Surface instability of multipulse laser ablation on a metallic target

6 Pages·0.378 MB·English

by  Ang L.K., Lau Y.Y., Gilgenbach R.M., Spindler H.L., Lash J.S., Kovaleski S.D.

JOURNALOFAPPLIEDPHYSICS VOLUME83,NUMBER8 15APRIL1998
Surface instability of multipulse laser ablation on a metallic target
L. K. Ang, Y. Y. Lau,a) R. M. Gilgenbach,a) H. L. Spindler,b) J. S. Lash,c)
and S. D. Kovaleski
IntenseEnergyBeamInteractionLaboratory,DepartmentofNuclearEngineering
andRadiologicalSciences,TheUniversityofMichigan,AnnArbor,Michigan48109-2104
(cid:126)Received 28 April 1997; accepted for publication 6 January 1998(cid:33)
Largescalewavelikepatternsareobservedonanaluminumsurfaceafteritisablatedbyaseriesof
KrFlaserpulses(cid:126)248nm,40ns,5J/cm2(cid:33).Thesesurfacestructureshaveawavelengthontheorder
of30(cid:109)m,muchlongerthanthelaserwavelength.Wepostulatethatthesewavepatternsarecaused
by the Kelvin–Helmholtz instability at the interface between the molten aluminum and the plasma
plume.Aparametricstudyisgivenintermsofthemoltenlayer’sthicknessandofthespatialextent
andkineticenergydensityinthelaser-producedplasmaplume.Alsoincludedisanestimateofthe
cumulative growth in a multipulse laser ablation experiment. These estimates indicate that the
Kelvin–Helmholtzinstabilityisaviablemechanismfortheformationofthelargescalestructures.
© 1998 American Institute of Physics. (cid:64)S0021-8979(cid:126)98(cid:33)00408-3(cid:35)
I. INTRODUCTION aged target surface for a number of pulses up to 4200 shots,
we observe a relatively uniform ripple formation in the cen-
Pulsed-laser deposition (cid:126)PLD(cid:33) is an efficient and versa- ter of the laser spot, with large surface structures formed
tile thin film deposition technique.1 The major concern of (cid:126)50–100 (cid:109)m(cid:33) in the outer edge. The spacing of the ripple is
PLD is the particulate formation that leads to the splashing much larger than the laser wavelength, on the order of 30
ofmaterialsonthetarget.Thereisconsiderableevidencethat (cid:109)m (cid:126)see Figs. 1 and 2 below(cid:33).
large particulate formation is preceded by the formation of The laser-produced plasma plumes have several effects
wavelike structures on the ablated surface.2 The surface on laser-target interactions. They might strengthen the large
modificationbycumulativelaserirradiationalsoaffectsboth scalestructuresontheonehand(cid:126)seebelow(cid:33),andtheymight
the film composition and deposition rate.3 The mechanisms absorb or reflect the laser energy,17 thereby preventing the
of the laser sputtering of materials have been studied.4
laser light from reaching the surface, with the result of re-
Roughly speaking, there are two types of surface struc-
ducingthethicknessofthemoltenlayer.Contrarytothecase
tures resulting from laser irradiation. The first type is of
ofsmallscalesurfacestructures,thesurfaceconditionsofthe
small scale, on the order of the laser wavelength. They are
pre-ablated metal, as well as whatever interference effects
observedduringthefirstfewpulsesorwhenthelaserfluence
with the incident laser light, are probably less crucial in the
isbelowthedamagethresholdofthesurface.Ingeneral,they
formation of the large scale structures, which were not ob-
are more dependent on the surface condition, such as the
servedforpolymersandothermaterialsusingthisKrFlaser.
optical and thermophysical properties of the material. There
The presence of large scale surface structures must have
are existing theories for the formation of these small scale
been created by a rather significant energy reservoir. The
periodic surface structures.5 The proposed mechanisms in-
fairly regular wavelike patterns look much like the wind-
clude inhomogeneous energy deposition due to the interfer-
driven surface wave in a pond (cid:126)see Fig. 1(cid:33). This recognition
ence of the incident laser beam and the surface scattering
naturally directs our attention to the Kelvin–Helmholtz
field.Excitationofsurfaceplasmonscanproduceanomalous
instability18 as a candidate for the creation of similar wave-
absorption under high fluence irradiation,6 and the laser-
like structures. In our case, the molten aluminum plays the
driven corrugation instability leads to a strong coupling
role of ‘‘water,’’ and the ‘‘wind’’ comes from expansion of
when the critical depth reaches the pump laser wavelength.
thehighpressureplasmaplume.Thelargesurfacestructures
The second type of surface structures, the object of the
occurwhenthesurfacewaves(cid:126)comingfromthecenterofthe
present study, has a scale much greater than the pump laser
laser spot(cid:33) are splashed and solidified at the edge. We may
wavelength. These large surface structures7,8 appear when
tentativelyidentifytheKelvin–Helmholtzinstabilityasavi-
thelaserfluenceisabovethedamagethresholdandthetarget
able candidate if the computed growth rate may explain the
is heated beyond the vapor phase to the plasma state. In the
multipulse experiments,2,9–16 a KrF laser (cid:126)248 nm, 40 ns, buildup of the large scale structures during the multipulse
5–10J/cm2(cid:33) is incident on an aluminum target. From the ablation, upon using a reasonable set of parameters consis-
scanning electron microscope (cid:126)SEM(cid:33) pictures of the dam- tent with the experiments.
In addition to Kelvin–Helmholtz (cid:126)KH(cid:33) instability, we
have also studied the possibilities of other hydrodynamic in-
a(cid:33)Alsoat:AppliedPhysicsProgram,UniversityofMichigan,AnnArbor,MI stabilities, such as capillary wave (cid:126)CW(cid:33) and Rayleigh–
48109.
b(cid:33)BoeingCorp.,Seattle,WA. Taylor (cid:126)RT(cid:33) instability. Brailovsky etal.8 considered all
c(cid:33)SandiaNationalLaboratory,Albuquerque,NM. three instabilities for the mechanisms of melt droplets. For
0021-8979/98/83(8)/4466/6/$15.00 4466 ©1998AmericanInstituteofPhysics
J.Appl.Phys.,Vol.83,No.8,15April1998 Angetal. 4467
(cid:108) ; it equals 4 (cid:109)m by estimating an acceleration force (cid:126)(cid:97)(cid:33)
m
of 3.2(cid:51)109 m/s2 (cid:126)Ref. 20(cid:33) in the liquid-vapor interface.
Moreover,theRTinstabilityusuallydoesnothaveitssigna-
tureintheformofaveryregularwavepatternasexhibitedin
Fig.1,althoughthisinstabilitymightwellbeacandidatefor
the formation of the individual droplets of molten materials
attheedgeofthelaserspot,2butdropletformationisbeyond
the scope of the present paper.
The growth rate of the thermocapillary instability21 is
tooslowtoinitiatethelargescalestructures.Thecorrugation
instability of plane evaporation waves21 in liquid also grows
too slowly. The above considerations of small (cid:108) (cid:126)less than
m
10 (cid:109)m(cid:33) and slow growth rate help us to eliminate the other
macroscopic instabilities in favor of KH instability. We note
that our model is different from the one previously consid-
eredbyBrailovskyetal.8inthattheirKHinstabilitymecha-
nism is caused by the perpendicular plume velocity stream-
ing along the vertical column of the molten layer. More
specifically, Brailovsky examined the KH instability on the
vertical columns that are already formed. Here we analyze
how these vertical columns are formed in the first place: the
parallel wind leads to growth of the vertical columns via the
KH instability. Once these vertical columns are formed, the
FIG.1. ASEMpicture(cid:126)at50(cid:51)magnification(cid:33)ofthelaserablationspotof (cid:126)vertical(cid:33)windthenprovidessecondaryripplesonthesecol-
1000 KrF excimer laser pulses on an aluminum target at a fluence of umns.Brailovkyanalyzedthesecondaryripplesthusformed.
10J/cm2(cid:64)fromRef.10(cid:35).
It is clear that when the amplitude of the vertical columns is
small (cid:126)which is the case during their initial growth that is
analyzed here(cid:33), Brailovsky’s mechanism is inoperative.
CWinstability,theyconsideredasubsonicvaporevaporated
Theuncertaintiesintheparameters,suchasthedepthof
from the surface with a perpendicular expansion velocity of
order104 cm/s, whichistwoordersofmagnitudelowerthan the molten layer and the density and velocity profiles of the
our measured velocity (cid:126)on the order of cm/(cid:109)s(cid:33) in the plasma wind at the liquid-plasma interface, force us to use a
experiments10–16 (cid:126)see below(cid:33). Their calculation for the case semiemperical approach on a much simplified model. We
ofbismuthablatedbylaserintensityof109 W/cm2yieldeda use a one-dimensional model with conveniently chosen den-
maximum instability increment ((cid:108) ) of 0.1 (cid:109)m, which is sity and velocity profiles for the two media: molten liquid
m
much lower than our experimental value of about 30 (cid:109)m. andplasmawind.Wepostulatethatthewavelikepatternthat
Unlike the RT instability discussed by Brailovsky,19 is observed in the experiment corresponds to the wave num-
ber that yields the highest growth rate. We then examine the
conventionalRTinstabilitymodelhasbeenusedtocalculate
dependence of this maximum growth on the parameters. We
next evaluate the cumulative growth for a sequence of laser
pulses, assuming that between pulses, the wave pattern so-
lidifies quickly so that the frozen pattern serves as the initial
condition at the time the next laser pulse arrives. The ranges
of the chosen parameters are guided by extensive, previous
experimental measurements of plasma plume
parameters.10–16 From Ref. 12 (cid:126)Figs. 9i,j(cid:33), one can infer a
transverse plasma wind velocity of 0.18 cm/(cid:109)s.
Finally, we remark that the laser inhomogeneity is un-
likely to produce wavelike patterns so regular over a broad
front (cid:126)cf. Fig. 1(cid:33) and these have not been seen in our previ-
ous experiments on polymer and ceramic ablation.
II. EXPERIMENTAL CONFIGURATION AND DATA
The laser ablation plume was produced by focusing a
pulse from a KrF excimer laser (cid:126)248 nm, 40 ns, (cid:44)1.2 J(cid:33) on
aluminum targets. The analyzed samples consisted of seven
FIG.2. ASEMpicture(cid:126)at500(cid:51)magnification(cid:33)inthemiddleofadamaged
99.999% pure solid aluminum targets. The targets were
Al target irradiated by 250 pulses of KrF excimer laser (cid:126)248 nm, 40 ns,
5J/cm2 on a pure aluminum target in vacuum condition ((cid:44)2 placed at a ninety degree angle to the incident laser beam.
(cid:51)10(cid:50)5 Torr). Thelaserfocalspotwas2.0by2.5mm,or0.05cm2inarea.
4468 J.Appl.Phys.,Vol.83,No.8,15April1998 Angetal.
The fluence was measured at regular intervals by inserting a
calorimeterinfrontoftheKrFlaserbeam.Theaveragelaser
fluence at the target was approximately 5J/cm2.
Fortheseexperiments,thestainless-steelvacuumsystem
was evacuated using a rotary pump-backed turbomolecular
pump.Thepressureremainedlessthan2(cid:51)10(cid:50)5 Torrduring
the laser ablation of aluminum.
Progressivelevelsofdamage,rangingfrom5upto4200
excimer laser pulses, were produced on each of seven tar-
gets.Theresultingdamageonthetargetswasinvestigatedby
placing each target in an SEM. At each stage of damage, an
SEM image was taken of the entire laser focal spot and a
second SEM image was taken at a higher magnification in FIG. 3. The model of 2 layers of fluids in relative motion in x-direction.
(cid:114)(z) and U(z) are the equilibrium mass density and horizontal velocity,
the middle of the damaged area. From our results, the sig-
wheresubscript‘1’isforthemoltenlayer(z(cid:44)0) and‘2’isfortheplasma
nificant uniform ripple began to occur at 250 laser pulses plume(z(cid:46)0).
irradiation.Here,weonlypresenttheSEMimage(cid:126)500(cid:51)(cid:33)in
the middle of the damaged area at 250 laser pulses (cid:126)see Fig.
2(cid:33). Figure 1 shows the damage in the middle of the spot at (cid:83) (cid:68)
1000 pulses and 50(cid:51) magnification. (cid:126)k U(cid:50)(cid:118)(cid:33) d2(cid:50)k2 u(cid:50)k u d2U(cid:49)1 d(cid:114)
This KrF laser ablated Al plasma has been extensively x dz2 x dz2 (cid:114)dz
(cid:83) (cid:68)
characterized in our previous research.11–16 Many different
du dU gk2
diagnostics have been used to investigate the expansion (cid:51) (cid:126)k U(cid:50)(cid:118)(cid:33) (cid:50)k u (cid:50)u
x dz x dz k U(cid:50)(cid:118)
velocity of the laser ablation plumes, such as resonant x
(cid:83) (cid:68)
holographic interferometry,11,12 resonance absorption k4(cid:115) d4 d2
photography,11,13,14 schlieren photography,14,15 and laser (cid:49)u (cid:100)(cid:126)z(cid:33)(cid:49)i(cid:110) (cid:50)2k2 (cid:49)k4 u(cid:53)0.
(cid:114)(cid:126)k U(cid:50)(cid:118)(cid:33) dz4 dz2
deflection.11,16 The electron density has been measured by x
laser deflection.11 From Ref. 12, the leading edge (cid:126)perpen- (cid:126)1(cid:33)
dicular to target(cid:33) expansion velocity of (cid:39)1.4 cm/(cid:109)s in Here, k2(cid:53)k2(cid:49)k2, g is the gravity acceleration, (cid:115)is surface
x y
vacuum has been measured which corresponds to an initial tension constant, (cid:110)is kinematic viscosity constant, and (cid:100)(z)
(cid:126)perpendicular to target(cid:33) plume temperature of 3.6 eV. It is is the Dirac delta function. To simplify Eq. (cid:126)1(cid:33), we compare
important to clarify that this perpendicular expansion veloc-
themagnitudeofvariousterms:gravity,surfacetension,and
ity is higher than the parallel velocity, which has been in-
viscosity. From the available experimental data, we notice
ferred from previous experimental measurements (cid:126)Ref. 12, that (cid:108)(cid:91)2(cid:112)/k is on the order of 30 (cid:109)m. We then find that
Figs. 9i, j(cid:33) to be about 0.18 cm/(cid:109)s. surface tension is the dominant term, with (cid:115)k3/(cid:114)(cid:64)((cid:110)k2)2
1
FromRef.11,theelectrondensityprofileoftheablation (cid:64)gk (cid:126)Ref. 23(cid:33).
plume has been measured at various times. Typically, at 50 In region I (z(cid:44)0), we assume that the molten layer has
ns, the measured electron density is about 3(cid:51)1017 cm(cid:50)3 at a thickness of H , with a uniform density (cid:114) and uniform
1 1
0.3mmabovethetargetsurfacesothisdensitycanapproach velocity U (cid:126)which may be taken to be zero(cid:33). Equation (cid:126)1(cid:33)
1018–1019 cm(cid:50)3 at the surface. Thus, in this paper, we con- 1
reduces to
sider a rather dense plasma (cid:126)residual plume(cid:33) moving up to 1 (cid:83) (cid:68)
cm/(cid:109)s parallel to the target surface, which produces the (cid:126)k U (cid:50)(cid:118)(cid:33) d2(cid:50)k2 u (cid:53)0. (cid:126)2(cid:33)
wavelike pattern. Contrary to the roughness at the edge, we x 1 dz2 1
have a rather smooth surface with a regular ripple pattern in In region II (z(cid:46)0), we assume that the high-pressure
the order 30 (cid:109)m spacing in the center of the laser spot. plasma plume gives rise to a wind, with density (cid:114)(cid:91)(cid:114)(z)
2 2
andvelocity,U (cid:91)U (z). Weassumethatthephasevelocity
2 2
of the surface wave, (cid:118)/k is much less than the equilibrium
x
III. THE MODEL velocity, U2 (cid:126)U2(cid:64)(cid:118)/kx, to be verified later(cid:33). Equation (cid:126)1(cid:33)
becomes
In a sharp boundary model (cid:126)Fig. 3(cid:33), the molten alumi- (cid:70) (cid:83)
d2 1 d(cid:114) d 1 d(cid:114) 1 dU
num is located in region I (z(cid:44)0) and the plasma plume is (cid:126)k U (cid:50)(cid:118)(cid:33) (cid:49) 2 (cid:50) k2(cid:49) 2 2
located in region II (z(cid:46)0); the interface at z(cid:53)0. In the x 2 dz2 (cid:114)2 dz dz (cid:114)2 dz U2 dz
(cid:68)(cid:71)
description of Kelvin–Helmholtz instability, we consider a 1 d2U
general density profile (cid:114)(z), and general velocity profile (cid:49) 2 u (cid:53)0. (cid:126)3(cid:33)
U dz2 2
U(z). We may also include the effects of surface tension, 2
viscosity,andgravity.Bycombiningtheequationofmotion, Inordertocalculatethegrowthrateoftheinstability,we
continuity equation, incompressible condition and perturba- solveEqs.(cid:126)2(cid:33)and(cid:126)3(cid:33)intheregionz(cid:44)0 andz(cid:46)0 foru and
1
tion of the form exp(ik x(cid:49)ik y(cid:50)i(cid:118)t), where (cid:118)(cid:53)((cid:118)(cid:49)i(cid:103)), u , respectively, and integrate Eq. (cid:126)1(cid:33) at the boundary from
x y r 2
we obtain the governing equation22 for the perturbed veloc- z(cid:53)0(cid:50) to 0(cid:49). To simplify the calculation, let (cid:114)(z)
2
ity, u: (cid:53)(cid:114) exp((cid:50)z/H ) and U (z)(cid:53)U exp((cid:50)z/H ), where H
2o 2 2 2o 3 2
J.Appl.Phys.,Vol.83,No.8,15April1998 Angetal. 4469
isthedensityscalelengthoftheplumeandH isthevelocity
3
shearscalelengthoftheplume.ItisclearthatU (cid:64)U and
2o 1
(cid:114)(cid:64)(cid:114) . We then obtain the growth rate
1 2o
(cid:65)
(cid:103)(cid:53) tanh(cid:126)(cid:76) (cid:33)(cid:64)(cid:126)(cid:70)(cid:114) U2 k2(cid:50)k3(cid:115)(cid:33)/(cid:114) (cid:35), (cid:126)4(cid:33)
1 2o 2o 1
and the real part of the frequency
(cid:70) (cid:71)
(cid:114) U
(cid:118)(cid:53)kU 2o tanh(cid:126)(cid:76) (cid:33)(cid:70)(cid:49) 1 , (cid:126)5(cid:33)
r 2o (cid:114) 1 U
1 2o
(cid:65)
where (cid:70)(cid:91)(cid:64)2 (cid:76)2(cid:49)(r(cid:49)1/2)2(cid:50)1(cid:35)/2(cid:76) (cid:62)0, (cid:76) (cid:91)kH , (cid:76)
2 2 1 1 2
(cid:91)kH , andr(cid:91)H /H arenormalizedparameters.Inobtain-
2 2 3
ing Eqs. (cid:126)4(cid:33) and (cid:126)5(cid:33), the boundary conditions u ((cid:50)H )(cid:53)0,
1 1
u ((cid:96))(cid:53)0 and u (0)(cid:50)u (0)(cid:53)U (0)(cid:50)U (0), as well as
2 2 1 2 1
the assumption kx(cid:39)k have been used. Note that Eq. (cid:126)4(cid:33) can FIG.4. Normalizedgrowthrate,(cid:103)¯(cid:91)(cid:103)/(cid:103)(cid:96) asafunctionofH2 forvarious
be extended to include the Rayleigh–Taylor instability and H at(cid:108)(cid:53)30(cid:109)mandr(cid:53)1(r(cid:91)H /H ). H , H , andH are,respectively,
1 2 3 2 3 1
gravitation effects, by adding the term(cid:114)k((cid:97)(cid:50)g) in the nu- the characteristic scale length of the plume’s density profile, the plume’s
1
merator in the square bracket of Eq. (cid:126)4(cid:33), where (cid:97)is the velocityprofileandmoltenlayerofAl.
accelerationforcewhichacceleratesverticallyfromthemol-
ten layer to the plasma plume layer, and g is gravitational
mate the growth rate with Eq. (cid:126)6(cid:33) and calculate the corre-
acceleration.Inthisarticle,weestimatethattheseeffectsare
sponding plasma energy density as a function of H , H ,
negligible due to the high plasma plume velocity.10–16 1 2
H .
Since there are many parameters that are not readily 3
By setting (cid:108)(cid:53)30 (cid:109)m, we show the dependence of the
available from experiments (cid:126)such as H , H and H (cid:33), to
1 2 3 growth rate on H and H . Figure 4 shows that the growth
proceedfurther,wepostulatethatthewavelikepatternthatis 1 2
rate increases with H and decreases with H for r
observed in experiments (cid:126)Fig. 1(cid:33) corresponds to the wave- 1 2
(cid:91)H /H (cid:53)1 (cid:126)spatialvariationoftheplumedensityprofileis
number that yields the maximum growth. Then by varying 2 3
assumed to be equal to that of parallel velocity profile(cid:33). The
H , H , andH , wemayinferwhatwouldbethetemporal
gr1owth2rate of3the Kelvin–Helmholtz instability, and the growth rate can be twice (cid:103)(cid:96) at high H1 and low H2, and
diminishes to zero at low H . We also calculate the corre-
plasma wind kinetic energy density (cid:68)(cid:91)(cid:114) U2 that is re- 1
2o 2o spondingenergydensityneededtodrivethesurfaceinstabil-
quired so as to produce such a growth with the observed
ity at (cid:108)(cid:53)30 (cid:109)m. The dependence of (cid:68)¯ on H and H are
wave number. Thus, by setting d(cid:103)/dk(cid:53)0, we obtain the 1 2
giveninFig.5;itincreaseswithH andH . However,fora
equationthatmaximizesthegrowthrateandtheenergyden- 1 2
wide range of H (cid:126)1–100 (cid:109)m(cid:33), (cid:68)¯ does not change much,
sitythatisrequiredtoyieldsuchagrowthwiththeobserved 1
wave number k. The normalized growth rate, (cid:103)¯, and the with an asymptotic value between 0.9 and 1.1 for H2
(cid:46)5(cid:109)m.
corresponding normalized plasma plume’s energy density,
(cid:68)¯, are given b(cid:65)y In order to calculate the growth rate of these large sur-
(cid:83) (cid:68) face structures and energy density of the ablation plume, we
(cid:76) have to estimate H , H , and H . In the fluence range of a
(cid:103)¯(cid:91) (cid:103)(cid:53) 2(cid:83)tanh (cid:76)1 (cid:70)(cid:50)(cid:126)(cid:68)2(cid:76)2(cid:70)2(cid:49)1(cid:33) , (cid:126)6(cid:33) fBeywsJe/tctimng2 (cid:108)of(cid:53)l3a0se(cid:109)r1mab,laHt2io(cid:53)n,2H(cid:109)1m3i,satnydpicra(cid:53)ll1y,athfeewnormmicarlioznesd.
(cid:103)(cid:96) (cid:70) 1(cid:49) (cid:76)1 (cid:49) (cid:76)2 1
2 sinh2(cid:76) 2(cid:76) (cid:70)(cid:49)1
1 2
(cid:70) (cid:71)
and
2(cid:76)
1(cid:49) 1
(cid:68) 3sinh2(cid:76)
(cid:68)¯(cid:91) (cid:53) (cid:83) (cid:68) 1 . (cid:126)7(cid:33)
(cid:68)(cid:96) (cid:70) 1(cid:49) (cid:76)1 (cid:49) (cid:76)2
2 sinh2(cid:76) 2(cid:76) (cid:70)(cid:49)1
1 2
Here (cid:64)(cid:103)(cid:96),(cid:68)(cid:96)(cid:35)(cid:53)(cid:64)((cid:115)k3/2(cid:114)1)1/2,3(cid:115)k/2(cid:35), the quantities corre-
sponding to H1, H2, H3!(cid:96). For (cid:108)(cid:53)30 (cid:109)m, we have (cid:103)(cid:96)
(cid:39)1.3(cid:109)s(cid:50)1, and (cid:68)(cid:96)(cid:39)0.272J/cm3, using (cid:114)(cid:53)2.37g/cm3,
(cid:115)(cid:53)0.865 N/m, (cid:110)(cid:53)1.055(cid:51)10(cid:50)2 cm2/s and g(cid:53)9.8m/s2
(cid:126)from Ref. 23(cid:33).
Traditionally, Eq. (cid:126)7(cid:33) gives the most probable period (cid:108)
of the surface wave when (cid:68), H , H , H and the thermo-
physicalpropertiesaregiven,and1 the2grow3thrateatthis(cid:108)is FIG.5. Normalizedenergydensity,(cid:68)¯(cid:91)(cid:68)/(cid:68)(cid:96)asafunctionofH2forvari-
ousH at(cid:108)(cid:53)30(cid:109)mandr(cid:53)1(r(cid:91)H /H ). H , H , andH are,respec-
calculated from Eq. (cid:126)6(cid:33). Here, we keep H , H , and H as 1 2 3 2 3 1
1 2 3 tively, the characteristic scale length of the plume’s density profile, the
free parameters, and use the experimental value of (cid:108) to esti- plume’svelocityprofileandmoltenlayerofAl.
4470 J.Appl.Phys.,Vol.83,No.8,15April1998 Angetal.
FIG.6. Normalizedgrowthrate,(cid:103)¯(cid:91)(cid:103)/(cid:103)(cid:96) andnormalizedenergydensity, FIG. 7. Calculated cumulative growth, as a function of N (cid:126)number of
(cid:68)¯(cid:91)(cid:68)/(cid:68)(cid:96) as a function of H2 at (cid:108)(cid:53)30 (cid:109)m, H1(cid:53)2(cid:109)m, and r(cid:53)1(r pulses(cid:33) of KrF excimer laser ablation (cid:126)248 nm, 40 ns, 5J/cm2(cid:33) on a pure
(cid:91)H2/H3).Thedashedlinesaretheupperandlowerlimitsofthemeasured aluminumtargetforH1(cid:53)1,2,3(cid:109)m.
(cid:68)¯ ((cid:125)n T ), where n (cid:39)1019cm(cid:50)3 and T (cid:39)1eV (cid:126)upper limit(cid:33) and 0.1 eV
e e e e
(cid:126)lowerlimit(cid:33).
3000 times for H (cid:53)3(cid:109)m, which may be deemed reason-
1
able, considering all the approximations involved. The issue
energydensityandgrowthratearegiveninFig.6.Toensure of saturation remains to be studied.
that KH instability is indeed a possible mechanism for the In ablation experiments, the plume’s density profile
growthat(cid:108)(cid:53)30(cid:109)m,wecomparethecalculated(cid:68)¯ withmea- is time dependent, which, roughly speaking, evolves from
sured(cid:68)¯, bysetting(cid:68)(cid:39)n T . Here,n istheelectrondensity exp((cid:50)z/H)2andtoaprofilewhosepeakdensityislocatedfar
e e e
at the target surface ((cid:39)1019 cm(cid:50)3) and T is electron tem- above the interface surface,26 after a much longer time scale
e
perature corresponding to the parallel velocity14 (cid:126)1 eV for thanthelaserpulselength(cid:126)duetoplumeexpansionfromthe
upperlimitand0.1eVforlowerlimit(cid:33),wherebothn andT interface surface(cid:33). We have assumed a constant profile
e e
were previously measured from this experiment.11–12,24 In withinthelaserpulselengthtimescaleinthismodel,butdue
Fig. 6, the upper and lower limit of the measured (cid:68)¯ are to the lower gradient (d(cid:114)/dz) at the interface surface of
shown. As can be seen, the calculated (cid:68)¯ lies within the ex- these evolved density profiles at later time, the contributions
perimental range, and the calculated growth rate is about of this expanding plume to growth become negligible.
0.66(cid:109)s(cid:50)1 at H2(cid:46)20(cid:109)m. To verify our assumption of U2(cid:64)(cid:118)/kx, under the con-
ditionsU (cid:64)U and(cid:114)(cid:64)(cid:114) , wefoundthat(cid:118)(cid:33)kU (cid:64)see
2o 1 1 2o r 2o
Eq. (cid:126)5(cid:33)(cid:35), and the maximum of (cid:103)/k (cid:126)and (cid:118) /k(cid:33) is about 1240
r
IV. CUMULATIVE GROWTH cm/s. Thus the phase velocity of the surface wave is indeed
muchslowerthananyvelocityintheplasmaplume,whichis
Theaboveparametricstudyofthetemporalgrowth,asa in the range of 105–106 cm/s.11,12
function of H , H , and H , allows us to assess the total
1 2 3
growth after N laser pulses, each pulse lasting 40 ns. We
wish to calculate the cumulative growth rate, (cid:103)*((cid:53)(cid:40)N(cid:103)) ACKNOWLEDGMENTS
i i
after N laser pulses of irradiation. As can be seen in Figs. 1 This research was supported by National Science Foun-
and 2, molten surface waves of material that have been so- dation Grant No. CTS-9522282. H.L.S. and J.S.L. acknowl-
lidified have a rather smooth ripple with period of about 30 edge previous support from National Science Foundation
(cid:109)m in the center of the laser spot. However, at the edge of Graduate Fellowships. The authors also acknowledge the
the crater, we found material piled up in conical structures support of Sandia National Laboratory. They wish to thank
with height 50 to 100 (cid:109)m (cid:126)see SEM image in Ref. 2(cid:33). Thus, the referee for many helpful comments.
weassumethatH (N)(cid:53)H (N) isalinearlyincreasingfunc-
2 3
tion with N, up to 100 (cid:109)m at N(cid:53)250 and H (N) is a con-
1
stant (cid:126)(cid:53)1, 2, 3 (cid:109)m(cid:33).25 The increase in the scales H and H 1D.B.Chrisey,andG.K.Hubler,PulsedLaserDepositionofThinfilms
2 3 (cid:126)Wiley,NewYork,1994(cid:33).
in the plasma plume, as N increases, is on account of the
2H. L. Spindler, R. M. Gilgenbach, and J. S. Lash, Appl. Phys. Lett. 68,
observed buildup of the surface roughness as N increases. 3245(cid:126)1996(cid:33).
Thespatialextentoftheplasma,asmeasuredbyH andH , 3S. R. Foltyn, R. C. Dye, K. C. Ott, E. Peterson, K. M. Hubbard, W.
2 3
isthenexpectedtoincreasewithN. Itturnsoutthatthefinal Hutchinson,R.E.Muenchausen,R.C.Estler,andX.D.Wu,Appl.Phys.
Lett.59,594(cid:126)1991(cid:33).
result is not sensitive to the precise values of H and H ,
2 3 4R.KellyandJ.E.Rothenberg,Nucl.Instrum.MethodsPhys.Res.B7/8,
with H2, H3(cid:46)10(cid:109)m, but it is more sensitive to the magni- 755(cid:126)1985(cid:33);R.Kelly,J.J.Cuomo,P.A.Leary,J.E.Rothenberg,B.E.
tude of H (cid:126)see Fig. 4(cid:33). Braren, and C. F. Aliotta, ibid. 9, 329 (cid:126)1985(cid:33); J. E. Rothenberg and R.
Using1suchamodel,weshowthegrowthofexp(cid:126)(cid:103)*(cid:116)(cid:33)in Kelly,ibid.1,291(cid:126)1984(cid:33).
5H.M.vanDriel,J.E.Sipe,andJ.F.Young,Phys.Rev.Lett.49,1955
Fig. 7, up to N(cid:53)250, where (cid:116)is set to be the laser pulse- (cid:126)1982(cid:33);J.E.Sipe,J.F.Young,J.S.Preston,andH.M.vanDriel,Phys.
lengthof40ns.Theeffectivegrowthfor250pulsesisabout Rev.B27,1141(cid:126)1983(cid:33).
J.Appl.Phys.,Vol.83,No.8,15April1998 Angetal. 4471
6F.Keilmann,Phys.Rev.Lett.51,2097(cid:126)1983(cid:33);S.R.J.Brueck,andD.J. 20T.D.Bennett,C.P.Grigoropoulos,andD.J.Krajnovich,J.Appl.Phys.
Ehrlich,ibid.48,1678(cid:126)1982(cid:33). 77,849(cid:126)1995(cid:33).Here,welinearlyinterpolatedtheaccelerationforce(cid:126)(cid:97)(cid:33)
7S.A.Akhmanov,V.I.Emel’yanov,N.I.Koroteev,andV.N.Seminogov, byusingtheEq.(cid:126)7(cid:33)inthisreferenceforourexperimentofanA1target
Sov. Phys. Usp. 28, 1084 (cid:126)1985(cid:33); O. Bostanjoglo and T. Nick, J. Appl. ablatedbylaserintensityof5J/cm2.Notethatevenwithoutinterpolation,
Phys.79,8725(cid:126)1996(cid:33). usingthevaluefromtheircaseof1J/cm2, wehave(cid:108) (cid:53)8(cid:109)m.
8A.B.Brailovsky,S.V.Gaponov,andV.I.Luchin,Appl.Phys.A:Solids 21S.I.AnisimovandV.A.Khokhlov,InstabilitiesinLasmer-MatterInterac-
Surf.61,81(cid:126)1995(cid:33). tion(cid:126)ChemicalRubberCo.,BocaRaton,1995(cid:33).
9L.K.Ang,Y.Y.Lau,R.M.Gilgenbach,andH.L.Spindler,Appl.Phys.
Lett.70,696(cid:126)1997(cid:33). 22See,e.g.,S.Chandrasekhar,inHydrodynamicandHydromagneticStabil-
ity(cid:126)Dover,NewYork,1961(cid:33),Chap6.Notethatviscositytermhasbeen
10J.S.Lash,Ph.D.dissertation,UniversityofMichigan,1996.
11R. M. Gilgenbach, C. H. Ching, J. S. Lash, and R. A. Lindley, Phys. included.
Plasmas1,1619(cid:126)1994(cid:33). 23Thedifferenceintheinequalityisoforder103, for(cid:114)(cid:53)densityofmolten
12R.A.Lindley,R.M.Gilgenbach,C.H.Ching,andJ.S.Lash,J.Appl. Al(cid:53)2.37g/cm3, (cid:115)(cid:53)0.865 N/m, (cid:110)(cid:53)1.055(cid:51)10(cid:50)2 cm2/s, and g
Phys.76,5457(cid:126)1994(cid:33). (cid:53)9.8m/s2.
13R. M. Gilgenbach and P. L. G. Ventzek, Appl. Phys. Lett. 58, 1597 24In the ablation plume, the ion component can been ignored as ion tem-
(cid:126)1991(cid:33). peratureismuchlowerthanelectrontemperature.Notethattheelectron
14P.L.G.Ventzek,R.M.Gilgenbach,C.H.Ching,andR.A.Lindley,J. densityisdifficulttomeasureatthetargetsurface,herewehaveestimated
Appl.Phys.72,1696(cid:126)1992(cid:33). itisabout1019cm(cid:50)3(cid:126)twoordershigherthanwhatwemeasuredat0.3mm
15P.L.G.Ventzek,R.M.Gilgenbach,J.A.Sell,andD.M.Heffelfinger,J. abovethetargetsurface(cid:33).
Appl.Phys.68,965(cid:126)1990(cid:33). 25Thedepthofthemoltenaluminum,H , islikewiseexpectedtoincrease
16P.L.G.Ventzek,R.M.Gilgenbach,D.M.Heffelfinger,andJ.A.Sell,J. 1
withN forsmallN. However,forlargervaluesofN, theplasmaplume
Appl.Phys.70,587(cid:126)1991(cid:33).
17X.MaoandR.E.Russo,Appl.Phys.A:SolidsSurf.64,1(cid:126)1997(cid:33). becomes substantial and it may begin to absorb (cid:126)and reflect(cid:33) the laser
18See,e.g.,D.Bauerle,inLaserProcessingandChemistry(cid:126)Springer,Ber- light,leavingamuchreducedfractionoflaserenergythatcouldreachthe
lin,1996(cid:33),p.409. aluminum surface (cid:126)Ref. 17(cid:33). Thus, H1 is expected to be reduced as N
19RT instability model from Ref. 8 is based on acceleration produced by becomes large. However, for simplicity we assume that H1 does not
centrifugalforceofmoltenflowatconvexliquid-solidinterface,whichis changemuch,whichisaround1–3(cid:109)m.
asecond-ordereffect(cid:126)thevelocityofmoltenflowisnothighenoughto 26A.Mele,A.G.Guidoni,R.Kelly,A.Miotello,S.Orlando,R.Teghil,and
produceasignificantforce(cid:33). C.Flamini,Nucl.Instrum.MethodsPhys.Res.B116,257(cid:126)1996(cid:33).