Nonlinear laser lithography for indefinitely large-
area nanostructuring with femtosecond pulses
Bu
¨
lent O
¨
ktem
1
†
, Ihor Pavlov
2,3
†
, Serim Ilday
4
, Hamit Kalaycıog
˘
lu
2
,AndreyRybak
2,3
,SeydiYavas¸
1
,
Mutlu Erdog
˘
an
1
and F. O
¨
mer Ilday
2
*
Dynamical systems based on the interplay of nonlinear feed-
back mechanisms are ubiquitous in nature
1–5
. Well-understood
examples from photonics include mode locking
6
and a broad
class of fractal optics
7
, including self-similarity
8
. In addition
to the fundamental interest in such systems, fascinating techni-
cal functionalities that are difficult or even impossible to
achieve with linear systems can emerge naturally from them
7
if the right control tools can be applied. Here, we demonstrate
a method that exploits positive nonlocal feedback to initiate,
and negative local feedback to regulate, the growth of ultrafast
laser-induced metal–oxide nanostructures with unprecedented
uniformity, at high speed, low cost and on non-planar or flexible
surfaces. The nonlocal nature of the feedback allows us to stitch
the nanostructures seamlessly, enabling coverage of indefi-
nitely large areas with subnanometre uniformity in periodicity.
We demonstrate our approach through the fabrication of tita-
nium dioxide and tungsten oxide nanostructures, but it can
also be extended to a large variety of other materials.
The fabrication of nanostructures on surfaces is of paramount
importance in nanotechnology and materials science
9
. There are
several established techniques, including photolithography, elec-
tron-beam lithography, imprint lithography
10
and laser interference
lithography
11
, as well as non-conventional approaches such as self-
assembly
12
and direct laser writing
13
. These techniques require
either high-cost, complex systems or offer limited flexibility. An
alternative flexible and potentially very low-cost method is laser-
induced periodic surface structuring (LIPSS). The first observation
of LIPSS dates back to 1965
14
. However, after almost 50 years and
a large body of published work that has demonstrated LIPSS on
various metals, semiconductors and glasses
15–19
, the method
has not found widespread use due to the stubborn problem of
quality control
18,19
.
Despite the evident role of self-assembly in the LIPSS process,
uniformity and long-range order remain poor, a problem we ident-
ified as originating from the fact that the structures are initiated
from multiple seed locations concurrently and independently,
thereby producing an irregular pattern. Because the process is irre-
versible, without self-correction, these irregularities become frozen.
Our solution to this relies on carefully exploiting feedback mechan-
isms to tightly regulate the formation of nanostructures induced by
ultrashort pulses. This process can be summarized in three steps.
(1) The laser beam, with a peak intensity close to the ablation
threshold for titanium, is focused on a titanium surface, where it
is scattered by existing nanostructures or any surface defects
15
.
The interference of the scattered and incident fields leads to inten-
sity variations in the immediate neighbourhood of the scattering
point. (2) At points where the threshold intensity for ablation is
exceeded, titanium reacts rapidly with O
2
from the air, forming tita-
nium dioxide (TiO
2
). The use of ultrashort pulses is necessary to
ensure this process occurs faster than heat diffusion, as this can
smear out the nanometre-scale localization of the deposited laser
energy. The first two steps constitute a positive feedback loop
(Fig. 1a). As the nanostructure grows, so does its scattering power.
(3) The growth mechanism also has an imbedded negative feedback
loop. As TiO
2
grows on top of the titanium, penetration of O
2
through the oxide layer decreases exponentially, decelerating and
eventually halting the growth process (Fig. 1b).
The experimental set-up (Fig. 2 and Methods) consists of an
ultrafast fibre laser
20
coupled to a microscope system for real-time
observation of the nanofabrication process. All experiments were
guided by a semi-phenomenological theoretical model developed
by us. The main features of the model are summarized in the follow-
ing and in the Methods, and the details are discussed in the
Supplementary Information. Scattering of the incident laser field
from a single point is modelled as dipole radiation
15,16
, with the rela-
tive height of the surface point setting the scattering amplitude. This
is confirmed experimentally (Fig. 3a) and numerically (Fig. 3b) by
the structure formed around an isolated scatterer. The polarization
of the laser sets the dipole radiation pattern, which results in regu-
larly spaced nanolines parallel to the laser polarization. Circular
polarization, which can be visualized as rotating linear polarization,
results in an array of nanocircles. The period of the structures ranges
between 600 and 900 nm, depending on the film thickness. Because
the film is much thinner than the wavelength of light, light experi-
ences a sort of a weighted average (effective) index of refraction
which depends not only on that of the thin film, but also on
those of the air and the substrate above and below the film, respect-
ively. The total field at any surface point is the sum of the incident
field and the total scattered field, which is given by the integral of the
product of the surface height and the incident field over the entire
surface. This surface integral is the mathematical origin of the non-
local feedback. The amplitude of the dipole radiation decays with
distance, which sets a finite range for this nonlocal feedback, such
that two distant points on the surface have negligible mutual influ-
ence. For this reason, processing a large area at once results in struc-
tures with poor long-range order, as seen experimentally (Fig. 3c)
and numerically (Fig. 3d). By limiting the size of the laser beam
to 10 wavelengths, we ensure that even the most distant points
under the beam have contributions to their mutual fields. This
way, the problem of independent structure initiation is solved.
At points where the total intensity exceeds the ablation threshold
(1 × 10
12
Wcm
22
), the metal (titanium) disassociates from the
solid phase under the non-equilibrium conditions created by the
ultrashort pulse and reacts with O
2
from the ambient atmosphere,
1
UNAM—Institute of Materials Science and Nanotechnology, Bilkent University, 06800 Ankara, Turkey,
2
Department of Physics, Bilkent University, 06800
Ankara, Turk ey,
3
Institute of Physics, National Academy of Science of Ukraine, Kiev, Ukraine,
4
Department of Micro and Nanotechnology, Middle East
Technical University, 06800 Ankara, Turkey;
†
These authors contributed equally to this work.
*
e-mail: ilday@bilkent.edu.tr
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PUBLISHED ONLINE: 20 OCTOBER 2013 | DOI: 10.1038/NPHOTON.2013.272
NATURE PHOTONICS | VOL 7 | NOVEMBER 2013 | www.nature.com/naturephotonics 897
© 2013 Macmillan Publishers Limited. All rights reserved.
Substrate
Ti film
TiO
2
y
x
z
y
Substrate
Ti film
O
2
O
2
O
2
Nanoline
width
Nanoline
period
z
a
b
Figure 1 | Conceptual model. a, Schematic of the nanostructure formation process as a laser beam is scanned ov er the surface. b, Schematic showing a
cross-sectional view of the surface, depicting the deceleration of the growth process due to negative feedback.
Similariton
fibre laser
Acousto-optic
modulator
Pump
diodes
Stretch fibre
Isolator
Multimode
combiner
Double-clad
Yb-doped fibre
Yb-fibre
preamplifier
Collimator
Halogen lamp
Half-wave and/or
quarter-wave plate
Low NA objective
(×10 magnification)
High NA objective
(×100 magnification)
Short-pass filter
cuto at 980 nm
Two-axis, motorized
translation stage
Beamsplitter
EMCCD
camera
Neutral density filter
Grating
compressor
Figure 2 | Experimental set-up. An amplified fibre laser is coupled to a custom-built, computer-controlled optical microscope set-up. EMCCD, electron-
multiplying charge-coupled device; NA, numerical aperture.
LETTERS
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forming metal oxide (TiO
2
) of an amount that is proportional to the
laser-activated metal (titanium) or available O
2
at that point, which-
ever is smaller. Here, we simply refer to this controlled transformation
as ablation, because similar physical processes underlie it, even
though the metal is not removed, but is chemically transformed. As
a result of the ablation threshold, no processing of the surface
should occur between the nanolines, where partially destructive inter-
ference leads to the total intensity being below the ablation threshold.
The presence of this threshold, which was confirmed experimentally
(Fig. 3; Supplementary Section ‘Experimental evidence for the
threshold for intensity’), is the main source of nonlinearity.
When scanning a small-diameter beam, the nanostructures are
created sequentially, with existing structures creating new structures,
similar to the toppling of dominoes. This enables the formation of
extremely uniform nanostructures (experimental and simulated
results are shown in Fig. 3e and f, respectively). Moreover, it is
possible to tile indefinitely large areas with nanostructures,
without a discernible reduction in long-range uniformity when
using a small laser beam. We scan the beam along a line, then
shift the beam laterally while still preserving a partial overlap with
the previous point, and then scan again parallel to the line of the
scan (with partial overlap being maintained all along the way with
the first line of the scan). This can be visually observed in
Supplementary Movie S1, where the red disk represents the beam
location and verified experimentally (Supplementary Movie S2).
Further evidence of the role of nonlocal feedback lies in the fact
that the new structures form a tilted front and the nanolines
become distorted into a wavy pattern at the end of each scan line
due to incomplete nonlocal feedback.
The nanostructure formation mechanism exhibits a significant
degree of robustness against distinct types of perturbations. First,
the resultant field at any point is formed collectively by the entire
surrounding area, so the contributions of isolated defects or rough
patches on the surface are easily overwhelmed. When a defect is
placed along the beam path (under conditions otherwise the same
as in Fig. 3f ), the nanolines suffer only minor distortions
(Fig. 3g). Defects encountered in Supplementary Movie S2
provide experimental confirmation. Second, Supplementary Movie
S2 shows that the beam focus was not maintained well during scan-
ning due to the poor mechanical stability of our set-up. However,
key features, such as nanoline period and width, are independent
of laser power (see Supplementary Section ‘Insensitivity of the
nanostructure features to laser power and exposure time’ for direct
experimental confirmation). Because of this insensitivity, a partial
loss of focus during scanning is inconsequential. In fact, we found
the standard and Allan deviations of the nanoline period of this
structure to be 0.9 nm and 0.14 nm, respectively (for details see
Supplementary Section ‘Characterization of the uniformity of the
nanostructures’). Third, as a result of the negative feedback
mechanism, the growth of the nanostructures saturates at a given
height. Even minutes-long exposure to a stationary beam or multiple
scans of the laser over the same area have no discernible effect
(Supplementary Movie S4). Robustness against a range of pertur-
bations is a coveted feature of nonlinear systems
5
that is extremely
difficult to achieve in strictly linear systems.
A diverse range of nanostructures have been fabricated using this
approach. A photograph of nanostructures covering a 3 mm
2
area,
fabricated on a thin and flexible glass slide, is presented in Fig. 4a.
0
10
0 20
0
10
0 50 100 150 200 250
40
0
10
0 50 100 150 200
x (µm)
02040
x (µm)
02040
x (µm)
y (µm)
e
f
g
0 4
0
4
8
0 100 200 300
8
0 4
0
4
8
0 50 100 150
8
a
b
c
d
Figure 3 | Nanostructure formation dynamics. a,b, SEM image of the experimental r esults (a) and numerical simulation results (b) of nanostructures formed
around an isolated scatter er by a few, high-energy pulses with linear polarization. c,d, SEM image of the experimental results (c) and numerical simulation
results (d) of nanostructures obtained with a large and stationary laser beam. e, SEM image of uniform nanostructures obtained by scanning a small laser
beam. f, Numerical simulation results of nanostructures obtained by scanning a small laser beam. g, Numerical simulation results showing robustness of the
nanostructure formation against a defect, showing minor distortion and quick subsequent recovery. Colour bars indicate height in nanometres.
NATURE PHOTONICS DOI: 10.1038/NPHOTON.2013.272
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A scanning electron microscope (SEM) image of a section of the
same structure is shown in Fig. 4b. A mesh structure of titanium
dots surrounded by a mesh of TiO
2
is obtained by scanning
with a linearly polarized beam, followed by a second pass with
908-rotated polarization (Fig. 4c). Using circularly polarized light,
a regular array of nanocircles is obtained (Fig. 4d, Supplementary
Movie S4). An important advantage of this method is the capability
to create these structures on non-planar surfaces due to the insensi-
tivity of the process to variations in laser intensity. This is in clear
contrast to conventional lithography techniques. As a demon-
stration, we scanned the beam over a titanium-coated optical fibre
(125 mm diameter), creating structures despite the very strong
surface curvature (Fig. 4e). Synchronously rotating the polarization
during a circular scan results in optical resonator-like patterns
(Fig. 4f), which could be interesting given the high index of TiO
2
.
The structures can be imprinted on a substrate such as silicon,
where the titanium film is used only as a transfer material
(Fig. 4g). If desired, titanium can be selectively etched away after-
wards. Although we focused on titanium in this work, our approach
should be applicable to other materials. Indeed, Fig. 4h shows tung-
sten oxide structures fabricated on a tungsten surface.
To conclude, we report a simple, low-cost and high-speed
method based on exploiting naturally occurring feedback mechan-
isms for the creation of metal–oxide nanostructures with femtose-
cond pulses. We have demonstrated periodic nanostructures
covering areas measuring square millimetres with 1 nm long-
range uniformity on bulk and thin metal films on flexible substrates,
as well as on the surface of an optical fibre, proving that non-planar
surfaces can be processed. These special features, primarily the
ability to process curved surfaces, are nominally not achievable
with conventional techniques. In addition, our technique exhibits
a substantial degree of robustness against defects and perturbations.
This constitutes another demonstration that unique technological
capabilities can emerge naturally by exploitation of nonlinear
photonic systems
7
. Although we optimized the process for the oxi-
dation of titanium and tungsten under a regular atmosphere, many
metals, semiconductors and dielectrics have been shown to support
LIPSS formation
15–19
. In principle, any of these materials can be sub-
jected to a variety of chemical reactions under a suitable atmosphere
to fabricate nanostructures from a virtually inexhaustible list of
material compositions. The fabricated nanostructures can find
applications in plasmonics
21
, plasmonic nanolithography
22
,
photon detection
23
, nanophotonics
24
, memristors
25
and metallic
nanostructures
26
for nanoelectronics, control of cell behaviour
through patterned surfaces
27
and in low-cost fabrication of highly
ordered TiO
2
structures, which have been shown to significantly
increase the efficiency of dye-sensitized solar cells
28
.
Methods
Laser set-up. The laser source was a home-built Yb-doped fibre laser, operating at a
central wavelength of 1,060 nm and generating pulses with up to 1 mJ energy at
1 MHz, which can be compressed to 100 fs (ref. 20). The powers incident on the
samples ranged from 100 mW to 1 W. The pulse-to-pulse power stability was on the
order of 0.05% (measured from 3 Hz to 250 kHz).
Integrated laser microscope set-up. The pulses from the laser were coupled into a
modified inverted microscope (Nikon Eclipse Ti) using a dichroic mirror with high
reflectivity for 1 mm and high transmission of visible light. The focused spot size was
set to 12 mm (full-width at half-maximum intensity) in most experiments. Beam
positioning was achieved by moving the sample on a dual-axis step-motor stage
(Thorlabs, MAX2 03) with a repeatability of 1 mm. The samples were illuminated
with a halogen source, and imaging was carried out with a ×100 oil-immersion
objective. The images were recorded with an electron-multiplying charge-coupled
device camera (Andor, Luca).
Theoretical model. The semi-phenomenological three-step model was based on an
integro-difference equation with decoupled timescales. The laser beam was modelled
as a Gaussian beam centred at a point (x
0
, y
0
) on the surface. When the nth pulse
of the pulse train was incident, it scattered from the surface protrusions and
depressions, described by the local height of titanium, h
n
(x, y ). The total laser
intensity was calculated for every point (x , y) on the surface by integrating the
contributions from the surrounding surface elements. Ablation occurs on a
picosecond timescale, much faster than thermal diffusion, which would otherwise
smear out the nanoscale localization of the absorbed laser energy. At points where
the laser intensity exceeded the ablation threshold, titanium was ablated from its top
surface down to the point where the intensity dropped below the ablation threshold.
The amount of O
2
available was calculated based on the thickness of the TiO
2
layer
at that point. Ablated titanium and O
2
react readily on a timescale much slower than
the ablation process, but faster than the arrival of the next pulse (1 ms). The amount
of TiO
2
formed was determined by the amount of ablated titanium and O
2
,
whichever was smaller. The surface profile was then updated as h
nþ1
(x, y). The entire
2 µm
30 µm
2 µm
30 µm
2 µm
50 µm
1 µm
30 µm
30 µm
2 µm
1 µm
3 mm
1 mm
a
c
e
g
b
d
f
h
Figure 4 | Examples of fabricated nanostructures. a, Photograph of
nanostructures covering an area of 1 mm × 3 mm (colouration is due to
diffraction of room light). b, SEM image of a portion of the same structure.
c, SEM image of mesh structure obtained by two scans of the beam with
orthogonal polarizations. d, Nanocircles (diameter, 370 nm) obtained with
circularly polarized light. e, Nanostructures fabricated on the side of a
titanium-coated optical fibre, demonstrating the capability to fabricate on
non-planar surfaces. f, Circular pattern of nanostructures obtained by
rotation of the polarization direction. g, Cross-sectional SEM image of
structures crea ted on a thin film of titanium on a silicon substra te,
showing imprinting of the nanostructures to the underlying substr ate.
h, Nanostructures obtained on a tungsten film ov er a glass substrate.
LETTERS
NATURE PHOTONICS DOI: 10.1038/NPHOTON.2013.272
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© 2013 Macmillan Publishers Limited. All rights reserved.
process was repeated for the (n þ 1)th pulse with an updated beam position (x
0
, y
0
).
A full account of the model is given in Supplementary Section ‘Detailed description
of the theoretical model’.
Received 13 November 2012; accepted 9 September 2013;
published online 20 October 2013
References
1. Bhalla, U. S. & Iyengar, R. Emergent properties of networks of biological
signaling pathways. Science 283, 381–387 (1999).
2. Hopfield, J. J. Neural networks and physical systems with emergent collective
computational abilities. Proc. Natl Acad. Sci. USA 79, 2554–2558 (1982).
3. Ferrell, J. E. Jr. Self-perpetuating states in signal transduction: positive
feedback, double-negative feedback and bistability. Curr. Opin. Cell Biol.
14, 140–148 (2002).
4. Mandelbrot, B. How long is the coast of Britain? Statistical self-similarity and
fractional dimension. Science 156, 636–638 (1967).
5. Kitano, H. Biological robustness. Nature Rev. Genet. 5, 826–837 (2004).
6. Haus, H. A. Theory of mode locking with a fast saturable absorber. J. Appl. Phys.
46, 3049–3058 (1975).
7. Segev, M., Soljac
ˇ
ic
´
, M. & Dudley, J. M. Fractal optics and beyond. Nature Photon.
6, 209–210 (2012).
8. Dudley, J. M., Finot, C., Richardson, D. J. & Millot, G. Self-similarity in ultrafast
nonlinear optics. Nature Phys. 3, 597–603 (2007).
9. Barth, J. V., Costantini, G. & Kern, K. Engineering atomic and molecular
nanostructures at surfaces. Nature 437, 671–679 (2005).
10. Ito, T. & Okazaki, S. Pushing the limits of lithography. Nature 406,
1027–1031 (2000).
11. Sreekanth, K. V., Chua, J. K. & Murukeshan, V. M. Interferometric lithography
for nanoscale feature patterning: a comparative analysis between laser
interference, evanescent wave interference, and surface plasmon interference.
Appl. Opt. 49, 6710–6717 (2010).
12. Whitesides, G. M. Self-assembly at all scales. Science 295, 2418–2421 (2002).
13. Gattass, R. R. & Mazur, E. Femtosecond laser micromachining in transparent
materials. Nature Photon. 2, 219–225 (2008).
14. Birnbaum, M. Semiconductor surface damage produced by ruby lasers. J. Appl.
Phys. 36, 3688–3689 (1965).
15. Temple, P. & Soileau, M. Polarization charge model for laser-induced
ripple patterns in dielectric materials. IEEE J. Quantum Electron. 17,
2067–2072 (1981).
16. Sipe, J. E., Young, J. F., Preston, J. S. & van Driel, H. M. Laser-induced periodic
surface structure I: theory. Phys. Rev. B 27, 1141–1154 (1983).
17. Bonch-Bruevich, A. M., Libenson, M. N., Makin, V. S. & Trubaev, V. V. Surface
electromagnetic waves in optics. Opt. Eng. 31, 718–730 (1991).
18. Sun, Q., Liang, F., Valle
´
e, R. & Chin, S. L. Nanograting formation on the surface
of silica glass by scanning focused femtosecond laser pulses. Opt. Lett. 33,
2713–2715 (2008).
19. Bonse, J., Kru
¨
ger, J., Ho¨hm, S. & Rosenfeld, A. Femtosecond laser-induced
periodic surface structures. J. Laser Appl. 24, 042006 (2012).
20. Kalaycioglu, H., Oktem, B., S¸enel, Ç., Paltani, P. P. & Ilday, F. O
¨
.
Microjoule-
energy, 1 MHz repetition rate pulses from all-fiber-integrated nonlinear chirped-
pulse amplifier. Opt. Lett. 35, 959–961 (2010).
21. Atwater, H. A. & Polman, A. Plasmonics for improved photovoltaic devices.
Nature Mater. 9, 205–213 (2010).
22. Srituravanich, W., Fang, N., Sun, C., Luo, Q. & Zhang, X. Plasmonic
nanolithography. Nano Lett. 4, 1085–1088 (2004).
23. Konstantatos, G. & Sargent, E. H. Nanostructured materials for photon
detection. Nature Nanotech. 5, 391–400 (2010).
24. Juan, M. L., Righini, M. & Quidant, R. Plasmon nano-optical tweezers. Nature
Photon. 5, 349–356 (2011).
25. Strukov, D. B., Snider, G. S., Stewart, D. R. & Williams, R. S. The missing
memristor found. Nature 453, 80–83 (2008).
26. Didiot, C., Pons, S., Kierren, B., Fagot-Revurat, Y. & Malterre, D. Nanopatterning
the electronic properties of gold surfaces with self-organized superlattices of
metallic nanostructures. Nature Nanotech. 2, 617–621 (2007).
27. Flemming, R. G., Murphy, C. J., Abrams, G. A., Goodman, S. L. & Nealey, P. F.
Effects of synthetic micro- and nano-structured surfaces on cell behavior.
Biomaterials 20, 573–588 (1999).
28. Kang, T.-S., Smith, A. P., Taylor, B. E. & Durstock, M. F. Fabrication of highly-
ordered TiO
2
nanotube arrays and their use in dye-sensitized solar cells. Nano
Lett. 9, 601–606 (2009).
Acknowledgements
The authors acknowledge support from the Scientific and Technological Research Council
of Turkey (TU
¨
BI
˙
TAK; grant nos 106G089 and 209T058) and a Distinguished Young
Scientist award from the Turkish Academy of Science s (TU
¨
BA). The authors thank G. Ertas¸
for help with Raman spectroscopy.
Author contributions
B.O
¨
. and I.P. conducted the experiments and analysed the data. I.P., S.I. and F.O
¨
.I.
developed the theoretical model and I.P. performed the simulations. I.P., B.O
¨
., A.R., S.Y.
and M.E. constructed the laser microscope set-up. H.K., B.O
¨
. and A.R. constructed the
laser system.
Additional information
Supplementary information is available in the online version of the paper.
Reprints and
permissions information is available online at www.nature.com/reprints. Correspondence and
requests for materials should be addressed to F.O
¨
.I.
Competing financial interests
The authors declare no competing financial interests.
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