On the generation of grooves on crystalline
silicon irradiated by femtosecond laser pulses
Shutong He,1,2 Jijil JJ Nivas,1,3 Antonio Vecchione,4
Minglie Hu,2 and Salvatore Amoruso1,3,*
1
Dipartimento di Fisica, Università di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Via Cintia,
I-80126 Napoli, Italy
2
Ultrafast Laser Laboratory, Key Laboratory of Opto-electronic Information Technical Science of Ministry of
Education, College of Precision Instruments and Opto-electronics Engineering, Tianjin University, Tianjin 300072,
China
3
CNR-SPIN, UOS Napoli, Complesso Universitario di Monte S. Angelo, Via Cintia, I-80126 Napoli, Italy
4
CNR-SPIN, UOS Salerno, Via Giovanni Paolo II 132, I-84084 Fisciano (SA), Italy
*
[email protected]
Abstract: Irradiation of crystalline silicon with femtosecond laser pulses
produces a variety of quasi-periodic surface structures, among which subwavelength ripples creation is largely studied. Here we report an
experimental investigation and a theoretical interpretation focusing on the
seldom considered issue of quasi-periodic, micron spaced grooves
formation. We characterize the morphological evolution of the grooves
generation and experimentally single out the variation of the threshold
fluence for their formation with the number of pulses N, while typical
ripples simultaneously produced in the irradiated area are always
considered for comparison. Our experimental findings evidence a power
law dependence of the threshold fluence on the number of pulses both for
ripples and grooves formation, typical of an incubation behavior. The
incubation factor and single pulse threshold are (0.76 ± 0.04) and (0.20 ±
0.04) J/cm2 for ripples and (0.84 ± 0.03) and (0.54 ± 0.08) J/cm2 for
grooves, respectively. Surface-scattered wave theory, which allows
modeling irradiation with a single pulse on a rough surface, is exploited to
interpret the observed structural modification of the surface textures. A
simple, empirical scaling approach is proposed associating the surface
structures generated in multiple-pulse experiments with the predictions of
the surface-scattered wave theory, at laser fluencies around the grooves
formation threshold. This, in turn, allows proposing a physical mechanism
interpreting the grooves generation as well as the coexistence and relative
prominence of grooves and ripples in the irradiated area.
©2016 Optical Society of America
OCIS codes: (140.3295) Laser beam characterization; (320.2250) Femtosecond phenomena;
(320.7130) Ultrafast processes in condensed matter, including semiconductors.
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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 subwavelength 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
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© 2016 OSA
Received 15 Oct 2015; revised 25 Nov 2015; accepted 26 Nov 2015; published 9 Feb 2016
22 Feb 2016 | Vol. 24, No. 4 | DOI:10.1364/OE.24.003238 | OPTICS EXPRESS 3239
[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 εSi = 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 (rR) and grooved
(rG) regions and the corresponding uncertainty is used as error bar.
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© 2016 OSA
Received 15 Oct 2015; revised 25 Nov 2015; accepted 26 Nov 2015; published 9 Feb 2016
22 Feb 2016 | Vol. 24, No. 4 | DOI:10.1364/OE.24.003238 | OPTICS EXPRESS 3240
Fig. 1. (a) Portion of a SEM micrograph of the Si target surface after N = 100, for E0≈14 µJ
(Φp≈0.8 J/cm2); (b) corresponding Gaussian spatial profile of the laser beam. The doubleheaded arrow indicates the incident laser pulse polarization.
3. Results and discussion
Considering the Gaussian spatial beam profile with a 1/e2-beam waist w0, the peak fluence is
Φp = (2E0)/(π w02 ) and the squared outer radius rk of the two patterned regions (k = R and G
for ripples and grooves, respectively) is related to the corresponding energy threshold Eth,k by:
rk2 =
1 2  E0
w0 ln 
E
2
 th, k
 1 2  Φp
 = w0 ln 
 2
 Φ th , k



(1)
where Eth,k and Φth,k are the threshold energy and fluence for ripples (k = R) and grooves (k =
G), respectively, and Φth,k = (2 Eth,k)/(π w02 ). Figure 2(a) reports rR and rG as a function of the
laser pulse energy E0, for N = 100, which are well described by Eq. (1). From fits we obtain
w0 = (34.2 ± 0.5) µm both from ripples and grooves, Eth,R(N = 100) = (1.22 ± 0.06) µJ and
Eth,G(N = 100) = (4.72 ± 0.06) µJ. Consequently, the threshold fluences are Φth,R(N = 100) =
(66 ± 5) mJ/cm2 and Φth,G(N = 100) = (260 ± 20) mJ/cm2. We would like to notice that the
experimental data of Fig. 2(a) are limited to a maximum laser pulse energy lower than about
50 μJ. At higher energies, the beam starts to be affected by instabilities, like plasma in air and
filamentation near to the target surface [14,15], which indeed lead to a more complex crater
morphology, which is out of the scope of the present study.
From SEM micrographs of the Si target irradiated with different number of pulses N, the
radii rR and rG 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 Φth,R and Φth,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 rG and not grooves rudiments. Figure 2(b) reports the
variation of the threshold fluences with N in the form NΦth,k(N) vs N, for Φp = 1.5 J/cm2,
where k is equal to R and G for ripples and grooves, respectively. A similar behavior is also
observed for Φp = 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]:
Φ th , k ( N ) = Φ th, k (1) N ξk −1
#251991
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(2)
Received 15 Oct 2015; revised 25 Nov 2015; accepted 26 Nov 2015; published 9 Feb 2016
22 Feb 2016 | Vol. 24, No. 4 | DOI:10.1364/OE.24.003238 | OPTICS EXPRESS 3241
where Φth,k(1) is the threshold fluence for N = 1 and ξk is the incubation factor, with k = R for
ripples and k = G for grooves, respectively.
Fig. 2. (a) Variation of rR and rG with pulse energy E0. (b) Threshold fluence variation with the
number of pulses N in the form NΦth,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.
Considering first ripples, fit to experimental data gives Φth,R(1) = (0.20 ± 0.04) J/cm2 and
ξR = (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 Φp = 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 Φth,G
starts at N = 50. Interestingly, when a groove pattern starts forming Φth,G(N) also follows Eq.
(2), with Φth,G(1) = (0.54 ± 0.08) J/cm2 and ξG = (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.
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Received 15 Oct 2015; revised 25 Nov 2015; accepted 26 Nov 2015; published 9 Feb 2016
22 Feb 2016 | Vol. 24, No. 4 | DOI:10.1364/OE.24.003238 | OPTICS EXPRESS 3242
Fig. 3. SEM micrographs of the Si target surface at N = 100 for (a) Φp = 0.8 J/cm2 and Φp = 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 (AL and BL) and
high (BH and CH) 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.
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 Φp = 0.8 J/cm2 and Φp = 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 Φp = 0.8 J/cm2 and Φp = 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 AL and BL. AL 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, BL is a central region with well-developed grooves where Φ is larger than Φth,G(N =
100)≈0.26 J/cm2. In Fig. 3(b) we recognize that grooves similar to those of the region BL only
appears in an annular area BH corresponding to 0.26 J/cm2 < Φ < 0.71 J/cm2, while larger
groove stripes occupy the central region CH (Φ > 0.71 J/cm2). In particular, the average width
of the grooves increases from ≈2 µm to ≈4 µm by passing from BH to CH, 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 AL shrinks to a very sharp boundary between rippled and grooved areas.
#251991
© 2016 OSA
Received 15 Oct 2015; revised 25 Nov 2015; accepted 26 Nov 2015; published 9 Feb 2016
22 Feb 2016 | Vol. 24, No. 4 | DOI:10.1364/OE.24.003238 | OPTICS EXPRESS 3243
Fig. 4. (a) Spatial profile of the laser pulse fluence Φ(r) for Φp = 0.8 J/cm2; the right vertical
axis shows the corresponding value of Φeff. (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 doubleheaded arrows show the laser polarization. (c) 2D map of η(κ) corresponding to condition Φeff,I.
The wave vectors κx and κy 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.
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 κx and κy parallel and orthogonal to the laser polarization,
respectively. The map of η(κ) is symmetric with respect to κx = 0 and κy = 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
#251991
© 2016 OSA
Received 15 Oct 2015; revised 25 Nov 2015; accepted 26 Nov 2015; published 9 Feb 2016
22 Feb 2016 | Vol. 24, No. 4 | DOI:10.1364/OE.24.003238 | OPTICS EXPRESS 3244
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.
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 Φeff that scales with the
experimental single-shot threshold fluence, Φth,G(1), in the same proportion as the
corresponding fluencies Φ and Φth,G(N) for N pulse, respectively. This reads Φeff/Φth,G(1) =
Φ/Φth,G(N), and consequently Φ eff = N 1−ξG × Φ .
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 Φp = 0.8 J/cm2. The right axis shows the
corresponding values of Φeff for N = 100. Φeff,I≈Φth,G(1) = 0.54 J/cm2 corresponds to the
transitional fluence from ripples to grooves. The free-carrier number density calculated at
Φeff,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 κx 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. Φeff,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
ΦI≈0.26 J/cm2 which corresponds to a radial position in the irradiated spot rI≈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 Φeff,I, namely Φeff,II = 0.5 J/cm2
and Φeff,III = 0.6 J/cm2. In the conditions of Φeff,II = 0.5 J/cm2 and Φeff,III = 0.6 J/cm2, the free-
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Received 15 Oct 2015; revised 25 Nov 2015; accepted 26 Nov 2015; published 9 Feb 2016
22 Feb 2016 | Vol. 24, No. 4 | DOI:10.1364/OE.24.003238 | OPTICS EXPRESS 3245
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 ΦII≈0.24
J/cm2 and ΦIII≈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 Φeff,II (ε* = –86.4 + 6i) and
Φeff,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 Φeff,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 quasiperiodic 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 CH 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
#251991
© 2016 OSA
Received 15 Oct 2015; revised 25 Nov 2015; accepted 26 Nov 2015; published 9 Feb 2016
22 Feb 2016 | Vol. 24, No. 4 | DOI:10.1364/OE.24.003238 | OPTICS EXPRESS 3246
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.
Acknowledgments
S.H. thanks the China National Scholarship Fund. M.H. acknowledges National Natural
Science Foundation of China (Grant No. 61322502) and Tianjin City S&T Project (Grant
No.13RCGFGX01122).
#251991
© 2016 OSA
Received 15 Oct 2015; revised 25 Nov 2015; accepted 26 Nov 2015; published 9 Feb 2016
22 Feb 2016 | Vol. 24, No. 4 | DOI:10.1364/OE.24.003238 | OPTICS EXPRESS 3247