Atomistic simulation of laser-pulse surface modification: Predictions of models with various length and time scales

Transcription

1 Atomistic simulation of laser-pulse surface modification: Predictions of models with various length and time scales Sergey V. Starikov and Vasily V. Pisarev Citation: Journal of Applied Physics 117, (2015); doi: / View online: View Table of Contents: Published by the AIP Publishing Articles you may be interested in The origins of pressure-induced phase transformations during the surface texturing of silicon using femtosecond laser irradiation J. Appl. Phys. 112, (2012); / Experimental study of femtosecond laser-stimulated electrical discharges in small gaps and surface modifications J. Appl. Phys. 105, (2009); / Periodic ordering of random surface nanostructures induced by femtosecond laser pulses on metals J. Appl. Phys. 101, (2007); / Time-resolved measurement on ablative acceleration of foil plates driven by pulsed laser beam Rev. Sci. Instrum. 72, 2032 (2001); / Space and time resolved temperature measurements in laser pulse-produced metal melts Rev. Sci. Instrum. 68, 2534 (1997); /

2 JOURNAL OF APPLIED PHYSICS 117, (2015) Atomistic simulation of laser-pulse surface modification: Predictions of models with various length and time scales Sergey V. Starikov 1,2,a) and Vasily V. Pisarev 1,2 1 Moscow Institute of Physics and Technology, Dolgoprudny , Russia 2 Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow , Russia (Received 3 December 2014; accepted 20 March 2015; published online 1 April 2015) In this work, the femtosecond laser pulse modification of surface is studied for aluminium (Al) and gold (Au) by use of two-temperature atomistic simulation. The results are obtained for various atomistic models with different scales: from pseudo-one-dimensional to full-scale three-dimensional simulation. The surface modification after laser irradiation can be caused by ablation and melting. For low energy laser pulses, the nanoscale ripples may be induced on a surface by melting without laser ablation. In this case, nanoscale changes of the surface are due to a splash of molten metal under temperature gradient. Laser ablation occurs at a higher pulse energy when a crater is formed on the surface. There are essential differences between Al ablation and Au ablation. In the first step of shock-wave induced ablation, swelling and void formation occur for both metals. However, the simulation of ablation in gold shows an additional athermal type of ablation that is associated with electron pressure relaxation. This type of ablation takes place at the surface layer, at a depth of several nanometers, and does not induce swelling. VC 2015 AIP Publishing LLC. [ I. INTRODUCTION Over the last ten years, there has been increasing interest in the interaction of femtosecond laser pulse with matter. The surface modification by laser pulse is one of the means for creation of nanoscale structures. Variety of the obtained nanostructures is large enough and includes craters, 1 6 nanojets, 7 voids under a surface, 8,9 and periodical structure on a surface. 10,11 However, the physical mechanisms of nanostructures fabrication in this way are unknown. Complete description of a surface modification by laser pulse must take into account many phenomena taking place in strongly nonequilibrium state. Absorption of the laser pulse initially leads to excitation of the electron subsystem (ES) In this case, initial state of the system is the two-temperature (2T) state, and the electron temperature (T e ) may be several orders higher than the ion temperature (T i ). The time of electron ion relaxation is comparable to the time of relaxation processes taking place in the ion subsystem (IS) such as heat transfer and phase transitions. One of the ways to simulate this situation is a continuum approximation with the two-temperature equation of state Such approach is a powerful tool for study of the surface modification by laser pulse. Nevertheless, this method does not take into account the phenomena existing at the atomistic level (such as decay of metastable phase or nucleation) that are essential for correct description of the surface modifications at threshold fluences. Another way to consider the problem is to apply atomistic simulation (AS). AS for 2T-system is proposed in Refs. 12 and 18. In these models, ions are simulated in the framework of classical molecular dynamics, while electrons are treated as continuous. a) Electronic mail: starikov@ihed.ras.ru This model was further modified (in Refs. 19 and 20) taking into account an influence of the electron pressure on ions dynamics. Over the past years, the experimental works focus on nonlocal character of the surface modification by laser pulse. Now it is clear that all irradiated surface is involved in the modification process. Complete description of the experimental data may be given by the full-scale AS of such process with lm-length scales in all three dimensions (3Dsimulation). At the present time, all similar simulations are performed with one-dimensional (1D hydrodynamic model) or pseudo-one-dimensional (AS with periodic boundaries) approaches. The surface mechanical or thermodynamic relaxation 5,7 and nucleation process 8,9 are not taken into account in these cases. Thereby, significant features of the surface modification are not considered in these models. The first step towards the account of the above-mentioned effects have been taken recently in Refs. 21 and 22. However, the full-scale 3D-simulation has not been performed yet. The size of 2D- and 3D-simulations corresponds from hundreds of millions to billions of atoms. In addition, such simulation requires about 10 6 calculation steps. Hence, such simulations are only achievable using massive parallelism and can be performed only on the world s top supercomputers. At this date, the examples of billion-atom MD simulations include investigation of cavitation, 23 nucleation, 24 nanovoid growth, 25 and nanohydrodynamics studies. 26 In this work, the femtosecond laser pulse modification of a surface is studied for aluminium (Al) and gold (Au) by use of two-temperature AS. There are some experimental features of surface laser modification for both studied metals which are not completely understood. In the recent experiments for aluminium, 8,9 swelling and formation of voids under the surface have been obtained as the first step of /2015/117(13)/135901/9/$ , VC 2015 AIP Publishing LLC

3 S. V. Starikov and V. V. Pisarev J. Appl. Phys. 117, (2015) ultrashort-pulse laser ablation. The substantial material removal required about 25% higher fluences. It might be supposed that the threshold fluence for the void formation may be calculated at 1D simulation as the ablation threshold, 9,15 but this approach does not give the possibility to describe all evolution of the matter. To all appearances, only full-scale model of laser ablation may simulate similar process. One of the features of the surface modification of gold is strong discrepancy between the experimental threshold fluence of surface modification and the calculated one. In the experiments, the threshold value of absorbed fluence F is about mj/cm 2 for creation of nanoscale ripples, 10,27 and producing nanoparticles and nanojets requires F about mj/cm 2. At the same time, the simulation gives threshold absorbed fluence for ablation about 150 mj/ cm 2. 1,2 A possible explanation of this discrepancy was given in Ref. 30 through the existence of the additional mechanism of ablation due to the electron pressure relaxation. Results of this work are obtained from simulation of various models at different scales: from 1D simulation to fullscale 3D simulation. The used two-temperature model is described in Sec. II. Section III reviews the details and results of the 1D simulation. Section IV is devoted to the surface modification of metal by laser pulse without ablation (2D-simulation). In Sec. V, the results for 2D- and 3Dsimulation of laser ablation are given. The comparison of simulation results with available data for the studied metals is discussed. II. TWO-TEMPERATURE ATOMISTIC MODEL Our model is implemented as a modification of the 2Tmodel in the LAMMPS code. 31,32 Heating and relaxation of the ES were simulated with a use of the 2T-formalism. Evolution of the ES was treated in the continuum model coupled with the atomistic model for the IS. 18,33,34 The ES was characterised by the temperature distribution T e ðx; y; zþ, temperature-dependent specific heat C e ðt e Þ, and heat conductivity j e ðt e Þ. The basic equation for the electron energy relaxation in this model is the thermal conductivity equation C e ðt e e ¼rj ð e rt e Þ nðt e ; T i Þþ It ðþe x=l ; l where the source nðt e ; T i Þ corresponds to the energy transfer between electronic and ionic subsystems, 18,34 I is the absorbed laser intensity of the pulse with width s (i.e., I s ¼ F), and l is the attenuation length. During the simulation time t < s ¼ 100 fs, heating of the ES is performed. The electron energy does not overflow through the surface which is normal to x-direction. We use C e from Ref. 35 for both studied metals and j e from Refs. 12 and 20 for Au and Al, respectively. The values of l are taken as 10 nm and 15 nm for Au and Al, respectively. It is significant to note that the ballistic transport of the excited electrons is not considered in the model. The energy flux in the ES is caused only by heat conductivity. Therefore, electroneutrality is conserved during the 2T-stage. However, the ballistic transport of the excited electrons may be significant for gold. 36,37 The question about role of the ballistic transport in the energy transport remains still open. The equations of motion for ions are modified to account for the electron-ion energy exchange m dv j dt ¼ r jur ð 1 ; :::r n Þþ F lang j ðt e T i Þ rp e ; (2) n i where m and v j are mass and velocity of the j-th atom, Uðr j Þ is potential energy of the system which is described by the potential, r j denotes differentiation with respect to the coordinates of the j-th atom, and F lang is the random force (Langevin thermostat) due to electron-phonon coupling. The last term is the electron blast force 19,20,34 of the electron pressure P e and n i is the ion density. In this work, we use embedded atom method interatomic potentials (EAM-potential). Aluminium is described with the EAM-potential from Ref. 38. For description of gold, we use the EAM-potential which is developed in Ref. 5 as a cold part of the electrontemperature-depended potential (i.e., ETD-potential at T e ¼ 0:1 ev). 39 The damping time parameter of the thermostat depends on local ion and electron temperatures. It was set to provide the total energy transfer per unit volume per one MD timestep equal to gðt e T i Þdt on an average, with g ¼ Wm 3 K 1 and g ¼ Wm 3 K 1 for Au and Al, respectively. The term n in Eq. (1) includes energy balance from both the Langevin force and electron blast force. It should be noted that there is significant uncertainty in the choice of g, especially for gold. In this work, the selection of g is based on a value averaged over the data from several works. 14,35,40 However, the given values of g must be regarded as an estimation. To solve the coupled equations (1) and (2), the scheme proposed by Duffy and Rutherford in Refs. 18 and 33 was used. The simulation volume is divided to smaller cells by a grid. Equation (1) is solved numerically on this grid. The velocities of atoms in a cell are used to calculate the local ion temperature and energy exchange term n. At the end of each ionic time step, the values of T i and n are calculated at all grid points, and Eq. (1) is then integrated numerically up to the same time moment, and the new electron temperature profile is calculated. The ES and IS are described separately only in 2T-stage. 10 ps for Al and 20 ps for Au are enough to achieve the balance between subsystems (T e T i ) for all cases simulated in this work. After that, the system is simulated only by classical molecular dynamics. The electron heat conduction in the metal after 2T-stage is not taken into account. For all types of simulations, the surface is assumed to be flat. The boundary between the atoms and vacuum determines position of the surface. At the deformation in 2Dand 3D-simulations, the surface position is defined by the position of the most shifted atom. This assumption is correct because during 2T-stage the surface deforms slightly. It should be noted that the heat flow term in Eq. (1) was calculated numerically via the heat flux difference between the neighbor j ert e Þ q x Dx q xþdx ; (3) Dx

4 S. V. Starikov and V. V. Pisarev J. Appl. Phys. 117, (2015) where q ¼ j e rt e is the heat flux density, dx is the grid space in x-direction (normal to the open surface). The boundary condition was set so that the heat fluxes from and to vacuum were zeroed, and the form (3) allowed us to treat grid points near the surface in the same way as the grid points in the bulk. The electron pressure is taken in the following form: P e ðt e Þ¼cC e T e. The coefficients c are chosen as 0.9 for Au and 0.4 for Al, to get the best agreement with the dependence P e ðt e Þ. 5,41,42 It should be noted that P e is described as delocalized pressure for both metals (i.e., the free electron gas approximation is used). To avoid large electron pressure gradients at the surface in numerical simulations, the electron pressure profile was smoothed near the surface (the surface is assumed to be flat) ¼ c C et e ðþk x ðx þ kþ 2 þ x # ðc e T e Þ xþdx ðc e T e Þ x ; x þ k Dx where x is the coordinate measured from an instantaneous surface position, k is the effective electron mean free path. 5,20 This expression reduces to the correct expression rp e ¼rðcC e T e Þ in the bulk (x k). The systems with various scales are simulated. At 1D-simulation, the size of the calculation box is set to nm in the x, y, and z directions, respectively. The ions form a crystal in one half of the calculation box, at x > 1000 nm. At 2D-simulation, the size of the calculation box is nm. We perform 3D-simulation only for Al, and the size of the calculation box in this case is nm in the x, y, and z directions (atoms form a crystal at x > 500 nm). The periodic boundary conditions in y and z directions are used in all simulations. Distribution of the absorbed fluence F on the surface is given by the Gaussian profile: FðrÞ ¼F 0 exp½ r 2 =R 2 e Š, where F 0 and R e are parameters of Gaussian and r is the distance from a centre of laser spot. In 3D-simulation, the absorbed energy E abs is connected with fluence by the equation E abs ¼ ¼ þ1 ð 0 þ1 ð III. 1D-SIMULATION 0 FðrÞ2prdr F 0 exp½ r 2 =R 2 e Š2prdr ¼ F 0pR 2 e : (4) Figure 1 shows the dependence of the modification depth d (ablation or melting) on absorbed fluence F obtained from 1D-simulation. The depth of ablation crater d is calculated as: d ¼ N r =ðn eq SÞ, where N r is the number of all ions removed during ablation, n eq is an equilibrium ion concentration, and S is a surface area. The different mechanisms of ablation are found at the simulation of gold. This result agrees well with the previous results 20,30 obtained with ETD-potential. For the absorbed fluence F < 150 mj/cm 2, ablation is due to the electron FIG. 1. Results of the 1D AS. The dependence of ablation/melting depth d on absorbed fluence F for the simulated metals: 1 melting depth for Al; 2 melting depth for Au; 3 ablation depth for Al; and 4 ablation depth for Au. pressure build-up, similarly to the electron-driven ablation in Refs. 43 and 44. At the initial moment of time, a high pressure is created in the near-surface layer due to increase of the electron temperature. The formation of a layer with negative pressure takes place as a result of joint action of two pressure-reducing processes: the mechanical expansion in vacuum and the decrease of T e due to relaxation processes. This type of ablation is described in detail in Refs. 30 and 43. Here, we name this type of ablation, the short type, as it occurs into short spatial and time scales: about 5 nm and 15 ps for the depth and the time duration, respectively. At higher F, the short type of ablation is present as well. However, in this case, it cannot be distinguished from much deeper long ablation due to the rarefaction wave formation. This type of ablation has place at F > 150 mj/cm 2 (like in Refs. 1 and 2). Therefore, the dependence d(f) for gold has the second ablation threshold (see Fig. 1). It should be noted that the separation of two mechanisms is impossible for the long laser pulse width s. If the time of electron-ion relaxation is comparable with s the short type of ablation does not occur explicitly. 30 Similar effect of two thresholds of ablation at the short laser pulse width has been obtained in several experiments. 4,29,45,46 Figure 2 illustrates the evolution of matter and the electron pressure profiles at short ablation of Au. It should be noted that the 1D-simulation without electron pressure gives only long ablation, in complete agreement with Ref. 1. In case of aluminium, the mechanism of ablation is fully determined by propagation of a shock wave as the value of electron pressure for Al is significantly lower than for Au at the identical absorbed fluences. In addition, the time of electron-ion relaxation for Al is smaller than for Au. However, the role of electron pressure in ablation of aluminium may rise at higher fluencies or for thin film. 47 Our results for aluminium ablation agree with the 1D-hydrodynamic simulation. 15 The ablation mechanism associated with boiling is not investigated in this work. The fluence required for realization of considerable boiling must be larger than the examined fluences.

5 S. V. Starikov and V. V. Pisarev J. Appl. Phys. 117, (2015) r 2 a ¼ R2 e lnðf 0=F abl Þ¼R 2 e lnðae=pr2 e F ablþ; (6) where F abl threshold fluence of ablation at 1D-simulation. Figure 3 illustrates this approach for the absorbed energy E abs ¼ 48 nj. Thus, experimental measurements of the dependencies r m ðeþ and r a ðeþ may provide values of F melt and F abl. IV. SURFACE MODIFICATION WITH MELTING FIG. 2. (a) Snapshots of short ablation of Au from 1D-simulation with F 0 ¼ 86 mj/cm 2. (b) The electron pressure profiles along x-direction at Au short ablation. For both figures, the numbers indicate the various moments of calculation time: 1 t ¼ 0.1 ps, 2 t ¼ 5ps,3 t ¼ 10 ps, and 4 t ¼ 20 ps. Along with the ablation process, we investigate melting of the metals by the laser pulse. The melt depth is calculated as depth of formed liquid layer: N l =ðn eq SÞ, where N l is the number of ions in liquid (i.e., disordered) state including the removed ions. The diagnostics used in this work for determination of liquid-solid boundary is similar to the approach from Ref. 48. The threshold fluences of melting for the studied metals differ in several times (see Figure 1). The reason of lower threshold fluence of melting for aluminium is in a small value of j e and a high value of g in comparison with gold. Aluminium accumulates absorbed energy of the laser pulse near the surface while in gold the energy spreads from the surface into bulk. In this case, the maximum of ion temperature for aluminium is higher than the maximum of ion temperature for gold at identical fluences. We believe that the threshold fluence of melting determines the size of surface modification area. At low energy of laser pulse, the nanoscale ripples may be induced on the surface by the melting without laser ablation. 5,10,27 The nanoscale changes of the surface are due to the splash of molten metal under fluence/temperature gradient of the laser beam. The depth of this modification is no more than several nanometers. The modification area radius r m in this case may be determined by the formula The 2D-simulation is performed to verify the formula (5). Figure 4 shows the snapshots of the evolution of Al surface at absorption of the laser pulse with F 0 ¼ 32 mj/cm 2 and R e ¼ 90 nm. Here, R e is several times smaller than the experimental value. However, the general features must appear at the used scales as the phenomenon is determined by hydrodynamics. It should be noted that the local value of melting depth in 2D- and 3D-simulations agrees with the local fluence F and with the result of 1D-simulation (see Figure 1). Also such agreement is observed for the depth of voids formation at ablation. The absorbed energy spreads on a surface (into yz-plane) weakly in comparison with the flow in x-direction. It is due to larger temperature gradient into x-direction, compared to y or z-directions. However, for the case with R e l, the melting depth in 2D- or 3D-simulation must be appreciably smaller than the estimation from 1D-smulation. The performed simulation demonstrates that the surface modification may be realized by splash of molten metal without ablation. There is an analogy of this modification with the capillary waves. The most appreciable changes occur on the boundary between the melt and the crystal. The calculated size of modification agrees well with the formula (5). It feels like the similar effect must appear also in 3Dsimulation. However, such 3D-simulation demands a computing resource larger than the one applied in this work. This phenomenon shows that new interesting features of matter may be studied at larger scales of simulation. It should be stressed that such type of modification is more appreciable at X-ray laser pulse 49,50 as local gradients of temperature may be larger than for optical pulse. r 2 m ¼ R2 e lnðf 0=F melt Þ¼R 2 e lnðae=pr2 2 F meltþ; (5) where a absorption coefficient, E total energy of the laser pulse (E abs ¼ ae), and F melt threshold fluence of melting at 1D-simulation. It should be noted that the profile of the modification strongly depends on the characteristic of laser pulse and irradiated matter. The ablation (or swelling as first step of ablation) occurs at a higher pulse energy. The radius of ablation area r a may be determined by the formula FIG. 3. The simulated profile of absorbed fluence F on a surface at absorbed energy E abs ¼ 48 nj. Numbered lines indicate the threshold values: 1 threshold fluence for melting of Al; 2 threshold fluence for melting of Au; 3 threshold fluence for ablation of Al; and 4 threshold fluence for ablation of Au (short type of ablation).

6 S. V. Starikov and V. V. Pisarev J. Appl. Phys. 117, (2015) FIG. 4. Results of the 2D AS. Evolution of the Al surface at absorption of the laser pulse with F 0 ¼ 32 mj/cm 2 and R e ¼ 90 nm: (a) t ¼ 100 ps; (b) t ¼ 200 ps; (c) t ¼ 500 ps; and (d) t ¼ 1.3 ns. White dashed lines indicate the boundaries of the melt zone. The red circles indicate the modification of the surface. V. 2D- AND 3D-SIMULATION OF ABLATION In this work, the 2D-simulation of ablation is performed for both metals. The 3D-simulation is carried out only for aluminium. A. Simulation of ablation in aluminium Figure 5 shows the pressure profiles along x-directions in various moments of 1D- and 2D-simulation at identical F 0 ¼ 65 mj/cm 2. In 2D-simulation, R e equals 90 nm. The character of the stresses evolution in matter agrees well with the description of laser ablation given in Refs. 1 and 2. In 2D-case, the moderate decrease of shock wave amplitude is obtained. In this case, the pressure amplitude changes according to the law x 1 and is twice lower than the value in 1D at x 5R e. The pressure wave overcomes the distance of about 22 R e from the front surface to the rear surface and back, during the long time of the simulation. The sphericity and the attenuation of stress waves appreciably decrease the influence of the wave reflection from a rear surface on the processes near the front surface. It is worth noting that such influence may disappear completely if a non-reflective rear surface is used. For instance, thermal boundary conditions were used in Ref. 51. The value of R e at 3D-simulation is smaller than at 2Dsimulation because of smaller size of the calculation cell. This fact is a consequence of the limitation of the computing resources. Figure 6 shows the pressure profiles for 3Dsimulation (F 0 ¼ 65 mj/cm 2 and R e ¼ 60 nm). The decreasing of pressure amplitude here is more substantial than in case of 2D-simulation. The pressure amplitude changes according to the law x 2 and is twice lower than the value in 1D at x 2R e. In addition, 3D-geometry of the simulation leads to smoother maximum of pressure wave than in 1D and 2Dcases. Nevertheless, nucleation of the voids is similar in all simulated systems. On the other hand, the relaxation after voids nucleation occurs in different ways for various simulations. FIG. 5. The pressure profiles along x-direction passing through the centre of laser spot for various moments of Al ablation simulation: (a) t ¼ 2 ps; (b) t ¼ 15 ps; (c) t ¼ 25 ps; and (d) t ¼ 35 ps. Blue dashed lines indicate the results of 1D simulation. Red lines indicate the results of 2D simulation. The absorbed fluence F 0 ¼ 65 mj/cm 2, the radius of laser spot for 2D simulation R e ¼ 90 nm.

7 S. V. Starikov and V. V. Pisarev J. Appl. Phys. 117, (2015) FIG. 6. The pressure profiles along x-direction passing through the laser spot centre for various moments of 3D simulation: 1 t ¼ 2 ps; 2 t ¼ 10 ps; 3 t ¼ 15 ps; and 4 t ¼ 20 ps. The absorbed fluence F 0 ¼ 65 mj/cm 2, radius of laser spot R e ¼ 60 nm. Nucleation of the voids occurs at a depth about 40 nm. This depth agrees with the results of 1D-simulation (see Figure 1). Thus, the first step of ablation is the swelling, in well agreement with the experiments. 8,9 At 3D-simulation, the voids are disconnected at the initial time and then combine into one spherical void (see Figure 7), and the frustrated ablation takes place. The material removal requires about 30% higher central fluences than F abl in agreement with the experiments. 8,9 At 2D-simulation, the evolution of voids is described less accurate as the surface tension can not organize stable spherical void. The results of simulation confirm correctness of the formula (6) for the swelling area. For the real values of R e, the frustrated ablation must correspond to porous structure with bulk voids placed at a depth about 40 nm. B. Simulation of ablation in gold The 2D-simulation of ablation in gold reveals some interesting features. As the short ablation takes place at a depth of several nanometers, the swelling does not appear here. Thus, the material removal occurs at central absorbed fluence F 0 ¼ F abl ¼ 60 mj/cm 2. The simulation results agree with the experiments where producing of nanoparticles and nanojets takes place at the absorbed fluences about mj/cm 2. In our simulation, the nanojets height may reach nm. The swelling takes place at F 0 ¼ 150 mj/cm 2 when the long type of ablation occurs. Figure 8 shows the snapshots of the evolution of Au surface at absorption of the laser pulse with F 0 ¼ 160 mj/cm 2 and R e ¼ 400 nm. First, the short ablation changes surface morphology. Then the voids are formed at a depth of about nm at the long ablation. In this case, the substantial material removal requires F 0 > 190 mj/cm 2. The question about the electron pressure description is a crucial aspect of simulation for gold. 30,52,53 Inclusion of the electron pressure in the model leads to the short type of ablation. At the same time, the detailed experimental study of the dependence of surface morphology on absorbed energy is not carried out for single laser pulse. Thus, the additional experimental data about surface morphology at laser ablation in gold are necessary for verification of the model. FIG. 7. The evolution of Al surface at absorption of the laser pulse with F 0 ¼ 65 mj/cm 2 and R e ¼ 90 nm for 2D-simulation (left snapshots) and R e ¼ 60 nm for 3D-simulation (right snapshots): (a) and (b) t ¼ 25 ps; (c) and (d) t ¼ 70 ps; (e) and (f) t ¼ 150 ps. FIG. 8. Results of the 2D atomistic simulation. The evolution of Au surface at absorption of the laser pulse with F 0 ¼ 160 mj/cm 2 and R e ¼ 400 nm: (a) t ¼ 10 ps; (b) t ¼ 80 ps; (c) t ¼ 160 ps; and (d) t ¼ 260 ps. The black dasheddotted line indicates the center of the laser spot.

8 S. V. Starikov and V. V. Pisarev J. Appl. Phys. 117, (2015) VI. CONCLUSION In this work, changes of the surface morphology at the interaction with laser pulse are studied for Al and Au. The 2D-simulation shows the possibility of the surface modification without ablation by the splash of molten metal. Such modification considerably depends on temperature/fluence gradient and may vary for different laser pulses. The depth of this modification is about several nanometers. This fact agrees with the experiments where the changes of surface morphology were observed as nanoscale ripples without ablation. 5,10,27 For both studied metals, swelling is obtained as initial stage of the long laser ablation. At the same time, the short type of ablation is revealed for gold. This type of ablation does not produce swelling and creates nanoparticles and nanojets at the threshold fluence. The low threshold fluence of this process is due to the build-up of the high electron pressure and the comparatively low rate of electron-ion energy relaxation in gold. It is possible that the short ablation is the reason of the existence of second threshold fluence leading to a change in slope of the dependence d(f) observed in the multiple-shot laser experiments. 29,45 ACKNOWLEDGMENTS The calculations were carried out on the computer clusters MVS-100 K of the Joint Supercomputer Center of RAS, K-100 of Keldysh Institute of Applied Mathematics of RAS, and Lomonosov of the Moscow State University. The work was supported by the Russian Science Foundation (Grant No ). APPENDIX: PERFORMANCE MEASURES The size of the 2D and 3D simulations corresponds to hundreds of millions to billions of atoms. Such simulations are only achievable using massive parallelism and to the day can be performed only on the world s top supercomputers. The classical molecular dynamics codes are reported to scale with high efficiency to hundreds of thousands Central processing units (CPU) cores and trillion particles. 54 Specifically, the LAMMPS code has recently been reported to scale up to particles. 24 The performance of the MSU Lomonosov supercomputing cluster for the ablation simulations with EAM potential has been tested. The cluster has a partition of nodes with 2 quad-core Intel Xeon 5570 CPUs per node (CPU partition) and a partition with 2 quad-core Intel Xeon 5570 CPUs and 2 Nvidia X2070 Graphics processing units (GPU) accelerators per node (GPU partition). We have tested simulation performance of the standard (CPU) and GPU-accelerated 55 versions of the LAMMPS code on CPU and GPU partitions, respectively. The LAMMPS executable was built with Intel Cþþ Compiler 13, with MPI support and GPU package enabled. One and the same executable file was used for both CPUonly and CPU þ GPU calculations. The choice of CPU only and CPU þ GPU calculations was made by a built-in command line option of the program. The tests consisted of the FIG. 9. LAMMPS performance at the MSU Lomonosov cluster with EAM potential for aluminium. NVE MD simulation of short length (1000 to timesteps) on a given number of computational nodes. The execution time was averaged over 3 consecutive runs. The LAMMPS performance results are shown in Fig. 9. We were primarily interested in the simulations of large systems, so the figures represent the weak scaling performance, i.e., the scaling when the system size changes proportionally to the number of cores used. For our tasks, the optimal load was about 30 K atoms/cpu core at CPU partition and 1M atoms/gpu at GPU partition, giving simulation speed 0.1 s/timestep. The results of GPU-accelerated molecular dynamics with LAMMPS show noticeable performance dependence on load (Fig. 10). The performance is sub-optimal at low GPU load, probably due to increased communication costs because of more frequent GPU-host data exchange. On the other hand, very high GPU loads (with higher theoretical efficiency) are not attainable due to memory limit. As a rule of thumb, the maximal GPU load is 1M atoms per GB video memory for a typical EAM metal simulation (cutoff radius ¼ 3rd coordination sphere), may be less with large cutoff radius potentials. Overall, both CPU and GPU LAMMPS versions demonstrated excellent scaling on the cluster. The CPU version scaling efficiency was above 95% up to 8192 cores and above 70% up to cores, and the GPU version showed over 90% efficiency up to 1280 GPUs. The GPU nodes FIG. 10. GPU-accelerated MD LAMMPS efficiency at the MSU Lomonosov cluster with EAM potential for aluminium.

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