Nanosphere Photolithography: The Inﬂuence of Nanopore Arrays

Disorder on Extraordinary Optical Transmission

Andrei Ushkov

1,2 a

, Olivier Dellea

, Isabelle Verrier

, Thomas Kampfe

, Alexey Shcherbakov

4 b

Jean-Yves Michalon

and Yves Jourlin

1 c

Univ. Lyon, UJM-Saint-Etienne, CNRS, Institut d’Optique Graduate School, Laboratoire Hubert Curien UMR 5516,

F-42023 Saint-Etienne, France

Center for Photonics and 2D Materials, Moscow Institute of Physics and Technology, 9 Institutsky Lane, Dolgoprudny

141700, Russia

Grenoble Alpes Univ., CEA-Liten, 17 rue des Martyrs, 38054 Grenoble, France

Department of Physics and Engineering, ITMO University, 49 Kronverksky Pr., 197101 St. Petersburg, Russia

Keywords:

Nanosphere Photolithohraphy, NPL, Extraordinary Optical Transmission, EOT, Disorder, Nanopore Array,

Diffraction Graing, Plasmonics, Numerical Simulations.

Abstract:

We analyze both experimentally and numerically the inﬂuence of nanopore arrays disorder on extraordinary

optical transmission in samples, fabricated via nanosphere photolithography. Two measures of disorder are

considered, the correlations between them are discussed using experimental and numerical data. We propose

a theoretical model which takes explicitly the disorder into account, and show how the concurrence between

nanopore depth and disorder level deﬁnes the quality of EOT excitation. Simulated spectra are in a good

agreement with experimental ones. Our results reveal the possibilities of NPL for EOT-based applications and

pave the way toward plasmonic devices with a polycrystalline design.

1 INTRODUCTION

Since its discovery in 1998 by Ebbessen (Ebbesen

et al., 1998), the Extraordinary Optical Transmission

(EOT) has been studied intensively for numerous ap-

plications in optical ﬁltering (Wen et al., 2019), sens-

ing (Yeh et al., 2011) and energy transfer (Andrew

and Barnes, 2004). Different EOT-compatible sam-

ple designs were considered, for example continuous

or perforated thin metal ﬁlms (Ushkov et al., 2019;

Jourlin et al., 2009; Sauvage-Vincent et al., 2013;

Wen et al., 2019; Park et al., 2020; Yue et al., 2014),

metallic slit arrays (Deng et al., 2018), deep undu-

lations for localized plasmon excitations (Genet and

Ebbesen, 2010). In order to fabricate samples and

study the EOT experimentally, various surface nanos-

tructuration approaches exist: Electron-Beam Lithog-

raphy (Li et al., 2010; Yue et al., 2014), Focused

Ion Beam Milling (Ebbesen et al., 1998; Hahn et al.,

2020; Liu et al., 2020b), Soft-Nanoimprinting (Cam-

https://orcid.org/0000-0001-8962-1599

https://orcid.org/0000-0002-9070-5439

https://orcid.org/0000-0002-7935-2150

pos et al., 2008) or Laser Interference Lithography

(Ushkov et al., 2020; Cao et al., 2018).

Nowadays the self-assembled colloidal mono-

layers attract more and more attention for practi-

cal plasmonic applications. Despite the polycrys-

talline geometry, structures fabricated via colloidal

self-assembly can support resonant optical effects.

Plasmon-mediated resonant transmission was ob-

served, for example, in samples prepared via metal

deposition into the intersticies between colloidal par-

ticles (Liu et al., 2020a; Jamiolkowski et al., 2019), or

in continuous metal ﬁlms covering a self-assembled

nanosphere mask (Farcau, 2019; Quint and Pacholski,

2014; Zhang et al., 2012) with or without the removal

of particles.

The deposition of close-packed self-assembled

colloidal monolayers on different substrates is per-

formed by various modiﬁcations of the Langmuir-

Blodgett technique (Ruan et al., 2007; Dell

ea et al.,

2014; Lotito and Zambelli, 2016; Vogel et al.,

2011). In comparison with conventional periodic

structuration methods these approaches possess a

high throughput, are well adapted for the curved and

non-conventional surfaces (Berthod et al., 2017; Pen-

Ushkov, A., Dellea, O., Verrier, I., Kampfe, T., Shcherbakov, A., Michalon, J. and Jourlin, Y.

Nanosphere Photolithography: The Inﬂuence of Nanopore Arrays Disorder on Extraordinary Optical Transmission.

DOI: 10.5220/0010344400460053

In Proceedings of the 9th International Conference on Photonics, Optics and Laser Technology (PHOTOPTICS 2021), pages 46-53

ISBN: 978-989-758-492-3

dergraph et al., 2013; Bhawalkar et al., 2010) and can

be integrated into industrial production lines (Dell

et al., 2014).

The disorder should be explicitly taken into ac-

count for the polycrystalline structures. It was shown

both numerically and experimentally (Quint and Pa-

cholski, 2014) that the disorder in thin gold ﬁlm un-

dulations ﬂattens and lowers the optical transmission;

the randomness in ﬁlm perforation positions leads to

a broadband absorption (Fang et al., 2015), polycrys-

talline structures were used as light absorbers (Qu and

Kinzel, 2016).

In this work we study the inﬂuence of disorder

on EOT in samples, prepared via an advanced sur-

face nanostructuring method called Nanosphere Pho-

tolithography (NPL) (Zhang et al., 2016). In con-

trast to other colloidal-based approaches mentioned

above, NPL is much more ﬂexible in the nanotopogra-

phy as it employs photonic nanojets for drawing sur-

face motifs. This feature makes it possible to control

the surface undulations depth, avoid the photoresist

layer perforations and produce nanopores - the ge-

ometry more ﬂexible for the tuning of plasmonic re-

sponse in comparison with nanoholes (Gartia et al.,

2013; Wang et al., 2013). We consider two measures

of nanopore arrays disorder, compare them and show

how to explicitly take the disorder into account in

numerical simulations. Experimental EOT measure-

ments are in a good correspondence with calculated

spectra. In addition, we propose a phenomenological

model, adapted from the 1D case (Nau et al., 2007),

for EOT calculations in disordered 2D structures. Our

results are promising to reveal the possibilities of NPL

for EOT-based applications and pave the way toward

plasmonic devices with a polycrystalline design.

2 FABRICATION AND

CHARACTERIZATION OF

SAMPLES

In Fig. 1 we present the main technological steps for

samples fabrication. On a surface of BK7 glass slides

3.7 × 2.5 cm, cleaned in ultrasonic acetone, ethanol

baths and DI-water bath, a 600 nm/250 nm-thick

Shipley S1805 photoresist layer is spin-coated for

1.1 µm/300 nm microsphere diameter, respectively,

see Fig. 1a. The resist was soft-baked at 60

◦

for 1 min. The Boostream process, developed in

CEA-Liten (Dell

ea et al., 2014), performs the self-

assembly of silica nano/micro particles with diam-

eters of σ

=1.1 µm or 300 nm into close-packed

monolayers on the water surface. The Boostream

process allows the transfer of these polycrystalline

monolayers onto the substrate in a continuous man-

ner, which is advantageous for industrial needs (Shav-

dina et al., 2015). The colloidal mask on the resist

surface acts as a microlens array for UV irradiation

(see Fig. 1b) and exposes the resist during a cer-

tain time t

exp

∼ 10 s. The exposed sample is then

cleaned in an ultrasonic bath from the colloidal parti-

cles and is developed in MF-319 developer at 8

◦

C for

dev

∼ 4 s. As a result, nanopore arrays appear in the

resist, see Fig. 1c. Final fabrication steps (Figs. 1d-e)

are 20 nm-thick aluminum layer deposition via mag-

netron sputtering, and the second 600 nm-thick resist

coating to protect the metal and create the symmet-

rical ”Insulator-Metal-Insulator” (IMI) structure with

improved EOT behavior.

Figure 1: Nanopore array fabrication: a) The glass slide

cleaning and a deposition of a photoresist ﬁlm; b) deposi-

tion of colloidal monolayer, UV irradiation; c) the removla

of colloidal particles, resist development and formation of

nanopores; d) surface metallization; e) second resist ﬁlm

deposition for the symmetrical ”Insulator-Metal-Insulator”

(IMI) structure.

An optical microscope and SEM were used to

visualize arrays with interpore distances 1.1 µm and

300 nm, respectively, before the ﬁnal resist coating in

Fig. 1e. Four samples S1-S4 were fabricated experi-

mentally with different interpore distances and disor-

der, see Figs. 2a-d. Nanopore depth was measured us-

ing AFM, transmission spectra of IMI structures were

measured using the UV/Vis/NIR spectrophotometer

Cary 5000.

Nanosphere Photolithography: The Inﬂuence of Nanopore Arrays Disorder on Extraordinary Optical Transmission

Figure 2: a)-c) Optical microscope photographs of NPL-

fabricated nanopore arrays samples S1-S3 with different

quality and a mean interpore distance σ

=1.1 µm. AFM-

measured nanopore depth is ∼ 220 nm; d) SEM photo-

graph of nanopore sample S4 with a mean interpore distance

= 300 nm, AFM-measured nanopore depth 50 nm; e)

Example of simulated polycrystalline sample; f) the mean

interpore distance σ

, average number N of nanopores in

grains and a measure of disorder 1/N for every sample S1-

S5. Values above the scale bars in a)-e) show the distances

in microns.

3 PARAMETERS OF DISORDER

In two-dimensional systems a number of param-

eter have been proposed to quantify the disor-

der: nanopore concentration and hole-to-hole spacing

(Reilly III et al., 2010), impurity concentration (Gray

et al., 2015), statistical control parameter (Richter

et al., 2011). In this work we consider two measures

of disorder p

and p

: nanopores per grain and the

normalized width of the structure factor peak, respec-

tively. In what follows these parameters are used for

EOT calculations, and the correlation between them

is discussed.

Numerical simulations of transmission spectra

were performed using a proprietary GSMCC code

(Shcherbakov and Tishchenko, 2017) and the Lumer-

ical FDTD software. In the FDTD method nanopores

have vertical walls, in the GSMCC simulations the

walls were slightly slanted. Both methods produced

similar spectra, which assures the attained numerical

results. The material dispersion is used for simula-

tions, the dispersion of the resist S1805 was measured

by ellipsometry.

3.1 Nanopores Per Grain

In the context of polycrystalline geometries a natu-

ral measure of disorder is an average number N of

nanopores per grain, because this value is dimension-

less, allows to compare samples with different char-

acteristic lengths and is easy to estimate from experi-

mental data. We use the inverse number of nanopores

per grain as the ﬁrst of two parameters of disorder:

≡ 1/N. The values p

for the samples S1-S4,

which are speciﬁed in Fig. 2f, conﬁrm the visual im-

pression that the disorder increases from S1 to S4.

In order to clarify the nanopore distribution in high-

quality samples, we performed the image-processing-

based statistical analysis of large 227 µm×170 µm mi-

croscope photographs, nanopore grains with differ-

ent orientations of hexagonal lattice are depicted by

different colors in Fig. 5b. These photographs al-

low estimating an average huge number of nanopores

per grain as ∼ 10

by deﬁning the grain size in S1

as 100 µm. This grain size, however, is still much

smaller than the spectrophotometer incident light spot

1 mm×3 mm, so in all samples S1-S4 it measures

a collective response of numerous randomly oriented

domains.

Figures 3a-b show the measured transmission

spectra at normal incidence through metallized sam-

ples S3 and S1, respectively. The pronounced EOT

peak exists in S1 only due to its long-range order;

the EOT resonant wavelength λ

EOT

≈ 1530 nm can

be estimated via the formula for hexagonal lattice

(Eks¸io

glu et al., 2016):

EOT

√

3σ

·Re(ε

)

+ Re(ε

)

, (1)

for 6 symmetrical ﬁrst diffraction orders (m,n) =

(±1,0),(0,±1),(±1,∓1); ε

and ε

are dielectric

permittivities of dielectric and metallic layers, respec-

tively, and σ

is the interpore distance deﬁned by the

diameter of the self-assembled particles. Although in

Fig. 3b the modeling of ideal hexagonal lattice is

enough for a good correspondence with experiment,

the disorder in Fig. 3a necessiates the simulation of

the periodical super cell, as shown in Fig. 3a inset.

The nanopore distribution from experimental data

was used in Fig. 3a, the cell size is adapted to include

the mean number of nanopores per grain N = 43 in

PHOTOPTICS 2021 - 9th International Conference on Photonics, Optics and Laser Technology

Figure 3: Transmission spectra at normal incidence with

and without EOT through samples with a mean interpore

distance 1.1 µm. Solid curves in a) and b) correspond to the

measured transmission through samples S3 and S1, respec-

tively. Dashed lines in a) and b) are the calculated spectra

of nanopore arrays arranged in periodical cells, shown as in-

sets in a) and b); red rectangles denote periodical boundary

conditions, its size in a) is 6816 × 5636 nm.

correspondence with values of Fig. 2f. Both experi-

mental and numerical results show that a high disor-

der in nanopore arrays effectively suppresses the EOT

peak.

Although the parameter p

is easy to estimate

from experimental data and allows to deﬁne properly

the size of super cells with disorder, it is a geometri-

cal value which is not directly connected with sample

diffraction properties. We believe that for EOT-based

devices another parameter of disorder is more appro-

priate, introduced in the next section.

3.2 Normalized Width of the Structure

Factor Peak

As it was mentioned above, the experimental samples

consist of a huge number of randomly oriented grains,

illuminated by normally incident light during spec-

tral measurements. We study the EOT caused by ﬁrst

diffraction orders; in polycrystalline samples these

orders, coming from different grains, create a circle

in reciprocal space with the radius k

≡

where b

and b

are basis reciprocal vectors for an

ideal hexagonal grating, see Fig. 4. To calculate

a Fourier transform ρ

of nanopore arrays we use a

set of two-dimensional Dirac delta functions ρ(r) =

∑

i=1

δ(r −r

), which are zero except nanopore cen-

ters r = r

, and get ρ

∑

i=1

exp(ik ·r

). The

blue proﬁle in Fig. 4 represents the radial-averaged

static structure factor S(k), which is proportional to

the squared modulus of Fourier amplitudes: S(k) =

hρ

−k

i/N.

If nanopore grains are large enough (as for the

sample S1), the circle is thin, and the measured EOT

is almost the same as for ideal hexagonal grating

(see Fig. 3b), even if the total number of illumi-

nated grains is big. The transmission through peri-

odical hexagonal lattices weakly depends to incident

light polarization due to the 6-fold rotational symme-

try (Zhao et al., 2017). Our preliminary calculations

show that transmission variations are well below 1%

for any linear polarization in hexagonally arranged

nanopores. For samples with smaller grains the recip-

rocal space circle is wider in analogy with diffraction

in amorphous liquids (Ziman, 1979; Rojas-Ochoa

et al., 2004). Consequently, the Full Width at Half

Maximum (FWHM) of the radial distribution can

serve as a measure of disorder, connected with the

structure diffraction properties. In this paper we con-

sider the dimensionless parameter of disorder p

≡

FWHM/k

Figure 4: Sketch of the ﬁrst Fourier harmonics circle for

polycrystalline gratings. Reciprocal basis vectors b

and b

and 6 ﬁrst diffraction orders denoted by blue points are de-

ﬁned by ideal hexagonal nanopore arrangement. The proﬁle

along the circles radius (in blue) represents the static struc-

ture factor S(k).

The both parameters p

and p

grow with the

growth of disorder, their values for experimental sam-

ples S1-S4 are shown in Fig. 5a. According to

this ﬁgure, the reciprocal space circle slows its width

growth with the increase of p

, it means that diffrac-

tion properties of structures with small crystallites do

not depend sufﬁciently on the disorder level, in con-

trast to samples with large crystallites and a long-

range order. In order to understand this behavior bet-

ter we developed a simple model of polycrystalline

nanopore arrays (see, for example, S5 in Fig. 2e).

For every simulation a set of points is chosen ran-

domly, and the Voronoi diagram of this set deﬁnes

Nanosphere Photolithography: The Inﬂuence of Nanopore Arrays Disorder on Extraordinary Optical Transmission

the nanopore grains boundaries. The space inside

grains is ﬁlled with hexagonally arranged elements

(nanopores), the lattice orientation is chosen ran-

domly in every grain. We leave the thin stripes along

boundaries empty to avoid the overlap of nanopores

from different grains. In such a way, numerous re-

alizations of nanopore arrays with different p

were

simulated, and corresponding values of p

were cal-

culated. In Fig. 5a parameters p

and p

of indi-

vidual simulated nanopore distributions are denoted,

together with a phenomenological power function ﬁt-

ting p

) = 0.63p

0.45

The comparison of experimental and modeled de-

pendences p

) in Fig. 5a allows to make two

observations. Firstly, the modeled monotone func-

tion generally repeats the experimental behavior, thus

the average number of nanopores per grain can, to

a ﬁrst approximation, determine a diffraction qual-

ity of samples. Secondly, the experimental values of

tend to be larger than those predicted by a sim-

ple polycrystalline model. It can be explained by

the presence of additional defects in nanopore arrays

along with randomly oriented crystallites, i.e. hexag-

onal lattice phase jumps (Avrutsky et al., 2000) (white

uncolored lines in Fig. 5b) and regions between

grains, ﬁlled with randomly distributed nanopores.

Although these defects can be introduced into the

modelling, it goes beyond the scope of this paper. In

the following section we use the ”diffraction” param-

eter of disorder for numerical simulation of EOT.

3.3 Inﬂuence of Nanopore Arrays

Disorder on EOT

In order to utilize the parameter p

and introduce

explicitly the disorder into numerical EOT calcula-

tions we propose a model, adapted from the 1D case

(Nau et al., 2007). A radial-symmetric structure fac-

tor S(k), calculated for experimental nanopore distri-

bution, is least square ﬁtted to a Gaussian to obtain

the value of p

. At the same time, the structure peak

width deﬁnes a set of effective ﬁrst diffraction orders

k, which come from different grains and give a con-

tribution α

(λ) to the total transmission T(λ) at a

wavelength λ. We assume a simple incoherent sum-

mation of these partial contributions because of nu-

merous randomly oriented and distributed grains. The

scaling factor α

depends on the density of excited

modes and is proportional to the corresponding value

S(k).

The total transmission is the sum of all par-

tial contributions with k around the structure factor

peak, where the α

is sufﬁciently non-zero: T(λ) =

∑

(λ). Partial spectra T

are obtained from the

Figure 5: a) Correlation between two disorder parameters

and p

for simulated (brown points and ﬁtting line) and

experimental nanopore distributions (green squares). Sam-

ples S1-S4 and the example of simulated distribution S5 are

shown in Figs. 2a-e. The phenomenological power function

ﬁtting p

= 0.63p

0.45

is used.

simulation of perfect samples (Nau et al., 2007).

Figure 6a shows several calculated transmission

spectra at normal incidence for 50 nm-depth nanopore

arrays, for different disorder levels p

. The ex-

perimentally measured value of EOT and its spec-

tral shape for sample S4 is in a good agreement

with theoretical results at appropriate disorder level,

compare with its value in Fig. 5a. The ”diffrac-

tion” parameter p

is convenient to study the inﬂu-

ence of continuously varying disorder on EOT. Fig-

ure 6b demonstrates the change of maximum EOT

value with nanopore depth at numerous disorder lev-

els. Generally, the disorder suppresses the resonant

transmission. Interestingly, it can also turn a trans-

mission decreasing with a depth growth into an in-

creasing one, for deep gratings (see the highest and

the lowest curves in Fig. 6b at depth>100 nm). The

3D-representation of calculated data in Fig. 6c re-

PHOTOPTICS 2021 - 9th International Conference on Photonics, Optics and Laser Technology

Figure 6: a) A set of calculated transmission spectra (tones

of green) at normal incidence with different parameter of

disorder p

. A red curve shows an experimentally mea-

sured transmission for the sample S4. Simulated and exper-

imental nanopore depth is 50 nm; b) calculated maximum

EOT transmission as a function of graing depth for a set of

; c) 3D-representation of data from b), showing a con-

currence between grating depth and disorder for the value

of EOT.

veals an interplay between grating depth and disorder

for establishing a EOT value.

4 CONCLUSIONS

In conclusion, we analyzed both experimentally and

numerically the inﬂuence of nanopore arrays disor-

der on extraordinary optical transmission in samples,

fabricated via nanosphere photolithography. We used

two measures of disorder: ”geometrical” parameter

and ”diffraction” parameter p

, and constructed a

simple model of nanopore distributions to understand

better the correlations between p

and p

. We con-

sider the value of p

as a more appropriate and con-

venient one for numerical simulation of disordered

samples in the context of EOT, and proposed a theo-

retical model which takes explicitly the disorder into

account. Simulated spectra are in a good agreement

with experimental ones. We have shown how the con-

currence between nanopore depth and disorder level

deﬁnes the quality of EOT excitation. We believe

that our results, which reveal the possibilities of NPL

for EOT-based applications, will pave the way toward

plasmonic devices with a polycrystalline design.

ACKNOWLEDGEMENTS

The work was funded by the SIS 488 doctoral school

of Saint-Etienne, university of Lyon (France), and

by RFBR, project number 19-32-90034. The au-

thors would like to thank CNRS engineers Marion

HOCHEDEL and Arnaud VALOUR for the technical

support.

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