Transfer-Matrix Method for Efficient Ablation by Pulsed Laser Ablation

ARTICLE pubs.acs.org/JPCC

Transfer-Matrix Method for Efficient Ablation by Pulsed Laser Ablation and Nanoparticle Generation in Liquids Ana Menendez-Manjon, Philipp Wagener, and Stephan Barcikowski* Laser Zentrum Hannover, Hollerithallee 8, Hannover 30419, Germany

bS Supporting Information ABSTRACT: Comparable low nanoparticle production is a weakness of femtosecond-pulsed laser ablation in liquids, but the process ablation rate can be maximized at optimal focusing conditions and liquid levels. Refraction at the air-liquid boundary, vaporization of the liquid, self-focusing, and optical breakdown in the liquid complicate the determination of these optimal parameters. A semiempirical method has been developed, allowing an a priori determination of the appropriate experimental setup (liquid layer over the target, focal length, and lens position) for efficient ablation. The presented work can be applied with high accuracy for tightly focused beams, whereas loosely focused ultrashort lasers should be avoided to induce effective fabrication of colloids via laser ablation in liquids.

’ INTRODUCTION Pulsed laser ablation in liquids (PLAL) started to be investigated in the late 80s as a method for processing of material surfaces.1 Since then, much effort has been done on understanding the differences of laser ablation mechanism in a gas atmosphere.2-10 By laser processing in gas or liquids, the energy density on the target is usually determined by the nominal energy delivered to the target and ablated spot area.11 However, the propagation of the laser beam from air to liquid phase and along the liquid produces several changes in the incident laser pulse energy12 and wavelength.13,14 Moreover, when ultrashort and high-energetic laser pulses are applied, self-focusing and filamentation appear as a result of the interaction of the laser radiation with the liquid in which the target is immersed.15-17 When nanoparticles are generated during the ablation process, absorption and nonlinear interaction are enhanced due to the larger linear and nonlinear absorption coefficients of the colloid.18-20 Although these effects limit the productivity of laser ablation, they are rarely considered during the experiments, and careful reading of the results should be done.2 The generation of nanoparticulate colloids by PLAL is attracting the attention of researchers, with a 15-fold increase in publication activity in the past decade21 due to the possibility to combine desired solid and liquid phases and obtain highly pure and stable colloids.22 Nevertheless, compared with other nanoparticle generation techniques, the laser-based method presents low productivities for longtime generation processes, and optimal parameters should be used to draw upon this technique. It has been shown that the ablated mass increases with fluence applied on the target23 so that high intensities are desired for the production of nanoparticles. However, when high energies are used, the determination of the focal plane in liquids by the ablated spots is not evident, and alternative procedures r 2011 American Chemical Society

have to be employed, like the measurement of sound intensity produced by the collapse of the laser-induced cavitation bubble.24 We present a semiempirical approach to the propagation of the laser beam from air to the liquid until it reaches the target to determine the optimal experimental parameters (focal length, liquid layer over the target...) for efficient PLAL and nanoparticle generation.

’ EXPERIMENTAL METHODS A Ti/sapphire laser (Spitfire Pro, Spectra Physics) of 800 nm central wavelength with 3.4 mm beam radius delivering pulses of 120 fs length and 400 μJ maximal pulse energy at a repetition rate of 5000 Hz was used for the ablation experiments and as a model for the propagation analysis in this work. The laser beam was focused with lenses of different focal lengths. The relative distance between the target and lens has been changed by moving the lens toward the target (dzL < 0) or away from it (dzL > 0), with dzL = 0 when the geometrical focal plane coincides with the target. This reference position of the lens has been determined through the measurement of ablated spots on a Si-wafer in air. The typical experimental setup for PLAL is shown in Figure 1. Gold targets of 100 μm thickness (99.99% Goodfellow) were cleaned with acetone in an ultrasonic bath and ablated in deionized water, acetone, and ethanol (Sigma-Aldrich). The resulting gold colloids generated by PLAL were analyzed spectroscopically (1650, Shimadzu) to determine the gold concentration in the solution from Special Issue: Laser Ablation and Nanoparticle Generation in Liquids Received: September 30, 2010 Revised: January 26, 2011 Published: March 01, 2011 5108

dx.doi.org/10.1021/jp109370q | J. Phys. Chem. C 2011, 115, 5108–5114

The Journal of Physical Chemistry C

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Figure 1. Typical experimental setup for ablation in liquid environment.

its interband absorption (A@ 380 nm for the case of gold).25 The calibration curve is shown in the Supporting Information (Figure S3). To determine the optical breakdown intensity threshold of different liquids, the laser beam was focused by a 40 mm focal length lens in the center of a quartz cuvette filled with the desired liquid, and the 90 scattered light from the focal volume has been measured with a fiber spectrometer (H2000þ, Ocean Optics).

’ RESULTS AND DISCUSSION The determination of the beam waist position of focused laser beams in gaseous atmosphere can be done directly from the ablated spots at different lens-target distances. In liquids and with ultrashort laser pulses this procedure is not so evident. The diameter of the ablated spots on a silicon wafer (5000 on 1) under different water layers is presented in Figure 2. It can be seen that when the ablation takes place in a liquid, the ablated spots diminish until they vanish with the increment of the lens position dzL. Experimentalists could interpret that analogously to air, the smaller the ablated spot, the higher the fluence, and hence expect high nanoparticle productivity. However, when nanoparticles are generated by ultrashort PLAL, the largest ablated mass does not occur for the lens position corresponding to the smallest ablated spot. For this reason, contrary to laser ablation in a gaseous atmosphere, the determination of the focal plane (i.e., the higher fluence on the target) is not possible by simple inspection of the ablated spots. One possible procedure is to define the focal plane as the position at which the largest mass is ablated. Typically, time-consuming experimental series are carried out for each new experimental setup. The simple variation of, for example, the liquid, requires refocusing and repetition of the focal plane determination experiments. One exemplifying measurement of this kind is shown in Figure 3a for the case of a 10 mm water layer over the target and the laser beam with 200 μJ pulse energy being focused by a lens of 40 mm focal length. The maximum nanoparticle productivity has been achieved for dzL = 2 mm. Note that according to Figure 2 the smallest spot found for these parameters was at dzL = 4 mm. The 2 mm difference in the lens position, even though it might not seem very significant, induces a 260 times higher gold concentration in the liquid. The ablated mass at varying lens position was measured for different liquid layers over the target. The optimal focusing conditions in each case have been derived from these types of measurements aiming at maximum nanoparticle productivity, that is, colloidal gold mass concentration. In Figure 3b, the relative lens position dzL at which the highest ablation rate is reached with different liquid layers over the target in water and in acetone and ethanol for the 10 mm liquid layer are shown. We see

Figure 2. Effect of lens position and water layer on ablated spot diameter on a silicon wafer (f = 40 mm). Top: photograph of ablated spots in air and with 10 mm water layer.

that the optimal focusing conditions are dependent on the liquid layer and what kind of liquid is used. As the liquid layer increases, the displacement of the lens with respect to its original position (the position at which the focal plane in air coincided with the target) should be increased. When the laser beam is focused by longer focal lengths (Figure 3c), the focusing conditions are very different, requiring a reduction in the relative distance between lens and target (dzL < 0). The principal phenomena causing this displacement of the focal plane with respect to the focal plane in air will be discussed below. The complex beam parameter q(z) characterizes a laser beam at any point along its propagation path. A detailed description of this parameter and its relation to the beam radius, wavefront radius, and Rayleigh length has been summarized in the Supporting Information. The analysis of the propagation of a laser beam through different optical elements, that is, the determination of its complex beam parameter q(z) at each point, can be accomplished by the ABCD-transfer-matrix method for Gaussian beams.26-28 This method has been applied to the typical experimental setup for ablation in liquids (Figure 1), where the relative distance between lens and target might be varied by displacing the lens a distance dzL. The complex beam parameter q of the incoming laser to the air-liquid frontier is q = -h þ dzL þ izR, where h is the liquid layer over the target and zR is the Rayleigh length of the beam after it was focused by a lens of focal length f. Combined with the corresponding transfer matrix along the liquid, the complex beam parameter in the liquid at a distance hp from the liquid surface is q0 ¼ hp þ nðdzL - hÞ þ inzR

ð1Þ

The beam radius along the liquid can be derived from q0 and results in sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 λ ðhp þ nðdzL - hÞÞ þ n2 z2R ð2Þ ω¼ π zR n2 Detailed mathematical derivation can be found in the Supporting Information. Equation 2 can be used to calculate the caustic of the beam along the system, as shown in Figure 4. In this Figure, the refraction of the laser beam in the liquid is evident. Moreover, it can be seen that when a focused laser beam is transmitted from air to a liquid, the beam waist will be shifted 5109

dx.doi.org/10.1021/jp109370q |J. Phys. Chem. C 2011, 115, 5108–5114


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Figure 3. (a) Concentration of gold nanoparticles in the colloid generated by PLAL as a function of the lens position for h = 10 mm, f = 40 mm. (b) Experimental and theoretical lens position (f = 40 mm) for a maximal ablation rate for different liquid layers over the target. (c) Experimental and theoretical lens position (h = 10 mm) for a maximal ablation rate in water with different focal lengths.

along the propagation direction independently of the focal length of the lens. The presence of liquid obviously requires modification of the focusing conditions (dzL) or displacement of the target to maximize the fluence and hence the nanoparticle productivity. We will analyze in the present work the first, with it being analogous to the second modification. At the beam waist of a focused laser, the complex beam parameter takes imaginary values. The fluence delivered to the target will be at a maximum if the condition Re[q0 ] = 0 is fulfilled on the target surface (hp = h). An analytical expression for the lens position dzL required to place the beam waist on the immersed target can then be derived form eq 1 dzL ¼ hð1 - 1=nÞ

ð3Þ

Only the refractive index n and liquid layer over the target h affect the displacement of the beam waist due to refraction, and as seen in Figure 4, it is independent of the focal length of the lens. As presented in Figure 4 and expressed in eq 3, for all cases, the distance between the lens and the ablation system should be increased to maximize the nanoparticle productivity. However, it should be considered that the fluence on the liquid’s surface increases if (dzL > 0). If the laser pulse energy density on the surface of the liquid exceeds a certain value, then it vaporizes and water vapor is ejected upward. A picture of this phenomenon can be found in the Supporting Information (Figure S3a). The pulse energy is then absorbed by the liquid and scattered by the vaporized liquid ejected from the surface along the beam propagation path. The ablation efficiency is hence drastically reduced, and for this reason, this focusing regime should be avoided. The lens position at which vaporization is induced can be related to a fluence threshold Fth of this phenomenon as follows rffiffiffiffiffiffiffiffiffiffiffiffiffiffi F0 -1 ð4Þ dzL ¼ h - zR Fth where F0 is the focal fluence of the incident laser beam. (Refer to the Supporting Information for mathematical derivation.) To determine the vaporization threshold fluence, the femtosecond laser beam with 200 μJ pulse energy was focused inside the liquid matrix with a 80 mm focal length lens for at least 10 s. The position of the lens relative to the geometrical focal plane at which vaporization occurs was visually determined for different liquid layers

Figure 4. Calculated caustic of the laser beam propagating linearly from air to water for different focal lengths.

of ethanol, water, and acetone. The best fits of eq 4 to the experimental data (Figure 5a), with zR = 141 μm and F0 = 355 J/cm2 (theoretical), allow the calculation of the fluence threshold for each liquid. These values are 0.33, 0.21, and 0.15 J/cm2 for water, ethanol, and acetone, respectively. Knowing the fluence threshold for the vaporization of the liquid, the lens position for every liquid layer, focal length, and pulse energy for which liquid vaporization will occur can be calculated. Figure 5b shows with solid lines the lens positions at which the vaporization of the liquid starts to be induced for different water layers. Note that the slopes of these lines are proportional to the square root of the pulse energy. The solid lines divide the plot in two regions: the vaporization region rffiffiffiffiffiffiffiffiffiffiffiffiffiffi F0 -1 " h ð5Þ dzL g h - zR F th over the lines and the maximal transmission region rffiffiffiffiffiffiffiffiffiffiffiffiffiffi F0 dzL < h - zR -1 " h F th

ð6Þ

under the lines. More explicitly, if we focus with a lens of 80 mm and the liquid layer is 2.5 mm (case 1 in Figure 5), then for all focusing conditions (dzL) vaporization of water will be induced, and the 5110



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Figure 5. (a) Lens position for which explosive vaporization is induced in water, acetone, and ethanol in dependence of the liquid layer. The lines result from the fit of eq 2 to the experimental data. (b) Calculated working diagram for optimal lens position (at different focal lengths) and liquid layer to avoid explosive evaporation and overcome focal shift produced by refraction of the laser beam (200 μJ/pulse). The colored dotted lines mark the minimal liquid layer required for maximal mass ablation.

ablation will be hindered. If we choose a thicker water layer, 10 mm as represented by the case 2 in Figure 5, then the lens position dzL can be varied in a long-range without inducing liquid vaporization because we are working in the (h,dzL) space below the threshold line. For a maximal delivery of the laser energy to the target, avoiding vaporization, and a proper focalization on the target’s surface, two different conditions have to be hence fulfilled (eqs 3 and 4). This fact can be also read from Figure 5b. The dashed line defines the required lens correction to focus the laser beam on a target immersed at 10 mm in water considering refraction at the air-liquid interface. Aiming at maximum ablation mass rate and, respectively, nanoparticle productivity, one should work along the dashed line but keeping always in the maximum transmission region. Considering the previous example, we can see in Figure 5b that for h = 2.5 mm (case 1) the lens position required to refocus the beam on the target is always in the vaporization zone of the 80 mm lens. PLAL experiments will not be productive for nanoparticle generation under these conditions, but if h = 10 mm (case 2), then the required lens position to focus on the target avoiding refraction (2.5 mm) is found in the high-energy transmission range. High-energy densities will reach the target, producing in this way large ablated masses. At this point, we can also see that the liquid layer is bounded from below by the intersection of both expressions (eqs 3 and 4). Therefore, the minimal liquid layer necessary to place the beam waist on the target’s surface, avoiding liquid vaporization, is expressed as rffiffiffiffiffiffi F0 -1 ð7Þ hmin ¼ nzR Fth For example, when focusing the laser beam in water with 200 μJ/pulse with a 40 mm lens, a minimal water layer of 3 mm is required, whereas for a 150 mm lens, at least 11.5 mm should be used. Using these expressions, we can determine the experimental setup (liquid layer, focusing conditions, lens) necessary for a productive ablation in liquids. The effect of refraction and liquid vaporization is common to all type of lasers; however, nonlinear interaction of the laser and liquid can be induced by ultrashort laser pulses, even at low pulse energies. Even though the coefficient of the nonlinear Kerr index n2 of most liquids is usually on the order of 10-15 cm2/W, the high intensities employed in this study (∼1013 W/cm2) clearly cause nonlinear effects such as self-focusing, supercontinuum

Figure 6. Calculated caustic of the femtosecond laser beam undergoing self-focusing in water at different focal lengths.

generation, or filamentation of the laser beam.29 The formation of white light is an indication of filamentation, and hence selffocusing can be easily identified. These effects complicate the prediction of the beam propagation through the liquid. A laser beam propagating in a dielectric medium will self-focus if the pulse power exceeds a critical power, which can be expressed for Gaussian beams as29 3:77λ2 ð8Þ 8πn0 n2 Great efforts have been done to study the self-focusing effect in liquids, especially in water.30-32 Several approximations have been proposed as an alternative to numerical solutions of the nonlinear Schr€odinger equation governing the propagation of intense light beams in Kerr media.33 We have applied the approximation proposed by Yariv and Yeh34 because it is appropriate to the PLAL experimental setup. They propose an extension of the matrix formalism to nonlinear propagation of focused Gaussian beams. Following the work of these authors, the caustic of the laser beam propagating along the liquid can be determined. The expression for the beam radius can be found in the Supporting Information. As an example of the results obtained through the nonlinear transfer-matrices, the caustic of a beam focused by different focal lengths in water is plotted in Figure 6. Pcr ¼

5111



Figure 7. (a) Calculated caustic of a laser beam with different pulse lengths focused in water. (b) Calculated caustic of a laser beam focused with two different lenses in water, acetone, and ethanol.

Notice that the position of the lens is dzL = 0, as in the case of Figure 4, but now the nonlinear propagation causes different shifts of the beam waist for the different focal lengths. Note also that this movement of the focus is more marked for long focal lengths (similarly low NA or focusing angles), as demonstrated by several authors experimentally.16,35 The propagation length of the selffocused beam until collapse depends on the square diameter of the laser beam at the entrance of the medium;29 hence the beam will self-focus more rapidly if previously focused with a long focal length lens. Some authors take advantage of these irradiation conditions to fragmentate colloidal nanoparticles.36 We would like to remark here that self-focusing becomes not negligible for ultrashort laser pulses, as can be seen in Figure 7a, on the caustics of laser beams of different pulse lengths but the same pulse energy. Typical nanosecond or picosecond laser beams are not affected by nonlinear propagation. The researchers working with long-pulsed laser systems can base their studies on the conventional ABCD matrix formalism for the calculation of the beam caustic along the liquid. The effect of the liquid, that is, its refractive index, gets more pronounced as the focal length of the lens increases and the pulse length shortens, as shown in Figure 7b. Several authors have notice experimentally the shifted focal plane, giving advice to selffocusing, filamentation, and plasma formation in the liquid.2,24,37 A common effect accompanying the laser irradiation of liquids is the formation of an electron plasma (optical breakdown) if an intensity threshold Ith is exceeded in the liquid. A picture of the plasma formation in liquid is presented in Figure S3 in the Supporting Information. A high portion of the energy will be deposited in the liquid, and because the plasma strongly scatters and absorbs the incoming pulses, the energy reaching the target will be reduced. The induction of plasma formation before the target should be for this reason also avoided if high ablation rates are desired. We have experimentally determined the optical breakdown intensity threshold of water, acetone, and ethanol, as explained in the Experimental Methods Section. For increasing pulse energy, the scattered intensity by laser-induced plumes in water, ethanol, and acetone as a function of input energy is shown in Figure 8. The saturation point of scattered light intensity from the plasma plume induced in the liquid has been used to define the optical breakdown intensity threshold of each liquid. The experimentally obtained optical breakdown intensity thresholds are 222, 94, and 35 1011 W/cm2 for water, ethanol, and acetone, respectively. From now on, using the nominal input energy and beam diameter, the intensity along the beam path can be determined. Applying the ABCD-matrix system to the focused laser beam, with nonlinear-propagation corrections in the case of peak

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Figure 8. Relative intensity scattered from the plasma plume induced by femtosecond laser pulses in water, ethanol, and acetone at increasing laser intensity.

powers exceeding the self-focusing critical power, we can determine the beam diameter along the propagation path in the liquid and compare the laser intensity along the propagation path with the optical breakdown intensity threshold of the liquid. As an example, the intensity distribution along the propagation path of a laser beam undergoing self-focusing, focused outside the liquid with two different focal lengths, is shown in Figure 9. The plasma is induced when the laser intensity overcomes the optical breakdown intensity threshold (I/Ith > 1), represented by black zones that can be seen in the gray scale pattern. The optimal focalization conditions can in this sense be determined a priori, varying dzL until the plasma formation occurs near the target surface. Considering this semiempirical analysis, a methodology can be established to determine the best working conditions (liquid layer over the target, position of the lens) for most efficient ablation in liquid media. For a fixed liquid and focal length, the minimal liquid layer can be calculated by eq 4. Assuming linear propagation of the laser beam, the position of the lens relative to the geometrical focal plane is determined by refraction and calculated with eq 3. High intensity lasers may produce nonlinear propagation, and the caustic of the beam can be determined by the implementation of an extension of the ABCD formalism to the nonlinear propagation.34 With the predicted caustic of the laser beam in the liquid, the intensity along the propagation path can be compared with the threshold intensity of the liquid and avoid the focusing conditions at which plasma might be induced before the target, inhibiting the complete delivery of the pulse energy to the target. The calculated lens position for maximum ablation in water, with dependence on the liquid layer over the target, and in acetone and ethanol is represented in Figure 3b, along with the experimentally obtained lens positions. A good correlation between the predicted values and the results obtained experimentally was found for short focal length lenses; however, the calculations fail to reflect the experimental results for loose focused beams (Figure 3.c). Productive nanoparticle generation is achieved with high power tightly focused beams, and long focal lenses should be avoided because they induce more easily complicated phenomena during PLAL (as obvious from Figure 6). The inaccurate results observed for the 80 and 200 mm focal lengths are probably attributed to the high peak powers used for the experiments (109 W), which are a factor 600 higher than the critical peak power. It has been shown experimentally that peak powers of the order 100Pcr induce collapse of the self-focused beam after a shorter propagation distance (proportional to 1/P) than √ at P < 100Pcr, where the collapse distance is proportional to 1/ P.38 5112



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Figure 9. Caustic (red lines) and intensity distribution (gray scale) of the laser beam inside water for two different focal lengths and focal conditions (h = 10 mm, Ep = 200 μJ).

Note that the particular case in which the target is displaced relative to the liquid surface can be analyzed in an analogous way. The case of ablation in closed chambers where a quartz window is at the entrance plane to the liquid of the laser beam, the evaporative explosion threshold of the liquid, should be substituted by the window damage threshold.

’ CONCLUSIONS Even though sufficient models describing the propagation of pulsed laser beams in condensed media are available, their application to PLAL for nanoparticle generation was lacking. Considering the effect of refraction, vaporization of the liquid, self-focusing, and optical breakdown, the optimal experimental parameters, like required minimal liquid layer, focal length, and focusing conditions for nanoparticle production, were determined a priori. Supported by experimental results, we have shown that time-lasting preliminary experiments to determine the focal position and best parameters for maximal nanoparticle generation during laser ablation in liquids can be avoided using the presented working diagrams. Loosely focused beams, advantageous for nanoparticle fragmentation, present more pronounced nonlinear phenomena, complicating the ablation and reducing the nanoparticle productivity in the case of ultrashort pulses. ’ ASSOCIATED CONTENT

bS

Supporting Information. Mathematical derivation of refraction, fluence on the liquid surface, and nonlinear-transfer matrix formalism and gold concentration in the liquid. This

material is available free of charge via the Internet at http://pubs. acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The German Research Foundation is gratefully acknowledged for financial support within the DFG-Projects SPP-1327 (BA358012-1) and excellence cluster REBIRTH. ’ REFERENCES (1) Patil, P.; Phase, D.; Kulkarni, S.; Ghaisas, S.; Kulkarni, S.; Kanetkar, S.; Ogale, S.; Bhide, V. Phys. Rev. Lett. 1987, 58, 238–241. (2) Daminelli, G.; Kruger, J.; Kautek, W. Thin Solid Films 2004, 467, 334–341. (3) Nichols, W. T.; Sasaki, T.; Koshizaki, N. J. Appl. Phys. 2006, 100, 1149111–1149116. (4) Smejkal, P.; Pfleger, J.; Vlckova, B.; Dammer, O. In COLA’05: 8th International Conference on Laser Ablation; Hess, W., Herman, P., Bauerle, D., Koinuma, H., Eds.; Journal of Physics Conference Series 59; IOP Publishing Ltd.: Bristol, England, 2007, pp 185-188. (5) Barcikowski, S.; Hahn, A.; Kabashin, A. V.; Chichkov, B. N. Appl. Phys. A: Mater. Sci. Process. 2007, 87, 47–55. (6) Sakka, T.; Saito, K.; Ogata, Y. H. J. Appl. Phys. 2005, 97. (7) Oguchi, H.; Sakka, T.; Ogata, Y. H. J. Appl. Phys. 2007, 102. (8) Zheng, Z. Y.; Zhang, J.; Zhang, Y.; Liu, F.; Chen, M.; Lu, X.; Li, Y. T. Appl. Phys. A: Mater. Sci. Process. 2006, 85, 441–443. 5113



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Transfer-Matrix Method for Efficient Ablation by Pulsed Laser Ablation

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