- Email: [email protected]
Monte Carlo simulation of the laser-induced plasma-plume expansion under vacuum and with a background gas
Applied Surface Science 138–139 Ž1999. 97–101
Monte Carlo simulation of the laser-induced plasma-plume expansion under vacuum and with a background gas F. Garrelie ) , A. Catherinot E.S.A. 6015 C.N.R.S. ‘Materiaux Ceramiques et Traitements de Surface’, ´ ´ LMCTS-PLM, Faculte´ des Sciences, 123 AÕenue A. Thomas, 87060 Limoges, France
Abstract The plasma-plume created above a copper target irradiated by a pulsed KrF laser beam Žwavelengths 248 nm, pulse durations 20 ns, fluences 17 Jrcm2 . is investigated by means of a Monte Carlo simulation. The plume expansion under both vacuum and background gas is followed in time by simulating particle motion and collisions in the gas phase. The expansion under vacuum of laser-ablated particles is dominated by the laser energy absorption by the evaporated particles during the laser pulse. A comparison between simulated time-of-flight curves and experimental curves obtained by spectroscopic time-of-flight measurements has shown that about 6% of the incoming laser energy was contributing to the expansion process through the time-delayed recombination of this energy into kinetic energy. The plasma-plume expansion under a residual argon pressure greater than 50 Pa has been found to be very much affected by collisions between laser-ablated and ambient gas particles. The compression of the ambient gas particles by the ejected particles in the leading edge of the plume Žsnowplow effect. is clearly observed. q 1999 Elsevier Science B.V. All rights reserved. PACS: 52.65.Pp; 52.50.Jm; 81.15.Fg Keywords: Ablation; Simulation; Monte Carlo; Laser; Plasma; Transport
1. Introduction Pulsed laser vaporization of materials from a target has attracted great attention over the past few years as a promising technique for depositing a wide variety of thin films w1x, as for instance high-temperature superconductors w2x. For a better understanding of the growth mechanisms, the nature and transport of species from the target to the substrate should be known and controlled. Theoretical studies, describ-
)
Corresponding author. Tel.: q33-5-55-45-75-08; Fax: q335-55-45-72-11; E-mail: [email protected]
ing the plume in terms of a continuous medium, have been developed both for the expansion under vacuum w3,4x, and with a residual ambient pressure of a few tens of pascal w5,6x. Monte Carlo simulations were already used to examine the effects of collisions among particles desorbing from solid surfaces when a few monolayers of material from the target were desorbed in vacuum w7–9x. Moreover, the transport of laser ablated atoms in a dilute gas has also been studied by a Monte Carlo method w10,11x but without a description of the collective motion of the ablated particles in the dilute gas. The latter can lead to the compression of the ambient gas particles in the leading edge of the plume due to collisions between
0169-4332r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 5 7 8 - 9
98
F. Garrelie, A. Catherinotr Applied Surface Science 138–139 (1999) 97–101
laser-ablated and ambient gas particles, corresponding to the snowplow of the leading edge of the plume observed experimentally w12x. In this paper, we present a three-dimensional Monte Carlo simulation of the laser-induced plasma-plume transport either under vacuum or with a background gas. The simulation is carried out under conditions similar to those used in pulsed-laser deposition of thin films, i.e., when more than a few monolayers of materials are evaporated per pulse and a plasma is created in the vapor of the ejected species.
2. Model The plasma-plume expansion is simulated by a Monte Carlo procedure based on Bird’s algorithm w13x. According to the high number of particles evaporated during the laser pulse, the plume is simulated on a reduced scale w14x, thus permitting the simulation with a reduced number of particles involved. This approach allows us to describe realistically the plume expansion for a high evaporation rate and large spot size, under conditions corresponding, for instance, to pulsed-laser deposition of thin films. The flow is supposed to be axially symmetric, the region above the target being divided into a network of cells specified by two coordinates, z, normal to the surface and passing through the center of the laser-spot area, and r, in the plane parallel to the surface and measuring the distance from the z-axis.
unit time and surface, evolves with both time and position within the laser spot area. The evolution with time has been estimated by a numerical computation w16x of laser–copper interaction based on the resolution of the heat-flow equation, and the radial profile of the evaporated depth has been taken as a hyperbolic function. The latter was based on profilometric measurements of the ablated volume when a copper target was irradiated by a KrF laser Žwavelength s 248 nm, pulse durations 20 ns, fluence s 17 Jrcm2 .. Because of the very high evaporation flux, the surface temperature is estimated by introducing the Clausius–Clapeyron law w17x, leading to a value close to the critical temperature of copper Ž8390 K., much higher than the vaporization temperature under standard conditions of temperature and pressure. The motion and the interactions among evaporated particles are computed by successive time steps w13x. The collisions are computed within each cell of the network with the use of the Time Counter method w13x, which defines the number of collisions to be performed per time step per cell. The elasticcollision cross-section depends on the collision energy, ´ , through an inverse square root law Ž s Ž ´ . A 1r6´ .. In order to simulate the laser-energy absorption by the dense plume and the effects induced on the expansion, we assume that a fraction of the ionized particles will redistribute the transported internal energy Žequal to the ionization energy. into kinetic energy through collisional recombinative processes w14x. 2.2. Expansion under background gas
2.1. Expansion under Õacuum The details of the method developed to simulate the plasma-plume expansion under vacuum have been described before w14x. In this section, we described only the details relevant to the present calculations. We start the simulation with all cells empty at t s 0. Until the end of the laser pulse, particles are evaporated by assuming a thermal evaporation process. As the involved processes are rather complicated, we have made the approximation of a pure thermal process, a detailed study of laser-surfaces interactions can be found in Ref. w15x. The evaporation rate, i.e., the number of particles evaporated per
The previously described method has been extended to the simulation of the plasma-plume expansion with a residual argon pressure. The evaporated particles and the background gas particles are followed in a similar way, by the uncoupling of particles motion and the collisions over the time interval D t. The proposed approach does not distinguish temporal stages during which only interactions among the evaporated particles or interactions of the ablated particles with the background gas particles are computed. The different kinds of interactions are allowed to arise during the same time step of the simulation.
F. Garrelie, A. Catherinotr Applied Surface Science 138–139 (1999) 97–101
The evaporation of the copper particles is simulated by the same way as previously ŽSection 2.1.. The initial positions of the background gas particles are randomly sampled into the simulated volume. The interactions among all particles contained in each cell of the network are computed by the Time Counter method w13x. The probability of each kind of collision Žcopper–copper, copper–argon, argon– argon. is determined on the basis of the collision cross-section and the particle density of each species. A random test, on the basis of these different probabilities, is used to determine the kind of event that must be computed. This allows us to follow simultaneously both the motion of the evaporated particles and the background-gas particles, which is not possible by a Monte Carlo simulation of random trajectories w10,11x. The simulated volume is divided into 45,000 cells of variable dimensions. In order to avoid statistical fluctuations at longer times when the particles density in the plume has strongly decreased, the number of copper particles is progressively increased from 60,000 up to 960,000 w14x. When the expansion occurs under a residual pressure, the number of background-gas particles used is increased in the same ratio.
3. Results As the algorithm allows us to simulate the photoablation phenomena with a relatively large spot size and great evaporated depth, calculations are performed with a spot size of 464 mm in diameter, an evaporated depth averaged over all the damaged area of 0.1 mm, and a laser fluence of 17 Jrcm2 . 3.1. Expansion under Õacuum Simulated time of flight distributions, performed with 35% of the total number of particles converting their internal energy Ži.e., ionization energy. into kinetic energy, and measurements w14x Žspectroscopic time of flight on CuI, l s 521.8 nm. are reported on Fig. 1 for different heights above the sample surface. For distances lower than 4 mm, a good agreement of the temporal location of the maximum of the curve is obtained, whereas the decrease of the curve is rela-
99
Fig. 1. Simulated Žsymbol B. and experimental w14x Žfull line. time-of-flight curves of copper particles at distances of 2 and 5 mm above the target obtained after a KrF irradiation under vacuum at a fluence of 17 Jrcm2 .
tively poorly described by the simulation. A good agreement between simulated curves and measurements is obtained for all distances greater than 4 mm. This indicates that, among the incident laser energy absorbed by the evaporated particles, 6% of the incident laser energy is absorbed in the plume and redistributed into kinetic energy by time-delayed recombination. This value leads to simulated results in good agreement with both experimental results obtained by spectroscopic time-of-flight measurements w14x and numerical results obtained by Ho et al. w18x. This approximation of time-delayed redistribution of energy carried only by a fraction of the species Žcorresponding to the recombination of ionized particles leading to a kinetic-energy transfer. leads to results which predict well the experimental velocities of particles. 3.2. Expansion with a background gas The simulation was carried out under the same conditions as previously ŽSection 3.1., except for the presence of the argon particles in the simulated volume above the target. Collisions among all particles Žcopper and argon. are computed by the method described in Section 2.2. Calculations have been done for different argon pressures extending from 1 to 200 Pa. The density distribution in the plasmaplume, which corresponds to the copper particle density, and the density distribution of background gas particles Žargon. at a delay of 1 ms after the
100
F. Garrelie, A. Catherinotr Applied Surface Science 138–139 (1999) 97–101
Fig. 2. Simulation of the density distribution of copper particles and background-gas particles at a delay of 1 ms after the beginning of the laser pulse and for various argon pressures. The corresponding laser fluence is 17 Jrcm2 . The size of each image is 3 cm = 3 cm.
beginning of the laser pulse are reported on Fig. 2 for various argon pressures. These results show clearly the effects of collisions between laser ablated and ambient-gas particles. Moreover, at the first stages of the expansion Žnot shown here., the plasma-plume shape is not much affected by the presence of ambient particles, due to the difference between the particle density in the plume and in the background gas. At later stages, ambient-gas particles are pushed out from the volume occupied by the copper particles, on account of kinetic-energy transfer during collisions between copper particles and argon particles. Argon particles are compressed in a higher density region in the front of the plume, which lead to a decrease of copper-particle velocities. Indeed, the instantaneous velocity of the leading edge of the plume at a delay of 1 ms and for an argon pressure of 100 Pa is about 1.0 = 10 4 m sy1 , to be compared with a value of 1.6 = 10 4 m sy1 obtained for the expansion under vacuum. These observations are in good agreement with experimental observations w12,19x of the expansion of the laser-induced plasma-plume under background gas and show clearly the snowplow of the leading edge of the plume. The threshold pressure value of about 10 Pa, leading to a decrease of the laser-ablated particle velocities, is also in good agreement with experimental observations on timeof-flight velocities w19x.
Moreover, these results show that the high-density region in the plume is deficient in background-gas particles, which is of great interest for thin film realization by pulsed-laser deposition.
4. Conclusion In this paper, we have reported a three-dimensional simulation of the laser-induced plasma-plume expansion under vacuum and with a background gas. Simulated results of the plasma-plume expansion under vacuum compare well with experimental results obtained on spectroscopic time-of-flight velocities w14x. The simulation of the expansion with a background gas leads, to our knowledge, for the first time by a Monte Carlo method, to the observation of the snowplow of the leading edge of the plume. This indicates that this method is appropriate to the description of the plasma-plume expansion under various residual background pressures. Simulated results show clearly the effects of the collisions between evaporated and background-gas particles. The influence of many experimental parameters, such as for instance the pressure and the nature of the background gas, may be easily deduced by simulations, with obvious applications to thin-film realization by pulsed-laser deposition.
F. Garrelie, A. Catherinotr Applied Surface Science 138–139 (1999) 97–101
References w1x D.B. Chrisey, C.K. Hubler, Pulsed Laser Deposition of Thin Films, Naval Research Laboratory, Washington, DC, 1994. w2x C. Champeaux, P. Marchet, J. Aubreton, J.P. Mercurio, A. Catherinot, Appl. Surf. Sci. 69 Ž1993. 335. w3x R.K. Singh, O.W. Holland, J. Narayan, J. Appl. Phys. 68 Ž1. Ž1990. 233. w4x J.C.S. Kools, T.S. Baller, S.T. de Zwart, J. Dieleman, J. Appl. Phys. 71 Ž9. Ž1992. 4547. w5x K.R. Chen, J.N. Leboeuf, R.F. Wood, D.B. Geohegan, J.M. Donato, C.L. Liu, A.A. Puretzky, J. Vac. Sci. Technol. A 14 Ž3. Ž1996. 1111. w6x R.F. Wood, K.R. Chen, J.N. Leboeuf, A.A. Puretzky, D.B. Geohegan, Phys. Rev. Lett. 79 Ž8. Ž1997. 1571. w7x I. Noorbatcha, R.R. Lucchese, Y. Zeiri, J. Chem. Phys. 86 Ž1987. 5816. w8x D. Sibold, H.M. Urbassek, J. Appl. Phys. 73 Ž12. Ž1993. 8544.
101
w9x T.E. Itina, V.N. Tokarev, W. Marine, M. Autric, J. Chem. Phys. 106 Ž21. Ž1997. 8905. w10x J.C.S. Kools, J. Appl. Phys. 74 Ž10. Ž1993. 6401. w11x T.E. Itina, W. Marine, M. Autric, J. Appl. Phys. 82 Ž7. Ž1997. 3536. w12x D.B. Geohegan, Appl. Phys. Lett. 60 Ž22. Ž1992. 2732. w13x G.A. Bird, Molecular Gas Dynamics, Clarendon, Oxford, 1976. w14x F. Garrelie, J. Aubreton, A. Catherinot, J. Appl. Phys. 83 Ž10. Ž1998. 5075, and references therein. w15x R. Kelly, A. Miotello, Nucl. Instrum. and Meth. in Phys. Res. B 122 Ž1997. 374. w16x R.K. Singh, J. Viatella, J.O.M. Ž1992. 20–23. w17x M. Aden, E. Beyer, G. Herziger, H. Kunze, J. Phys. D: Appl. Phys. 25 Ž1992. 57. w18x J.R. Ho, C.P. Grigoropoulos, J.A.C. Humphrey, J. Appl. Phys. 79 Ž9. Ž1996. 7205. w19x B. Angleraud, C. Girault, C. Champeaux, F. Garrelie, C. Germain, A. Catherinot, Appl. Surf. Sci. 96–98 Ž1996. 117.
Monte Carlo simulation of the laser-induced plasma-plume expansion under vacuum and with a background gas F. Garrelie ) , A. Catherinot E.S.A. 6015 C.N.R.S. ‘Materiaux Ceramiques et Traitements de Surface’, ´ ´ LMCTS-PLM, Faculte´ des Sciences, 123 AÕenue A. Thomas, 87060 Limoges, France
Abstract The plasma-plume created above a copper target irradiated by a pulsed KrF laser beam Žwavelengths 248 nm, pulse durations 20 ns, fluences 17 Jrcm2 . is investigated by means of a Monte Carlo simulation. The plume expansion under both vacuum and background gas is followed in time by simulating particle motion and collisions in the gas phase. The expansion under vacuum of laser-ablated particles is dominated by the laser energy absorption by the evaporated particles during the laser pulse. A comparison between simulated time-of-flight curves and experimental curves obtained by spectroscopic time-of-flight measurements has shown that about 6% of the incoming laser energy was contributing to the expansion process through the time-delayed recombination of this energy into kinetic energy. The plasma-plume expansion under a residual argon pressure greater than 50 Pa has been found to be very much affected by collisions between laser-ablated and ambient gas particles. The compression of the ambient gas particles by the ejected particles in the leading edge of the plume Žsnowplow effect. is clearly observed. q 1999 Elsevier Science B.V. All rights reserved. PACS: 52.65.Pp; 52.50.Jm; 81.15.Fg Keywords: Ablation; Simulation; Monte Carlo; Laser; Plasma; Transport
1. Introduction Pulsed laser vaporization of materials from a target has attracted great attention over the past few years as a promising technique for depositing a wide variety of thin films w1x, as for instance high-temperature superconductors w2x. For a better understanding of the growth mechanisms, the nature and transport of species from the target to the substrate should be known and controlled. Theoretical studies, describ-
)
Corresponding author. Tel.: q33-5-55-45-75-08; Fax: q335-55-45-72-11; E-mail: [email protected]
ing the plume in terms of a continuous medium, have been developed both for the expansion under vacuum w3,4x, and with a residual ambient pressure of a few tens of pascal w5,6x. Monte Carlo simulations were already used to examine the effects of collisions among particles desorbing from solid surfaces when a few monolayers of material from the target were desorbed in vacuum w7–9x. Moreover, the transport of laser ablated atoms in a dilute gas has also been studied by a Monte Carlo method w10,11x but without a description of the collective motion of the ablated particles in the dilute gas. The latter can lead to the compression of the ambient gas particles in the leading edge of the plume due to collisions between
0169-4332r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 Ž 9 8 . 0 0 5 7 8 - 9
98
F. Garrelie, A. Catherinotr Applied Surface Science 138–139 (1999) 97–101
laser-ablated and ambient gas particles, corresponding to the snowplow of the leading edge of the plume observed experimentally w12x. In this paper, we present a three-dimensional Monte Carlo simulation of the laser-induced plasma-plume transport either under vacuum or with a background gas. The simulation is carried out under conditions similar to those used in pulsed-laser deposition of thin films, i.e., when more than a few monolayers of materials are evaporated per pulse and a plasma is created in the vapor of the ejected species.
2. Model The plasma-plume expansion is simulated by a Monte Carlo procedure based on Bird’s algorithm w13x. According to the high number of particles evaporated during the laser pulse, the plume is simulated on a reduced scale w14x, thus permitting the simulation with a reduced number of particles involved. This approach allows us to describe realistically the plume expansion for a high evaporation rate and large spot size, under conditions corresponding, for instance, to pulsed-laser deposition of thin films. The flow is supposed to be axially symmetric, the region above the target being divided into a network of cells specified by two coordinates, z, normal to the surface and passing through the center of the laser-spot area, and r, in the plane parallel to the surface and measuring the distance from the z-axis.
unit time and surface, evolves with both time and position within the laser spot area. The evolution with time has been estimated by a numerical computation w16x of laser–copper interaction based on the resolution of the heat-flow equation, and the radial profile of the evaporated depth has been taken as a hyperbolic function. The latter was based on profilometric measurements of the ablated volume when a copper target was irradiated by a KrF laser Žwavelength s 248 nm, pulse durations 20 ns, fluence s 17 Jrcm2 .. Because of the very high evaporation flux, the surface temperature is estimated by introducing the Clausius–Clapeyron law w17x, leading to a value close to the critical temperature of copper Ž8390 K., much higher than the vaporization temperature under standard conditions of temperature and pressure. The motion and the interactions among evaporated particles are computed by successive time steps w13x. The collisions are computed within each cell of the network with the use of the Time Counter method w13x, which defines the number of collisions to be performed per time step per cell. The elasticcollision cross-section depends on the collision energy, ´ , through an inverse square root law Ž s Ž ´ . A 1r6´ .. In order to simulate the laser-energy absorption by the dense plume and the effects induced on the expansion, we assume that a fraction of the ionized particles will redistribute the transported internal energy Žequal to the ionization energy. into kinetic energy through collisional recombinative processes w14x. 2.2. Expansion under background gas
2.1. Expansion under Õacuum The details of the method developed to simulate the plasma-plume expansion under vacuum have been described before w14x. In this section, we described only the details relevant to the present calculations. We start the simulation with all cells empty at t s 0. Until the end of the laser pulse, particles are evaporated by assuming a thermal evaporation process. As the involved processes are rather complicated, we have made the approximation of a pure thermal process, a detailed study of laser-surfaces interactions can be found in Ref. w15x. The evaporation rate, i.e., the number of particles evaporated per
The previously described method has been extended to the simulation of the plasma-plume expansion with a residual argon pressure. The evaporated particles and the background gas particles are followed in a similar way, by the uncoupling of particles motion and the collisions over the time interval D t. The proposed approach does not distinguish temporal stages during which only interactions among the evaporated particles or interactions of the ablated particles with the background gas particles are computed. The different kinds of interactions are allowed to arise during the same time step of the simulation.
F. Garrelie, A. Catherinotr Applied Surface Science 138–139 (1999) 97–101
The evaporation of the copper particles is simulated by the same way as previously ŽSection 2.1.. The initial positions of the background gas particles are randomly sampled into the simulated volume. The interactions among all particles contained in each cell of the network are computed by the Time Counter method w13x. The probability of each kind of collision Žcopper–copper, copper–argon, argon– argon. is determined on the basis of the collision cross-section and the particle density of each species. A random test, on the basis of these different probabilities, is used to determine the kind of event that must be computed. This allows us to follow simultaneously both the motion of the evaporated particles and the background-gas particles, which is not possible by a Monte Carlo simulation of random trajectories w10,11x. The simulated volume is divided into 45,000 cells of variable dimensions. In order to avoid statistical fluctuations at longer times when the particles density in the plume has strongly decreased, the number of copper particles is progressively increased from 60,000 up to 960,000 w14x. When the expansion occurs under a residual pressure, the number of background-gas particles used is increased in the same ratio.
3. Results As the algorithm allows us to simulate the photoablation phenomena with a relatively large spot size and great evaporated depth, calculations are performed with a spot size of 464 mm in diameter, an evaporated depth averaged over all the damaged area of 0.1 mm, and a laser fluence of 17 Jrcm2 . 3.1. Expansion under Õacuum Simulated time of flight distributions, performed with 35% of the total number of particles converting their internal energy Ži.e., ionization energy. into kinetic energy, and measurements w14x Žspectroscopic time of flight on CuI, l s 521.8 nm. are reported on Fig. 1 for different heights above the sample surface. For distances lower than 4 mm, a good agreement of the temporal location of the maximum of the curve is obtained, whereas the decrease of the curve is rela-
99
Fig. 1. Simulated Žsymbol B. and experimental w14x Žfull line. time-of-flight curves of copper particles at distances of 2 and 5 mm above the target obtained after a KrF irradiation under vacuum at a fluence of 17 Jrcm2 .
tively poorly described by the simulation. A good agreement between simulated curves and measurements is obtained for all distances greater than 4 mm. This indicates that, among the incident laser energy absorbed by the evaporated particles, 6% of the incident laser energy is absorbed in the plume and redistributed into kinetic energy by time-delayed recombination. This value leads to simulated results in good agreement with both experimental results obtained by spectroscopic time-of-flight measurements w14x and numerical results obtained by Ho et al. w18x. This approximation of time-delayed redistribution of energy carried only by a fraction of the species Žcorresponding to the recombination of ionized particles leading to a kinetic-energy transfer. leads to results which predict well the experimental velocities of particles. 3.2. Expansion with a background gas The simulation was carried out under the same conditions as previously ŽSection 3.1., except for the presence of the argon particles in the simulated volume above the target. Collisions among all particles Žcopper and argon. are computed by the method described in Section 2.2. Calculations have been done for different argon pressures extending from 1 to 200 Pa. The density distribution in the plasmaplume, which corresponds to the copper particle density, and the density distribution of background gas particles Žargon. at a delay of 1 ms after the
100
F. Garrelie, A. Catherinotr Applied Surface Science 138–139 (1999) 97–101
Fig. 2. Simulation of the density distribution of copper particles and background-gas particles at a delay of 1 ms after the beginning of the laser pulse and for various argon pressures. The corresponding laser fluence is 17 Jrcm2 . The size of each image is 3 cm = 3 cm.
beginning of the laser pulse are reported on Fig. 2 for various argon pressures. These results show clearly the effects of collisions between laser ablated and ambient-gas particles. Moreover, at the first stages of the expansion Žnot shown here., the plasma-plume shape is not much affected by the presence of ambient particles, due to the difference between the particle density in the plume and in the background gas. At later stages, ambient-gas particles are pushed out from the volume occupied by the copper particles, on account of kinetic-energy transfer during collisions between copper particles and argon particles. Argon particles are compressed in a higher density region in the front of the plume, which lead to a decrease of copper-particle velocities. Indeed, the instantaneous velocity of the leading edge of the plume at a delay of 1 ms and for an argon pressure of 100 Pa is about 1.0 = 10 4 m sy1 , to be compared with a value of 1.6 = 10 4 m sy1 obtained for the expansion under vacuum. These observations are in good agreement with experimental observations w12,19x of the expansion of the laser-induced plasma-plume under background gas and show clearly the snowplow of the leading edge of the plume. The threshold pressure value of about 10 Pa, leading to a decrease of the laser-ablated particle velocities, is also in good agreement with experimental observations on timeof-flight velocities w19x.
Moreover, these results show that the high-density region in the plume is deficient in background-gas particles, which is of great interest for thin film realization by pulsed-laser deposition.
4. Conclusion In this paper, we have reported a three-dimensional simulation of the laser-induced plasma-plume expansion under vacuum and with a background gas. Simulated results of the plasma-plume expansion under vacuum compare well with experimental results obtained on spectroscopic time-of-flight velocities w14x. The simulation of the expansion with a background gas leads, to our knowledge, for the first time by a Monte Carlo method, to the observation of the snowplow of the leading edge of the plume. This indicates that this method is appropriate to the description of the plasma-plume expansion under various residual background pressures. Simulated results show clearly the effects of the collisions between evaporated and background-gas particles. The influence of many experimental parameters, such as for instance the pressure and the nature of the background gas, may be easily deduced by simulations, with obvious applications to thin-film realization by pulsed-laser deposition.
F. Garrelie, A. Catherinotr Applied Surface Science 138–139 (1999) 97–101
References w1x D.B. Chrisey, C.K. Hubler, Pulsed Laser Deposition of Thin Films, Naval Research Laboratory, Washington, DC, 1994. w2x C. Champeaux, P. Marchet, J. Aubreton, J.P. Mercurio, A. Catherinot, Appl. Surf. Sci. 69 Ž1993. 335. w3x R.K. Singh, O.W. Holland, J. Narayan, J. Appl. Phys. 68 Ž1. Ž1990. 233. w4x J.C.S. Kools, T.S. Baller, S.T. de Zwart, J. Dieleman, J. Appl. Phys. 71 Ž9. Ž1992. 4547. w5x K.R. Chen, J.N. Leboeuf, R.F. Wood, D.B. Geohegan, J.M. Donato, C.L. Liu, A.A. Puretzky, J. Vac. Sci. Technol. A 14 Ž3. Ž1996. 1111. w6x R.F. Wood, K.R. Chen, J.N. Leboeuf, A.A. Puretzky, D.B. Geohegan, Phys. Rev. Lett. 79 Ž8. Ž1997. 1571. w7x I. Noorbatcha, R.R. Lucchese, Y. Zeiri, J. Chem. Phys. 86 Ž1987. 5816. w8x D. Sibold, H.M. Urbassek, J. Appl. Phys. 73 Ž12. Ž1993. 8544.
101
w9x T.E. Itina, V.N. Tokarev, W. Marine, M. Autric, J. Chem. Phys. 106 Ž21. Ž1997. 8905. w10x J.C.S. Kools, J. Appl. Phys. 74 Ž10. Ž1993. 6401. w11x T.E. Itina, W. Marine, M. Autric, J. Appl. Phys. 82 Ž7. Ž1997. 3536. w12x D.B. Geohegan, Appl. Phys. Lett. 60 Ž22. Ž1992. 2732. w13x G.A. Bird, Molecular Gas Dynamics, Clarendon, Oxford, 1976. w14x F. Garrelie, J. Aubreton, A. Catherinot, J. Appl. Phys. 83 Ž10. Ž1998. 5075, and references therein. w15x R. Kelly, A. Miotello, Nucl. Instrum. and Meth. in Phys. Res. B 122 Ž1997. 374. w16x R.K. Singh, J. Viatella, J.O.M. Ž1992. 20–23. w17x M. Aden, E. Beyer, G. Herziger, H. Kunze, J. Phys. D: Appl. Phys. 25 Ž1992. 57. w18x J.R. Ho, C.P. Grigoropoulos, J.A.C. Humphrey, J. Appl. Phys. 79 Ž9. Ž1996. 7205. w19x B. Angleraud, C. Girault, C. Champeaux, F. Garrelie, C. Germain, A. Catherinot, Appl. Surf. Sci. 96–98 Ž1996. 117.