Femtosecond Laser‐Induced Periodic Surface Structuring of the Topological Insulator Bismuth Telluride

Surface structuring of topological insulator Bi2Te3 single crystals with femtosecond laser by varying pulses N and energy E is reported. Interesting effects related to laser‐induced periodic surface structures formation in this class of materials are evidenced. At low pulse energy, a clear formation of periodic, subwavelength ripples oriented orthogonally to the laser polarization is observed; those are restricted to an annular region surrounding a featureless central disk as the laser energy progressively increases. The structural analysis shows that some degree of crystallinity is preserved in the rippled area, but the central disk is amorphous resembling what is observed for germanium (Ge) and is associated with the hindering of surface structure formation due to a thick melted surface layer. Interestingly, at larger fluence or number of pulses, a transition to suprawavelength grooves occurs within the annular region covered by surface structures. The findings demonstrate a clear incubation behavior, suggesting that the formation of laser‐induced periodic surface structures is coherent with the general features of the process already reported for other materials. However, the disappearance of these structures in the central area, possibly resulting from the influence of the depth of the melt layer, indicates a mixed behavior for Bi2Te3.


Introduction
In the modern world femtosecond (fs) pulses act as a key tool in the surface processing of a variety of solid materials due to formation of LIPSS is generally rationalized due to a periodic intensity modulation of the absorbed energy, resulting from the interference between incident laser radiation and roughnessinduced scattered waves propagating at the target surface. [1,3,6]hrough periodic modulation of the intensity distribution, processes like melting and ablation are triggered preferentially at local intensity maxima, imprinting a permanent periodic pattern on the material surface.However, other phenomena have also been proposed to explain LSFL generation, for example, self-organization of surface instabilities, hydrodynamics, etc. [6,[11][12][13] As for HSFL, theories based on second-harmonic generation, the involvement of specific types of plasmon modes, self-organization, etc., have been considered as possible involved mechanisms. [1,14]nother kind of LSFL that lately got attention, named grooves, is found in semiconductors (e.g., InP and Si) and metals, particularly in the region of higher fluence and for large number of pulses. [1,15,16][17] According to Tsibidis et al., the generation of grooves is attributed to hydrothermal waves propagating between the wells of the ripples, rather than thermocapillary waves typically associated with regular ripple formation. [11]t is well known that the material bandgap plays an influential role in the nature of the interaction as well as on the kind of generated LIPSS, especially at subablation conditions.For example, HSFLs are predominantly observed when the target surface is irradiated with photons whose energy is below the bandgap of the material. [18,19]In that perspective, laser irradiation of materials with a particular band structure such as topological insulators (TI) is particularly stimulating, since they present insulating bulk states and topologically protected metallic surface states characterized by Dirac dispersion and spin-momentum locking of carriers. [20]These materials are attractive both when reduced to low dimensions as well as when used as thermoelectric (TE) materials, particularly for electronic, spintronic, and photonic applications, where light can be coupled to topologically protected surface carriers to reveal several interesting phenomena.Its impressive thermoelectric characteristics make it highly suitable for various applications, including thermoelectric refrigeration, thermoelectric generator (TEG), thermoelectric cooling (TEC), and thermal sensing.Lately, it has gained substantial attention in the field of material science due to its potential applications in energy harvesting, chip cooling, chip sensing, and related areas. [21]s the generation of periodic surface structures has been used to impart functional properties to the surface of many materials, it may also find interesting applications in this class of materials that have not been explored extensively.Therefore, addressing the formation of LIPSS in such poorly investigated materials is worthwhile and holds significant potential.Moreover, the distinct saturable absorption properties of layered TI open up their use in mode locked fiber lasers for fs pulse generation across the visible, near-infrared, and mid-infrared wavelengths by tuning the layer thickness. [22]s laser irradiation of TI is particularly interesting to explore the influence of the material properties on the modification of target surface and formation of surface structures as well as in view of possible development of functional materials.However, this topic remains still scarcely investigated.Bi 2 Te 3 is a potential TE material and TI with highly complex band structure and lattice dynamics as well as strong spin-orbit interaction and band inversion.However, there are only very few reports on fs laser irradiation of Bi 2 Te 3 or other TI.Zhou et al. investigated the selective ablation and direct writing of thick films of n-type Bi 2 Te 3 and p-type Sb 2 Te 3 by 290 fs laser pulses at  ≈ 343 nm, addressing the fluence threshold and optimal conditions for selective etching to be used in the fabrication of micro-TE devices for chip thermal management and self-powered energy harvesting. [23]Yue et al. carried out an analysis of laser-induced photoexcitation of thin film of Bi 2 Te 3 by using 100 fs pulses at 800 nm, inducing a significant change in the refractive index of the material potentially interesting for the elaboration of flat optical devices. [24]Here we report on fs laser irradiation and generation of periodic surface structures on Bi 2 Te 3 , addressing some peculiar features observed in the formation of subwavelength periodic surface structures on this material.

Morphological and Structural Analysis
Laser irradiation and surface structuring of the Bi 2 Te 3 target was carried out by exploiting different sequences of N pulses (1≤ N ≤1000) with different values of the pulse energy E, in the range 3-60 J, at a repetition rate of 100 Hz.The Gaussian laser beam was focused on the target surface at normal incidence, in air.The beam waist, measured by following the method proposed by Liu, [24,25] was estimated to be w 0 = (58±2) m.The corresponding value of the peak fluence is F p = (2E)∕(w 2 0 ) .Examples of the morphology of the Bi 2 Te 3 sample surface after laser irradiation are illustrated by the scanning electron microscopy (SEM) and atomic force microscopy (AFM) images displayed in Figure 1, as representative of low and high energy cases.Panels (a) and (c) of Figure 1 report SEM images of the surface irradiated at an energy E ≈ 5 J (F p ≈ 95 mJ cm -2 ), whereas panels (b) and (d) refer to E ≈ 60 J (F p ≈ 1.1 J cm -2 ), the highest pulse energy value investigated in the present study.The number of pulses is N = 10 for panels (a) and (b) and N = 100 for (c) and (d), respectively.A significant change in the shape of the area covered by surface structures is observed at the two values of the pulse energy, for both pulse numbers.Although the incident beam has a Gaussian intensity profile, at low pulse energy the structured region appears to be more elongated in the direction of the laser beam polarization (horizontal direction in Figure 1) and characterized by rougher edges along this direction with respect to the top and bottom boundaries, as depicted in panels (a) and (c) of Figure 1.Instead, at the highest pulse energy the surface structures only form in an annular region, as illustrated in panels (b) and (d) of Figure 1 suggesting that the generation of surface structures is limited to a small fluence range in these experimental conditions.The AFM images on the sides of panels (a-d) in Figure 1 further depict the surface morphology of the LIPSS formed in each case: at low energy (panels (a) and (c)) subwavelength ripples preferentially oriented in a direction orthogonal to the laser polarization are formed.Instead, at high energy ripples are also observed for N = 10, but at N = 100 the orientation of the surface structures tends to become more parallel to the laser polarization evidencing the formation of supra-wavelength grooves.Moreover, when N passes from 10 to 100, the depth of the surface structures , estimated from the AFM data by using Gwyddion software, [26,27] increases from (47±8) to (204±15) nm at E≈5 J and from (99±6) to (509±21) nm at E≈60 J.Therefore,  shows an almost fivefold rise for N going from 10 to 100, at a fixed pulse energy, whereas an almost ten times growth of the pulse energy, at a fixed pulse number, results in an increase of  of about a factor 2. Moreover, also the spatial period Λ of the ripples and grooves depend on E and N, as will be detailed later in Section 3.2.
For the case displayed in panel (d) of Figure 1, the AFM image (I) reports a 3D-view of a portion of the annular rippled region, whereas the insets (II) and (III) display zoomed views of the structured annular region and of the central part of the irradiated area, respectively.From image (I), a clear rim seems to be formed on the inner side of the annular structured region, whereas the structures progressively disappear going further away toward the external part, which does not present surface structures but only a decoration with dispersed nanoparticles.Image (II) evidences that in the external periphery of the annular structured area the ripples become separated in small bumps before disappearing.Instead, the image (III) shows that no surface structures are formed in the inner circular region hit by the most intense part of the Gaussian beam, but the surface is decorated with some nanoparticles and nanohole-like features.
Figure 2 reports SEM images illustrating the morphological variations induced by a progressive variation of the laser energy E, at fixed pulse number N = 100.In particular, the upper row shows a series of SEM images illustrating the gradual changes in the surface structures, whereas middle and lower rows display SEM images acquired at higher magnification at the edge and in the central part, respectively, of the corresponding SEM image reported in the upper raw.
It is evident from the SEM images in row (i) that the structured region evolves from a noncircular shape that elongates parallel to laser polarization to a nearly circular shape and, finally, to a welldefined annulus around a central part without any significant surface structure.The formation of a structured annulus encircling an almost featureless disk was observed earlier by Casquero et al. in Ge target irradiated by Ti:Sa fs and ns laser pulses. [27]Also in that case, the ringed structured region was formed at higher values of the pulse number and peak fluence and two different types of LIPSS featuring orthogonal orientations were observed.However, HSFL were generated at low pulse number and LSFL were namely present in the ringed region; [27] instead, here we observe standard subwavelength ripples (LSFL) as well as grooves.At relatively low pulse energy, the LIPSS form over a region more elongated along the laser polarization, just as observed in Figure 1a,c; this shape likely ensues from the more efficient generation of the roughness-induced scattered waves in the direction of the laser polarization vector. [28,29]As the pulse energy increases, as shown in column (c) of Figure 2, the surface structures are generated over a nearly circular area presenting ripples (LSFL) encompassing a central region decorated with grooves.The gradual evolution from ripples to grooves is clearly displayed in the lower row (iii).Such a behavior resembles the one typically observed for Si, InP, and metals irradiated by a Gaussian beam, at high values of the fluence and number of pulses. [16,30,31]However, differently from those materials, for Bi 2 Te 3 a further increase of the pulse energy results in the formation of the ring-shaped structured region surrounding an almost featureless central disk, as can be seen in columns (d) and (e) of Figure 2. The comparatively smoother central region observed in the SEM images displayed in column (e) seems to evidence clear signatures of thermal effect, ablation, melt formation, and resolidification.
According to Yue et al., irradiation of Bi 2 Te 3 thin film with 800 nm fs laser pulses induces giant changes to its refractive index and transparency, and the formation of TeO 2 and Bi 2 O 3 is evidenced by Raman analysis. [24]Here, to better clarify how the fs pulses irradiation influences the pristine Bi 2 Te 3 sample, SEM imaging combined with electron back scattered diffraction (EBSD) [32] was carried out to discriminate the presence of polycrystalline, single crystalline, and amorphous regions.Through this technique the electron beam scans a selected area of the sample; and for crystalline sample's regions Kikuchi electron diffraction patterns [33] are generated.During EBSD analysis, the sample was typically tilted at 70°to the horizontal plane to optimize both the contrast in the diffraction pattern and the fraction of electrons scattered from the sample.Then, the crystallographic orientation of Bi 2 Te 3 samples structured with various number of pulses and pulse energy were studied.It is worth to mention that the Bi 2 Te 3 crystals used for laser structuring were obtained by cleavage in air.According to the crystal structure of this material [34] they exhibited smooth (0001) cleaved surface with an excellent crystalline quality, as confirmed by EBSD measurements.The crystallographic cell of the Bi 2 Te 3 , BiTe, and Bi 4 Te 3 compounds were entered in the software database for the phase identification. [35,36]he Kikuchi electron diffraction pattern corresponding to a smooth Bi 2 Te 3 surface is provided in Figure 3a, which can be used as a reference in the determination of crystalline properties over the analyzed region.Figure 3b reports a SEM image of the area irradiated by N = 500 pulses at an energy E = 10 J (F p ≈ 0.2 J cm -2 ).The morphology of the irradiated area, obtained with the electron beam impinging on the sample surface at an angle of 20°, clearly shows that the central disk is located below the pristine surface of the sample with a shallow hump formation around the center.In the bottom panel (Figure 3c), the EBSD phase distribution map confirms the presence of Bi 2 Te 3 phase, while no other phases were indexed.The black area in Figure 3c, corre- sponding to nonindexed points, might be due to a wrinkled region giving a weak pattern for the LIPSS (II), whereas the absence of a diffraction pattern in the central disk (I) and in the annular region (III) can be ascribed to amorphization (see Figure 3b).It is worth mentioning that the electron diffraction pattern quality (EDPQ) of the pristine sample (corresponding to the region IV) The central region of the shallow crater formed on the sample surface does not show a diffraction pattern, suggesting the formation of an amorphous phase.On the contrary, the surface features in the annular structured area show the presence of small crystalline domains, whose sizes varies from 500 nm to 2 m.Furthermore, the EBSD measurements reveal the presence of an amorphous ring, with a width of few m, outside the annular structured region.The abovementioned amorphous ring borders the area modified by the laser irradiation from the fully crystalline outer surface retaining the crystalline properties of the pristine sample.
This analysis suggests that the formation of the featureless central disk can result from a melting and resolidification process induced by the intense beam part of the fs pulse train.This seems also clear from the surface morphology observed in the SEM images of the panels (iii) in Figure 2d,e, in the region marked as I in Figure 3b) as well as from the AFM analysis shown in the inset (I) of Figure 1d.On the other hand, the ringed amorphous region encircling the annulus covered by surface structures resembles the typical change induced to the target surface by the low fluence wings of the Gaussian laser beam before reaching values below the threshold for surface modification. [31]igure 4 reports EBSD analyses carried out on the sample surface for N = 100 pulses at two different values of the laser pulse energy, namely E = 3.5 J (F p ≈ 65 mJ cm -2 ) and E = 43 J (F p ≈ 0.8 J cm -2 ).At the low energy E = 3.5 J, the results reported in Figure 4a evidence a central region covered by surface structures that still retains a certain degree of crystallinity.Instead, at E = 43 J Figure 4b indicates the formation of the featureless amorphous region in the central area surrounded by the structured annular region.The latter is indeed somewhat crystalline, similar to the structured region of the low energy case in Figure 4a, whereas the latter present an amorphous state possibly due to melting and resolidification processes occurring in the part hit by the most intense part of the laser beam.The variation of the size of these various regions will be illustrated later in Section 3.4 by following the dependence of the inner and outer radii of the structured annulus on the pulse number N and pulse energy E.

Surface Features for a High Pulse Number of N = 1000
It is interesting to clarify the change of the surface morphology occurring at a relatively higher number of pulses at low energy, an experimental condition for which the central part of the irradiated surface displays the clear formation of subwavelength ripples for N = 100 pulses, as shown in Figure 2a,b.As an example, Figure 5a reports a SEM image of the sample surface after irradiation with a sequence on N = 1000 laser pulses at an energy E = 5 J (F p ≈ 90 mJ cm -2 ), i.e., a value of the pulse number N larger by an order of magnitude with respect to Figure 2. Figure 5a clearly demonstrates the formation of LIPSS even for N = 1000 at low pulse energy.
The LIPSS appear well-developed over a large part of the irradiated surface; in the central region, where the local fluence is larger, the ripples appear thicker and more disconnected into individual, shorter units.Panel (e) of Figure 5 displays a 3D view of the ripples obtained by AFM measurements in the area covered by LIPSS.The values of the ripples period estimated both by a direct measurement and using 2D-FFT (see bottom rightcorner of panel (a)) of the SEM image result to be (714 ± 75) and (734 ± 42) nm, respectively.The insets (b-d) in Figure 5 report zoomed views of the left and upper edges as well as interior part of the rippled area.As can be observed, the surface structure at the edges are more elongated along the direction of laser polarization (inset (b)) as a consequence of the roughness-induced scattered waves in the direction of the laser polarization. [28,29]Similar features were observed earlier in the case of silicon samples processed either at reduced ambient pressure or in ambient air at low number of pulses. [37]For sample processed in air such a feature is typically hampered at large number of laser pulses (N>>10) as a consequence of the redeposition of ablated nanoparticles that get accumulated over and in the surrounding of the irradiated spot [28,38,39] and enhances the surface absorption limiting such an observation. [40]Instead, in high vacuum irradiation of Si such an effect is still recognizable, due to the negligible nanoparticles back-deposition. [41]Strikingly, such an effect is still well visible in Bi 2 Te 3 even at N = 1000 pulses even for atmospheric pressure conditions.This observation suggests a very limited influence of nanoparticles redeposition at the low laser energy used here, even in air.In fact, the SEM image shows a small number of nanoparticles decorating the processed surface.This is likely due to the reduced ablation threshold of the Bi 2 Te 3 at the used laser wavelength, such that the redeposited particles may get melted and resolidifies back on the original surface.For the same reason a rippled area more elongated along the direction of laser polarization is formed at the low fluence used here; in fact, for other materials processed in ambient air such an effect was observed only at low number of pulses (N < 5), but as N increased the structured region became progressively more circular thanks to the roughness-aided absorption mediated by the accumulation of nanoparticles around the crater.Finally, for the sake of comparison the SEM image of Figure 5f shows the surface morphology produced by a sequence of N = 1000 pulses at a high energy value of E = 43 J (F p ≈ 0.8 J cm -2 ).The SEM image was acquired at an angle of 40°and demonstrates the generation of a deep ablation crater whose edge presents a groove-like periodic surface modulation parallel to the laser polarization as shown by the SEM images in panel (g).

Variation of the Structured Area and LIPSS Period with E and N
Here, we illustrate the variation of the area covered by surface structures as a function of the pulse energy E and number of pulses N. Typically, surface structures start to form above a minimum threshold value of the laser fluence, F th,min .Moreover, they exist within a range of laser fluences and when the local pulse fluence exceeds a particular value F th,max a transition to other type of structures or surface modifications typically occur. [30,42,43]Both the threshold fluence values depend on the pulse number N. This occurrence, indicated as incubation, is ascribed to the multipulse feedback effects related to the progressive variation of the surface properties during the pulse sequence. [30,42]s an example, Figure 6a   The variation of the external and internal radii of the annular structured area as a function of pulse energy E, for N = 100 is illustrated in Figure 6b.The experimental datapoints are described rather well by the solid lines representing the energy dependence of a position r th at which a threshold energy value E th is achieved for a Gaussian beam spatial profile where w 0 is the beam spot size and the corresponding peak threshold fluence is F th = (2E th )∕(w 2 0 ) .For the case in Figure 6a, the estimated values of the fluence threshold corresponding to the external and internal radii are F th,ex ≈ 40 mJ cm -2 and F th,in ≈ 250 mJ cm -2 .Figure 6c illustrates the dependence of the external and internal radii on the pulse number N for an energy E = 60 J.An increase in the number of pulses N leads to a progressive reduction in the energy threshold E th due to a multipulse feedback effect mechanism generally described by a simple incubation behavior as E th (N) = E th (1)N  − 1 , where  is the incubation factor and E th (1) the threshold energy for a single pulse.Physically the incubation behavior is related to the creation of laser-induced defects that increase the absorption and lower the threshold for the subsequent pulses, as for example the occupation of trap states and the creation of laser-induced-states in dielectrics or the progressive formation of surface structures and redeposition of nanoparticle for metals and semiconductors.Substitution of the simple incubation trend for E th (N) in Equation ( 1) allows obtaining the following dependence for the radius r th The solid line in Figure 6c is a fit to Equation (2) demonstrating that the external radius is well described by such an incubation model with  = (0.93 ± 0.05) and E th (1) = (3.8± 0.4) J.Instead, in Figure 6c the internal radius follows a different dependence characterized by a gradual decrease as a function of N and a progressive detachment from an incubation trend passing through the experimental datapoint at low pulse numbers shown as a dashed line.This observation further suggests that the formation of a featureless central area without surface structures is likely related to the fact that the fluence values in that region overpass a threshold leading to a condition that hinders their formation.Recalling the similarity of the observed behavior with Ge, it is worth observing that according to the time resolved studies carried out by Ehrlich et al. in germanium samples, the formation of LIPSS is supported only when the melt layer thickness is less than ≈20 nm. [44]More recently, Casquero et al. conducted similar experiments on Ge, confirming the influence of the thickness of the melt layer. [27]Hence, the formation of a central disk without periodic structures could be possibly associated to an increased depth of the melt layer formed in the inner region where the local intensity is higher.This interpretation is consistent with the observation of ripples in the internal part of the irradiated area for low energy values and the progressive restriction of their presence in a peripheric annular region as the fluence increases.The different dependence of the radii encircling the surface structured area of the sample with the pulse number is rationalized as a change in the mechanisms occurring at low and high fluence.However, further investigation is needed in the future to fully clarify such an aspect of laser surface structuring of Bi 2 Te 3 .
Finally, we illustrate the variation of ripples and grooves period Λ on the pulse energy E and the number of pulses N. The experimental conditions allowed to identify clear ripples and grooves for several values of E and N and then measure their period.The results are reported in Figure 7, in which panel (a) shows the dependence of Λ on E for a number of pulses N = 50, whereas panel (b) reports Λ as a function of N for a pulse energy E = 3.5 J (F p ≈ 90 mJ cm -2 ).In agreement with previous reports on other materials, [16,17,45,46] Figure 7a the dependencies of period Λ on E shows very weak for the ripples (the energy variation mainly influences the region where ripples are formed, as observed above) and a progressive increase for the grooves.However, as can be observed in Figure 7b, ripples and grooves evidence clear opposite trends of the period Λ on N, coherently with the behavior observed for other materials. [16,17,45,46]

Conclusions
Topological insulators constitute an interesting class of materials for their peculiar properties as well as their potential applications in functional materials.In this respect, the generation of surface structures by irradiation with fs laser pulses has become a wellestablished method to impart new surface functionalities once the fundamental aspects concerning the formation of LIPSS and the window of the experimental parameters for their generation have been ascertained.However, studies devoted to fs laser surface structuring of a specimen of this class of materials are still missing.
Here we have reported an experimental investigation on fs laser surface structuring of a Bi 2 Te 3 target by irradiation with ≈800 nm, ≈35 fs laser pulses, in air.The target sample was cleaved from a single crystal grown by the floating zone method and irradiated with sequences of N laser pulses at various values of the laser energy E. Our experimental findings evidenced a variety of effects related to fs laser irradiation of Bi 2 Te 3 .At low pulse energy, SEM and AFM analyses demonstrated the clear formation of subwavelength ripples oriented in direction orthogonal to the laser polarization over the target surface.Strikingly, at fixed N, the progressive increase of the laser energy E led to the restriction of surface structures only to an annular region surrounding a featureless central disk.Structural analysis of the sample with EBSD showed that the central disk is amorphous, whereas some degree of crystallinity was retained in the structured area.The absence of surface structures in an amorphized central region surrounded by a structured ring was observed earlier in Ge irradiated by fs laser pulses; this characteristic of Ge was ascribed to its specific feature of supporting LIPSS formation only for a limited thickness of the melt layer induced by laser irradiation.A similar effect could be at play also for Bi 2 Te 3 , even if further investigations should be needed to fully clarify such an aspect for this material.For instance, this effect does not occur in Si, the most studied material for LIPSS generation, which instead showed the formation of a central area covered by suprawavelength grooves parallel to the laser polarization.Interestingly, grooves also formed on Bi 2 Te 3 at larger fluence or number of pulses, but they remained still restricted within the annular region covered by surface structures.
The analysis of the external radius of the annular structured region demonstrated a clear incubation behavior with an incubation coefficient  ≈ 0.93 and a single shot ablation threshold fluence F th (1) ≈ 36 mJ cm -2 .Instead, the variation of the internal radius on the pulse number showed a trend different from the one expected for incubation.This, in turn, suggests that the LIPSS formation is coherent with the general features of the process already reported for other materials, but their disappearance in the central area derived from other mechanisms, as for example the influence of the melt layer depth.Finally, we addressed the dependence of ripples and grooves period Λ on both pulse energy E and number of pulses N (Figure 7) observing features similar to those reported for other materials and explained by current models on surface structures formation.
Our experimental findings have evidenced a variety of effects associated with the laser irradiation of Bi 2 Te 3 with fs laser pulses that can be of interest in laser processing and structuring of this interesting material.The results suggest a distinct behavior of Bi 2 Te 3 regarding the excitation of surface scattered waves and melting dynamics, which subsequently lead to the formation of ripples and grooves, respectively, that should deserve further, in depth analysis in the future.

Experimental Section
Experiments of fs laser irradiation and surface structuring on Bi 2 Te 3 were performed with a regeneratively amplified Ti:Sapphire laser source (Legend, Coherent Inc.) delivering linearly polarized ≈35 fs pulses at a central wavelength of ≈800 nm.The laser pulse energy, E, was varied by means of a system of half-wave plate and polarizer.The Gaussian beam was focused on the target surface by means of a plano-convex lens with a nominal focal length of 75 mm.The pulse energy was measured after the focusing lens using an OPHIR pyroelectric energy meter.Experiments were conducted by exploiting different sequences of N pulses (1≤ N ≤1000) with different values of the pulse energy E, in the range 3-60 J, at a repetition rate of 100 Hz.
The target was a piece of Bi 2 Te 3 cleaved from a single crystal grown in a sealed quartz ampoule using an infrared image furnace with double elliptical mirrors (NEC Machinery, model SC1-MDH11020).Single crystals of Bi 2 Te 3 were grown by the floating zone method from metallic bismuth and tellurium, in stoichiometric ratio.The target sample was mounted on a computer controlled two-axis motorized piezo stage (Micronix-USA Ltd) whose movement was synchronized with an electromechanical shutter and a custom software allowed firing the required number of pulses N at any selected location on the target surface.
The sample surface was characterized after irradiation by field emission scanning electron microscopy (FE-SEM).SEM images were typically acquired by registering secondary electrons (SE) with an Everhart-Thornley (ET) type detector.To inspect surface features more precisely, the In-Lens (IL) detector, located inside the electron column of the microscope and arranged rotationally symmetric around its axis, was also used.The SEM images were analyzed using the software Gwyddion ascertaining the periodic features of surface modulations both visually and through 2D fast Fourier transform (2D-FFT) analysis of the SEM micrographs.In some cases, atomic force microscopy was also carried out to get information on the morphology of specific areas of the irradiated target surface.Finally, EBSD measurements were carried out on different regions of the irradiated sample to analyze the modification of the sample crystallinity.The EBSD measurements were performed using an Inca Crystal 300 EBSD system added to a SEM LEO (Zeiss, model EVO 50) with a LaB6 gun.During EBSD measurements, the SEM was operated using an aperture size of 30 m, a working distance of 18 mm, an accelerating voltage of 20 kV and a probe current of 5 nA.It is worth to mention that EBSD results reported in the following are affected by the surface roughness induced by the laser treatment.

Figure 1 .
Figure 1.SEM and AFM images of the irradiated sample for two different values of the pulse energy E and pulse number N-panels (a) and (c): E ≈ 5 J (F p ≈ 90 mJ cm −2 ), N = 10; panels (b) and (d): E ≈ 60 J (F p ≈ 1.1 J cm −2 ), N = 100.The SEM images display the irradiated region over a larger area, whereas the AFM images show the morphology of the LIPSS in the area marked on the corresponding SEM image.The double headed arrow indicates the polarization direction of the laser beam.

Figure 2 .
Figure 2. SEM micrographs of the laser irradiated region for different values of the pulse energy E, from 3.5 J (F p ≈ 65 mJ cm −2 ) to 43 J (F p ≈ 0.8 J cm −2 ), at a fixed number of pulses N = 100.The upper panels (i) illustrate the changes of the irradiated area as the pulse energy varies.The rows (ii and ii) display high-resolution SEM images of the edge of the structured area and of the central part of the irradiated region, respectively.The black and white scale bars correspond to 20 and 5 m, respectively.The double-headed arrow in red indicates the direction of the linear polarization.

Figure 3 .
Figure 3. a) Kikuchi Electron diffraction pattern collected on the crystalline area of structured Bi 2 Te 3 .b) SEM image of Bi 2 Te 3 sample irradiated with N = 500 pulses at a pulse energy E = 10 J (F p ≈ 0.25 J cm −2 ).c) EBSD phase distribution map showing the presence of Bi 2 Te 3 phase only.d) EDPQ map with dark and light regions related to the different crystallinity of the inspected area.

Figure 4 .
Figure 4. SEM Image, EBSD quality pattern and phase distribution map of the irradiated sample surface for N = 100 pulses and for pulse energies of a) 3.5 J (F p ≈ 65 mJ cm −2 ) and b) 40 J (F p ≈ 65 mJ cm −2 ), respectively.By comparing the pattern quality, corresponding to the EBSD patter formation, for the two different laser energies, it is evident the amorphous central featureless region only forms at larger values of the pulse energy.

Figure 5 .
Figure 5. a) In-Lens SEM image of the Bi 2 Te 3 after irradiation with N = 1000 laser pulses at a pulse energy E = 5 J (F p ≈ 90 mJ cm −2 ) showing the formation of LIPSS.The insets (b) and (c) display zoomed images of the left and top edges of the rippled area, whereas inset (d) reports a magnified view of the ripples inside the spot.A 3D visualization of the ripples obtained by AFM is shown in panel (e).A 2D-FFT map of the structured spot is given in the lower-right corner of panel (a).The red double headed arrow in panel (a) indicates the direction of the laser polarization.For the sake of comparison, the surface morphology observed at E = 43 J (F p ≈ 0.8 J cm −2 ) for N = 1000 is illustrated in the SEM images of panels (f) and (g).The SEM image of panel (f), acquired at an angle of 40°, showcases the formation of a deep crater, whereas panel (g) evidence groove-like periodic surface modulation parallel to the laser polarization at the edge of the formed crater.
reports a SEM micrograph of the sample surface after irradiation with a sequence of N = 100 pulse at E = 20 J and the Gaussian profile of the laser fluence illustrating the two threshold values, F th,in and F th,ex , for the formation of the surface structures delimiting the area indicated as I and the featureless central region marked as II.

Figure 6 .
Figure 6.a) Fluence spatial profile and SEM image illustrating the thresholds F th,min and F th,max corresponding to the formation of the external and internal rings limiting the annular area covered by surface structures, indicated as I.The example refers to E = 20 J (F p ≈ 0.4 J cm −2 ) and N = 100.The featureless central disk is marked as II.Panels (b) and (c) report the variation of the internal and external radii as a function of the pulse energy E (at N = 100) and number of pulse N (at E = 60 J), respectively.The solid lines in panel (b) are fits according to Equation (1).The solid line in panel (c) is a fit according to Equation (2), whereas the dashed curve represents a similar dependence passing through the first experimental points for the internal radius evidencing an experimental trend different from the one expected for incubation.The uncertainties on the experimental datapoints of panels (b) and (c) are contained within their respective size.

Figure 7 .
Figure 7. Variation of the ripples and grooves period Λ with respect to the pulse energy E (panel (a)) and number of pulses N (panel (b)).