# Liquid-assisted laser nanotexturing of silicon: onset of hydrodynamic
processes regulated by laser-induced periodic surface structures

Yulia Borodaenko  Institute of Automation and Control Processes, Far Eastern
Branch, Russian Academy of Science, 5 Radio Str., Vladivostok 690041, Russia
Dmitriy Pavlov  Institute of Automation and Control Processes, Far Eastern
Branch, Russian Academy of Science, 5 Radio Str., Vladivostok 690041, Russia
Artem Cherepakhin  Institute of Automation and Control Processes, Far Eastern
Branch, Russian Academy of Science, 5 Radio Str., Vladivostok 690041, Russia
Eugeny Mitsai  Institute of Automation and Control Processes, Far Eastern
Branch, Russian Academy of Science, 5 Radio Str., Vladivostok 690041, Russia
Andrei Pilnik  Pacific Quantum Center, Far Eastern Federal University,
Vladivostok, Russia  Institute of Automation and Control Processes, Far
Eastern Branch, Russian Academy of Science, 5 Radio Str., Vladivostok 690041,
Russia  Sergey Syubaev  Institute of Automation and Control Processes, Far
Eastern Branch, Russian Academy of Science, 5 Radio Str., Vladivostok 690041,
Russia  Image Processing Systems Institute of RAS Branch of the FSRC
Crystallography and Photonics RAS, Samara, Russia  Stanislav O. Gurbatov
Institute of Automation and Control Processes, Far Eastern Branch, Russian
Academy of Science, 5 Radio Str., Vladivostok 690041, Russia  Far Eastern
Federal University, Vladivostok, Russia  Evgeny Modin  CIC NanoGUNE BRTA, Avda
Tolosa 76, 20018 Donostia-San Sebastian, Spain  Aleksey P. Porfirev  Image
Processing Systems Institute of RAS Branch of the FSRC Crystallography and
Photonics RAS, Samara, Russia  Svetlana N. Khonina  Image Processing Systems
Institute of RAS Branch of the FSRC Crystallography and Photonics RAS, Samara,
Russia  Aleksandr V. Shevlyagin  Institute of Automation and Control
Processes, Far Eastern Branch, Russian Academy of Science, 5 Radio Str.,
Vladivostok 690041, Russia  Evgeny L. Gurevich<EMAIL_ADDRESS>Laser
Center (LFM), University of Applied Sciences Munster, Stegerwaldstra?e 39,
48565 Steinfurt, Germany  Aleksandr A. Kuchmizhak<EMAIL_ADDRESS>Institute of Automation and Control Processes, Far Eastern Branch, Russian
Academy of Science, 5 Radio Str., Vladivostok 690041, Russia  Pacific Quantum
Center, Far Eastern Federal University, Vladivostok, Russia

###### Abstract

Ultrashort laser exposure can push materials to transient highly
nonequilibrium states driving their subsequent morphology self-organization
stimulated by excited electromagnetic and hydrodynamic processes. Laser
processing parameters regulate these processes defining the resulting surface
nano-morphologies demanding for diverse applications. Here, upon systematic
studies of femtosecond-laser processing of monocrystalline Si in oxidation-
preventing methanol, we showed that the electromagnetic processes dominating
at initial steps of the progressive morphology evolution define the onset of
the hydrodynamic processes and resulting morphology upon subsequent multi-
pulse exposure. In particular, under promoted exposure quasi-regular
subwavelength laser-induced periodic surface structures (LIPSSs) were
justified to evolve through the template-assisted development of the Rayleigh-
Plateau hydrodynamic instability in the molten ridges forming quasi-regular
surface patterns with a supra-wavelength periodicity and preferential
alignment along polarization direction of the incident light. Subsequent
exposure promotes fusion-assisted morphology rearrangement resulting in a
spiky surface with a random orientation, yet constant inter-structure distance
correlated with initial LIPSS periodicity. Along with the insight onto the
physical picture driving the morphology evolution and supra-wavelength
nanostructure formation, our experiments also demonstrated that the resulting
quasi-regular and random spiky morphology can be tailored by the
intensity/polarization distribution of the incident laser beam allowing on-
demand surface nanotexturing with diverse hierarchical surface morphologies
exhibiting reduced reflectivity in the visible and shortwave IR spectral
ranges. Finally, we highlighted the practical attractiveness of the suggested
approach for improving near-IR photoresponse and expanding operation spectral
range of vertical p-n junction Si photo-detector operating under room
temperature and zero-bias conditions $via$ single-step annealing-free laser
nanopatterning of its surface.

##  I Introduction

Surface micro- and nanostructuring represents an important technological
procedure allowing to improve basic characteristics of critical materials or
even endow them with new functionalities. Bright examples of such material
improvement can be readily found in almost all aspects of modern engineering
and device fabrication, where appropriate patterning allows to control
electrical, optical, biological, tribological and wetting properties of the
processed surfaces. Direct laser processing of materials using pulsed
radiation represents non-lithographic straightforward technique exhibiting
continuously growing importance for both scientific and industrial
communities. Such interest is largely boosted by the development of the laser
market offering cheaper, high-speed and stable pulsed sources, more precise
beam shaping and scanning systems as well as the growth of fundamental
understanding of laser-matter interaction $via$ development of computer-aided
simulation tools and analysis techniques based on machine learning Sugioka and
Cheng (2014); Vorobyev and Guo (2013); Wei  _et al._ (2020); Stratakis  _et
al._ (2020); Dalloz  _et al._ (2022); Porfirev  _et al._ (2023); Brandao  _et
al._ (2023).

Apart from a common direct patterning of the surface with a tightly focused
laser beam along the computer-defined trajectory, the formation of surface
features $via$ laser-driven self-organization phenomena has gained significant
research interest during past decades owing to practically attractive
simplicity, fabrication scalability and ability of such an approach to create
diverse regular or random surface morphologies with characteristic nanoscale
footprints Stoian and Colombier (2020); Stoian and Bonse (2023). Laser-induced
periodic surface structures (LIPSSs; also referred to as ripples) discovered
in 1965 Birnbaum (1965) shortly after intensification of the studies related
to laser-matter interaction represent remarkable example of such self-
organization driven by pulsed (or even CW Nemanich  _et al._ (1983)) laser
radiation on the surface of practically all types of materials Buividas  _et
al._ (2014); Bonse  _et al._ (2016); Bonse and Gräf (2020). LIPSSs usually
appear as a (quasi)regular grating-type surface morphology aligned
perpendicularly or along the polarization vector of the incident radiation
depending on the dominating contribution of the effects driven self-
organization. In most cases, these effects have ”electromagnetic” nature
explaining the periodical surface ordering $via$ interference of the incident
radiation with the surface/scattered waves that yield a characteristic LIPSSs
periodicity $\Lambda$ close to the laser wavelength $\lambda$ used. Specific
experimental conditions (such as texturing in liquids) or processing regimes
driving the laser-irradiated material into the nonequlibrium state and
facilitating interference of the counter-propagating surface waves allow to
shrink the grating periodicity down to deep subwavelength values
($\Lambda<<\lambda$; high spatial frequency LIPSSs). Supra-wavelength surface
patterns with the periodicity $\Lambda>\lambda$, which formation indeed falls
outside electromagnetic scenario, were also reported on the surface of diverse
material manifesting themselves as universal phenomenon and unveiling
complexity of the laser-driven self-organization processes that are yet far
from complete understanding Tsibidis  _et al._ (2016); Xu  _et al._ (2019);
Zhang  _et al._ (2021).

Monocrystalline Si (c-Si), a critically important semiconductor widely applied
in variety of optoelectronic and nanophotonic devices Green  _et al._ (2021);
Baranov  _et al._ (2017), was widely studied in the context of LIPSSs
formation revealing the ability to produce on its surface both high spatial
frequency LIPSSs Le Harzic  _et al._ (2005); Shen  _et al._ (2008); Le Harzic
_et al._ (2011); Straub  _et al._ (2012); Hamad  _et al._ (2014); Meng  _et
al._ (2017); Yiannakou  _et al._ (2017); Zhang and Sugioka (2019); Kesaev  _et
al._ (2021); Borodaenko  _et al._ (2021, 2022) as well as quasi-regular supra-
wavelength patterns Ma  _et al._ (2014); Zayarny  _et al._ (2016); Nivas  _et
al._ (2017, 2018); Allahyari  _et al._ (2020); Nivas  _et al._ (2021); Hu  _et
al._ (2022); Kawabata  _et al._ (2023). The latter type of the structures was
generally explained by hydrodynamic processes Tsibidis  _et al._ (2015a), yet
their ordering along polarization direction and evident correlation between
the characteristic periodicity and laser wavelength were established Nivas
_et al._ (2018) reflecting the lack of complete understanding of the
underlying physical processes driven morphology self-organization. In this
respect, more systematic studies targeted at unveiling the role of
hydrodynamic and electromagnetic processes in formation of supra-wavelength
structures are required to achieve full-scale control over the surface
morphology crucial for obtaining desired optical properties as well as device
performance optimization.

In this paper, we systematically studied fs-laser processing of c-Si immersed
in methanol revealing that the electromagnetic processes dominating at initial
steps of the progressive morphology evolution define the onset of the
hydrodynamic processes and resulting morphology upon subsequent multi-pulse
exposure. In particular, under promoted exposure regular subwavelength LIPSSs
were shown to evolve through the template-assisted development of the
Rayleigh-Plateau (R.-P.) hydrodynamic instability in the molten ridges
creating quasi-regular surface patterns with supra-wavelength periodicity and
alignment along polarization direction of the incident light. Subsequent
exposure promotes fusion-assisted morphology rearrangement resulting in spiky
surface with random orientation, yet constant inter-structure distance
connected with LIPSS. Along with the insight onto the physical picture driving
the morphology evolution, our experiments also demonstrate that the resulting
quasi-regular and random spiky morphology can be tailored by the
intensity/polarization distribution of the incident laser beam allowing to
achieve diverse hierarchical surface morphologies with reduced reflectivity in
the visible and shortwave IR (SWIR) spectral ranges. In contrast to the well-
studied fs-laser texturing of c-Si in air demonstrating similar combination of
the electromagnetic and hydrodynamic processes driving morphology evolution,
the methanol strongly reduces efficiency the silicon oxidation as well as
allows to achieve larger density of nanostructures per surface cite defined by
initially subwavelength LIPSSs periodicity. Finally, using the developed
single-step fabrication strategy we produced a vertical p-n junction Si
photodetector with an active laser-patterned area providing enhanced near-IR
photoresponse and expanded operation window without annealing post-treatment
under room temperature conditions and zero bias voltage.

##  II Results and discussion

Figure 1:  (a) Schematically illustrated procedure of fs-laser nanotexturing
of monocrystalline Si in methanol. (b,c) Series of top-view SEM images of the
spotted Si surface modifications produced by linearly polarized Gaussian beam
and azymuthally polarized CV beam at fixed fluence of $F$=0.18 J/cm2 and
variable number of applied pulses per site $N$ (that is indicated near each
image). Scale bar in panels (b) and (c) corresponds to 0.5 and 2 $\mu$m,
respectively. One quarter of the circle-shape morphology produced with the CV
beam is shown for clarity. (d) Sketch demonstrating key steps behind laser-
driven morphology transition of the Si surface from the ordered subwavelength
LIPSSs to self-organized spikes. (e) In-plane maps of the absorbed laser
energy $\propto$E${}^{2}\cdot$Im[$\epsilon$] in the vicinity of the LIPSS
ridges of variable morphologies. White contour highlights the modeled
morphologies (elongated elliptical pitches in the Si wafer and circularly
shaped protrusions). Double-side arrows indicate the polarization direction.
The obtained maps were averaged over several cross-sections calculated at
variable depth below Si surface. (f) Schematic representation of one half of
the period of the instability used for the estimations.

###  II.1 Formation of spiky Si under static irradiation conditions: onset of
hydrodynamic processes in LIPSSs

We started from systematic studies of the fs-laser ablation of Si in methanol
under static (or spotted) irradiation conditions, where laser beams with
either a Gaussian- or a donut-shape intensity profiles and variable
polarization distributions (further referred to as Gaussian and cylindrical
vector (CV) beams) were applied to expose certain sites of the Si surface
(Fig. 1a). For simplicity, to illustrate the key processes underlying the
morphology modulation, namely, transition from the LIPSSs to randomly arranged
spiky morphology, we fixed laser fluence at $F$=0.18 J/cm2 (that is larger
than the single-pulse ablation threshold of Si in liquid; Borodaenko  _et al._
(2021)) and varied the number of applied pulses per site $N$. Under such
irradiation conditions, any substantial modifications of the surface start at
$N>$5 appearing as the subwavelength LIPSSs that exhibit periodicity
$\Lambda$=260$\pm$30 nm and are arranged perpendicularly to the polarization
direction (left panel, Fig. 1b). Consequently, azimuthally polarized CV beam
imprints donut-shaped areas containing radially oriented LIPSSs (left panel,
Fig. 1c). The LIPSSs were previously suggested to originate from interference
of the incident radiation with surface plasma waves supported at the interface
between surrounding liquid (methanol, in this case) and photoexcited layer of
Si with the dielectric permittivity modified by increased concentration of
free carriers Borodaenko  _et al._ (2021). Subsequently incident laser pulses
are absorbed by the LIPSS ridges resulting in their heating and partial
melting. Molten ridges of a certain size are expected to become
hydrodynamically unstable that results in modulations of their height with a
characteristic period $\Lambda_{R.-P.}\approx$ 550-700 nm associated with the
development of the R.-P. instability Plateau (1873); Rayleigh (1892); Kulchin
_et al._ (2014); Pavlov  _et al._ (2020). These height/width modulations are
clearly seen on the surface morphologies imprinted with both Gaussian and CV
beams at $N>$25 (middle panels, Fig. 1b,c) and are expected to facilitate
light absorption of the subsequently incident laser pulses. This results in
local fusion of the neighboring protrusions to spiky features. The process
continues upon subsequent surface irradiation eventually leading to the
formation of self-organized nanotextured surface covered with a randomly
arranged protrusions (further referred to as spiky Si). Sketch provided in the
Figure 1d graphically illustrates the main steps behind transition from the
ordered subwavelength LIPSSs to self-organized textures. To justify the
deductions regarding such laser-induced morphology evolution, its effect on
the modification of the laser radiation absorption was first analyzed by
numerically solving Maxwell equations with a commercial electromagnetic solver
(Lumerical, Ansys). As initial step, we considered smooth Si LIPSSs in the
form of the nanotrenches with semi-elliptical cross-section arranged with a
periodicity of 260 nm perpendicularly to the polarization direction of the
normally incident plane wave and calculated in-plane near-surface distribution
of the absorbed laser energy $\propto$E${}^{2}\cdot$Im[$\epsilon$] (E is an
EM-field amplitude; $\epsilon$ is dielectric permittivity of silicon) in their
vicinity. These calculations clearly show preferential absorption of the
deposited laser energy by the LIPSSs ridges (left panel, Fig. 1e) as well as
rearrangement of the absorbed energy profile once the R.-P. modulations and
larger fused nanostructures appear (middle and right panels, Fig. 1e). In
additional, both types of structures appeared to enhance laser radiation
absorption promoting material melting and fusion.

Let us next justify the onset of the R.-P. instability developing in the
molten LIPSS ridges with a characteristic period $\Lambda_{R.-P.}\approx$
550-700 nm according to the experimental data (middle panels; Fig. 1b,c). We
considered a ridge having at the initial state (i.e., before the instability
starts developing) a half-cylindrical shape, as shown in the top panel of Fig.
1f, while at the final state each half-period of the destabilised ridge was
approximated with a half-cone. The precise estimation of the Rayleigh-Plateau
destabilisation requires the information about the contact angle of liquid
silicon on solid silicon substratePavlov  _et al._ (2020), which is not known
and most probably cannot be precisely identified due to the presence of
silicon dioxide Fujii  _et al._ (1999). Hence, we assessed the characteristic
destabilisation time $t_{i}$ and possible range of the characteristic periods
$\Lambda_{R.-P.}$ based on the comparison between the surface energy in the
initial and final states. In doing this, we supposed that the volume of the
considered ridge does not change during the R.-P. destabilisation enabling the
estimation of the ratio between the initial radius $R_{0}$ and the maximal
radius of the cone in the final state $R_{1}$. From $\frac{1}{2}\pi
R_{0}^{2}\ell=\frac{1}{2}\frac{1}{3}\pi R_{1}^{2}\ell$ follows that
$R_{1}=\sqrt{3}R_{0}$. A destabilisation is only possible if it is
energetically advantageous for the system. Only such periods of the
instability $\Lambda$ can develop, for which the surface energy decreases upon
the shape transformation. No other kinds of energy are considered, since the
surface tension dominates on the submicrometer scale. The surface energy of
the side surface of a half-cylinder is $\mathcal{E}_{0}=\pi R_{0}\ell\sigma$
and in the final state the energy of the side surface of the half-cone is
$\mathcal{E}_{1}=\frac{1}{2}\pi R_{1}a\sigma$, where the surface tension of
liquid silicon $\sigma\approx 0.7\,...\,0.8\,N/m$ Eustathopoulos and Drevet
(2013) and the side wall of the cone is $a=\sqrt{\ell^{2}+R_{1}^{2}}$. From
the conditions that the energy difference must be
$\mathcal{E}_{0}-\mathcal{E}_{1}>0$ and $\ell=\Lambda_{R.-P.}/2$ follows that
only periods with $\Lambda_{R.-P.}>6R_{0}$ are possible. This estimation well
fits the experimentally observed periods of the instability $\approx
0.6\,...\,0.7\,\mu m$ at $R_{0}\approx 0.1\,\mu m$.

For the estimation of time $t_{i}$ the instability with a given period
$\Lambda_{R.-P.}$ is needed to develop, we supposed that the gain in the
energy due to the reduction of the surface limits the work of the friction
forces $A=Fs$, which appears due to the motion of the viscous melt Gurevich
(2016). Here $s\sim\ell$ is the distance, at which Si atoms are transported
upon the instability, and the friction force is estimated with the Newton’s
law as $F=\eta Av/R_{0}$, where the viscosity of liquid silicon
$\eta=0.7\,...\,0.9\,mPa\,s$ Sasaki  _et al._ (1995), the average flow
velocity of the melt on the surface is $v\approx s/t_{i}$, and the area of the
moving liquid $A\approx\pi R_{0}\ell$. With $\ell=\Lambda_{R.-P.}/2$ this
criterion can be rewritten as:

$\dfrac{\eta\pi\Lambda_{R.-P.}^{3}}{8t_{i}}\lesssim\sigma\pi
R_{0}\dfrac{\Lambda_{R.-P.}}{2}\left(1-\dfrac{\sqrt{3}}{2}\left(1+12\dfrac{R_{0}^{2}}{\Lambda_{R.-P.}^{2}}\right)\right).$
(1)

The term in the brackets in the equation (1) is of the order of one, and the
equation can be simplified as

$t_{i}\gtrsim\dfrac{\eta\Lambda_{R.-P.}^{2}}{\sigma R_{0}}.$ (2)

Substituting the experimentally observed period of $\Lambda_{R.-P.}\approx
0.6\,...\,0.7\,\mu m$ we obtain that the instability develops within few
nanoseconds that agrees with the experimental assessments of the
characteristic solidification time $t_{m}$ during which the Si exposed with a
fs-laser pulse remains in the molten state, thus allowing the instability to
develop Gundrum  _et al._ (2007). This time can be roughly estimated based on
the assumption that the temperature in the molten Si ridge is $T_{1}\approx
2T_{m}$, while the temperature of the solid substrate in the proximity of the
molten ridge $T_{2}\approx T_{m}$, where the $T_{m}$ is the Si melting point.
We supposed that after the end of the laser pulse the heat conduction is the
only mechanism of cooling and use the Fick’s laws of diffusion, in which the
Laplace operator is approximated as $\nabla^{2}T\approx T_{m}/R_{0}^{2}$ and
the time derivative of the temperature $\dot{T}\approx T_{m}/t_{m}$. With the
thermal diffusivity in liquid silicon $D_{T}\approx 0.1\,cm^{2}/s$ Yamamoto
_et al._ (1991) we estimate $t_{m}\approx R_{0}^{2}/D_{T}\sim 10^{-9}\,s$,
which is of the order of estimated time required for the development of the
instability and agrees with the previously reported data Gundrum  _et al._
(2007).

According to the performed analysis, the development of the instabilities with
larger periods is evidently limited by the solidification time $t_{m}$ as well
as the characteristic LIPSSs morphology (periodicity and ridge size; Eq.
(2))). This means that the regulation of the laser-processing conditions that
define the surface morphology at initial state (i.e. before the instabilities
start to develop) allows to control the resulting morphology of the self-
organized textures, such as average size and density of the spiky features. At
the same time, larger applied fluences as well as destabilization of the
LIPSSs through a fusion-assisted formation of the higher light-absorbing
features evidently will increase the size of the molten pool and its
solidification time making possible the development of the instabilities with
larger wavelengths (Fig. 1e).

###  II.2 Formation of spiky Si under dynamic irradiation conditions:
correlation between irradiation conditions, nanomorphology evolution and
optical properties

Figure 2:  (a) Schematic illustration of the Si wafer texturing in methanol
using dynamic irradiation conditions and various laser beams. (b-d) Evolution
of the surface morphology of the Si wafer processed in methanol by Gaussian-
shape linearly polarized fs-laser pulses at $F$=0.146 J/cm2 (regular LIPSSs),
0.155 J/cm2 (destabilized LIPSSs) and 0.177 J/cm2 (spiky Si). Bottom panels
provide FFT analysis of the main image as well as close-up tilt-view SEM
images of the corresponding surface morphologies. Fixed scanning speed
$\nu$=50 $\mu$m/s and pulse repetition rate $\kappa$=1 kHz were used for
surface patterning. Scale bar in top-view and tilt-view SEM images in the
panels (b)-(d) corresponds to 2 and 0.5 $\mu$m, respectively.

The observed surface morphologies including regular and destabilized LIPSSs as
well as disordered spiky Si can be expanded over practically relevant areas
under dynamic irradiation conditions, namely, by scanning the Si surface by a
laser beam diameter $d$ at a constant speed $\nu$ and pulse repetition rate
$\kappa$ (Fig. 2a). In fact, both parameters define the number of pulses
$N$=$d\kappa$/$\nu$ applied per surface site, similarly to the case of static
irradiation conditions discussed in the previous section. Moreover, once the
instability development is related to the amount of the molten phase of the
material, tailoring the laser fluence $F$ within a certain range above the
ablation threshold also allows to tune the resulting surface morphology.
Series of top- and side-view SEM images in Fig. 2b-d illustrate the ability to
reproduce the main discussed morphologies by scanning the Si surface with a
linearly polarized Gaussian beam along meander-like trajectory at the inter-
line spacing of 2.5 $\mu$m, $\kappa$=1 kHz, $\nu$=50 $\mu$m/s and varying $F$
(Fig. 2b-d). The obtained SEM images of the surface morphologies were also
subjected to Fast Fourier Transform (FFT) analysis clearly showing peaks
related to the regular LIPSSs as well as those associated with the periodic
modulations caused by the R.-P. instability (Fig. 2c,d). FFT analysis shows
that the intensity of the latter peaks grows with the applied fluence $F$,
while protrusions mainly follow the direction perpendicular to the LIPSS
orientation. At laser fluence of $F$=0.18 J/cm2 completely disordered spiky Si
surface can be produced as evidenced from the FFT analysis (Fig. 2d).

Performed analysis also highlights that upon increasing the number of applied
pulses electromagnetic processes underlying formation of the ordered LIPSSs
are gradually replaced by the hydrodynamic ones that evidently dominate at
larger $N$. Noteworthy, further increase of the number of applied pulses
(and/or laser fluence $F$) promotes melting and fusion of the neighboring
protrusions resulting in increase of their geometric size and corresponding
decrease of their density. In fact, increase of the laser fluence $F$ from
0.166 (minimal fluence required to achieve spiky Si at $\nu$=50 $\mu$m/s) to
0.199 J/cm2 decreases twice the density of the spiky features (from 2.9 to
1.53 structures per $\mu$m2). The increase in the average distance between the
spiky features with time agrees with the theory of coarsening droplets on a
plane predicting the distance growth $\propto t^{\beta}$ with $\beta\lesssim
3/8$ Otto  _et al._ (2006). At the same time, at moderate fluence (or $N$) the
simultaneous contribution of electromagnetic and hydrodynamic processes drives
formation of unique quasi-regular hierarchical morphologies, where LIPSSs
ridges act as sites for templated dewetting _via_ development of the R.-P.
instability resulting in the largest density of structures per surface area.

Figure 3:  (a) Series of top-view SEM images of the spotted Si surface
modifications produced by circularly polarized Gaussian beam at fixed fluence
and variable number of applied pulses per site $N$. (b) SEM images of the Si
surface morphology processed in methanol by circularly polarized fs-laser
pulses at variable number of applied pulses per site $N$. Bottom panels
provide FFT analysis of the main image as well as close-up tilt-view SEM
images of the corresponding surface morphologies. Fixed laser fluence $F$=0.16
J/cm2 and pulse repetition rate $\kappa$= 1 kHz was used for surface
patterning. Scale bars in panels (a) and (b) corresponds to 1 and 2 $\mu$m,
respectively.

Once the LIPSSs formation governs the subsequent morphology evolution, it is
reasonable to suppose that control over the morphology at the initial step
(that is largely defined by electromagnetically driven self-organization
processes) will substantially affect the resulting relief at the steps when
hydrodynamic processes will come into action. To support this deduction, we
carried out parametric studies on the Si wafer patterning in methanol using
circularly polarized Gaussian-shaped beam under static and dynamic irradiation
condition. Such irradiation conditions suppress the efficiency of the LIPSSs
formation along a certain direction as well as deepening of the nanotrenches
by subsequently incident pulses. This leads to the formation of the shallow
LIPSSs with azimuthally varying orientation at $N$=10 and $F$=0.16 J/cm2 (Fig.
3a, left panel). Noteworthy, similar relief was obtained by double-pulse
exposure of the Si wafer using ps-scale time delay between pulses and
orthogonal polarization direction Liu  _et al._ (2021). The produced
morphology is much less pronounced being compared to those obtained by
linearly polarized beam and same irradiation conditions ($N$ and $F$) (see
Fig. 1b). Subsequent laser exposure of this morphology promotes formation of
the disordered LIPSSs which height modulation can be driven by the
interference of the diverging/converging plasmon waves or R.-P. instabilities
with $\Lambda_{R.-P.}\approx\Lambda$ defined by reduced size of the ridges.
Eventually, further irradiation ($N>$50) initiates merging of the neighboring
elevations resulting in formation of rather smooth surface protrusions, which
size increases $via$ fusion upon subsequent exposure. Similar surface
morphologies were also produced with circularly polarized Gaussian beam under
dynamic irradiation conditions at fixed $F$ and $\kappa$ varying scanning
speed $\nu$ to provide the number of applied pulses $N$ per site ranging from
50 to 200 (Fig. 3b). These morphologies were analyzed with the FFT revealing
their complete directional independence as well as constant average distance
between spiky features that raises with $N$. In contrast to the surface
patterning with the linearly polarized beam, utilization of the circularly
polarized one can not provide regimes where evident formation of the LIPSSs
destabilized by the R.-P. instability can be justified. Additionally, the
obtained morphologies exhibit more shallow and smooth profile under
irradiation conditions similar to those used with linearly polarized beam,
revealing clear difference in the onset of hydrodynamic processes affected by
the LIPSSs formation at initial steps that confirms the previously made
deductions.

Figure 4:  (a) Schematic illustration of the CV beam clarifying the origin of
the inhomogeneous patterning of the Si surface under dynamic irradiation
conditions (scanning along a linear trajectory). (b-d) SEM images of the Si
surface patterned in methanol with an azimuthally polarized CV beam at fixed
fluence $F$=0.16 J/cm2 and variable scanning speed $\nu$= 150, 100, 50
$\mu$m/s respectively. (e) Scheme of the uniform Si surface patterning with a
CV beam at an offset between the linear scans equal to the half of the beam
diameter (approx. 5 $\mu$m). (f) SEM image of the surface morphology produced
using such scanning procedure, $F$=0.16 J/cm2 and $\nu$=100 $\mu$m/s as well
as FFT analysis of this image. Scale bar corresponds to 2 $\mu$m on the main
panels and 0.2 $\mu$m on the inset.

Similar Si patterning experiments were also carried out with an azimuthally
polarized CV beam under dynamic irradiation conditions revealing even broader
diversity of the obtained surface morphologies (see Fig. 4). In particular,
near-threshold fluence and moderate number of applied pulses allows to produce
the patterned tracks containing the radially arranged LIPSSs. Once the $F$ (or
$N$) increases, the observed grating-type morphology of the peripheral areas
of the track changes to densely arranged spiky surface. The feature can be
explained by the donut-shape intensity profile of the CV beam, allowing to
sequentially expose the Si surface by the front and back parts of the donut
upon scanning along linear direction. In the central parts of the linear scans
the polarization distribution appears to be identical for the front and the
back parts of the donut, being almost perpendicular to the scanning direction.
However, for peripheral area the front and the back part of the donut have
different polarization direction as it is schematically illustrated in Fig.
4a. Evidently, in the peripheral areas of the scan this creates two overlapped
LIPSS gratings with almost perpendicular orientations resulting in spiky
surface with the largest density of the surface features per surface area
(Fig. 4b). Further increase of the dose ($F$, $N$) leads to the previously
discussed hydrodynamic R.-P. destabilization and fusion-assisted formation of
larger surface features. Noteworthy, unveiled nanotexturing regime with the
overlapping LIPSSs can be expanded over larger surface areas upon scanning the
surface with CV beam along the meander-like trajectory and keeping the offset
between the linear scans equal to the half of the CV beam diameter (approx. 5
$\mu$m; Fig. 4e). The resulting surface morphology produced at $F$=0.16 J/cm2
and $\nu$=100 $\mu$m/s as well as FFT analysis of this image are illustrated
in Fig. 4f indicating presence of both the regular and hydrodynamically
destabilized LIPSSs with a random orientation in the formed surface pattern.

Figure 5:  (a) Representative FTIR reflectance spectra of the pristine and
laser-patterned monocrystalline Si. Various types of the surface morphologies
(regular #1 and destabilized LIPSSs #2 as well as the spiky Si #3) were
fabricated at $F$=0.16 J/cm2 and $\kappa$=1 kHz varying only the scanning
speed $\nu$ controlling the number of applied pulses per site $N$. Inset shows
SEM image of the FIB cross-sectional cut made perpendicularly to the ridge
orientation. (b) Average visible and SWIR reflectivity of various types of the
surface morphologies (regular #1 and destabilized LIPSSs #2 as well as the
spiky Si #3) produced using linearly (L), circularly (C) and azimuthally (A)
polarized beams and variable $F$ and $\nu$. (c) High-resolution TEM image of
the LIPSS ridges with their well-seen amorphous interface layer.(d)
Corresponding averaged Raman spectra of the laser-patterned Si surface sites
related to the mentioned morphologies before (solid curves) and after (dashed
curves) annealing at 600oC and 10-5 torr for 30 min. (e) Series of SEM images
of the Si surface processed in air at variable number of applied pulses $N$
and fixed $F$=0.16 J/cm2. Scale bar corresponds to 2 $\mu$m.

The produced spatially homogeneous surface morphologies were further analysed
through the way they interact with the incident unpolarized electromagnetic
waves. More specifically, we first compared the average reflectivity of the
laser-patterned surfaces produced with a linearly polarized beam in the
visible (0.5 - 0.7 $\mu$m) and shortwave IR (SWIR; 1 - 3 $\mu$m) spectral
regions (Fig. 5a). These studies showed that SWIR reflectivity gradually drops
once the morphology evolves from the regular subwavelength LIPSSs to the spiky
Si, which reflects the formation of the larger supra-wavelength structures.
Noteworthy, in the SWIR spectral range the regular LIPSSs satisfy the
criterion of the subwavelength grating, for which at wavelengths $\lambda_{R}$
larger than $\Lambda n_{Si}$ ($n_{Si}\approx$3.5 is refractive index of Si in
the SWIR spectral range Aspnes and Studna (1983)) this surface morphology can
be approximated by an effective medium with a gradually decreasing refractive
index when moving from the air interface towards the bulk. In this respect,
the removal of the refractive index jump decreases the Fresnel reflection at
the interface. However, optimal anti-reflective performance can be achieved
when the thickness of this effective medium defined by the height of the
surface structures $h$ will be larger than
$\lambda_{R}$(4$\sqrt{n_{Si}})^{-1}$. Considering the average height of the
ridges $\approx$ 200 nm for regular LIPSSs (inset; Fig. 5a), this explains the
increase of the reflectivity at $\lambda_{R}>$1 $\mu$m. Onset of hydrodynamic
processes allows to create dense supra-wavelength surface features that
efficiently traps the IR light through multiple reflections resulting in
average reflectivity R${}_{SWIR}\approx$ 6% for spiky Si ($vs$ only
$\approx$11 and 14 % for destabilized and regular LIPSSs, respectively; Fig.
5b). Noteworthy, all the considered types of the structures demonstrate rather
low reflectivity in the visible spectral range (down to 5% for destabilized
LIPSS; Fig. 5b), that can be associated with their light trapping performance
as well as certain structural transformation of the near surface layer
confirmed by combining transmission electron microscopy and Raman
microspectroscopy (Fig. 5c,d). In particular, both methods revealed the
formation of thin amorphous Si layer ($\alpha$-Si) with its thickness being
about 10-25 nm for the regular LIPSSs according to TEM studies. Moreover,
systematic Raman studies showed that the $\alpha$-Si amount decreases with the
increasing amount of laser pulses applied per surface site (decreasing $\nu$)
as evidenced from gradually decaying intensity of the corresponding Raman band
centered near 480 cm-1 (Fig. 5d; solid curves) Borodaenko  _et al._ (2021);
Liu  _et al._ (2023). Importantly, this observation indicates that promoted
laser exposure creates continuously growing amount of the molten Si that
recrystallizes over longer time period required for minimization of the
amorphous phase. In this respect, spiky Si morphology exhibits the smallest
amount of the $\alpha$-Si almost unaffected by annealing of the patterned Si
wafers in an oxygen-free (10-5 torr) atmosphere at 600oC for 30 min (dashed
curves; Fig. 5d). As can be seen, effect of the annealing is more evident for
regular and destabilized LIPSSs where initial content of the $\alpha$-Si is
larger. Systematically studied SWIR and visible-range reflectivity of the main
types of the surface structures (marked as #1 - #3 for regular and
destabilized LIPSSs as well as the spiky Si) produced using various laser
beams with linear (L), circular (C) and azimuthal (A) polarization within a
certain range of laser processing parameters ($F$,$\nu$) are summarized in
Fig. 5b revealing the ability to control optical properties of the Si surface
within the demanding spectral range upon proper surface micro-
(nano-)texturing.

Finally, let us highlight additional benefits of the Si laser texturing in
methanol. In fact, most of the studies on fs-laser processing of Si was
carried out under ambient environment revealing ability to create supra-
wavelength structures (also referred to as grooves) under accumulated
exposure. These structure manifested themselves as a universal phenomenon
being observed under diverse experimental conditions (such as visible and IR
laser wavelengths Allahyari  _et al._ (2020), angled excitation Nivas  _et
al._ (2021), shaped beams Nivas  _et al._ (2015), GHz bursts Kawabata  _et
al._ (2023), vacuum conditions Hu  _et al._ (2022), etc.) with their supra-
wavelength periodicity generally correlating with the incident wavelength
Nivas  _et al._ (2018). These structures at the initial step of their
formation are believed to originate from the similar hybrid
electromagnetic/hydrodynamic scenario unveiled here, yet alternative
explanation based on hydrothermal waves were also reported Tsibidis  _et al._
(2015b). Irrespectively of the chosen laser wavelength and processing
parameters, the reported characteristic distance between the supra-wavelength
grooves that evidently defines the average density of the spiky features in
between is about twice larger compared to the corresponding LIPSS period
$\Lambda\approx$0.8$\lambda$ upon processing in air. Taking into account the
observed LIPSS periodicity of $\Lambda\approx$0.55$\lambda$ and suggested
scenario of the morphology evolution $via$ destabilization and fusion of the
neighboring LIPSS ridges, more denser arrangement of the spiky features are
expected for Si surface processed in methanol. To provide direct comparison,
we performed laser texturing experiments of Si wafer using similar processing
parameters under ambient environment and static/dynamic irradiation conditions
(Fig. 5e). These results confirm the made deductions regarding (i) similarity
of the physical processes driving morphology reorganization revealed under
dynamic exposure that results in (ii) notably lower maximal density of the
spiky features (less than 1 structure per $\mu$m2; Fig. 5e) in the textures
produced in air. Moreover, increase of the dose results in contentiously
growing amount of the oxidized Si that can be crucial for certain applications
and is to be removed by ultrasonication or HF etching, in a sharp contrast to
the surface textures produced in methanol requiring no additional cleaning
procedures. Comparative energy-dispersive X-ray (EDX) analysis indicates an
order of magnitude larger content of oxygen (30$\pm$7 wt.% $vs.$ 3 wt.% at
$N$=50, $F$=0.16 J/cm2) in the surface textures patterned under ambient
environment, with a content of oxygen in the pristine Si wafer stored in air
of 2 wt.%. Additionally, processing in methanol leads to an small increase of
the carbon content only to 6 wt.% ($vs.$ 5 wt.% for non-patterned Si wafer)
that can be related to a thermal decomposition of the methanol molecules or
substitution of the OH-groups on the silicon surface with -OCH3 Wovchko  _et
al._ (1995).

###  II.3 Laser-patterned Si p-n junction photo-detector

Discussed benefits of the liquid-assisted laser texturing of Si highlight
practical attractiveness of the developed approach for diverse applications.
For example, nanotextured Si surface can be further functionalized with noble-
metal films (nanoparticles) to act as a substrate for optical sensing, where
the ability to control morphological/optical properties are highly demanded to
optimize the device performance for a certain pump wavelength Diebold  _et
al._ (2009); Borodaenko  _et al._ (2022); Erkızan  _et al._ (2022).
Alternatively, metal-free sensing and light-emitting devices empowered by the
rich optics of Mie resonances and benefiting from the absence of luminescence
quenching effects are also becoming popular research direction Alessandri and
Lombardi (2016); Tittl  _et al._ (2018); Mitsai  _et al._ (2018); Mironenko
_et al._ (2019); Dostovalov  _et al._ (2020). Silicon also represent an
important material applied in solar cells and photodetectors where the proper
laser-assisted nanotexturing can not only remove optical coupling losses
associated with an inherently high refractive index of the material, but also
provide additional defect-mediated light-absorption channels boosting the
device performance Sher  _et al._ (2011); Zielke  _et al._ (2012).

Figure 6:  (a) Schematically illustrated vertical p-n junction Si
photodetector with a laser-patterned active area. (b) Optical photograph of
the fabricated device. (c) Spectral dependence of the photoresponse (markers)
of the pristine $R_{flat}$ and laser-patterned $R_{spiky}$ devices. Solid
curve demonstrates spectral dependence of the photoresponse ratio
$r$=$R_{spiky}$/$R_{flat}$. (d) Normalized photoresponse as a function of the
laser pump power measured for pristine device at 850 nm pump wavelength (gray
markers) as well as for laser-patterned device at 850 (red markers) and 1250
nm pump wavelengths (orange markers).

We justified applicability of the developed liquid-assisted fs-laser texturing
of Si for improvement of the characteristics of the p-n junction Si
photodetector. Usually, extending the operation wavelength range and/or
enhancement of the absolute photoresponse are the most demanded outputs, that
are commonly achieved by nanostructuring-induced near-surface (shallow)
junction formation Juntunen  _et al._ (2016); Garin  _et al._ (2020); Seta?la?
_et al._ (2023) and Si hyperdoping accompanied with surface texturing Zhao
_et al._ (2023, 2020) when dealing with low photo-detection performance of the
pristine (unprocessed) Si-based devices in the UV and NIR/SWIR ranges,
respectively. Scheme of the resulted Si photo-detector and photograph of the
chip-packaged device with laser-patterned light-sensitive areas are presented
in Fig. 6a,b. For device realization, we choose the destabilized LIPSS
morphology providing the lowest reflectivity near 1000 nm as well as moderate
morphology-affected depth that is to be carefully control considering low
thickness (approx. 2 $\mu$m) of the top p-Si. Excessive texturing of this
layer can deteriorate the crystallinity of p-n junction area (space charge
region near the interface between n- and p-Si layers).

Measurements of the photoresponse as a function of the incident laser
wavelength (Fig. 6c) revealed the improved performance of the laser-textured
device (Rspiky) over pristine one (Rflat). For clarity, the obtained data is
also plotted as photo-response ratio, r=Rspiky/Rflat, showing its fast
increase with the incident light wavelength, with the maximal 2-fold
enhancement of the photoresponse at 1200 nm. Importantly, the laser patterning
makes the Si p-n junction to be sensitive to sub-band gap illumination at
least down to 1300 nm with the room-temperature photoresponse of about several
mA/W under zero bias condition (self-powered mode). The mechanism of such
improved NIR photo-sensitivity can be attributed to Urbach states and laser-
induced structural defects generated in morphology-modified and underlying
layers during the laser processing Li  _et al._ (2018). This results in a
lower photo-response of laser-patterned device as compared to the pristine
one, when shifting to the shorter wavelengths due to the pronounced surface
recombination rate for photo-generated carriers near the edge and side walls
of the Si protrusions facilitated by lower penetration depth of the laser
radiation. In accordance with Fig. 6c the specific threshold wavelength is 750
nm, where photoresponse ratio is equal to 1. As wavelength of the incident
light exceeding threshold value becomes comparable with characteristic period
of the Si featured ($\approx\Lambda_{R.-P.}$), the higher photoresponse could
be detected. This period matching results in spectral shifting of the
photoresponse peak value from the 750 to 850 nm with an additional local
maximum at $\approx 1100$ nm for the flat and spiky Si p-n junction photo-
detectors, respectively. An additional confirmation of the defect-related
enhancement of the NIR photoresponse is provided in Fig. 6d, demonstrating
dependencies of the normalized photoresponse as a function of the incident
laser power measured for both patterned and pristine devices at 850 and 1250
nm characteristic pump wavelengths. As can be seen, at photon energy above the
Si bandgap (850 nm pump), both devices demonstrate power exponents close to 1,
yet the data obtained for the laser-patterned device shows slightly sub-linear
trend, evidently owing to enhanced surface recombination. At the same time,
photoresponse of the laser-patterned device at sub-band photon energy (at 1250
nm) can be characterized by a relatively sharp, yet clear sub-linear power
dependence with exponential factor of 0.74, while the pristine Si p-n junction
is completely insensitive to such illumination due to the absence of the
defect states.

##  III Conclusions

Here, we demonstrated how simultaneous action of electromagnetic and
hydrodynamic processes driven by ultrashort multi-pulse laser exposure at the
monocrystalline Si interface can be used to control the resulting micro- and
nanoscale surface nanomorphology spanning from the regular LIPSSs to quasi-
ordered (or randomly arranged) spikes. Our studies clearly showed that the
electromagnetic processes (such as polarization-dependent excitation and
interference of the surface waves) dominating at initial steps of the
morphology evolution define the onset of the hydrodynamic processes and
resulting morphology upon promoted multi-pulse exposure. This results in
appearance of the quasi-regular morphologies having the surface features
defined by the hydrodynamic instability and oriented parallel to the
polarization vector of the incident radiation. Our studies add an important
brick into fundamental understanding of the interaction of ultrashort laser
pulses with the silicon that has been used for a long time as a key benchmark
material for such studies. In particular, our results clarify the origin of
formation of widely reported supra-wavelength surface features following
polarization direction of the incident radiation.

From application point of view, our work highlights practical benefits of
liquid-assisted laser processing of Si. In a sharp contrast to the well
studied processing of Si under ambient environment, methanol not only reduces
the efficiency of Si oxidation and removes debris from the nanotextured
surface without any post-processing steps but also facilitates formation of
the regular plasmon-mediated subwavelength LIPSSs with the periodicity
$\approx\lambda/2$ as well as denser quasi-ordered spiky features. Considering
wide applicability of silicon in optoelectronics, all-dielectric photonics and
optical sensors, such advanced maskless and straightforward nanotexturing
procedure is expected to be of high demand for future applications. As a good
demonstration of the practical applicability of the developed approach, using
direct laser patterning without any post-annealing and cleaning steps we
realized the self-powered vertical p-n junction Si photodetector with twice
larger photoresponse at sub-bandgap photon energies and expanded NIR operation
range.

##  IV Methods

###  IV.1 Laser patterning

Monocrystalline Si wafers were placed into a quartz cuvette filled with a
methanol and directly processed with a second-harmonic (515 nm) fs-laser (200
fs) pulse generated at 1 kHz pulse repetition rate by a regeneratively
amplified laser system (Pharos, Light Conversion). For certain experiments,
as-generated linearly polarized Gaussian-shape laser beam was shaped into a CV
beam by passing through a radial polarization converter ($S$-waveplate;
Beresna  _et al._ (2011)). The laser texturing was performed through the
static 4-mm thick layer of isopropanol with a Gaussian/CV beam focused onto
the sample surface with a dry microscope objective having numerical aperture
(NA) of 0.13. The size of the focal spot $D_{th}$ in the case of Gaussian-
shape beam was evaluated using Liu method Liu (1982). More specifically, we
plotted the squared diameter of the single-pulse Si surface modification as a
function of the incident pulse energy in logarithmic scale $D^{2}$-ln[$E$].
The beam size $D_{th}\approx$5 $\mu$m was obtained from the slope of the
linear fit of the obtained dependence. In the case of CV beam generated by the
$S$-waveplate, we used the Lambert function $W$ to calculate the inner and
outer radii of the focal-plane annular distribution Zhang  _et al._ (2017):

$r_{inner}=\sqrt{\frac{m}{2}}\sqrt{-W\left(0,-\frac{\left(e^{-m-2}m^{m}\right)^{1/m}}{m}\right)}\omega,$
(3)

and

$r_{outer}=\sqrt{\frac{m}{2}}\sqrt{-W\left(-1,-\frac{\left(e^{-m-2}m^{m}\right)^{1/m}}{m}\right)}\omega$
(4)

Then, the ratio of the areas of the Gaussian beam $S_{gauss}$=$\pi
D^{2}_{th}/4$ and the CV beam
$S_{CV}=\pi\left(r_{outer}^{2}-r_{inner}^{2}\right)$ for the focusing
conditions ($NA$=0.13) can be assessed to be $S_{CV}/S_{gauss}=$2.2.

###  IV.2 Characterization

Structural and morphological features of the laser-patterned surfaces were
characterized using SEM device (Ultra 55+, Carl Zeiss) equipped with an EDX
modality for chemical analysis. TEM studies (Titan 60-300, Thermo Fisher) were
carried out with a thin lamella prepared using using dual-beam (electron/ion)
device (Helios 450, Thermo Fisher). Preparation steps include (i) coverage of
the sight of interest with a protective Pt layer, (ii) FIB cutting and
thinning down to electron transparency and (iii) lamella extraction for TEM
imaging.

Micro-Raman spectroscopy (Integra Spectra II, NT-MDT) was carried out with a
CW laser pump centered at 473 nm. Linearly polarized laser radiation was
focused onto the sample surface with a dry microscope objective having
NA=0.28. Raman spectra were averaged over at least 20 surface sites for each
laser-patterned area.

Fast Fourier Transform (FFT) analysis of the SEM images of the LIPSSs and
spiky Si produced at variable irradiation conditions was performed with an
ImageJ package. The same software was applied to evaluate average density of
the self-organized structures using a find maxima tool.

Finite-difference time domain simulations were carried out to calculate the
absorption (E2Im[$\epsilon$], where E is an EM field amplitude and
Im[$\epsilon$] is the dielectric permittivity of Si) of the incident laser
pulses by the LIPSSs with variable morphologies. In particular, we considered
the smooth Si surface having several pitches with a semi-elliptical profile
(depth of 200 nm and width of 150 nm) arranged at the period of 260 nm that is
fully consistent with the experimental data. Destabilizations of the grating
morphology were modeled either as a local elliptical-shape protrusions
decorating the ridges or larger protrusions filling the space between
neighboring ridges (Fig. 1e). Si grating was placed in the background medium
with a refractive index of 1.33 corresponding to those for methanol Moutzouris
_et al._ (2014) and exposed from the top by a Gaussian-shape (1/e-diameter of
3 $\mu$m) pulse having the polarization perpendicular with respect to the
ridge orientation. Computational volume was limited by perfectly matched
layers.

Reflectivity of the laser-patterned surface in the visible (0.5 - 0.7 $\mu$m)
and SWIR (1 - 3 $\mu$m) spectral ranges was assessed using an integrated-
sphere spectrometer (Cary 5000, Varian) and Fourier-Transform IR spectrometer
(Vertex 80, Bruker) coupled to the IR microscope (Hyperion 2000, Bruker),
respectively.

###  IV.3 Fabrication and characterization of a Si photo-detector with a
vertical p-n junction

Monocrystalline n-type (resistivity of 0.1 Ohm$\cdot$cm) Si wafer with a
lateral size of 6$\times$6 mm2 with an epitaxially grown 2 $\mu$m thick p-type
Si top layer (resistivity of 10 Ohm$\cdot$cm) was laser-textured following the
previously described procedure to create a destabilized LIPSS morphology
within certain surface areas (Fig. 6a,b). Then, 200 nm thick Al film was
magnetron sputtered through the shadow mask to create a patched square-loop
top electrode. Similarly, 2 nm of Sb film covered with 100 nm thick Au layer
was deposited to form a filled square bottom electrode. Resulting device was
annealed in vacuum (base pressure of 5$\times$10-6 Torr) for 30 min at 400∘C
to improve surface adhesion and reduce contact resistance. Same procedure was
used to produce non-patterned (pristine) reference photodetector. Pristine and
patterned Si photo-detectors were chip-packaged using ultrasonic welding with
Al microwires.

The photo-responsivity of the Si p-n junction devices was probed under room
tempereture and zero bias voltage using spectrally tunable laser radiation
generated at 80 MHz pulse repetition rate by a femtosecond optical parametric
oscillator (TOPOL, Avesta Project LTD.). The output laser beam was shaped by a
lens to yield a pump spot diameter $\approx$ 60 $\mu$m. Different sites of the
laser-patterned and pristine devices were probed for statistical averaging of
the results. The incident power at the selected wavelength within the spectral
range from 700 to 1300 nm was measured by a Ge optical power meter (Newport).
The photocurrent was directly captured by a Keithley sourcemeter from the
illuminated devices. Photoresponse was calculated as the generated
photocurrent divided by the power of incident light. Attenuated laser lines
from the TOPOL setup were used to register the photoresponse $versus$ incident
optical irradiation power for the patterned and pristine Si p-n junction
photo-detectors.

## Conflict of interest

The authors declare no competing financial interests.

## Acknowledgements

This work was supported by the Russian Science Foundation (Grant no.
21-79-20075).

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