- Email: [email protected]
Study of ultrashort laser ablation of metals by molecular dynamics simulation and experimental method
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 3 ( 2 0 0 8 ) 202–207
journal homepage: www.elsevier.com/locate/jmatprotec
Study of ultrashort laser ablation of metals by molecular dynamics simulation and experimental method Xuan Liu a,c,∗ , Weimin Zhou b , Changxin Chen a , Lijie Zhao c , Yafei Zhang a a
National Key Laboratory of Nano/Micro Fabrication Technology, Research Institute of Micro/Nanometer Science & Technology, Shanghai Jiao Tong University, Shanghai, PR China b Shanghai Nanotechnology Promotion Center, Shanghai, PR China c College of mechanical engineering, Jiamusi University, PR China
a r t i c l e
i n f o
a b s t r a c t
Article history:
The dynamics of fs-laser ablation of monocrystalline copper has been investigated by molec-
Received 22 December 2006
ular dynamics simulation and experimental method. A simulation model is developed by
Received in revised form 8 July 2007
taking the laser energy absorption, the thermal transport of free electrons as well as the
Accepted 26 September 2007
energy exchange between electrons and lattice into account. The propagation of laserinduced stress wave in the simulation model is studied. The velocity of stress wave is predicted to be nearly equal to sound velocity of copper 4400 m/s. The mechanisms of
Keywords:
ablation responsible for individual atoms and clusters are analyzed as the thermal fluc-
Ultrashort laser ablation
tuations in the kinetic energy and tensile stresses, respectively. The rates of ablation at
Molecular dynamics
different fluences obtained from molecular dynamics calculations support the experimental
Monocrystalline copper
observations of two different ablation regimes. © 2007 Elsevier B.V. All rights reserved.
1.
Introduction
Ultrashort laser ablation becomes more and more important in materials processing due to the advantages such as high energy intensity, controlled thermal load, non-thermal nature of ablation process as well as short thermal penetration depth (Tae et al., 2002; Atansov and Nedialkov, 2002; Herrmann et al., 1997; Meunier et al., 2003; Momma et al., 1996, 1998; Chichkov et al., 1996; Gotz and Stuke, 1997). Recently, ultrashort laser ablation has been used widely for surface micromaching of materials (Mao et al., 1993; Zhu et al., 2001; Noevodin et al., 1997; Weissmantel et al., 1998; Marcinkevicius et al., 2001), removal of tissue in surgery (Vogel et al., 2005; Nolte et al., 1999); producing particles for subsequent mass spectrometric ¨ investigations (Dreisewerd et al., 2005; Schurenberg et al., 2005; Fuso et al., 1996), and radioactive surface cleaning (Furukawa and Hashida, 2002). A study of the basic mechanism involved
∗
Corresponding author. Tel.: +86 21 62932092; fax: +86 21 62823631. E-mail address: [email protected] (X. Liu). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.09.084
in femtosecond laser ablation of metals is of great significance in terms of improving the efficiency of laser micro-machining and minimizing laser-induced damage. However, it is difficult to elucidate such mechanism by experiments only due to the complexity and diversity of the processes involved during laser irradiation. Molecular dynamics (MD) method has solved this problem and demonstrated its potential for the further investigation of the subject, which has been mentioned above. In this paper, MD simulations combined with experimental method is used to study a laser of 120-fs pulse at = 800 nm interaction with monocrystalline Cu. The laser energy absorption, the thermal transport sustained by free electrons, and the energy exchange between electrons and lattice are taken into account in this simulation model. The mechanisms of material removal and the thermodynamic states of matter during laser ablation are studied. The rates of ablation at different fluences are obtained from simulations and experiments.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 3 ( 2 0 0 8 ) 202–207
2.
Methods
2.1.
Initial model in molecular dynamics simulations
203
Monocrystalline Cu is chosen as a model system, which is composed of 6 unit cells in the x and y directions, and 500 unit cells in the z direction containing approximately 70,000 atoms. The particles interact with one another through Morse potential (Girifalco and Weizer, 1959). The potential U between two atoms is given by U (r) = D[exp{−2a(r − r0 )} − 2exp{−a(r − r0 )}]
(1) Fig. 1 – Schematic sketch of simulation model.
where D is the dissociation energy, a is constant, r0 is equilibrium distance of atoms, and r is the distance between atoms. Values of the parameters used in the MD simulations are listed in Table 1. Velocity-Verlet algorithm (Swope et al., 1982) is used in the simulations, which can predict positions, velocities and accelerations at the same time without compromising precision. Cell linked-list (Allen and Tidesley, 1987) is necessary in order to shorten the time spending in the force calculations. Gaussian pulse enters the bulk targets in the z direction, which is perpendicular to (1 0 0) plane in the cubic lattice. The initial velocities of atoms are given at random with a Gaussian distribution at 300 K, and follow the Maxwellian distribution at the same temperature in thermal equilibrium state through thermalizing for 100 ps before laser heating. Periodic boundary conditions are applied in the direction parallel to the surface. The velocity dampening technique is used at the bottom of the model to minimize the effect of shock wave reflection. The sketch map of model is shown in Fig. 1. Laser energy absorption is achieved by adding a velocityproportional force to the equation of each atom mi r¨ i = Fi + mi vi
(2)
where = (g/Ca )[(Te − Ta )/Ta ] is derived from two-step radiation heating model developed by Qiu (Qiu and Tien, 1993). Ca is the heat capacities (per unit volume) of the lattice subsystems, Te and Ta are the local temperature of the electron and the lattice subsystems, g is the electron–phonon coupling constant. The
values of Ca and g are also shown in Table 1. The expression of has been used in the studies of ultrashort laser ablation ¨ of metals with MD method (Schafer et al., 2002; Liu and Wang, 2004, 2005). The obtained simulation results agree with experiments well, proving the initial model to be fully acceptable. Laser energy absorbed by atoms in a system contributes to the increase of kinetic energy.
2.2.
Experimental set-up
The laser used in experiments was a Ti:sapphire amplifier system, which delivers 120-fs pulses with a center wavelength of 800 nm and repetition rate of 1 kHz. The irradiation number of pulses was controlled by means of a fast mechanical shutter. The laser fluence was determined by the spot size on the sample plane and the pulse energy by using a dielectric attenuator with adjustable transmission. The ablation depth per pulse was defined as the hole depth per laser pulse. The monocrystalline copper with single side polished was mounted on a rotating holder and placed in a vacuum chamber evacuated to a residual pressure less than 10–3 Torr. Microcraters were induced with the laser fluences of 600, 450, 400, 300, 260, 220 and 180 mJ/cm2 , respectively, and with increasing number of pulses per irradiated spot (125, 250, 500 and 1000). In measurements, the total depths of the holes were measured via stylus profilometer and the sample was further inspected by optical and scanning electron microscopy (SEM).
3.
Results and discussion
3.1.
Simulation results
Table 1 – Simulation parameters Parameter Metal Lattice constant, (nm) Equilibrium distance of atoms, r0 (nm) Dissociation energy, D (ev) Constant, a (1/nm) Mass of atom, m (kg) Laser penetration depth, p (nm) Time step, h (fs) Heat capacities (per unit volume) of the lattice subsystems, Ca (J/m3 K) Electron–phonon coupling constant, g (W/m3 K)
Value Cu 0.361 0.287 0.3429 13.588 1.055e−25 12 2 4.1 × 106 3.6 × 1017
Laser heating in the metal targets is achieved in two steps (Anisimov et al., 1974). First, electron subsystem is thermalized quickly due to laser energy absorption; second, lattice subsystem is warmed up through energy coupling with electron subsystem. So the electrons play an important role in thermal transport under laser irradiation. The maximal temperatures of electrons subsystem in copper at different laser fluences are shown in Fig. 2, which are calculated from the two-step radiation heating model. These maximal temperatures increase with the increasing laser fluences and reach 72,110 K at laser fluence of 600 mJ/cm2 , indicat-
204
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 3 ( 2 0 0 8 ) 202–207
Fig. 2 – The maximal temperature of electrons at different fluences.
ing a strong influence of laser fluence on the temperature of electrons. The snapshots from the MD simulations of laser irradiation Cu with laser fluence of 0.3 J/cm2 are shown in Fig. 3. The atoms are colored based on local temperature in units of melting point of Cu, Tm = 1358 K. As can be seen from the figure, a complete microscopic description of the dynamics processes involved in laser ablation is provided. The temperature of surface increases to be about 1000 K when pulse is just over, while there is no thermal expansion in the direction of depth. This indicates the pulse energy is absorbed nearly in constant volume and the heating takes place in the stress confinement region (Zhigilei, 2003; Zhigilei et al., 2003). The expansion is accelerated after 5 ps since a period of time is needed for the laser energy deposited in the form of kinetic energy to turn into the potential energy and result in displacement. The relaxation of the laser-induced stress in the stress
Fig. 3 – Snapshots of laser ablation Cu at fluence of 300 mJ/cm2 : (a) t = 0.12 ps; (b) t = 5 ps; (c) t = 100 ps; (d) t = 120 ps; (e) t = 160 ps; (g) f = 200 fs.
Fig. 4 – Snapshots of laser ablation Cu at fluence of 400 mJ/cm2 : (a) t = 0.12 ps; (b) t = 5 ps; (c) t = 100 ps; (d) t = 120 ps; (e) t = 160 ps; (g) f = 200 fs.
confinement region causes elastic vibrations. The temperature distributions are very complex as a result of the intense influence of elastic vibrations on the temperature evolution of the target. Before spallations, a peak of temperature at the depth of around 58 nm appears owing to the transformation of potential energy into kinetic energy and a decrease in the number of atoms in the local region, which indicates a spallation will occur. Ablation products consist of both individual atoms and a big cluster. Firstly, a noticeable number of atoms are ejected from the surface in succession due to thermal fluctuations in the kinetic energy. Then a big cluster breaks off from the target at about 117.4 ps. Another small cluster is also ejected from the cluster after 4.8 ps, while combines with the upper one into a cluster during the course of moving upward. This phenomenon has not been found in previous simulations of laser ablation metals (Leveugle et al., 2004). The reason for clusters ejection is that the interaction of the incident release wave corresponding to the unloading of the front face and reflected stresses wave generates resultant tensile
Fig. 5 – Ablation rate of individual atoms vs. fluence.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 3 ( 2 0 0 8 ) 202–207
205
Fig. 6 – Peak values of stress wave obtained form the MD simulations.
Fig. 7 – Propagations of the stress wave and the longitudinal wave.
stresses exceeding the strength of the material. The ablation process by fs-laser has mechanical character. In order to investigate the ablation characteristics at different laser fluences, several fluences below and above 300 mJ/cm2 are taken in the simulations. Fig. 4 shows the snapshots of laser irradiation Cu with a fluence of 400 mJ/cm2 . Compared with Fig. 2, the target tears at more locations resulting in the formation of more clusters, and the spallations all occur in the target rather than in the clusters. These clusters move apart from each other, so there is no combining of two clusters into one. The formation of multispallation leads to a collective ejection of clusters, which is an obvi-
ous character of the so-called stress confinement regime of laser ablation (Zhigilei and Garrison, 1999). Many individual atoms also appear between clusters, while there is almost no individual atom between clusters for the case of low fluence irradiation. The fluence dependence of the ablation rate for individual atoms is shown in Fig. 5. The ablation rates increase at low fluences until point A where there is a jump to point B. The higher laser fluence, the more intensive thermal fluctuations in the kinetic energy of atoms in surface area are obtained. So more atoms are ejected form the surface. Moreover, the presence of individual atoms between clusters due to the breaking of metallic bonds also increases the yield of individual atoms.
Fig. 8 – Dependences of ablation depth on the pulse number.
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j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 3 ( 2 0 0 8 ) 202–207
4.
Conclusions
The dynamics of femtosecond laser ablation of Cu is investigated by means of experimental and MD methods. The main mechanisms responsible for ablation are found to be resultant tensile stresses exceeding the strength of the material and thermal fluctuations in the kinetic energy. The velocity of stress wave is predicted to be nearly equal to sound velocity. The character of collective ejection of atoms and clusters for fs-laser ablation is found. This proves ablation occurs in the stress confinement region. The rates of ablation at different fluences obtained from MD simulations are 1–2 times higher than those from experiments as a result of a well-defined crystalline surface irradiated by a single pulse. Fig. 9 – Ablation rates obtained from experiments and MD simulations.
During laser–material interaction, a stress wave is produced and propagates into the irradiated material. In the MD simulations, the stress is calculated from the virial and compressive stress is denoted by positive value. The peak values of stress wave shown in Fig. 6 are increasing before 30 ps, and then attenuating as a result of the release wave. These peak values are increasing with the depths in the course of propagating into the target. Fig. 7 compares the propagation of stress wave in the model system and the longitudinal wave. Based on the locations of the peaks at different times, the velocity of stress wave can be predicted to be about 4400 m/s, which is nearly equal to the sound velocity in Cu.
3.2.
Comparison to experimental results
The experiments were performed with a different number of pulses at certain fluences. The dependences of ablation depth on the pulse number are shown in Fig. 8. The ablation rate at each certain fluence decreases with the increasing pulse number by and large, especially for the case of large numbers of pulses irradiation, which is also been found by Nolte (Nolte et al., 1997). By linear least squares fitting of experimental data, the ultimate ablation rates are determined to be 4.006, 6.741, 11.3, 19.5, 28.7, 38.0 and 42.7 nm/pulse for laser fluences 180, 220, 260, 300, 400, 450 and 600 mJ/cm2 , respectively. The relationship between ablation rate and laser fluence is presented in Fig. 9. The ablation rates obtained from MD simulations are 1–2 times higher than those from experiments. This may be related to using a well-defined crystalline surface irradiated by a single pulse in MD simulations. In contrast, the experimental data were taken as an average over many laser pulses. The target tears at several locations at high fluences lead to the formation of more clusters and higher ablation rates. Consequently, two different regimes of ablation rates appear. There is also a jump from point C to point D, while the jump begins at the fluence of 260 mJ/cm2 different from 300 mJ/cm2 in Fig. 5. The same regularity is also found for experimental data, which has been also reported by other research groups (Nolte et al., 1997; Furusawa et al., 1999; Hirayama and Obara, 2002). The formation of more than one cluster is primarily responsible for the jump of ablation rates.
Acknowledgements This work is supported by National Natural Science Foundation of China No.50730008, and Shanghai Science and Technology Grant No. 0752nm015 and National Basic Research Program of China No. 2006CB300406.
references
Allen, M.P., Tidesley, D.J., 1987. Computer Simulation of Liqueds. Clarendon Press, Oxford. Anisimov, S.I., Kapeliovich, B.L., Perelman, T.L., 1974. Sov. Phys. JETP 39, 375. Atansov, P.A., Nedialkov, N.N., 2002. Appl. Surf. Sci. 186, 369. Chichkov, B.N., Momma, C., Nolte, S., 1996. Appl. Phys. A 63, 109. Dreisewerd, K., et al., 2005. Anal. Chem. 77, 4098. Furukawa, H., Hashida, M., 2002. Appl. Surf. Sci. 197–198, 114. Fuso, F., et al., 1996. Appl. Surf. Sci. 96–98, 181. Furusawa, K., Takahashi, K., Kumagai, H., 1999. Appl. Phys. A 69, S359. Girifalco, L.A., Weizer, V.G., 1959. Phys. Rev. 114, 687. Gotz, T., Stuke, M., 1997. Appl. Phys. A 64, 539. Herrmann, F.W.R., Gerlach, J., Campbell, E.E.B., 1997. Nucl. Instr. Meth. B 122, 401. Hirayama, Y., Obara, M., 2002. Appl. Surf. Sci. 197/198, 741. Leveugle, E., Ivanov, D.S., Zhigilei, L.V., 2004. Appl. Phys. A 79, 1643. Liu, X., Wang, Y., 2004. The 6th Int. Conf. on Frontiers of Design and Manufacturing (ICFDM’04), Xi’an. Liu, X., Wang, Y., 2005. Chin. Opt. Lett. 3, 57. Mao, X., et al., 1993. J. Appl. Phys. 74, 4915. Marcinkevicius, A., et al., 2001. Opt. Lett. 26, 277. Meunier, M., et al., 2003. SPIE Proc. 4978, 169. Momma, C., Chichkov, B.N., Nolte, S., 1996. Opt. Commun. 129, 134. Momma, C., Nolte, S., Kamalage, K., 1998. Appl. Phys. A 67, 517. Noevodin, A., Donley, M., Zabinski, J., 1997. Surf. Coat. Technol. 92, 42. Nolte, S., Momma, C., Jacobs, H., 1997. J. Opt. Soc. Am. B 14, 2716. ¨ Nolte, S., et al., 1999. Physikalische Blatter 55, 41. Qiu, T.Q., Tien, C.L., 1993. J. Heat Transfer 115–124. ¨ Schafer, C., Urbassek, H.M., Zhigilei, L.V., 2002. Phys. Rev. B 66, 115404. ¨ Schurenberg, M., et al., 2005. Int J. Mass Spectrom. Ion Proc. 172, 89. Swope, W.C., Anderson, H.C., Berens, P.H., 1982. J. Chem. Phys. 76, 637.
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Tae, Y.C., David, J.H., Costas, P.G., 2002. Appl. Surf. Sci. 197–198, 720. Vogel, A., et al., 2005. Appl. Phys. B 81, 1015. Weissmantel, S., et al., 1998. Appl. Surf. Sci. 127–129, 444.
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Zhu, C., Qin, Y., Yang, H., 2001. Chin. Phys. Lett. 18, 59. Zhigilei, L.V., 2003. Appl. Phys. A 76, 339. Zhigilei, L.V., Leveugle, E., Garrison, B.J., 2003. Chem. Rev. 103, 321. Zhigilei, L.V., Garrison, B.J., 1999. Appl. Phys. A 69, 75.
journal homepage: www.elsevier.com/locate/jmatprotec
Study of ultrashort laser ablation of metals by molecular dynamics simulation and experimental method Xuan Liu a,c,∗ , Weimin Zhou b , Changxin Chen a , Lijie Zhao c , Yafei Zhang a a
National Key Laboratory of Nano/Micro Fabrication Technology, Research Institute of Micro/Nanometer Science & Technology, Shanghai Jiao Tong University, Shanghai, PR China b Shanghai Nanotechnology Promotion Center, Shanghai, PR China c College of mechanical engineering, Jiamusi University, PR China
a r t i c l e
i n f o
a b s t r a c t
Article history:
The dynamics of fs-laser ablation of monocrystalline copper has been investigated by molec-
Received 22 December 2006
ular dynamics simulation and experimental method. A simulation model is developed by
Received in revised form 8 July 2007
taking the laser energy absorption, the thermal transport of free electrons as well as the
Accepted 26 September 2007
energy exchange between electrons and lattice into account. The propagation of laserinduced stress wave in the simulation model is studied. The velocity of stress wave is predicted to be nearly equal to sound velocity of copper 4400 m/s. The mechanisms of
Keywords:
ablation responsible for individual atoms and clusters are analyzed as the thermal fluc-
Ultrashort laser ablation
tuations in the kinetic energy and tensile stresses, respectively. The rates of ablation at
Molecular dynamics
different fluences obtained from molecular dynamics calculations support the experimental
Monocrystalline copper
observations of two different ablation regimes. © 2007 Elsevier B.V. All rights reserved.
1.
Introduction
Ultrashort laser ablation becomes more and more important in materials processing due to the advantages such as high energy intensity, controlled thermal load, non-thermal nature of ablation process as well as short thermal penetration depth (Tae et al., 2002; Atansov and Nedialkov, 2002; Herrmann et al., 1997; Meunier et al., 2003; Momma et al., 1996, 1998; Chichkov et al., 1996; Gotz and Stuke, 1997). Recently, ultrashort laser ablation has been used widely for surface micromaching of materials (Mao et al., 1993; Zhu et al., 2001; Noevodin et al., 1997; Weissmantel et al., 1998; Marcinkevicius et al., 2001), removal of tissue in surgery (Vogel et al., 2005; Nolte et al., 1999); producing particles for subsequent mass spectrometric ¨ investigations (Dreisewerd et al., 2005; Schurenberg et al., 2005; Fuso et al., 1996), and radioactive surface cleaning (Furukawa and Hashida, 2002). A study of the basic mechanism involved
∗
Corresponding author. Tel.: +86 21 62932092; fax: +86 21 62823631. E-mail address: [email protected] (X. Liu). 0924-0136/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2007.09.084
in femtosecond laser ablation of metals is of great significance in terms of improving the efficiency of laser micro-machining and minimizing laser-induced damage. However, it is difficult to elucidate such mechanism by experiments only due to the complexity and diversity of the processes involved during laser irradiation. Molecular dynamics (MD) method has solved this problem and demonstrated its potential for the further investigation of the subject, which has been mentioned above. In this paper, MD simulations combined with experimental method is used to study a laser of 120-fs pulse at = 800 nm interaction with monocrystalline Cu. The laser energy absorption, the thermal transport sustained by free electrons, and the energy exchange between electrons and lattice are taken into account in this simulation model. The mechanisms of material removal and the thermodynamic states of matter during laser ablation are studied. The rates of ablation at different fluences are obtained from simulations and experiments.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 3 ( 2 0 0 8 ) 202–207
2.
Methods
2.1.
Initial model in molecular dynamics simulations
203
Monocrystalline Cu is chosen as a model system, which is composed of 6 unit cells in the x and y directions, and 500 unit cells in the z direction containing approximately 70,000 atoms. The particles interact with one another through Morse potential (Girifalco and Weizer, 1959). The potential U between two atoms is given by U (r) = D[exp{−2a(r − r0 )} − 2exp{−a(r − r0 )}]
(1) Fig. 1 – Schematic sketch of simulation model.
where D is the dissociation energy, a is constant, r0 is equilibrium distance of atoms, and r is the distance between atoms. Values of the parameters used in the MD simulations are listed in Table 1. Velocity-Verlet algorithm (Swope et al., 1982) is used in the simulations, which can predict positions, velocities and accelerations at the same time without compromising precision. Cell linked-list (Allen and Tidesley, 1987) is necessary in order to shorten the time spending in the force calculations. Gaussian pulse enters the bulk targets in the z direction, which is perpendicular to (1 0 0) plane in the cubic lattice. The initial velocities of atoms are given at random with a Gaussian distribution at 300 K, and follow the Maxwellian distribution at the same temperature in thermal equilibrium state through thermalizing for 100 ps before laser heating. Periodic boundary conditions are applied in the direction parallel to the surface. The velocity dampening technique is used at the bottom of the model to minimize the effect of shock wave reflection. The sketch map of model is shown in Fig. 1. Laser energy absorption is achieved by adding a velocityproportional force to the equation of each atom mi r¨ i = Fi + mi vi
(2)
where = (g/Ca )[(Te − Ta )/Ta ] is derived from two-step radiation heating model developed by Qiu (Qiu and Tien, 1993). Ca is the heat capacities (per unit volume) of the lattice subsystems, Te and Ta are the local temperature of the electron and the lattice subsystems, g is the electron–phonon coupling constant. The
values of Ca and g are also shown in Table 1. The expression of has been used in the studies of ultrashort laser ablation ¨ of metals with MD method (Schafer et al., 2002; Liu and Wang, 2004, 2005). The obtained simulation results agree with experiments well, proving the initial model to be fully acceptable. Laser energy absorbed by atoms in a system contributes to the increase of kinetic energy.
2.2.
Experimental set-up
The laser used in experiments was a Ti:sapphire amplifier system, which delivers 120-fs pulses with a center wavelength of 800 nm and repetition rate of 1 kHz. The irradiation number of pulses was controlled by means of a fast mechanical shutter. The laser fluence was determined by the spot size on the sample plane and the pulse energy by using a dielectric attenuator with adjustable transmission. The ablation depth per pulse was defined as the hole depth per laser pulse. The monocrystalline copper with single side polished was mounted on a rotating holder and placed in a vacuum chamber evacuated to a residual pressure less than 10–3 Torr. Microcraters were induced with the laser fluences of 600, 450, 400, 300, 260, 220 and 180 mJ/cm2 , respectively, and with increasing number of pulses per irradiated spot (125, 250, 500 and 1000). In measurements, the total depths of the holes were measured via stylus profilometer and the sample was further inspected by optical and scanning electron microscopy (SEM).
3.
Results and discussion
3.1.
Simulation results
Table 1 – Simulation parameters Parameter Metal Lattice constant, (nm) Equilibrium distance of atoms, r0 (nm) Dissociation energy, D (ev) Constant, a (1/nm) Mass of atom, m (kg) Laser penetration depth, p (nm) Time step, h (fs) Heat capacities (per unit volume) of the lattice subsystems, Ca (J/m3 K) Electron–phonon coupling constant, g (W/m3 K)
Value Cu 0.361 0.287 0.3429 13.588 1.055e−25 12 2 4.1 × 106 3.6 × 1017
Laser heating in the metal targets is achieved in two steps (Anisimov et al., 1974). First, electron subsystem is thermalized quickly due to laser energy absorption; second, lattice subsystem is warmed up through energy coupling with electron subsystem. So the electrons play an important role in thermal transport under laser irradiation. The maximal temperatures of electrons subsystem in copper at different laser fluences are shown in Fig. 2, which are calculated from the two-step radiation heating model. These maximal temperatures increase with the increasing laser fluences and reach 72,110 K at laser fluence of 600 mJ/cm2 , indicat-
204
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 3 ( 2 0 0 8 ) 202–207
Fig. 2 – The maximal temperature of electrons at different fluences.
ing a strong influence of laser fluence on the temperature of electrons. The snapshots from the MD simulations of laser irradiation Cu with laser fluence of 0.3 J/cm2 are shown in Fig. 3. The atoms are colored based on local temperature in units of melting point of Cu, Tm = 1358 K. As can be seen from the figure, a complete microscopic description of the dynamics processes involved in laser ablation is provided. The temperature of surface increases to be about 1000 K when pulse is just over, while there is no thermal expansion in the direction of depth. This indicates the pulse energy is absorbed nearly in constant volume and the heating takes place in the stress confinement region (Zhigilei, 2003; Zhigilei et al., 2003). The expansion is accelerated after 5 ps since a period of time is needed for the laser energy deposited in the form of kinetic energy to turn into the potential energy and result in displacement. The relaxation of the laser-induced stress in the stress
Fig. 3 – Snapshots of laser ablation Cu at fluence of 300 mJ/cm2 : (a) t = 0.12 ps; (b) t = 5 ps; (c) t = 100 ps; (d) t = 120 ps; (e) t = 160 ps; (g) f = 200 fs.
Fig. 4 – Snapshots of laser ablation Cu at fluence of 400 mJ/cm2 : (a) t = 0.12 ps; (b) t = 5 ps; (c) t = 100 ps; (d) t = 120 ps; (e) t = 160 ps; (g) f = 200 fs.
confinement region causes elastic vibrations. The temperature distributions are very complex as a result of the intense influence of elastic vibrations on the temperature evolution of the target. Before spallations, a peak of temperature at the depth of around 58 nm appears owing to the transformation of potential energy into kinetic energy and a decrease in the number of atoms in the local region, which indicates a spallation will occur. Ablation products consist of both individual atoms and a big cluster. Firstly, a noticeable number of atoms are ejected from the surface in succession due to thermal fluctuations in the kinetic energy. Then a big cluster breaks off from the target at about 117.4 ps. Another small cluster is also ejected from the cluster after 4.8 ps, while combines with the upper one into a cluster during the course of moving upward. This phenomenon has not been found in previous simulations of laser ablation metals (Leveugle et al., 2004). The reason for clusters ejection is that the interaction of the incident release wave corresponding to the unloading of the front face and reflected stresses wave generates resultant tensile
Fig. 5 – Ablation rate of individual atoms vs. fluence.
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 3 ( 2 0 0 8 ) 202–207
205
Fig. 6 – Peak values of stress wave obtained form the MD simulations.
Fig. 7 – Propagations of the stress wave and the longitudinal wave.
stresses exceeding the strength of the material. The ablation process by fs-laser has mechanical character. In order to investigate the ablation characteristics at different laser fluences, several fluences below and above 300 mJ/cm2 are taken in the simulations. Fig. 4 shows the snapshots of laser irradiation Cu with a fluence of 400 mJ/cm2 . Compared with Fig. 2, the target tears at more locations resulting in the formation of more clusters, and the spallations all occur in the target rather than in the clusters. These clusters move apart from each other, so there is no combining of two clusters into one. The formation of multispallation leads to a collective ejection of clusters, which is an obvi-
ous character of the so-called stress confinement regime of laser ablation (Zhigilei and Garrison, 1999). Many individual atoms also appear between clusters, while there is almost no individual atom between clusters for the case of low fluence irradiation. The fluence dependence of the ablation rate for individual atoms is shown in Fig. 5. The ablation rates increase at low fluences until point A where there is a jump to point B. The higher laser fluence, the more intensive thermal fluctuations in the kinetic energy of atoms in surface area are obtained. So more atoms are ejected form the surface. Moreover, the presence of individual atoms between clusters due to the breaking of metallic bonds also increases the yield of individual atoms.
Fig. 8 – Dependences of ablation depth on the pulse number.
206
j o u r n a l o f m a t e r i a l s p r o c e s s i n g t e c h n o l o g y 2 0 3 ( 2 0 0 8 ) 202–207
4.
Conclusions
The dynamics of femtosecond laser ablation of Cu is investigated by means of experimental and MD methods. The main mechanisms responsible for ablation are found to be resultant tensile stresses exceeding the strength of the material and thermal fluctuations in the kinetic energy. The velocity of stress wave is predicted to be nearly equal to sound velocity. The character of collective ejection of atoms and clusters for fs-laser ablation is found. This proves ablation occurs in the stress confinement region. The rates of ablation at different fluences obtained from MD simulations are 1–2 times higher than those from experiments as a result of a well-defined crystalline surface irradiated by a single pulse. Fig. 9 – Ablation rates obtained from experiments and MD simulations.
During laser–material interaction, a stress wave is produced and propagates into the irradiated material. In the MD simulations, the stress is calculated from the virial and compressive stress is denoted by positive value. The peak values of stress wave shown in Fig. 6 are increasing before 30 ps, and then attenuating as a result of the release wave. These peak values are increasing with the depths in the course of propagating into the target. Fig. 7 compares the propagation of stress wave in the model system and the longitudinal wave. Based on the locations of the peaks at different times, the velocity of stress wave can be predicted to be about 4400 m/s, which is nearly equal to the sound velocity in Cu.
3.2.
Comparison to experimental results
The experiments were performed with a different number of pulses at certain fluences. The dependences of ablation depth on the pulse number are shown in Fig. 8. The ablation rate at each certain fluence decreases with the increasing pulse number by and large, especially for the case of large numbers of pulses irradiation, which is also been found by Nolte (Nolte et al., 1997). By linear least squares fitting of experimental data, the ultimate ablation rates are determined to be 4.006, 6.741, 11.3, 19.5, 28.7, 38.0 and 42.7 nm/pulse for laser fluences 180, 220, 260, 300, 400, 450 and 600 mJ/cm2 , respectively. The relationship between ablation rate and laser fluence is presented in Fig. 9. The ablation rates obtained from MD simulations are 1–2 times higher than those from experiments. This may be related to using a well-defined crystalline surface irradiated by a single pulse in MD simulations. In contrast, the experimental data were taken as an average over many laser pulses. The target tears at several locations at high fluences lead to the formation of more clusters and higher ablation rates. Consequently, two different regimes of ablation rates appear. There is also a jump from point C to point D, while the jump begins at the fluence of 260 mJ/cm2 different from 300 mJ/cm2 in Fig. 5. The same regularity is also found for experimental data, which has been also reported by other research groups (Nolte et al., 1997; Furusawa et al., 1999; Hirayama and Obara, 2002). The formation of more than one cluster is primarily responsible for the jump of ablation rates.
Acknowledgements This work is supported by National Natural Science Foundation of China No.50730008, and Shanghai Science and Technology Grant No. 0752nm015 and National Basic Research Program of China No. 2006CB300406.
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