Investigation of the sensitivity enhancement of nanowire-based surface plasmon resonance biosensors

Abstract

In this paper, we theoretically investigate the sensitivity enhancement of nanowire-based surface plasmon resonance (SPR) biosensors using rigorous coupled-wave analysis (RCWA). For a higher sensitivity, we are particularly interested in the size, period, and geometry of gold nanowires. When the nanowire period is less than 300 nm, the calculated sensitivity enhancement of a nanowire-based SPR configuration is more than ten-fold compared with that of a conventional one. Moreover, for a reliable performance, we study a modified SPR structure with periodic patterns of nanowires deposited onto a gold film. In such a schematic of nanowire-enhanced SPR biosensor, the sensitivity enhancement induced by nanowires with a T-profile is better than that of nanowires with an inverse T-profile.

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INVESTIGATION OF THE SENSITIVITY ENHANCEMENT OF
NANOWIRE-BASED SURFACE PLASMON RESONANCE BIOSENSORS

Kyung Min Byun1, Donghyun Kim2, and Sung June Kim1
1School of Electrical Engineering and Computer Science, Seoul National University, Korea
2School of Electrical and Electronic Engineering, Yonsei University, Korea
e-mail : calli8@helios.snu.ac.kr

ABSTRACT

In this paper, we theoretically investigate the
sensitivity enhancement of nanowire-based surface
plasmon resonance (SPR) biosensors using rigorous
coupled-wave analysis (RCWA). For a higher
sensitivity, we are particularly interested in the size,
period, and geometry of gold nanowires. When the
nanowire period is less than 300 nm, the calculated
sensitivity enhancement of a nanowire-based SPR
configuration is more than ten-fold compared with
that of a conventional one. Moreover, for a reliable
performance, we study a modified SPR structure with
periodic patterns of nanowires deposited onto a gold
film. In such a schematic of nanowire-enhanced SPR
biosensor, the sensitivity enhancement induced by
nanowires with a T-profile is better than that of
nanowires with an inverse T-profile.

Keywords: Nanowire-based
resonance (SPR) biosensor, Sensitivity enhancement,
Rigorous coupled-wave analysis (RCWA)

INTRODUCTION

Surface plasmons are excited when a thin
conducting metal film is placed between the two
optical media. At a specific incident angle, the surface
plasmons resonantly couple with a light in an
appropriate polarization. Since the energy of the
incident light is absorbed in this resonance, the
reflected intensity shows a minimum at the resonance
angle. Such a phenomenon has been widely used in a
variety of sensing applications, since it provides rapid,
label-free and array-based sensing capability in real-
time for biochemical reactions on a surface [1], [2].
surface plasmon
θθ
Prism Prism
BiomaterialBiomaterial
Gold filmGold film
TM modeTM mode

Figure 1. Schematic diagram of a conventional SPR
biosensor. The incident light is monochromatic and
TM-polarized.

In a conventional schematic of SPR biosensors as
shown in Figure 1, a glass slide with a thin gold
coating is mounted on a prism. Light passes through
the prism and slide, then reflects off the gold film and
passes back through the prism to a detector. Changes
in reflectivity versus angle or wavelength give a
signal that is proportional to the concentration of
biomaterial near to the surface. By measuring the
resonance shift, it is possible to quantify the surface
reactions of interest. These biochemical reactions
include antibody-antigen
hybridization, biomaterial
interactions, and other adsorption processes.
The highest sensitivity of an SPR biosensor based
on a conventional configuration is approximately 1
pg/mm2 [3], corresponding to a change of 5 × 10-7 in
refractive index unit. Although an SPR biosensor is
extremely simple in structure and commercially
available as an economic alternative to more
expensive sensing techniques, it suffers from
insufficient sensitivity in some applications, for
example, those that require the sensing of aerosol
release of toxins. To get over the limitation on the
sensitivity, nanoparticle-based SPR biosensors have
drawn tremendous interests in recent years. It has
been empirically shown that applying nanoparticles
may significantly enhance the sensitivity by 1-2
orders of magnitude [4].
Noble metal nanostructures allow strong optical
coupling of incident light, possibly through surface
plasmon polaritons (SPPs) excited on a thin metal
film, to resonances of collective electron oscillations,
so called localized surface plasmons (LSPs). The
optical properties of LSPs are dependent on the size
and shape as well as on the dielectric function of gold
nanostructures. For an ensemble of nanostructures,
the electromagnetic coupling between nanostructures
arises and this interaction is generally enhanced with
a decrease of the period. Thus, among many design
parameters, we are particularly interested in the size,
shape, and period of nanostructures.
Based on the reports that nanostructures of the size
ranging from 20 nm to 50 nm produce the strongest
and sharpest SPR enhancement [5], the nanowires of
this study are sized in this range. The nanowire period
is scanned in a range of 50-200 nm. The goal of our
study is to theoretically investigate the sensitivity
enhancement of nanowire-based SPR biosensors
using RCWA.
Also, for better sensitivity, we propose a modified
structure of nanowires adsorbed on a smooth gold
interactions,
and
DNA
receptor cell

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film. We form periodic patterns of one-dimensional
nanowires with a T-profile or an inverse T-profile and
explore the design parameters of nanowires that can
provide reliable performance. Our study demonstrates
the potential for significant improvement in the
sensitivity of SPR biosensors by designing a structure
of nanowires.

NUMERICAL MODEL

In our numerical model, RCWA is applied to
analyze a periodic structure of one-dimensional gold
nanowires on a smooth metal film. In Maxwell’s
equations, the linearly polarized light can always be
divided into two mutually independent polarizations,
transverse electric (TE) and transverse magnetic (TM)
modes. Once, one of the two transverse field
components is known, the other may be obtained from
the curl relation of the Maxwell’s equations.
Among many existing rigorous methods, the
coupled-wave analysis formulated by Moharam and
Gaylord is unique because of its versatility and
simplicity [6]. Its numerical implementation uses only
elementary Maxwell’s equations, and do not require
any sophisticated numerical
approximations. RCWA may be applied to one-
dimensional nanowires
continuous or discontinuous permittivity variations.
The permittivity in a metallic grating region is written
as a Fourier series expansion

∑
m
where Λ is the grating period, εm is the Fourier
component of the grating dielectric function, 2π/Λ is
the grating vector, and j = (-1)1/2. The light source is
assumed as a unit-amplitude monochromatic plane
wave with a wavelength λ and incident at an angle θ
relative to the z-axis. And the electromagnetic fields
inside a grating are given by wave equations
∇
⋅∇+∇
zxkEE
ε
ε
∇
+∇
zxkHH
ε
ε
where E is the electric field, H is the magnetic field,
ε(x, z) is the complex permittivity, k (= 2π/λ) is the
wave number in vacuum. One of the above two
general wave equations may be selected and
simplified for particular incident wave polarizations.
The electric or magnetic field inside a grating region
is expanded in terms of space harmonic components.
And at the boundaries of each layer, the tangential
components of the electric and magnetic fields must
be continuous.
When the size of a nanostructure is smaller than
100 nm, the calculation becomes difficult and the
convergence problem is not easy to solve due to
extremely rapid variations of the field that occur on
techniques or
(gratings) that have
Λ=Λ+=
m
mxjzzxzx
)/2 exp()(),(),(
πεεε
, (1)
0),()(
22
=+
E
ε
, (2)
0),(
22
=+×∇×
H
ε
, (3)
very short distances. However, the RCWA has been
successfully applied for numerical calculations to
explain experimental results of nanostructures [7], [8].
Also, convergence can be achieved in a calculation
work of every case by including a sufficient number
of harmonics. Note that our RCWA routine was found
to corroborate experimental results of earlier SPR
studies based on nanowires [9].

θθ
11
22
33
44
55
xx
zz


Figure 2. Schematic diagram of a nanowire-based
multilayer model used in our numerical calculations.

A schematic diagram of a nanowire-based SPR
biosensor model is shown in Figure 2, where
nanowires are represented as one-dimensional array of
gold wires orient along the y-axis. The incident and
reflected lights are in the xz-plane of the coordinate
system shown. Layers 1, 2, 3, 4, and 5 represent a
BK7 glass prism, a binding film of chromium, the
SPP supporting gold film, a layer of target analytes,
and one-dimensional gold nanowires, respectively.
Target analytes are assumed to sit on top of a thin film
of a 40 nm thick gold layer, where SPPs are excited,
as well as an attachment layer of chromium with 2 nm
thickness. The binding with analyte is modeled with a
1 nm thick self-assembled monolayer (SAM) that is
supported by a gold film. In the previous studies,
nanoparticles or nanowires binding with target
analytes are randomly distributed onto a biomaterial
layer. However, in this study, the randomly patterned
gold nanoparticles are approximated to one-
dimensional nanowires whose directions are parallel
to x-axis. The complex indices of refraction of the
BK7 glass prism substrate, chromium film, gold film
and nanowires, and the binding layer with analytes
were determined respectively as 1.515, 3.48 + 4.36i,
0.18 + 3.0i, and 1.526 at λ = 633 nm [10]. A SAM is
extremely thin compared with the wavelength, so that
the layer is essentially a lossless dielectric, and its
extinction coefficient is ignored. The model in Figure
2 assumes an illumination with a TM-polarized
monochromatic plane wave at a fixed wavelength λ =
633 nm as the incidence angle θ is scanned with an
angular resolution of 0.01º

RESULTS AND DISCUSSION

Page 3

We calculate a conventional SPR configuration
with or without a SAM and the results of the
resonance angles are
respectively. As shown in Figure 3, only minor
change of 0.17° is observed, and thus it is confirmed
that the presence of a SAM layer only weakly affects
the conventional SPR response. However, use of gold
nanowires on a surface of SAM results in a resonance
angle of 46.380° and a dramatic shift 1.255° of a
resonance angle. In this calculation, the size of a gold
nanowire is 20 nm in width and height, and the
nanowire period is set to 500 nm. The shiftness
induced by these nanowire gratings is about 7.4 times
larger than that of the conventional SPR biosensor.
45.295° and 45.125°,
40 424446 48 50
0.0
0.2
0.4
0.6
0.8
1.0


Reflectivity
Incident Angle [degree]
Without SAM
With SAM
With SAM + Nanowires

Figure 3. SPR curves (reflectivity vs. incident angle)
of a 40 nm thick gold metal film on a dielectric glass
prism (solid line), a SAM adsorbed on a bare gold
film (dotted line), and the nanowire layer is
additionally adsorbed onto a SAM (dashed line). The
one-dimensional nanowires of having the width and
height 20 nm are deposited on a SAM that is adsorbed
on gold film substrate. In the calculation, the
nanowire period is 500 nm.

While fixing the geometry of nanowires, varying
nanowire period from 200 nm to 1 um affects the SPR
response as shown in Figure 4. In the results we find
that, as the nanowire period is decreased, the response
of the biosensor becomes more sensitive.
404244 4648 50
0.0
0.2
0.4
0.6
0.8
1.0


Reflectivity
Incident Angle [degree]
Without SAM
With SAM
With SAM + N.P. 200 nm
With SAM + N.P. 400 nm
With SAM + N.P. 600 nm
With SAM + N.P. 800 nm
With SAM + N.P. 1000 nm
N.P. = Nanowire Period

Figure 4. SPR curves (reflectivity vs. incident angle)
of a 40 nm thick gold metal film on a dielectric glass
prism (solid line), a SAM adsorbed on a bare gold
film (dotted line), and the nanowire layer is
additionally adsorbed onto a SAM (the other dashed
lines).

We define a parameter of sensitivity enhancement
factor (SEF) to represent the influence of nanowires.
This parameter is given by

θ
θ
∆
where θC_SPR is the plasmon resonance angle of a
conventional SPR scheme with a bare gold film,
θC_SPR_SAM is that of a conventional SPR scheme with
a bare gold film coated with a SAM, and θN_SPR_SAM is
that of one-dimensional
configuration shown in Figure 2. Using RCWA, it was
already computed that θC_SPR is 45.125° and θC_SPR_SAM
is 45.295°. Therefore the numerical results of Figure 4
may be presented in Figure 5 by use of SEF.
SPRC SAMSPRC
SPRC SAM SPRN
SPRC
SPRN
SEF
___
___
_
_
θθ
θθ
−
−
=
∆
=
, (4)
nanowire-based SPR
100200300400
Nanowire Period [nm]
5006007008009001000
0
10
20
30
40


Sensitivity Enhancement Factor

Figure 5. SEF curve of a nanowire-based SPR
biosensor. The dimension of one-dimensional
nanowires is 20 nm in width and height, and the
nanowire period varies from 100 nm to 1 um.

As described previously, decreasing the nanowire
period from 1000 nm to 100 nm brings about an
improvement of SEF. Comparison of the reflectivity
minimums’ positions shows that a change of nanowire
period from 100 nm to 1000 nm shows the decrease
of SEF from 31.85 to 5.47 as shown in Figure 5.
When the period is less than 300 nm, the calculated
sensitivity enhancement of the nanowire-based SPR
biosensor is more than ten-fold compared with the
sensitivity of a conventional one. These results may
be explained as a superposition of the following two
effects.
As the period is decreased, the coverage or surface
concentration of the nanowires gets higher. The large
number density of nanowires per unit area may induce
more localized plasmon resonances. Thus, this effect
results in a damping of surface plasmon polaritons
(SPPs) and a dominant excitation of localized surface
plasmons (LSPs) that leads to the emergence of strong

Page 4

extinction bands and to a giant amplification of the
local electromagnetic field.
For an ensemble of nanowires, the electromagnetic
coupling between nanowires arises and the interaction
of nanowires is enhanced with a decrease of inter-
nanowire spacing. Thus a strong interaction effect can
present different resonance properties, resulting in an
additional shift of resonance angle. In our calculation
results of Figure 5, when the period is over 300 nm,
the sensitivity enhancement effect by interacting
nanowires is limited and insignificant. Thus it is
confirmed that there is no distinguishable difference
of SEF in this range. However, as the period is
decreased less than 300 nm, the strong interactions
between nanowires may induce an enormous
enhancement of sensitivity.
Moreover, we investigated a modified nanowire-
based SPR biosensor in which nanowires are adsorbed
on a gold film and bind with target analytes. Using
this configuration, it is possible to guarantee the
reproducibility of the performance by a precise
control of geometrical parameters of nanowires.
When a nanowire is adhered to a gold film, the
interactions between SPPs, excited on the substrate,
and LSPs of nanowires take place, thus the
interference area between a gold film and a nanowire
may be considered as an important design parameter.
While the detailed calculation results are not shown in
this paper, the calculated SEF of nanowires with a T-
profile gets higher than that of an inverse T-profile.
For a T-profile, we may attain maximum SEF of
47.35, however, for an inverse T-profile, the SEF has
the largest value of 19.29.
Considering a practical structure that is relatively
easy to fabricate and insensitive to a fabrication
process error in period, we optimized design
parameters of nanowire-enhanced SPR biosensors.
Among various geometries of nanowires with a range
of 20 nm–40 nm, the optimized performance of
nanowires with a T-profile is that the peak SEF is
28.17 and the nanowire period is 140 nm.

CONCLUSION

We have investigated the sensitivity enhancement
of nanowire-based SPR biosensors using RCWA
method. An application of RCWA to a SPR biosensor
configuration involving gold nanowires onto a
dielectric SAM shows a dramatic shift of a resonance
angle. When the period of nanowire gratings is less
than 300 nm, the calculated sensitivity enhancement
is more than ten-fold compared with the sensitivity of
a conventional SPR biosensor’s configuration. These
results are the superposition of the two effects, the
increased density of nanowires exciting LSPs and the
strong interactions between nanowires resulting in an
additional shift of a resonance angle. Additionally, it
is found that in a proposed nanowire-enhanced SPR
biosensor in which nanowires are adsorbed on a gold
film, nanowires with a T-profile show a higher SEF
characteristic than those with an inverse T-profile. The
peak sensitivity enhancement factor of the optimized
geometry of nanowires comes up to 28.17 when
nanowire has a T-profile and the period is 140 nm.
Our study presents the potential for significant
improvement in the sensitivity of SPR biosensors by
designing a structure of nanowires.

Acknowledgements

This work is supported by the Nano Bioelectronics
and Systems Research Center of Seoul National
University, which is an ERC supported by the Korean
Science and Engineering Foundation (KOSEF).

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