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Using highly coherent radiation at a wavelength of 13.9 nm from a Ag-plasma soft X-ray laser, we constructed a pump-and-probe interferometer based on a double Lloyd's mirror system. The spatial resolutions are evaluated with a test pattern, showing 1.8-μm lateral resolution, and 1-nm depth sensitivity. This instrument enables a single-shot observation of the surface morphology with a 7-ps time-resolution. We succeeded in observing a nanometer scale surface dilation of Pt films at the early stage of the ablation process initiated by a 70 fs near infrared pump pulse.
©2010 Optical Society of America
1. Introduction
The dynamics of photo-induced phenomena, namely laser-induced melting, annealing, ablation [1], and ripple formation [2] on solid surfaces, is the central issue for photon-aided advanced technologies for nanometer-scale fabrication. Photo-induced phase transitions [3], as well as photochemical and biological processes in nanometer space, also have to be clarified from a dynamic point of view. These phenomena often accompany changes in surface morphology proceeding in very short (nano- to femtosecond) time scale, and thus are hard to explore using ordinary experimental techniques. The nonreversible and nonrepetitive nature of these phenomena adds more difficulties to time-resolved observation.
The scanning electron microscope (SEM), scanning tunneling microscope (STM), and atomic force microscope (AFM) are well-established tools for observing surface morphology on nanometer to sub-nanometer scales. However, it is impossible for these techniques to capture time-resolved information, because they rely on scanning of the probe in two-dimensional space. On the other hand, a number of ultrafast experimental techniques have been developed in optical spectroscopy, X-ray diffraction [4,5], and electron diffraction [6], enabling investigations in pico- and femto-second regimes. Most of these methods basically probe the bulk properties and collect little information about surface morphology.
The optical method based on interference phenomena provides information on surface deviation and can be operated in a time-resolved mode when we use pulsed light sources. For example, Temnov et al. [7] constructed a Linnik interference microscope, using mode-locked 100 fs pulses at 400 nm, and realized lateral resolution of a few micrometers and depth resolution of a few nanometers with or without a reference light wave. Surface dilation due to laser-induced melting and expansion of the ablation front after laser irradiation has been observed for GaAs [7].
Since spatial resolution is directly related to the wavelength of the probe light, drastic improvement of resolution is challenged in extreme ultraviolet and soft X-ray regions by utilizing new light sources to investigate the structures of biological cells, magnetic domains, nano-particles/tubes, and fabricated devices. On the other hand, the attenuation length of the electromagnetic wave rapidly increases toward kiloelectronvolt region in many materials. Thus the 100 eV (λ = 12.4 nm) region is optimum for microscopy of solid surfaces.
The highest lateral resolution is pursued utilizing mainly a very stable synchrotron radiation. Resolutions of 15 nm [8] and 12 nm [9] have been realized at 600 eV with Fresnel zone plate optics. Applications in time-resolved measurements have also been reported. A time-resolved observation of the ablation process of a free-standing thin film has been demonstrated by Barty et al. [10] with a free electron laser (FEL). The time evolution of the periodic patterns emerging on the film during evaporation was retrieved from a speckle pattern by numerical processing with a spatial resolution of 50 nm and a time resolution of 10 ps.
The laser-driven plasma soft X-ray laser (SXRL) is an attractive light source for this purpose, because it has outstanding properties such as high monochromaticity, coherence and short duration, which are beneficial for scientific applications. Attempts to improve the phase coherence have been made by Wang et al. [11] with seeding from HHG (high harmonic generation), and by the Japan Atomic Energy Agency (JAEA), which used a double target configuration [12,13]. Utilizing the soft X-ray pulses at a wavelength 40 times shorter than that of visible light and an up-to-date soft X-ray microscope technique, lateral resolution of 10 nm and depth resolution below 30 pm will be achieved. As for the pump-and-probe interferometry in the soft X-ray region, plasma diagnostics through the change in the refractive index with the soft X-ray interferometer has been reported at wavelengths of 46.9 nm [14] and 14.7 nm [15]. Disappearance of interference fringes due to plasma has been demonstrated for silica glass [16]. However, observation of the surface deviation has not been reported, as far as the authors know.
In this paper, we report on the construction of an interferometer that is based on the double Lloyd's mirror system and that can observe 1 nm deviation in a single-shot measurement. The early stage of the ablation process of the Pt film was observed, and a small dilation of the surface just below the ablation threshold was found in the picosecond region.
2. Experimental setup
At JAEA, we used an SXRL based on Ni-like Ag plasma that has extremely high spatial coherence owing to the double target system [13]. The spectral purity is also high (Δλ/λ < 10−4), because it utilizes the atomic energy level as the lasing state. It delivers soft X-ray photons at 89 eV (13.9 nm) with a photon number exceeding 1010 (equivalent to 500 nJ/pulse), which is sufficient to obtain a single-shot interferogram. The system provides 7 ps pulses at a repetition rate of 0.1 Hz [17]. Thus, there is practically no waiting time for single-shot experiments.
Figure 1(a) shows the optics of the pump and probe interferometer constructed in a vacuum space. The coherent 13.9 nm radiation from the plasma is focused 460 mm before the sample by a concave imaging mirror A with a magnification ratio of about unity. The beam is incident on the sample at a grazing angle of 24 degrees. The sample image is then transferred onto an X-ray CCD camera by a second concave imaging mirror B with a magnification factor of 21.3. The principle of interferometry is illustrated in Fig. 1(b). The soft X-ray from the sample is divided into two parts by the double Lloyd's mirror placed between imaging mirror B and the CCD, and is focused on the CCD with a small angle to get the interference fringes. The “source” is the transferred plasma image (50 μm in diameter). The double Lloyd's mirror brings about two virtual “sources” 1 and 2, and the interference fringes appear on the detector plane within the interference area, where the sample (red cones) and reference (blue cones) beams overlap. The fringe spacing X on the CCD camera is expressed as,
where L and δ are defined in Fig. 1(b). λ is the wavelength of soft X-ray, a is the distance between the virtual sources 1, 2 and the double Lloyd's mirror. The shift of the fringe on the CCD, ΔX, is related to the height difference h on the sample surface through,where θ is the grazing angle at the sample [defined in Fig. 1(c)]. As seen from Eq. (2), larger θ gives higher vertical resolution. However, by increasing θ, the reflectance of the sample decreases rapidly. Thus we have chosen θ = 24 degrees in our measurement as a compromise.
Fig. 1 (a) Schematic of the soft X-ray laser (SXRL) interferometer. (b) Principle of interferometry based on the double Lloyd's mirror system. δ is the angle between Lloyd's mirrors 1 and 2. (c) Details of the optical arrangement on the sample. Here, θ is the grazing incidence angle.
The timing between the pumping and the soft X-ray pulses was roughly adjusted by observing the scattered light of the pump pulse and the driving laser pulse from the sample surface by using a PIN photodiode and an oscilloscope within several hundred picoseconds. The timing was further adjusted by observing the same signal with a streak camera. Since the precise adjustment between the soft X-ray and the 800-nm pumping pulse was difficult, we performed a fine adjustment by ablating the sample and observing the burned crater by soft X-ray imaging. To estimate the peak fluence of the pumping pulses, we assumed a Gaussian-like beam with an elliptic spatial profile, and evaluated the long and short axes of the ellipse by using the so-called D2-method [18].
We used 100-nm Pt films evaporated on fused silica substrates as samples. To test the spatial resolution, grooves are fabricated on the Pt film by a focused ion beam (FIB) tool. The broadening of the edge of the grooves is within 500 nm, which is better than the resolution of the soft X-ray measurements. In the retrieval process of the landscape, the high-frequency components were removed from the image of the interferogram by a Fourier low-pass filter and smoothed in the x and y directions with appropriate widths. Then the local phase shifts of the fringes were calculated from the maximum positions of brightness.
3. Results and discussion
The sample (100-nm-thick Pt film plated on a fused silica substrate) is pumped by a 70-fs pulse at a wavelength of 800 nm from a Ti:sapphire laser, which is electronically synchronized with the SXRL by a common master oscillator. The typical pump energy and the excitation density on the sample surface were 130 μJ and 3×1013 W/cm2, respectively.
3.1 Static interferometry with a test pattern
The spatial resolution was tested with the grooves made on the Pt film. Figure 2(a) shows the SEM image of the test pattern. The single-shot interference image is shown in Fig. 2(b), where an upward shift indicates a negative deviation of the surface. At a grazing angle of 24 degrees, a shift of one period corresponds to 17.1 nm. The landscape is retrieved from this image by numerical processing, and is shown in Fig. 2(c). The cross section along the white dotted line measured by AFM [Fig. 2(d)] agrees well with that deduced from the retrieved landscape [Fig. 2(e)]. The vertical resolution is estimated from RMS (root mean square) deviation in the flat area (not shown) of the same sample, and we obtained 0.50-0.81 nm, confirming the resolution better than 1 nm. The lateral resolution is evaluated as 1.8 μm from the edge, indicated by a green arrow. The deviation as small as 6 nm can be detected as a large fringe shift, which is discernible from a single fringe without any signal processing.
Fig. 2 (a) SEM image of the test patterns with a depth of 6 nm and various line widths. Shown are 8- and 6-μm single lines and pairs of 4-, 2-, 1.5-, 1- and 0.5-μm lines from the left. (b) Single-shot interferogram of the test pattern. (c) Retrieved landscape. (d) Cross section of the test pattern along the dotted white line in (a) measured by AFM. (e) Cross section of the retrieved landscape shown in (c) along the dotted white line. The blue arrow on the right side of (b) shows the direction of the incident soft X-ray.
3.2 Ablation dynamics of Pt film
The ablation phenomena are investigated for a 100-nm Pt film on a fused silica plate. For one ablation event, we took three images: before pumping (t < t0), upon pumping (t) with an appropriate time delay and after pumping (t = ∞). Figures 3(a) , 3(b) and 3(c) correspond to this series. At t = t0 + 50 ps [Fig. 3(b)], the fringes are shifted to the right, implying positive deviation of the surface, while at t = ∞ [Fig. 3(c)], they are bent to the left, indicating negative deviation due to a crater formation. Figures 3(e)–3(h) are the images upon pumping at various time delays. Since a fringe shift is not discernible at t = t0 and is clearly observable at t = t0 + 25 ps near the bottom edge of the ablation area, we expect the true time origin is located between these two time points. Hereafter, we tentatively locate the origin at t0, which may involve an uncertainty of less than 25 ps. At 650 ps, the image is the same as that at t = ∞ (not shown), indicating that the transient phenomena are over.
Fig. 3 Interferograms of the Pt films on fused silica plate. (a) before irradiation, (b) at t = t0 + 50 ps, (c) after irradiation. (d) Microscope images (field size 150 μm×150 μm) of the sample surface after ablation corresponding to Figs. (b) and (c). (e)-(h): Time-resolved interferograms. The same image is shown in (b) and (g) for a convenient comparison. The red closed curves represent the ablation areas observed by an optical microscope. Pumping energies are 112.4, 112.8, 130 and 240 μJ for (e), (f), (g) and (h), respectively. The blue arrow shows the direction of the incident soft X-ray (common to all figures).
Since plasma might be ejected from the surface at a high pumping fluence exceeding 1013 W/cm2, we evaluated the time-space behavior of the electron density by using the hydrodynamic code HYADES [19], assuming rectangular pulse with a width of 100-200 fs and power density of 1013 W/cm2 for pumping. According to this calculation, a layer several tens of nanometers from the top starts to expand around 10 ps, and the plasma expands to a height of 60 nm at 40 ps. However, the density is far smaller than the reflection limit of the 13.9 nm light ( = cm−3), and reflectance will be negligible at 24 degrees. Another contribution of the plasma may be the modification of the refractive index, which may distort the wave front of the soft X-ray reflected from the sample. However, the plasma thickness at 50 ps will be less than 100 nm and the phase shift inside the plasma layer will be far smaller than 2π, because the refractive index is estimated to lie between 1.0 and 0.999. Thus the fringes seen in the ablation area are interpreted as a contribution from the reflection of the ablation front, which has a density close to solid Pt.
Figure 4 shows the results of the analysis. Figure 4(a) is the image at t = t0 + 50 ps, while (d) is an average of three shots of soft X-ray after pumping for the crater shown in Fig. 3(c) to obtain a better S/N ratio. To understand the large fringe shifts in the ablation area (red enclosure), we simulate the fringe pattern from the Dektak (a scan probe with a stylus) image obtained after the experiment [Fig. 4(f)], where we can see a crater (dark blue) surrounded by a bank (red to yellow) and a small core circle (light blue ring) near the beam center. As can be seen in Fig. 4(d), the simulated contour lines well reproduce the experimental image, including the curved fringes inside the crater and the steep rightward shift just below the bottom edge of the enclosure. It should be noted that the fringes in the crater have the same color (red or orange) as the flat area far to the right of the enclosure. This means that the phase shift amounts to three periods, which is equivalent to 52 nm. Thus, the retrieved landscape [Fig. 4(e)] is not meaningful inside the enclosure, where the fringes have such discontinuous shifts. However, it is reliable outside the enclosure, where the fringes are continuous. These results show that the surface morphology is correctly reflected in the interference patterns in a single-shot measurement.
Fig. 4 Single-shot interferograms and retrieved landscapes for t = t0 + 50 ps (a, b) and t = ∞ (d, e). The interferogram at t = ∞ is an average of the images taken with three soft X-ray pulses for the same spot after ablation. The red enclosure in 4a, as well as the gray silhouettes in 4b and 4e, show the ablated areas observed by an optical microscope after irradiation. The green curves in 4a are the calculated fringe patterns based on the Gaussian dome (c) for t = t0 + 50 ps. The colored contours in 4d represent the simulated fringes based on the Dektak image (f) for t = ∞. The cross sections along the white dotted lines in (b) and (e) are shown in Fig. 5.
Next we discuss the interference image at t = t0 + 50 ps. The retrieved landscape is shown in Fig. 4(b). The landscape is determined near and outside of the enclosure, while it is hardly retrieved near the center of the pump beam. Then we attempted to simulate the fringe pattern from the assumed shape of the ablation front. Linde et al. [20] reported that the ablation front is a fluidic thin layer and has a density close to the solid, while inside is more dilute (bubble-like structure). A domelike shape was observed at 1.4 ns for Si. Using time-resolved Newton ring measurements, those authors also showed that the behavior is more or less the same for various materials, e.g., Si, Ti, Au and Al [21]. We approximate the dome with a Gaussian function having an elliptic envelope within the surface plane [Fig. 4(c)]. The result (green lines) is in good agreement with the experiment as shown in Fig. 4(a). From the best fitting, the height of the ablation front at t = t0 + 50 ps is estimated to be 35 nm. In Si, the height of the ablation front at 500 ps was 500 nm [20]. Using this value and assuming a constant velocity motion of the ablation front, the height at 50 ps will be 50 nm, which is consistent with our observation. Thus we conclude that the observed dilation corresponds to the very early stage of the formation of a bubble-like structure [7].
The high vertical resolution of our method revealed a small positive deviation of the surface slightly outside the enclosure. The cross sections along the line A-B-C-D in Figs. 4(b) and 4(e) are shown in Fig. 5 for t = t0 + 50 ps (red squares) and t = ∞ (blue squares). At t = t0 + 50 ps, the surface deviation is + 8 nm, which corresponds to 8% expansion of the 100 nm Pt film, on the boundary of the ablation area C and the height reaches 10 nm at D. It is interesting to note that the landscape has no discontinuity on boundary C. At t = ∞, the height further increases to 20 nm between C and D, showing the formation of a ridge structure, which is commonly observed on the boundary of the ablated area in various materials [22]. In contrast, the surface slightly deviates toward the negative direction from B to the point 10 μm before C, the maximum depth being 2.5 nm. It is noteworthy that the starting point B of this dip area coincides with that of the dilated area. We define the area between B and C as the “preablation area” because ablation does not occur, while some trace of structural change remains.
Fig. 5 The cross-sections of the landscapes along the dotted white line connecting A,B, C and D in Figs. 4(b) and 4(e) are shown. The origin of the abscissa is defined at point A. The vertical dotted lines B and C correspond to the boundary of the preablation and ablation areas, respectively.
At t = t0 + 650 ps [Fig. 3(h)] already, this gentle bending of the fringes outside the ablation area, i.e., the dilation of the surface, is not found. Thermal expansion may be one candidate for dilation. However, it will be only 2 nm if we assume that the temperature of the 100 nm Pt layer rises from room temperature to the melting point. Furthermore, the penetration depth of the pumping light is only 10-20 nm, and it takes about 1 ns for the heat to diffuse from the top to the bottom of the 100 nm Pt film. In a time-resolved X-ray diffraction experiment on GaAs, 0.2% elongation of the unit cell in the picosecond region was found and interpreted basically in terms of thermal expansion [23]. This will give only 0.2 nm dilation of the surface for a 100 nm film, even if the thermal expansion coefficient is 50% larger in Pt. Therefore, thermal expansion cannot be the origin.
The volume change from the solid at room temperature to molten Pt is about 8.5% and could explain the 8 nm change in thickness for 100-nm-thick Pt film. For example, 47 nm dilation of the surface in 1 ns due to thermal melting and its recovery due to re-crystallization in 4 ns were found in GaAs [24]. If the melting front propagates into the film at the speed of sound [25], the onset time will be around 100 ps, which may not be contradictory to our observation. Nevertheless, the re-crystallization will take much more time, typically more than nanoseconds, because thermal diffusion into the substrate should remove the latent heat from the film at solidification.
One possible cause of the observed ultrafast dilation is a phenomenon similar to electronic melting. A numerical simulation by Stamphli et al. [26] showed that the lattice constant of Si crystal will increase by 0.1 nm within 100 fs due to weakening of the bonding under high-density optical excitation. Within the ablation area, it has been suggested that two interfaces (ablation front and melting front) are formed in 40 ps [20], and that the interfaces are filled with a fluidic matter. We observed no discontinuity on boundary C (Fig. 5) at t = t0 + 50 ps, suggesting that the phenomenon outside the ablation area is qualitatively the same. Therefore, we can speculate that a structure similar to the “ablation front” is formed in the preablation region (B-C in Fig. 5), too. This could then return to nearly the original position at the speed of sound, if the bonding is not fully destroyed.
In conclusion, we successfully captured 7-ps snapshots of nanometer dilations of a solid surface by using an interferometer combined with a highly coherent high-photon-flux soft X-ray laser. The early stage of the expanding ablation front of the Pt film (around 50 ps) was taken and a small surface dilation was found in the preablation area, where the fluence is slightly below the ablation threshold. This is an important milestone toward time-resolved observation at an atomic layer resolution. Combining this method with the free electron laser, 10-fs snap-shot with monoatomic-layer resolution will become possible.
4. Conclusions
In this paper we have presented a pump-and-probe soft X-ray interferometer for observing surface morphology based on a double Lloyd's mirror system. Lateral resolution of 1.8 μm, depth resolution of 1 nm, and a time resolution of 7 ps have been achieved. We applied this technique to the ablation dynamics of platinum film and found nanometer scale surface dilation inside and outside the ablation area at the early stage of the ablation process for the first time.
Acknowledgments
Development of the SXRL interferometer was supported by a Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (20740326). The authors acknowledge the support of the JAEA X-ray Laser staff.
References and links
1. S. K. Sundaram and E. Mazur, “Inducing and probing non-thermal transitions in semiconductors using femtosecond laser pulses,” Nat. Mater. 1(4), 217–224 (2002). [CrossRef]
2. J. Reif, F. Costache, and M. Bestehorn, in “Recent Advances in Laser Processing of Materials,” (ed. J. Perriere, E. Millon, and E. Fogarassy, Chap 9, pp. 275–290 (Elsevier, Oxford U.K., 2006).
3. K. Nasu, H. Ping, and H. Mizouchi, “Photoinduced structural phase transitions and their dynamics,” J. Phys. Condens. Matter 13(35), 201 (2001). [CrossRef]
4. A. Cavalleri, C. Tóth, C. W. Siders, J. A. Squier, F. Ráksi, P. Forget, and J. C. Kieffer, “Femtosecond Structural Dynamics in VO2 during an Ultrafast Solid-Solid Phase Transition,” Phys. Rev. Lett. 87(23), 237401 (2001). [CrossRef] [PubMed]
5. K. Sokolowski-Tinten, C. Blome, J. Blums, A. Cavalleri, C. Dietrich, A. Tarasevitch, I. Uschmann, E. Förster, M. Kammler, M. Horn-von-Hoegen, and D. von der Linde, “Femtosecond X-ray measurement of coherent lattice vibrations near the Lindemann stability limit,” Nature 422(6929), 287–289 (2003). [CrossRef] [PubMed]
6. P. Baum, D.-S. Yang, and A. H. Zewail, “4D visualization of transitional structures in phase transformations by electron diffraction,” Science 318(5851), 788–792 (2007). [CrossRef] [PubMed]
7. V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, and D. von der Linde, “Femtosecond time-resolved interferometric microscopy,” Appl. Phys., A Mater. Sci. Process. 78(4), 483–489 (2004). [CrossRef]
8. W. Chao, B. D. Harteneck, J. A. Liddle, E. H. Anderson, and D. T. Attwood, “Soft X-ray microscopy at a spatial resolution better than 15 nm,” Nature 435(7046), 1210–1213 (2005). [CrossRef] [PubMed]
9. W. Chao, J. Kim, S. Rekawa, P. Fischer, and E. H. Anderson, “Demonstration of 12 nm resolution Fresnel zone plate lens based soft x-ray microscopy,” Opt. Express 17(20), 17669–17677 (2009). [CrossRef] [PubMed]
10. A. Barty, S. Boutet, M. J. Bogan, S. Hau-Riege, S. Marchesini, K. Sokolowski-Tinten, N. Stojanovic, R. Tobey, H. Ehrke, A. Cavalleri, S. Düsterer, M. Frank, S. Bajt, B. W. Woods, M. M. Seibert, J. Hajdu, R. Treusch, and H. N. Chapman, “Ultrafast single-shot diffraction imaging of nanoscale dynamics,” Nat. Photonics 2(7), 415–419 (2008). [CrossRef]
11. Y. Wang, E. Granados, F. Pedaci, D. Alessi, B. Luther, M. Berrill, and J. J. Rocca, “Phase-coherent, injection-seeded table-top soft-X-ray lasers at 18.9 nm and 13.9 nm,” Nat. Photonics 2(2), 94–98 (2008). [CrossRef]
12. M. Tanaka, M. Nishikino, T. Kawachi, N. Hasegawa, M. Kado, M. Kishimoto, K. Nagashima, and Y. Kato, “X-ray laser beam with diffraction-limited divergence generated with two gain media,” Opt. Lett. 28(18), 1680–1682 (2003). [CrossRef] [PubMed]
13. M. Nishikino, N. Hasegawa, T. Kawachi, H. Yamatani, K. Sukegawa, and K. Nagashima, “Characterization of a high-brilliance soft x-ray laser at 13.9 nm by use of an oscillator-amplifier configuration,” Appl. Opt. 47(8), 1129–1134 (2008). [CrossRef] [PubMed]
14. J. J. Rocca, C. H. Moreno, M. C. Marconi, and K. Kanizay, “Soft-x-ray laser interferometry of a plasma with a tabletop laser and a Lloyd’s mirror,” Opt. Lett. 24(6), 420–422 (1999). [CrossRef]
15. J. Filevich, J. J. Rocca, M. C. Marconi, S. J. Moon, J. Nilsen, J. H. Scofield, J. Dunn, R. F. Smith, R. Keenan, J. R. Hunter, and V. N. Shlyaptsev, “Observation of a multiply ionized plasma with index of refraction greater than one,” Phys. Rev. Lett. 94(3), 035005 (2005). [CrossRef] [PubMed]
16. G. Jamelot, D. Ros, B. Rus, M. Kozlova, K. Cassou, S. Kazamias, A. Klisnick, T. Mocek, P. Homer, J. Polan, and M. Stupka, “X-ray laser interference microscopy for advanced studies of laser-induced damages,” Proc. X-ray Lasers 2006 (ed. Nickles, P. V., and Janulewicz, K. A.), 571–576 (Springer, Netherlands, 2007).
17. Y. Ochi, T. Kawachi, N. Hasegawa, M. Nishikino, T. Ohba, M. Tanaka, M. Kishimoto, T. Kaihori, K. Nagashima, and A. Sugiyama, “Demonstration of submicro Joule, spatially coherent soft-X-ray laser pumped by 0.1 Hertz, 10 Joule, picosecond laser,” Jpn. J. Appl. Phys. 48(12), 120212 (2009). [CrossRef]
18. J. M. Liu, “Simple technique for measurements of pulsed Gaussian-beam spot sizes,” Opt. Lett. 7(5), 196–198 (1982). [CrossRef] [PubMed]
19. J. T. Larsen and S. M. Lane, “HYADES - A plasma hydrodynamic code for dense plasma studies,” J. Quant. Spectrosc. Radiat. Transf. 51(1-2), 179–186 (1994). [CrossRef]
20. D. von der Linde and K. Sokolowski-Tinten, “The physical mechanisms of short-pulse laser ablation,” Appl. Surf. Sci. 154–155(1-4), 1–10 (2000). [CrossRef]
21. K. Sokolowski-Tinten, J. Bialkowski, A. Cavalleri, D. von der Linde, A. Oparin, J. Meyer-ter-Vehn, and S. I. Anisimov, “Transient states of matter during short pulse laser ablation,” Phys. Rev. Lett. 81(1), 224–227 (1998). [CrossRef]
22. Y. Izawa, Y. Setuhara, M. Hashida, M. Fujita, and Y. Izawa, “Ablation and amorphization of crystalline Si by femtosecond and picosecond laser irradiation,” Jpn. J. Appl. Phys. 45(7), 5791–5794 (2006). [CrossRef]
23. C. Rose-Petruck, R. Jimenez, T. Guo, A. Cavalleri, C. W. Siders, F. Rksi, J. A. Squier, B. C. Walker, K. R. Wilson, and C. P. J. Barty, “Picosecond-milliangstrom lattice dynamics measured by ultrafast X-ray diffraction,” Nature 398(6725), 310–312 (1999). [CrossRef]
24. V. V. Temnov, K. Sokolowski-Tinten, P. Zhou, and D. von der Linde, “Ultrafast imaging interferometry at femtosecond laser-excited surfaces,” J. Opt. Soc. Am. B 23(9), 1954–1964 (2006). [CrossRef]
25. B. Rethfeld and K. Sokolowski-Tinten, “von D. der Linde, and S. I. Anisimov, “Timescales in the response of materials to femtosecond laser excitation,” Appl. Phys., A Mater. Sci. Process. 79, 767–769 (2004).
26. P. Stampfli and K. Bennemann, “Time dependence of the laser-induced femtosecond lattice instability of Si and GaAs: Role of longitudinal optical distortions,” Phys. Rev. B 49(11), 7299–7305 (1994). [CrossRef]
