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).

References

[1] D. Bäuerle, Laser Processing and Chemistry, Springer-Verlag, Berlin, Heidelberg, 2000.

[2] C.R. Phipps (Ed.), Laser Ablation and its Application, Springer, New York, 2007.

[3] B.N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, A. Tünnermann, Appl. Phys. A 63

(1996) 109-115.

[4] A. Miotello, R. Kelly, Appl. Phys. A 69 (1999) S67-S73.

[5] V. Craciun, D. Craciun, M.C. Bonescu, C. Boulmer-Leborgne, J. Hermann, Phys. Rev. B 58

(1998) 6787-6790.

[6] J.H. Yoo, S.H. Jeong, X.L. Mao, R. Greif, R.E. Russo: Appl. Phys. Lett. 76 (2000) 783-785.

[7] N.M. Bulgakova, A.V. Bulgakov, Appl. Phys. A 73 (2001) 199-208.

[8] C. Porneala, D.A. Willis, J. Phys. D: Appl. Phys. 42 (2009) 155503.

[9] Y. Zhou, B. Wu, S. Tao, A. Forsman, Y. Gao, Appl. Surf. Sci. 257 (2011) 2886-2890.

[10] A.V. Bulgakov, N.M. Bulgakova, Quantum Electron. 29 (1999) 433-437.

[11] S. Gurlui, M. Agop, P. Nica, M. Ziskind, C. Focsa, Phys. Rev. E 78 (2008) 026405.

[12] S. Paul, S.I. Kudryashov, K. Lyon, S.D. Allen, J. Appl. Phys. 101 (2007) 043106.

[13] T.V. Kononenko, S.V. Garnov, S.M. Pimenov, V.I. Konov, V. Romano, B. Borsos, W.P.

Weber, Appl. Phys. A 71 (2000) 627-631.

[14] N.M. Bulgakova, A.V. Bulgakov, L.P. Babich, Appl. Phys. A 79 (2004) 1323-1326.

[15] J.F. Ready, Effects of High-Power Laser Radiation, Academic Press, New York, 1971.

[16] J.A. McKey, J.T. Schriempf, Appl. Phys. Lett. 35 (1979) 433-434.

[17] A.M. Prokhorov, V.I. Konov, I. Ursu, I.N. Mihailescu, Laser Heating of Metals, Adam

Hilger, Bristol, 1990.

[18] C. Körner, R. Mayerhofer, M. Hartmann, H.W. Bergmann, Appl. Phys. A 63 (1996) 123-

131.

[19] S. Lazare, V. Tokarev, Ultraviolet laser ablation of polymers and the role of liquid

formation and expulsion, in: J. Perrière, E. Millon, E. Fogarassy (Eds.), Recent Advances in

Laser Processing of Materials, E-MRS Series Elsevier, 2006. pp. 137-180.

[20] M. Stafe, C. Negutu, I.M. Popescu, Appl. Surf. Sci. 253 (2007) 6353-6358.

[21] A.A. Ionin, S.I. Kudryashov, L.V. Seleznev, Phys. Rev. E 82 (2010) 016404.

[22] V. Semak, A. Matsunawa, J. Phys. D: Appl. Phys. 30 (1997) 2541-2552.

[23] A.V. Bulgakova, N.M. Bulgakov, J. Phys. D: Appl. Phys. 28 (1995) 1710-1718.

[24] J.R. Ho, C.P. Grigoropoulos, J.A.C. Humphrey, J. Appl. Phys. 79 (1996) 7205-7215.

[25] A. Bogaerts, Z. Chen, R. Gijbels, A. Vertes, Spectrochim. Acta Part B 58 (2003) 1867-

1893.

[26] V.I. Mazhukin, V.V. Nossov, G. Flamant, I. Smurov, J. Quant. Spectrosc. Radiat. Transfer

73 (2002) 451-460.

[27] V.I. Mazhukin, V.V. Nossov, I. Smurov, G. Flamant, J. Phys. D: Appl. Phys. 37 (2004)

185-199.

[28] V.I. Mazhukin, V.V. Nossov, I. Smurov, Appl. Surf. Sci. 253 (2007) 7686-7691.

[29] M. Aghaei, S. Mehrabian, S.H. Tavassoli, J. Appl. Phys. 104 (2008) 053303

[30] L.A. Artsimovich, R.Z. Sagdeev, Plasma Physics for Physicists, Atomizdat, Moscow, 1979

(in Russian).

[31] A.V. Bulgakov, A.B. Evtushenko, Yu.G. Shukhov, I. Ozerov, W. Marine, Quantum

Electron. 40 (2010) 1021-1033.

[32] A.Y. Basharin, M.V. Brykin, M.Y. Marin, I.S. Pakhomov, S.F. Sitnikov, High Temper. 42

(2004) 60-67.

[33] A.I. Savvatimskiy, Carbon 47 (2009) 2322-2328.

[34] N.M. Bulgakova, L.A. Zakharov, A.A. Onischuk, V.G. Kiselev, A.M. Baklanov, J. Phys. D:

Appl. Phys. 42 (2009) 065504.

[35] E.D. Palik (Ed.), Handbook of Optical Constants of Solids, Academic Press, Orlando FL,

1998.

[36] A.M. Malvezzi, M. Romanoni, Int. J. Thermophys. 13 (1992) 131-140.

[37] N.M. Bulgakova, A.V. Bulgakov, Proc. SPIE 6732 (2007) 67320G.

[38] Ya.B. Zel’dovich and Yu. P. Raizer, Physics of Shock Waves and High Temperature

Hydrodynamics Phenomena, Academic, New York, 1967.

[39] L.M. Biberman, G.E. Norman, J. Quant. Spectrosc. Radiat. Transfer 3 (1963) 221-245.

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.