Physics Letters A 302 (2002) 182–189

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Plume dynamics during film and nanoparticles depositionby pulsed laser ablation

Min Hana,∗, Yanchun Gongb, Jianfeng Zhoua, Chunrong Yina, Fengqi Songa,Nakiko Mutoc, Toshio Takiyac, Yasushi Iwatac

a National Laboratory of Solid State Microstructures and Department of Materials Science, Nanjing University, Nanjing 210093, Chinab Institute of Sciences, PLAUST, Nanjing 211101, China

c Cluster Advanced Nanoprocesses CRT, National Institute of Advanced Industrial Science and Technology, AIST Tsukuba Central 2,Tsukuba 305-8568, Japan

Received 21 June 2002; received in revised form 21 June 2002; accepted 15 August 2002

Communicated by B. Fricke

Abstract

The gas dynamics of pulsed laser ablation of silicon target in the helium gas ambient is investigated via direct simulationMonte Carlo method with a real physical scale of target-substrate configuration. A shock driven process is clearly observed. Itis shown that the interaction of the shock front with the target surface and the vapor front induce significant backward flux ofablated particles and oscillating behavior of vapor front. A confined layer mixed with high density Si and He atoms is formedaround the contact front. Its behavior is important to the nanoparticle formation and deposition. 2002 Elsevier Science B.V. All rights reserved.

PACS: 61.46.+w; 81.15.Fg; 47.40.Nm; 05.10.Ln

Keywords: Pulsed laser ablation; DSMC; Nanoparticle; Gas dynamics

Pulsed laser deposition (PLD) has been an impor-tant technique for depositing a wide variety of thinfilms and nanoscale particles such as fullerenes andsilicon nanoclusters [1]. Ambient gas is typically usedfor PLD to improve the qualities of the films pro-duced or to accelerate the condensation and growth ofthe nanoclusters. The introduction of background gasduring pulsed laser ablation (PLA) leads to consider-ably complicated gas dynamics processes for the ex-

* Corresponding author.E-mail address: sjhanmin@nju.edu.cn (M. Han).

pansion and propagation of the ablated plume, whichinclude the formation and evolution of shock waves[2,3], the plume oscillations [4], and “plume splitting”into fast and background-slowed components [5,12].The knowledge of the constitution and dynamical be-havior of the ablated plume over real temporal andspatial scales is of crucial importance to optimize thefilm growth and nanoparticle synthesis by varying thelaser parameters, the ambient gas pressure and target-substrate distance.

The velocity, density, temperature and fluid dy-namics of the PLA plume have been studied widely.

0375-9601/02/$ – see front matter 2002 Elsevier Science B.V. All rights reserved.PII: S0375-9601(02)01116-7

M. Han et al. / Physics Letters A 302 (2002) 182–189 183

A number of fundamental details have been success-fully explored by a variety of experimental techniques,such as the ICCD photography, TOF mass spectrome-try as well as the emission spectroscopy [6], and the-oretical studies which involve Monte Carlo simulation[7,8], the shock layer model [9] as well as fluid dy-namic models [10,11]. However, to our knowledge,few attentions have been given to the interaction ofthe plume with the substrate surface, which may ev-idently alter the gas dynamics behavior of the plumenear the substrate during film deposition or nanopar-ticle growth. The target-substrate configuration is im-portant to the PLD practice. The density and kineticenergy profile of the particles arriving at the substrateare key processing parameters for film growth. In thePLA supersonic expansion cluster source of the Smal-ley type [13], complex plume dynamics within thecondensation cell may induce large dispersions of thegas flow condition and the residence time for clustergrowth, as a result the generated clusters have a rela-tively broad size distribution.

In this Letter, a direct simulation Monte Carloapproach is described and applied to demonstratethe main features of the gas dynamics of the PLDprocess in a real physical scale of target-substrateconfiguration from molecular (microscopic) level. Theobserved dynamics may help optimize the productionand collection of gas-condensed nanoparticles by laserablation.

Formation of Si film and nanoparticles by PLA iswidely explored both experimentally and theoreticallydue to its important technological applications. Herewe also choose silicon as target materials. In thesimulation, Si wafer is assumed to be ablated by aNd:YAG laser (λ = 532 nm, focused to an energydensity of 5 J/cm2 in flat-topped 10 ns pulse). Thelaser spot on the target surface is 1 mm in diameter.The target and substrate are coaxially arranged witha 20 mm space between. The ambient gas of He ismaintained at 1000 Pa. Such conditions are typical forPLA experiments.

In the view of gas dynamics, the PLA process canbe classified into (1) evaporation of the target materialand (2) hydrodynamic expansion of the ablated plumeinto the ambient gas (here we make the approxima-tion of a pure thermal evaporation process and neglectthe interaction between the evaporated plume and theincident laser beam). For the fairly short laser pulses

(∼10 ns) that are typical for PLD experiments, it isreasonable to consider the above two processes as ad-jacent stages. The energy of the laser irradiation isspent on heating, melting and evaporating the targetmaterial. The surface temperature of the target can becomputed by using the heat flow equation [14]. Forlaser fluence higher than 4× 108 W/cm2, the surfacetemperature approaches the maximum rapidly duringthe initial few nanoseconds of the pulse. Evaporationprocess becomes important when the surface tempera-ture of target approaches the melting pointTm (for Si,Tm = 1693 K). For the laser fluence and pulse durationwe considered, the thermally activated surface vapor-ization can reasonably be used to describe the evapo-ration due to pulsed laser irradiation of the target [15].The saturated vapor pressurepv in equilibrium at thetarget surface can be calculated using the Clausius–Clapeyron equation from the surface temperatureTs .The flux of vapor atoms leaving the surface can bewritten as:

J = βpv

(2πkTsm)1/2,

whereβ (≈1) denotes the sticking coefficient of sur-face atoms,m is the atomic mass of the vapor atom.The total ablated atom number is an integration ofJ

over time and surface area. With the laser irradiationconditions we consider, the surface temperature of Sitarget can be raised to 9400 K. 1× 1015 Si atoms areevaporated from the target surface within each laserpulse.

To obtain the initial condition for vapor expansion,we perform a Knudsen layer analysis [16,17] to getthe idealized states of the gas just leaving the Knudsenlayer (KL). The local densityn0, mean velocityu0 andtemperatureT0 of the vapor just outside the KL canbe calculated from the jump conditions and may bededuced very simply:

T0

Ts=

[√1+ π

(g

8

)2

− √π

g

8

]2

,

n0

ns

=√

Ts

T0

[(g2 + 1

2

)eg2

erfc(g) − g√π

]

+ 1

2

Ts

T0

[1− √

π geg2erfc(g)

],

(1)u0 =√

γkT0

m,

184 M. Han et al. / Physics Letters A 302 (2002) 182–189

Table 1Surface temperature of Si target, total number of ablated vapor atoms and the states of the vapor just outside the Knudsen layer

Laser fluence Surface temperature Vapor temperature Vapor density Flux velocity Total number(MW/cm2) of target (K) after KL (K) after KL(m−3) after KL (ms−1) of vapor atoms

500 9400 6280 1.66× 1026 1760 1.01× 1015

wherens is the saturated vapor density at the targetsurface, γ is the adiabatic index. The calculatedidealized states just beyond the KL are listed in Table 1together with the total number of ablated vapor atoms.

To get the detail knowledge of the particulatestructure and thermodynamical states of the ablatedplume at all times from molecular level, the directsimulation Monte Carlo (DSMC) method [18,19] isthe appropriate tool. We start the DSMC calculationfrom the out edge of KL. The following assumptionsare used in the simulation: (1) since the ablatedplume is significantly forward peaked, we adopt anone dimensional DSMC scheme. In the calculation,velocities and the collision kinetics are considered asthree-dimension, however, the motion of the particlesis only allowed to along the direction normal tothe target surface; (2) expansion starts from a cloudwith the densityn0. The ablated atoms are uniformlydistributed within a cylindrical space of the laserspot diameter. And the range of distribution dependson the total ablated atom number listed in Table 1.The particles in the cloud have a Maxwell velocitydistribution with the temperatureT0; (3) the particlesof the vapor and the ambient gas may interact as elastichard-spheres (HS) scattering with a total collisioncross sectionσ , which is independent of the scatteringangle, andσij = π(ri + rj )

2, whereri andrj are theradii of the colliding particles.

In the DSMC simulation, the time evolution ofthe vapor cloud and the ambient gas is obtainedby following a number of simulated particles thatundergo elastic collision. The volumes between thetarget and substrate are subdivided into a networkof cells with cell sizes less than the local meanfree path. Simulated particles are only allowed tocollide between each other within the same cell.The particle evolution is integrated in time stepsof duration �t , which is a fraction of mean freetime. The positions and velocities of the particles areevolved in time by two independent steps: advectionand collision. During each Monte Carlo time step

the particles are first allowed to move according totheir velocity and the time step length�t . Thenpairs of nearby particles are randomly selected withinthe cell for collision using the acceptance-rejectionmethod. Their post-collision velocities are evaluatedstochastically with the conservation of momentumand energy. To simulate the dense HS gas flow inthe PLA process, we adopt the so-called ConsistentBoltzmann Algorithm (CBA) [20]. With the Enskogapproximation, an enhanced probability is introducedto express the mean free path for a dense gas as

(2)λE = 1√2πnYd2

,

wheren is the particle number density,d = ri + rjis the effective collision diameter. The collision rateof the dense gas is then given by the Enskog rateΛE = YΛ, whereΛ is the normal collision rate of adilute HS gas. The EnskogY -factor is

Y (n) = (1+ 0.05556782b2n + 0.0139445b2

2n2

− 0.0013396b32n

2)/(1− 0.56943218b2n

(3)+ 0.08289011b22n

2),whereb2 = (2/3)πd3 is the HS second virial coeffi-cient.

In Fig. 1 we present a time sequence of the radialdensity distribution of the pulsed laser ablated siliconplume under expansion (lines) and the helium carriergas under compression (dots) over the entire flowfield. The evolution of gas dynamical behavior ontime may be well split into several temporal stages.At the early stage of the vapor expansion (e.g., forshort delays up to 100 ns), the density of Si vapor isstill much high compared to that of the He gas, thedensity profile of the Si vapor can be characterizedby a simple expansion. The expansion is quite free,the fluid velocity increases linearly with the expansionrange, as shown in Fig. 2, where the velocity profiles atseveral typical temporal stages are plotted. However,at the contact front, which separates the ablated plume

M. Han et al. / Physics Letters A 302 (2002) 182–189 185

Fig. 1. A time sequence of the radial density distribution of the pulsed laser ablated silicon plume (lines) and the helium carrier gas (dots) overthe entire flow field. The laser fluence is 500 MW/cm2, and ambient helium pressure is 1000 Pa.

186 M. Han et al. / Physics Letters A 302 (2002) 182–189

Fig. 2. Velocity profiles of silicon plume propagation at several typical temporal stages.

from the ambient gas, there is a sudden drop of thevapor density, which shows the counteraction effectsof the ambient He gas. The ambient gas particlesare pushed forward from the volume occupied by thevapor particles and the gas is compressed, leading tothe formation of a high-density peak of the He gas. Atthis stage, the fluid velocity near the contact front ishigher than 8000 m/s, which is a factor of 2–3 fasterthan predicted from the adiabatic expansion modeland consistent with the observation of laser-ablationexperiments [21,22].

With expansion, the density of the Si vapor de-creases continuously. The kinetic energy transfer dur-ing collisions between the particles induces a groupvelocity in the He gas in front of the high density Hepeak and compress the gas into high density. The high-density peaks propagate forward. During this stage,the process is a typical shock wave phenomenon. Thecompression of the He gas can be considered as ashock compression process. The shock front (the front

of the high density He peak) has a distribution width ofseveral mean free path. Before the shock front reachesthe substrate located at 20 mm away from the tar-get, the shock wave is quite stable. The density ofthe shock-compressed layer is about 3 times increased.For delays greater than∼100 ns, a high-density peakof vapor plume appears at the contact front due to thecounteraction of the He gas. And the fluid velocity ofthe vapor flux decreases continuously (curves 2, 3 inFig. 2). The Si density within this peak is higher than1024 m−3 and the width of the peak increases with thedelay time.

After about 2.3 µs, the shock front reaches the sub-strate surface. A second high-density peak is formedin the shock compressed He gas layer near the sub-strate. The front of this peak propagates backward, andthe fluid velocity within the peak drops to zero. Thisprocess is equivalent to a shock wave that is formeddue to the reflection of the incoming shock front on thesubstrate surface. The reflected shock wave induces

M. Han et al. / Physics Letters A 302 (2002) 182–189 187

Fig. 3. Positions of the contact front and shock wave front during the propagation of the pulsed laser ablated Si plume. The inset graph showsthe steady propagation behavior of shock front in detail.

a second shock compression of the He gas, the den-sity of which is increased by about 2 times. Behindthe reflected shock front, the He gas is left to be quietagain.

The reflected shock front collides with the incom-ing vapor front at about 3.5 µs and is reflected from thevapor front again. But the new reflected shock wavebecomes much weaker. After a number of oscillatingcycles between the vapor front and the substrate, theshock wave in the He gas completely ceases out. Thevapor front is also stopped at about 3.8 mm in front ofthe substrate.

Because the density within the vapor is muchhigher than that behind the vapor front, a backwardpropagating flux of ablated particles is observed andthe contact front is also pushed back towards thetarget due to the backward flow formation (curve 4of Fig. 2). After the backward flux front reaches thetarget surface, the density distribution behavior of theplume and ambient gas becomes stationary over the

entire flow space although a rather slow oscillation ofthe contact front position is still remained. As shownin Fig. 2 (curve 5), the fluid velocity of the Si vaporapproaches zero over the entire flow field. The ablatedparticles can approach the target surface only throughdiffusion process, much slower than the shock waveprocess.

We plot the positions of the contact front as wellas the shock fronts as a function of time in Fig. 3.The propagation, reflection of the shock front is clearlyshown. The oscillating behavior of the vapor front andthe backward flow formation are also quite obvious.A similar contact front oscillation phenomenon wasreported recently as an experimental study and ex-plained as an overexpansion effect [23,24]. The back-ward flux of the ablated particles was also observedin several experiments by TOF spectroscopy or time-resolved imaging and used for cluster and thin film de-position [25,26]. From the curves in Fig. 3, we canfind that the propagation of the incoming and the re-

188 M. Han et al. / Physics Letters A 302 (2002) 182–189

flected shock front can be linearly fitted. The veloc-ity of the shock front estimated from the slope of thecurve is consistent with the estimation of the shockwave model [27]. This means the gas dynamics ofhelium gas under PLA process is quite steady, and aone-dimensional stationary analysis of the shock wavemodel is an appropriate approach.

The shock wave formation and reflection phenom-ena due to the introduction of a buffer gas play im-portant roles in the nanoparticle formation and deposi-tion process. In Fig. 1, there is a region at the contactfront where the high density Si vapor peak and the Hegas peak is overlapped, in other words, the Si and Heatoms are mixed within this region. Due to the highdensity of the Si and He atoms, the mean free pathof the atoms in this region is very short. And this re-gion is also compressed both by the incoming vaporpeak and the reflected shock waves. It is reasonable toconsider that within this region, the atoms are locallyconfined. According to the vapor condensation andcluster formation theory (see, for example, Ref. [28]),the cluster formation efficiency is determined by therate of collisions among cluster nucleus, vapor atomsand buffer gas, which is controlled by the densitiesof the vapor atoms as well as the buffer gas atoms.We can expect that effective cluster condensation andgrowth process is constrained in the confined region.This region is the dominant for cluster condensationand growth. The condensation process starts when theconfinement region becomes saturated and stops whenthe clusters are ejected from the confinement region orthe condensation condition become negligible due tothe long time expansion and diffusion. The nanoparti-cles collected on substrates are formed in the gas phasewithin the confinement region far from the substrateand transported to the substrate by diffusion process.Diffusion is driven by gradients in density and temper-ature. The diffusion velocities of the ablated particlesare much slower than the primary expansion velocityof the plume. Comparing to the PLD process in vac-uum, the nanoparticles formed by the PLA process un-der moderate buffer gas pressure are deposited on thesubstrate surface with sufficient low kinetic energy.

In summarize, the gas dynamics during the expan-sion of silicon PLA plume in ambient He gas havebeen investigated by a direct simulation Monte Carlocalculation in a real physical scale from molecularlevel. A shock driven process is clearly observed. The

interaction of the shock front with the substrate sur-face and its effect to the feature of PLA plume iscarefully analyzed. The backward flow formation andvapor front position oscillation phenomena give wellagreement with experimental results. It is shown thata confined layer with high particle density is formedaround the contact front of the expanded vapor andcompressed ambient gas due to the reflection of theshock front on the substrate. The behavior of suchconfined layer is important to the film deposition andnanoparticle formation. The nanoparticles collected onthe substrates are formed within the confinement re-gion and transport to the substrate by diffusion processwith rather low kinetic energy.

References

[1] P.R. Willmott, J.R. Huber, Rev. Mod. Phys. 72 (2000) 315.[2] J.L. Bobin, Y.A. Durand, Ph.P. Langer, G. Tonon, J. Appl.

Phys. 39 (1968) 4184.[3] D.B. Geohegan, Appl. Phys. Lett. 60 (1992) 2732.[4] A.V. Bulgakov, A.P. Mayorov, M.R. Predtechensky,

A.V. Roshchin, Tech. Phys. Lett. 20 (1994) 74.[5] D.B. Geohegan, A.A. Puretzky, Appl. Phys. Lett. 67 (1995)

197.[6] D.B. Chrisey, G.K. Hubler (Eds.), Pulsed Laser Deposition of

Thin Films, Wiley-Interscience, New York, 1994.[7] J.C.S. Kools, J. Appl. Phys. 74 (1993) 6401.[8] F. Garrelie, A. Catherinot, Appl. Surf. Sci. 138/139 (1999) 97.[9] M.R. Predtechensky, A.P. Mayorov, Appl. Superconductivity 1

(1993) 2011.[10] R. Kelly, A. Miotello, Appl. Phys. B 57 (1993) 145.[11] D. Sibold, H.M. Urbassek, Phys. Fluids A 4 (1992) 165.[12] R.F. Wood, K.R. Chen, J.N. Leboeuf, A.A. Puretzky,

D.B. Geohegan, Phys. Rev. Lett. 79 (1997) 1571.[13] J.R. Heath, Y. Liu, S.C. O’Brien, Q.L. Zhang, R.F. Curl,

F.K. Tittel, R.E. Smalley, J. Chem. Phys. 83 (1985) 5520.[14] M. Han, Y.C. Gong, C.R. Yin, J.F. Zhou, F.Q. Song, unpub-

lished.[15] R. Kelly, A. Miotello, A. Mele, A.G. Guidoni, J.W. Hastie,

P.K. Schenck, H. Okabe, Appl. Surf. Sci. 133 (1998) 251.[16] C.J. Knight, AIAA J. 17 (1979) 519.[17] A. Peterlongo, A. Miotello, R. Kelly, Phys. Rev. E 50 (1994)

4716.[18] G.A. Bird, Molecular Gas Dynamics, Clarendon, Oxford,

1976.[19] F.J. Alexander, A.L. Garcia, B.J. Alder, in: J. Brey, J. Marro,

M. Rubi, M. San Miguel (Eds.), 25 Years of Non-EquilibriumStatistical Mechanics, Springer, Berlin, 1995.

[20] F.J. Alexander, A.L. Garcia, B.J. Alder, Phys. Rev. Lett. 74(1996) 5212.

[21] R. Kelly, J. Chem. Phys. 92 (1990) 5047.

M. Han et al. / Physics Letters A 302 (2002) 182–189 189

[22] K.R. Chen, J.N. Leboeuf, R.F. Wood, D.B. Geohegan, J.M. Do-nato, C.L. Liu, A.A. Puretzky, Phys. Rev. Lett. 75 (1995) 4706.

[23] A.V. Bulgakov, M.R. Predtechensky, A.P. Mayorov, Appl.Surf. Sci. 96–98 (1996) 159.

[24] Y. Iwata, M. Kishida, S.W. Yu, S. Kiyama, A. Fukuda,M. Muto, T. Swada, T. Takiya, A. Komura, K. Nakajima,K. Yoshioka, JETRO (2001) 11.

[25] D.B. Geohegan, A.A. Puretzky, G. Duscher, S.J. Pernycook,Appl. Phys. Lett. 72 (1998) 2987.

[26] I.A. Movtchan, W. Marine, R.W. Dreyfus, H.C. Le, M. Sentis,M. Autric, Appl. Surf. Sci. 96–98 (1996) 251.

[27] M. Han, T. Takiya, M. Muto, A. Fukada, T. Sawada, Y. Iwata,unpublished.

[28] W. Marine, L. Patrone, B. Luk’yanchuk, M. Sentis, Appl. Surf.Sci. 154–155 (2000) 345.