Post on 20-Jan-2023
Published in Applied Surface Science 257 (2011) 10876– 10882
Role of laser-induced plasma in ultradeep drilling of materials by nanosecond laser pulses
Nadezhda M. Bulgakova,1 Anton B. Evtushenko,1 Yuri G. Shukhov,1 Sergey I. Kudryashov,2
Alexander V. Bulgakov1
1Institute of Thermophysics SB RAS, 1 Lavrentyev Ave., 630090 Novosibirsk, Russia
2P.N. Lebedev Physical Institute RAS, 53 Leninsky Ave., 119991 Moscow, Russia
Abstract. Radiative effects of the laser-induced ablative plasma on the heating and ablation
dynamics of materials irradiated by nanosecond laser pulses are studied by the example of
graphite ablation. On the basis of combined thermal and gasdynamic modeling, the laser-induced
plasma plume is shown to be a controlling factor responsible for ultradeep laser drilling due to
plasma radiation, both bremsstrahlung and recombinative. We demonstrate that plasma radiative
heating of the target considerably deepens the molten layer, thus explaining the observed crater
depths.
I. Introduction
Pulsed laser ablation (PLA) has become an effective tool for microprocessing of different
materials, including cutting, drilling, surface patterning, etc. [1-3]. It has been established that,
for nanosecond laser pulses, a transition from the normal (surface) vaporization mechanism to a
violent ejection of a mixture of vapor and liquid droplets from the irradiated target (called
usually phase explosion or, more appropriate, explosive vaporization) occurs at a threshold laser
irradiance (typically of the order of 109 W/cm2 for inorganic materials) [4-9]. The latter
mechanism is stimulated by a homogeneous nucleation of the vapor phase within a molten layer
superheated relative to the surface when the growing vapor bubbles tear the liquid matter into
pieces. In such explosive ablation regime, the surface vaporization of particles is developed
during the laser pulse action resulting in the formation of a hot light-absorbing plasma in the
ablation products [7,10,11]. The subsequent, often dominant by amount, volumetric ejection of
the vapor-droplet phase happens after the pulse termination [6,8,9]. The ablative craters
produced in the regimes of volumetric material ejection can be very deep reaching, in some
cases, several or even tens micrometers in depth per pulse [6,7,12]. Such ultradeep laser drilling
cannot result from a common heat conduction transport into the target bulk and is suggested to
be due to ablative laser plasma effects [12]. The laser-produced plume shields the target from the
laser beam that results in a saturation of the mass removal in the surface vaporization regimes
[7,10,13]. Studies of the laser energy balance show that, at fluences near the transition to the
volumetric material ejection, the plasma plume can accumulate more than 40% of the laser beam
energy [14]. Such a hot plasma induces ejection of molten matter due to the plasma recoil
pressure [1]. On the other hand, plasma radiation (both recombinative and bremsstrahlung) can
lead to additional heating of the target material [12,15-17].
While the role of the recoil pressure of plasma plumes under PLA is extensively
discussed in the literature (see, e.g., [8,18-22]), detailed theoretical studies of the plasma
reradiation effects in ultradeep crater formation are still missing. The radiation heat transfer in
laser-ablation plasma plumes produced at moderate laser intensities (108–109 W/cm2) was the
subject of numerous works focused mainly on plasma absorption effects and their role in the
plume expansion dynamics [23-29]. Therewith some information was obtained about plasma
emission during ablation of metals, including bremsstrahlung and blackbody radiation, and also
emission in distinct spectral lines [24,26,29]. One of the results of these works is that the plasma
radiation has only a minor influence on the target heating [24,26]. We argue, however, that this
does not necessarily represent the facts for many situations. First, the authors [24,26] considered
highly reflective metal targets (Al, Cu) while good absorbers, like graphite, can be heated by
plasma emission much more efficiently. Second, most of the previous works neglected the
recombinative radiation of the plasma which is the main emission mechanism for plasmas at
relatively low temperatures (below ~10 eV) [30], typical for the considered ablation conditions.
It should be underlined that the expanding laser plasma radiates energy both during and after the
laser pulse action that can lead to prolonged stages of target heating and vaporization.
In this paper we make an attempt to evaluate radiative effects of laser-induced plasmas on
heating and ablation dynamics of materials irradiated by nanosecond laser pulses. For this
purpose we have performed experimental and theoretical studies of laser ablation of graphite
which is considered as a representative example. The theoretical analysis is performed in three
stages. First, the conventional thermal model refined by accounting for the effects of target
melting and plasma shielding is applied for evaluating the energy accumulated by the laser-
generated plasma. We show that, in the explosive vaporization regimes, this model cannot
explain the observed ablation depths whose values are higher than the sum of the calculated
ablation and melting depths. Hence, we have undertaken further analysis and considered the
expansion of the recombining plasma plume using the data obtained at the first stage as the
initial conditions for the plasma modeling. As a result, the recombination and bremsstrahlung
emissions of the plasma are derived as a function of time. At the third stage, we have introduced
the plasma radiation as an additional source term to the thermal model in order to elucidate
changes in the material melting depths caused by the radiating plasma upon expansion. Modeling
has been performed for polycrystalline graphite irradiated by the second harmonics of a Nd:YAG
laser in a wide range of laser fluences covering ablation regimes from the ablation threshold to
the regimes of volumetric material ejection. The simulations are compared with measurements of
the laser-induced mass removal. The influence of the laser-induced radiative plasma on the
material ablation is discussed.
2. Experimental
The experimental arrangement has been described in detail elsewhere [7,10,31]. In brief,
ablation of the target material was carried out under vacuum conditions (10-5 Pa) with a
frequency doubled Nd:YAG laser (532-nm wavelength, pulse of a Gaussian temporal profile of
7-ns (FWHM) duration). A 10×10-mm2 area, 3-mm thick plate of polycrystalline graphite (1.67
g/cm3 mass density, 99.99% purity) was used as the target. The laser beam was focused at
normal incidence by a glass lens (100-mm focal length) into a circular spot of a diameter in the
range 0.1–0.3 mm (1/e2-level). The pulse energy was monitored by a pyroelectric detector Ophir-
PE25BB-DIF and varied independently of the irradiation spot size. Laser fluence F0 on the target
surface was varied in the range of 1–50 J/cm2. The ablation measurements were performed
translating the target to avoid formation of a crater on its surface and thus to have the same
irradiation conditions during multipulse ablation series. The ablation mass was accumulated over
103–104 laser shots. The average mass removal per pulse was determined by measuring the target
weight before and after irradiation using a precision balance GH-202-A&D (10-µg resolution).
The ablation depth was determined by normalizing the measured mass to the target mass density
and spot area. In addition, separate craters were produced for visualization purposes by
irradiating the static target with a fixed number of laser shots (less than 50). The craters were
examined with an optical microscope (a CCD camera Toshiba IK-M50H equipped with a
Mitutoyo M-Plan APO 10× objective and a Navitar Zoom 4× lens).
The experimental data on the ablation depth as a function of incident laser fluence F0 are
presented in Fig. 1 by dark squares. The ablation threshold can be determined as Fabl ≈ 1.5 J/cm2.
Note that with 532-nm laser pulses we have not found a distinct saturation of the ablation depth
which is observed under ablation of graphite at 1064 nm [7,10]. However, the secondary
threshold fluence value Fexp for the transition to explosive vaporization is very similar, ~22
J/cm2.
Fig. 1.
Fig. 2.
Photographs of typical craters produced by 30 laser shots in low- and high-fluence regimes
are shown in Fig. 2. Frozen capillary waves are distinctly seen, unambiguously indicating
melting of graphite even at relatively low laser fluences, near the ablation threshold Fabl. At high
laser fluences above the explosive vaporization threshold Fexp, one can recognize in the center of
the irradiation spot a distinct area of ultradeep ablation with a smooth bottom surrounded by a
zone of the re-solidified material. The depth in the center reaches 2–3 µm per pulse (note that in
Fig. 1 the ablation depth averaged over the irradiated spot area is given). The obvious melting of
graphite indicates that, during the ablation, the carbon vapor pressure above the target reaches, at
least, 100 bar [32,33]. Hence, the observed transition to the ultradeep ablation can be attributed
to the formation of a thick layer of molten graphite whose explosive vaporization together with
the high recoil pressure leads to sharp deepening of the crater starting from Fexp. The following
theoretical analysis is aimed at elucidating the dynamics of heating, melting, and ablation of
graphite under these experimental conditions in order to get an insight into a possible role of the
laser ablation plasma in the ultradeep ablation process.
3. Theoretical analysis
The theoretical analysis is performed in three stages, based on two models previously
developed by the authors, i.e., the thermal model of pulsed laser ablation with effective plasma
plume absorption [7,10] and the spherical model of the laser-induced plasma which takes into
account the ionization/recombination dynamics [23]. The latter model implies that local
ionization equilibrium can be violated, as indeed occurs in the simulations. The advantage of this
model is that it allows calculating the energy balance in plasma including radiative losses of the
energy. Here we will dwell only on the main features of the models used (see [7,10,14,23] for
more details).
3.1. First stage: Thermal model with plasma shielding
At the first stage we apply the thermal model whose final form was described in [14]. The
model is based on solving a heat flow equation in its one-dimensional form that allows analyzing
the evolution of the temperature profiles T(t,z) toward the target depth z:
( )( ) ( )ztSzT
zzTtu
tTTTLc mmp ,)( +
∂∂
∂∂
=⎟⎠
⎞⎜⎝
⎛∂∂
−∂∂
−+ λδρ , (1)
).exp()()1(),(),( L ztIRztSztS bb αα −−== (2)
Here ρ, cp, λ, αb, and R are the mass density, the heat capacity, the thermal conductivity, and the
absorption and reflection coefficients of the irradiated bulk material respectively. The term
Lmδ(T – Tm) allows the calculations across the liquid-solid interface, having the temperature Tm.
Here Lm is the latent heat of fusion, δ(T – Tm) is δ-function whose computational domain is
usually about 5 computational cells [14]. The vaporization rate u(t) is defined under the
assumption that the flow of vaporized molecules from the surface follows the Hertz-Knudsen
equation and the vapor pressure above the vaporized surface can be estimated using the
Clausius-Clapeyron equation [7]. An important feature of our model is that it takes into account
the effect of plasma plume shielding of laser radiation by considering not only the amount of
vaporized material but also vapor/plasma heating. This allows modeling the ablation process and
the laser energy balance over the fluence range where the normal vaporization mechanism is
dominant.
The temporal shape of the Nd:YAG laser pulse used in our ablation experiments can be
described by the Gaussian function
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛−=
2
00 2ln4exp2ln2)(
LL
tFtIτπτ
, (3)
where I0(t), F0, and τL are the incident laser intensity, fluence and pulse duration, respectively.
Under the conditions of plasma shielding, the intensity of laser light reaching the target surface
can be presented in the form [7,10]
[ ] ⎥⎦
⎤⎢⎣
⎡−=Λ−= ∫
∞
000 ),(exp)()(exp)()( dzTntIttItI ppα , (4)
where Λ(t) is the total optical thickness of the PLA plasma, and α(np,Tp) is the plasma absorption
coefficient dependent on the plasma density and temperature. It has been shown that Λ(t) can be
approximated as [7,10]
Λ(t) = aΔz(t) + bEa(t), (5)
where Δz(t) is the ablation depth and Ea(t) is the laser energy absorbed by the plasma by the time
moment t. The time-independent coefficients a and b, being the only free parameters in the
model, are to be determined by comparison with experimental data. In specific cases, when the
plasma absorption mechanisms are well established and the α(np,Tp) dependence is available, the
a and b parameters can be estimated theoretically [7]. The values Δz(t) and Ea(t) are calculated
by solving the system of Eqs. (1)-(5) with the following initial and boundary conditions
T(0, z) = T0, )(0
tLuzT
z
=∂
∂
=
λ (6)
where T0 is the initial temperature of the target and L is the latent heat of vaporization.
To calculate the laser energy balance, we note that the incident pulse energy E0 is
partially reflected from the target surface (ER), lost to the target heating (Et), absorbed by the
emerging plasma (Eab), and used for surface vaporization (EL is the part corresponding to the
latent heat of vaporization and Eth is the thermal energy of the vaporized particles). The
particular fractions Ei of the laser energy are determined by integration of the corresponding
time-dependent quantities, found in the model calculations, during and after the laser pulse
action as follows [14]:
∫=ct
dttItRE0
R )()( , (7)
000
t )(),()( TTcdztzTTcE p
Z
cp
m
−= ∫ , (8)
∫ Λ−−===
c
c
t
ttadtttIEE
00ab ))](exp(1)[( , (9)
)()(0
L c
t
tzLdttuLEc
Δ== ∫ , (10)
( )∫ −=ct
s dttuTtTkE0
0th )()(23 . (11)
The time moment tc was chosen so that the vaporization had stopped at this time. The target
depth Zm was deep enough to satisfy the condition T(Zm,tc) = T0. The fulfillment of the energy
balance condition, ∑ = 0EEi , was checked in the calculations and found to be perfectly
satisfied. Note that the factor 3/2 in the expression for Eth accounts for atomic vaporization. In
the case of vaporization of molecules or polyatomic particles, one should take into account
excitation of vibrational and rotational degrees of freedom as it was made in [34].
The simulations have been performed in the range of laser fluences from the ablation
threshold Fabl (~1.5 J/cm2) to fluence values slightly above the experimentally determined
explosive vaporization threshold Fexp. The absorption and reflection coefficients of graphite at
the laser wavelength of 532 nm are respectively 3.3×105 cm-1 and 0.3 for solid graphite [35,36]
and 1.4×105 cm-1 and 0.06 for the liquid phase [36]. The other target properties are summarized
in [7]. It should be noted that already at the ablation threshold Fabl the calculated saturation
pressure at the vaporization peak (corresponding to the maximum surface temperature) exceeds
100 bar and hence graphite can melt. The calculated ablation depth and the maximum depth of
the molten layer as functions of laser fluence are given in Fig. 1 by solid and dashed lines
respectively. Figure 3 shows the calculated fractions Ei of the pulse energy (Eqs. 7-11).
It is notable that for 532-nm ablation, contrary to modeling of IR laser irradiation regimes
[14], a satisfactory agreement between the experimental data and simulation results on mass
removal is obtained with an only adjustable parameter in Eq. (5), a = 20000 cm-1, while b = 0.
Intentionally, we modeled irradiation regimes slightly above the explosive vaporization
threshold. In view that the explosive vaporization occurs mainly after the laser pulse termination
[6,8,9], such simulations allow estimating the normally vaporized material fraction (we note
however that, at fluences of the order of 50 J/cm2 and higher, the explosive ablation can be
observed already during the laser pulse [11]). Surprising is that the measured ablation depth in
the regimes of explosive vaporization is even deeper than the maximum thickness of the molten
layer obtained in the simulations. Hence, such a deep ablation cannot be reached under the
assumption that the whole molten layer is ejected from the target. A plausible explanation of this
fact is that, as mentioned above, the conventional thermal model underestimates the melting
depth at fairly high laser fluences since the target can be additionally heated by radiation, both
bremsstrahlung and recombinative, of the ablation plasma plume [12,15-17]. The laser energy
balance calculations show (Fig. 3) that, at fluences near Fexp, plasma absorbs ~50% of the
incident laser energy and we can assume that a considerable part of plasma radiation is coupled
to the target. Moreover, hot laser-induced plasmas efficiently emit in the UV spectral range
[12,30] where the reflection coefficient of materials is smaller as compared to IR and visible
ranges and thus this additional heating can considerably increase the molten layer.
To evaluate the effect of plasma radiation on target heating, melting, and vaporization,
we have further developed our model accounting for the hot ablative plasma as an additional heat
source. For this aim we have exploited the spherical model of laser plume expansion [23] which
allows us to simulate ionization/recombination dynamics of the plasma and its energy balance
and, hence, to evaluate the temporal dynamics of plasma radiation.
Fig. 3.
3.2. Second stage: Radiation of expanding laser plasma
According to the model [23] we assume that, by the end of laser pulse, the vaporized
atoms are distributed uniformly in a half-sphere volume. The initial temperature of the neutral
carbon vapor is estimated on the basis of the above energy balance as Tin = T0 + 2/3×(Eab +
Eth)/(kBNvap). Here T0 = 300 K; Nvap is the number of vaporized carbon atoms; kB is the
Boltzmann constant. Assuming the local ionization equilibrium, the plasma temperature and the
ionization degree are determined with an iterative procedure as described in [23], when the
electron and energy sources in the continuum and energy equations are set equal to zero. The
spherical plasma plume with the pre-determined parameters is allowed to expand freely into
vacuum and we follow the evolution of the plume parameters (the electron and ion densities and
temperatures, ionization degree) and plasma radiation. Figure 4 illustrates the radial distributions
of the electron and ion temperatures, Te and Ti, of such carbon plasma produced at a laser fluence
of 15 J/cm2 at a time moment of 25 µs. The initially equal Te and Ti values become considerably
different at late stages of expansion.
Here we would like to draw attention to a controversial aspect of laser plasma dynamics.
In numerous studies, evolution of the laser-ablation plasmas is described by the Saha equation,
assuming that the local ionization equilibrium is kept during expansion. However, this is true
only for initial expansion stages when the plasma plume is fairly dense and hot. Already after
several microseconds (depending on the initial conditions), the expanding plasma can be driven
out of the equilibrium due to a disbalance between the collisional ionization and recombination
channels (Fig. 4). In the outer plasma region where the density drops rapidly (typical density
profiles in carbon plasmas obtained with the spherical model can be found in [37]), the
collisional ionization is suppressed while the plume electrons receive some energy in the
recombination events and do not have enough time to exchange their energy with ions and
neutrals. As a result, the electron temperature is higher as compared to that of the heavy plasma
particles. In contrast, the electron temperature is well below than the ion/neutral temperature in
denser plume regions. In these regions, the electron energy losses in the continuing events of
collisional ionization and bremsstrahlung are not compensated by the electron-ion energy
exchange and heating-up in the three-particle recombination. The disbalance between the
electron and ion temperatures results also in the fact that the ionization degree calculated using
the kinetic approach [23] does not correspond to that estimated by the Saha equation. Moreover,
in different plume regions the ionization degree can be higher or lower than the corresponding
equilibrium values. Hence, application of the Saha equation to the laser-ablation plasmas
requires some caution.
Fig. 4.
Basing on the kinetic considerations [23], we can calculate fractions of the laser energy
transferred to the plume kinetic energy and lost from the plume via recombinative radiation of
the plasma. For a singly ionized plasma (Z = 1), the photo-recombinative losses can be expressed
as [23] 5.013
rec )5.1(102 −− +⋅= eiee TnenITq W/cm3. (12)
Here e is the unit charge, the electron and ion densities (ne, ni) and the electron temperature Te
are measured in cm-3 and eV respectively. On the other hand, the radiation power densities of the
bremsstrahlung and photo-recombination processes can be estimated as [30]: 5.0234
brem 105.1 eie TZnnq −⋅= W/cm3, (13)
5.0429rec 105 −−⋅= eie TZnnq W/cm3. (14)
Here the electron temperature is measured in Kelvins. Simulations have shown that Eqs. (12) and
(14) give at Z = 1 the same recombinative radiation power. To calculate the total plasma
emission, the bremsstrahlung (Eq. (13)) and photo-recombinative (Eqs. (12) or (14)) power
densities were integrated over space and time during our simulations of the plasma expansion
dynamics. We neglect here the blackbody plasma radiation and spectral plasma emission since
these radiant energy losses represent only a minor fraction in a continuous plasma spectrum
produced by the bremsstrahlung and photo-recombination mechanisms [24,29,38,39]. Note also
that, besides recombinative and bremsstrahlung radiation, other radiative processes take place in
plasmas such as, e.g., bremsstrahlung in the field of neutral atoms (not considered here) which
can be important at low ionization degrees [38,39]. Figure 5 shows the fraction of the plasma
energy radiated during the plume expansion. Comparing with Fig. 3, we note that the efficiency
of the reemission of the laser energy absorbed by the plasma increases with increasing laser
fluence.
Fig. 5.
Thus, a considerable fraction of the plasma energy is reemitted (mainly in the UV range)
and coupled back to the irradiated target. Hence, a plasma radiative heat term can be constructed
and added to the heat flow equation (1) as a heat source additional to the laser pulse. As an upper
estimate, we assume that a half of plasma radiation reaches the target (this likely occurs for fairly
large irradiated spots when the plasma has a disk-like shape at the initial expansion stages). The
obtained bremsstrahlung (Ibrem(t)) and recombinative radiation (Irec(t)) intensities of the plasma
radiation in the direction to the target are shown in Fig. 6. We note that the recombinative
emission is dominant that is typical for plasmas with relatively low electron temperatures (a few
eV), while the opposite situation is realized in plasmas at high Te [30]. Indeed, the Ibrem(t)/Irec(t)
ratio increases with laser fluence (i.e., with plasma temperature) as can be seen in Fig. 6. The
main portion of such plasma re-radiation occurs during ~20 ns after the expansion start,
whereupon it decreases by several orders of magnitude. A similar time interval for laser-induced
plasma emission was obtained in [29] for the case of copper ablation. The drop in the radiation
intensity is connected with the involvement of the whole plasma into the expansion process
when the rarefaction wave reaches the plume center. In the further modeling stage we use the
obtained Ipl(t) dependencies as the plasma radiative heat terms in Eq. (1).
Fig. 6.
3.3. Third stage: Thermal model with effective plasma heating
To account for the additional target heating by the plasma radiation, the laser energy
source in Eq. (1) is changed to the form ),(),(),( plL ztSztSztS += with
)()1(),( plplplpl tIRztS α−= where )(pl tI is the sum of the recombinative radiation and
bremsstrahlung emission intensities (Fig. 6). Here Rpl and αpl are the effective values of the
reflection and absorption coefficients for graphite at wavelengths of plasma emission. Since the
recombinative radiation dominates under the considered ablation conditions, we arbitrarily
assume, for rough estimative calculations, that the plasma radiates at ~950 Å. The corresponding
photon energy is ~13 eV that is the ionization potential of carbon atoms plus an average electron
energy of ~2 eV at early expansion stages as obtained in the calculations of the plasma expansion
dynamics (see Sec. 3.2). Thus we use Rpl = 0.18 and αpl = 7.7×105 cm-1 [35]. The simulations
described in Section 3.1 were repeated with this new energy source term, assuming that the
plasma radiation starts at the moment of the incident laser intensity maximum when the plasma
plume is already developing. Surprisingly, the ablation depth of normally vaporized graphite is
almost insensitive to the introduction of this additional heating term while the depth of the
molten layer is notably increasing at F0 > 10 J/cm2. As a result, at fluences near the Fexp value,
the total depth of ablated and molten material is approaching the experimentally observed
ablation depth (Fig. 1, dash-dotted line). Assuming that in the regime of explosive vaporization
the whole molten layer becomes superheated and is ejected from the target surface, we obtain a
convincing explanation of the ultradeep ablation effect.
4. Discussion
The model presented here, although being considerably simplified, has nevertheless
demonstrated that at relatively high laser fluences the energy absorbed by the plasma plume can
be efficiently coupled back to the target, representing an additional heating source. Thus, for the
considered conditions of graphite ablation at fluences of 20–25 J/cm2 the target obtains ~15%
more laser energy than predicted by the conventional thermal model (compare Figs. 3 and 5,
taking into account the target reflectivity). The latter model predicts too shallow melting depths
and cannot explain the observed ablation rates in the explosive vaporization regime (Fig. 1,
dashed line). Obviously, the explosively ejected layer cannot exceed the depth of the molten
layer. The extra energy supplied by the plasma radiation causes considerably deeper melting and
explains the ultradeep explosive ablation of graphite.
For the sake of simplicity, in modeling we considered plasma radiation at a photon
energy of ~13 eV assuming the dominance of the recombinative emission and a ~2-eV average
energy of the recombining electrons. In fact, both the recombinative and bremsstrahlung
radiations produce continuum spectra whose maxima are shifted towards smaller photon energies
upon plasma cooling. For a more rigorous consideration, one has to integrate the plasma
emittance over the spectral distributions and to take into account the wavelength-dependent
optical properties of the target. However, the reflection coefficient of graphite remains almost
unchanged (within 10–20%) while the absorption coefficient, being more profoundly altered, is
of minor importance as the temperature distribution in the target is essentially governed by the
heat conduction at the nanosecond scale. Hence, we expect that a more refined model can
somewhat change the quantitative results while will leave the main conclusions made here
unchanged.
Another important issue concerns the spatial manifestation of the ablation/modification
mechanisms on the irradiated surface (Fig. 2). We have performed one-dimensional modeling for
laser fluences averaged over the irradiation spot. However, a Gaussian distribution of the laser
pulse energy across the beam implies the dominance of different ablation mechanisms in
different zones within the irradiated spot. On exceeding the explosive ablation threshold, the
regime of ultradeep drilling is observed first at the central part of the spot where the laser fluence
reaches its maximal value (almost twice higher than that assumed by the spot-averaged
modeling). The deep crater originating from the explosive ejection of matter (zone 4 in Fig. 2b)
is surrounded by an annular zone with evident traces of melting (zone 3) where the local laser
fluence is below Fexp and ablation has a normal vaporization character during the entire laser
pulse. Beyond the melting region one can clearly see a surface modification region where
sublimation of matter took place (zone 2), which gradually transforms into the zone 1 where the
surface experiences only some mechanical spallation and, at larger distances from the irradiation
spot center, no traces of modification are seen. At the central part of the irradiated spot, where
the local value of laser fluence exceeds the explosive vaporization threshold, all the above
ablation mechanisms occur consecutively and are changing each other during and after the laser
pulse action – from sublimation to normal vaporization upon melting and, finally, to ejection of a
vapor-melt mixture.
Comments should be made on the observed delay of explosive ablation relative to the
laser pulse [6,8,9]. Obviously, during the laser pulse when normal vaporization occurs, the high
pressure of the hot laser plasma absorbing the laser radiation prevents the target superheating
(the molten layer stays in near-binodal states [7]). After the laser pulse termination when the
plasma pressure drops due to plume expansion, the thermodynamic state of the molten layer
evolves towards superheating, making an explosive decay of the melt possible. On the other
hand, the expanding plasma additionally heats the target upon recombination thus increasing the
superheating degree of the molten matter. Hence, a conclusion can be made that, depending on
the laser fluence range, the laser-induced plasma affects the ablation rate in opposite ways. At
moderate fluences, the plasma shields partially the target from the incident laser radiation, thus
decreasing the ablation efficiency. In contrast, at fairly high fluences the plasma plays a
stimulating role in explosive ablation.
6. Conclusions
In this study we have undertaken an effort to clarify how the laser-induced plasma plume
influences the ablation process of graphite. It is shown that the experimental observations in the
ultradeep drilling irradiation regimes cannot be explained by the conventional thermal model
accounting for the only plasma shielding effect. Within such considerations, the calculated
ablation and melting depths altogether are considerably smaller than the experimentally observed
ablation depths. Taking into account the recombinative and bremsstrahlung radiation of the laser
ablation plasma allows to describe convincingly such ultradeep ablation process. We show that a
considerable part of the laser energy absorbed by the plasma is reradiated back toward the target
in a spectral range which is even better absorbed by the target than the incident laser radiation.
Depending on the laser beam energy and pulse duration, the laser-induced plasma plume can act
as a factor suppressing the explosive ablation and, on the contrary, can stimulate the latter
ablation process leading to ultradeep drilling. The results of this study performed for the specific
case of graphite have however a general character which should be valid for laser ablation of any
materials when developed plasma plumes are formed upon ablation.
Acknowledgments
This work was supported by the Russian Foundation for Basic Research (RFBR) (projects Nos.
08-08-00756, 10-08-00880, 10-08-00941 and 10-03-00441) and by the Federal Target Program
“Research and research-pedagogical personnel of innovative Russia for 2009–2013” (State
contracts No. 02.740.11.0109 and No. 02.740.11.0562).
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Figure captions
Fig. 1. Measured ablation depth (averaged over the irradiation spot) as a function of laser fluence
(dark squares). Modeling results on the ablation depth are shown by solid line. Onset of
“ultradeep drilling” (phase explosion) is ~22 J/cm2. The other lines show the calculated
maximum depths of melting (with respect to the initial target surface) obtained with the thermal
model taking into account plasma shielding (dashed line) and, additionally, with contribution of
plasma radiative heating (dot-dashed line). Details of the calculations are given in the text.
Fig. 2. Optical microscope images of craters formed on the graphite surface by 30 consecutive
laser shots at fluences (a) 3 J/cm2 and (b) 24 J/cm2. The scale bar corresponds to an irradiated
spot size (1/e2 level) for both cases. Several zones can be marked out: (1) non-damaged surface,
(2) an external area of the irradiated spot where laser energy is insufficient to induce melting, (3)
a zone with clear traces of melting, and (4) a deep area in the middle of the irradiated spot with a
smooth bottom where melting traces are hardly distinguished.
Fig. 3. The laser energy balance as a function of laser fluence: Et, Eab, EL, Eth, and ER are the
fractions of the energy dissipated in the graphite target, absorbed by the plasma, spent for
vaporization as the latent heat and the particle energy, and reflected from the target surface,
respectively. At fluences above the explosive vaporization threshold (~22 J/cm2), redistribution
between the channels occurs (not considered here), mainly between Et and Eth, due to ejection of
the vapor-droplet phase that is usually delayed in respect to the laser pulse.
Fig. 4. The spatial profiles of the electron and ion/atom temperatures in the expanding carbon
plasma at a time moment of 25 µs after the expansion onset. The initial conditions correspond to
the experimental conditions of graphite ablation at F0 = 15 J/cm2: Te = Ti = 34510 K; ionization
degree is ~48%.
Fig. 5. The total energy Erad radiated by the plasma plume during its expansion into vacuum as a
function of laser fluence.
Fig. 6. The plasma radiation intensities in the direction to the target calculated on the basis of the
spherical model of the plasma plume expansion for two laser fluences, (a) 20 and (b) 25 J/cm2.
The recombinative radiation and bremsstrahlung emission intensities are shown by solid and
dashed lines, respectively. The time moment t = 0 corresponds to the plume expansion start.