ISSN 00213640, JETP Letters, 2014, Vol. 99, No. 9, pp. 518–522. © Pleiades Publishing, Ltd., 2014. Original Russian Text © V.I. Emel’yanov, D.A. Zayarniy, A.A. Ionin, I.V. Kiseleva, S.I. Kudryashov, S.V. Makarov, T.H.T. Nguyen, A.A. Rudenko, 2014, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2014, Vol. 99, No. 9, pp. 601–605.
Nanoscale Hydrodynamic Instability in a Molten Thin Gold Film Induced by Femtosecond Laser Ablation V. I. Emel’yanova, D. A. Zayarniyb, A. A. Ioninb, I. V. Kiselevab, c, S. I. Kudryashovb, *, S. V. Makarovb, **, T. H. T. Nguyenb, c, and A. A. Rudenkob a
Faculty of Physics, Moscow State University, Moscow, 119991 Russia * email:
[email protected] ** email:
[email protected] b Lebedev Physical Institute, Russian Academy of Sciences, Leninskii pr. 53, Moscow, 119991 Russia c Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudnyi, Moscow region, 141700 Russia Received April 1, 2014
A mechanism of the formation of a nanotip with a nanoparticle at its top that appears in a thin metal film irradiated by a single femtosecond laser pulse has been studied experimentally and theoretically. It has been found that the nanotip appears owing to a melt flow and a nanojet formation, which is cooled and solidified. Within a proposed hydrodynamic model, the development of thermocapillary instability in the melted film is treated with the use of the Kuramoto–Sivashinskytype hydrodynamic equation. The simulation shows that the nanojet nucleates in the form of a nanopeak in a pit on the top of a microbump (linear stage) and, then, grows in a nonlinear (explosive) regime of an increase in thermocapillary instability in good agreement with experimental data. DOI: 10.1134/S0021364014090057
1. A metallic nanotip is one of the most important nanostructures because it can locally enhance an elec tromagnetic field owing to the socalled lightning rod effect [1]. It was previously shown that an array of laserinduced nanotips (nanojets) has resonant optical absorption [2] and exhibits an increased photoemis sion of charged particles under irradiation by an intense ultrashort laser pulse [3]. One of the promising methods for creating surface metallic nanotips is the use of strongly focused nanosecond [4], picosecond [5], and femtosecond [6] laser pulses. This method makes it possible to create a single nanotip on a microbump pedestal on the surface of a thin metallic film per pulse. Another remarkable method for the formation of nanotips involves the excitation and focusing of intense surface electromagnetic waves on metallic surface microrings [3, 7]. This method allows the creation of an array of numerous disordered (the entire array per two pulses at weak focusing) or ordered (numerous pairs of strongly focused ultrashort pulses at pointbypoint writing of the array) nanotips on the surface of a bulk metal without the attendant forma tion of microbumps. It is noteworthy that the forma tion of nanotips in both cases is accompanied by the formation of a nanosphere on the top of a nanotip, which is pinchedoff at a certain threshold fluence and can be deposited on another surface [8]. The formation of laserinduced nanotips refers to phenomena of the hydrodynamic flow in a melted
shell of a microbump [9], pressure of evaporated vapor [5], and thermoelastic and plastic deformation at the expansion of a heated film [10]. At the same time, the effect of the thickness of a metallic film, as well as of focusing of ultrashort laser pulse (width of the melt pool), on the geometric parameters of appearing nanostructures has not yet been systematically stud ied. Therefore, the physical mechanism of the laser induced formation of these nanostructures remains unknown. In this work, the formation of a nanotip under irra diation by a single ultrashort laser pulse with various energies is experimentally studied and a hydrody namic model of the formation and development of a nanojet with the appearance of a nanoparticle is pro posed. 2. As a sample, we used a film of an 80/20 gold– palladium alloy with the thickness h ≈ 60 nm deposited in an argon atmosphere on a CaF2 substrate by magne tron sputtering (SC7620, Quorum Technologies). A fiber laser facility based on Yb+ ions (Sutsuma, Amplitude Systems) [11] was used as a source of ultrashort laser pulses. The frequency of the 1030nm fundamental harmonic of the laser is doubled in a BBO crystal yielding the ultrashort laser pulse of the second harmonic with a wavelength of 515 nm, FWHM of about 200 fs, and a maximum energy in the pulse up to 4 μJ. The spatial distribution of radiation at the output from a singlemode fiber corresponded to
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Fig. 2. Scanning electron microscopy image of the surface of the gold film irradiated by a single ultrashort laser pulse with the fluence F ≈ 0.18 J/cm2 at an angle of view of 42°. The white squares indicate the regions of the surface where the chemical composition was examined (given in at %).
Fig. 1. Scanning electron microscopy images of the surface of the gold film irradiated by single ultrashort laser pulses with the fluence F ≈ (a) 0.11, (b) 0.13, (c) 0.15, and (d, f) 0.18 J/cm2. The dashed line in panel (a) indicates the melted region of the film. Panel (f) shows the magnified image of the nanoparticle seen in panel (e) from the other side. Angles of view with respect to the normal to the sur face are (a, b) 42° and (c, d) 55°.
the TEM00 mode. Laser radiation was focused onto a spot with the radius R1/e ≈ 1.5 μm on the surface of the sample in air through the objective of a microscope with NA = 0.25. The sample was placed on a three dimensional motorized translating stage with a mini mum translating step of 150 nm. The relief of the sur face was visualized by a JEOL 7001F scanning elec tron microscope (SEM) with integrated detector for energydispersive Xray spectroscopy (EDS). 3. The incidence of ultrashort laser pulses with var ious energies on the goldfilm surface results in differ ent types of its modification (Fig. 1). Traces of the melting of the surface and recrystallization of metal nanocrystallite grains after the irradiation by a single ultrashort laser pulse with the fluence F ≈ 0.11 J/cm2 are seen in Fig. 1a. It is remarkable that this is not accompanied by visible separation of the film from the substrate. However, the irradiation by an ultrashort laser pulse with the fluence F ≈ 0.13 J/cm2 results in not only the melting of the film but also in exfoliation in the form of a microbump (Fig. 1b). A further increase in the fluence leads to the growth of the microbump and the appearance of a nanotip in the pit on the top of the microbump (Fig. 1c). Then (at JETP LETTERS
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F > 0.18 J/cm2), the film in its central part (darker region) becomes visibly thinner, and a submicron jet and a nanoparticle are formed immediately at the top of the microbump (Figs. 1d and 1e). The energydispersive Xray spectroscopic analysis of the film with a high spatial resolution showed that the dark region at the center of the microbump is attributed to the significant thinning of the film. At a cathode voltage of 15 kV, the characteristic depth of penetration of electrons into gold is about 0.2 μm and the initial thickness of the film under study is about 60 nm. This should give comparable signals from the film and substrate (Fig. 2). The contribution from the film in the dark region to the total signal is weakened by an order of magnitude (Fig. 2b). This indicates the significant thinning of the film because of the transi tion of the material to the formed particle whose dimensions are significantly larger than the thickness of the film. Indeed, the average radius of the nanopar ticle (Fig. 1c) is 0.43 μm, the corresponding volume is V ≈ 0.33 μm3, the radius of the dark region is approxi mately 1.3 μm, and the corresponding area is S ≈ 5.31 μm2. In terms of these data, the average thickness of the thin region can be estimated as d = h – V/S ≈ 0⎯10 nm. Thus, the thickness of the film decreases by almost an order of magnitude in agreement with the EDS data. After the irradiation by the ultrashort laser pulse with the fluence F ≈ 0.18 J/cm2, a nanotip (a solidified nanojet of metal melt) is observed under the nanopar ticle (Fig. 1d); this nanotip ejects the nanoparticle to a certain distance from the microbump until finally total separation (Fig. 1e). This effect is successfully applied to create regular arrays of nanoparticles by their depo
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Fig. 3. Scanning electron microscopy images of the surface of the gold film irradiated by a single ultrashort laser pulse with the fluence F ≈ (a) 0.23 and (b) 0.25 J/cm2 at an angle of view of 55°. (c) Magnified images of the separated nanoparticle with the nanojet.
sition directly on an additional substrate [9, 12]. How ever, the formation of nanoparticles with a complex shape, e.g., with a notch (Fig. 1f), has not yet been reported. The notch can appear at the place of separa tion of the nanoparticle from the nanojet, because the nanojet is solidified owing to the electron heat con duction to the film before the solidification of the nanoparticle connected to the jet through a point con tact (Fig. 1d). Because of the later solidification of the nanoparticle, its mechanical contact with the nanotip is weak (Fig. 3c). Nanoparticles with a hollow can exhibit additional plasmon resonances and a strong magnetic response to the irradiation by visible radia tion [13]. The separation of the nanoparticle together with the jet, which is accompanied by the formation of a hole on the top of a hollow microbump, occurs already at the fluence F ≈ 0.23 J/cm2 (Fig. 1f). At higher flu ences, the diameter of the formed hole increases
Fig. 4. Diameters of the regions of formation of (squares) microbumps and (triangles) holes versus the natural loga rithm of the laser energy. The inset shows the scanning electron microscopy image of the surface of the gold film irradiated by a single ultrashort laser pulse with the fluence F ≈ 0.27 J/cm2.
monotonically, and the nanoparticle together with the nanojet leaves the irradiation region (Fig. 3). In a cer tain case, the nanoparticle remains on the bottom of the microbump at the center of the hole (Fig. 3a). Under other conditions, the nanoparticle leaves the hole (Fig. 3b). The measured energy dependences of the diameter of microbumps and holes on the surface of the gold film have the formation thresholds Fbump ≈ (0.10 ± 0.02) J/cm2 and Fhole ≈ (0.22 ± 0.02) J/cm2, respec tively, and the characteristic radius of the distribution T of the introduced energy R 1/E ≈ (2.0 ± 0.1) μm T
(Fig. 4). Since the radius R 1/e is about 0.5 μm larger than the optical focusing radius R1/e ≈ 1.5 μm, this indicates significant lateral heat transport at these scales at nanosecond times τ of the formation of the microbump and hole ( 4χτ ~ 1 μm for τ ~ 10–8 s [14] and the known hightemperature thermal diffusivity of gold χ(1000 K) ≈ 1.1 cm2/s [15]) in agreement with our previous studies of other materials [16, 17]. To understand the mechanism of formation of microbumps, nanotips, and nanoparticles, it is impor tant that their formation thresholds slightly above the melting threshold of the film can occur without defor mation of the surface (Fig. 1a). This experimental fact cannot be explained by the existing models based either on the molecular dynamics method [18, 19] or on the solution of a continuous problem of the propa gation of elastic waves and plastic deformations in a heated film [10]. At the same time, the appearance of the transition region in the form of a step between a thinned top and the melted edge of the microbump (Figs. 1c–1e) was predicted in [19]. Below, we discuss a possible mechanism of formation of nanotips from a melted film. We assume that the formation and development of a nanojet and the formation of a nanoparticle are due to the thermocapillary instability of the melted film. Because of a low thermal conductivity of a dielectric substrate under the film with the thickness h, the laser JETP LETTERS
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Fig. 5. Calculated profiles of the nanojet at the (a) quasilinear (solution by Eq. (2) with ε = θ = 1) and (b) nonlinear (numerical solution of onedimensional equation (1) disregarding the term ~(∇H)2) stages of its formation.
melting of the film results in the appearance of the normal gradient of the temperature T directed from the irradiated surface into the film along the z axis. As a result, the relief of the surface of the melt becomes unstable: at a local increase in the thickness of the melt h(r, t) = hm + h1(r, t), where hm = const, h1(r) Ⰶ hm, and r = {x, y}, thermocapillary forces generate rising flows enhancing fluctuations. Fluctuation h1(r, t) sat isfies the twodimensional Kuramoto–Sivashinsky type hydrodynamic equation obtained in the long wavelength approximation [20]: 2 2 2 ∂H = – εΔH – Δ H – ε [ ( ∇H ) + ( ΔH ) ], ∂θ
(1)
where H = 2h1/hm; θ = t(D1, l2) is the dimensionless time; ε = D/D1 > 0 is the control parameter; D = 2
( σ T h m × 2ρη) ∂T/∂z z = hm > 0; D1 = σhm/3ρη > 0; ρ, η, and σ are the density, kinematic viscosity, and sur face tension coefficient of the melt, respectively; l|| = hm/ 3 is the scaling parameter; σT = ∂σ/∂T < 0; and Δ and ∇ are the twodimensional Laplace and gradient operators with respect to the dimensionless coordi nates X = x/l|| and Y = y/l||. In the quasilinear regime (at small times) under the phase matching condition for the harmonics of the relief (qx and qy), the solution of Eq. (1) is represented in the form of the superposi tion of harmonics: +∞ +∞
H ( X, Y, θ ) =
∫∫
2
2
2
2 2
exp { [ ε ( q X + q Y ) – ( q X + q Y ) ]θ }
–∞ –∞
(2)
× cos ( q X X + q Y Y )dq X dq Y . It describes the appearance and growth of an axisym metric peak (Fig. 5a) with a diameter of about the JETP LETTERS
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thickness of the melt hm, which is experimentally observed at the initial stage of the formation of the nanojet (Fig. 1c). In the nonlinear regime (at a quite high laser flu ence), the last term of Eq. (1) dominates in the case of strong axisymmetric focusing. The resulting nonlinear equation in the onedimensional approximation was numerically analyzed in [21], where an “explosive” solution with the subsequent growth of a nanopeak and the formation of a nanotip was demonstrated (Fig. 5b). Upward flows of the cooled melt within the nanojet are responsible for the accumulation of the material at the end of the nanojet with the subsequent formation of a spherical nanoparticle, which mini mizes the surface energy (Rayleigh instability can be an alternative mechanism of the formation of the nanoparticle [14, 22]). The motion of the melt from the central region of the surface (x = 0, Fig. 5b) upward along the nanotip initiates flows of the melt along the surface toward the base of the nanotip, which result in the thinning of the melted film near this base (Figs. 1c–1e). 4. To summarize, the hydrodynamic instability of a thin gold film melted by a single ultrashort laser pulse has been studied experimentally and theoretically. This instability is manifested in the appearance of a nanojet of the melt at the linear stage and its develop ment at the nonlinear stage of instability with the sub sequent decomposition of the nanojet into nanoparti cles. A new principle of the formation of nanoparticles with nanonotches, which are promising for the cre ation of nanoantennas with unique optical properties, has been demonstrated. This work was supported by the Russian Founda tion for Basic Research (project no. 130200971) and
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Translated by R. Tyapaev
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