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228 Microsyst Technol (2018) 24:227–233
1 3
extinction characteristics of LSPRs. But the Ag thin film is
unstable because as Ag thin film is put in ambient atmos-
phere, the relative permittivity of the Ag thin film will be
definitely changed due to the oxidation (forming the Ag
2
O)
and sulfuration (forming the Ag
2
S). For that, the optical
performance of the LSPRs fabricated by periodic Ag nano-
particle arrays (PNAs) will be critically changed.
Therefore, the oxidation and sulfuration problems have
become an important issue for the properties of LSPRs
based on the Ag PNAs. In order to overcome this prob-
lem, many researchers have used a protective thin film on
the Ag PNAs to form a hybrid bi-layer. For example, Au–
Ag PNAs with gold thin film coated on the surfaces of Ag
thin film the Au thin film can protect the pure Ag thin film
from being oxidation and sulfuration. Liu et al. investi-
gated a type of quadrangular frustum pyramid composition
nanostructure with silver in bottom layer and gold in top
layer (Liu et al. 2010). They well investigated the extinc-
tion spectra and refractive index sensitivity (RIS) of the
hybrid Au–Ag quadrangular frustum pyramid nanostruc-
ture. Fu et al. introduced a hybrid Au–Ag subwavelength
metallic zone plate-like structure and showed that thick-
nesses of both the Au and Ag thin films had significantly
tailoring function (Fu and Zhou 2009). Recently, Mathpal
et al. deposited titanium dioxide (TiO
2
) thin film by a sim-
ple thermal pyrolysis method, which could be further used
as a base matrix for the deposition of gold nanoparticles
(Mathpal et al. 2015). They found that the fabrication of
a plasmonic metamaterial structure is a new approach for
increasing the absorption and trapping of light in semi-
conducting oxide based thin film. Research by Rani et al.
found that the variations of the thicknesses of Ag and TiO
2
medium can tune the surface plasmon resonance (SPR)
wavelength in a large range (Rani et al. 2014). For that, in
order to enhance the sensitivity of nanocomposite based
fiber optic SPR sensor further, numerous innovative nano-
composites comprising nanoparticles of gold (Au), silver
(Ag), and copper (Cu) with their varying volume fractions
embedded in host dielectric matrices of TiO
2
and InN were
considered in their study. However, as we know, so far there
are no works investigating TiO
2
as the upper layer to pro-
tect Ag thin film from preventing oxidation and sulfuration.
Also, so far there are no any researches discuss the effect
of thickness of TiO
2
layer on optical properties and sens-
ing performance of Ag-based PNAs. The refractive index
sensitivity (RIS) and figure of merit (FOM) of the LSPRs
sensors (Joshi et al. 2012; Sekhon et al. 2013; Spackova
et al. 2013; Chan et al. 2008; Novo et al. 2008; Jin et al.
2001) are sensitive to the thickness of TiO
2
layer, for that
the influence of the thickness of TiO
2
layer on the optical
properties and sensing performance of the Ag-based hybrid
PNAs is important and it would be the main topic of this
study.
In this paper, we first considered and investigated the
influences of the oxidation and sulfuration processes of
Ag thin films on the properties of triangular PNAs from
their extinction spectra of the LSPRs. The discrete dipole
approximation (DDA) is a method being used to compute
scattering of radiation for particles or periodic nanoparticle
arrays having arbitrary shapes and having periodic struc-
tures. Typical metals that support surface plasmons in the
nanoparticle arrays’ structure are the single-layer structure
of silver (Ag), gold (Au), and chromium (Cr) nanoparti-
cle arrays and the bi-layer structure of hybrid Ag–Au and
hybrid Ni-Au nanoparticle arrays (Liu et al. 2015a). We
had used the DDA method to calculate the extinction spec-
tra of the structures with the bi-layer materials of Ag
2
O–Ag
and Ag
2
S–Ag. Because the Au and TiO
2
thin films could be
used to protect and prevent Ag thin films from the oxida-
tion and sulfuration, the extinction spectra of the structures
with bi-layer materials of Au–Ag and TiO
2
–Ag were also
investigated by using DDA method for simulation. After
the certification of DDA method, we calculated the RIS
and FOM of the hybrid Au–Ag and TiO
2
-Ag nanostructure
arrays with different thicknesses of Au and TiO
2
thin films.
2 Simulation structure and materials
The discrete dipole approximation (DDA) is a flexible and
powerful technique for computing scattering and absorp-
tion of radiation by targets of arbitrary geometry and by
periodic structures, and DDA method can provide a con-
venient method to describe the light scattering for nanopar-
ticles in arbitrary shapes. The basic idea of DDA method
was introduced by DeVoe (1964), who applied DDA
method to study the optical properties of molecular aggre-
gates, but the retardation effects were not included. For
that, DeVoe’s treatment was limited to aggregate the mate-
rials that were small compared with the wavelength. DDA
method has then been developed to simulate the proper-
ties of the continuum target by a finite array of polarizable
points, which acquire dipole moments in response to the
local electric field. In DDA formalism, for a finite array of
point dipoles the scattering problem may be solved exactly,
so the only approximation that is present in DDA method
is the replacement of the continuum target by an array of
electric dipoles (N-point dipoles), in which the polarizabil-
ity (αi) and position vector (ri) of each dipole are specified,
respectively. The detail used equations can be found in our
past researches (Liu et al. 2014, 2015b, c).
An implementation of electrodynamic theory called
DDA method can be used to model the experimentally
measured extinction spectra. In this study, DDA method
was used to design and simulate the hybrid bi-layer hex-
agonal lattice of triangular periodic nanoparticle arrays