sensors
Article
Characterization of a Functional Hydrogel Layer
on a Silicon-Based Grating Waveguide for a
Biochemical Sensor
Yoo-Seung Hong 1 , Jongseong Kim 2, * and Hyuk-Kee Sung 1, *
1
2
*
School of Electronic and Electric Engineering, Hongik University, Seoul 121-791, Korea;
[email protected]
Department of Neurology, Molecular Imaging and Neurovascular Research (MINER) Laboratory,
Dongguk University Ilsan Hospital, Goyang 10326, Korea
Correspondence: [email protected] (J.K.); [email protected] (H.-K.S.);
Tel.: +82-31-961-8418 (J.K.); +82-2-320-3037 (H.-K.S.)
Academic Editor: Alexandre François
Received: 7 April 2016; Accepted: 15 June 2016; Published: 18 June 2016
Abstract: We numerically demonstrated the characteristics of a functional hydrogel layer on a
silicon-based grating waveguide for a simple, cost-effective refractive index (RI) biochemical sensor.
The RI of the functional hydrogel layer changes when a specific biochemical interaction occurs
between the hydrogel-linked receptors and injected ligand molecules. The transmission spectral
profile of the grating waveguide shifts depends on the amount of RI change caused by the functional
layer. Our characterization includes the effective RI change caused by the thickness, functional
volume ratio, and functional strength of the hydrogel layer. The results confirm the feasibility of, and
set design rules for, hydrogel-assisted silicon-based grating waveguides.
Keywords: waveguides; diffraction gratings; biological sensing and sensors; optical sensing
and sensors
1. Introduction
The quantification of a refractive index (RI) change has been shown to be an effective method of
developing a biochemical sensor that measures biomolecular interactions [1–4]. The method exhibits
significant advantages such as no fluorescent labeling, high throughput, and improved sensitivity
than other biochemical sensors [5–9]. Several approaches have been proposed and successfully
demonstrated to quantify the RI change induced by the concentration change of biochemical molecules.
They include surface plasmon resonance (SPR) [10], ring resonators [11], long-period fiber grating [12],
a grating coupler [13], grating waveguides [14], and metallic photonic crystal sensors [15,16].
The proposed techniques utilize the resonance frequency shift of a transmission spectral profile
that occurs when a fraction of the guided mode interacts with receptors and targeted molecules
on the waveguide surface [4,5,17]. Among these techniques, a silicon-based grating waveguide
is especially promising because of its fabrication compatibility with the standard complementary
metal-oxide-semiconductor (CMOS) processes, the simplicity of the structure, and the corresponding
cost competitiveness as well as its superior sensitivity [14]. Pham et al. utilized the shift of a sharp
fringe in the transmission spectrum near the stop-band edge of the grating [14]. They successfully
demonstrated a direct and label-free protein biosensor based on the grated waveguide.
Detection and quantification of the multivalent binding of proteins is a crucial step for a better
understanding of the fundamental mechanisms in the immune system, cancer, and thrombosis [18–20].
To detect multivalent binding efficiently as well as to distinguish it from the monovalent case, Kim et al.
utilized hydrogel micro-particles as a functional layer [21]. They successfully demonstrated the
Sensors 2016, 16, 914; doi:10.3390/s16060914
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RI change of the microgels through a ligand-induced receptor dimerization that accompanies the
multivalent binding process. Typically, the capability of distinguishing multivalent binding from
monovalent is limited in most current analytical technologies without labeling fluorescence molecules.
Isothermal titration calorimetry (ITC) could be used, but this consumes a relatively large amount of
purified proteins. On the other hand, when microgels containing appropriate receptors are used as
functional layers, their RI changes significantly because of a dimerization between injected target
proteins and receptors, and a corresponding local deswelling of the functional layer [21]. It has been
reported that the RI of the functional microgel layer changes by 0.05 from its original value because of
the multivalent binding and the deswelling of the microgel layer [22].
Herein, we propose a compact and inexpensive biochemical sensor prototype using a silicon-based
grating waveguide assisted by a hydrogel top cladding layer as a functional layer. We perform a
numerical simulation focusing on the characterization of the functional layer that is dedicated to
detecting and quantifying the multivalent binding of proteins. The proposed biochemical sensor
consists of a typical silicon-on-insulator (SOI) bottom layer, a silicon-based grating waveguide core,
and a hydrogel functional layer on top of the grating waveguide. The waveguide core is designed as a
grating structure to achieve Fabry–Perot resonances of the Bloch modes. The transmission spectral
profile exhibits multiple resonance peaks due to optical interference between guided modes in the
grating waveguide. The RI of the hydrogel layer changes as a result of a biochemical interaction
(e.g., multivalent binding of proteins) between the functional layer, receptor, and targeted molecules.
Consequently, the effective RI of the waveguide changes and is followed by a shift in the resonance
wavelength of the spectral transmission profile. We calculated the waveguide effective RI as a function
of several parameters of the functional layer. These parameters include the thickness, functional
volume ratio, and functional strength of the hydrogel layer. We determined the optimized hydrogel
layer thickness when a double-layer model was employed. We calculated the dynamic range of
the waveguide effective RI and performed a comparison between single- and double-layer models.
The results demonstrate the feasibility of, and set design rules for, silicon-based grating waveguide
sensors assisted by a functional hydrogel layer. The proposed configuration is a promising candidate
for a low-cost, CMOS-compatible sensor for detecting the multivalent binding of proteins.
2. Principles
2.1. Silicon-Based Grating Waveguide Sensor
Figure 1 shows the schematic of a grating waveguide structure and its sensing principle.
The waveguide core consists of Si3 N4 on top of a SiO2 bottom cladding layer. A 200-period structure,
having a 490-nm pitch with 50% duty cycle and 75-nm etch depth, is used as a grating waveguide.
The transmission profile near the 1550-nm wavelength is shown in the inset of Figure 1. Fabry–Perot
resonance modes with a stopband are formed by the distributed feedback nature of the periodic
grating structures. The resonance mode closest to the stopband exhibits the narrowest bandwidth
(i.e., the highest quality factor), so that a high sensitivity can be achieved by utilizing the fringe mode.
When the RI of the top cladding changes, the effective RI of the core waveguide changes, causing the
transmission profile to shift [23]. We carried out a numerical investigation of the grating waveguide
using a 2-D finite-difference time-domain (FDTD) method and a finite-difference method (FDM) for
transverse electric (TE) mode using software from Lumerical Solutions, Inc. (Vancouver, BC, Canada).
We incorporated a 2-D FDTD simulation-window of 110 µm in the x-direction (propagation direction)
and 4 µm in the y-direction (cross-section direction), using perfectly matched layers in boundary
conditions for a grating waveguide of 98 µm by 275 nm. In order to obtain accurate transmission of the
grating waveguide, a mesh grid size of ∆x = 40 nm in the x-direction and ∆y = 4 nm in the y-direction
as well as a time-step size of ∆t = 1.3 ˆ 10´17 s were used in the FDTD simulation.
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Figure
Schematicofofaagrating
gratingwaveguide
waveguide for
for aa refractive
principle.
Figure
1.1.Schematic
refractive index
index(RI)
(RI)sensor
sensorand
anditsitssensing
sensing
principle.
Figure
2aSchematic
shows the
simulation
result for
effectiveindex
RI, 𝑛𝑐,𝑒𝑓𝑓
, of aand
waveguide
a function of
Figure 1.
a grating waveguide
forthe
a refractive
its sensingasprinciple.
Figure
2a shows
theofsimulation
result for
the
effective RI, (RI)
nc,e fsensor
f , of a waveguide as a function of
the top cladding RI for the structure shown in Figure 1. Here, 𝑛𝑐,𝑒𝑓𝑓
is defined as a spatial average of
the top cladding RI for the structure shown in Figure 1. Here, nc,e f f is defined as a spatial average of
Figure 2a
simulation
resultcore
for the
RI, top
𝑛𝑐,𝑒𝑓𝑓
, of a waveguide
a function
of
the effective
RIsshows
of thethe
entire
waveguide
[24].effective
When the
cladding
RI varies,as𝑛𝑐,𝑒𝑓𝑓
changes
the effective RIs of the entire waveguide core [24]. When the top cladding RI varies, nc,e f f changes
theshown
top cladding
RI2a.
forFigure
the structure
shown
in Figure 1. Here,
𝑛𝑐,𝑒𝑓𝑓 iswavelength
defined as aofspatial
average
of
as
in Figure
2b shows
the corresponding
resonance
the fringe
mode.
as shown in Figure 2a. Figure 2b shows the corresponding resonance wavelength of the fringe mode.
the effective
RIs
entirewaveguide
waveguideiscore
When
the top
cladding
RI avaries,
𝑛𝑐,𝑒𝑓𝑓
changes
The
sensitivity
ofof
thethe
grating
176 [24].
nm/RIU,
where
RIU
stands for
refractive
index
unit.
The sensitivity of the grating waveguide is 176 nm/RIU, where RIU stands for a refractive index unit.
as shown
Figure 2a.
Figure
2b shows thebetween
corresponding
wavelength
of thegiven
fringeby
mode.
The
result in
coincides
with
the relationship
𝑛𝑐,𝑒𝑓𝑓 resonance
and resonance
wavelength
[25].
The
result
coincides
with
the
relationship
between
n
and
resonance
wavelength
given
by [25].
c,e
f
f
The
of thestructure,
grating waveguide
is 176
nm/RIU, where
stands
In
thesensitivity
Bragg grating
the resonance
wavelength
𝜆𝐵 isRIU
written
as for
[25]a refractive index unit.
In The
the Bragg
structure,
resonance
wavelength
written as wavelength
[25]
B is resonance
result grating
coincides
with the the
relationship
between
𝑛𝑐,𝑒𝑓𝑓 λand
given by [25].
𝜆𝐵 = 2Λ𝑛𝑐,𝑒𝑓𝑓
(1)
In the Bragg grating structure, the resonance wavelength 𝜆𝐵 is written as [25]
λ
“
2Λn
B
c,e fthe
f Bragg resonance wavelength 𝜆 is given(1)
where Λ is a grating period. The corresponding
shift of
𝐵
𝜆𝐵 = 2Λ𝑛𝑐,𝑒𝑓𝑓
(1)
by
where
Λ
is
a
grating
period.
The
corresponding
shift
of
the
Bragg
resonance
wavelength
λ
is
given
where Λ is a grating period. The corresponding shift of the Bragg resonance wavelength 𝜆B𝐵 is given by
Δ𝜆𝐵 = 2ΛΔ𝑛𝑐,𝑒𝑓𝑓
(2)
by
∆λ B “ 2Λ∆nc,e f f
(2)
Δ𝜆𝐵 = 2ΛΔ𝑛𝑐,𝑒𝑓𝑓
(2)
(a)
(b)
Figure 2. (a) Effective(a)
RI of the waveguide core and (b) resonance wavelength
(b)of a fringe mode as a
function of the top cladding RI.
Figure 2. (a) Effective RI of the waveguide core and (b) resonance wavelength of a fringe mode as a
Figure 2. (a) Effective RI of the waveguide core and (b) resonance wavelength of a fringe mode as a
function
of the top
cladding
RI.
The
resonance
shift
is attributed
to evanescent waveguide modes that penetrate and interact
function of the top cladding RI.
with the top cladding layer. As shown in Figure 2a,b, the resonance shift of the transmission response
resonance
shift is
to evanescent
waveguide
that effective
penetrateRI.
and
interact
of theThe
grating
waveguide
is attributed
directly related
to the change
in the modes
waveguide
Therefore,
The
resonance
shift
is
attributed
to
evanescent
waveguide
modes
that
penetrate
and
interact
with
with
the top cladding
layer. As
shown RI
in Figure
2a,b, the
resonance
of the transmission
we
calculate
the waveguide
effective
using FDM
instead
of theshift
resonance
shift in thisresponse
paper to
theoftop
cladding
layer.
As
shown
in
Figure
2a,b,
the
resonance
shift
of
the
transmission
response
of
the grating
waveguide
directly
related
to the change
in the
waveguide effective
provide
physical
insight asiswell
to save
calculation
effort. The
figure-of-merit
(FOM) ofRI.
theTherefore,
RI sensor
thewe
grating
waveguide
is directly related
the change
in theof
waveguide
effective
RI.this
Therefore,
calculate
the by
waveguide
RI to
using
FDM
instead
the resonance
shift
in
towe
can be
calculated
dividing effective
the sensitivity
by the
full-width
at half-maximum
(FWHM)
of paper
a Fabry–
calculate
waveguide
effective
RI save
using
FDM instead
ofThe
the figure-of-merit
resonance shift(FOM)
in thisof
paper
tosensor
provide
providethe
physical
insight
as well to
calculation
effort.
the RI
can be insight
calculated
by dividing
sensitivityeffort.
by theThe
full-width
at half-maximum
(FWHM)
of a Fabry–
physical
as well
to savethe
calculation
figure-of-merit
(FOM) of
the RI sensor
can be
Sensors 2016, 16, 914
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calculated by dividing the sensitivity by the full-width at half-maximum (FWHM) of a Fabry–Perot
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resonance mode. Although the sensitivity is not great compared with some previous work [16], the
narrow
transmission
resonance
the
Fabry–Perot
provides with
a high
FOM
of 400.
It should
Perot resonance
mode.
Althoughofthe
sensitivity
is notmode
great compared
some
previous
work
[16],
also
be
noted
that,
although
the
calculated
sensitivity
in
Figure
2b
might
be
slightly
lower
than
the narrow transmission resonance of the Fabry–Perot mode provides a high FOM of 400. It should
that
of
other
RI
sensors
in
[4],
the
significant
top
cladding
RI
change
of
a
functional
hydrogel
layer
also be noted that, although the calculated sensitivity in Figure 2b might be slightly lower than that
canofprovide
sufficient
change
of the waveguide
effective
RI [22,26],
and the silicon-based
other RIasensors
in [4],
the significant
top cladding
RI change
of a functional
hydrogel layergrating
can
waveguide
a functional
layer can be
a promising
solution
to the
enable
a low-cost,grating
compact,
provide acombined
sufficientwith
change
of the waveguide
effective
RI [22,26],
and
silicon-based
waveguide combined
with a sensor
functional
layer can be a promising solution to enable a low-cost,
CMOS-compatible
biochemical
platform.
compact, CMOS-compatible biochemical sensor platform.
2.2. Modeling of a Functional Layer for Sensing the Multivalent Binding of Proteins
2.2. Modeling of a Functional Layer for Sensing the Multivalent Binding of Proteins
Figure 3 shows the conceptual diagrams of the grating waveguide with a functional hydrogel layer
Figure
3 shows the
conceptual
diagrams
a functional
hydrogel
for sensing
multivalent
binding
of proteins.
Aof
Si3the
N4grating
gratingwaveguide
waveguidewith
with
the same dimensions
forFigure
sensing
of proteins.
3N4 grating
waveguide
same
as layer
that of
1 ismultivalent
used as a binding
waveguide
core, andA aSihydrogel
layer
on top ofwith
the the
waveguide
dimensions
that of Figure
is usedthe
as receptors
a waveguide
core,hydrogel
and a hydrogel
layer
on toptoofligand
the
serves
as the as
functional
layer. 1 When
in the
layer are
exposed
waveguide
serves
as
the
functional
layer.
When
the
receptors
in
the
hydrogel
layer
are
exposed
to
proteins, ligand-induced receptor dimerization occurs, yielding a local deswelling of the hydrogel
ligand
proteins,
ligand-induced
receptor
dimerization
occurs,
yielding
a
local
deswelling
of
the
layer. Subsequently, the RI of the hydrogel layer is reported to change by about 0.05 [22]. The local
hydrogel of
layer.
the
RI of thetakes
hydrogel
reported
to change
by about
0.05 [22].
deswelling
the Subsequently,
hydrogel layer
typically
placelayer
at itsistop
surface.
Therefore,
both singleand
The local deswelling of the hydrogel layer typically takes place at its top surface. Therefore, both
double-layer
models are considered to provide accurate characterization and design guidelines for
single- and double-layer models are considered to provide accurate characterization and design
the functional layer. In the single-layer model, the RI of the functional hydrogel layer nh is assumed
guidelines for the functional layer. In the single-layer model, the RI of the functional hydrogel layer
to change uniformly to nh,up as a result of the multivalent binding of proteins. In contrast, the RI of
𝑛ℎ is assumed to change uniformly to 𝑛ℎ,𝑢𝑝 as a result of the multivalent binding of proteins. In
the hydrogel layer in the double-layer model is assumed to form two separate values, nh,up and nh ,
contrast, the RI of the hydrogel layer in the double-layer model is assumed to form two separate
respectively, where nh,up is the RI of the reacted hydrogel that results from the multivalent binding
values, 𝑛ℎ,𝑢𝑝 and 𝑛ℎ , respectively, where 𝑛ℎ,𝑢𝑝 is the RI of the reacted hydrogel that results from the
process. Only the upper layer RI changes while the bottom layer RI remains the same as its original
multivalent binding process. Only the upper layer RI changes while the bottom layer RI remains the
value
nh .asAits
functional
a is definedvolume
as the ratio
reacted as
volume
to the
hydrogel
same
original volume
value 𝑛ℎratio
. A functional
ratio of𝑎 the
is defined
the ratio
of total
the reacted
volume.
that
thehydrogel
effect of volume.
biological
crosslinking
on hydrogel
shrinkage
is significantly
lower
volumeNote
to the
total
Note
that the effect
of biological
crosslinking
on hydrogel
than
that
of
hydrogel
volume
phase
transitions
caused
by
changes
in
temperature,
pH,
and
shrinkage is significantly lower than that of hydrogel volume phase transitions caused by changesionic
in
strength
[27,28].pH, and ionic strength [27,28].
temperature,
Figure
Conceptual diagram
diagram showing
showing the
thethe
Figure
3. 3.Conceptual
the RI
RI change
change ofof aa functional
functionalhydrogel
hydrogellayer
layerafter
after
multivalent
binding
of
proteins.
A
single-layer
and
a
double-layer
model
are
considered
for
multivalent binding of proteins. A single-layer and a double-layer model are considered for comparison.
comparison.
h:
hydrogel
layer
thickness;
a:
functional
volume
ratio,
𝑛
:
RI
of
a
hydrogel
layer
before
ℎ
h: hydrogel layer thickness; a: functional volume ratio, nh : RI of a hydrogel
layer before the multivalent
the multivalent
binding
or RI ofhydrogel
the non-reacted
after the
multivalent
ℎ,𝑢𝑝 :
binding
or RI of the
non-reacted
volumehydrogel
after thevolume
multivalent
binding;
nh,up : binding;
RI of the 𝑛
reacted
RI of thevolume
reactedafter
hydrogel
volume after
the multivalent binding.
hydrogel
the multivalent
binding.
3. Simulation Results
3. Simulation
Figure 4aResults
shows the waveguide effective RI 𝑛𝑐,𝑒𝑓𝑓 as a function of the thickness of the hydrogel
layer for single- and double-layer models. The RI of the Si3N4 waveguide and SiO2 bottom cladding
Figure 4a shows the waveguide effective RI nc,e f f as a function of the thickness of the hydrogel
layers are 1.989 and 1.444, respectively. All the RIs and effective RIs in this paper are specified at a
layer for single- and double-layer models. The RI of the Si3 N4 waveguide and SiO2 bottom cladding
wavelength of 1550 nm. The RI of the hydrogel layer before the multivalent binding 𝑛ℎ is 1.34. It is
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layers are 1.989 and 1.444, respectively. All the RIs and effective RIs in this paper are specified at a
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wavelength
1550 nm. The RI of the hydrogel layer before the multivalent binding nh is 1.34.
assumed to change to 1.35 for the single-layer model (=nh,s ) after the multivalent binding. In the
assumed to change
to 1.35
single-layer
model
the multivalent
In the
ℎ,𝑠 ) after
double-layer
model, the
RI offor
thethe
reacted
hydrogel
nh,up(=𝑛
changes
to 1.39,
while that ofbinding.
the non-reacted
double-layer
RI of the reacted
hydrogel
to 1.39, while
that of the
nonℎ,𝑢𝑝 changes
layer
remainsmodel,
at 1.34 the
as previously
reported
on the 𝑛basis
of experimental
observations
[21,26,29].
reacted
layer
remains
at
1.34
as
previously
reported
on
the
basis
of
experimental
observations
The functional volume ratio a is set at 0.2 for the double-layer model, so that the volume RI change
[21,26,29].
functional
ratio and
𝑎 is double-layer
set at 0.2 for the
double-layer
so that thebinding
volumeof
remains
theThe
same
for bothvolume
the singlemodels.
Before model,
the multivalent
RI changen remains
the same for both the single- and double-layer models. Before the multivalent
proteins,
c,e f f increases with the hydrogel thickness owing to the extension of the region where
binding
of
proteins,
𝑛𝑐,𝑒𝑓𝑓 increases with the hydrogel thickness owing to the extension of the region
evanescent fields exist
(dotted curve). After the multivalent binding, nc,e f f also increases with the
where
evanescent
fields
exist
(dotted
curve).(black
After the
multivalent
binding,
𝑛𝑐,𝑒𝑓𝑓 also increases with
hydrogel thickness for both
the
single-layer
dashed
curve) and
double-layer
(black solid curve)
the hydrogel thickness for both the single-layer (black dashed curve) and double-layer (black solid
models. In the double-layer model, the increase of nc,e f f starts to saturate at about 300 nm because
curve) models. In the double-layer model, the increase of 𝑛𝑐,𝑒𝑓𝑓 starts to saturate at about 300 nm
surface sensing utilizing evanescent fields becomes less effective
as a result of the increased non-reacted
because surface sensing utilizing evanescent fields becomes less effective as a result of the increased
volume. The nc,e f f of the single-layer model is larger than that of the double-layer model because
non-reacted volume. The 𝑛𝑐,𝑒𝑓𝑓 of the single-layer model is larger than that of the double-layer model
the entire volume is reacting
in the single-layer model. Therefore, the bulk hydrogel with a uniform
because the entire volume is reacting in the single-layer model. Therefore, the bulk hydrogel with a
RI change in the entire volume is preferable to achieve a higher sensitivity. We also consider the
uniform RI change in the entire volume is preferable to achieve a higher sensitivity. We also consider
shrinkage effects of hydrogel (gray dashed and gray solid curves, respectively) after multivalent
the shrinkage effects of hydrogel (gray dashed and gray solid curves, respectively) after multivalent
binding on the basis of previous studies [27]. We assume that the maximum thickness change of the
binding on the basis of previous studies [27]. We assume that the maximum thickness change of the
reacted hydrogel layer is 10% based on the previous report. For a single-layer model, we assume a
reacted hydrogel layer is 10% based on the previous report. For a single-layer model, we assume a
2% decrease in a hydrogel thickness because an equal amount of biological reaction is assumed for
2% decrease in a hydrogel thickness because an equal amount of biological reaction is assumed for
double-layer (20% of reactive volume) and single-layer models (100% of reactive volume). This results
double-layer (20% of reactive volume) and single-layer models (100% of reactive volume). This
in
the maximum
thicknessthickness
changes changes
of the reacted
layer being
2%being
and 10%
singleand
results
in the maximum
of thehydrogel
reacted hydrogel
layer
2% for
andthe
10%
for the
double-layer
model,
respectively.
Note
that
the
functional
volume
ratio
of
the
double
layer
model
is
single- and double-layer model, respectively. Note that the functional volume ratio of the double0.2.
The
solidand
dashed-gray
show nc,e f f considering
shrinkage, while the black lines exhibit
layer
model
is 0.2.
The solid-lines
and dashed-gray
lines show 𝑛the
𝑐,𝑒𝑓𝑓 considering the shrinkage, while the
nblack
considering
shrinkage
for singledouble-layer
respectively.
Themodels,
two gray
c,e f f without
lines exhibit
𝑛𝑐,𝑒𝑓𝑓 the
without
considering
theorshrinkage
for models,
single- or
double-layer
lines
present
trends
similar
to
the
corresponding
black
lines
while
exhibiting
a
slightly
lower
value
respectively. The two gray lines present trends similar to the corresponding black lines while
because
of
the
thickness
decrease
after
the
deswelling.
exhibiting a slightly lower value because of the thickness decrease after the deswelling.
(a)
(b)
Figure
Figure4.4.Cont.
Cont.
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(c)
Figure 4. (a) Waveguide effective RI 𝑛𝑐,𝑒𝑓𝑓 for various hydrogel thicknesses (dotted curve: before
Figure 4. (a) Waveguide effective RI nc,e
f f for various hydrogel thicknesses (dotted curve: before
functionalization, solid curve: after functionalization using a double-layer model ( 𝑛
= 1.39,
functionalization, solid curve: after functionalization using a double-layer model ℎ,𝑢𝑝
(nh,up = 1.39,
𝑛ℎ = 1.34), dashed curve: after functionalization using a single-layer model ( 𝑛ℎ,𝑠 = 1.35)) and
nh = 1.34), dashed curve: after functionalization using a single-layer model (nh,s = 1.35)) and (b) effective
(b) effective RI change 𝑛𝑐,𝑒𝑓𝑓 for various hydrogel thicknesses (solid curve: double-layer model
RI change nc,e f f for various hydrogel thicknesses (solid curve: double-layer model (nh,up = 1.39,
(𝑛ℎ,𝑢𝑝 = 1.39, 𝑛ℎ = 1.34), dashed curve: single-layer model (𝑛ℎ,𝑢𝑝 = 1.35)). The functional volume
nh = 1.34), dashed curve: single-layer model (nh,up = 1.35)). The functional volume ratio a is 0.2 for
ratio 𝑎 is 0.2 for the double-layer model. The black and gray curves represent the cases with and
the double-layer model. The black and gray curves represent the cases with and without considering
without considering hydrogel shrinkage after deswelling. Shrinkages of 2% and 10% in thickness are
hydrogel shrinkage after deswelling. Shrinkages of 2% and 10% in thickness are assumed for a
assumed for a single- and double-layer model, respectively. (c) Effect of the hydrogel shrinkage on
single- and double-layer model, respectively. (c) Effect of the hydrogel shrinkage on the waveguide
the waveguide effective RI change for single- and double-layer models.
effective RI change for single- and double-layer models.
Figure 4b shows the corresponding waveguide effective RI difference, ∆𝑛𝑐,𝑒𝑓𝑓 , before and after
theFigure
multivalent
binding
for the shrinkage
and non-shrinkage
cases.
The ∆𝑛𝑐,𝑒𝑓𝑓
single-layer
4b shows
the corresponding
waveguide
effective RI
difference,
∆nc,eoff f the
, before
and after
is largerbinding
than thatfor
of the
model,
and the ∆𝑛𝑐,𝑒𝑓𝑓
of the
double-layer
reaches
themodel
multivalent
thedouble-layer
shrinkage and
non-shrinkage
cases.
The
∆nc,e f f of model
the single-layer
its maximum
at a that
thickness
about 150 nm.
Thisand
result
thedouble-layer
optimal thickness
the
model
is larger than
of theof
double-layer
model,
the determines
∆nc,e f f of the
modelofreaches
is needed
to ensure
multivalent
binding produces
the highest
possible
its functional
maximumlayer
at a that
thickness
of about
150that
nm.the
This
result determines
the optimal
thickness
of the
change
in
effective
RI
∆𝑛
.
In
considering
the
shrinkage
effects
of
hydrogel
due
to
multivalent
𝑐,𝑒𝑓𝑓
functional layer that is needed to ensure that the multivalent binding produces the highest possible
binding,
we observed
almost. the
same results for the single-layer model and slightly lower effective
change
in effective
RI ∆n
c,e f f In considering the shrinkage effects of hydrogel due to multivalent
RI
changes
for
the
double-layer
model
than for
those
non-shrinkage
cases.
undergo
a
binding, we observed almost the same
results
theof
single-layer
model
andHydrogels
slightly lower
effective
volume phase transition upon changes in temperature, pH, and ionic strength, which induces
RI changes for the double-layer model than those of non-shrinkage cases. Hydrogels undergo a
dramatic changes in volume and optical density. Thus, one can easily measure the changes using
volume phase transition upon changes in temperature, pH, and ionic strength, which induces dramatic
Dynamic Light Scattering (DLS) or optical microscopy. In contrast, biological crosslinking causes
changes in volume and optical density. Thus, one can easily measure the changes using Dynamic
significantly smaller changes in volume and thus is hardly detectable using DLS. We have calculated
Light Scattering (DLS) or optical microscopy. In contrast, biological crosslinking causes significantly
the effects of hydrogel shrinkage on waveguide effective RI with and without shrinkage owing to
smaller
changes in volume and thus is hardly detectable using DLS. We have calculated the effects
multivalent binding as shown in Figure 4c. It shows the effect of the shrinkage on top of the RI change
of hydrogel
shrinkage
oneffect
waveguide
effectiveisRI
with and
without
shrinkage owing to multivalent
by the deswelling.
The
of the shrinkage
defined
as (∆𝑛
𝑐,𝑒𝑓𝑓 − ∆𝑛𝑐,𝑒𝑓𝑓,𝑠 )/∆𝑛𝑐,𝑒𝑓𝑓 , where ∆𝑛𝑐,𝑒𝑓𝑓
binding
as
shown
in
Figure
4c.
It
shows
the
effect
of
the
shrinkage
on top of the
RI change
by the
is the difference of waveguide RI before and after deswelling without considering
hydrogel
shrinkage,
deswelling.
The
effect
of
the
shrinkage
is
defined
as
(∆n
´
∆n
)/∆n
,
where
∆n
f f after c,e
f f ,s
c,econsidering
ff
c,e f f is the
and ∆𝑛𝑐,𝑒𝑓𝑓,𝑠 is the difference of waveguide RI before c,e
and
deswelling
hydrogel
difference
of waveguide
and after
deswelling
without
considering
shrinkage,
and
shrinkage.
The effect ofRI
thebefore
shrinkage
ranges
from about
2% to 5%
and 11% tohydrogel
13% depending
on an
∆ninitial
is
the
difference
of
waveguide
RI
before
and
after
deswelling
considering
hydrogel
shrinkage.
c,e f f ,s hydrogel thickness for a single-layer and double-layer model, respectively. The results suggest
The
effect
the shrinkage
rangesexperience
from about
2%shrinkage
to 5% and
11% to
depending model,
on an initial
that
the of
thinner
hydrogel layers
more
effects.
In 13%
the double-layer
the
hydrogel
thickness
single-layer
double-layer
respectively.
Thebecause
results suggest
that the
shrinkage
effectsfor
area much
more and
significant
than inmodel,
the single-layer
case
the thickness
thinner
hydrogel
experiencemodel.
more shrinkage effects. In the double-layer model, the shrinkage
changes
more inlayers
the double-layer
a can
In
actual
biochemical
applications,
volume
controlled
by changing
effects are much more significant than inthe
thefunctional
single-layer
case ratio
because
thebe
thickness
changes
more in
layer composition
thethe
double-layer
model. properties, applying various receptors, or both. Figure 5a shows ∆𝑛𝑐,𝑒𝑓𝑓 for
various
hydrogel
thickness
and functional
volume ratios.
Inratio
all further
in this
paper,the
In actual
biochemical
applications,
the functional
volume
a can becalculations
controlled by
changing
hydrogel
shrinkage
is
not
considered
because
the
shrinkage
does
not
seem
to
significantly
affect
the
layer composition properties, applying various receptors, or both. Figure 5a shows ∆nc,e f f for various
major
trend
of
the
waveguide
effective
RI
change.
The
value
of
∆𝑛
reaches
its
maximum
at
a
𝑐,𝑒𝑓𝑓
hydrogel thickness and functional volume ratios. In all further calculations
in this paper, hydrogel
thickness
150 nm,because
coinciding
the result
in Figure
4a. It increases
becomes
shrinkage
is of
notabout
considered
the with
shrinkage
doesshown
not seem
to significantly
affect as
the𝑎 major
trend
larger,
as
shown
in
Figure
5b.
The
value
of
𝑛
is
assumed
to
be
a
constant
of
1.39
for
all
ℎ,𝑢𝑝
of the waveguide effective RI change. The value of ∆nc,e f f reaches its maximum at a thickness 𝑎of. The
about
largest ∆𝑛𝑐,𝑒𝑓𝑓 was exhibited by the 150-nm-thick layer, and it increased monotonically for 𝑎 values
150 nm, coinciding
with the result shown in Figure 4a. It increases as a becomes larger, as shown
from 15% to 25% as shown in Figure 5b.
in Figure 5b. The value of nh,up is assumed to be a constant of 1.39 for all a. The largest ∆nc,e f f was
exhibited by the 150-nm-thick layer, and it increased monotonically for a values from 15% to 25% as
shown in Figure 5b.
Sensors 2016, 16, 914
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Sensors 2016, 16, 914
Sensors 2016, 16, 914
7 of 9
7 of 9
(a)
(a)
(b)
(b)
Figure 5. (a) ∆𝑛𝑐,𝑒𝑓𝑓 as a function of the functional volume ratio 𝑎 for various hydrogel thicknesses
Figure
a function
various
Figure5.5.(a)
(a)∆n
∆𝑛
a functionofofthe
thefunctional
functionalvolume
volumeratio
ratioa 𝑎forfor
varioushydrogel
hydrogelthicknesses
thicknessesand
c,e f f asas
and (b) ∆𝑛𝑐,𝑒𝑓𝑓 𝑐,𝑒𝑓𝑓
for specific hydrogel thicknesses of 20, 150, and 600 nm. The RI of the reacted
(b)and
∆nc,e
for
specific
hydrogel
thicknesses
of
20,
150,
and
600
nm.
The
RI
of
the
reacted
hydrogel
nh,up
(b)f f ∆𝑛𝑐,𝑒𝑓𝑓 for specific hydrogel thicknesses of 20, 150, and 600 nm. The RI of the reacted
hydrogel 𝑛ℎ,𝑢𝑝
has a constant value of 1.39 for all 𝑎.
has
a constant
value
1.39 for value
all a. of 1.39 for all 𝑎.
hydrogel
𝑛ℎ,𝑢𝑝
has of
a constant
We performed a more precise quantification on the ∆𝑛𝑐,𝑒𝑓𝑓 within a small RI variation of the
Weperformed
performedaamore
more precise quantification
quantification on
within a asmall
RIRI
variation
of the
𝑐,𝑒𝑓𝑓
We
on the
the ∆𝑛
∆n
variation
of the
c,e
f f within
hydrogel.
Here, the RI of the precise
hydrogel layer varies from
1.385
to
1.395
for both small
the singleand doublehydrogel.
Here,
the
RI
of
the
hydrogel
layer
varies
from
1.385
to
1.395
for
both
the
singleand
doublehydrogel.
Here,
the RIinof
the hydrogel
varies from
1.385
to 1.395
for bothlayer
the provides
single- and
layer models
as shown
Figures
6a–d. For layer
the single-layer
model,
a thicker
functional
layer modelsmodels
as shown
inshown
Figuresin
6a–d.
For the
single-layer
model,
a thicker
functional
layer provides
double-layer
as
Figure
6a–d.
For
the
single-layer
model,
a
thicker
a larger ∆𝑛𝑐,𝑒𝑓𝑓 that yields a larger dynamic range of ∆𝑛𝑐,𝑒𝑓𝑓 . For the double-layer model, a functional
150-nm
a larger
∆𝑛𝑐,𝑒𝑓𝑓 that yields a larger dynamic range of ∆𝑛𝑐,𝑒𝑓𝑓 . For the double-layer model, a 150-nm
layer
provides
a larger
∆nc,e f f ∆𝑛
that
yields
a
larger
dynamic
range
of
∆n
.
For
the
double-layer
c,e
f
f
thickness
provides
the largest
,
which
corresponds
to
the
results
shown
in
Figures
4a
and 5a.
thickness provides the largest ∆𝑛𝑐,𝑒𝑓𝑓
𝑐,𝑒𝑓𝑓 , which corresponds to the results shown in Figures 4a and 5a.
model,
a 150-nm
thicknessofprovides
∆nc,e f fmodel
, which
corresponds
to the
results
shown in
The amount
and variation
∆𝑛𝑐,𝑒𝑓𝑓 ofthe
thelargest
double-layer
is smaller
than that
of the
single-layer
The amount and variation of ∆𝑛𝑐,𝑒𝑓𝑓 of the double-layer model is smaller than that of the single-layer
Figures
4a
and
5a.
The
amount
and
variation
of
∆n
of
the
double-layer
model
is
smaller
than that
model because the grating waveguide is essentially
c,e f fa surface sensor that detects a biochemical
model because the grating waveguide is essentially a surface sensor that detects a biochemical
ofprocess
the single-layer
thetop
grating
waveguide
is essentially
a surface
sensor
that detects
occurring model
at the because
waveguide
surface.
Therefore,
a larger dynamic
range
of ∆𝑛
is
process occurring at the waveguide top surface. Therefore, a larger dynamic range of ∆𝑛𝑐,𝑒𝑓𝑓
𝑐,𝑒𝑓𝑓 is
aattained
biochemical
occurring than
at the by
waveguide
top surface.model.
Therefore,
a larger
range of
by process
the single-layer
the double-layer
It will
be dynamic
an interesting
attained by the single-layer than by the double-layer model. It will be an interesting
future
to by
characterize
and than
compare
monovalent
∆n
attained
the single-layer
by thequantitative
double-layersignals
model. between
It will be an
interestingand
future
c,e f f isstudy
future
study to characterize and compare quantitative signals between monovalent and
multivalent
bindings.and
Each
binding
may produce
a significantly
different amount
of effective
RI
study
to characterize
compare
quantitative
signals
between monovalent
and multivalent
bindings.
multivalent
bindings. Each
binding
may produce
a significantly
different amount
of effective
RI
change
in a waveguide.
Each
binding
may
produce
a
significantly
different
amount
of
effective
RI
change
in
a
waveguide.
change in a waveguide.
(a)
(a)
(b)
(b)
(c)
(c)
(d)
(d)
Figure
within a small RI variation of the functional layer for various hydrogel thicknesses
Figure6.6.∆𝑛
∆𝑛𝑐,𝑒𝑓𝑓
𝑐,𝑒𝑓𝑓 within a small RI variation of the functional layer for various hydrogel thicknesses
Figure
6.(a)∆n
withinand
a smalldouble-layer
RI variation of the functional
for hydrogel
various hydrogel
thicknesses
c,e
f
f
for
the
single-layer
forlayer
specific
thicknesses
of 20,
for the (a) single-layer and(c)
(c) double-layermodels.
models. ∆𝑛
∆𝑛𝑐,𝑒𝑓𝑓
𝑐,𝑒𝑓𝑓 for specific hydrogel thicknesses of 20,
for
the
(a)600
single-layer
and
(c)
double-layer
models.
∆nc,e f f for
specific hydrogel thicknesses of 20, 150,
150,
and
nm
for
the
(b)
single-layer
and
(d)
double-layer
models.
150, and 600 nm for the (b) single-layer and (d) double-layer models.
and 600 nm for the (b) single-layer and (d) double-layer models.
Sensors 2016, 16, 914
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4. Conclusions
We evaluated the characteristics of a functional hydrogel layer on a silicon grating waveguide
for use as a simple, low-cost, CMOS-compatible biochemical sensor. Such functionalization of the
hydrogel layer provides a significant RI change in response to a specialized biochemical interaction,
namely, the multivalent binding of proteins. Characterization of the functional layer was performed
numerically by exploring effective RI changes of the proposed grating waveguide including both a
single- and double-layer model of the hydrogel. The effective RI change of the waveguide is larger
for the single-layer model than for the double-layer model because the surface sensing mechanism
utilizes a waveguide evanescent field. We found that an optimal thickness exists for the double-layer
model. Our results demonstrate that the waveguide effective RI difference between before and after
the multivalent binding process increases with the functional volume ratio. The investigation of a
waveguide effective RI caused by a small RI variation of the functional layer allows us to obtain the
dynamic range of the proposed biochemical sensor. The characterization of the functional hydrogel
layer could be the foundation for the application of a silicon-based grating waveguide sensor to a wide
variety of biochemical sensors.
Acknowledgments: This work supported in part by the National Research Foundation of Korea (NRF) under the
Basic Science Research Program (No. 2014R1A1A2053587) and the National Research Foundation of Korea (NRF)
under the Global Research Lab. (GRL) Program (NRF-2015K1A1A2028228).
Author Contributions: All authors contributed considerably to this article. The article was conceived and
structured by all the authors. Jongseong Kim and Hyuk-Kee Sung conceived the simulation, analyzed the data,
and wrote the paper. Jongseong Kim and Hyuk-Kee Sung are also co-corresponding authors of the manuscript.
Yoo-Seung Hong performed the simulations and analyzed the data.
Conflicts of Interest: The authors declare no conflict of interest.
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