Fabrication of periodic structures in thin metal films by pulsed laser irradiation

Yuri Kaganovskii, Haim Vladomirsky, and Michel Rosenbluh

Department of Physics, The Jack and Pearl Resnick Institute of Advanced Technology, Bar-Ilan University, Ramat-Gan 52900, Israel.

kagany@mail.biu.ac.il

Abstract. We developed a technique for the fabrication of 1D and 2D periodic structures in thin gold and silver films by irradiation with two and four intersecting beams of a nanosecond pulsed laser. The periodically alternating intensity distribution caused by interference induces mass transfer in thin metal films. The mechanisms and kinetics of mass transfer depend on the film thickness, morphology, and laser intensity. In the films thinner than some transitional value, h*, redistribution of material between "hot" and "cold" regions on the substrate occurs as a result of melting and beading of the film in "hot" regions and subsequent motion of liquid drops towards "cold" regions in the optically induced temperature gradient. In the films thicker h* redistribution of the film material occurs by hydrodynamic flow of the molten film in the temperature gradient, with subsequent crystallization in the "cold" regions and formation of tall and narrow ridges or rims. Theoretical models were developed that allowed us to calculate the time dependent temperature distributions around irradiated regions of the film. From the temperature distributions we calculated the expected speed of liquid beads, as well the distances between the ridges, the rim diameters and found good agreement with the measured values. Keywords: pulsed laser irradiation, thin metal films, periodic structures. 1 INTRODUCTION

Formation of nanoscale periodic structures in Au and Ag films has generated much attention due to its importance to many areas in microelectronics, micromechanics, optical recording, circuit patterning, and mask generation [1-4]. These films might be used in sub-wavelength optics based on excitation of surface plasmons and their coupling with light [5-8]. Understanding of the interaction of laser irradiation with island metal films is also important for laser manipulation of composing nanoparticles.

A high intensity short laser pulse can result in significant heating, melting, and vaporization of thin metal films deposited on a dielectric substrate. By variation of laser intensity and its spatial distribution along the substrate one can observe and control a variety of physical processes in thin films, such as capillary beading, motion of separate liquid beads in a temperature gradient, atomic mass transfer induced by capillarity, and hydrodynamic redistribution of the molten region. Thus laser treatment can be used for precise modifications of metallic thin films on dielectric substrates [9].

Previously we studied the peculiarities of laser beading of molten Au films on glass substrate and hydrodynamic redistribution of film material induced by capillary driving forces [10]. In this work, the interaction of an intense laser pulse with thin gold and silver films deposited on a glass or silicon nitride substrates. Our research goal is to find optimal conditions for the fabrication of periodic holes and lines by pulsed laser irradiation and to obtain a better understanding of the basic mechanisms involved in this process.

Journal of Nanophotonics, Vol. 1, 011690 (27 December 2007)

© 2007 Society of Photo-Optical Instrumentation Engineers [DOI: 10.1117/1.2824477]Received 21 Jun 2007; accepted 12 Nov 2007; published 27 Dec 2007 [CCC: 19342608/2007/$25.00]Journal of Nanophotonics, Vol. 1, 011690 (2007) Page 1

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We have found that mechanism of mass transfer in thin films depends critically on the film thickness. There exists a "transitional" film thickness h*, so that if the film thickness h < h*, fast beading (de-wetting) of molten film occurs, with subsequent motion of the beads from hot to cold regions of the film. With h > h*, melting of the film, instead of beading, is accompanied by hydrodynamic flow of the melt to cold regions and formation of linear ridges or circular rims at the boundaries of molten regions.

We have calculated the characteristic time of beading as a function of the film thickness. We also calculated the temperature distribution along the surface, both for island and continuous films, the speed of beads moving in a temperature gradient and the speed of the hydrodynamic motion of the edge of molten film driven by capillary forces. We have found the results of our calculations to be in good agreement with the experimental data.

2 EXPERIMENTAL

Gold and silver films were deposited onto glass substrates (microscope cover glasses) in a vacuum 5×10-6 Pa, by thermal evaporation at a rate of 0.1 nm/s. The samples were mounted on an x-y-z stage that positioned the sample with a resolution of 2.5 µm relative to a focusing lens and were then irradiated by the third harmonic of a Nd:YAG laser (λ = 354 nm) with pulse duration of 7 ns and 10 Hz repetition rate. As the reflectivity of metallic thin films in the UV is lower than at longer wavelengths, the coupling of laser energy into the thin films is enhanced as compared to visible and infrared irradiation.

Two and four intersecting beams were used to create an intensity-modulated pattern at the surface. Two-beam interference produces a spatially modulated light field, an interference grating [11], with a period )2/sin(2/ θλ=l (λ is the wavelength, θ is the angle between two beams) and the spatial intensity distribution

I(x) = 2 I0 [1+ cos (2πx/l)] (1)

oscillating from 0 to Imax = 4 I0 (I0 is the intensity of the beams). The four-beam interference produces a 2D modulated light field, with a spatial intensity distribution [12] ranging from 0 to Imax = 16 I0 and periodicity equal 2l :

I(x,y) = 4I0 [cos (2πx/l)+cos (2πy/l)]2. (2)

N d :Y A G 3 5 5 n m

7 n s

GL 1 L 2

D 1 D 2

S

θ / 2

Fig. 1. Scheme of two- and four-beam irradiation. D1 and D2 – diaphragms; G – grid of 35-µm period; L1 and L2 – lenses; S – sample.

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To obtain the multiple interfering beams, we diffracted the 354 nm laser beam on a 2D square metallic grid and masked the resulting diffraction pattern with either two or four holes open in the mask (see scheme in Fig. 1). By adjusting the mask position to correspond to the first diffraction orders, and then passing the selected orders through two lenses, we obtained a focused interference pattern on the sample surface with a diameter of 80 – 280 µm depending on the focal length of the lenses. The average power in each of the diffracted beams varied in the range 2.5 – 70 µW, corresponding to peak intensities, I0, in the range 1010 – 1012 W/m2.

All irradiation experiments were performed in air. The redistribution of gold or silver on the substrate after the laser irradiation was studied by optical microscopy and by atomic force microscope (AFM) operating in tapping mode.

3 RESULTS The initial film thickness, h, in our experiments varied in the range of 5 – 50 nm. AFM analysis of the film morphology showed that films with h > 12 – 15 nm were continuous, with a surface roughness of the order of 2 – 3 nm, while the thinner films were discontinuous with a granular structure.

(a)

(b)

(c)

(d)

Fig. 2. Optical microphotographs obtained from Au films of two different thicknesses after irradiation by two (a, b) and four (c, d) intersecting beams. (a, c) – I0 = 1.3×1011 W/m2; (b, d) – I0 = 1.5×1011 W/m2; 1 pulse; film thicknesses: h1 = 8 nm (a, c); h2 = 18 nm (b, d). High intensity lines (spots) create white lines (circles) in the 8-nm film and black lines (circles) in the 18-nm film.

Typical optical images of the linear and square gratings obtained by two- and four-beam irradiation are shown in Fig. 2. As seen, the contrast in the photographs, as well as positions of white and black (grey) regions depends on the film thickness. For films thinner than some "transitional" thickness h* (17 nm for Au films and ~20 nm for Ag films) white lines (spots) are observed in the "hot" regions on the surface (corresponding to high intensity of interference field), whereas for films thicker than h* in the same hot regions one can observe black spots or lines.

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2 µm

50 nm

100 nm

0

(a)

(b)

Fig. 3. AFM micrographs showing beading of thin (8 nm) Au film under two-beam (a) and four-beam (b) laser irradiation. 1 pulse, Imax = 1.5×1011 W/m2. In Fig. 3a an edge of irradiated spot is shown to distinguish hot and cold regions.

Analysis of the AFM images of these structures shows that the films are molten in the hot

regions and if the film thickness h < h*, de-wetting (beading) of the molten films is observed (Fig. 3). Formation of relatively large beads in the hot regions leads to the increase of reflection compared to that for initial film and thus these regions look brighter in the optical micrographs (Figs. 2a, c). With an increase in the number of pulses we observed motion of the beads from the hot regions (where the film was molten) towards cold regions (Fig. 4). The period of the structures had no noticeable effect on the structure formation and beading provided the structure spacing was more than about 1 µm.

(a) (b)

(d)

1.5 µm

2 µm 2 µm

(c)

10 µm

Fig. 4. AFM images of beaded lines (a – c) produced by irradiation with increasing number of pulses: (a) – 1 pulse, (b) – 30 pulses, (c) – 100 pulses. Imax = 2.5×1011 W/m2. Particles move from hot to cold and thus lines become wider. Larger particles move faster and concentrate at the boundaries of molten zones. (d) – one of the circular spots obtained under four-beam irradiation; 30 pulses, Imax = 4.2×1011 W/m2.

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The average rate of bead motion depended on the particle radius (larger particles moved faster), laser intensity and periodicity of the structure and varied in a range 2 – 20 nm/pulse. The motion was accompanied by partial evaporation of the material and its re-deposition after the end of the pulse onto the surrounding area. Due to particle motion, the lines consisting of molten islands become wider and moving particles concentrate at the boundaries of molten zones. Finally, after a large number of pulses (the number depends on the pulse intensity), all particles are collected along "cold" lines, whereas hot regions become free from particles (Fig. 4c).

For thicker films (h ≥ h*), instead of beading, one can observe a complete removal of the film material from hot regions and its hydrodynamic flow to cold areas where the material crystallizes. Crystallization is accompanied by the formation of high and narrow ridges (Fig. 5).

Removal of the material from the hot regions of films results in the decrease of reflection in comparison with the initial film and these regions look darker in the optical images (Fig. 2 b, d). To avoid the effects of multiple evaporation and re-condensation on the surface, the structures shown were obtained with irradiation by a single laser pulse. Previously [10] we found that the minimum intensity, Imin (threshold intensity), required for morphological changes in the films and the fabrication of periodic structures, depends on the film thickness and the periodicity of the structures.

(a) (b)

(c) (d)

Fig. 5. Ridges (a) and rims (c) produced in 18-nm Au film by two- and four-beam irradiation, respectively. 1 pulse; (a) – Imax = 6.5×1010 W/m2; (c) – 1.7×1011 W/m2. (b) and (d) – appropriate surface profiles.

With irradiation at the lowest intensity, Imin, the absorbed light energy is just sufficient to melt the films. Irradiation with intensities I > Imin leads to an increasing size of the molten zone. For films with thickness h > h*, this results in the increase of the rim diameter (for four-beam interference) or the width of the uncovered substrate between the ridges (for two-beam interference). At a particular intensity (for two-beam interference), the width of the molten zone becomes close to the period of the grating, and the "cold strips" (where the film remains solid) become very narrow. Finally, adjacent ridges coalesce (Fig. 6), and periodic metallic lines of nanoscale width are fabricated.

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0 1 2 3 4 5 6 7 80

50

100

150

200

250

300

350

400

(a)

(b)

Fig. 6. Coalescence of adjacent ridges and formation of nanolines. 18-nm Au film; 1 pulse; Im = 1.25×1011 W/m2.

4 THEORETICAL MODELS AND DISCUSSION Theoretical analysis of these phenomena requires knowledge of the temperature distribution in the film, which depends on the film morphology. In island films, each island is heated under laser irradiation independently of adjacent islands; however one has to take into account heat losses caused by heat flow to the substrate. The problem can be solved using two scales: on a microscopic scale we consider the heating of a separate island, whereas on a macroscopic scale, in which any small element ∆x contains many islands, we consider a temperature distribution, which results from the superposition of temperature distributions obtained for each separate island. In the continuous films we can consider only the macro scale taking into account heat conductivity along the film, as well as heat losses to the substrate. 4.1 Temperature distribution around a particle in island film

On the microscale, we first consider the temperature distribution around a separate hemispherical metal nanoparticle, which absorbs laser radiation. As it was previously shown, the particle temperature, Tp, during the laser pulse can be estimated from the equation

( )qp

p JRIRCdt

dT 22 21 πεπ −≈ . (3)

Here, R is the particle radius, Cp = 2πcpR3/3 is the heat capacity of the particle, cp is the heat capacity per unit volume of particle, I is the light intensity, e is the spectral emissivity of the particle that depends on the particle radius, Jq = -κc(dT/dr)r = R is the heat flux from the particle to the bulk of the glass, c is the heat capacity per unit volume of glass, κ is the thermal diffusivity of the glass. If the radius R << (κτ)1/2 (τ is the pulse duration), during the laser pulse a steady state temperature distribution [13] is formed in the glass under the particle:

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T(r) ≈ Tp R / r. (4)

Then we obtain from Eq. (3) with dTp/dt = 0 that a particle reaches the temperature:

Tp ≈ εI R / 2κc, (5) where ε is the spectral emissivity. Equation (5) is valid for particles having radius R > α-1 (α is the absorption coefficient). Substituting in Eq. (5) κ ≈ 3⋅10-7 m2/s [13] and R ≈ 20 nm, we obtain κ/2R ≈ 1.3 ns, i.e. characteristic time for forming a steady state heat distribution around metal islands is indeed less than the pulse duration (7 ns). With εI ≈ 1011 W/m2, c ≈ 3.8⋅106 J/m3K, and R ≈ 20 nm, we have Tp ≈ 900 °C.

The above estimates are valid for particle radii smaller than (κτ)1/2. With particle radii larger than (κτ)1/2 (for our parameters R ≥ 50 nm), the characteristic time for the formation of a steady state heat distribution becomes longer than the pulse duration and Eqs. 4 and 5 cannot be used for estimates of particle temperature. For this case we solved Eq. 3 with the heat conduction equation for substrate; i.e.,

sss Tt

T ∆=∂

∂ κ , (6)

where κs is the heat diffusivity of the glass substrate. Eqs. (3) and (6) were solved numerically using MATLAB. We assumed that the particle is a round cylinder with the radius R and height h and intensity I is constant for t ≤ τ. Dependence ε (h) was calculated using well-known formulas [14] and optical constants [15] both for Au and Ag particles. As a result of the calculations we could find the particle temperature as a function of time, Tp(t), for various particle radii (Fig. 7) and light intensities, as well as the temperature distributions in the glass directly under the particle (see example in Fig. 8). We have found that numerical calculations of Tp made for particles with the radii R < (κτ)1/2 agree with those calculated from Eq. (5).

The temperature distribution in the ensemble of nanoparticles is defined as superposition of temperature distribution from separate particles and thus depends essentially on the average distance between the particles, l, as well as on average particle radius, R. Rigorous calculations are very complicated, however estimates can be easily done. For instance, if mono-dispersed nanoparticles form two-dimensional hexagonal lattice with period l, the resulting particle temperature increases by factor ( )lRf /121+≈ compared to the value of Tp in Eq. (5). Approximately the same factor can be obtained for a square lattice. The above estimates are valid for a random particle location and can be applied to island films. With

1.0/ ≈lR we obtain Tp = 1980 oC, whereas with 2.0/ ≈lR we have Tp = 3060 oC. Estimates of the minimal surface temperature of the substrate give 800 and 1700 oC, respectively, for the same values R/l. It is clear from these estimates that starting with some minimum laser power, the metal particles become liquid and under each particle a hemispherical layer of liquid glass is formed.

To estimate the thickness of the liquid layer, δ, we can use Eq. (4) and assume that the glass becomes liquid at the temperature about TL. We obtain

LLp cTIRfTRT κεδ 2// 2≈≈ . (7)

Assuming TL ≈ 900 °C and setting into Eq. (7) other parameters used above, we obtain a layer thickness δ ≈ 2R under the particle of 20 nm radius. With increasing laser intensity, the liquid

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zones around adjacent particles overlap, so that the glass surface is fully covered by a liquid film.

(ns)

T p(o

C)

1 1

2

3

4

5

Fig. 7. Particle temperature as a function of irradiation time calculated by rigorous numerical solution of heat conduction equations. 1 – R = 20 nm; 2 – 40 nm; 3 – 60 nm; 4 – 80 nm; 5 – 120 nm. I = 4.2×1011 W/m2. A steady state particle temperature, which can be calculated from Eq. (5), is formed during the pulse for particles with R ≤ 50 nm, in accordance with our estimates.

4.2 Motion of beads

Taking into account the formation of a liquid glass layer under the particle and melting of the particle itself we can suggest the following mechanism of the bead motion. The beads move in a temperature gradient created in the island film by the beam interference. As seen from Eq. 5, the particle temperature is proportional to the laser intensity, which periodically varies between 0 and maximum value (see Eqs. (1) and (2)). This means that the particle temperature in the film follows spatial intensity distribution and thus each particle is to be found in a macroscopic temperature gradient. It is known that in a temperature gradient a force is applied to each unit surface parallel to T∇ (γ is the surface tension)

TdTdF ∇= γ . (8)

As dγ/dT < 0, the force is directed opposite to T∇ . A force applied to a liquid bead half submerged in a glass is of the order of

TdT

dRF bg

b ∇+

≈)(2 γγ

π , (9)

where γ is the surface tension of the bead and γgb is the tension of the bead – glass interface. Under this force, a bead can move similar to Stokes motion of sphere in a viscous liquid. The difference is only that liquid glass layer is created by hot particle absorbing the light energy. The speed of the bead motion can be estimated from the formula

TdT

dRv gb

g∇

+≈

)(2

γγη

. (10)

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Time 7 ns

x10-7 m

x10-7 m

Fig. 8. Temperature distribution in a substrate under cylindrical particle with R = h =60 nm at the end of the pulse (t = 7 ns). Laser intensity I = 5 1011 W/m2; Tp = 2500oC.

Here, ηg is the dynamic viscosity of liquid glass. Substituting into Eq. 10 dγ/dT ≈ dγgb/dT ≈ 10-4 N/m K [16], ηg ≈ 10-3 Pa s (for T ≈ 2000 K), R = 50 nm, and T∇ ≈ 109 K/m we obtain v ≈ 1 m/s or 7 nm/pulse, in a good agreement with our experimental observations. 4.3 Temperature distribution in continuous film

The temperature distribution in continuous thin films has been previously investigated under various approximations as applied to thin film micro machining [17, 18]. The temperature distribution in the film, Tf(x,y,z,t), can be calculated from the equation:

fff

f

cztyxIT

tT )exp(),,()1( ⋅−ℜ−+∆=∂

∂ αακ . (11)

The temperature distribution in the substrate, Ts(x,y,z,t), is calculated from Eq. (6). Here α is the absorption coefficient of the particle and cf is the heat capacity per unit volume of the film, ℜ is the film reflectivity, which is a function of the film thickness. The second term in Eq. (11) represents a heat source in the film, due to the absorbed light energy.

As we consider the problem using a macroscopic scale, the intensity I(x,y,z,t) in Eq. (11), is a function of coordinates and time. We have calculated the temperature distributions in the Au and Ag films of various thicknesses irradiated both by two- and four-beam interference [10]. The intensity I(x,y,t) in Eq. (11) was taken as the product )()( txI φ⋅ or )(),( tyxI φ⋅ where )(xI and ),( yxI were defined by Eqs. (1) and (2) for two- and four-beam interference, respectively. The time-dependent factor, φ(t), described a rectangular pulse of 7 ns duration.

Equations (11) and (6) were solved numerically using MATLAB both for two-beam interference (in this case the light intensity and the temperature distribution are independent of y) and for four-beam interference (for which we assumed that the two-dimensional temperature distribution around each hot spot was cylindrically symmetric). The material parameters used in the calculations were taken from the literature [13]: absorption coefficients

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α were determined from our experimental data on transmission and reflection; the same values were obtained theoretically [14]). The reflectivity, ℜ , was measured as a function of the film thickness h.

Figure 9 shows examples of temperature distributions, T(x,t) , for 18 nm Au thin film on a glass substrate z = h) during the heating (t = 4 and 7 ns) and cooling cycle (t = 10 and 20 ns) under two-beam interference for grating periods: 5 and 1 µm. During the heating, the temperature distribution qualitatively follows the incident laser beam intensity profile and the temperature reaches a maximum at the end of the pulse. After the end of the pulse, the temperature profile rapidly smoothens simultaneously with a gradual decrease of the temperature. The smoothening of the temperature distribution occurs because of the high heat conductivity of the gold film, whereas the temperature decrease is caused by heat flow to the substrate. The maximum film temperature at the end of the pulse is proportional to the beam intensity I0; it depends also on the period l of intensity variation (see Eq. (1)), especially when the period becomes close to the heat diffusion distance d = (κfτ)1/2. With κf = 1.26·10-4 m2/s and τ = 7 ns we obtain for Au film d = 0.94 µm. For the period 5 µm (l 2 >> d 2) noticeable smoothening is observed only after the end of the pulse, whereas for l = 1 µm (l2 ≈ d2) smoothening is seen even during the heating. As is clear from this estimate and our simulation, the heat diffusion distance d defines a minimum period in the structure, which can be created by modulated intensity of nanosecond duration. To reduce the period d, one can decrease the pulse duration keeping the pulse energy constant. For instance, with a pulse duration τ = 500 ps we would expect to obtain d ≈ 250 nm.

The temperature distributions in a film irradiated by four-beam interference are similar to those under two-beam interference irradiation, although the maximum temperature at the end of the pulse is a little bit higher than that for two-beam irradiation with the same maximum intensity (4I0 and 16I0 for two- and four-beam irradiation, respectively).

4.4 Beading of the continuous film and hydrodynamic flow

Immediately after melting is initiated at the center of a hot line or spot, the melting zone rapidly expands. A thin liquid metal film on a dielectric substrate is unstable (because the wetting angle differs from zero) and thus de-wetting of the liquid film has to take place. From theoretical considerations [19], there are two different mechanisms of de-wetting: nucleation and subsequent growth of holes and film instability against thermally activated surface waves.

Nucleation of the holes in metal films occurs as a rule at triple points between three adjacent grains. The critical radius of the hole nucleus should exceed the film thickness. The growth of the hole (at a given temperature) leads to the accumulation of material along the perimeter of the hole thus building up an elevated rim. The cross-section of the rim is close to spherical segment with contact angleθ and radius of curvature Rr.

Due to Laplace pressure of order of γ/Rr (γ is the surface tension of the liquid metal) the rim will move with a speed, V, which is practically independent of the rim radius [20]

ηγ /≈V . (12) Here, η is the dynamic viscosity of the molten film. Substituting in Eq. (9) γ = 1.15 N/m [16] and η ≈ 10-3 Pa s (for liquid gold near the melting temperature [21]), we obtain V ≈ 103 m/s. With such speed the rim can pass over the half-period of the grating in about 1 ns, i.e. the liquid reaches the solid film, and crystallizes, practically instantly (compared to the pulse duration). This means that the final radius of the hole or the distance between the linear ridges can be estimated from the temperature distributions (Fig. 9) as the distance to the isotherm corresponding to the melting temperature of Au. The calculated values are in very good agreement with the experimental data [10].

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Distance ( µm)

T (o

C)

(a)

1

2

3

4

Distance (µm)(b)

T (o

C)

2

1

3

4

Fig. 9. Calculated temperature profiles at z = 0 for various times during irradiation (4 and 7 ns) and after irradiation (10 and 20 ns) of 18-nm Au film with peak intensity 8×1010 W/m2 and periods of 5 µm (a) and 1 µm (b). 1 – 4 ns; 2 – 7 ns; 3 – 10 ns; 4 – 20 ns.

The second mechanism of de-wetting – instability of the film against thermally activated surface waves – ruptures the film spontaneously. Due to thermal motion of atoms, spontaneous mass redistribution occurs in a thin liquid film that leads to film thickness fluctuations – surface waves. The amplitude of the unstable surface waves grows exponentially in time and the rise time τm is [20]

Vh

m 4

5

34

βτ = , (13)

where the parameter β is a characteristic of the material combination substrate – film; for Au films it was measured to be 4.3 nm [20]; speed V is given by Eq. (12).

The rise time depends very strongly on the film thickness; with V = 103 m/s and β = 6.2 nm, we obtain τm = 0.7 ns for h = 15 nm and 1.7 ns for h = 18 nm. These estimates explain why rims and ridges are not observed in the films thinner than h*. Due to instability against

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capillary waves, de-wetting (beading) of the film with h < h* occurs faster than the time it takes for the rim to reach the solid region of the film. The experimentally determined value h* = 17 nm is in a good agreement with the above estimates.

In our experiments, as the multi-beam interference results in an inhomogeneous temperature distribution, nucleation and subsequent growth of holes in liquid metal films occurs first at the highest temperatures. Subsequently, the ridge or rim of the hole moves to cold regions, mainly under Laplace pressure, with some contribution to the driving force caused by the temperature gradient. 5 CONCLUSIONS We present simple techniques for the fabrication of periodic lines and holes in thin gold and silver films by nanosecond pulsed laser irradiation. The technique is based on irradiation of the films by two or four intersecting laser beams, which create interference pattern on the film surface, with periodic spatial intensity distribution. In the hot regions films melt and the film material transfers towards cold regions.

We have analyzed mechanisms of the mass transfer along the substrate during a laser pulse and found that they are quite different for different film thicknesses. There exists a "transitional" film thickness h*, so that if the film thickness h < h*, beading of molten film occurs, with subsequent motion of the beads from hot to cold regions of the film. With h > h*, melting of the film, instead of beading, is accompanied by hydrodynamic flow of the melt to cold regions and formation of linear ridges or circular rims at the boundaries of molten regions.

Numerical solution of the heat equation with the source of heat caused by a modulated laser-intensity distribution is obtained both for island and continuous films and temperature distribution inside the irradiated area is found as a function of coordinates and time. On the basis of the solution the laser intensities necessary for fabrication of periodic structures are calculated for various film thicknesses and periodicities. The calculations are in a good agreement with the experimental results and give us confidence in the validity of the models presented for laser induced pattern formation in thin metallic films.

The conditions necessary for hydrodynamic redistribution of the liquid film material are analyzed. Hydrodynamic flow is possible only when the liquid film is thick enough and is therefore stable against surface capillary waves. Under such conditions the time for de-wetting (beading), which is proportional to h5, is longer than the time necessary for the hydrodynamic redistribution of liquid between hot and cold regions.

Acknowledgments This work was supported by the Israel Science Foundation (grant #1196/05).

References [1] I. Miyamoto and H. Hayashi, "Process of thin Cu film removal by KrF excimer laser,"

Rev. Laser Eng. 23, 1081-1089 (1995). [2] Z. Toth, B. Hopp, Z. Kantor, F. Ignacz, T. Szoerenyi, and Z. Bor, "Dynamics of

excimer laser ablation of thin tungsten films monitored by ultrafast photography," Appl. Phys. A 60, 431-436 (1995) [doi:10.1007/BF01538765].

[3] J. Solis, K.A. Rubin, and C. Ortiz, "Structural and optical transformations by laser irradiation of InSb-based thin films," J. Mater. Res. 5, 190-210 (1990) [doi:10.1557/JMR.1990.0190].

[4] V. P. Veiko, I. M. Karpman, M. N. Libenson, and E. B. Yakovlev, "Optimal regime for forming topological patterns when processing films with laser radiation," Sov. J. Quantum Electron. 12, 1408-1411 (1982) [doi:10.1070/QE1982v012n11ABEH006087].

Downloaded From: http://nanophotonics.spiedigitallibrary.org/ on 12/17/2013 Terms of Use: http://spiedl.org/terms

Journal of Nanophotonics, Vol. 1, 011690 (2007) Page 13

[5] T. W. Ebbesen, H. J. Lezec, H. F. Ghaemi, and T. Thio, and P. A. Wolff, "Extraordinary optical transmission through sub-wavelength hole arrays," Nature 391, 667-669 (1998) [doi:10.1038/35570].

[6] H. F. Ghaemi, T. Thio, D. E. Grupp, T. W. Ebbesen, and H. J. Lezec, "Surface plasmons enhance optical transmission through subwavelength holes," Phys. Rev. B 58, 6779-6782 (1998) [doi:10.1103/PhysRevB.58.6779].

[7] A. Krishnan, T. Thio, T. J. Kim, H. J. Lezec, T. W. Ebbesen, P. A. Wolff, J. Pendry, L. Martin-Moreno, and F. J. Garcia-Vidal, "Evanescently coupled resonance in surface plasmon enhanced transmission," Opt. Commun. 200, 1-7 (2001) [doi:10.1016/S0030-4018(01)01558-9].

[8] A. Degiron, H. J. Lezec, W. L. Barnes, and T. W. Ebbesen, "Effects of hole depth on enhanced light transmission through subwavelength hole arrays," Appl. Phys. Lett. 81, 4327-4329 (2002) [doi:10.1063/1.1526162].

[9] R. Ranjan, D.N. Lambeth, M. Tromel, P. Goglia, and Y. Li, "Laser texturing for low-flying-height media," J. Appl. Phys. 69, 5745-5747 (1991) [doi:10.1063/1.347908].

[10] Yu. Kaganovskii, H. Vladomirsky, and M. Rosenbluh, "Periodic lines and holes produced in thin Au films by pulsed laser irradiation," J. Appl. Phys. 100, 044317 (2006) [doi:10.1063/1.2234548].

[11] H. J. Eichler, P. Gunter, and D. W. Pohl, Laser-Induced Dynamic Gratings, Springer-Verlag, Berlin, Germany (1986).

[12] T. Kondo, S. Matsuo, S. Juodkazis, and H. Misawa, "Femtosecond laser interference technique with diffractive beam splitter for fabrication of three-dimensional photonic crystals," Appl. Phys. Lett. 79, 725-727 (2001) [doi:10.1063/1.1391232].

[13] H. S. Carslaw and J. C. Jaeger, Conduction of Heat in Solids, Clarendon Press, Oxford, UK (1989).

[14] J. E. Nestell, Jr. and R. W. Christy, "Derivation of optical constants of metals from thin-film measurements at oblique incidence," Appl. Opt. 11, 643-651 (1972).

[15] J. H. Weaver, C. Krafka, D. W. Lynch, and E. E. Koch, Optical Properties of Metals (OPM), Vols. I and II, Physics Data, Nr. 18-1 and 18-2, Fachinformationzentrum, Karlsruhe, Germany (1981).

[16] I. Egry, G. Lohoefer, and G. Jacobs, "Surface tension of liquid metals: results from measurements on ground and in space," Phys. Rev. Lett. 75, 4043-4046 (1995) [doi:10.1103/PhysRevLett.75.4043].

[17] V. J. Zaleckas and J. C. Koo, "Thin-film machining by laser-induced explosion," Appl. Phys. Lett. 31, 615-617 (1977) [doi:10.1063/1.89801].

[18] U. C. Paek and A. Kestenbaum, "Thermal analysis of thin-film micromachining with lasers," J. Appl. Phys. 44, 2260-2268 (1973) [doi:10.1063/1.1662547].

[19] F. Brochard-Wyart and J. Daillant, "Drying of solids wetted by thin liquid films," Can. J. Phys. 68, 1084-1088 (1990).

[20] J. Bischof, D. Scherer, S. Herminghaus, and P. Leiderer, "Dewetting modes of thin metallic films: nucleation of holes and spinodal dewetting," Phys. Rev. Lett. 77, 1536-1539 (1996) [doi:10.1103/PhysRevLett.77.1536].

[21] T. Iida and R. I. L. Guthrie, The Physical Properties of Liquid Metals, Oxford University Press, Oxford, UK (1987).

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