Technical Physics Letters, Vol. 31, No. 5, 2005, pp. 361–363. Translated from Pis’ma v Zhurnal Tekhnicheskoœ Fiziki, Vol. 31, No. 9, 2005, pp. 6–13. Original Russian Text Copyright © 2005 by Kask, Michurin.
Percolation in Laser Ablation of Binary Mixtures N. E. Kask* and S. V. Michurin Skobel’tsyn Institute of Nuclear Physics, Moscow State University, Moscow, 119899 Russia * e-mail:
[email protected] Received November 3, 2004
Abstract—We have studied the optical emission of plasma expanding from a target made of a binary alloy or a pressed powder mixture and ablated by nanosecond laser pulses of moderate power. The intensity of spectral lines has been studied for the first time as dependent on the target composition. It is established that a threedimensional percolation takes place in the plasma, with a percolation threshold determined by the atomic density of a metal component in the target composition. © 2005 Pleiades Publishing, Inc.
Introduction. The formation of nanodimensional clusters during pulsed laser ablation of targets has been extensively studied in recent years in the context of solving certain problems of nanotechnology. The laser plasma parameters depend on the irradiation conditions and rapidly vary after termination of a single laser pulse. The dynamics of plasma expanding into the gas phase, the plasma composition, and the characteristics of various processes (absorption of laser radiation, heating, ionization, recombination, condensation, and clusterization) in the plume depend on various factors, in particular, on the pressure produced by the ambient (buffer) gas. According to Harilal et al. [1], laser plasma exhibits adiabatic expansion at pressures below 1 Pa. The collisions of plasma particles with atoms of the ambient gas become significant at a pressure of ~10 Pa, as manifested by a significant increase in the intensity of emission from the plume observed 1–2 µs after termination of the laser pulse. In the case of a plasma expanding into vacuum during the ablation of aluminum [1] and silicon [2] targets, the relative intensities of ion emission lines show that the plasma temperature reaches a maximum (~104 K) at the end of the laser pulse and then decays at a characteristic time of ~10–7 s. Evidently, the increase in intensity of emission observed with microsecond intervals in the course of plasma expansion into a surrounding gas is related to a change in the emissivity (and absorption) of the plasma as a result of the condensation and clusterization processes. According to the results of our previous investigations [3–5], the intensity of continuous emission in the case of millisecond laser pulses is correlated with a threshold behavior of the high-frequency conductivity as a function of the laser composition (this behavior is characteristic of percolation) and with the appearance of fractal nanostructures. As the ambient gas pressure increases, the effective brightness and color temperatures (characterizing the continuous emission) exhibit a jumplike increase to a level above the boiling point of
the target material [6]. This is accompanied by a change in the shape and size of the plume and by the formation of a macroscopic fractal shell in its peripheral layers [5]. The continuous emission spectrum and a high microwave conductivity of the plasma are related to the presence of percolation clusters in the plume volume. These clusters, in contrast to compact ones, do not vanish when the temperature increases above the boiling point. For such clusters to exist, it is necessary that the density of medium exceed a certain critical value. Percolation must also take place when targets are ablated by shorter laser pulses, since the greater the flux intensity, the higher the density of the near-surface plasma. Experimental investigations of the plasma formed in the nanosecond range of laser pulse durations encounter difficulties related to plasma degradation and to the requirement of high temporal resolution of the measuring equipment. An alternative approach to the study of clusterization phenomena is offered by methods developed previously [3–6] for the investigation of percolation in laser plumes at the surface of composite targets and the analysis of spectral features of the continuous emission. This paper presents the results of experimental investigation of the phenomenon of percolation in the plasma formed at the surface of a binary target ablated by nanosecond laser pulses. Experimental setup and methods. The experimental setup used for the investigation of emission from the plume in a broad range of the buffer gas pressures (1−107 Pa) was described in detail elsewhere [6]. In this study, binary targets were ablated by single pulses of a Nd:YAG laser with λ = 1.06 µm, a pulse duration of ~10 ns, a pulse energy of ~10 mJ, and a power density of ~108 W/cm2 in the laser spot. We have measured the spectra of emission from plumes formed at the surface of binary targets representing either pressed powder mixtures or binary alloys (CuxAl1 – x and CuxNi1 – x). The powder mixtures were
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Fig. 1. Plots of the atomic spectral line intensity I versus composition (x is the atomic fraction of copper) for a binary alloy target ablated by nanosecond laser pulses at a buffer gas pressure of 105 Pa: (a) CuxAl1 – x alloy in argon; (b) CuxNi1 – x in air; (1) Cu, λ ≈ 0.5105 µm; (2) Al, λ ≈ 0.3964 µm; (3) Ni, λ ≈ 0.5477 µm; (4) effective color temperature Tcol of the plume.
melted in electric arc between tungsten electrodes in argon at normal pressure. The results of control experiments using repeated laser pulses allowed the optimum conditions of irradiation to be selected to ensure reproducibility of the emission caused by two sequential laser pulses. These were the first and second pulses in the case of alloys, and the second and third pulses for powder mixtures, after which the target was shifted. The geometry of irradiation and the laser pulse parameters in the course of these measurements remained unchanged. The emission was taken in the direction perpendicular to the plume axis, from a plasma region spaced by ≈1 mm from the target surface. In the course of investigation of the effects of target composition, the size and shape of the plume (which depend predominantly on the laser pulse intensity and the ambient gas pressure [2]) also remained unchanged. One aim of this study was to determine the effect of the target composition on the effective temperatures in the laser plume. The observed significant excess of the effective color temperature (Tcol ≥ 5000 K) over the brightness temperature (Tbr ≤ 3000 K) in the visible spectral range indicates that the plasma layer is optically thin. The absorption of emis-
sion at discrete frequencies was also ignored, since the measurements were performed for low-intensity spectral lines corresponding to the transitions of subordinate series. In the analysis of experimental data, it was assumed that (i) the target components are uniformly distributed in the plume volume and (ii) their relative densities in the evaporated substance are the same as in the target. The fraction of free atoms in the laser plasma was determined using the intensity of discrete atomic emission lines. Experimental results and discussion. During the laser ablation of binary copper-based alloys with aluminum and nickel, we monitored the intensities of spectral lines belonging to Cu (λ = 0.5105 µm), Al (λ = 0.3964 µm), and Ni atoms (λ = 0.5477 µm). Figures 1a and 1b show plots of these intensities versus the relative number of Cu atoms in the target composition. These experimental data were obtained for a normal pressure of the buffer gas (Ar for CuxAl1 – x; air for CuxNi1 – x). In the absence of absorption, the intensity of each spectral line must be proportional to the density of the corresponding metal component in the plume volume (provided that the line widths and shapes exhibit no significant variations). The full widths at half maximum (FWHM) of the monitored spectral lines were independent of the target composition and the buffer gas pressure and amounted to 0.37 ± 0.04, 1 ± 0.05, and 0.4 ± 0.04 nm for Cu, Al, and Ni, respectively. As can be seen from Fig. 1, deviations from the proportionality between the line intensity and the component density in the plasma are observed when the relative atomic density exceeds na ~ 0.15, which is a level characteristic of the three-dimensional percolation threshold [7]. Therefore, it was natural to assume that saturation of the intensity of the atomic spectral lines (Fig. 1) is related to a limitation on the number of free atoms in the plasma as a result of the formation of bound structures (clusters). Since the model of compact clusters is inconsistent with a rather high gas temperature (~1 eV) of the plasma at the moment of laser pulse action (when the intensities of spectral lines are at maximum [2]), the formation of “hot” bound structures is most probably explained in terms of the model of gaslike clusters [8] and the model of percolation cluster. If the percolation threshold on the axis of compositions is determined as the position of a local maximum or a bending point, the binary metal alloys are characterized by the following values: 0.5 ± 0.05, 0.4 ± 0.04, and 1.3 ± 0.2 nm for Cu, Ni, and Al, respectively. During the laser ablation of binary metal targets (both alloys and powder mixtures), the percolation thresholds appear separately for each metal component and do not influence the behavior of the other components. In the case of a metal–salt mixture, the spectrum of the plume contains both the discrete lines of the metal component, the continuum, and the atomic spectrum of metal atoms entering into the salt molecules. The maximum intenTECHNICAL PHYSICS LETTERS
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Fig. 2. Plots of the atomic spectral line intensity I versus composition (x is the atomic fraction of aluminum) for a pressed powder mixture target ablated by nanosecond laser pulses at a buffer gas (air) pressure of 105 Pa: (a) Al–LiF mixture; (b) Al–MgF2 mixture; (1) Al, λ ≈ 0.3964 µm; (2) Li, λ ≈ 0.4273 µm; (3) Mg, λ ≈ 0.3838 µm; (4) effective color temperature Tcol of the plume.
sity of the spectral lines of aluminum in a mixture with salt was observed for a relative atomic density of n 'a ~ 0.3 (Figs. 2a and 2b). This value is about one and half times the percolation threshold for aluminum in the binary mixtures. This difference is probably related to a decrease in the content of free aluminum atoms, which is explained by their involvement in chemical reactions with the formation of fluorides AlFn (n ≤ 3) and by the liberation of metal atoms from salt molecules. In contrast to the results for alloys, the spectral line intensity in the case of pressed metal–salt powder mixtures sharply decreases above the percolation threshold. This can be interpreted as being due to the fact that aluminum atoms entering into a percolation cluster do not participate in chemical reactions. It should be noted that a target made of a powder mixture can also be considered as a medium featuring three-dimensional percolation. However, the percolation threshold in such objects is determined by the volume ratio of the mixture components, rather than by their atomic densities [7]. Representation of the experimental results in Figs. 1 and 2 as functions of the volume fractions of components in the target leads to a much greater difference between percolation thresholds TECHNICAL PHYSICS LETTERS
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of the given metal (e.g., of copper in different alloys or aluminum in mixtures with different salts). An alternative model for hot structures formed in a dense vapor is offered by the model of a gaslike cluster with the minimum number of bonds between atoms [8]. At a sufficiently high temperature, such structures appear as spontaneously formed (virtual) atomic chains. Since the critical density for the formation of one-dimensional chains (percolation threshold) is close to unity, this model is inconsistent with the experimental results obtained in this study. Our results are also at variance with the two-phase cluster model [9], according to which the outer monolayer of a compact cluster consists of particles with small numbers of bonds. Indeed, percolation in a two-dimensional layer is characterized by a threshold of 0.5. Zhukhovitskiœ [10] proposed a generalized model of virtual chains, in which a cluster comprising a fractallike system of bound atomic chains has a topology close to that of the percolation cluster. Conclusions. The results of our investigation showed that plasma generated during ablation of targets by nanosecond laser pulses and expanding into a buffer gas contains three-dimensional percolation clusters. The percolation threshold is determined by the critical atomic density of each evaporated metal component of the target. Such “hot” percolation clusters determine the absorption capacity, temperature, and spectral continuum of emission from the laser plasma. Acknowledgments. This study was supported by the Russian foundation for Basic Research (project no. 03-02-17026) and the Program of Support for Leading Scientific Schools in Russia (NSh-1771.2003.2). REFERENCES 1. S. S. Harilal, C. V. Bindhu, M. S. Tillack, et al., J. Appl. Phys. 93, 2380 (2003). 2. M. S. Tillack, D. W. Blair, and S. S. Harilal, Nanotechnology 15, 390 (2004). 3. H. E. Kask, Pis’ma Zh. Éksp. Teor. Fiz. 60, 204 (1994) [JETP Lett. 60, 212 (1994)]. 4. N. E. Kask, S. V. Michurin, and G. M. Fedorov, Zh. Éksp. Teor. Fiz. 116, 1979 (1999) [JETP 89, 1072 (1999]. 5. N. E. Kask, E. G. Leksina, S. V. Michurin, et al., Kvantovaya Élektron. (Moscow) 32, 437 (2002). 6. N. E. Kask, S. V. Michurin, and G. M. Fedorov, Kvantovaya Élektron. (Moscow) 34, 524 (2004). 7. B. I. Shklovskii and A. L. Efros, Electronic Properties of Doped Semiconductors (Nauka, Moscow, 1979; Springer-Verlag, New York, 1984). 8. D. I. Zhukhovitskiœ, Zh. Éksp. Teor. Fiz. 113, 181 (1998) [JETP 86, 101 (1998)]. 9. D. I. Zhukhovitskiœ, Zh. Éksp. Teor. Fiz. 121, 396 (2002) [JETP 94, 336 (2002)]. 10. D. I. Zhukhovitskiœ, Zh. Fiz. Khim. 75, 1159 (2001).
Translated by P. Pozdeev
