Analysis of nascent silicon phase-change gratings induced by femtosecond laser irradiation in vacuum

The formation of periodic surface structures is a general effect of femtosecond laser irradiation of solid targets showing promising interest in material science and technology. However, the experiments are typically carried out in air, a condition in which the target surface becomes densely decorated with nanoparticles that can influence the formation of the surface structures in the early stage of the irradiation process. Here we report an investigation of structures generation on a silicon surface irradiated in vacuum (10−5 mbar) with a low number of laser pulses (N ≤ 10) that exploits several microscopy techniques (optical, atomic force, electron and Raman). Our analyses allow identifying the creation of silicon phase-change gratings consisting of alternating amorphous and crystalline periodic lines, with almost no material removal, located at the periphery of a shallow ablation crater. These gratings originate from two different kinds of defects: (i) the first is characterized by a peculiar lobed shape that is produced by the first few laser pulses; (ii) the second is provided by the one-dimensional, linear singularity defined by the ablation edge of the nascent crater. Both kind of defects lead to grating structures extending outwards the amorphous central area of the crater along the direction of the laser polarization. Comparative analysis with the surface formed in air, in the same experimental conditions, evidences the important role played by nanoparticles densely decorating the target in air and the striking variation occurring in vacuum.

S1. Optical image of the sample surface. Figure S1 shows an optical image of the sample after irradiation with N=4 laser pulses at an energy E0=140 J, in high vacuum. One can observe that the morphology of the ripples located inside the inner crater also influences the optical images of the target surface inducing a spatial modulation of its reflectivity. Interestingly, reflectivity modulations are also observed outside the shallow ablation crater, namely in the fringed verge area around the crater and in the area of the gratings departing from the elliptical defects seen in the SEM image. The AFM analysis discussed in the main text indicates that these regions are not characterized by significant topographic changes of the surface, thus suggesting that the reflectivity changes in such areas can be ascribed to a change of the local physical properties of the surface, as confirmed by micro-Raman imaging. Figure S1. Optical image of the sample surface after an irradiation sequence of N=4 laser pulses at an energy E0=140 J, in high vacuum.

S2. Consistency analysis on surface scattered wave.
Here we report a consistency analysis about the formation of the amorphous-crystalline fringes through the generation of a surface scattered wave (SSW). Under ultrashort laser pulses irradiation, the complex refractive index of silicon can be noticeably modified as a consequence of the high density of generated electrons. In such excited conditions, surface roughness and defects can act as scattering centers for the formation of SSW, as e.g. Surface Plasmon Polariton (SPP) [1][2][3] , that interfering with the incident laser beam give rise to a modulation of the absorbed energy. This scenario is typically associated to the formation of the morphological ripples generated during fs laser irradiation of solid targets. In particular Huang et al. proposed SPP as a mechanism explaining the typical decrease of ripples period with number of laser pulses N through a grating-assisted influence on the ripples period 2 . However, a similar effect has been rationalized on a more general SSW approach by Zhang et al. 4 , thus indicating SSW as a general aspect of the feedback mechanisms involved in ripples generation by fs laser irradiation, which is further enhanced for SPP-active targets as silicon under ultrashort laser pulses 3 . Hereafter we try to support a scenario where a SSW in form of SPP can generate an energy modulation leading to the formation of the a-Si/c-Si surface grating. The relative dielectric constant of the excited silicon surface εex, at the laser wavelength ωL, can be expressed as 2,5,6 : = ,1 + ,2 = 0 ( ) − (1), one can derive for the real and imaginary part of the dielectric constant εex: while the SPP propagation length Ls along the surface is given by:

S3. Double-interface model for the analysis of Raman spatial profiles.
In  The intensity IR of the light generated into layer 2 by Raman scattering is given by: where R is an efficiency factor of the Raman scattering process. Then, the backscattered light at the shifted Raman wavelength travels the layer and is eventually detected as Idet:  Table I.

S4. Confocal microscopy and double-interface model for the analysis of reflectivity spatial
profiles.   Fig. S3(a). R/R has been obtained by subtracting from the local reflectivity signal, R(x), the asymptotic reference value, Rref, registered at larger distance from defects, where the reflectivity becomes constant, and then normalizing it to Rref, i.e.
R/R=(R(x)-Rref)/Rref. The reflectivity profile of Fig. S3(b) shows a series of fringes associated to the progressive passage from a-Si to c-Si superimposed over an average variation of the local reflectivity (red curve). Moreover, in Fig. S3(b) two localized defects and the crater edge can be identified by the two sudden dips, at x55 m and x33 m, and a shoulder, at x31 m, respectively. Moving outwards the spot, the reflectivity variation reaches a maximum which is then followed by a progressive decay towards the reference value corresponding to c-Si.
The reflectivity of fs laser irradiated silicon was analyzed earlier by considering a thin film optical model to address the influence of the a-Si layer thickness for modified regions of the Si surface extending over several m 12,13 . A similar analysis has been carried out to rationalize the spatial profiles of the observed reflectivity registered by confocal microscopy, as e.g. in Fig. S3.  Fig. S4 and p-polarized light is considered, as in our experimental conditions.
The reflectivity of the double-interface is given by 8 : where ↔ and ↔ are the single-boundary complex Fresnel coefficients for the passage at the interface n, l (n and l =0,1,2, with n l) in the propagation direction indicated by the arrow and 1 is the angle of propagation in layer 1. Hence, the reflectivity ratio ∆ shown in Fig. S4, for various angle of incidence 0, is obtained. One can observe a damped oscillating behavior of the reflectivity ratio due to both absorption and interference effects of the double-interface. By considering the average reflectivity values in Fig. S3(b) for x >55 m, a maximum a-Si depth of 24 nm can be inferred for the fringes produced around the intense defect. As for fringes produced by the crater edge (x <30 m), R/R reaches average values larger than that expected for normal incidence of the probing beam of the confocal microscope. In first instance, a normal incidence can be considered for the confocal microscope measurements; however, the non-monotonic character of the relative reflectivity ratio dependence on the a-Si layer thickness makes such approach less reliable than the micro-Raman one. Experimental results (shown in Fig. S3(b)) indicate a maximum value of the average R/R in the fringe pattern at the right of the defect of 20%, which might correspond to a maximal depth of 24 nm if the decreasing part after first maximum is considered in Fig. S4. This value is consistent with the estimate obtained by micro-Raman imaging, however sizeable oscillations around the average values of the reflectivity ratio are observed experimentally, in agreement with previous reports concerning larger surface area modification of silicon with ultrashort laser pulses 10 . There can be various reasons for such a behavior. First, deviations from the normal incidence of the confocal probing radiation, related to the high numerical aperture of the objective, might lead to a larger variation of the reflectivity ratio, as predicted by the model at increasing incident angles in Fig. S.4. Second, differences might also arise from the fact that a double-interface air/a-Si/c-Si system with perfectly parallel surfaces exploited in the model cannot completely describe subtleties coming from undulations and reduced sharpness of the real structure in the description of the surface reflectivity. In the real case both interfaces should present undulations and reduced sharpness. However, the fringes can be associated to a thickness modulation of the a-Si overlayer around its average value, which is larger for fringes produced by the SSW induced at the local defect than for the crater edge. This can be likely ascribed to a superposition of several scattered wavelets, each with a different phase, interfering with the Gaussian spot in the region around the extended crater edge, while a more localized source of SSW with well-defined phase can be considered for the punctual defect. Further analyses should be necessary to completely clarify such an aspect.