1. Introduction

Direct femtosecond (fs) laser surface nano- and micro-structuring is a versatile method to tailor material surface morphologies, which enhance diverse interesting physical properties. These include the ability to permanently modify the surface absorption spectrum or change appearing colors of metals and semiconductors without any addition of pigments, the possibility to fabricate super-hydrophobic and self-cleaning surfaces, etc [1–7]. In this context, the formation of laser-induced periodic surface structures in the form of sub-wavelength ripples is extensively studied [1,8]. Instead, detailed investigations of the other supervening quasi-periodic surface structure named as grooves [9], which usually forms at higher fluence and larger number of incident laser pulses than ripples, are still rather scarce. Contrary to the ripples orientation that is perpendicular to laser polarization, the grooves show a characteristic alignment parallel to the laser polarization and, hence, orthogonal to ripples [9–11]. Several mechanisms are proposed to rationalize ripples formation, e.g. excitation of surface plasmon polaritons (SPPs) or self-organization of surface instabilities, and no general consensus has been reached yet (see e.g. Refs. 1 and 8, and references therein quoted), meanwhile grooves generation mechanisms are still overlooked.

Here we investigate micron spaced grooves formation on crystalline silicon irradiated with fs laser pulses, in air. Silicon is selected because it is a case study for surface structures formation and the most relevant semiconductor material. Moreover, its physical properties are well-known and available for modeling of the laser-target interaction process. In particular, we single out the dependence of the threshold fluence for grooves formation on the number of pulses N, while taking the typical ripples simultaneously produced in the irradiated area as reference. We find that the grooves formation threshold fluence variation with N follows a dependence similar to that previously reported by Bonse et al. for the laser induced modification threshold of silicon, and ascribed to incubation effects [9]. Moreover, we evidence a simple way to associate the surface structures generated in multiple-pulse experiments with the predictions of surface-scattered wave theory [12,13], that allows modeling irradiation of a rough sample surface with a single pulse, thus interpreting the observed structural modification of the silicon surface texture. This, in turn, allows proposing a physical mechanism for grooves formation addressing the coexistence and relative prominence of grooves and ripples in the irradiated area.

2. Experimental methods

We use linearly polarized laser pulses of ≈35 fs with a Gaussian beam spatial profile provided by a Ti:Sapphire fs laser source, at 100 Hz repetition rate. The target is a single-crystalline Si (100) plate (dielectric constant ε_Si = 13.64 + 0.048i at 800 nm). The laser beam is focused by a lens onto the Si target sample mounted on a computer-controlled XY-translation stage at normal incidence. An electromechanical shutter controls the number of laser pulses, N, irradiated on the target surface. The morphological modifications of the irradiated surface are studied by using a field emission scanning electron microscope.

Anticipating our experimental findings, Fig. 1 reports a section of the SEM micrograph of the Si surface after irradiation with N = 100 laser pulses at an energy E₀≈14 µJ, and the Gaussian spatial profile of the fluence, Φ(r). At this number of pulses, one can easily recognize the diverse surface textures developed in the ablated crater. In particular, one can identify sub-wavelength ripples and micro-grooves covering the external and central part of the crater, respectively. These two regions are separated by a very thin annulus where ripples and rudiments of grooves coexist. For easiness of identification, in Fig. 1(a) the outer edges of the rippled and grooved areas are marked by two double-circles. These correspond to the wider and narrower circles that can be drawn to surround the corresponding region, and takes into account uncertainty due to both a slightly elliptical beam spatial profile and a variability of circle recognition obtained in repeated measurements by different individuals in our team. From each double-circles one obtains the mean outer radius of the rippled (r_R) and grooved (r_G) regions and the corresponding uncertainty is used as error bar.

 

Fig. 1 (a) Portion of a SEM micrograph of the Si target surface after N = 100, for E₀≈14 µJ (Φ_p≈0.8 J/cm²); (b) corresponding Gaussian spatial profile of the laser beam. The double-headed arrow indicates the incident laser pulse polarization.

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3. Results and discussion

Considering the Gaussian spatial beam profile with a 1/e²-beam waist w₀, the peak fluence is Φ_p = (2E₀)/(π$w_0^2$) and the squared outer radius r_k of the two patterned regions (k = R and G for ripples and grooves, respectively) is related to the corresponding energy threshold E_th,k by:

 

Fig. 2 (a) Variation of r_R and r_G with pulse energy E₀. (b) Threshold fluence variation with the number of pulses N in the form NΦ_th,k(N) vs N (k = R for ripples and k = G and grooves). The lines in (a) and (b) are fits according to Eqs. (1) and (2), respectively.

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From SEM micrographs of the Si target irradiated with different number of pulses N, the radii r_R and r_G are estimated, and the corresponding fluence is determined from the spatial fluence profile of the laser beam. These values of the fluence at the margin of the rippled and grooved regions correspond to the threshold fluences Φ_th,R and Φ_th,G for ripples and grooves formation, respectively, as illustrated in Fig. 1(a). It should be noted that we considered only well-developed grooves for measuring r_G and not grooves rudiments. Figure 2(b) reports the variation of the threshold fluences with N in the form NΦ_th,k(N) vs N, for Φ_p = 1.5 J/cm², where k is equal to R and G for ripples and grooves, respectively. A similar behavior is also observed for Φ_p = 0.5 J/cm². The experimental data are well described by a linear dependence on a semi-logarithmic plot, supporting a power law dependence of the threshold fluence typical of an incubation behavior [9]:

Considering first ripples, fit to experimental data gives Φ_th,R(1) = (0.20 ± 0.04) J/cm² and ξ_R = (0.76 ± 0.04) (see Fig. 2(b), square symbols). As for the grooves, we notice that for N lower than ≈50 only isolated groove rudiments are observed at Φ_p = 1.5 J/cm². Moreover, the value of the number of pulses at which well-developed grooves starts appearing varies with laser pulse peak fluence indicating that a minimum pulse number is needed for grooves formation, in agreement with earlier reports [9,16]. Therefore, in Fig. 2(b) the values of Φ_th,G starts at N = 50. Interestingly, when a groove pattern starts forming Φ_th,G(N) also follows Eq. (2), with Φ_th,G(1) = (0.54 ± 0.08) J/cm² and ξ_G = (0.84 ± 0.03).

In previous studies, the incubation behavior has been applied to rationalize the variation of the threshold fluence needed to induce modification or ablation of the target surface [9,16–18]. We have extended it to describe the dependence of the grooves formation threshold on N. Our experimental findings strikingly indicate that it also describes rather well the dependence on N of the threshold fluence for the formation of both ripples and grooves. Moreover, the estimates of the incubation coefficient are consistent with the value ξ≈0.84 reported by Bonse et al. for the modification threshold of silicon [9], slight differences being expected to depend on specific experimental conditions, e.g. wavelength and duration of laser pulses, and repetition rate.

We turn now to the dependence of the grooves features on fluence. Figures 3(a) and 3(b) report SEM micrographs of the Si target surface for N = 100 at Φ_p = 0.8 J/cm² and Φ_p = 2.3 J/cm², respectively, with the corresponding spatial profile of the laser pulse fluence. In each figure, the upper panels display zoomed views of specific areas. We associate the selected laser peak fluencies Φ_p = 0.8 J/cm² and Φ_p = 2.3 J/cm² to low and high excitation levels, respectively. In both cases, the rippled area is located in an outer annular region. Besides the rippled area, in Fig. 3(a) we identify the two other regions A_L and B_L. A_L presents groove rudiments in form of isolated islands, constituting a transitional region between ripples and grooves, and corresponds to local values of the fluence Φ in the range 0.14–0.26 J/cm². Instead, B_L is a central region with well-developed grooves where Φ is larger than Φ_th,G(N = 100)≈0.26 J/cm². In Fig. 3(b) we recognize that grooves similar to those of the region B_L only appears in an annular area B_H corresponding to 0.26 J/cm² < Φ < 0.71 J/cm², while larger groove stripes occupy the central region C_H (Φ > 0.71 J/cm²). In particular, the average width of the grooves increases from ≈2 µm to ≈4 µm by passing from B_H to C_H, suggesting a broadening of their period with the fluence. Moreover, the larger peak fluence of Fig. 3(b) also results in a dramatic decrease of the width of the transitional annulus and the region corresponding to A_L shrinks to a very sharp boundary between rippled and grooved areas.

 

Fig. 3 SEM micrographs of the Si target surface at N = 100 for (a) Φ_p = 0.8 J/cm² and Φ_p = 2.3 J/cm². Below each image the corresponding spatial profile of the laser pulse fluence is shown. The squares mark regions characterized by different surface structures at low (A_L and B_L) and high (B_H and C_H) excitation levels. Top panels show zoomed images of the part evidence by the square with the same color in the corresponding SEM image. The double-headed arrows indicate the laser polarization.

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In an attempt to theoretically interpret the morphological evolution of the surface with the fluence and rationalize the role of the pulse number we exploit the Sipe-Drude model [19,20]. The Sipe approach [12,13] interprets the generation of periodic surface structures in terms of a spatially-modulated pattern of energy deposition on a rough target surface. This is expressed by means of an “efficacy factor” η(κ) that is function of the characteristic wave-vector κ of the induced periodic structure in the Fourier spatial frequency domain (i.e. κ = 2π/Λ, Λ being the spatial period of the surface structure in the real space). For linearly-polarized laser pulses at normal incidence the main features of η(κ) are rather independent of the specific parameters used to describe the surface roughness, i.e. the shape factor s and the filling factor f [19]. Hence, the standard values of the Sipe theory for the shape (s = 0.4) and filling (f = 0.1) factors are generally exploited, which depict the surface roughness as spherical shaped islands [12,13,16,19]. η(κ) is represented in the form of a two-dimensional (2D) map describing the modulation of laser energy distribution in the κ-space (see e.g. Fig. 4(c)), with wave vectors components κ_x and κ_y parallel and orthogonal to the laser polarization, respectively. The map of η(κ) is symmetric with respect to κ_x = 0 and κ_y = 0. More recently, this theory has been extended to take into account the variation of the dielectric permittivity ε of the silicon target surface induced by the laser pulse irradiation [19,20], and is generally refereed as Sipe-Drude model. The variation of ε is obtained by exploiting two-temperature model and free-carrier number density equations [21–23], and the results show that ε plays the most important role in determining the features of the efficacy factor η(κ). In particular, during irradiation with a fixed pulse fluence Φ, the temporal variation of the free-carrier number density reaches a maximum value at a certain time t*. In other words, t* represents the particular time that the free-carrier number density need to increase to the maximum value. The overall scale of t* is ≈50 fs after the peak of the incident pulse, and the value of t* will differ for each fluence. Consequently, at t* the real part of the dielectric permittivity reaches its minimum value. The value of the dielectric permittivity ε* at time t* is used in our simulations to calculate the efficacy factor distribution η(κ) according to Sipe theory. It is worth mentioning that the surface modification mechanism was also interpreted by a hydrodynamics-based theory, which also explained the narrowing effect of the ripples period with laser pulse energy increasing [22]. However, also in such an approach the spatial modulation of the absorbed energy was taken into account as a key factor for the surface structures formation.

 

Fig. 4 (a) Spatial profile of the laser pulse fluence Φ(r) for Φ_p = 0.8 J/cm²; the right vertical axis shows the corresponding value of Φ_eff. (b) 2D-IFT maps (lower panels) and corresponding SEM images (upper panels) for conditions I, II, III. The 2D-IFT maps are normalized to the corresponding maximum intensity according to the scale shown on the right. The double-headed arrows show the laser polarization. (c) 2D map of η(κ) corresponding to condition Φ_eff,I. The wave vectors κ_x and κ_y are in units of 2π/λ, where λ is the laser wavelength. (d) 2D-IFT map in condition III: the regions with a value of the intensity ranging from 2/3 to 1 (corresponding to the maximum intensity value) are colored in red, while the regions with lower intensity are shown in green. (d) Sketch of ripples and grooves formation: the upper panel shows a SEM image of the transitional region from ripples to grooves registered at an acquisition angle of 20° while the lower panel is a schematic diagram showing the alternating structure of ripples and grooves.

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Sipe-Drude model cannot directly simulate multi-pulse irradiation conditions typically used in experiments. Here, we discuss a simple, empirical way to introduce in this approach the possible effects related to the progressive reduction with N of the laser threshold fluence for the formation of the grooves discussed above (see e.g. Fig. 2(b)). In particular, we suggest to take into account the diverse excitation level associated to N-pulse irradiation at fluence Φ by considering in the model an effective single-shot fluence Φ_eff that scales with the experimental single-shot threshold fluence, Φ_th,G(1), in the same proportion as the corresponding fluencies Φ and Φ_th,G(N) for N pulse, respectively. This reads Φ_eff/Φ_th,G(1) = Φ/Φ_th,G(N), and consequently ${\Phi }_{eff}=N^{1-{\xi }_G}\times \Phi$.

Hereafter, we compare the variation of the surface textures associated to the experimental transition from ripples to grooves with model predictions. Figure 4(a) reports the fluence spatial profile Φ(r) corresponding to a peak fluence Φ_p = 0.8 J/cm². The right axis shows the corresponding values of Φ_eff for N = 100. Φ_eff,I≈Φ_th,G(1) = 0.54 J/cm² corresponds to the transitional fluence from ripples to grooves. The free-carrier number density calculated at Φ_eff,I = 0.54 J/cm² and t* is 4.82 × 10²² cm^–3, corresponding to ε* = –95.7 + 6.5i. The corresponding map of η(κ) is shown in Fig. 4(c). One can observe the appearance of very sharp intensity peaks distributed over a sickle-shaped feature. It can be recognized the presence of two sharp peaks in the Fourier spatial frequency domain whose wave vectors are located at angles of 5.5° and 26.5°, respectively, measured with respect to the laser polarization direction that is parallel to the κ_x axis. These angles account for the bending and bifurcation phenomena of ripples, as discussed earlier in a previous report [23]. For an easier visualization of the corresponding energy modulation and a more direct comparison with experimental observations, a mapping of η(κ) distribution into the real space is obtained by discrete 2D inverse Fourier transformation (2D-IFT). The 2D-IFT map corresponding to Fig. 4(c) (i.e. Φ_eff,I = 0.54 J/cm²) is reported in the lower-left panel of Fig. 4(b); the normalized intensity scale is shown on the right of the figure. The corresponding experimental fluence is Φ_I≈0.26 J/cm² which corresponds to a radial position in the irradiated spot r_I≈26 µm, in the transitional region from ripples to grooves. A corresponding SEM image is reported in the upper-left panel of Fig. 4(b), and shows subwavelength ripples decorated with grooves rudiments. The 2D-IFT main feature is a pattern of relatively linear, quasi-periodic stripes perpendicular to the laser polarization corresponding to the ripples. In fact, region of higher intensity (in black) corresponds to locations where a more effective ablation creates deeper rifts, while material remaining on their sides gives rise to ripples. Moreover, the 2D-IFT also presents a secondary, quasi-periodic pattern parallel to laser polarization and with larger period that tend to blur the underlying ripples. We associate this secondary pattern to the region where grooves rudiments start forming. To better illustrate the transition from ripples to grooves, we consider two other fluences within ± 10% of Φ_eff,I, namely Φ_eff,II = 0.5 J/cm² and Φ_eff,III = 0.6 J/cm². In the conditions of Φ_eff,II = 0.5 J/cm² and Φ_eff,III = 0.6 J/cm², the free-carrier number densities at t* are 3.19 × 10²² cm^–3 and 4.95 × 10²² cm^–3, resulting in ε* = –86.4 + 6i and ε* = –108.4 + 7.2i, respectively. The corresponding SEM images at Φ_II≈0.24 J/cm² and Φ_III≈0.29 J/cm² are reported in the upper panels of Fig. 4(b), and clearly show the passage from tidy ripples to grooves. The corresponding 2D-IFT at Φ_eff,II (ε* = –86.4 + 6i) and Φ_eff,III (ε* = –108.4 + 7.2i) are shown in the lower panels of Fig. 4(b). One can observe that the secondary pattern is almost absent in case II, while it is more marked in case III. Moreover, residual ripples can be recognized under the grooves in the SEM image of case III, indicating that grooves forms on top of ripples. In previous literature, the height information on ripples and grooves was measured by AFM and it is clear that the grooves lie above the ripples [20].

Recent reports address the formation of linear ripples through the progressive aggregation of nanoparticles [24,25]. In particular, Talbi et al. observed the formation of subwavelength ripples by coalescence of randomly redeposited nanoparticles during irradiation of mesoporous silicon with UV ps laser pulses at low irradiance, i.e. for fluence below the ablation threshold [24]. These ripples were oriented in a direction orthogonal to the laser polarization [24]. It was also reported recently that grooves can form through aggregation of the nanoparticles, which usually decorate the ripples [1–3], at flunces higher than the ablation threshold [23]. Figure 4(d) reports the 2D-IFT at Φ_eff,III (ε* = –108.4 + 7.2i). For ease of illustration, the regions with a value of the intensity ranging from 2/3 to 1 (corresponding to the maximum intensity value) are colored in red, while the regions with lower intensity are shown in green, respectively. These lower intensity regions correspond to the second quasi-periodic energy deposition pattern where grooves tend to appear. The energy absorbed in these lower intensity regions is likely not high enough to induce an effective ablation. Instead, it can favor aggregation of the nanoparticles and nanostructures progressively forming grooves rudiments, which eventually fuse together leading to the creation of grooves stripes oriented along the laser polarization. On the contrary, the region of higher energy deposition, where more effective ablation occurs, is characterized by gaps between grooves where ripples residuals persist. This scenario is schematically depicted in Fig. 4(e): the lower panel reports a sketch with grooves rudiments and stripes on the top of the ripples, while the upper panel shows a SEM image of the transitional region from ripples to grooves registered at an acquisition angle of 20°. In our experimental conditions, the energy deposited in the high intensity regions is high enough to produce nanoparticles by ablation, while in the lower energy regions the redeposited nanoparticles tend to aggregate forming quasi-periodic grooves whose preferential orientation along the laser polarization is driven by the redistribution of the deposited energy. Hence, the alternating structure of grooves and ripples illustrated by SEM image of case III is generated. Finally, at still higher fluence, as e.g. region C_H in Fig. 3, further fusion of the nanostructures present between adjacent groove stripes likely leads to the observed widening of the grooves period. As a final remark, we would like to underline that the secondary quasi-periodic patterns of energy distribution oriented along the laser polarization only forms in condition of high excitation. Therefore, it is likely that in the case of very low fluence irradiation analyzed by Talbi at al [24], the nanoparticle aggregation is driven by the more standard periodic spatial energy pattern observed at lower excitation level leading to the formation of the ripples orthogonal to the laser polarization.

4. Summary

In conclusions, the seldom analyzed generation of quasi-periodic grooves on crystalline silicon irradiated by fs laser pulses was investigated experimentally evidencing a regular variation of the threshold fluence for their formation with the number of pulses N. Then, a simple, empirical scaling approach was proposed to introduce the diverse excitation levels associated to N-pulse irradiation within the frame of a Sipe-Drude model, at laser fluencies around the grooves formation threshold. This results in a rather good agreement with the experimental findings, paving the way to a deeper understanding of the mechanisms involved in the generation of quasi-periodic surface structures and further fostering direct fs laser fabrication of surface structures with complex morphologies.