Two-dimensional laser-induced periodic surface structures formed on crystalline silicon by GHz burst mode femtosecond laser pulses

Femtosecond laser pulses with GHz burst mode that consist of a series of trains of ultrashort laser pulses with a pulse interval of several hundred picoseconds offer distinct features in material processing that cannot be obtained by the conventional irradiation scheme of femtosecond laser pulses (single-pulse mode). However, most studies using the GHz burst mode femtosecond laser pulses focus on ablation of materials to achieve high-efficiency and high-quality material removal. In this study, we explore the ability of the GHz burst mode femtosecond laser processing to form laser-induced periodic surface structures (LIPSS) on silicon. It is well known that the direction of LIPSS formed by the single-pulse mode with linearly polarized laser pulses is typically perpendicular to the laser polarization direction. In contrast, we find that the GHz burst mode femtosecond laser (wavelength: 1030 nm, intra-pulse duration: 220 fs, intra-pulse interval time (intra-pulse repetition rate): 205 ps (4.88 GHz), burst pulse repetition rate: 200 kHz) creates unique two-dimensional (2D) LIPSS. We regard the formation mechanism of 2D LIPSS as the synergetic contribution of the electromagnetic mechanism and the hydrodynamic mechanism. Specifically, generation of hot spots with highly enhanced electric fields by the localized surface plasmon resonance of subsequent pulses in the bursts within the nanogrooves of one-dimensional LIPSS formed by the preceding pulses creates 2D LIPSS. Additionally, hydrodynamic instability including convection flow determines the final structure of 2D LIPSS.

In the meantime, Kerse et al recently demonstrated that femtosecond laser pulses with GHz burst mode, which deliver trains of femtosecond laser pulse (intra-pulse) with a pulse interval of several hundred ps, can achieve high-efficiency and high-quality ablation of materials [35]. They said that GHz burst mode can ablate the material before the heat generated by preceding pulses diffuse away from the processed area, which improves ablation efficiency by an order of magnitude. They further stated that the thermal energy contained in the ablated mass can be carried away due to the physical removal of ablated materials, which is called ablation cooling for high-quality ablation with minimized thermal effects. This result has a significant impact on the community of laser materials processing to push researchers to follow the experiments using GHz burst mode [36]. Some groups showed that GHz burst mode femtosecond laser is a promising tool for higher efficiency ablation than the conventional irradiation scheme of ultrashort laser pulses (single-pulse mode) [37][38][39][40][41] and high-quality material processing with minimal thermal damage [41][42][43].
Thus, GHz burst mode femtosecond laser pulses offer distinct features in materials processing due to more controlled energy deposition as compared with the single-pulse mode. However, the most of experiments on the GHz burst mode processing reported so far are focused on ablation, while few works have been investigated on other types of materials processing. Giannuzzi et al demonstrated LIPSS formation on stainless steel by the GHz burst mode, which showed formation of similar LIPSS to the single-pulse mode [44]. In this paper, we apply GHz burst mode femtosecond laser pulses to the formation of LIPSS on silicon to show the ability of GHz burst for formation of unique nanostructures in comparison with the single-pulse mode and discuss the possible formation mechanism. Figure 1 shows a schematic illustration of the experimental setup for LIPSS formation by using GHz burst mode femtosecond laser pulses. Experiments were carried out on a polished p-doped crystalline silicon wafer (100) with 625 µm thickness and resistivity of 3.11-3.41 Ω cm using linearly polarized femtosecond laser pulses. The laser system, based on Yb: KGW (Light conversion Ltd, Pharos), emitted laser pulses with a pulse duration of 220 fs at a central wavelength of 1030 nm. This system could also be operated with GHz burst mode that contained a series of pulse trains (burst pulses) composed of multiple intra-pulses with the same pulse duration of 220 fs, wavelength of 1030 nm and polarization direction. The number of intra-pulses P in each burst pulse used in this experiment varied from 1 (single-pulse mode) to 10. The time interval between each intra-pulse in the burst was constant at 205 ps corresponding to a repetition rate of 4.88 GHz. The envelope of burst, in other words, the distribution of intra-pulse fluence, was adjustable. LIPSS were formed at number of burst pulses N = 50 and 200 with a 200 kHz repetition rate, for which the p-polarized laser beam reflected by a polarizing beam splitter (PBS) was focused on silicon substrates placed on an XYZ stage with a PC control by using an achromatic lens with a focal length of 50 mm. A part of the laser beam transmitted through PBS was directed to an ultrafast photodiode to monitor the shape of the burst pulses on an oscilloscope. The burst pulse energy (laser power) was controlled by polarizing optics elements consisting of a half-wave plate and PBS.

Formation of LIPSS
To calculate the laser fluence, the focused spot radius ω 0 at the position where the intensity decreases to 1/e was estimated from the equation for the laser beam possessing using Gaussian spatial distribution with experimental data of single-pulse mode (supplementary figure S1) [45]: Here, r, E, and E th are the radius of the modified area, the irradiated pulse energy, and the threshold of the modification, respectively. Then, the focused spot size and the melting threshold fluence were estimated to be 12.5 µm in diameter and 113 mJ cm −2 , respectively. We have further confirmed that the numerical aperture of lens (0.05) and M 2 ∼ 1.2 of the laser used in this study theoretically give almost the same diameter. Meanwhile, in another experiment, the ablation threshold was evaluated to be 190 mJ cm −2 . For LIPSS formation, ablation threshold fluences were first determined for each condition, different N and P by directly observing the ablation spots formed on silicon using a CMOS camera. Then, the burst pulse fluence was increased by 20 mJ cm −2 from the threshold to form the LIPSS almost on the entire focused spots.

Characterization
The surface morphologies of the LIPSS formed on silicon substrates were observed using a scanning electron microscope (SEM). In addition, we analyzed the cross-section of the formed one-dimensional (1D) LIPSS with a scanning transmission electron microscope (STEM) to determine its dimensions for simulation of the electric field enhancements.

Simulation of electric field enhancements on 1D LIPSS
The simulation of electric field enhancement was carried out with a commercial software using limitary element analysis (COMSOL, Multiphysics). The electric field enhancement was simulated on a 1D LIPSS irradiated by a 1030 nm fs laser whose polarization direction was perpendicular to the 1D LIPSS (supplementary figure S3) The dimensions of the 1D LIPSS were set at a period of 760 nm and a nanogroove width and depth of 250 nm and 700 nm, respectively, according to the observation using SEM and STEM, as shown in supplementary figure S4. The permittivity of silicon used for the simulation was calculated based on the estimation of carrier density generated by femtosecond laser pulse (details of calculation are shown in supporting information). Other parameters used for the simulation were referred from [41,[46][47][48][49][50][51]. The details of simulation are shown in supplementary data. . For this experiment, the ablation threshold fluences for each condition were first determined experimentally. LIPSS were then produced at the burst pulse fluences increased by 20 mJ cm −2 from each threshold. The threshold intra-pulse fluence for the formation of LIPSS by the burst was significantly lower than the singlepulse mode and decreased as P increased, which is consistent with the work on silicon ablation [41]. In this experiment, the intensity of the intra-pulses in the burst was adjusted to be almost same, as shown in figure 3(a) and supplementary figure S2.

Results and discussion
The single-pulse mode creates 1D LIPSS whose direction was perpendicular to the laser polarization direction (figures 1(a) and (f)) as already observed in the previous studies [4,5,13,16]. The periods of LIPSS at N = 50 and 200 were measured to be approximately 870 nm and 830 nm, respectively. The GHz burst mode also created 1D LIPPS when P = 2 (figures 1(b) and (g)). However, the periods of LIPSS formed at N = 50 and 200 decreased to 740 nm and 690 nm, respectively. The lower pulse intensity in the burst might reduce the periods. For the GHz burst mode, the total number of pulses introduced for LIPSS formation can be considered as the product of P and N. Therefore, the total number  of pulses for the GHz burst with N = 2 is double that of the single-pulse mode. Some studies have reported that the period of LIPSS created by the single-pulse mode decreases as the pulse number increases [2,11,14,16]. It has been explained that increasing pulse number changes the surface properties, such as permittivity and topography, due to amorphization and modification, which induce higher interactions with the incident laser to efficiently excite SPP, decreasing the period of LIPSS [11,14,16]. Additionally, other studies have theoretically or experimentally demonstrated that the lower intensity creates the smaller period [2,6,7]. Consequently, the period of LIPSS by GHz burst becomes shorter than that of the singlepulse mode due to a larger number of total pulses and lower fluence of intra-pulses.
More interestingly, GHz burst mode with P larger than three fabricated two-dimensional (2D) LIPSS (figures 2(c)-(d), (h)-(j)) with another periodic surface structure parallel to the laser polarization direction in addition to the regular LIPSS. The period of LIPSS was larger when parallel to the laser polarization direction than when perpendicular. For example, the periods perpendicular and parallel to the laser polarization direction of 2D LIPSS formed with N = 50 and P = 5 (figure 1(j)) were measured to be approximately 770 nm and 1790 nm, respectively. 2D LIPSS shows melting and resolidification, particularly at the center of processed regions, and the resolidification is more pronounced as P increases. This may be attributed to heat accumulation by GHz burst mode since ablation in LIPSS formation is restrictive, which reduces the ablation cooling effect. Specifically, ablation only takes place at the grooves of LIPSS while the other parts (ridges) remain unablated to accumulate the thermal energy. However, we considered that hot spots with a highly enhanced electric field generated in the nanogrooves should be more responsible for the melting and resolidification as discussed later. Thus, we have shown that GHz burst-mode femtosecond laser pulses can form unique 2D LIPSS. We speculate that the 2D LIPSS formation is attributed to the 'hot spots' generated in the nanogrooves of 1D LIPSS by localized surface plasmon resonance (LSPR). Specifically, 1D LIPSS was first fabricated on the silicon surface by the first two intra-pulses in the burst because the intra-pulse fluence is smaller than the threshold of single-pulse mode for LIPSS formation as shown in figure 3(a). The collaborative contribution of first two intrapulses enables 1D LIPSS formation even at the intra-pulse fluence smaller than the threshold similarly to the case of ablation [41]. At the same time, these two intra-pulses generate a high density of free electrons in the formed 1D LIPSS to make the surface metallic-like. Since the lifetime of free electrons in silicon is longer than several tens of nanoseconds [52], the generated free electrons are still in the conduction band when the latter part of the intra-pulses in the burst is introduced. When the light beam is incident on 1D LIPSS of some kinds of metals such as gold and silver, hot spots with highly enhanced electric fields are generated in the nanogrooves of 1D LIPSS due to LSPR [24]. The enhancement is greatest when the light with a polarization perpendicular to the direction of 1D LIPSS is incident. Consequently, when the third and subsequent intra-pulses in the burst, whose polarization directions were perpendicular to that of LIPSS, are irradiated onto the metal-like silicon surface of 1D LIPSS formed by the first two intra-pulses, hot spots were generated, as shown in figure 4(b). The hot spots were generated periodically at the sidewalls of nanogrooves in the 1D LIPSS, which ablate the sidewalls periodically to create 2D LIPSS as shown in figure 4(c). To discuss the validity of our speculation, we first estimated the free electron density generated when a single pulse femtosecond laser with the intensity same as the intra-pulse fluence used in this experiment (N = 50, P = 5), which was approximately 1.94 × 10 22 electrons cm −3 (the details of calculations are shown in supplementary information). The estimated electron density is comparable to that in metals. This result implies that the first two intra-pulses in GHz burst can create a metal-like surface in the formed 1D LIPSS. Based on the above estimation, we examined the possibility of generating hot spots in the 1D LIPSS by third and subsequent intra-pulses in GHz bursts. To this end, we simulated the electric field enhanced in the nanogrooves of silicon with the free electron density calculated above. The dimensions of nanogrooves used for this simulation, such as the period and groove width and depth, were determined as averages from the observed 1D LIPSS (shown in supplementary information, figure S4(a), N = 50, P = 2) using SEM and a scanning transmission electron microscope (STEM) (supplementary figures S4(b) and (c)). The conditions of the irradiated laser beam for the simulation were same as the fabrication conditions in figure 1(b). The simulation was carried out based on some [41,[46][47][48][49][50][51] and its details are shown in supporting information. Figure 5 shows the simulated results of the electric field enhancements in the nanogroove in 1D LIPSS. It is obvious that give the enhancement was not constant along the nanogroove ( figure 5(a)). The highest electric field was periodically obtained to generate the hot spots where the electric field was enhanced by a factor of more than 5. The period was estimated to be approximately 1300 nm by measuring the distance between the points of the highest electric field in the figure. Although silicon is a nonmetal material, the simulated result shows that hot spots can be generated when high density of free electrons is excited. As described above, the period parallel to the polarization direction in 2D LIPSS formed with N = 50 and P = 5 was 1790 nm, which is larger than the simulated period of hot spots. The difference may originate from the dimensions of 1D LIPSS, such as the width, depth, and period of the nanogrooves used in the simulation, which influence the period. In fact, the dimensions of the 1D LIPSS obtained by the experiment had more complex shapes than what was used in the simulation. Meanwhile, from the simulation, the electron density in silicon did not affect the period as much, but it did affect the enhancement of electric field. From figure 5(b), the highest electric field was obtained at the top of sidewalls of nanogroove, and the electric field at the bottom is also highly enhanced. Therefore, it is considered that ablation takes place at the top and the bottom of nanogrooves, resulting in creation of 2D LIPSS.
The similar mechanism was proposed for formation of 1D and 2D nanohole arrays on silicon by single-pulse mode at a relatively low repetition rate of 1 kHz [53]. In this case, the depth of grooves of LIPSS first formed was shallower than 200 nm, so that the electric enhancement at the hot spots (<0.5) was much smaller than >5 simulated in our study. Additionally, the hot spots were generated at the center of grooves along the width direction. As a result, the authors considered that ablation at the hot spots created 1D and 2D nanohole arrays.
In the above discussion, we assumed the solid-state. However, SEM observation indicated melting during LIPSS formation. Therefore, silicon surface could be melted by the first two intra-pulses in the burst, and the subsequent intra-pulses could interact with molten silicon. Even if it is the case, molten silicon is metal-like and plasmonically active, enabling generation of hot spots.
Another possible mechanism of 2D LIPSS formation is hydrodynamic instability such as convection flow due to surface temperature instability and lattice temperature modulation on the surface [25][26][27]. Irradiation of femtosecond laser double pulses of orthogonal linearly polarized beams or counter-rotating circularly polarized beams enabled creation of controlled 2D nanostructures on stainless steel, whose mechanism was regarded as nonlinear convection flow [27]. However, the geometric patterns and their periods on silicon were much different from 2D LIPSS formed on stainless steel. More importantly, 2D structures were not formed on stainless steel when the parallel linearly polarized double pulses were irradiated. Additionally, GHz burst mode irradiation on stainless steel created 1D LIPSS similar to the case of singlepulse mode [44]. The difference between silicon and stainless steel may be due to little hot spot generation in stainless steel. Meanwhile, since 2D LIPSS formed in our study showed melting and resolidification, the hydrodynamic mechanism could be involved in the formation mechanism. In fact, the created 2D structure is different from that expected from the electromagnetic mechanism based on hot spot generation as discussed later (also see figure 4). Therefore, the synergetic contribution of the electromagnetic mechanism and the hydrodynamic mechanism is likely for 2D LIPSS formation on silicon.
S. Höhm et al have demonstrated irradiation of doublepulses with the same polarization direction for LIPSS formation on silicon at delay times from several hundred femtoseconds to picoseconds [54]. A careful look at the structure created (for example, figure 4 in [54]) exhibits 2D-like LIPSS, although the authors have not mentioned this fact in their literature. The creation of such structures may rely on the same mechanism we proposed. Meanwhile, the double-pulse irradiation of femtosecond laser beams with orthogonal polarization directions was demonstrated, in which transient changes on surface conditions after femtosecond laser irradiation due to laser-induced electrons in the conduction band was discussed and different types of 2D LIPSS was formed on silicon [55]. LIPSS formation using the double-pulses was also demonstrated for some other materials. For example, two-color (400 and 800 nm) double pulse irradiation with parallel polarization on fused silica was demonstrated, which showed that the first pulse exciting electrons into the conduction band in a spatially modulated pattern (low spatial frequency LIPSS), while the second pulse would give further energy to these pre-excited carriers [56]. As already described above, the double pulse irradiation with different conditions (polarization, interpulse delay) enabled controlling 2D nanostructuring [27]. Figure 5(a) further shows that the electric field is enhanced by approximately two times even at the center between the hot spots, which may not be high enough to induce ablation but be able to melt the side walls. This might cause melting and resolidification at the centers of the 2D LIPSS observed in figures 2(c)-(e) and (h)-(j). To suppress the melting and thereby create more defined 2D LIPSS, we performed the experiment using the GHz burst in which the intensities of the intra-pulses were gradually decreased, as shown in figure 3(b). The reduced intensities of the latter intra-pulses could reduce the electric field at the sidewalls between the hot spots to the intensity low enough to avoid melting, while generating the hot spots with the intensity high enough to induce ablation. Figures 6(a) and (b) show the SEM images of silicon processed by GHz burst pulses at P = 3 and N = 50 with flat and negatively sloped distribution of intra-pulse intensity (shown in figure 3), respectively. For the negatively sloped distribution, the intensities of second and third intra-pulses were adjusted to be approximately 73% and 50% of the first intrapulse, respectively. Obviously, the negatively sloped distribution can suppress the melting to create much better defined 2D LIPSS as compared with the flat distribution. This result supports the proposed mechanism based on the hot spots for 2D LIPSS formation. However, the morphology of the fabricated 2D LIPSS differs from the illustration shown in figure 3(c), which is expected by the hot spot mechanism. Specifically, figure 3(c) exhibits an array of square dot structures of ridges, while the created structure has rather a lattice structure as illustrated in figure 3(d). Additionally, the width of the ridges perpendicular to the laser polarization direction is much narrower than the 1D LIPSS. These results suggest that the hot spots cannot ablate the entire width of ridges in 1D LIPSS, but narrow them. Meanwhile, the other parts of the sidewalls melted together, resulting in the formation of the lattice structure. A more tailored envelope of the GHz burst will further improve the quality of 2D LIPSS.

Conclusion
We applied GHz burst mode femtosecond laser processing to formation of LIPSS to examine its ability of creating unique micro and nanostructures. Then, we revealed that the GHz burst mode can fabricate a unique 2D LIPSS. The fabricated 2D LIPSS was composed of both periodic surface structures parallel and perpendicular to the laser polarization direction. We speculate the formation mechanism of 2D LIPSS as the synergetic contribution of the electromagnetic mechanism and the hydrodynamic mechanism. Specifically, regular 1D LIPSS were formed on silicon by first and second intra-pulses in the GHz burst. Then, the periodic hot spots with a highly enhanced electric field were generated in the nanogrooves of 1D LIPSS due to LSPR by third and following intra-pulses to create 2D LIPSS. Simulation of the enhancement of electric fields on 1D LIPSS supported validity of the proposed mechanism. Additionally, the electric field enhancement induced surface melting which determined the final structure of 2D LIPSS due to the hydrodynamic effects such as convection flow. Nevertheless, further investigation is necessary to explore the exact mechanism. Based on this hypothesis, we successfully created more defined 2D LIPSS by tailoring the envelope of GHz burst, in which the intensity of three intra-pulses was gradually reduced. Further optimization of the envelopes will create much more defined 2D LIPSS with designed periods. Such 2D structures would provide better surface properties than regular 1D structures [24]. Our results show that GHz burst-mode femtosecond laser pulses offer unique characteristics for not only ablation but also other types of processing, such as LIPSS formation to open a new avenue for micro and nanofabrication.