Plasma temperature for various metallic targets.
During the last decade, our groups have performed systematic experimental studies on the characterization of plasma plumes generated by laser ablation in various temporal regimes (ns, ps, fs) on materials ranging from simple metals (Al, Cu, Mn, Ni, In, W, …) to more complex compounds (ceramics, chalcogenide glasses, ferrites). Optical (fast imaging and space- and time-resolved emission spectroscopy) and electrical (mainly Langmuir probe) methods have been applied to experimentally investigate the dynamics of the plasma plume and its constituents. Influence of the target physical (thermodynamic and electrical) parameters on the plasma dynamics has been studied. A mathematical correlation between the local and global plasma parameters and the physical properties of the target was proposed for the first time. Peculiar behaviors like plume splitting or plasma oscillations have been evidenced for high laser fluence ablation in vacuum. Along with results from the literature, our findings provide convincing arguments for the existence of multiple double-layers in the laser ablation plasma plume, in a scenario including two-temperature electrons. New fractal-based theoretical approaches have been developed to qualitatively and quantitatively account for the observed phenomena. The space and time evolution of expansion velocity, particle number, current density and plasma temperature were theoretically investigated.
- laser ablation
- transient plasma dynamics
- plasma oscillations
- Langmuir probe
- optical emission spectroscopy
- plasma simulation
Despite its widespread use in a large number of applications (e.g. pulsed laser deposition , generation of nanoparticles [2, 3], chemical analysis [4, 5] or cleaning of delicate artwork ), a comprehensive picture of laser ablation remains a challenge for both experimentalists and theoreticians. The difficulty arises from the multi-physics nature of the ablation process, coupling optics and electrodynamics (absorption of light by the target material), thermodynamics (heating, phase transitions, cooling), gas dynamics (expansion of ablation plume into vacuum or background gas), plasma physics (collisions, electric interactions) and laser-plume interaction (plasma heating by absorption of laser photons, inverse Bremsstrahlung, multi-photon ionization), some of these evolving on very short time scales, which can make it challenging to find the adequate resolving probe. Moreover, the fundamental mechanisms involved in the ablation process and the properties and dynamics of the subsequent laser-produced plasmas depend strongly on the laser beam parameters (pulse duration, fluence, wavelength or beam profile) and also on the properties of the irradiated material (thermal/electrical conductivity, reflectivity, heat of vaporization, binding energy, etc.).
Fundamental differences can be revealed when investigating the role of the laser pulse duration with respect to the specific timescales of the irradiated material response . For instance, in nanosecond ablation regime, the laser pulse is significantly longer than the usual electron cooling time (∼10 fs) and the lattice heating time (∼ps). In this case, the energy absorbed by the electrons has enough time to be transferred to the lattice. The electrons and the lattice can further reach thermal equilibrium, and the main energy loss is the heat conduction into the solid target. Consequently, the mechanisms involved in this ablation regime are mainly thermal (e.g. phase explosion, normal vaporization, etc.) [8, 9]. Most notably, the subsequent plasma generated in this ablation regime absorbs a significant percentage of the beam energy (pulse “tail”, during several nanoseconds), leading to an important heating of the plume. In the case of ultra-fast laser ablation (∼fs), when the laser pulse duration is shorter than (or on the same scale as) the electron cooling time, the electrons in the surface layer suffer cooling by heat diffusion and by heat transfer to the lattice ions. This stage continues for several picoseconds. The picture changes in the case of a semiconductor target which is heated by an ultrashort pulse. In the latter case, laser energy is transferred into the solid by creating a “bath” of hot electrons and holes . Hot carriers subsequently transfer energy to the lattice by creating optical and acoustic phonons. In the case of both metals and semiconductors, the thermalization of laser energy in the hot carrier bath takes place within a few femtoseconds, while the typical time-scale for lattice heating falls within the 1–10 ps range, where thermal conduction is negligible . For low fluence fs-laser irradiation, the Coulomb explosion  is the dominant ejection mechanism, while at sufficiently high laser intensities the phase explosion is followed by non-thermal vaporization of the bulk material and becomes the main mechanism for material removal . A particular case of ultra-fast laser ablation is represented by ps-laser ablation. This temporal regime acts like a bridge between the previous cases manifesting characteristics from both regimes. The pulse duration is long enough so that some thermal damage occurs due to the heating of the lattice. If the laser pulse width is in the 1–10 ps range, the particle ejection is still dominated by the Coulomb explosion with minimal contribution from the thermal mechanism and no interaction between the plasma plume and the incoming laser beam. For longer pulse durations (∼100 ps) the balance is “tipped” in favor of thermal mechanisms coupled with a brief absorption of the laser beam by the ejected cloud .
Extensive efforts have been fostered by many research groups in the last decades for unveiling this complexity. Most of them were dedicated to characterizing the laser-produced plasma dynamics and to establishing a link between the local/global plasma parameters and the fundamental ablation mechanisms, some also addressed the link with the physical properties of the irradiated material (see, e.g., [14–48]). In order to draw a comprehensive picture of the laser-produced transient plasma evolution, one needs detailed space- and time-resolved information on the chemical and electrical composition of the expanding plume (ions, electrons, neutral atoms, molecules, clusters, with associated number densities, ionization stages, etc.), the plasma dynamics—expansion regime (plasma as a whole), kinetic energies (of every individual species), etc. Optical (fast photography, shadowgraphy, interferometry, optical emission and absorption spectroscopies, laser-induced fluorescence, resonant ionization spectroscopy, Thomson scattering) and electrical (Langmuir probes (LP), Faraday cups, electrostatic analyzers, mass spectrometry) methods [49, 50] are available for undertaking this complex investigation. The difficulty in getting a complete description of the laser ablation plasma plume arises mostly from its transient character, with a lifetime typically on the 10 μs scale, but with inner rapid phenomena (e.g. oscillations) which can exhibit sub-nanosecond timescales. Consequently, extreme care must be taken for the specific application of well-known steady state plasma characterization tools (e.g. Langmuir probes) to this transient case. Moreover, not all of the above-mentioned techniques can be applied for probing the great variety of laser ablation plasmas (nor even one given plasma plume along its spatial and temporal evolution). For instance, higher electron number densities are needed to get an effective response when using interferometry or Thomson scattering than when Langmuir probes are used. Typical irradiation conditions (in the range of GW/cm2) will result in laser ablation plasmas which can be considered as cold (electron temperature in the eV range, number densities roughly in the 1013–1018 cm−3 range). Higher irradiation values (exceeding 1 PW/cm2) can lead to hot plasmas with higher electron temperature and number densities, usually studied in a laser inertial confinement nuclear fusion context .
During the last decade, our groups have performed systematic experimental and theoretical studies on the fundamental characterization and applications (mainly pulsed laser deposition of thin films) of plasma plumes generated by laser ablation in various temporal regimes (ns, ps, fs) on materials ranging from simple metals (Al, Cu, Mn, Ni, In, W, etc.) to more complex compounds (ceramics, chalcogenide glasses, ferrites) [52–79]. Optical (fast gate Intensified Charge Coupled Device (ICCD) camera imaging and space- and time-resolved emission spectroscopy) and electrical (mainly Langmuir probe) methods have been applied to experimentally investigate the dynamics of the plasma plume and its constituents. The analysis of probe current-voltage characteristics at various delays after the laser pulse gave access to the temporal evolution of ion density, electron temperature and plasma potential. The recording time-scales are analyzed by coupling the distribution functions of electrons and ions through an effective mass. The space and time evolution of expansion velocity, particle current density and plasma temperature were theoretically investigated by a fractal hydrodynamic model. We present here a short overview of these experimental and theoretical studies, with a special focus on the characterization of transient laser-produced plasmas by electrical methods and on recent developments of the fractal hydrodynamic model.
2. Experimental details
A schematic view of the experimental set-up often used in our studies is given in Figure 1. The solid targets (usually 20 mm diameter, 1 mm thick disks) of various chemical composition were placed on a translation-rotation stage in vacuum or controlled atmosphere and irradiated by ns, ps or fs laser pulses at various wavelengths (usually 532 nm Nd:YAG and 800 nm Ti:Sa, Quantel, Continuum, Spectra Physics). We used laser fluences spanning the 10−1–103 J/cm2 range, corresponding to irradiances in the 106–1014 W/cm2 limits for laser spot dimensions on the target in the range 0.1–1 mm and laser pulse durations in the range 40 fs–10 ns.
The electric diagnostics mainly used were Langmuir probes immersed at various positions in the plasma plume to record the ionic or electronic currents, depending on the probe biasing voltage (
To record the plasma optical emission, three configurations have been often used: plasma plume imaging (ICCD fast photography), space- and time-resolved optical emission spectroscopy (OES) and temporal evolution of a given spectral line intensity [54–57, 62, 64, 66–68, 73, 75]. For the imaging experiments, ICCD gate widths of 5 ns were usually employed in order to catch as much as possible sharp temporal snapshots in the space-time evolution of the plume. For space-resolved OES, a 1 mm × 5 mm translating slit was placed in the vacuum chamber, at 40 mm from the normal to the target, to observe plasma plume “slices” of 1 mm width . Finally, the temporal evolution of a given spectral line intensity was recorded with a fast (sub-ns rise-time) photomultiplier tube (PMT, Hamamatsu) placed on the second output port of the monochromator (Acton Princeton Instruments), once the spectral line has been selected and isolated with appropriate entrance and exit slit widths and diffraction grating positions [54, 57].
3. Experimental results
Both our optical and electrical investigations on the dynamics of the transient plasmas produced by laser ablation in vacuum revealed some peculiar phenomena as the plume splitting in (at least) two components or the occurrence of oscillations in the currents recorded by the Langmuir probe or on the irradiated target. We have recently presented an overview of these peculiar findings, along with similar results from the literature, in a review paper . We will therefore orient the presentation below more on the extraction of significant plasma parameters (to be compared with the theoretical model predictions) from the time-of-flight profiles of the currents recorded by the LP.
The typical time-evolution of the ion current recorded by the probe placed at various distances (axial, radial) with respect to the center of the laser irradiation spot shows that it extends in the μs range and it generally consists in a fast part having an oscillatory behavior, and a slower tail which arrives at longer times (see some examples in Figure 2, for ns-ablation and
The currents induced in the target by the ablation process (displayed in Figure 3a for various laser energies/pulse) can be correlated with the probe signal, as the positive charging arises through the electrons escaping from the expanding plasma to the grounded chamber, while the negative charging is given by the ions escaping from the target. The asymmetry of the laser intensity distribution and non-uniform target absorptivity can also lead to the generation of considerable currents along a conductive target . Experiments revealed two possible mechanisms: induction due to the magnetic dipole moment of the plasma and a second mechanism resulting from the phenomena at the plasma-target interface [85–87]. From these experimental results, we observed that the amplitudes of the fast peak increase rapidly with the laser energy and the fast electron contribution becomes dominant above
When extracting the oscillatory part from the original signal (Figure 2), that is, subtracting the smoothed temporal trace, the resulted time-dependence revealed a good fitting with a usual damp oscillator [48, 60]. Thus, one can assume that in the electric field near the probe the ion equation of motion is , where the dissipative term is given by the electron-ion collision frequency, , and is the plasma ion frequency [49, 60]. We applied this procedure also for studying the LP current oscillations in the case of fs-laser ablation of Al. In a more detailed analysis, we observed that biasing the target can influence the oscillation frequency, two regimes being observed, corresponding to the fast and slow components, respectively. For example, in Figure 4a and b we observed good fitting for
During these measurements, a discussion has arisen on the use of low or high oscilloscope impedance for recording the transient signals. Both configurations have advantages and disadvantages. Using low impedance ensures good temporal resolution, while using a high input impedance has the advantage of improving the signal amplitude, although the temporal trace
The consequence of applying a positive voltage on the metallic target,
|Target||Atomic weight||Average charge state (|
|Al||27||14.21 ± 2.15||2.63 ± 0.74|
|Mn||55||8.15 ± 0.79||1.08 ± 0.42|
|Ni||59||6.72 ± 1.03||1.29 ± 0.37|
|Cu||64||6.54 ± 0.45||1.59 ± 0.23|
|In||115||8.66 ± 1.29||2.23 ± 0.94|
|Te||128||8.04 ± 0.84||1.44 ± 0.24|
|W||184||5.29 ± 0.53||0.92 ± 0.17|
Another approach used by our group is based on the treatment of the current-voltage characteristics (
The electron temperature (
We applied this particular method to study the dynamics of the plume at relatively long delays (>1 μs) after the laser pulse. Based on our previous ICCD fast camera imaging and space- and time-resolved optical emission spectroscopy measurements, we know that these times are characteristic for the observation of the slow plasma component [55, 56, 67]. As expected, it resulted that all studied parameters have a significant space-time decrease, due to the cooling process and rarefaction during expansion (Figure 7). Comparing the values for the electron temperatures determined using time-sampling methods with the ones given by the previous method, some notable differences occur. The time-resolved method only captures the cold tail arriving at the probe surface as the sampling is done after 1 μs, and thus the values of the electron temperatures are considerably lower than the ones derived from the total collected charge versus probe potential representation.
The same technique has been implemented for the study of transient plasmas generated by laser ablation in three different temporal regimes (ns, ps, fs) on a series of six metallic targets (Al, Ti, Mn, Ni, Cu, Zn). Figure 8a shows the decrease of the saturation ion density (recorded at 5 mm from the target and after 1 μs with respect to the laser pulse) with the melting point of the target material. Other groups have reported similar evolutions for ns-laser-produced plasmas. A significant decrease of the ablation efficiency (estimated as a function of the ablated crater depth) with the increase of the melting point was reported in . A similar influence of the melting point on the ablation yield was found by Schou et al. [29, 95], who discussed the decrease in the ablation yield as a consequence of the target cohesive energy increase. Both melting point and cohesive energy are considered as a measure of the degree of volatility. The same dependence proposed by previously mentioned authors was also found by our group for fs-laser ablation of various metallic targets (W, Te, In, Cu, Ni, Mn, Al) . The decrease of the ionic density with the increase of the melting point (or cohesive energy) appears to be a general characteristic of the laser-produced plasmas as it is confirmed by our current systematic study on the ns, fs and ps ablation for a wide range of metallic targets.
Figure 8b displays the evolution of the electronic temperature with the target electrical conductivity for the three ablation regimes. The values derived at
Let us note that in the results presented above only single-element targets were used to better understand the fundamental processes involved in laser-target interaction and subsequent plasma evolution. When using complex (multi-component) targets, the interpretation of the LP temporal profiles is more difficult. For example, we present in Figure 9 the results for laser ablation of a chalcogenide glass (Ge9.5Sb28.6Se61.9) , where three plasma structures are recorded, each of them oscillating with a specific frequency. These structures are also present in ICCD images (see the inset of Figure 9), displaying various expansion velocities.
An extensive investigation of plasmas generated by ns laser ablation of chalcogenide targets was presented in . We reported there a strong evolution of the global expansion velocity of all three plasma components (derived from ICCD fast camera imaging) and of the excitation temperatures (determined through optical emission spectroscopy) with the thermal and electrical properties of the complex chalcogenide target. More precisely, the increase of the Sb2Se3 content led to a quasilinear increase of the expansion velocities and average plasma temperature. The results were interpreted in the frame of the target structural changes. Previous reports on the properties of similar systems revealed that the addition of Sb leads to the decrease of the bandgap energy , the increase of the glass transition temperature and consequently the increase of the weak bonds concentration . The increase in the weak bonds concentration leads to increase in the thermal and electrical conductivity of the glass. This is in good agreement with our reported results on pure metallic targets , where the increase in the electrical/thermal conductivity of the materials led to the increase of electron temperatures and ion drift velocities.
4. Theoretical investigations
Continuing our previous work [55, 58, 59, 63] on the fractal hydrodynamic model for laser ablation plasma dynamics, we recently proposed a compact version for the analysis of the spatial and temporal evolution of some plasma dynamic variables . This version of our model was obtained by using normalized variables of the particle density, velocities, current density, etc., and by choosing adequate scale resolutions. In our initial model describing the evolution of the fractal fluid [59, 63, 98], we took into account a high number of factors (experimental ones by means of the width of the laser pulse Gaussian distribution, probe or target bias, etc., and theoretical ones by means of the fractal-non-fractal transition coefficient, resolution scale, fractal dimension of the movement curves, etc.), which increased the difficulty in performing a complete analysis of the plume dynamics. Through a viable choice of normalized dynamic variables with respect to the previous factors, we simplified the interpretation of the plume dynamics.
In the frame of fractal hydrodynamics with an arbitrary fractal dimension of the motion curves,
for the velocity field and
for the particular initial and boundary conditions given by:
Thus, we assumed that at
the current density takes the approximate form:
through the following identities:
Given the dependences of the multiple dynamic variables (
This allows us to re-write the dependencies of the plasma dynamic variables on the external factors as follows :
Normalized particle density:
Normalized current density:
Let us analyze the influence of the
In this context, in Figure 10a and b the current densities given by Eq. (16) are plotted versus time (
The validation of our model comes from the comparison with the time-dependence of plasma parameters obtained from LP measurements. In Figure 11a one observes that the time-decrease of the ion density is well fitted by the dependence (15), with the parameters
In the “classical” LTE model, the plasma temperature (
The normalization of the plasma dynamic variables led us to a more compact and simple form of the fractal theoretical model, by allowing the use of a single control parameter that embodies the contributions of several external parameters on the dynamics of the ejected particles. In its compact form, we were able for the first time  to define some clear associations between fractal model variables and specific plasma parameters (electron temperature, thermal velocity, particle density). Moreover, when compared with experimental data depicting the temporal evolution of the plasma parameters determined though the Langmuir probe method, the model satisfactorily reproduces the experimental traces. From the theoretical fit, we determined a range of values for the fractalization degree which describes the laser-produced plasmas in the ns ablation regime. The success of this non-differential approach is also seen from the fact that the model is able to “recognize” the probe—target distance at which the experimental data was recorded. Further studies are required in order to test the generality of the model, by comparing it against other “classical” theoretical models and also against data extracted from ps and fs laser-produced plasmas in various experimental conditions (target-probe distance, laser fluence, background pressure).
In the classical concepts, the theoretical models (hydrodynamic, kinetic, etc.) are built assuming that the dynamics of individual elements are characterized by continuous and differentiable motion variables (energy, momentum, density, etc.). These variables are exclusively dependent on the spatial coordinates and time. In the real situation, the complex system dynamics is much more complicated and the classical theoretical models failed in the attempt to explain all the concerned aspects. These difficulties can be overcome in a complementary approach, using fractal concepts, describing “exotic” shapes that did not fit the patterns of Euclidean geometry. Moreover, the depth analysis of different complex systems evolution showed that most of the phenomena are nonlinear and, therefore, new mathematical tools were required. These have been provided by the Scale Relativity Theory (SRT) and by Extended Scale Relativity Theory (ESRT) , that is, the SRT with an arbitrary constant fractal dimension. These theories consider that the motions of the complex systems structural units take place on continuous but non-differentiable curves (fractal curves). In this situation, Euclidean dynamics of a complex system subjected to external constraints is replaced by a fractal dynamics characterizing the same system free of any external constraints. More precisely, Euclidian constraints dependent motions, that is, on continuous but differentiable curves, are substituted by constraints independent motion in a fractal space, that is, on continuous but non-differentiable (fractal) curves (a free motion).
The dynamics of the transient laser-produced plasma in vacuum was investigated using electrical (Langmuir probe, target current) and optical (fast gate intensified CCD camera imaging) measurements for various ablation regimes and simple target materials. The typical time-evolution of the ion current recorded by the probe placed at various distances (axial, radial) with respect to the center of the laser irradiation spot shows that it extends in the μs range, and it generally consists in a fast part having an oscillatory behavior, and a slower tail which arrives at longer times. For the expansion velocities, values in the range of 104 m/s for the first (fast) structure and of 103 m/s for the second (slow) one were found, both from electrical and optical methods, which are in agreement with experimental results given in the literature and rough calculations performed in simple thermodynamic framework.
Measurements of the current induced in the target by the ablation process showed that it is correlated with the probe signal, as the positive charging arises through the electrons escaping from the expanding plasma to the grounded chamber, while the negative charging is given by the ions escaping from the target. Biasing the target by an external voltage source, the negative part of the target current, which is given by the ion contribution, acquires an oscillatory behavior of the same frequency as previously recorded for the Langmuir probe current. Consequently, such periodic fluctuations are assumed to be induced by the probe/target electric field, with a target bias threshold for their occurrence.
Extracting the oscillatory part from the original temporal trace of Langmuir probe, the resulted time-dependence revealed a good fitting with a usual damped oscillator, while its frequency is connected with the plasma ion frequency. Moreover, we observed that biasing the target can influence the oscillation frequency, two regimes being inferred, corresponding to the fast and slow components, respectively.
Electrical measurements can be successfully used to calculate the global temperature and average charge state for the fast plasma structure, through time-integration of probe current intensity to obtain the total collected charge dependence
Another approach used by us to study the dynamics of the plume at relatively long delays is based on the treatment of the current-voltage characteristics (
Theoretically, a compact version using normalized variables of our previous fractal hydrodynamic model was proposed for the analysis of the spatial and temporal evolution of some plasma dynamic variables. In this context, a new parameter named fractalization degree was introduced to account for the contribution of all external factors, that is, the fractal-non-fractal transition coefficient, the scale resolution, and the fractal dimension of the movement curves. When compared with experimental data depicting the temporal evolution of the plasma parameters determined through the Langmuir probe method, the model satisfactorily reproduces the experimental traces. In the compact form of the model, we were able to define some clear associations between fractal model variables and specific plasma parameters. From the theoretical fit, we determined a range of values for the fractalization degree which describes the laser-produced plasmas in the ns ablation regime, while more efforts are required to elucidate some features associated with femtosecond laser ablation (e.g. evolution of the oscillation period with the target atomic mass).
This work has been partially supported by the Agence Nationale de la Recherche through the LABEX CEMPI (ANR-11-LABX-0007), as well as by the Ministry of Higher Education and Research, Hauts de France Council and European Regional Development Fund (ERDF) through the Contrat de Projets Etat-Region (CPER Photonics4Society). S.A.I. thanks the Institut Français de Bucharest for a BGF cotutelle PhD grant.