- Email: [email protected]
Ablation threshold dependence on pulse duration for copper
Applied Surface Science 197±198 (2002) 862±867
Ablation threshold dependence on pulse duration for copper M. Hashidaa,d,*, A.F. Semeroka, O. Gobertb, G. Petitec, Y. Izawad, J.F-. Wagnera a
CEA Saclay, DPC/SCPA/LALES, 91191 Gif sur, Yvette Cedex, France CEA Saclay, DSM/DRECAM/SPAM, 91191 Gif sur, Yvette Cedex, France c Ecole Polytechnique, DSM/DRECAM/LSI, 91128 Gif sur, Yvette Cedex, France d Institute of Laser Engineering, Osaka University, 2-6 Yamadaoka, Suita, Osaka 565-0871, Japan b
Abstract Laser ablation of Cu by short pulse laser (800 nm wavelength, 70 fs pulse duration, 0.01±28 J/cm2 ¯uence range) in air was studied. Three different ablation thresholds were distinguished in all metals. The ablation thresholds for Cu were found to be 0.018, 0.18, and 0.25 J/cm2. The lowest ablation threshold was of one order of magnitude lower than the one observed previously. In the ¯uence range of 0.018±0.18 J/cm2 the ablation rate was 0.01 nm per pulse. A dependence of the threshold on the pulse duration was demonstrated in the range of 70 fs±5 ps. As the laser pulse duration increased, the ablation threshold had the tendency to be higher. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Femtosecond ablation; Ablation threshold; Metal
1. Introduction Laser ablation is categorized by two different regimes which are distinguished by the comparison of the laser pulse duration with the characteristic time of electron±phonon interaction in metal. When the laser pulse duration is shorter than this characteristic time (te p several picosecond) [1±3], the ablation threshold is smaller than that of longer pulses and the ablation rate is increased. A large amount of both experimental and theoretical works on laser ablation with ultra short laser pulses has been done until recently [4±9]. However, the process of controlled ablation of matter has not been clearly understood and needs further investigation. Additionally, laser ablation has been used for various kinds of applications, for example, diagnosis of the
target composition, removal of small space debris and radioactive surface, and material processing for microstructure. To establish these application more accurately, a detailed knowledge of the mechanism of laser ablation is important. Laser ablation occurs when the laser ¯uence exceeds a certain threshold typical of a given condensed matter, which also depends on the laser parameters, such as the pulse duration. Thus the ablation threshold is seen as an important parameter for understanding the physical mechanism underlying laser ablation. The purpose of our study was to investigate the ablation threshold of a metal sample with sub-ps laser pulses. In this paper, the ablation thresholds, ablation rates and crater shapes for copper with short laser pulse are reported. 2. Experimental
*
Corresponding author. Tel.: 81-6-6879-8736; fax: 81-6-6878-1568. E-mail address: [email protected] (M. Hashida).
The ablation experiments were carried out with Ti± Al2O3 laser emitting at a 800 nm wavelength. The
0169-4332/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 ( 0 2 ) 0 0 4 6 3 - 4
M. Hashida et al. / Applied Surface Science 197±198 (2002) 862±867
minimum pulse duration was of 70 fs, and could be adjusted in 70 fs±5 ps ranges by an appropriate choice of the distance between the pulse compressor gratings. The pulse duration was de®ned with the second-order autocorrelator. The contrast of the pulse was measured with a high dynamic cross-correlator. The energy contrast ratio of pre-pulse to main-pulse was estimated to be less than 10%. Cu sample with well-known physical parameters was chosen to study the laser ablation threshold. In the experiment, the laser beam was focused onto the metal target surface with a quartz lens (f 10 cm) in normal incidence. The beam pro®le was veri®ed to be nearly Gaussian by measuring the laser spatial distribution at the surface target position with a SPIRICON beam analyzer. On the target surface, the Gaussian laser beam took the shape of an ellipse with horizontal and vertical width of 41.5 and 65.7 mm, respectively, at 1/e in intensity. The laser energy was varied from 0.21 to 600 mJ (0.01±28 J/ cm2) by a half-wave plate with polarizer. At maximum ¯uence, nonlinear laser beam/air interaction was not observed. The energy stability was kept 5% during our experiments. The laser repetition rate was of 20 Hz. An electromechanical shutter was used to choose the desired number of laser shots for crater production. In the experiment, the target could be easily placed in a desired laser beam diameter spot within 5% precision. The craters obtained were measured with an optical microscope pro®lometer (MicroXamPhase Shift Technology) with lateral resolution of 1 mm and depth resolution of 0.01 mm.
863
laser beam, the ablation threshold is expressed by [11] as: ( ) G 2 (2) Fth Fexp a where G is the crater diameter, a the laser beam diameter. The ablation threshold could be roughly estimated by the laser ¯uence resulting in the minimal crater diameter. Fig. 1 shows typical crater pro®les for Cu sample at different laser ¯uence. The horizontal central section of the crater pro®les was always used to determine the ablation threshold because the horizontal pro®le of the laser beam was in a fairly good agreement with the Gaussian shape. At each ¯uences, the crater pro®le was very reproducible. In the ¯uence range of 0.2±0.6 J/ cm2, the pro®les of the craters were quite different from the laser beam pro®le and demonstrated a sharp peak in the center of the crater.
3. Experimental results The ablation threshold was determined by two different methods. The ®rst one was to study the ablation rate dependence on the laser ¯uence. The ablation rate L have been well expressed by [8,10] as: 1 F L ln (1) a Fth where a-optical absorption or heat penetration coef®cient, F-laser ¯uence. The ablation threshold (Fth) was determined by the laser ¯uence where the ablation rate was suffering rapid changes. The second method was applied to study the crater surface diameter dependence on the laser ¯uence. With the Gaussian
Fig. 1. Typical Cu crater pro®les at different laser ¯uence with 70 fs.
864
M. Hashida et al. / Applied Surface Science 197±198 (2002) 862±867
Fig. 2. Ablation depth obtained with Cu by multi laser shots for 70 fs laser pulse.
The experiment was performed with a different number of laser shots. Fig. 2a and b show the increase of the crater depth for Cu sample. The ablation rate was de®ned as the crater depth per laser shot. In this experiment, the ablation rates were 0.33 mm per pulse and 0.0093 nm per pulse for laser ¯uences 13.4 and 0.073 J/cm2, respectively. The inaccuracy of measurements was due to the crater structure with small spikes. Fig. 3 shows the ablation rate dependence on the laser ¯uence. Each ablation rate was obtained by the crater depth dependence on the number of laser shots. The number of laser shots, that could result in the ablation depth detectable with a microscope pro®l-
ometer, was in the range 1±128 shots for F > 4 J/cm2 and >128 shots for F < 4 J/cm2. In the laser ¯uence range of 0.018±0.2 J/cm2, the crater depth per pulse was so low that it was necessary to use 144 000 laser shots to determine the ablation rate. For the low ¯uence range, the ablation threshold was found to be 0.018 J/cm2. The ablation rates were 0.01 nm per pulse in the ¯uence range of 0.018±0.2 J/cm2. The ablation rate was suffering rapid changes at the ¯uence of 0.18 J/cm2. Thus this ¯uence value was second ablation threshold. Fig. 4 illustrates the dependence of the surface crater diameter on the incident laser ¯uence. Each
Fig. 3. Dependence of the Cu ablation rate on incident laser ¯uence with 70 fs pulse. The dotted and dashed-dotted curves are the calculated ablation rates based on a thermal model (logarithmic dependence). The solid curve is the calculated ablation rate obtained with the assumption of a 3-photon absorption.
M. Hashida et al. / Applied Surface Science 197±198 (2002) 862±867
Fig. 4. Dependence of the Cu crater diameter on incident laser ¯uence with 70 fs. The curves are the calculated to be ®tted well with experimental data.
crater diameter was con®rmed by the crater diameter dependence on the number of laser shots. As increasing the number of laser shots, the crater diameter remained constant while crater depth lineally increased. Near the ¯uence of 0.25 J/cm2, the interesting feature of the crater structure was the appearance of a bigger and shallower concentric hole in the case of more than 10 000 laser shots. The onset of this phenomenon is clearly visible in the diameter measurements. The curves ®tting the diameter as a function of laser ¯uence are simply obtained from Eq. (2) and expressed as G afln F=Fth g0:5 . Crater diameter values demonstrate two different dependencies with minimum diameters of 14 and 24 mm for the laser ¯uence of 0.02 and 0.25 J/cm2, respectively. From the extrapolation of these two dependencies to G 0, the ablation thresholds were estimated as Fth 0:018 and 0.18 J/cm2, respectively. The obtained ablation threshold values were equal to the thresholds obtained by the ablation rate dependence on laser ¯uence. The diameter of the sharp peak in the center of the crater (0.2± 0.6 J/cm2) is assumed to be produced by the contribution of ablation with another threshold. The diameter of such sharp peaks gives the threshold ¯uence Fth 0:250 J/cm2. Fig. 5 gives the pulse duration dependencies of the three obtained ablation thresholds. The ablation thresholds F2,th and F3,th were determined by two different methods mentioned above and were found to be of the same value. The lines were determined by
865
Fig. 5. Dependence of the ablation threshold on incident laser pulse duration.
the method of the least square ®tting applied to the results obtained for each threshold. The ®tting 1=4 lines show that the dependencies are F1;th b1 tp , 1=2 2=3 F2;th b2 tp , and F3;th b3 tp , respectively. 4. Discussion and conclusion The dependence of the ablation rate for Cu has been measured and could be expressed by two differd ent logarithmic functions [9]: L d ln F=Fth and 2 l d l L l ln F=Fth , where Fth 0:14 J/cm and Fth 2 0:46 J/cm . They were characterized by the optical penetration depth (d 10 nm) and the electronic thermal conduction (l 80 nm), respectively. This treatment of the ablation rate was used to analyze our experimental results. Fig. 3 presents the best ®tting of the calculated dependencies of the ablation rate with the experimental results obtained with d 7 nm d and Fth 0:22 J/cm2 for medium ¯uence regime, l l 80 nm and Fth 1:0 J/cm2 for high ¯uence regime, respectively. The calculation was done by d l adjusting d, Fth , l, and Fth . The experimental results and the calculated values of ablation thresholds were d found to be different as 1.2 for F2,th and Fth and 4 l for F1,th and Fth , respectively. Besides, with the ablation thresholds experimentally observed, the calculated dependencies of the ablation rate were not found to be in agreement with the experimental results in a wide range of laser ¯uences.
866
M. Hashida et al. / Applied Surface Science 197±198 (2002) 862±867
The lowest ablation threshold F3;th 0:018 J/cm2 (Fig. 3) in our experiments was of one order of d magnitude lower than Fth . The obtained ablation rates near F3,th could not be explained by the logarithmic dependency based on the thermal diffusion model as the ablation rate was less than one atomic layer in our experiments. It was also reported in [9] that for pulses longer than 1 ps, the absence of the ®rst logarithmic regime d L d ln F=Fth results from the electronic heat diffusion during the laser pulse. However, the analytical relationship between the ablation threshold and the pulse duration was not presented. The results of our work might suggest that the pulse duration dependence of the ablation thresholds could be explained by the process of m-photon absorption [12]. For m-photon absorption and incident laser pulse I(0, t) of a rectangular shape, the ablation rate Lm can be analytically solved and expressed as: ( 1 m ) 1 Eth 1 m=m F Lm ; m 1xm tp t p xm m2
(3)
where xm is the m-photon absorption coef®cient, Eth the ablation threshold energy per unit volume, F the incident laser ¯uence, and tp is the incident laser pulse duration. The threshold ¯uence dependence on laser pulse duration can be obtained from Eq. (3) at the condition of Lm 0 as: 1=m Eth Fth t m p xm
1=m
bm t m p
1=m
(4)
The ablation threshold values obtained experimentally (Fig. 5) were in good agreement with the function of 1=4 1=2 2=3 b1tp for F1,th, b2tp for F2,th, b3tp for F3,th. Thus, the ablation thresholds of F3,th and F2,th may be resulting from 3-photon and 2-photon absorption process, respectively. To explain the observed ablation rate dependence with the ablation threshold of F3,th, the ablation rate L was calculated with the assumption that the ablation is resulting from 3-photon absorption process. The absorption coef®cients of m-photon absorption (xm) for Cu are not known. The x3 was determined by the parameter b3, obtained by the best ®tting with experimental data, and Eth 1840 J/cm3 for Cu at room temperature [13]. The calculated
ablation rate with x3 1:0 10 18 cm3/W2 is shown as a solid curve in Fig. 3. It agrees within a factor of two with experimental results. The ablation rate of F2,th was calculated analogously. However, the calculated ablation rates are of two orders of magnitude lower than the experimental ones. We found that the ablation rate dependence on the laser ¯uence can be well enough approximated by superposition of three different curves for all metals under study in our experiments: 1. L3 k3 1 ln F=F3;th in low ¯uence regime; 2. L2 k2 1 ln F=F2;th 2 in medium ¯uence regime; 3. L1 k1 1 ln F=F1;th 3 in high ¯uence regime. A reasonable explanation of the fact that the curves are in a fairly good agreement with the experimental results has not been found yet. In conclusion, three ablation thresholds were determined in the experiments with 70 fs laser pulses. The pulse duration dependencies of the ablation thresholds were obtained for Cu sample. They were found to be in good agreement with the functions of 1=4 1=2 2=3 b1tp for F1,th, b2tp for F2,th, b3tp for F3,th. Experimental results were analyzed within the framework of thermal laser ablation model that could not explain suf®ciently well the obtained results. The ablation model with multi-photon absorption was applied to explain some particular features of ablation rate with low energy pulses. Acknowledgements The authors would like to acknowledge the technical assistance of SPAM and LSLA laboratories, CEA Saclay, France. References [1] S.D. Bronson, A. Kazeroonian, J.S. Moodera, D.W. Face, T.K. Cheng, Phys. Rev. Lett. 64 (1990) 2172. [2] G.L. Eesley, Phys. Rev. B 33 (1986) 2144. [3] M.I. Kaganov, I.M. Lifshitz, L.V. Tanatarov, Sov. Phys. JETP 4 (1957) 173. [4] H. Strehlow, Appl. Phys. A 65 (1977) 355. [5] P.P. Pronko, S.K. Dutta, D. Du, R.K. Singh, J. Appl. Phys. 78 (1995) 6233. [6] B.C. Stuart, M.D. Feit, S. Herman, A.M. Rubenchik, B.W. Shore, M.D. Perry, J. Opt. Soc. Am. B 13 (1996) 459.
M. Hashida et al. / Applied Surface Science 197±198 (2002) 862±867 [7] S.I. Anisimov, N.A. Inogamov, A.M. Opartin, B. Rethfeld, T. Yabe, M. Ogawa, V.E. Fortov, Appl. Phys. A 69 (1999) 617. [8] B.N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, A. Tunnermann, Appl. Phys. A 63 (1996) 109. [9] S. Nolte, C. Momma, H. Jacobs, A. Tunnermann, B.N. Chichkov, B. Wellegehausen, H. Welling, J. Opt. Soc. Am. B 14 (1997) 2716.
867
[10] S. Preuss, M. Demchuk, M. Stuk, Appl. Phys. A 61 (1995) 33. [11] J. Jamdeleit, G. Urbasch, H.D. Hoffmann, H.-G. Treush, E.W. Kreutz, Appl. Phys. A 63 (1996) 117. [12] S. Preuss, M. Spath, Y. Zhang, M. Stuke, Appl. Phys. Lett. 62 (1993) 3049. [13] R.C. Weast (Ed.), CRC Handbook of Chemistry and Physics, 68th Edition, CRC press, Boca Raton, 1987±1988, p. E-379.
Ablation threshold dependence on pulse duration for copper M. Hashidaa,d,*, A.F. Semeroka, O. Gobertb, G. Petitec, Y. Izawad, J.F-. Wagnera a
CEA Saclay, DPC/SCPA/LALES, 91191 Gif sur, Yvette Cedex, France CEA Saclay, DSM/DRECAM/SPAM, 91191 Gif sur, Yvette Cedex, France c Ecole Polytechnique, DSM/DRECAM/LSI, 91128 Gif sur, Yvette Cedex, France d Institute of Laser Engineering, Osaka University, 2-6 Yamadaoka, Suita, Osaka 565-0871, Japan b
Abstract Laser ablation of Cu by short pulse laser (800 nm wavelength, 70 fs pulse duration, 0.01±28 J/cm2 ¯uence range) in air was studied. Three different ablation thresholds were distinguished in all metals. The ablation thresholds for Cu were found to be 0.018, 0.18, and 0.25 J/cm2. The lowest ablation threshold was of one order of magnitude lower than the one observed previously. In the ¯uence range of 0.018±0.18 J/cm2 the ablation rate was 0.01 nm per pulse. A dependence of the threshold on the pulse duration was demonstrated in the range of 70 fs±5 ps. As the laser pulse duration increased, the ablation threshold had the tendency to be higher. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Femtosecond ablation; Ablation threshold; Metal
1. Introduction Laser ablation is categorized by two different regimes which are distinguished by the comparison of the laser pulse duration with the characteristic time of electron±phonon interaction in metal. When the laser pulse duration is shorter than this characteristic time (te p several picosecond) [1±3], the ablation threshold is smaller than that of longer pulses and the ablation rate is increased. A large amount of both experimental and theoretical works on laser ablation with ultra short laser pulses has been done until recently [4±9]. However, the process of controlled ablation of matter has not been clearly understood and needs further investigation. Additionally, laser ablation has been used for various kinds of applications, for example, diagnosis of the
target composition, removal of small space debris and radioactive surface, and material processing for microstructure. To establish these application more accurately, a detailed knowledge of the mechanism of laser ablation is important. Laser ablation occurs when the laser ¯uence exceeds a certain threshold typical of a given condensed matter, which also depends on the laser parameters, such as the pulse duration. Thus the ablation threshold is seen as an important parameter for understanding the physical mechanism underlying laser ablation. The purpose of our study was to investigate the ablation threshold of a metal sample with sub-ps laser pulses. In this paper, the ablation thresholds, ablation rates and crater shapes for copper with short laser pulse are reported. 2. Experimental
*
Corresponding author. Tel.: 81-6-6879-8736; fax: 81-6-6878-1568. E-mail address: [email protected] (M. Hashida).
The ablation experiments were carried out with Ti± Al2O3 laser emitting at a 800 nm wavelength. The
0169-4332/02/$ ± see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 9 - 4 3 3 2 ( 0 2 ) 0 0 4 6 3 - 4
M. Hashida et al. / Applied Surface Science 197±198 (2002) 862±867
minimum pulse duration was of 70 fs, and could be adjusted in 70 fs±5 ps ranges by an appropriate choice of the distance between the pulse compressor gratings. The pulse duration was de®ned with the second-order autocorrelator. The contrast of the pulse was measured with a high dynamic cross-correlator. The energy contrast ratio of pre-pulse to main-pulse was estimated to be less than 10%. Cu sample with well-known physical parameters was chosen to study the laser ablation threshold. In the experiment, the laser beam was focused onto the metal target surface with a quartz lens (f 10 cm) in normal incidence. The beam pro®le was veri®ed to be nearly Gaussian by measuring the laser spatial distribution at the surface target position with a SPIRICON beam analyzer. On the target surface, the Gaussian laser beam took the shape of an ellipse with horizontal and vertical width of 41.5 and 65.7 mm, respectively, at 1/e in intensity. The laser energy was varied from 0.21 to 600 mJ (0.01±28 J/ cm2) by a half-wave plate with polarizer. At maximum ¯uence, nonlinear laser beam/air interaction was not observed. The energy stability was kept 5% during our experiments. The laser repetition rate was of 20 Hz. An electromechanical shutter was used to choose the desired number of laser shots for crater production. In the experiment, the target could be easily placed in a desired laser beam diameter spot within 5% precision. The craters obtained were measured with an optical microscope pro®lometer (MicroXamPhase Shift Technology) with lateral resolution of 1 mm and depth resolution of 0.01 mm.
863
laser beam, the ablation threshold is expressed by [11] as: ( ) G 2 (2) Fth Fexp a where G is the crater diameter, a the laser beam diameter. The ablation threshold could be roughly estimated by the laser ¯uence resulting in the minimal crater diameter. Fig. 1 shows typical crater pro®les for Cu sample at different laser ¯uence. The horizontal central section of the crater pro®les was always used to determine the ablation threshold because the horizontal pro®le of the laser beam was in a fairly good agreement with the Gaussian shape. At each ¯uences, the crater pro®le was very reproducible. In the ¯uence range of 0.2±0.6 J/ cm2, the pro®les of the craters were quite different from the laser beam pro®le and demonstrated a sharp peak in the center of the crater.
3. Experimental results The ablation threshold was determined by two different methods. The ®rst one was to study the ablation rate dependence on the laser ¯uence. The ablation rate L have been well expressed by [8,10] as: 1 F L ln (1) a Fth where a-optical absorption or heat penetration coef®cient, F-laser ¯uence. The ablation threshold (Fth) was determined by the laser ¯uence where the ablation rate was suffering rapid changes. The second method was applied to study the crater surface diameter dependence on the laser ¯uence. With the Gaussian
Fig. 1. Typical Cu crater pro®les at different laser ¯uence with 70 fs.
864
M. Hashida et al. / Applied Surface Science 197±198 (2002) 862±867
Fig. 2. Ablation depth obtained with Cu by multi laser shots for 70 fs laser pulse.
The experiment was performed with a different number of laser shots. Fig. 2a and b show the increase of the crater depth for Cu sample. The ablation rate was de®ned as the crater depth per laser shot. In this experiment, the ablation rates were 0.33 mm per pulse and 0.0093 nm per pulse for laser ¯uences 13.4 and 0.073 J/cm2, respectively. The inaccuracy of measurements was due to the crater structure with small spikes. Fig. 3 shows the ablation rate dependence on the laser ¯uence. Each ablation rate was obtained by the crater depth dependence on the number of laser shots. The number of laser shots, that could result in the ablation depth detectable with a microscope pro®l-
ometer, was in the range 1±128 shots for F > 4 J/cm2 and >128 shots for F < 4 J/cm2. In the laser ¯uence range of 0.018±0.2 J/cm2, the crater depth per pulse was so low that it was necessary to use 144 000 laser shots to determine the ablation rate. For the low ¯uence range, the ablation threshold was found to be 0.018 J/cm2. The ablation rates were 0.01 nm per pulse in the ¯uence range of 0.018±0.2 J/cm2. The ablation rate was suffering rapid changes at the ¯uence of 0.18 J/cm2. Thus this ¯uence value was second ablation threshold. Fig. 4 illustrates the dependence of the surface crater diameter on the incident laser ¯uence. Each
Fig. 3. Dependence of the Cu ablation rate on incident laser ¯uence with 70 fs pulse. The dotted and dashed-dotted curves are the calculated ablation rates based on a thermal model (logarithmic dependence). The solid curve is the calculated ablation rate obtained with the assumption of a 3-photon absorption.
M. Hashida et al. / Applied Surface Science 197±198 (2002) 862±867
Fig. 4. Dependence of the Cu crater diameter on incident laser ¯uence with 70 fs. The curves are the calculated to be ®tted well with experimental data.
crater diameter was con®rmed by the crater diameter dependence on the number of laser shots. As increasing the number of laser shots, the crater diameter remained constant while crater depth lineally increased. Near the ¯uence of 0.25 J/cm2, the interesting feature of the crater structure was the appearance of a bigger and shallower concentric hole in the case of more than 10 000 laser shots. The onset of this phenomenon is clearly visible in the diameter measurements. The curves ®tting the diameter as a function of laser ¯uence are simply obtained from Eq. (2) and expressed as G afln F=Fth g0:5 . Crater diameter values demonstrate two different dependencies with minimum diameters of 14 and 24 mm for the laser ¯uence of 0.02 and 0.25 J/cm2, respectively. From the extrapolation of these two dependencies to G 0, the ablation thresholds were estimated as Fth 0:018 and 0.18 J/cm2, respectively. The obtained ablation threshold values were equal to the thresholds obtained by the ablation rate dependence on laser ¯uence. The diameter of the sharp peak in the center of the crater (0.2± 0.6 J/cm2) is assumed to be produced by the contribution of ablation with another threshold. The diameter of such sharp peaks gives the threshold ¯uence Fth 0:250 J/cm2. Fig. 5 gives the pulse duration dependencies of the three obtained ablation thresholds. The ablation thresholds F2,th and F3,th were determined by two different methods mentioned above and were found to be of the same value. The lines were determined by
865
Fig. 5. Dependence of the ablation threshold on incident laser pulse duration.
the method of the least square ®tting applied to the results obtained for each threshold. The ®tting 1=4 lines show that the dependencies are F1;th b1 tp , 1=2 2=3 F2;th b2 tp , and F3;th b3 tp , respectively. 4. Discussion and conclusion The dependence of the ablation rate for Cu has been measured and could be expressed by two differd ent logarithmic functions [9]: L d ln F=Fth and 2 l d l L l ln F=Fth , where Fth 0:14 J/cm and Fth 2 0:46 J/cm . They were characterized by the optical penetration depth (d 10 nm) and the electronic thermal conduction (l 80 nm), respectively. This treatment of the ablation rate was used to analyze our experimental results. Fig. 3 presents the best ®tting of the calculated dependencies of the ablation rate with the experimental results obtained with d 7 nm d and Fth 0:22 J/cm2 for medium ¯uence regime, l l 80 nm and Fth 1:0 J/cm2 for high ¯uence regime, respectively. The calculation was done by d l adjusting d, Fth , l, and Fth . The experimental results and the calculated values of ablation thresholds were d found to be different as 1.2 for F2,th and Fth and 4 l for F1,th and Fth , respectively. Besides, with the ablation thresholds experimentally observed, the calculated dependencies of the ablation rate were not found to be in agreement with the experimental results in a wide range of laser ¯uences.
866
M. Hashida et al. / Applied Surface Science 197±198 (2002) 862±867
The lowest ablation threshold F3;th 0:018 J/cm2 (Fig. 3) in our experiments was of one order of d magnitude lower than Fth . The obtained ablation rates near F3,th could not be explained by the logarithmic dependency based on the thermal diffusion model as the ablation rate was less than one atomic layer in our experiments. It was also reported in [9] that for pulses longer than 1 ps, the absence of the ®rst logarithmic regime d L d ln F=Fth results from the electronic heat diffusion during the laser pulse. However, the analytical relationship between the ablation threshold and the pulse duration was not presented. The results of our work might suggest that the pulse duration dependence of the ablation thresholds could be explained by the process of m-photon absorption [12]. For m-photon absorption and incident laser pulse I(0, t) of a rectangular shape, the ablation rate Lm can be analytically solved and expressed as: ( 1 m ) 1 Eth 1 m=m F Lm ; m 1xm tp t p xm m2
(3)
where xm is the m-photon absorption coef®cient, Eth the ablation threshold energy per unit volume, F the incident laser ¯uence, and tp is the incident laser pulse duration. The threshold ¯uence dependence on laser pulse duration can be obtained from Eq. (3) at the condition of Lm 0 as: 1=m Eth Fth t m p xm
1=m
bm t m p
1=m
(4)
The ablation threshold values obtained experimentally (Fig. 5) were in good agreement with the function of 1=4 1=2 2=3 b1tp for F1,th, b2tp for F2,th, b3tp for F3,th. Thus, the ablation thresholds of F3,th and F2,th may be resulting from 3-photon and 2-photon absorption process, respectively. To explain the observed ablation rate dependence with the ablation threshold of F3,th, the ablation rate L was calculated with the assumption that the ablation is resulting from 3-photon absorption process. The absorption coef®cients of m-photon absorption (xm) for Cu are not known. The x3 was determined by the parameter b3, obtained by the best ®tting with experimental data, and Eth 1840 J/cm3 for Cu at room temperature [13]. The calculated
ablation rate with x3 1:0 10 18 cm3/W2 is shown as a solid curve in Fig. 3. It agrees within a factor of two with experimental results. The ablation rate of F2,th was calculated analogously. However, the calculated ablation rates are of two orders of magnitude lower than the experimental ones. We found that the ablation rate dependence on the laser ¯uence can be well enough approximated by superposition of three different curves for all metals under study in our experiments: 1. L3 k3 1 ln F=F3;th in low ¯uence regime; 2. L2 k2 1 ln F=F2;th 2 in medium ¯uence regime; 3. L1 k1 1 ln F=F1;th 3 in high ¯uence regime. A reasonable explanation of the fact that the curves are in a fairly good agreement with the experimental results has not been found yet. In conclusion, three ablation thresholds were determined in the experiments with 70 fs laser pulses. The pulse duration dependencies of the ablation thresholds were obtained for Cu sample. They were found to be in good agreement with the functions of 1=4 1=2 2=3 b1tp for F1,th, b2tp for F2,th, b3tp for F3,th. Experimental results were analyzed within the framework of thermal laser ablation model that could not explain suf®ciently well the obtained results. The ablation model with multi-photon absorption was applied to explain some particular features of ablation rate with low energy pulses. Acknowledgements The authors would like to acknowledge the technical assistance of SPAM and LSLA laboratories, CEA Saclay, France. References [1] S.D. Bronson, A. Kazeroonian, J.S. Moodera, D.W. Face, T.K. Cheng, Phys. Rev. Lett. 64 (1990) 2172. [2] G.L. Eesley, Phys. Rev. B 33 (1986) 2144. [3] M.I. Kaganov, I.M. Lifshitz, L.V. Tanatarov, Sov. Phys. JETP 4 (1957) 173. [4] H. Strehlow, Appl. Phys. A 65 (1977) 355. [5] P.P. Pronko, S.K. Dutta, D. Du, R.K. Singh, J. Appl. Phys. 78 (1995) 6233. [6] B.C. Stuart, M.D. Feit, S. Herman, A.M. Rubenchik, B.W. Shore, M.D. Perry, J. Opt. Soc. Am. B 13 (1996) 459.
M. Hashida et al. / Applied Surface Science 197±198 (2002) 862±867 [7] S.I. Anisimov, N.A. Inogamov, A.M. Opartin, B. Rethfeld, T. Yabe, M. Ogawa, V.E. Fortov, Appl. Phys. A 69 (1999) 617. [8] B.N. Chichkov, C. Momma, S. Nolte, F. von Alvensleben, A. Tunnermann, Appl. Phys. A 63 (1996) 109. [9] S. Nolte, C. Momma, H. Jacobs, A. Tunnermann, B.N. Chichkov, B. Wellegehausen, H. Welling, J. Opt. Soc. Am. B 14 (1997) 2716.
867
[10] S. Preuss, M. Demchuk, M. Stuk, Appl. Phys. A 61 (1995) 33. [11] J. Jamdeleit, G. Urbasch, H.D. Hoffmann, H.-G. Treush, E.W. Kreutz, Appl. Phys. A 63 (1996) 117. [12] S. Preuss, M. Spath, Y. Zhang, M. Stuke, Appl. Phys. Lett. 62 (1993) 3049. [13] R.C. Weast (Ed.), CRC Handbook of Chemistry and Physics, 68th Edition, CRC press, Boca Raton, 1987±1988, p. E-379.