomena , ( Hemisphere, Washington , 1992 )

]:

Jhn(t)=Nl3χπ·mexp(16πχ3kBTl(t)(pve(Tl)pl(Tl)))exp(τhn(Tl)t)
(1)

The surface tension χ, the mass of one atom/molecule m and the number of liquid molecules per unit volume Nl are material dependent parameters. The pressure in the vapor embryo pve and in the liquid pl are both functions of the temperature Tl in the melt as described in Ref. [14

14 . V. P. Carey , Liquid-Vapor Phase-Change Phenomena , ( Hemisphere, Washington , 1992 )

]. For temperatures Tl above 0.8 Tc the thermodynamic stability vanishes and drastically affects a lot of material properties [10

10 . X. Xu and D. A. Willis , “ Non-Equilibrium Phase Change in Metal Induced by Nanosecond Pulsed Laser Irradiation ,” J. Heat Transfer 124 , 293 – 298 ( 2002 ) [CrossRef]

]. The thermodynamic critical temperature Tc, above which it is no longer possible to liquefy a substance by increasing the pressure, can be estimated to about 6000 K for the metals aluminum, copper and iron [15

15 . N. M. Bulgakova and A. V. Bulgakov , “ Pulsed laser ablation of solids: transition from normal vaporization to phase explosion ,” Appl. Phys. A 73 , 199 – 208 ( 2001 ) [CrossRef]

].

Beside these aforementioned processes material can be ablated on nanosecond timescale and longer by evaporation and “normal” boiling after heterogeneous nucleation [9

9 . R. Kelly and A. Miotello , “ Contribution of vaporization and boiling to thermal-spike sputtering by ions or laser pulses ,” Phys. Rev. E 60 , 2616 – 2625 ( 1999 ) [CrossRef]

]. Surface evaporation can be approximated by the Hertz-Knudsen equation and the Clausius-Clapeyron relation, which describes the saturated vapor pressure [2

2 . D. Bäuerle , Laser Processing and Chemistry , 3rd ed. ( Springer, Berlin-Heidelberg , 2000 )

]. However, calculations for metals above the boiling temperature result in a removal of only several atom layers in 100 ns [9

9 . R. Kelly and A. Miotello , “ Contribution of vaporization and boiling to thermal-spike sputtering by ions or laser pulses ,” Phys. Rev. E 60 , 2616 – 2625 ( 1999 ) [CrossRef]

]. Therefore, this process seems to be negligible for short timescales. Concerning normal boiling heterogeneous nucleation in the liquid is involved. Vapor embryos are initiated from a variety of disturbances such as gas or solid impurities, defects or an enclosing solid surface [9

9 . R. Kelly and A. Miotello , “ Contribution of vaporization and boiling to thermal-spike sputtering by ions or laser pulses ,” Phys. Rev. E 60 , 2616 – 2625 ( 1999 ) [CrossRef]

]. Once formed they grow rapidly (~t) and tend to diffuse and escape from the outer surface. Here, calculations for metals at twice the melting temperature result in diffusion distances of below 1 nm in 100 ns [9

9 . R. Kelly and A. Miotello , “ Contribution of vaporization and boiling to thermal-spike sputtering by ions or laser pulses ,” Phys. Rev. E 60 , 2616 – 2625 ( 1999 ) [CrossRef]

]. Therefore, normal boiling is also not expected to have significant contribution for short time scale <1 μs [9

9 . R. Kelly and A. Miotello , “ Contribution of vaporization and boiling to thermal-spike sputtering by ions or laser pulses ,” Phys. Rev. E 60 , 2616 – 2625 ( 1999 ) [CrossRef]

].

In contrast to these calculations experiments on gallium arsenide with 100 fs ablation pulses at fluences below the plasma formation threshold show bubble-like structures in the liquid [7

7 . K. Sokolowski-Tinten , J. Bialkowski , M. Boing , A. Cavalleri , and D. von der Linde , “ Bulk phase explosion and surface boiling during short pulse laser ablation of semiconductors ,” in Quantum Electronics and Laser Science Conference ( OSA Technical Digest, Optical Society of America, Washington, DC , 1999 ) pp. 231 – 232

]. These bubbles appear about 20 ns after the ablation pulse and grow linear in time. Both observations lead to the assumption of heterogeneous nucleation at the surface of the nonablated liquid [7

7 . K. Sokolowski-Tinten , J. Bialkowski , M. Boing , A. Cavalleri , and D. von der Linde , “ Bulk phase explosion and surface boiling during short pulse laser ablation of semiconductors ,” in Quantum Electronics and Laser Science Conference ( OSA Technical Digest, Optical Society of America, Washington, DC , 1999 ) pp. 231 – 232

]. Based on these contradictory results heterogeneous nucleation should not be neglected ab initio.

4. Results and discussion

4.1 Plasma luminescence

In order to measure the luminescence of the ablation plume of C75 steel 200 fs pulses with a fluence of 20 J/cm2 have been focused onto the sample surface, and the plasma luminescence has been recorded using the ICCD camera with a gate time of 4 ns. Curve fitting with a Gaussian distribution for the vertical and horizontal cross section through the maximum yields the intensity and the width for each delay time.

Fig. 2. Temporal evolution of the plasma luminescence in horizontal and vertical direction for the ablation of C75 steel with a pulse duration of 200 fs and a fluence of 20 J/cm2.

In Fig. 2 the relative intensity and width of the plasma luminescence is shown for delay times up to 120 ns. The intensity and the horizontal width each show two maxima at 20 ns and 50 ns. After the second maximum the intensity decreases nearly according to ~t -1,9. The same time dependence was observed for the continuum emission in laser-induced plasma spectroscopy experiments for the ablation of aluminum using pulses with a duration of 500 fs and 5 ps duration and a fluence of about 20 J/cm2 [16

16 . B. Le Drogoff , J. Margot , Vidal F. , S. Laville , M. Chaker , M. Sabsabi , T. W. Johnson , and O. Barthelemy , “ Influence of the laser pulse duration on laser-produced plasma properties ,” Plasma Sources Sci. Technol. 13 , 223 – 230 ( 2004 ) [CrossRef]

]. In the vertical direction this behavior is by far not that much pronounced, which is probably due to the fact that the particle emission is not isotropic.

Based on this it can be concluded that the ablation process can be divided into two stages of emission from the target surface separated about 30 ns. The stronger plasma emission at about 50 ns after the ablation pulse supports the assumption of a higher temperature or a higher mass density in the second stage of ablation.

4.2 Expansion of ablated material

The expansion R(t) of the ablated material at a certain time t can be obtained from images of the fast ICCD-camera in the pump-probe transmission setup shown in Fig. 1. The normalized spatial distribution of the transmitted light 4 ns after the ablation pulse (pulse duration 200 fs, fluence 20 J/cm2) is shown in Fig. 3(a). The width of the attenuation region is about the spot diameter and the height amounts to ~13 μm. With increasing time this region is expanding and the transmission increases. After 40 ns a second region can be observed in the images, which expands with nearly the same velocity. Fig. 3(b) shows these two regions 90 ns after the ablation pulse. At this time the first region is nearly faded and shows a higher transmission than the inner region. In the following we call the leading barrier between atmosphere and the faded region “shock wave front” and the barrier to the following region “vapor front”. This terminology is analog to the case of nanosecond ablation and will be explained below.

Fig. 3. (a) Transmission through the plasma 4 ns after the ablation pulse at a probe wavelength of 400 nm. (b): Transmission through the plasma 90 ns after the ablation pulse at a probe wavelength of 525 nm. The shock wave front is marked with a red dotted line on the left side of the image. Both Images were taken with a gated ICCD-Camera during the ablation of C75 steel with 200 fs pulses at an energy density of 20 J/cm2. The target surface is marked with a white line.

The expansion R(t) of the ablated material was determined based on the ICCD-camera images at different delay times and plotted in Fig. 4 for the horizontal, i.e. parallel to the surface, and vertical direction. The expansion of shock wave and vapor front is symmetric to the beam axis, but not completely spherical. Vertical expansion is in this case faster than horizontal. Shock wave and vapor front are expanding with a time delay of about 40 ns.

Fig. 4. Expansion of shock wave and vapor front during the ablation of C75 steel using a pulse duration of 200 fs and an energy density of 20 J/cm2. Expansion of the shock wave is plotted in blue colors, dark blue for vertical, i.e. normal to surface, and light blue for horizontal directions. Expansion of the second ablation front is plotted in red colors.

The vertical expansion can be described well by a combined propagation model of shock wave and vapor plume in gas for nanosecond laser pulses [2

2 . D. Bäuerle , Laser Processing and Chemistry , 3rd ed. ( Springer, Berlin-Heidelberg , 2000 )

]. This model assumes a linear expansion of the shock wave in the first nanoseconds similar to the vacuum case like Eq. (2). A transition from free expansion like in vacuum to expansion in gases occurs, when the mass of the vapor plume Mv is comparable to the mass of the shock wave ρg Rsw and is described by Eqs. (3).

linearexpansionsimilartovacuum0<t<(M5ρg2Esw3)16R(t)(EswζgMv)12·t
(2)
expansioningases(Mv5ρg2Esw3)16<t<(Esw2ρg3pg5)16R(t)ξsw(Eswρg·t2)n
(3)

Here Esw is the total energy of the shock wave, ρg the density of the ambient gas, ζg, ξsw and n are coefficients depending on the ambient gas and the expansion symmetry [2

2 . D. Bäuerle , Laser Processing and Chemistry , 3rd ed. ( Springer, Berlin-Heidelberg , 2000 )

]. In the case of an isentropic plume, spherical expansion and air atmosphere these coefficients can be approximated by ζg≈3/20, ξsw≈1 and n= 1/5 [2

2 . D. Bäuerle , Laser Processing and Chemistry , 3rd ed. ( Springer, Berlin-Heidelberg , 2000 )

].

Curve fitting of R(t) to the experimental data for the different regimes according to Eqs. (2)–(3) is shown in Fig. 4. The obtained values are Esw,≈5.5 μJ (≈1% of laser pulse energy), Mp≈5·10-12 kg (^ 0,2 μm average ablation depth). This results in an initial expansion velocity of 2.8 km/s normal to the sample surface and about 1.5 km/s parallel to surface direction for the ablation of C75 steel with 200 fs pulses at an energy density of 20 J/cm2. The transition from linear expansion to expansion in gases occurs at t≈30 ns.

Similar values of 4.6 km/s in longitudinal and 3 km/s in transversal direction were obtained for the ablation of copper with pulse durations between 70 fs and 10 ps at a fluence of 21 J/cm2 using luminosity measurements [5

5 . B. Salle , O. Gobert , P. Meynadier , M. Perdrix , G. Petite , and A. Semerok , “ Femtosecond and picosecond laser microablation: ablation efficiency and laser microplasma expansion ,” Appl. Phys. A 69 , S381 – S383 ( 1999 ) [CrossRef]

]. No dependency on the pulse duration was observed in that case. The graphs of plasma evolution shown in Ref. [5

5 . B. Salle , O. Gobert , P. Meynadier , M. Perdrix , G. Petite , and A. Semerok , “ Femtosecond and picosecond laser microablation: ablation efficiency and laser microplasma expansion ,” Appl. Phys. A 69 , S381 – S383 ( 1999 ) [CrossRef]

] indicate a reduction of expansion velocity after 25 ns. This is in rather good agreement with the transition from linear expansion to expansion in gases and confirms our results of shock wave expansion.

The interpretation of expansion based on the images at different time delays and the theoretical model leads to the assumption that the ablation process consists of two parts. These parts are separated in time by about 40 ns, what is close to the aforementioned results of the plasma luminescence measurements. Based on the theoretical expansion model of nanosecond pulse ablation and the described processes of ultrashort pulse ablation in section 3 we assume in the first stage plasma formation by direct ionization, sublimation, photoelectric and thermionic electron emission. The high temperatures and pressures cause further gas- and hydrodynamic effects and are the origin of the observed shock wave. Slower thermal processes like vaporization and boiling cause the formation of an expanding vapor plume.

4.3 Plasma Transmission

Collecting the transmitted light of laser pulses with defined temporal separation on a fast photodiode allows to trace the plasma transmission in the probe region. For a probe region directly above the sample surface, i.e., from the target surface up to about 14 micrometers, the plasma transmission measurements reveal a distribution of two minima as shown in Fig. 5(a) for an Aluminum target.

Fig. 5. (a) Temporal transmission of probe pulses with a wavelength of 400 nm for the ablation of Aluminum with 200 fs pulses at a fluence of 17 J/cm2. (b): Temporal transmission of probe pulses with a wavelength of 1050 nm for ablation with 3.3 ps pulses at 18 J/cm2. Data for copper are marked red, data for steel (1.00344) blue. In both graphs the experimental data are plotted in dots, while results of simulations are shown as lines.

The first transmission minimum is reached after about 5 ns and reaches almost 100% attenuation for an ablation pulse energy density of 17 J/cm2 (i.e. 160 μJ pulse energy at 35 μm beam diameter) within the experimental variance.

The second minimum with a reduction in transmission down to 60% follows 100 – 200 ns later. After the second minimum the transmission increases to the initial value after about 2 – 3 μs.

In Fig. 5(b) the plasma transmission is recorded for copper and steel targets. Both materials show the same two minima as observed for aluminum in Fig. 5(a). In case of steel the probe pulse attenuation after about 150 ns is 20% higher than for the copper target.

Detailed investigations using different laser energy densities show a significant influence on the height of the second transmission minimum, as seen in Fig. 6(a). The transmission is reduced from about 90% at 0,4 J/cm2 to 65% at 18 J/cm2 in the interval of the second minimum. No difference between pulse durations of 200 fs and 3,3 ps could be observed in further measurements.

By frequency doubling the probe laser beam the transmission through the plasma plume at a wavelength of 525 nm has been determined (Fig. 6(b)). Because a synchronization of these two mode-locked laser systems was not possible, the resolution is limited by the pulse repetition time of 14 ns. Thus changes in the transmission for the first minimum within 10 ns can not be resolved in this case. However, even in the second transmission minimum no obvious differences compared to a probe wavelength of 1050 nm are visible. Thus the source of this attenuation peak can not be caused by free electrons, which would give rise to a strong wavelength dependence. A similar argument holds true for scattering and reflection from particles smaller than the wavelength λ (i.e. Rayleigh scattering). In this case the transmitted intensity I should show a dependency ~λ -4. However, Mie scattering from particles larger than the wavelength λ is a possible description. Thus, we assume that the attenuation of the probe beam is dominated by Mie scattering from ablated clusters and droplets, similar to results in Ref. [3

3 . R. E. Russo , X. L. Mao , H. C. Liu , J. H. Yoo , and S. S. Mao , “ Time-resolved plasma diagnostics and mass removal during single-pulse laser ablation ,” Appl. Phys. A 69 , S887 – S894 ( 1999 ) [CrossRef]

].

Fig. 6. (a) Temporal transmission of probe pulses with a wavelength of 1050 nm in a steel (1.00344) plasma ablated with 3.3 ps pulse duration. The fluence was changed from 0.4 J/cm2 (green dots), 4 J/cm2 (red dots), 11 J/cm2 (blue dots) to 18 J/cm2 (black dots). (b): Attenuation curves for different probe wavelengths of 525 nm (green) and 1050 nm (red). Calculations are plotted as lines.

According to the abovementioned ablation processes and the time scales in our measurements we assume attenuation of the probe pulses in the first nanoseconds by absorption in a dense plasma. This plasma evolves from surface electron emission, sublimation and direct transition in the plasma state of a skin layer on the order of the optical absorption depth lopt.

Ablation by a rarefaction wave is also a possible process, but the existence at the fluence used is not proven [8

8 . B. Rethfeld , K. Sokolowski-Tinten , V. V. Temnov , S. I. Kudryashov , J. Bialkowski , A. Cavalleri , and D. von der Linde , “ Ablation dynamics of solids heated by femtosecond laser pulses ,” in Nonresonant Laser-Matter Interaction , M. N. Libenson , ed., Proc. SPIE 4423 , 186 – 196 ( 2001 ) [CrossRef]

]. Nevertheless, it can be expected that the heated material will expand and be ablated if the pressure conditions allow this.

For the theoretical description of the first nanoseconds in our experiments we assume absorption in the plasma plume by inverse Bremsstrahlung with a high degree of single ionization, described by [2

2 . D. Bäuerle , Laser Processing and Chemistry , 3rd ed. ( Springer, Berlin-Heidelberg , 2000 )

]:

αIB[cm1]1.37·1035λ[μm]3Ne[cm3]2Te[K]{1exp(ħωkBTe)}
(4)

Electron density Ne and temperature Te decrease with expansion of the plasma R(t) from the heated skin layer with thickness lopt. This can be approximated including Eq. (2) and assuming linear expansion by [3

3 . R. E. Russo , X. L. Mao , H. C. Liu , J. H. Yoo , and S. S. Mao , “ Time-resolved plasma diagnostics and mass removal during single-pulse laser ablation ,” Appl. Phys. A 69 , S887 – S894 ( 1999 ) [CrossRef]

, 18

18 . W. Theobald , R. Häβner , R. Kingham , R. Sauerbrey , R. Fehr , D. O. Gericke , M. Schlanges , W.-D. Kraeft, and K. Ishikawa , “ Electron densities, temperatures, and the dielectric function of femtosecond-laser-produced plasmas ,” Phys. Rev. E 59 , 3544 – 3553 ( 1999 ) [CrossRef]

]:

Ne=Ne0·lopt(lopt+R(t))
(5)
Te=Te0·(lopt(lopt+R(t)))531
(6)

For an initial electron density and temperature of Ne0=5·1022 cm-3 and Te0=1·105 K after the laser pulse there is excellent agreement with the experimental data. These values are on the order of former experiments and theoretical calculations [3

3 . R. E. Russo , X. L. Mao , H. C. Liu , J. H. Yoo , and S. S. Mao , “ Time-resolved plasma diagnostics and mass removal during single-pulse laser ablation ,” Appl. Phys. A 69 , S887 – S894 ( 1999 ) [CrossRef]

, 16

16 . B. Le Drogoff , J. Margot , Vidal F. , S. Laville , M. Chaker , M. Sabsabi , T. W. Johnson , and O. Barthelemy , “ Influence of the laser pulse duration on laser-produced plasma properties ,” Plasma Sources Sci. Technol. 13 , 223 – 230 ( 2004 ) [CrossRef]

, 18

18 . W. Theobald , R. Häβner , R. Kingham , R. Sauerbrey , R. Fehr , D. O. Gericke , M. Schlanges , W.-D. Kraeft, and K. Ishikawa , “ Electron densities, temperatures, and the dielectric function of femtosecond-laser-produced plasmas ,” Phys. Rev. E 59 , 3544 – 3553 ( 1999 ) [CrossRef]

] and confirm therefore the assumption of an expanding dense plasma in the first nanoseconds.

With the plasma expansion the probe beam is more and more blocked up to a time of about 5 ns, when the plasma expansion is high enough to block the whole probe beam. Since the electron density decreases with increasing time, the transmission through the plasma will start to increase from this moment. Thus, the transmission trace follows up to the minimum according to the Gaussian intensity profile of the beam and increases after that due to further electron diffusion and recombination.

In addition to this ablation plasma all our measurements show a second ablation component after about 30–50 ns. In luminescence measurements a second maximum after 50 ns is obvious, so we can assume a rise in temperature of the ablated material at this time. This is confirmed by the expansion of a second component after 40 ns with similar velocity as the shock wave. Also the plasma transmission starts to decrease after about 40 ns to a minimum at a time delay of 100 – 200 ns.

We assume for this time delayed ablation a thermal process of nucleation and following ejection of vapor and droplets. Possible are the processes of heterogeneous or homogenous nucleation. For heterogeneous nucleation disturbances in the material are necessary to initiate the growing of vapor embryos. By use of technical materials like in our case this is surely fulfilled, but the aforementioned slow diffusion velocity of the bubbles seems to be to short for reaching the surface [9

9 . R. Kelly and A. Miotello , “ Contribution of vaporization and boiling to thermal-spike sputtering by ions or laser pulses ,” Phys. Rev. E 60 , 2616 – 2625 ( 1999 ) [CrossRef]

].

Contrary to this argument experiments with lasers in the nanosecond pulse duration regime [19

19 . V. Craciun , N. Bassim , R. K. Singh , D. Craiciun , J. Hermann , and C. Boulmer-Leborgne , “ Laser-induced explosive boiling during nanosecond laser abaltion of silicon ,” Appl. Surf. Sci. 186 , 288 – 292 ( 2002 ) [CrossRef]

] support the ablation by heterogeneous nucleation and explain this by the fast growing rate of several m/s. Assuming 30 ns for establishment of stationary bubble nucleation and a growing rate of 5 m/s [19

19 . V. Craciun , N. Bassim , R. K. Singh , D. Craiciun , J. Hermann , and C. Boulmer-Leborgne , “ Laser-induced explosive boiling during nanosecond laser abaltion of silicon ,” Appl. Surf. Sci. 186 , 288 – 292 ( 2002 ) [CrossRef]

] a vapor embryo in 50 nm depth will reach the surface in 10 ns. These are the same time scales involved in our experiments.

This argumentation is confirmed by aforesaid femtosecond laser ablation experiments of GaAs up to delay times of 1 μs [7

7 . K. Sokolowski-Tinten , J. Bialkowski , M. Boing , A. Cavalleri , and D. von der Linde , “ Bulk phase explosion and surface boiling during short pulse laser ablation of semiconductors ,” in Quantum Electronics and Laser Science Conference ( OSA Technical Digest, Optical Society of America, Washington, DC , 1999 ) pp. 231 – 232

]. Ablation due to a rarefaction wave is observed in the first nanoseconds, followed by a formation of bubble like structures in the liquid after 20–30 ns.

On the other hand experiments on nanosecond pulse ablation give evidence for homogenous nucleation at the same time scales and longer [3

3 . R. E. Russo , X. L. Mao , H. C. Liu , J. H. Yoo , and S. S. Mao , “ Time-resolved plasma diagnostics and mass removal during single-pulse laser ablation ,” Appl. Phys. A 69 , S887 – S894 ( 1999 ) [CrossRef]

, 6

6 . K. Sokolowski-Tinten , J. Bialkowski , A. Cavalleri , M. Boing , H. Schüler , and D. von der Linde , “ Dynamics of femtosecond laser induced abaltion from solid surfaces ,” in High-Power Laser Ablation , C. R. Phipps , ed., Proc. SPIE 3343 , 46 – 57 ( 1998 ) [CrossRef]

, 10

10 . X. Xu and D. A. Willis , “ Non-Equilibrium Phase Change in Metal Induced by Nanosecond Pulsed Laser Irradiation ,” J. Heat Transfer 124 , 293 – 298 ( 2002 ) [CrossRef]

, 14

14 . V. P. Carey , Liquid-Vapor Phase-Change Phenomena , ( Hemisphere, Washington , 1992 )

]. For testing this we tried to calculate a similar transmission trace as observed in our measurements on the basis of Eq. (1). In Fig. 5 and Fig. 6 the results are drawn as solid lines. To fit the simulation it was necessary to reduce the surface tension at the boiling point by a factor 10-4, what is reasonable near the critical temperature [20

20 . A. Yoshida , “ Critical phenomenon analysis of surface tension of liquid metals ,” J. Jpn. Inst. Met. 58 , 1161 – 1168 ( 1994 )

]. We set the time lag τhn to 15–40 ns, what is near to theoretical and experimental values in literature [9

9 . R. Kelly and A. Miotello , “ Contribution of vaporization and boiling to thermal-spike sputtering by ions or laser pulses ,” Phys. Rev. E 60 , 2616 – 2625 ( 1999 ) [CrossRef]

, 10

10 . X. Xu and D. A. Willis , “ Non-Equilibrium Phase Change in Metal Induced by Nanosecond Pulsed Laser Irradiation ,” J. Heat Transfer 124 , 293 – 298 ( 2002 ) [CrossRef]

]. The pressure in the liquid is approximated by the recoil pressure out of the saturation pressure according to the Clausius-Clapeyron relation. Temperature evolution of the liquid is calculated with the above mentioned one-dimensional heat equation.

With these approximations neither heterogeneous nor homogenous nucleation can be excluded to explain our measurements. Both processes can be the origin for a second ablation phase after a few 10 ns under reasonable assumptions and further theoretical and experimental research is necessary to clarify this.

5. Conclusion

Ultrashort laser pulse ablation is a process with emission of particles up to several hundred nanoseconds after the laser pulse in at least two steps.

In the first step a thin layer of the surface on the order of the optical penetration depth of the laser pulse is ablated by electron emission, sublimation, transition to the plasma state and hydrodynamic/gasdynamic effects. This ablation processes proceed on nanosecond time scale or faster. The expansion can be described by a shock wave model developed for nanosecond ablation. In the first 30 ns linear expansion with about 3 km/s is measured, followed by a slow down to a dependency of ~t2/5.

The remaining heat is meanwhile diffusing in the material and thermal effects on longer time scales can occur. Therefore, we assume the second ablation step by boiling after heterogeneous or homogeneous nucleation. In our opinion neither of these processes can be excluded at first view. In our experiments this second step starts after about 40 ns with emission of hot material, increases to a maximum after about 150 ns and vanishes after a few microseconds. The main ablation products seem to be metal vapor and droplets with diameters greater than 1 μm. Variation of pulse duration in the range of 200 fs to 3.3 ps shows no significant effect on attenuation behavior.

Based on these results an upper limit for metal processing by ultrashort laser pulses can be assumed due to plasma shielding. The limit can be expected at a few hundred kHz and depends on ablation pulse fluence, target material and further process parameters like the geometry of the ablation spot/hole.

Acknowledgments

We are grateful to Prof. K. Sokolowski-Tinten for the helpful discussion. This work is supported financially in part by the German Ministry of Science, Education, Research and Technology (BMBF) projects 13N8576 and 13N8579 (PROMPTUS).

References and links

1 .

F. Dausinger , F. Lichter , and H. Lubatschowski , Femtosecond Technology for Technical and Medical Applications , ( Springer, Heidelberg , 2004 ) [CrossRef]

2 .

D. Bäuerle , Laser Processing and Chemistry , 3rd ed. ( Springer, Berlin-Heidelberg , 2000 )

3 .

R. E. Russo , X. L. Mao , H. C. Liu , J. H. Yoo , and S. S. Mao , “ Time-resolved plasma diagnostics and mass removal during single-pulse laser ablation ,” Appl. Phys. A 69 , S887 – S894 ( 1999 ) [CrossRef]

4 .

S. S. Mao , X. Mao , R. Greif , and R. E. Russo , “ Initation of an early-stage plasma during picosecond laser ablation of solids ,” Appl. Phys. Lett. 77 , 2464 – 2466 ( 2000 ) [CrossRef]

5 .

B. Salle , O. Gobert , P. Meynadier , M. Perdrix , G. Petite , and A. Semerok , “ Femtosecond and picosecond laser microablation: ablation efficiency and laser microplasma expansion ,” Appl. Phys. A 69 , S381 – S383 ( 1999 ) [CrossRef]

6 .

K. Sokolowski-Tinten , J. Bialkowski , A. Cavalleri , M. Boing , H. Schüler , and D. von der Linde , “ Dynamics of femtosecond laser induced abaltion from solid surfaces ,” in High-Power Laser Ablation , C. R. Phipps , ed., Proc. SPIE 3343 , 46 – 57 ( 1998 ) [CrossRef]

7 .

K. Sokolowski-Tinten , J. Bialkowski , M. Boing , A. Cavalleri , and D. von der Linde , “ Bulk phase explosion and surface boiling during short pulse laser ablation of semiconductors ,” in Quantum Electronics and Laser Science Conference ( OSA Technical Digest, Optical Society of America, Washington, DC , 1999 ) pp. 231 – 232

8 .

B. Rethfeld , K. Sokolowski-Tinten , V. V. Temnov , S. I. Kudryashov , J. Bialkowski , A. Cavalleri , and D. von der Linde , “ Ablation dynamics of solids heated by femtosecond laser pulses ,” in Nonresonant Laser-Matter Interaction , M. N. Libenson , ed., Proc. SPIE 4423 , 186 – 196 ( 2001 ) [CrossRef]

9 .

R. Kelly and A. Miotello , “ Contribution of vaporization and boiling to thermal-spike sputtering by ions or laser pulses ,” Phys. Rev. E 60 , 2616 – 2625 ( 1999 ) [CrossRef]

10 .

X. Xu and D. A. Willis , “ Non-Equilibrium Phase Change in Metal Induced by Nanosecond Pulsed Laser Irradiation ,” J. Heat Transfer 124 , 293 – 298 ( 2002 ) [CrossRef]

11 .

B.N. Chichkov , C. Momma , S. Nolte , F. von Alvensleben , and A. Tünnermann , “ Femtosecond, picosecond and nanosecond laser ablation of solids ,” Appl. Phys. A 63 , 109 – 115 ( 1996 ) [CrossRef]

12 .

S. Nolte , C. Momma , H. Jacobs , A. Tünnermann , B. N. Chichkov , B. Wellegehausen , and H. Welling , “ Ablation of metals by ultrashort laser pulses ,” J. Opt. Soc. Am. B. 14 , 2716 – 2722 ( 1997 ) [CrossRef]

13 .

S. I. Anisimov and B. S. Luk’yanchuk , “ Selected problems of laser ablation theory ,” Physics-Uspekhi 45 3 , 293 – 324 ( 2002 ) [CrossRef]

14 .

V. P. Carey , Liquid-Vapor Phase-Change Phenomena , ( Hemisphere, Washington , 1992 )

15 .

N. M. Bulgakova and A. V. Bulgakov , “ Pulsed laser ablation of solids: transition from normal vaporization to phase explosion ,” Appl. Phys. A 73 , 199 – 208 ( 2001 ) [CrossRef]

16 .

B. Le Drogoff , J. Margot , Vidal F. , S. Laville , M. Chaker , M. Sabsabi , T. W. Johnson , and O. Barthelemy , “ Influence of the laser pulse duration on laser-produced plasma properties ,” Plasma Sources Sci. Technol. 13 , 223 – 230 ( 2004 ) [CrossRef]

17 .

C. J. Nonhoff , Material Processing with Nd-Lasers , ( Electrochemical Publications Lim., Ayr , 1998 )

18 .

W. Theobald , R. Häβner , R. Kingham , R. Sauerbrey , R. Fehr , D. O. Gericke , M. Schlanges , W.-D. Kraeft, and K. Ishikawa , “ Electron densities, temperatures, and the dielectric function of femtosecond-laser-produced plasmas ,” Phys. Rev. E 59 , 3544 – 3553 ( 1999 ) [CrossRef]

19 .

V. Craciun , N. Bassim , R. K. Singh , D. Craiciun , J. Hermann , and C. Boulmer-Leborgne , “ Laser-induced explosive boiling during nanosecond laser abaltion of silicon ,” Appl. Surf. Sci. 186 , 288 – 292 ( 2002 ) [CrossRef]

20 .

A. Yoshida , “ Critical phenomenon analysis of surface tension of liquid metals ,” J. Jpn. Inst. Met. 58 , 1161 – 1168 ( 1994 )

OCIS Codes
(140.3390) Lasers and laser optics : Laser materials processing
(160.3900) Materials : Metals
(320.7120) Ultrafast optics : Ultrafast phenomena
(350.5400) Other areas of optics : Plasmas

ToC Category:
Research Papers

Citation
J. König, S. Nolte, and A. Tünnermann, "Plasma evolution during metal ablation with ultrashort laser pulses," Opt. Express 13, 10597-10607 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-26-10597


Sort:  Journal  |  Reset  

References

  1. F. Dausinger, F. Lichter and H. Lubatschowski, Femtosecond Technology for Technical and Medical Applications (Springer, Heidelberg, 2004). [CrossRef]
  2. D. Bäuerle, Laser Processing and Chemistry, 3rd ed. (Springer, Berlin-Heidelberg, 2000)
  3. R. E. Russo, X. L. Mao, H. C. Liu, J. H. Yoo and S. S. Mao, "Time-resolved plasma diagnostics and mass removal during single-pulse laser ablation," Appl. Phys. A 69, S887-S894 (1999) [CrossRef]
  4. S. S. Mao, X. Mao, R. Greif and R. E. Russo, "Initiation of an early-stage plasma during picosecond laser ablation of solids," Appl. Phys. Lett. 77, 2464-2466 (2000) [CrossRef]
  5. B. Salle, O. Gobert, P. Meynadier, M. Perdrix, G. Petite and A. Semerok, "Femtosecond and picosecond laser microablation: ablation efficiency and laser microplasma expansion," Appl. Phys. A 69, S381-S383 (1999) [CrossRef]
  6. K. Sokolowski-Tinten, J. Bialkowski, A. Cavalleri, M. Boing, H. Schüler and D. von der Linde, "Dynamics of femtosecond laser induced abaltion from solid surfaces," in High-Power Laser Ablation, C. R. Phipps, ed., Proc. SPIE 3343, 46-57 (1998) [CrossRef]
  7. K. Sokolowski-Tinten, J. Bialkowski, M. Boing, A. Cavalleri and D. von der Linde, "Bulk phase explosion and surface boiling during short pulse laser ablation of semiconductors," in Quantum Electronics and Laser Science Conference (OSA Technical Digest, Optical Society of America, Washington, DC, 1999) pp. 231-232
  8. B. Rethfeld, K. Sokolowski-Tinten, V. V. Temnov, S. I. Kudryashov, J. Bialkowski, A. Cavalleri and D. von der Linde, "Ablation dynamics of solids heated by femtosecond laser pulses," in Nonresonant Laser-Matter Interaction, M. N. Libenson, ed., Proc. SPIE 4423, 186-196 (2001) [CrossRef]
  9. R. Kelly and A. Miotello, "Contribution of vaporization and boiling to thermal-spike sputtering by ions or laser pulses," Phys. Rev. E 60, 2616-2625 (1999) [CrossRef]
  10. X. Xu and D. A. Willis, "Non-Equilibrium Phase Change in Metal Induced by Nanosecond Pulsed Laser Irradiation," J. Heat Transfer 124, 293-298 (2002) [CrossRef]
  11. B. N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben and A. Tünnermann, "Femtosecond, picosecond and nanosecond laser ablation of solids," Appl. Phys. A 63, 109-115 (1996) [CrossRef]
  12. S. Nolte, C. Momma, H. Jacobs, A. Tünnermann, B. N. Chichkov, B. Wellegehausen and H. Welling, "Ablation of metals by ultrashort laser pulses," J. Opt. Soc. Am. B 14, 2716-2722 (1997) [CrossRef]
  13. S. I. Anisimov and B. S. Luk’yanchuk, "Selected problems of laser ablation theory," Physics-Uspekhi 45 3, 293-324 (2002) [CrossRef]
  14. V. P. Carey, Liquid-Vapor Phase-Change Phenomena, (Hemisphere, Washington, 1992)
  15. N. M. Bulgakova and A. V. Bulgakov, "Pulsed laser ablation of solids: transition from normal vaporization to phase explosion," Appl. Phys. A 73, 199-208 (2001) [CrossRef]
  16. B. Le Drogoff, J. Margot, F. Vidal, S. Laville, M. Chaker, M. Sabsabi, T. W. Johnson and O. Barthelemy, "Influence of the laser pulse duration on laser-produced plasma properties," Plasma Sources Sci. Technol. 13, 223-230 (2004) [CrossRef]
  17. C. J. Nonhoff, Material Processing with Nd-Lasers, (Electrochemical Publications Lim., Ayr, 1998)
  18. W. Theobald, R. Häßner, R. Kingham, R. Sauerbrey, R. Fehr, D. O. Gericke, M. Schlanges,W.-D. Kraeft and K. Ishikawa, "Electron densities, temperatures, and the dielectric function of femtosecond-laser-produced plasmas," Phys. Rev. E 59, 3544-3553 (1999) [CrossRef]
  19. V. Craciun, N. Bassim, R. K. Singh, D. Craiciun, J. Hermann and C. Boulmer-Leborgne, "Laser-induced explosive boiling during nanosecond laser abaltion of silicon," Appl. Surf. Sci. 186, 288-292 (2002) [CrossRef]
  20. A. Yoshida, "Critical phenomenon analysis of surface tension of liquid metals," J. Jpn. Inst. Met. 58, 1161-1168 (1994)

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited