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Laser-assisted growth of microstructures on spatially confined substrates
Applied Surface Science 253 (2007) 7987–7991 www.elsevier.com/locate/apsusc
Laser-assisted growth of microstructures on spatially confined substrates S.I. Dolgaev, N.A. Kirichenko, A.V. Simakin, G.A. Shafeev * Wave Research Center, General Physics Institute of the Russian Academy of Sciences, 38, Vavilov Street, 117942 Moscow, Russian Federation Available online 25 February 2007
Abstract Laser-assisted growth of microstructures on spatially confined substrates is experimentally studied. The experiments are performed using a copper-vapor laser with pulse duration of 20 ns, and repetition rate of 7.5 kHz. Ropes made of Ni–Cr wires with diameter of 50–100 mm, as well as the edge of 50 mm thick Ni foils were exposed to multiple laser pulses. The morphology of structures that grow on these targets drastically differs from periodic array of micro-cones observed on semi-infinite targets made of the same materials. In case of wires the structures have radial symmetry and do not show any periodicity, while in case of a foil the periodic structures are aligned along its edges. The model of micro-structures formation in spatially confined conditions is elaborated based on the numerical solution of the heat conduction and hydrodynamics equations. It is shown that boundary conditions imposed by confined target onto melt flow strongly affect the structure morphology. The micro-structure formation is related to the confinement of melt flow under combined action of both capillary forces and gradients of surface tension. # 2007 Elsevier B.V. All rights reserved. Keywords: Ni–Cr; Micro-cones; SEM
1. Introduction Multi-pulse laser exposure of solids leads to the formation of a periodic structure that consists of densely packed micro-cones [1–6]. These structures are observed on a large variety of materials under exposure both in vacuum or gases. Typical period of micro-cones observed under nanosecond laser pulses is about 20 mm, and this period varies with the laser pulse duration [7]. The periodicity of micro-cones was associated with capillary waves in the melt produced on the solid under laser radiation [5]. Later a self-consistent model has been developed that describes the initial stages of the micro-cones growth from the periodic relief of the solid surface [8]. Microcones on Si exhibit low-threshold of field emission of electrons [9–12]. Another interesting feature of micro-cones is the proximity of their thermal emission to that of an ideal black body [13,14]. In typical conditions, the lateral dimensions of the targets exceed far the period of micro-cones. A priori one may expect the influence of the lateral dimensions of the target onto the morphology of structures if these dimensions are comparable
* Corresponding author. E-mail address: [email protected] (G.A. Shafeev). 0169-4332/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2007.02.074
with the period of micro-cones grown on semi-infinite substrates. Confinement of the melt bath may lead to new morphology of structures that are developed under multi-pulse laser exposure. The aim of this paper is the description of new types of structures that are developed under laser exposure of solid targets whose lateral dimensions are comparable with the period of micro-cones and at the same time are smaller than the laser spot size. The modelling of the process is performed on the basis of numerical solution of both heat conduction and melt flow equations. 2. Experimental Two types of spatially confined targets were used in the experiments. Wires made of either nickel–chromium alloy or copper were gathered in a rope, and the rope was exposed to laser radiation along its axis. In another set of experiments the target was made of 50 mm thick Ni foils assembled into a brick. Each Ni foil was thermally isolated from its neighbours. A Cu vapor laser was used as a laser source operating at wavelengths of 510 and 578 nm, pulse width of 20 ns, repetition rate of 7.5 kHz. The laser spot size in the plane of the composite target was 100 mm resulting in a fluence of 5 J/cm2. Laser exposure of extended areas of the composite target was carried out in air via scanning the laser beam. Typical number of laser shots
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delivered to the target was about 103. The morphology of laserexposed targets, either semi-infinite or spatially confined was characterized by a scanning electron microscopy (SEM). 3. Results Laser exposure of a semi-infinite Ni target results in development of periodic micro-cones having the period of 20 mm [4]. Micro-cones protrude above the initial surface of the target, which is typical for structures observed on many other substrates [4,5]. Structures grown on a 50 mm thick Ni foil have completely different morphology (Fig. 1). Two rows of microcones are formed along the length of the foil. In some cases the third row of micro-cones appears in between the first two rows. The spacing between adjacent cones in rows is close to their period on a semi-infinite Ni plate and is about 20 mm. Spacing between two rows of symmetric micro-cones is less than the foil thickness and is about 30–35 mm. Similar difference of morphology is observed for a Ni–Cr alloy. Micro-cones grown under multi-pulsed laser exposure of a semi-infinite substrate made of this material are typical (Fig. 2a) with average period of 25 mm. Their surface is oxidized by air oxygen, and the thin oxide film is covered by a network of micro-cracks. Laser exposure of a rope made of Ni– Cr wires results in completely different structure morphology though the wire diameter of 100 mm is 4 times greater than the period of the micro-cones on a semi-infinite Ni–Cr substrate. These structures are shown in Fig. 2b and c. At the initial stages of laser exposure of the wire tips the material is replaced from the wire center to its periphery so that the wire surface becomes concave. At this stage a slight decrease of the wire diameter is well visible. With further exposure symmetric pits become visible within the wire area. Their number varies from 3 to 4, and in some cases they have a triangle cross section. With further increase of the number of laser pulses these pits are deepened, and a central protrusion appears at the wire axis. Micro-structures that develop on Cu wires under multipulsed laser exposure in air do not show any symmetry with
respect to wire axis (see Fig. 3). Most frequently, several microcones appear on within the wire diameter. Most likely, they contain copper oxides rather than metallic Cu, since laser exposure is carried out in air. Similarly, periodic structures on semi-infinite Cu substrates that appear under multi-pulsed laser exposure also contain copper oxide, and their periodicity of 20 mm is due to the periodicity of the cracks in oxide layer. 4. Modelling of the process Let us consider a model that describes the contribution of main mechanisms leading to formation of micro-structures on spatially confined targets under their laser exposure. In the present paper we discuss only the case of foils. Let x coordinate is directed along the target surface, while the width of the target is L (L/2< x < L/2). Respectively, z coordinate is directed normally to the surface. Laser pulse induces melting of the target surface. Assuming the melt to be an uncompressible liquid, the melt thickness h can be found from the following equation: @h @ðvhÞ ¼ u0 ðx; tÞ ; @t @x
(1)
where v is an average velocity of the melt flow along the surface, u0(x, t) is the rate of thickness variations due to melting/solidification process. v(x, t) can be expressed from the Navier–Stokes equation: 1 @P 1 @a þ h : hv ¼ h2 3 @x 2 @x
(2)
Here h stands for viscosity of the melt, while the pressure in the liquid P ¼ PV a
@2 h @x2
(3)
is composed from the external component (vapor pressure) and the capillary pressure imposed by the surface tension coefficient a = a(TS) depending on the surface temperature TS. The second term in the right-hand side of (2) takes into account the thermocapillary forces that arise due to inhomogeneity of temperature distribution along the melt surface. In a wide range of temperature a(T) = a0 + a1(T T0), where a0 and a1 are constants, so @a/@x = a1(@TS/@x) in (2). The confinement of the target is given by the boundary conditions: v = 0 and h = 0 at x = L/2. The problem of the melt flow should be solved jointly with the problem of laser heating of the target taking into account the heating of the target to melting point, formation of the melt, and its evaporation. Temporal behavior of the intensity I(t) of the laser beam used in calculations is as follows: t t IðtÞ ¼ I 0 exp ; (4) t t where
Fig. 1. SEM view of micro-structures on a 50 mm thick Ni foil. Laser fluence of 5 J/cm2, 2 103 laser pulses. Scale bar denotes 50 mm, image tilt of 208.
t ¼ 2 108 s; I 0 ¼ 1:2 108 W=cm2 :
(5)
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Fig. 2. Periodic micro-cones grown on a semi-infinite Ni–Cr target by scan-irradiation with a Cu vapor laser (a). Pits on Ni–Cr wires, 2 103 laser pulses at 3 J/cm2. Scale bar denotes 50 mm, top view (b). Ni–Cr wires subjected to 3 103 laser pulses at 3 J/cm2. Scale bar denotes 50 mm, image tilt of 208 (c).
The relative deformation of the target surface is small during first several laser pulses. Assuming, as a first approximation, the surface to be flat, one can estimate both the characteristic melt thickness and the role of evaporation. According to estimations, the melt thickness is about 1 mm, and since the penetration depth of radiation into metals is of order of 102 mm, one can assume that the absorption of laser radiation takes place in the superficial layer of the target. Let the metal occupy the half-space z 0. Let us designate the coordinate of the melt front as z = s(t). Then the temperature T(z, t) can be found from the following equation: @T @ @T ds ¼ cr k rLm dðz sÞ; 0 < z < 1; @t @z @z dt
(6)
where k is the coefficient of thermal conductivity, c stands for specific heat capacity, Lm is the specific heat of melting of the metal, r is its density. d-function heat source in this equation accounts for heat absorption at the melt front. The position of the melt front s(t) is determined from the condition Fig. 3. SEM view of micro-cones on a Cu wire. 2 103 laser pulses at 5 J/cm2, image tilt 208.
TðsðtÞ; tÞ ¼ T m ;
(7)
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Fig. 5. Target profile that appears after the action of the first (dashed) and after the second (solid) laser pulse.
Fig. 4. Temporal behavior of the target temperature (a) and melt thickness (b) following one laser pulse.
where Tm is melting temperature. It is known that the evaporation is significant at the intensities used in the present calculations. However, numerical calculations show that the evaporated thickness per pulse is small, so that the boundary condition can be written on a static external surface: @T k ¼ I rLv u: (8) @z z¼0 Let u(t) is the velocity of motion of the boundary due to evaporation. The rate of evaporation depends on the surface temperature TS and is given by well-known expression: rffiffiffiffiffiffiffiffiffiffiffiffiffi Tv Tv P0 mT b uðT S Þ ¼ u0 ðTÞexp : (9) ; u0 ðTÞ ¼ Tb TS rT S 2pkB Here P0 is the atmospheric pressure, Tb is boiling temperature at atmospheric pressure, m is the mass of the evaporated particle (that can be assumed to be the mass of an atom), r is the density of the solid metal, kB is Boltzman constant, while the characteristic temperature of evaporation Tv is related to the heat of evaporation as follows: T v ¼ mLv =rkB . In the calculations the parameters of Ni were used. Fig. 4a shows the temporal dependence of the target temperature, and Fig. 4b shows the temporal behavior of the melt thickness derived from Eq. (7). Using the data from Fig. 4a, one can calculate the thickness D ofRthe metal evaporated per laser pulse 1 using the expression D ¼ 0 uðTð0; tÞÞ dt, where the function u(T) is given by expression (9). In our experimental conditions D 0.02 mm. The solution of a self-consistent problem of laser heating of the target and melt flow it is necessary to take into account the variation of the temperature along the surface. pffiffiffiffiffiDuring the laser pulse the heat propagates to distances lT at 1 mm, which is significantly smaller than the spatial scale of temperature inhomogeneity along the surface. In these conditions the
temperature field reproduces the profile of the heat source at the boundary. Due to surface deformation the normal to the surface is inclined to z-axis at angle w(x), and cos w = [1 + (@h/@x)2]1/2. Accordingly, the local value of the absorbed laser intensity can be expressed as 2 1 @h I abs I 1 : (10) 2 @x The temperature field can be divided into two terms Tðx; z; tÞ ¼ T 0 ðz; tÞ þ DTðx; z; tÞ;
(11)
where the first term corresponds to a flat target surface, while the second accounts for the modulation of the relief and can be written as follows: 2 1 @h DTðx; z; tÞ ¼ Fðz; tÞ: (12) 2 @x This approximation is valid provided that profile varies slowly during one laser pulse. This suggestion is confirmed by calculations. The function F(z, t) satisfies the following boundary problem: @F @ @F @F cr k ¼ 0; 0 < z < 1; k @t @z @z @z z¼0 du ¼ AI rLv F: (13) dT T¼T 0 The above-formulated model has been numerically solved. The target width was taken equal to 50 mm. Fig. 5 shows the surface profile after the first laser pulse (dashed line) and after the second pulse (solid line). The thickness of the evaporated layer is small since the laser pulse is short. 5. Discussion Initially flat surface becomes concave after the very first laser pulse. This effect is due to high capillary pressure in the vicinity of target edges at the initial stages of structure development. The melt moves from target periphery to its center. The velocity of this displacement from edges is rather high (about 200 cm/s), while the melt in the target center is almost immobile. High velocity allows the melt to displace for tens of mm during the time of its existence. As a result, the melt forms a kind of splash on the periphery of the target that fixes
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the relief profile upon solidification of the melt. For the same reason a small local maximum appears in the center of the target. The change of the surface profile gained with each laser pulse is of order of 0.1 mm. However, since each point of the sample is subjected to hundreds of laser shots, so the final deformation may amount to several tens of mm. Capillary pressure plays major role in mass transfer during first several pulses while the curvature of the surface is high due to splash. The curvature decreases with the increase of number of laser shots, since the result of consecutive action of following pulses is cumulative. In turn, the temperature gradients along the surface increase which stipulates the thermocapillary mass transfer. At late stages of exposure the curvature of the surface target further increases. The calculations show that the relief inclination of the order 0.3 is reached after some 50 pulses. This is sufficient for the re-reflection of laser radiation and these reflections of the laser beam in the relief lead to the significant re-distribution of laser intensity on the target surface. The formation of symmetric pits visible in Fig. 2b, may be due just to this intensity re-distribution. A flat target surface is unstable under multi-pulse laser exposure. Small inward displacement of the surface due to material transport from the target center to its periphery is amplified under exposure to subsequent laser pulse. The positive feedback for instability development is provided by the increase of fraction of laser radiation reflected to the surface, temperature rise and hence evaporation of the bottom of the pit. Higher temperature inside the pit enhances the radial thermocapillary flow to the periphery of the target. The formation of the rows of micro-cones along the sides of Ni foil (Fig. 1) can be explained by the minimization of the surface energy. Indeed, due to capillary pressure a sharp edge within the laser spot is molten simultaneously, and minimization of the surface energy requires equal curvature of the structure in both perpendicular directions. 6. Conclusions Thus, it has been experimentally demonstrated that microstructures that develop under multi-pulsed laser exposure of spatially confined metal targets such as Ni or Ni–Cr are completely different from periodic micro-cones observed on semi-infinite targets of the same materials. Preferential material displacement to the periphery of the confined targets is observed independently on their geometry. A self-sustained theoretical model of the process without any fitting parameter is
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elaborated. The model takes into account capillary forces in the melt, its evaporation and redistribution along the target. Spatial confinement of the target manifests itself mainly in boundary conditions for the melt flow. Initial stages of the structure formation (first few pulses) are governed by capillary melt flows towards the target center due to high curvature of the surface at almost constant temperature along the target. The calculated profiles of spatially confined targets after several laser pulses are in good agreement with experimentally observed micro-structures.
Acknowledgements The work was partially supported by the Russian Foundation for Basic Researches, grants ##04-02-81021 and 05-02-08311 and Scientific School 8108.2006.2.
References [1] F. Sa´nchez, J.L. Morenza, R. Aguiar, J.C. Delgado, M. Varela, Appl. Phys. Lett. 69 (1996) 620. [2] T.H. Her, R.F. Finlay, C. Wu, S. Deliwala, E. Mazur, Appl. Phys. Lett. 73 (1998) 1673. [3] A.J. Pedraza, J.D. Fowlkes, D.H. Lowndes, Appl. Phys. Lett. 74 (1999) 2322. [4] V.V. Voronov, S.I. Dolgaev, S.V. Lavrischev, A.A. Lyalin, A.V. Simakin, G.A. Shafeev, Quantum Electronics 30 (2000) 710.. [5] S.I. Dolgaev, S.V. Lavrischev, A.A. Lyalin, A.V. Simakin, V.V. Voronov, G.A. Shafeev, Appl. Phys. A 73 (2001) 177. [6] S.I. Dolgaev, J.M. Ferna´ndez-Pradas, J.L. Morenza, P. Serra, G.A. Shafeev, Appl. Phys. A83 (2006) 417. [7] M. Skantzakis, V. Zorba, D.G. Papazoglou, I. Zergioti, C. Fotakis, Appl. Surf. Sci., in press. [8] S.I. Dolgaev, N.A. Kirichenko, A.V. Simakin, G.A. Shafeev, Quantum Electronics 34 (2004) 771. [9] A.V. Karabutov, V.D. Frolov, E.N. Loubnin, A.V. Simakin, G.A. Shafeev, Appl. Phys. A 76 (2003) 413. [10] A.V. Karabutov, V.D. Frolov, A.V. Simakin, G.A. Shafeev, J. Vac. Sci. Technol. B 21 (2003) 449. [11] V. Zorba, I. Alexandrou, I. Zergioti, A. Manousaki, C. Ducati, A. Neumeister, C. Fotakis, G.A.J. Amaratunga, Thin Solid Films 453/454 (2004) 492. [12] A.V. Karabutov, G.A. Shafeev, N. Badi, A.M. Nair, A. Bensaoula, Appl. Surf. Sci. 252 (2006) 4453–4456. [13] D. Starikov, C. Boney, R. Pillai, A. Bensaoula, G.A. Shafeev, A.V. Simakin, Infr. Phys. Technol. 45 (2004) 159. [14] D. Starikov, C. Boney, R. Pillai, A. Bensaoula, G.A. Shafeev, A.V. Simakin, Appl. Phys. A79 (2004) 973.
Laser-assisted growth of microstructures on spatially confined substrates S.I. Dolgaev, N.A. Kirichenko, A.V. Simakin, G.A. Shafeev * Wave Research Center, General Physics Institute of the Russian Academy of Sciences, 38, Vavilov Street, 117942 Moscow, Russian Federation Available online 25 February 2007
Abstract Laser-assisted growth of microstructures on spatially confined substrates is experimentally studied. The experiments are performed using a copper-vapor laser with pulse duration of 20 ns, and repetition rate of 7.5 kHz. Ropes made of Ni–Cr wires with diameter of 50–100 mm, as well as the edge of 50 mm thick Ni foils were exposed to multiple laser pulses. The morphology of structures that grow on these targets drastically differs from periodic array of micro-cones observed on semi-infinite targets made of the same materials. In case of wires the structures have radial symmetry and do not show any periodicity, while in case of a foil the periodic structures are aligned along its edges. The model of micro-structures formation in spatially confined conditions is elaborated based on the numerical solution of the heat conduction and hydrodynamics equations. It is shown that boundary conditions imposed by confined target onto melt flow strongly affect the structure morphology. The micro-structure formation is related to the confinement of melt flow under combined action of both capillary forces and gradients of surface tension. # 2007 Elsevier B.V. All rights reserved. Keywords: Ni–Cr; Micro-cones; SEM
1. Introduction Multi-pulse laser exposure of solids leads to the formation of a periodic structure that consists of densely packed micro-cones [1–6]. These structures are observed on a large variety of materials under exposure both in vacuum or gases. Typical period of micro-cones observed under nanosecond laser pulses is about 20 mm, and this period varies with the laser pulse duration [7]. The periodicity of micro-cones was associated with capillary waves in the melt produced on the solid under laser radiation [5]. Later a self-consistent model has been developed that describes the initial stages of the micro-cones growth from the periodic relief of the solid surface [8]. Microcones on Si exhibit low-threshold of field emission of electrons [9–12]. Another interesting feature of micro-cones is the proximity of their thermal emission to that of an ideal black body [13,14]. In typical conditions, the lateral dimensions of the targets exceed far the period of micro-cones. A priori one may expect the influence of the lateral dimensions of the target onto the morphology of structures if these dimensions are comparable
* Corresponding author. E-mail address: [email protected] (G.A. Shafeev). 0169-4332/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.apsusc.2007.02.074
with the period of micro-cones grown on semi-infinite substrates. Confinement of the melt bath may lead to new morphology of structures that are developed under multi-pulse laser exposure. The aim of this paper is the description of new types of structures that are developed under laser exposure of solid targets whose lateral dimensions are comparable with the period of micro-cones and at the same time are smaller than the laser spot size. The modelling of the process is performed on the basis of numerical solution of both heat conduction and melt flow equations. 2. Experimental Two types of spatially confined targets were used in the experiments. Wires made of either nickel–chromium alloy or copper were gathered in a rope, and the rope was exposed to laser radiation along its axis. In another set of experiments the target was made of 50 mm thick Ni foils assembled into a brick. Each Ni foil was thermally isolated from its neighbours. A Cu vapor laser was used as a laser source operating at wavelengths of 510 and 578 nm, pulse width of 20 ns, repetition rate of 7.5 kHz. The laser spot size in the plane of the composite target was 100 mm resulting in a fluence of 5 J/cm2. Laser exposure of extended areas of the composite target was carried out in air via scanning the laser beam. Typical number of laser shots
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delivered to the target was about 103. The morphology of laserexposed targets, either semi-infinite or spatially confined was characterized by a scanning electron microscopy (SEM). 3. Results Laser exposure of a semi-infinite Ni target results in development of periodic micro-cones having the period of 20 mm [4]. Micro-cones protrude above the initial surface of the target, which is typical for structures observed on many other substrates [4,5]. Structures grown on a 50 mm thick Ni foil have completely different morphology (Fig. 1). Two rows of microcones are formed along the length of the foil. In some cases the third row of micro-cones appears in between the first two rows. The spacing between adjacent cones in rows is close to their period on a semi-infinite Ni plate and is about 20 mm. Spacing between two rows of symmetric micro-cones is less than the foil thickness and is about 30–35 mm. Similar difference of morphology is observed for a Ni–Cr alloy. Micro-cones grown under multi-pulsed laser exposure of a semi-infinite substrate made of this material are typical (Fig. 2a) with average period of 25 mm. Their surface is oxidized by air oxygen, and the thin oxide film is covered by a network of micro-cracks. Laser exposure of a rope made of Ni– Cr wires results in completely different structure morphology though the wire diameter of 100 mm is 4 times greater than the period of the micro-cones on a semi-infinite Ni–Cr substrate. These structures are shown in Fig. 2b and c. At the initial stages of laser exposure of the wire tips the material is replaced from the wire center to its periphery so that the wire surface becomes concave. At this stage a slight decrease of the wire diameter is well visible. With further exposure symmetric pits become visible within the wire area. Their number varies from 3 to 4, and in some cases they have a triangle cross section. With further increase of the number of laser pulses these pits are deepened, and a central protrusion appears at the wire axis. Micro-structures that develop on Cu wires under multipulsed laser exposure in air do not show any symmetry with
respect to wire axis (see Fig. 3). Most frequently, several microcones appear on within the wire diameter. Most likely, they contain copper oxides rather than metallic Cu, since laser exposure is carried out in air. Similarly, periodic structures on semi-infinite Cu substrates that appear under multi-pulsed laser exposure also contain copper oxide, and their periodicity of 20 mm is due to the periodicity of the cracks in oxide layer. 4. Modelling of the process Let us consider a model that describes the contribution of main mechanisms leading to formation of micro-structures on spatially confined targets under their laser exposure. In the present paper we discuss only the case of foils. Let x coordinate is directed along the target surface, while the width of the target is L (L/2< x < L/2). Respectively, z coordinate is directed normally to the surface. Laser pulse induces melting of the target surface. Assuming the melt to be an uncompressible liquid, the melt thickness h can be found from the following equation: @h @ðvhÞ ¼ u0 ðx; tÞ ; @t @x
(1)
where v is an average velocity of the melt flow along the surface, u0(x, t) is the rate of thickness variations due to melting/solidification process. v(x, t) can be expressed from the Navier–Stokes equation: 1 @P 1 @a þ h : hv ¼ h2 3 @x 2 @x
(2)
Here h stands for viscosity of the melt, while the pressure in the liquid P ¼ PV a
@2 h @x2
(3)
is composed from the external component (vapor pressure) and the capillary pressure imposed by the surface tension coefficient a = a(TS) depending on the surface temperature TS. The second term in the right-hand side of (2) takes into account the thermocapillary forces that arise due to inhomogeneity of temperature distribution along the melt surface. In a wide range of temperature a(T) = a0 + a1(T T0), where a0 and a1 are constants, so @a/@x = a1(@TS/@x) in (2). The confinement of the target is given by the boundary conditions: v = 0 and h = 0 at x = L/2. The problem of the melt flow should be solved jointly with the problem of laser heating of the target taking into account the heating of the target to melting point, formation of the melt, and its evaporation. Temporal behavior of the intensity I(t) of the laser beam used in calculations is as follows: t t IðtÞ ¼ I 0 exp ; (4) t t where
Fig. 1. SEM view of micro-structures on a 50 mm thick Ni foil. Laser fluence of 5 J/cm2, 2 103 laser pulses. Scale bar denotes 50 mm, image tilt of 208.
t ¼ 2 108 s; I 0 ¼ 1:2 108 W=cm2 :
(5)
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Fig. 2. Periodic micro-cones grown on a semi-infinite Ni–Cr target by scan-irradiation with a Cu vapor laser (a). Pits on Ni–Cr wires, 2 103 laser pulses at 3 J/cm2. Scale bar denotes 50 mm, top view (b). Ni–Cr wires subjected to 3 103 laser pulses at 3 J/cm2. Scale bar denotes 50 mm, image tilt of 208 (c).
The relative deformation of the target surface is small during first several laser pulses. Assuming, as a first approximation, the surface to be flat, one can estimate both the characteristic melt thickness and the role of evaporation. According to estimations, the melt thickness is about 1 mm, and since the penetration depth of radiation into metals is of order of 102 mm, one can assume that the absorption of laser radiation takes place in the superficial layer of the target. Let the metal occupy the half-space z 0. Let us designate the coordinate of the melt front as z = s(t). Then the temperature T(z, t) can be found from the following equation: @T @ @T ds ¼ cr k rLm dðz sÞ; 0 < z < 1; @t @z @z dt
(6)
where k is the coefficient of thermal conductivity, c stands for specific heat capacity, Lm is the specific heat of melting of the metal, r is its density. d-function heat source in this equation accounts for heat absorption at the melt front. The position of the melt front s(t) is determined from the condition Fig. 3. SEM view of micro-cones on a Cu wire. 2 103 laser pulses at 5 J/cm2, image tilt 208.
TðsðtÞ; tÞ ¼ T m ;
(7)
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Fig. 5. Target profile that appears after the action of the first (dashed) and after the second (solid) laser pulse.
Fig. 4. Temporal behavior of the target temperature (a) and melt thickness (b) following one laser pulse.
where Tm is melting temperature. It is known that the evaporation is significant at the intensities used in the present calculations. However, numerical calculations show that the evaporated thickness per pulse is small, so that the boundary condition can be written on a static external surface: @T k ¼ I rLv u: (8) @z z¼0 Let u(t) is the velocity of motion of the boundary due to evaporation. The rate of evaporation depends on the surface temperature TS and is given by well-known expression: rffiffiffiffiffiffiffiffiffiffiffiffiffi Tv Tv P0 mT b uðT S Þ ¼ u0 ðTÞexp : (9) ; u0 ðTÞ ¼ Tb TS rT S 2pkB Here P0 is the atmospheric pressure, Tb is boiling temperature at atmospheric pressure, m is the mass of the evaporated particle (that can be assumed to be the mass of an atom), r is the density of the solid metal, kB is Boltzman constant, while the characteristic temperature of evaporation Tv is related to the heat of evaporation as follows: T v ¼ mLv =rkB . In the calculations the parameters of Ni were used. Fig. 4a shows the temporal dependence of the target temperature, and Fig. 4b shows the temporal behavior of the melt thickness derived from Eq. (7). Using the data from Fig. 4a, one can calculate the thickness D ofRthe metal evaporated per laser pulse 1 using the expression D ¼ 0 uðTð0; tÞÞ dt, where the function u(T) is given by expression (9). In our experimental conditions D 0.02 mm. The solution of a self-consistent problem of laser heating of the target and melt flow it is necessary to take into account the variation of the temperature along the surface. pffiffiffiffiffiDuring the laser pulse the heat propagates to distances lT at 1 mm, which is significantly smaller than the spatial scale of temperature inhomogeneity along the surface. In these conditions the
temperature field reproduces the profile of the heat source at the boundary. Due to surface deformation the normal to the surface is inclined to z-axis at angle w(x), and cos w = [1 + (@h/@x)2]1/2. Accordingly, the local value of the absorbed laser intensity can be expressed as 2 1 @h I abs I 1 : (10) 2 @x The temperature field can be divided into two terms Tðx; z; tÞ ¼ T 0 ðz; tÞ þ DTðx; z; tÞ;
(11)
where the first term corresponds to a flat target surface, while the second accounts for the modulation of the relief and can be written as follows: 2 1 @h DTðx; z; tÞ ¼ Fðz; tÞ: (12) 2 @x This approximation is valid provided that profile varies slowly during one laser pulse. This suggestion is confirmed by calculations. The function F(z, t) satisfies the following boundary problem: @F @ @F @F cr k ¼ 0; 0 < z < 1; k @t @z @z @z z¼0 du ¼ AI rLv F: (13) dT T¼T 0 The above-formulated model has been numerically solved. The target width was taken equal to 50 mm. Fig. 5 shows the surface profile after the first laser pulse (dashed line) and after the second pulse (solid line). The thickness of the evaporated layer is small since the laser pulse is short. 5. Discussion Initially flat surface becomes concave after the very first laser pulse. This effect is due to high capillary pressure in the vicinity of target edges at the initial stages of structure development. The melt moves from target periphery to its center. The velocity of this displacement from edges is rather high (about 200 cm/s), while the melt in the target center is almost immobile. High velocity allows the melt to displace for tens of mm during the time of its existence. As a result, the melt forms a kind of splash on the periphery of the target that fixes
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the relief profile upon solidification of the melt. For the same reason a small local maximum appears in the center of the target. The change of the surface profile gained with each laser pulse is of order of 0.1 mm. However, since each point of the sample is subjected to hundreds of laser shots, so the final deformation may amount to several tens of mm. Capillary pressure plays major role in mass transfer during first several pulses while the curvature of the surface is high due to splash. The curvature decreases with the increase of number of laser shots, since the result of consecutive action of following pulses is cumulative. In turn, the temperature gradients along the surface increase which stipulates the thermocapillary mass transfer. At late stages of exposure the curvature of the surface target further increases. The calculations show that the relief inclination of the order 0.3 is reached after some 50 pulses. This is sufficient for the re-reflection of laser radiation and these reflections of the laser beam in the relief lead to the significant re-distribution of laser intensity on the target surface. The formation of symmetric pits visible in Fig. 2b, may be due just to this intensity re-distribution. A flat target surface is unstable under multi-pulse laser exposure. Small inward displacement of the surface due to material transport from the target center to its periphery is amplified under exposure to subsequent laser pulse. The positive feedback for instability development is provided by the increase of fraction of laser radiation reflected to the surface, temperature rise and hence evaporation of the bottom of the pit. Higher temperature inside the pit enhances the radial thermocapillary flow to the periphery of the target. The formation of the rows of micro-cones along the sides of Ni foil (Fig. 1) can be explained by the minimization of the surface energy. Indeed, due to capillary pressure a sharp edge within the laser spot is molten simultaneously, and minimization of the surface energy requires equal curvature of the structure in both perpendicular directions. 6. Conclusions Thus, it has been experimentally demonstrated that microstructures that develop under multi-pulsed laser exposure of spatially confined metal targets such as Ni or Ni–Cr are completely different from periodic micro-cones observed on semi-infinite targets of the same materials. Preferential material displacement to the periphery of the confined targets is observed independently on their geometry. A self-sustained theoretical model of the process without any fitting parameter is
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elaborated. The model takes into account capillary forces in the melt, its evaporation and redistribution along the target. Spatial confinement of the target manifests itself mainly in boundary conditions for the melt flow. Initial stages of the structure formation (first few pulses) are governed by capillary melt flows towards the target center due to high curvature of the surface at almost constant temperature along the target. The calculated profiles of spatially confined targets after several laser pulses are in good agreement with experimentally observed micro-structures.
Acknowledgements The work was partially supported by the Russian Foundation for Basic Researches, grants ##04-02-81021 and 05-02-08311 and Scientific School 8108.2006.2.
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