Probabilistic estimation of detection characteristics for surface-enhanced localized

surface plasmon resonance biosensing

Heejin Yang

The Graduate School

Yonsei University

Department of Electrical and Electronic Engineering

Probabilistic estimation of detection characteristics for surface-enhanced localized

surface plasmon resonance biosensing

A Master’s Thesis

Submitted to the Department of Electrical and Electronic Engineering

and the Graduate School of Yonsei University

in partial fulfillment of the

requirements for the degree of

Master of Science

Heejin Yang

December 2014

This certifies that the master’s thesis of

Heejin Yang is approved.

____________________________________ Thesis Supervisor: Donghyun Kim ___________________________________ Thesis Committee Member: Taewon Hwang ___________________________________ Thesis Committee Member: Dong Ha Kim

The Graduate School

Yonsei University

December 2014

i

Acknowledgments

First and foremost, I would like to express my deepest appreciation to my advisor,

Professor Donghyun Kim, who has supported me throughout my Master’s course.

Without his devoted and constant support, it would have been impossible for me

to complete my Master’s course. In spite of busy works of his own, he was

willing to take time to listen to my thoughts, help me on a better path of life, give

advice on my research, and provide the best environment for my research.

I would also like to express my warm thanks to my thesis committee.

Professor Taewon Hwang helped me find the basic concept of my study. With

constructive questions, Professor Dong Ha Kim helped me see the things I would

have otherwise overlooked. This dissertation would have never been

accomplished without their support.

I am also thankful for the past two years that I have spent with my colleagues

in the Biophotonics Engineering Laboratory. Even though I have not had an

opportunity to work with Dr. Jongryul Choi, Dr. Yeonsoo Ryu, Mr. Yonghwi Kim,

and Taewoong Lee, my research has been largely inspired by their research. Dr.

Youngjin Oh has helped me with the fabrication of nanostructure using e-beam

lithography and advised me, from research to my religious faith. I have to mention

Wonju Lee for giving me great help in RCWA calculation, illustration of

detection models, and my life in the laboratory. My time working with Taehwang

Son and Hongki Lee was an extraordinary experience. Also, I am grateful to

Haena Kim, Kiheung Kim, Changheon Lee, and Hyunwoong Lee.

ii

I thank Kangsoo Kim, Minki Kim, and Hojung Jin as well for their

encouragement and advice.

I would like to express my deepest thanks to my family for always staying

on my side.

Lastly, I would like to thank God for being my savior..

iii

Table of Contents

Acknowledgments

List of tables

List of figures

List of acronyms

Abstract

Chapter 1 Introduction

1. Biosensors

2. Surface plasmon resonance biosensors

2.1 Theoretical background

2.2 Detection characteristics

2.3 Enhancement of detection characteristics and colocalization

3. Overlap integral

Chapter 2 Probabilistic estimation of detection characteristics

1. Method and model

1.1 Electromagnetic field amplitude: nanoisland and its nearfield

1.2 Permittivity modeling: Poisson distribution

1.3 Three detection models

2. Probabilistic interpretation of detection characteristics

2.1 Non-specific detection

2.2 Non-colocalized detection

2.3 Colocalized detection

iv

2.4 Noise characteristics of nanoplasmonic detection

3. Results and discussion

3.1 Detection characteristics of three detection models

3.4 Wavelength dependence

3.5 Discussion

Chapter 3 Conclusion

References

국문요약

v

List of tables

Table 1.1 Historical landmarks in the biosensor and its development

Table 1.2 Type of transducers with property

Table 2.1 RCI at 95% CL for concentration and 2.03E11 selected as the

target concentration that produces normalized OI = 0.001 in non-

specific detection with target size = 25 nm

vi

List of figures

Figure 1.2.1 Two semi-infinite dielectric media with ε1 and ε2 separated by a

interface plane at z = 0.

Figure 1.2.2 Dispersion curve for SP.

Figure 1.2.3 Prism configuration with dielectric constants ε1 < ε2 (a) Otto

configuration (b) Kretschmann configuration.

Figure 1.2.4 Concept of a SPR biosensor.

Figure 2.1.1 Comparison of fabrication process: (a) e-beam lithography for

customized nanostructure. (b) Thermal annealing for nanoisland.

Figure 2.1.2 SEM images of nanoisland with varied thickness of evaporated

film.

Figure 2.1.3 Correlation length: (a) correlation coefficient of nanoisland (2 2

m2) (b) profile of correlation coefficient along the horizontally

dashed axis, and (c) profile of correlation coefficient along the

vertically dashed line.

Figure 2.1.4 Schematic process of near field calculation.

Figure 2.1.5 Schematic illustration of probability density function given by

Poisson distribution when concentration C (same as χS) = 1 in

arbitrary unit (histogram in blue) and 10 (in red).

Figure 2.1.6 Schematics of three different detection models.

Figure 2.3.1 (a) Normalized OI for non-specific detection of targets of varying

size. A color band is CI with 95% CL. (b) Magnified image of a

rectangle in Figure 2.1.6a. The vertical arrow is the range of

normalized OI to be possible at the concentration producing

normalized OI =1. The horizontal arrow is the range of producible

concentration of normalized OI = 1.

vii

Figure 2.3.2 (a) Normalized OI for non-colocalized detection of targets of

varying size. A color band is CI with 95% CL. (b) Magnified

image of a rectangle in (a).

Figure 2.3.3 Normalized OI for colocalized specific detection. Although there is

a CI with 95% CL, the CI appears as a line and thus is hard to

distinguish between the CL and the mean.

Figure 2.3.4 Comparison of normalized OIs generated by three models with

varying concentrations with target size at 25 nm.

Figure 2.3.5 RCI curves of varying concentration with target size = 25 nm in the

three models.

Figure 2.3.6 RCI curves of varying concentration with target size = 25 nm in the

three models.

Figure 2.3.7 Near field patterns of same nanoisland at various wavelengths. (a)

Incident wavelength λ = 488 nm, (b) 633 nm, and (c) 760 nm.

Figure 2.3.8 Histograms of normalized fields of nanoislands at various

wavelengths.

Figure 2.3.9 Normalized OI of the colocalized detection at different

wavelengths λ = 488 nm, 633 nm, and 760 nm of varying

concentration with target size 25 nm.

Figure 2.3.10 (a) RCI at different wavelengths λ = 488 nm, 633 nm, and 760 nm.

(b) Magnified RCI at undistinguishable wavelengths arget size 25

nm.

viii

Figure 2.3.11 List of abbreviations

CI CL CLT EMT LOD OI PR RCI RCWA SAM SEM SP SPP SPR

confidence interval confidence level central limit theorem effective medium theorem limit of detection overlap integral photo resist relative confidence interval rigorous coupled-wave analysis self-assembled monolayer scanning electron microscope surface plasmon surface plasmon polariton surface plasmon resonance

ix

Abstract

The present study is on detection characteristics of surface-enhanced surface

plasmon resonance biosensors. The random nature of near-field generated by

nanoisland brings the need for probabilistic modeling. Detection characteristics,

represented by overlap integral, of three detection models - non-specific, non-

colocalized, and colocalized detection models - were calculated based on the

probability theory. The calculated overlap integral is proportional to the target

concentration. The effect of target size on the reliability of normalized overlap

integral is limited compared to that of target concentration. Overlap integral is the

highest and confidence interval is the lowest in colocalized detection. Compared

to the non-specific detection model, the colocalized detection model got the

detection limit enhanced by four more orders.

Keywords: biosensor, surface plasmon resonance (SPR), SPR biosensor, semicontinuous nanostructure, random nano island, probability theory

1

Chapter 1

Introduction

1. Biosensors

A sensitive and selective recognition of materials has always been an important

issue in scientific research.

This is an important research topic also in the fields of biomedical

engineering, biochemistry, and biophysics, because of the need regarding drug

development, medical diagnostics, environmental issues, and more. Recent

demands in many fields have required biosensing for detecting biomolecules,

microorganisms, and macromolecular interactions.

High sensitivity and selectivity have usually been achieved by high-liquid

chormatography, gas chromatography, and mass spectrometry, and high cost and

preparation of samples for these useful techniques have accelerated development

of economical methods that are easy to use. Biosensors may be one such solution

[1,2].

The term "Biosensor" was introduced by Karl Cammmann in 1977 [3]. He

defined a biosensor as a chemical sensor where the detecting system uses a

biochemical mechanism. Leland C. Clark is known to be the inventor of the first

biosensor [4]. Clark published his paper on glucose biosensor in 1956. The device

was made up of an oxygen electrode coated with glucose oxidase. The electrode

2

measures the oxygen concentration. The reduced amount of oxygen concentration

is converted into the amount of glucose.

Table 1.1 Historical landmarks of biosensor and its development.

Year Event References

1962 First glucose enzyme electrode Clark, L. C. & Lyons, C. [1]

1973 Glucose enzyme electrode based on

peroxide detection Guilbault, G. G. & Lubrano, G. J. [2]

1975 Launch of the first commercial glucose

sensor system

Yellow Springs Instruments glucose

biosensor

1977 Karl Cammann introduced the term

“ biosensor ” Cammann, K. [3]

1980 First fibre optic pH sensor for in vivo

blood gases Peterson. [5]

1982 First fibre optic-based biosensor for glucose : Demonstration of in vivo

glucose monitoring

Shichiri, M. et al. [6]

1983 First surface plasmon resonance (SPR)

immunosensor Liedberg, [7]

1990 SPR based biosensor by Pharmacia

BIACore Jonsson

2001 Ellipsometric Biosensors Arwin [8]

Present Quantum dots, nanoparticles,

nanowires, nanotubes, etc Ghoshal [9-10]

A biosensor is generally defined as a device to detect chemical or biological

molecules, or microorganisms. A biosensor consists of a biological active

substance and a transducer. The biological active substance, called a receptor, is

used to selectively bind the analyte or functional group of interest, which may be

either organic or inorganic. Antibody, enzyme, and DNA are widely used as

receptors in biosensors [11-15]. A transducer is a platform to transform chemical

3

or physical responses of a biological recognition event into measureable

parameters. Optical biosensors are biosensors with transduction based on optical

principles. They are classified not only by the basis but also by whether the label

association attaches to the target or not.

Table 1.2 Type of transducers with properties Type Property

Optics

Luminescence Fluorescence Adsorption

Phosphorescence Surface enhanced Raman scattering

Dispersion Refraction spectroscopy

Electrochemistry Impedimetry Amperometry Voltammetry

Thermodynamics Heat of reaction

Adsorption

4

2. Surface plasmon resonance biosensors

2.1 Theoretical background

2.1.1 Excitation

Free electrons excited by the electromagnetic field at a metal/dielectric interface

collectively and coherently oscillate; such oscillations, are called SP oscillations

[16,17]. Consider two semi-infinite nonmagnetic media with dielectric functions

ε1 and ε2 are separated by a planar interface at z = 0. Maxwell’s equations without

external sources can be expressed as follows [18]:

Figure 1.2.1 Two semi-infinite dielectric media with ε1 and ε2 separated by an

interface plane at z = 0.

(1.2.1)

(1.2.2)

∙ ∙ 0 (1.2.3)

and

ε2ε1

z = 0

5

∙ 0 (1.2.4)

where i is i-th media. Media 1 is below z = 0 and media 2 is above z = 0.

Solutions of Eqs. (1.2.1) ~ (1.2.4) can be analyzed in the s-polarized and p-

polarized electromagnetic modes. For an ideal surface, if waves propagate along

the interface, there must be a component of the electric field normal to the surface.

Thus, the p-polarized wave is considered. The conditions in which a travelling

wave with the magnetic field H parallel to the interface (p-polarized wave) may

propagate along the surface (z = 0), with the fields declining in the positive (z > 0)

and negative (z < 0) directions are caculated.

, 0, | | (1.2.5)

and

0, , 0 | | (1.2.6)

qi represents the magnitude of a wave vector parallel to the surface.

When Eqs. (1.2.1) and (1.2.6) are substituted into Eqs. (1.2.1) ~ (1.2.4), the results

are as follows:

1 1 1 1 , (1.2.7)

2 2 2 2 , (1.2.8)

and

2 2

2 . (1.2.9)

In the boundary conditions, the component of the electric and magnetic fields

parallel to the surface must be continuous. From Eqs. (1.2.7) and (1.2.8),

6

1

11

2

22 0 (1.2.10)

and

1 2 0 (1.2.11)

are derived. For Eqs. (1.2.10) and (1.2.11), a solution exists only when the

determinant is zero, i.e.

1

1

2

20 (1.2.12)

This is the SP condition.

The 2D wave vector q from the boundary conditions is entered into Eq.

(1.2.9), i.e. q1=q2=q. Thus, Eq. (1.2.12) can be expressed as follows [19]

, (1.2.13)

w/c represents the magnitude of the light wave vector.

7

2.1.2 Dispersion relation

Consider a Drude semi-infinite metal in vacuum. Dielectric functions of medium

is

1 12

(1.2.14)

and ε2 = 1 [18], where η represents a positive infinitesimal. Thus, Eq. (1.2.13) can

be expressed as follows:

(1.2.15)

The blue line shows the light line ω = cq in free space and the red solid line

shows the SPP in the dispersion relation of Eq. (1.2.15). There is no intersection

between the red line and the blue line at low frequency. Thus, the incident light

cannot directly excite the SPP in free space. The red solid line approaches the

surface plasma frequency line. Because the dispersion curve of photons in metal

can lie across the red line at the point where the momenta match, SPPs can be

excited in metal.

8

Figure 1.2.2 Dispersion curve for SP.

ω=ckx

kx=

1

0.6

0.8

0.4

0.2

0

ωsp=ωp/

0 0.5 1 1.5 2 2.5 3

ω/ωp

Kx (arbitrary units)

momentum matching

9

2.1.3 Penetration depth

From Eqs. (1.2.13) and (1.2.9) (with q1 = q2 = q), the SP decay constant ki normal

to the interface is derived as follows

2

1 2. (1.2.16)

Eq (1.2.16) can define a penetration depth or attenuation length L = 1/ki where the

electromagnetic field becomes 1/e.

10

2.2 Surface plasmon resonance

To demonstrate SP excitation, Otto and Kretschmann independently propose

prism configuration [21,22]. The difference between the two proposals is the

location of low refractive index media between a metal film and the prism. In

Otto’s configuration which is for SP of solid phase media, low refractive index

media are inserted under the metal, whereas in Kretschmann’s configuration, the

metal adheres to the surface of the prism without low refractive index media. The

latter configuration is a more efficient structure for the creation of SP. There is

also a grating configuration, but its inaccuracy places the grating-configuration-

based sensor at a disadvantage; because the incident light passes through the

sample, it may have an accuracy issue when the sample is absorptive.

Figure 1.2.3 Prism configurations with dielectric constants ε1 < ε2 (a)

Otto configuration and (b) Kretschmann configuration.

As previously stated, the momentum of incoming photons and the SP can be

matched. Such matching is called SPR, and the incident angle of photons is called

θε0

ε1

ε2

prism

SP

θε0

ε1

ε2

prism

SP

(a) (b)

re

an

w

fu

ph

re

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Th

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11

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biosensors

ton

17)

ric

ted

The

his

as

is

12

(1.2.18)

where P is the measured output of the sensor; I is the sensor input; n is the

refractive index of the sensor platform; SRI is the sensitivity on refractive index

change; and ESF is the efficiency of the surface functionalization. Thus, the S is

the ratio of the change in the sensor output (e.g., wavelength or resonance angle)

to the change in the input (e.g., concentration of analyte). The S can be divided

into SRI and ESF. SRI is related to a method of modulation and excitation of SP, but

not ESF [23].

LOD is a metric with respect to the resolution of a biosensor and indicates

the minimum concentration of analyte that can be detected from the absence of

analyte [23]. LOD is calculated from the measured output of the sensor and the

standard deviation of a blank sample. The concentration of analyte that generates

the sensor output of three standard deviations is the LOD [24].

13

2.4 Enhancement of detection characteristics and colocalization

SPR biosensors are advantageous in being real-time and label-free. However, they

are not sensitive enough to detect a single molecule because of its label-free

nature. Several techniques have been proposed to improve the sensitivity, such as

conjugation with gold, silver, magnetic, or carbon-based nanoparticles, surface

modification with nanostructure and metamaterials; and colocalization of the

biointeractions of interest [11,25-28].

Colocalization is a technique to make an overlap between biointeraction and

a field localized by nanostructure. Dielectric or metal is evaporated at an angle to

coat the nanostructure except the regions very nearby the nanostructure. It is

similar as the situation where a shadow is formed right near the building which

receives the sunlight. The exposed regions of the surface are used as the binding

regions to capture the functionalized targets, allowing colocalization. Experiments

have discovered that the sensitivity increases by 1000 times compared to the

traditional detection [11,29-33].

Despite the sensitivity enhancement by colocalization is experimentally

proven the sensitivity characteristics is generally vague to understand [26]. Due to

the difficulty of alignment and the limitation of the prediction on the localized

near-field position, exact colocalization is difficult to achieve.

14

3. Overlap integral

SPR biosensors are founded on an enhanced evanescent field in the

metal/dielectric interface. The field distribution in the region where the enhanced

evanescent field exists determines the sensor sensitivity for a perturbation in the

analyte. Shalabney and Abdulhalim demonstrate that a shift in the wavevector k

corresponds to the OI, which corresponds to the interaction volume Vin [34,35]

δ∙∗∙ ∙

∙∗∙ ∙

(1.3.1)

where Ei and ki represent the electrical field and its wave vector before the

refractive index variation from perturbation in analyte; Ef is the changed electrical

field after the perturbation.; and δk is the change in the wave vector because of the

change of the dielectric constant from ε to ε + δε. Since δk represents the change

in the incident angle or the wavelength change, δk/δε indicates the sensitivity of

the sensor corresponding to the OI normalized by the total energy. An

enhancement of the sensitivity can be mathematically accomplished by enlarging

the interaction volume to increase the evanescence depth, improving the field

intensity, and using a material with a high electric constant.

Based on Eq. (1.3.1), the OI can be simplified as follows [34]:

OI | | (1.3.2)

Et is the normalized tangential electromagnetic field amplitude and ε is the

permittivity. Therefore, Eq. (1.3.2) has the unit of energy. The total energy on the

surface with the localized target can be related to the radiative energy which can

15

be measured with the SPR signal. Hence, the near-field quantities in the

interaction volume may be transduced into the far-field characteristics. For

example, the LOD can be molecularly interpreted as the number of target

molecules (N) generating a reference change in the reflectance (R) in the SPR

biosensor. Based on the OI, the redefined LOD is closely related to the

perturbation in the OI from the biointeraction of interest. In addition, the detection

sensitivity can be redefined as the ratio of the change in the OI to the number of

target molecules.

Thus, OIs help understand the relation between the near-field and the far-

field. In previous research, OIs have been used to optimize the nanostructure in

different features and structural parameters and predict the sensitivity of the

experimental model [26,36].

OIs have been deterministically treated, but the far-field characteristics of a

SPR biosensor can calculated with the simplified OI Eq. (1.3.2) in the manner of

the probabilistic approach. If the sampling function for the numerical calculation

is larger than one target molecule, the target permittivity may be approximately

derived as follows:

ε ∑ (1.3.3)

ε and ε each represent the permittivity of the target and the buffer

(ε2 2 and ε2 2 ). represents the locations of Nt target

molecules. When Eq. (1.3.3) is put into Eq. (1.3.2), the result is as follows:

OI ∑ | | | | (1.3.4)

16

From Eq. (1.3.4), the sensitivity is derived as follows:

∆

∆∑ | | ∑ | | ⁄ (1.3.5)

This is because the right hand side of Eq. (1.3.4) is a constant. Although the OI

becomes a simple integral form, two components, the permittivity and the field,

remain to analytically evaluate the OI. Due to the complex action of targets such

as contact inhibition or aggregation, it is complicated to precisely model the target

and its distribution. Also, the field is largely unknown.

The permittivity of the target and the buffer solution is treated as a

permittivity of a layer derived from the EMT [26,36]. Not considering the nature

of a random variable, however, the EMT-based evaluation is deterministic. In this

thesis, the probabilistic aspect of OI is focused on the colocalization. The

reliability in estimating the concentration of a target is also discussed.

17

Chapter 2

Probabilistic estimation of detection

characteristics

1. Method and Model

1.1 Electromagnetic field amplitude: nanoisland and its nearfield

To produce highly localized SP, the nanostrucutures on the metal surface are

fabricated by Focused-ion beam, e-beam lithography, or others. For example, e-

beam lithography is the practice of SEM by focusing a beam of electrons to draw

customized shapes on a surface coated with an electron-sensitive resist which can

be either positive or negative. Exposed to the e-beam, the electron resistor is

transformed into either more or less soluble structure. Due to the difference in the

solubility, either the exposed or non-exposed regions of the resistor are selectively

removed, with the surface immersed in the developing solution. After the

developer is rinsed on the surface, the vapor metal or dielectric covers the opening

region, and the residual resistor is removed. Although this practice is powerful in

that it can draw the patterns of nanostructure without mask, it has low throughput,

is not cost-effective, and is time-consuming. Also, the SEM, the evaporator for

vapor deposition, and various chemicals are required for the e-beam lithography.

18

Figure 2.1.1 Comparison of fabrication process: (a) e-beam lithography for

customized nanostructure. (b) Thermal annealing for nanoisland.

Random nanoisland, which is a semi-continuous structure, can be simply

synthesized by annealing the surface covered with the metal. It increases the cost-

effectiveness and reduces the synthesizing time [15]. Also, the excitation of the

highly localized SPs on the random nanoisland is experimentally observed [22]. It

is applied in various ways such as resonance energy transfer [37,38], surface-

enhanced Raman spectroscopy [39-42], enhancement and quenching of

fluorescence and photoluminescence [43-48], highly luminescent light emitting

diodes [49], solar cells [50,51], spontaneous light emission [52], and far-field

super-resolution microscopy [53].

Evaporation

PR spincoating

e-beam lithography

Development

Evaporation

Removal

Customized nanostructure

Thermal annealing

(a) (b)

Semicontinuousnanoisland

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22

1.2 Permittivity modeling: Poisson distribution

The distribution of target molecules at a certain concentration in space can be

analyzed with the stochastic geometry which is for random spatial patterns. In

enhancing sensing characteristics, where the target molecules are exactly located

is less important than whether they exist inside the highly localized near-field; one

target molecule in the highly localized near-field increases the sensing

characteristics more than a target molecule located outside does. In the stochastic

geometry, the number of points at a given rate is a random variable and is known

to follow the Poisson distribution [59]. The Poisson distribution is a discrete

probability distribution that demonstrates the probability of a given number of

events occurring in a fixed interval or space when these events occur with a

known average rate and independently of the time since the last event [60].

If the target molecules show no preference for any point and the total

volume of the target molecules is small that it is negligible compared to that of the

highly localized near-field, the random variable of target molecules can be

modeled according to the Poisson point distribution. In this case, the probability

mass function is

P!

. (2.1.1)

χ is the known average number of target molecules per unit volume, which is the

F

P

Figure 2.1.

oisson distr

.5 Schemat

ribution wh

(h

ic illustrati

hen concen

histogram i

23

ion of prob

ntration C (

in blue) and

bability den

(same as χ

d 10 (in red

nsity functio

χS) = 1 in ar

d).

on given by

rbitrary un

y

nit

24

1.3 Three detection models

Non-specific and specific detection have been considered. Randomness in the

non-specific detection arises from the distribution of target objects and the

intrinsic nature of nanoislands. Randomness in the specific detection is related to

the probability of binding target molecules to probe layer on the surface. The

binding process in the specific detection is stochastic and is considered as a

negligible factor in this study [61,62].

Figure 2.1.6 shows a simple model used to calculate the characteristics of

SPR detection in the non-specific and the specific models on nanoislands. The

models have a 20-nm thin underlying silver film. The dielectric permittivity and

the size of target biomolecules have been treated the same as those of adenovirus

particles (dielectric, nav = 1.366). The notation of target concentration has

followed En (n: integer) represents 10n /L = 10n-9 /m3 which is normally used

for the virus concentration. The non-specific detection model in Figure 2.1.6a has the probabilistically

distributed target in 3D. In the specific detection model illustrated in Figure 2.1.6b,

the distribution of target molecules is planar on the recognition layer with

antibodies that selectively capture the target. The binding position on the layer

follows the probabilistic distribution. In the colocalized detection model shown in

Figure 2.1.6c, the target molecules are bound to the localized field inside the

recognition layer and the binding position is probabilistically distributed. For

th

na

in

us

hese three m

anoislands.

F

We obs

ncident light

sed for SP

models, the

Figure 2.1.

served dete

t at = 48

PR sensing.

e randomne

6 Schemati

ction chara

8, 633, and

. The refle

25

ess of near

ics of three

acteristics a

d 760 nm. T

ectance cha

r-field distr

e different d

and localiza

These three

ange occurr

ibutions fo

detection m

ation on th

wavelength

ring as the

ollows that

models

he p-polariz

ths are wide

e result of

of

zed

ely

f a

26

biointeraction was calculated at the fixed incident angle of 60. It is assumed that

a 2.3-nm chromium layer adhered to an SF10 substrate (refractive index ns =

1.723) in the ambient buffer solution (nbuffer = 1.33). Also, we assumed that

nanoislands were made of a thermally annealing 5-nm silver film on top of the

chromium layer. Optical constants of silver and chrome at = 488, 633, and 760

nm were taken [63].

27

2 Probabilistic interpretation of detection characteristics

2.1 Non-specific detection

To make the analysis simple, it is assumed that is divided into four levels,

while ε is divided into two levels depending on the location , i.e.,

, ∈ |0.75 max min max, ∈ |0.50 max min 0.75 max min, ∈ |0.25 max min 0.50 max min

, ∈ |min 0.25 max min

(2.2.1)

and

ε ∈

(2.2.2)

Hence, Eq. (21) can be expressed as follows:

{ } { }∑∑ ≈-3

0= 12

023

0= 12

02 ++)(= i itiiii itiitii KAεESεEKAεEKASεEOI (2.2.3)

represents the number of target molecules in the i-th region (i = 0, 1, 2, 3)

which is an area corresponding to one of the four levels. At is the volume of one

target, and S represents the total volume of the i-th region. In this case, S and is

disjoint and independent of each other. Therefore, can be treated as the

independent Poisson random variable with parameter Si. Eq. (2.2.3) is

approximated based on the same assumption in Eq. (2.1.1) that S ≫ Eq.

(2.1.1) can be converted into

P!

. (2.2.4)

28

The OI is normalized by the optical signature of ambient buffer solution

without any target molecules. Normalized optical signature OIis interpreted as

follows:

OI∑ 2

0S21

30

OI , (2.2.5)

where OI ∑ 230 0Si. OI is a new Poisson random variable with a

parameter ∑ S30 , where 2

0S OI and

21A OI . Because each is independent of each other, OIcan be

modeled as a Gaussian random variable by the CLT [64]. The CLT is a theory in

which a Gaussian random variable is approximated from the summation of

sufficient independent random variables. As the number of independent random

variables becomes sufficient, their sum approaches a Gaussian random variable.

Inversely speaking, it is hard to model the sum of insufficient random variables

into a Gaussian random variable. In this case, the number of random variables is

close to insufficient. Nonetheless, OI can be converted into a Gaussian random

variable because 0 and 1 are Poisson random variables, and a Poisson

random variable is close to a Gaussian random variable. The mean and the

variance of OI are given by

OI2 ∑ ∑3 0

30 (2.2.6)

and

OI2 ∑ 23

0 (2.2.7)

From Eqs. (2.2.6) and (2.2.7), the area concentration of target, χ, is derived as follows:

29

OI ∑3 0∑ S3

0 (2.2.8)

Because of the Gaussian random variable, OI, also is a Gaussian random

variable with expectation and variance

(2.2.9)

and

σ 2 ∑2S3

0

∑ S30

2 (2.2.10)

Thus, the reliability of estimating the target concentration can be calculated in the

given CL [64]. The 95% CI of χ is

1.960 χ 1.960 . (2.2.11)

The 99% CI of χ is

2.575 χ 2.575 . (2.2.12)

Corresponding to a target concentration with 95% CL, the CI of the estimated

≡ is given by

1.960 OI 1.960 . (2.2.13)

The CI of the estimated ≡ with 99% is given by

2.575 OI 2.575 . (2.2.14)

The averages derived from the probabilistic model are consistent with those

from the deterministic model described in Eqs. (1.3.3) - (1.3.5) with the limited

ranges of target size up to 25 nm. If the target size exceeds 25 nm, the correlation

between the probabilistic and the deterministic models decreases. This is because

the assumption that the target size is small enough to be neglected compared to

30

the size of the localized field is repudiated above 25 nm. Thus, this study

performed the estimation for the target size 1 to 25 nm.

31

2.2 Non-colocalized detection

Non-colocalized detection is achieved by a probe layer on the metal surface

capturing target molecules. The influence of a probe layer on the near-field

distribution is imperceptibly small. Hence, in non-colocalized detection is

approximately identical to that in non-specific detection. The permittivity of the

outside volume to capture target molecules is treated to be ε0. The OI outside the

binding layer is constant at 20S . Eq. (2.2.3) in non-specific detection is given

by

OI ∑ S , A ∑ S , (2.2.15)

Si,inside is the volume of the i-th region in the binding layer, and Si, outside is that of

the outside. Si in non-specific detection is the sum of Si, inside and Si, outside in this

case. Furthermore, Eqs. (2.2.4) ~ (2.2.8) can be explained as follows:

P ,

!, (2.2.16)

OI∑ 2

0S ,21

30 ∑ 2

0S ,30

OI (2.2.17)

OI2 ∑ , ∑3 0

30 ∑ 2

0S ,30 OI (2.2.18)

OI2 ∑ 2

,30 (2.2.19)

OI ∑3 0 ∑ 20S , OI

30

∑ S ,30

(2.2.20)

OI ∑ S , 20S , OI , and 2

1A OI . Finally,

the CI with CLs can be obtained through Eqs. (2.2.9) ~ (2.2.14).

32

2.3 Colocalized detection

In colocalized detection, the effect of the probe layer on the approximation of

is negligible. Thus, remains identical. S2 and S3 are the regions

covered with the probe layer. The OI is expressed as

OI ∑ S , A ∑ S , ∑ S , .

(2.2.21)

Also, Eqs. (29) ~ (32) are changed to

OI∑ , ∑ , ∑ ,

(2.2.22)

, S , S , OI

(2.2.23)

∑ , (2.2.24)

∑ ∑ , ∑ ,

∑ , (2.2.25)

Then, the CI can be obtained through Eqs. (2.2.9) ~ (2.2.14).

33

2.4 Noise characteristics of nanoplasmonic detection

There are two factors that can bring noise to SPR biosensors. One such factor is

related to the technical performance, such as instrumentation from vibration or

stray light, for example. The other noise factor is related to the intrinsic noise

associated with the fundamental phenomena such as thermodynamic refractive

index fluctuation. If the noise sources are assumed to be probabilistically

independent of each other, the noise sources affect perturbations of the target

permittivity and the field amplitude that, consequently, bring noise to the OI.

Thus,

OI OI O (2.2.26)

Due to CLT, the noise term on the right hand side which is the sum of

various independent noise sources is treated as a Gaussian random variable with

expectation μ 0 and variance σ2 2 [65]. Because OI and

O can be considered independent and OI as the sum of the two

independent Gaussian random variables, OI becomes another Gaussian

random variable with mean μ Exp OI and variance σ2 2OI2. The

probability density function p is written as

ε, . (2.2.27)

and represent the statistical deviation in the tangential field amplitude

and target permittivity. The variance of OI is larger than that of OI without

O . The variance is the key factor for CI; an increase in the variance

34

increases the CI. The effects of noise factors are inversely proportional to the

LOD and, thus, the lower noise factor increases the LOD. Because the present

study demonstrates a particular model of detector, the LOD should be considered

as a relative scale rather than an absolute scale. Then, it is meaningful to relatively

compare the LODs of detection scenarios because noise factors in the scenarios

are independent of each other. Therefore, the LOD is evaluated with the relative

magnitude of optical signature generated in each of the detection scenarios.

35

3 Results and discussion

3.1 Detection characteristics of three detection model

3.1.1 Non-specific detection model

Consider a rectangular parallelepiped and assume that its base is a lateral plane of

2 2 m2 and the height is one penetration depth from the surface. If the

penetration depth is 100 nm, four target molecules exist inside the box at E10.

Figure 2.3.1 (a) describes the detection sensitivity as the optical signatures that

cause non-specific detection at a specific concentration evaluated for nanoislands.

The optical signatures are obtained by dividing the calculated OI into that of

ambient buffer without target molecules.

It is found that optical signatures monotonically increase with the size and

the target concentration. Optical signatures significantly changes with the target

size and are almost proportional to the target concentration. Because OI and

ΔOI/ΔN may be associated with the LOD and the detection sensitivity, the results

in Figure 2.3.1 imply that the LOD and the sensitivity for detecting targets of

larger size are enhanced. Such enhancement is related to the growth of effective

volume which is exposed to the near-field and occupied by the target.

Figure 2.3.1 shows the average characteristics using effective medium and

probabilistic characteristic as CI in the non-specific detection. An increase of CI

with target size shows that a larger target causes higher uncertainty at the same

concentration. For example, the CI with 95% CL for targets of ϕ = 25 nm at a

concentration of 2.03E11 is from 0.00075195 to 0.001248 with an average of

36

0.001, i.e., the relative confidence interval (RCI) defined by dividing the CI into

an average to be 0.5. The target concentration producing OI = 0.001 ranges from

1.594E11 to 2.631E11 with an average of 2.03E11, i.e., the RCI in the target

concentration of0.49. An identical concentration (2.03E11) produces the almost

constant RCI of 0.5 with target size of ϕ = 10, 15, and 20 nm although the CI at

the concentration increases with target size. This is because target size increases to

the average optical signature at the concentration. However, CI remains the same

as the target concentration changes. Hence, the RCI is inversely proportional to

the target concentration.

r

ho

Figur

varying s

rectangle in

to be po

orizontal a

e 2.3.1 (a) N

size. A color

n Figure 2.

ossible at th

arrow is the

Normalized

r band is C

1.6a. The v

he concentr

e range of p

37

d OI for no

CI with 95%

vertical arr

ration prod

producible

1.

on-specific

% CL. (b) M

ow is the ra

ducing norm

concentrat

detection o

Magnified i

ange of nor

malized OI

tion of norm

of targets of

image of a

rmalized O

I =1. The

malized OI

f

OI

I =

38

3.1.2 Specific detection model

The probe layer for the target recognition is assumed to uniformly cover the

surface in the specific detection model. The detection is limited to the target

molecules, although they are randomly captured by the layer. In other words, the

number of bindings can be identical to the target concentration. Computationally,

the target molecules are laterally distributed beneath the surface on top of the

binding layer. For simplicity, the specific detection model is estimated with

different scenarios, the non-colocalized and the colocalized detection models.

In the specific detection model, it is assumed that target molecules do not

prefer the surface as described in Figure 2.3.2. Figure 2.3.2 shows the calculated

optical signature with various target concentrations. The tendency in the results of

the non-colocalized detection is similar to the case of non-specific detection. On

the other hand, the magnitude of optical signature in non-colocalized detection is

much larger than that of optical signature in non-specific detection, which is due

to the nature of the surface. Following the evanescent nature, the near-field

exponentially decays of the surface. Thus, the optical signature is enhanced

compared to that of non-specific detection. Also, the number of target molecules

captured by the probe layer is generally larger in specific detection; as the target

concentration increases, the effective are is enlarged at a faster pace. Hence, the

stronger near-field and the wider effective area contribute to amplify the optical

signature in specific detection.

de

sp

0.

co

Figure 2

varying s

Compar

etection is s

patial rando

046857 to

oncentration

2.3.2 (a) No

size. A color

red to non-

smaller than

omness. On

0.050386

n of targets

ormalized O

r band is C

re

-specific de

n that in non

n the 95%

with an a

are ϕ = 25

39

OI for non-

CI with 95%

ectangle in

etection, th

n-specific de

CL, an op

average of

5 nm and E

-colocalized

% CL. (b) M

(a)

he variance

etection bec

ptical signa

0.048622

11. Also, th

d detection

Magnified i

e in no

cause of a d

ature range

when the

he uncertain

n of targets

image of a

on-colocaliz

decrease in t

es from OI

size and t

nty is 7.3%

of

zed

the

I =

the

in

te

In

sp

t

m

w

op

si

lo

to

erms of the R

n other wor

pecific detec

Figure

there is the

Colocali

molecules ex

would be ha

ptical trapp

gnificant b

ocalization w

The opt

o the target

RCI, compa

rds, the cert

ction.

e 2.3.3 Norm

e CI with 9

ized detect

xclusively b

rd to exper

ing in the c

because the

with an arbi

ical signatu

concentratio

ared with R

tainty in de

malized OI

5% CL, it

between

tion can be

bind in the l

rimentally p

calculation.

probabilist

itrary structu

ure in coloc

on. Because

40

RCI = 71%

etection is d

I for coloca

appears as

n the CL an

e probabili

localized fi

perform col

. Neverthele

tic interpre

ure.

calized detec

e the target

in the non-s

drastically i

lized specif

s a line so it

nd mean.

istically tre

elds as desc

localization

ess, the res

etation can

ction can be

molecules

specific det

improved b

fic detectio

t is hard to

eated in th

cribed in Fi

n on nanoisl

ults are pro

be applied

e calculated

bind to th

tection mod

by conducti

on. Althoug

distinguish

hat the targ

igure 2.3.3.

lands witho

obabilistica

d to the fie

d with respe

he probe lay

del.

ing

gh

h

get

. It

out

lly

eld

ect

yer

in

nu

de

ca

ca

th

ca

fo

op

be

de

n the locali

umber of ta

etection. Ca

an achieve t

alculation fo

he trend of

alculated op

ollows that o

ptical signa

ecause the d

etection than

Figure

w

zed field, t

arget molec

alculated t

the highest

or average b

f average o

ptical signa

of non-colo

ature is the

distribution

n in the oth

e 2.3.4 Com

with varyin

the target c

cules to the

this way, t

estimation

based on an

optical sign

atures. The

ocalized and

e highest a

n of the nea

er two scen

mparison of

ng concentr

41

concentratio

e volume o

the optical

with nanois

n effective m

natures. Fig

e overall tr

d non-specif

among the

ar-field has

narios.

f normalize

rations wit

on correspo

of the locali

signature f

slands. The

medium are

gure 2.3.3

rend of av

fic detection

three dete

a stronger

ed OIs gene

h target siz

onds to the

ized field i

for colocali

results of t

meaningfu

shows the

erage optic

ns; however

ction scena

influence i

erated by th

ze at 25 nm

e ratio of t

in colocaliz

ized detecti

the tradition

ul in followi

trend of t

cal signatur

r, the value

arios. This

in colocaliz

hree model

m.

the

zed

ion

nal

ing

the

res

of

is

zed

ls

42

Figure 2.3.3 illustrates that CI’s end-point and start-point are hard to

distinguish and that the CI is narrower than in non-specific and non-colocalized

detection. For the case where the targets are ϕ = 25 nm and the concentration is

E11, an optical signature ranges from OI = 1.5206 to 1.537 with an average of

1.5288 and the uncertainty is 1.1% in RCI. The RCI for this case is shown in

Table 2.1 for the detection models. It is confirmed RCI decreases with the order

from non-specific, non-colocalized, and to colocalized detection models. The

lowest uncertainty in the colocalized detection is achieved by limiting the freedom

of where target molecules are located. In other words, the distributable dimension

is relatively reduced from 3-dimension in non-specific detection and 2-dimension

in non-colocalized detection to 1-dimension in colocalized detection. Thus, the CI

is minimum and the value of optical signatures is maximum in colocalized

detection. Also, RCI slightly changes with target size.

Table 2.1 RCI at 95% CL for concentration and 2.03E11 selected as the

target concentration that produces normalized OI = 0.001 in non-specific

detection with target size of 25nm

Target concentration

Non-specific Non-colocalized Colocalized

9E 7.5023 0.7706 0.1170 10E 2.3723 0.2436 0.03695 11E 0.7118 0.07259 0.01078

2.03 x 11E 0.4963 0.05061 0.007514 12E 0.2372 0.02443 0.003717

ta

is

w

sc

in

re

ge

fo

de

an

The RC

argets of ϕ =

monotonic

while the opt

cale are alm

nterpretation

elated to th

enerating R

or non-spec

etection am

nd non-spec

Figure

CIs of the th

= 25 nm at

cally reduce

tical signatu

most identi

n based on

he resolutio

RCI = 1. The

ific, non-co

mplifies LOD

cific detectio

e 2.3.5 RCI

hree detect

the 95% CL

ed with targ

ure largely d

cal for the

the Poisson

on of biose

e LOD beco

olocalized,

D by 120 a

on.

I curves of

nm in

43

tion models

L by varyin

get concentr

decreases. T

e three dete

n process. I

ensors is d

omes 7.0E1

and coloca

and 11700

varying co

the three m

s in Figure

ng the target

ration becau

The slopes o

ection mod

In the prese

defined as t

10, 7.2E8, a

alized detec

times comp

oncentration

models.

2.3.5 are o

t concentrat

use CI sligh

of the RCI l

dels due to

ent study, L

the target

and 0.60E7,

ctions. Then

pared to no

n with targ

obtained w

tion. The R

htly increas

lines on a lo

o probabilis

LOD which

concentrati

, respective

n, colocaliz

on-colocaliz

get size = 25

ith

RCI

es,

og-

stic

h is

ion

ly,

zed

zed

5

44

In summary, colocalized detection enhances the optical signatures,

detection uncertainty related sensitivity, and LOD, compared to other detection

models, based on the probabilistic interpretation which are results obtained by the

traditional methods.

3.

A

at

sh

at

co

be

Th

or

ta

F

4 Waveleng

According to

t longer wav

horter wave

t an adva

olocalized d

enefit at a

hus, SPR se

rder to inve

arget size of

Figure 2.3.6

(a) In

gth depende

o previous re

velengths [5

elength. Alth

antage in

detection m

longer wav

ensing usin

estigate this

f 25 nm at li

6 Near field

ncident wav

ence

esearch, con

53-55]. How

hough non-

SPR sensi

may decrease

velength is

g colocalize

nature, opt

ight wavelen

d patterns

velength a =

45

nventional

wever, near

-specific an

ing at a lo

e at the sam

offset by

ed detection

tical signatu

ngth λ = 48

of same na

= 488 nm, (

SPR detecti

r-fields are

d non-coloc

onger wav

me wavelen

the weaker

n may have

ures from co

88, 633, and

anoisland a

(b) 633 nm,

ion has high

efficiently

calized dete

elength, th

ngth. This i

r near-field

e the best w

olocalized d

760 nm we

t various w

, and (c) 76

her sensitiv

localized a

ection may

he benefit

is because t

d localizatio

wavelength.

detection w

ere compare

wavelengths

60 nm.

ity

t a

be

of

the

on.

In

ith

ed.

s.

id

at

Fi

co

de

at

th

Figure

Figure 2

dentical in sp

t three diffe

igure 2.3.6

oncentration

ecreases as

t λ = 633 an

he effect of n

e 2.3.7 Hist

wavelen

2.3.8 shows

pite of diffe

ferent wave

6. On the

n and as the

the wavelen

nd 760 nm

near-field lo

tograms of

ngths at= 4

s that the o

erent wavele

elengths dem

other han

e wavelengt

ngth further

are compar

ocalization

46

normalized

488 nm, 633

overall tren

engths. The

monstrate n

nd, optical

th shifts fro

r shifts to 7

red, the diff

on optical s

d fields of n

3 nm, and 7

nds of optic

e distributio

noticeable d

l signature

m 488 to 6

760 nm. Wh

fferent shifts

signature is

nanoisland

760 nm.

cal signature

ns of near-f

differences

increases

33 nm. Opt

hen the opti

s in the grap

dominant.

ds at variou

es are almo

fields induc

as shown

with targ

tical signatu

ical signatur

aph imply th

us

ost

ced

in

get

ure

res

hat

=

nm

0.

O

stu

si

pr

ra

Figu

wavelengt

For the

25 nm, the

m)/OI(760

0108, and 0

I is highest

udy, the d

gnatures. T

robability th

atio of the

ure 2.3.8 No

ths aveleng

optical sign

e calculated

nm) = 1.67

0.0133 resp

t with the lo

distribution

Then, RCI

hat target m

volume of

ormalized O

gths ifferen

vary

natures at λ

d ratios ar

7. The RCI

ectively for

owest RCI a

of near-fie

decreases

molecules e

f target mo

47

OI of the co

nt waveleng

ying concen

= 488, 633

re OI(633 n

Is at E11 s

r λ = 488, 6

at λ = 633 n

eld strongl

in more a

exist in a sp

olecule to

olocalized d

gths λ = 488

ntrati

3 and 760 n

nm)/OI(488

hown in Fi

633 and 760

nm. Accordi

ly influenc

a localized

pecific regi

the volum

detection at

8, 633, and

m with th

nm) = 1.74

igure 2.3.9

0 nm. It is in

ing to the an

es the tren

field. The

ion S is

me of the r

t different

760 nm of

he targets of

4 and OI(6

are 0.013

nteresting th

nalysis in th

nd of optic

e geometric

defined as

region, whi

f ϕ

33

35,

hat

his

cal

cal

s a

ich

de

th

ne

ecreases and

he field cha

ear-field are

Figure

760 nm. (b

d reduces th

aracteristics

e closely rel

e 2.3.9 (a) R

b) Magnifie

he uncertain

such as in

lated to OI a

RCI at diff

d RCI at u

48

nty at a mor

ntensity and

and RCI.

ferent wave

undistinguis

760 nm.

re localized

d the total

elengths =

shable wav

d field. This

volume of

= 488, 633,

velengths λ

s suggests th

the localiz

and 760 nd

λ = 488 and

hat

zed

d

d

49

3.5 Discussion

Researchers in the field of biosensors are interested in whether a single molecule

may be detected by their systems. In this chapter, plasmonic detection has been

discussed with the probabilistic approach. Whether a nanoisland-based SPR

sensor is able to detect a single molecule using colocalized detection was studied;

the results indicate that the capacity of detectable binding is lower than fg/mm2. If

a molecule weights 100 kDa and the size of the localized field is 1 mm2, the LOD

would be a few hundred molecules under the best conditions. This implies that it

is quite challenging to detect a single molecule with nanoisland based on

colocalized detection. Nevertheless, OI conceptually signifies that colocalization

is able to further enhance LOD by optimizing the size of the target molecule and

localizing the strong near-field over the total field of detection.

Colocalized detection produces the highest optical signature and the lowest

uncertainty compared to the other detection models. However, there is a tradeoff

because, despite the advantages of colocalized detection, it takes an additional

experimental process to demonstrate colocalization. For sensing that requires

moderate detection characteristics, non-specific and non-colocalization can be an

alternative solution.

50

Chapter 3

Conclusions

Surface-enhanced SPR biosensors’ detection characteristics based on a

probabilistic model are researched. The randomness arising from near field

distribution of being produced by nanoisland increases to the need for

probabilistic approach. Non-specific, non-colocalized and colocalized detection

models were considered and calculated their detection characteristics. The

tendency of calculated OI shows proportional increase with target concentration.

It follows the previous research based on EMT. However the effect of target

concentration on uncertainty of SPR signal represented by normalized OI is

limited than that of target size. In other words, the CI is less affected by target

concentration than target size. Detection characteristics represented by the CI and

the amplitude of normalized OI were the optimum in colocalized detection. Based

on the probabilistic models, LOD of colocalized detection model was enhanced by

more 4 orders than that of non-specific detection model.

51

References

[1] X. Luo, J. Xu, W. Zhao, and H. Chen, “Glucose biosensor based on ENFET

doped with SiO2 nanoparticles,” Sensors and Actuators B: Chemical 97,

249-255 (2004).

[2] W. Sant, M. Pourciel, J. Launay, T. Do Conto, A. Martinez, and P. Temple-

Boyer, “Development of chemical field effect transistors for the detection of

urea,” Sensors and Actuators B: Chemical 95, 309-314 (2003).

[3] K. Cammann, “Bio-sensors based on ion-selective electrodes,” Fresenius’

Zeitschrift for Analytische Chemie 287, 1-9 (1977).

[4] L. C. Clark, and C. Lyons, “Electrode systems for continuous monitoring in

cardiovascular surgery,” Annals of the New York Academy of Sciences 102,

29-45 (2006).

[5] G. G. Guilbault, and G. J. Lubrano, “An enzyme electrode for the

amperometric determination of glucose,” Analytica Chimica Acta 64, 335-

346 (1973).

[6] J. I. Peterson, S. R. Goldstein, and R. V. Fitzgerald, “Fiber optic pH probe

for physiological use,” Analytical Chemistry 52, 864-869 (1980).

[7] M. Shichiri, Y. Yamasaki, R. Kawamori, N. Hakui and H. Abe, “Wearable

artificial endocrine pancreas with needle-type glucose sensor,” The Lancet

320, 1129-1131 (1982).

[8] B. Liedberg, C. Nylander and I. Lundstrom, “Surface plasmon resonance

for gas detection and biosensing,” Sensors Actuators A 4, 299-304 (1983).

[9] H. Arwin, “Ellipsometry on thin organic layers of biological interest:

characterization and applications,” Thin Solid Films 377, 48-56 (2000).

[10] S. Ghoshal, D. Mitra, S. Roy and D. D. Majumder, “Biosensors and

biochips for nanomedical applications: a review,” Sensors & Transducers

Journal 113, 1-17 (2010).

52

[11] S. Zeng, D. Baillargeat, H.-P. Ho and K.-T. Yong, “Nanomaterials

enhanced surface plasmon resonance for biological and chemical sensing

applications,” Chemical Society Reviews 43, 3426-3452 (2014).

[12] O. Shliom, M. Huang, B. Sachais, A. Kuo, J. W. Weisel, C. Nagaswami, T.

Nassar, K. Bdeir, E. Hiss, S. Gawlak, S. Harris, A. Mazar, and A. A. Higazi,

“Novel interactions between urokinase and its receptor,” The Journal of

Biological Chemistry 275, 24304-24312 (2000).

[13] J. G. Quinn, S. O’Neill, A. Doyle, C. McAtamney, D. Diamond, B. D.

MacCraith, and R. O’Kennedy, “Development and application of surface

plasmon resonancebased biosensors for the detection of cell-ligand

interactions,” Analytical Biochemistry 281, 135-143 (2000).

[14] K. A. Peterlinz and R. M. Georgiadis, “Observation of hybridization and

dehybridization of thiol-tethered DNA using two-color surface plasmon

resonance spectroscopy,” Journal of the American Chemical Society 119,

3401-3402 (1997).

[15] A. W. Peterson, L. K. Wolf, and R. M. Georgiadis, “Hybridization of

mismatched or partially matched DNA at surfaces,” Journal of the

American Chemical Society 124, 14601-14607 (2002).

[16] S. Maier, Plasmonics: Fundamental and Applications (Springer, 2007).

[17] A. V. Zayats, I. I. Smolyaninov, A. A. Maradudin, “Nano-optics of surface

plasmon polaritons,” Physics Reports 408, 131-314 (2005).

[18] J. D. Jackson, Classical Electrodynamics (Wiley, 1962)

[19] R. H. Ritchie and H. B. Eldridge, “Optical Emission from Irradiated Foils. I,”

Physical Review Letters 126, 1935 (1962)

[20] N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, 1976)

[21] A. Otto, “Excitation of surface plasma waves in silver by the method of

frustrated total reflection,” Zeitschrift für Physik 216, 398-410 (1968).

[22] E. Kretschmann and H. Raether, “Radiative decay of non-radiative surface

plasmons excited by light,” Zeitschrift für Naturforschung 23A, 2135-2136

(1968).

53

[23] J. Homola, “Present and future of surface plasmon resonance biosensors,”

Analytical and Bioanalytical Chemistry 377, 528-539 (2003).

[24] M. E. Stewart, C. R. Anderton, L. B. Thompson, J. Maria, S. K. Gray, J. A.

Rogers, and R. G. Nuzzo, “Nanostructured Plasmonic Sensors,” Chemical

Reviews 108, 494-521 (2008).

[25] Y. Oh, W. Lee, Y. Kim, and D. Kim, “Self-aligned colocalization of 3D

plasmonic nanogap arrays for ultra-sensitive surface plasmon resonance

detection,” Biosensors and Bioelectronics 51, 401-407 (2014).

[26] H. Yu, K. Kim, K. Ma, W. Lee, J.-W. Choi, C.-O. Yun, and D. Kim,

“Enhanced detection of virus particles by nanoisland-based localized

surface plasmon resonance,” Biosensors and Bioelectronics 41, 249-255

(2013).

[27] K. Kim, S. J. Yoon, and D. Kim, “Nanowire-based enhancement of

localized surface plasmon resonance for highly sensitive detection: a

theoretical study,” Optics Express 14, 12419-12431 (2006).

[28] R. J. Chen, H. C. Choi, S. Bangsaruntip, E. Yenilmez, X. Tang, Q. Wang, Y.

L. Chang, and H. Dai, “An investigation of the mechanisms of electronic

sensing of protein adsorption on carbon nanotube devices,” Journal of the

American Chemical Society 126, 1563-1568 (2004).

[29] Y. Kim, K. Chung, W. Lee, D. H. Kim, and D. Kim, “Nanogap-based

dielectric-specific colocalization for highly sensitive surface plasmon

resonance detection of biotin-streptavidin interactions,” Applied Physics

Letters 101, 233701 (2012).

[30] K. M. Byun, S. M. Jang, S. J. Kim, and D. Kim, “Effect of target

localization on the sensitivity of a localized surface plasmon resonance

biosensor based on subwavelength nanostructures,” Journal of the Optical

Society of America A 26, 1027-1034 (2009).

[31] X. D. Hoa, A. G. Kirk, and M. Tabrizian, “Enhanced SPR response from

patterned immobilization of surface bioreceptors on nano-gratings,”

Biosensors and Bioelectronics 24, 3043-3048 (2009).

54

[32] K. Ma, D. J. Kim, K. Kim, S. Moon, and D. Kim, “Target-localized

nanograting-based surface plasmon resonance detection toward label-free

molecular biosensing,” IEEE Journal of Selected Topics in Quantum

Electronics 16, 1004-1014 (2010).

[33] Y. Oh, W. Lee, and D. Kim, “Colocalization of gold nanoparticle-

conjugated DNA hybridization for enhanced surface plasmon detection

using nanograting antennas,” Optics Letters 36, 1353-1355 (2010).

[34] A. Shalabney and I. Abdulhalim, “Electromagnetic fields distribution in

multilayer thin film structures and the origin of sensitivity enhancement in

surface plasmon resonance sensors,” Sensors and Actuators A: Physical 159,

24-32 (2010).

[35] I. Abdulhalim, Biosensing configurations using guided wave resonant

structures, Optical Waveguide Sensing and Imaging, NATO Science for

Peace and Security Series B, Physics and Biophysics, edited by W. J. Bock,

I. Gannot, and S. Tanev (Springer-Verlag).

[36] W. Lee and D. Kim, “Field-matter integral overlap to estimate the

sensitivity of surface plasmon resonance biosensors,” Journal of the Optical

Society of America A 29, 1367-1376 (2012).

[37] J. Malicka, I. Gryczynski, J. Fang, J. Kusba, and J. R. Lakowicz, “Increased

resonance energy transfer between fluorophores bound to DNA in

proximity to metallic silver particles,” Analytical Biochemistry 315, 160-

169 (2003).

[38] E. Giorgetti, S. Cicchi, M. Muniz-Miranda, G. Margheri, T. Del Rosso, A.

Giusti, A. Rindi, G. Ghini, S. Sottini, A. Marcelli, and P. Foggi, “Forster

resonance energy transfer (FRET) with a donor-acceptor system adsorbed

on silver or gold nanoisland films,” Physical Chemistry Chemical Physics

11, 9798-9803 (2009).

[39] D. A. Weitz, S. Garoff, and T. J. Gramila, “Excitation spectra of surface-

enhanced Raman scattering on silver-island films,” Optics Letters 7, 168-

170 (1982).

55

[40] W. Yuan, H. P. Ho, R. K. Y. Lee, and S. K. Kong, “Surface-enhanced

Raman scattering biosensor for DNA detection on nanoparticle island

substrates,” Applied Optics 48, 4329-4337 (2009).

[41] A. Urich, A. Pospischil, M. M. Furchi, D. Dietze, K. Unterrainer, and T.

Mueller, “Silver nanoisland enhanced Raman interaction in graphene,”

Applied Physics Letters 101, 153113 (2012).

[42] Y. H. Jang, K. Chung, L. N. Quan, B. Spackova, H. Sipova, S. Moon, W. J.

Cho, H. Y. Shin, Y. J. Jang, J. E. Lee, S. T. Kochuveedu, M. J. Yoon, J.

Kim, S. Yoon, J. K. Kim, D. Kim, J. Homola, and D. H. Kim,

“Configuration-controlled Au nanocluster arrays on inverse micelle nano-

patterns: versatile platforms for SERS and SPR sensors,” Nanoscale 5,

12261-12271 (2013).

[43] C. D. Geddes, H. Cao, I. Gryczynski, Z. Gryczynski, J. Fang, and J. R.

Lakowicz, “Metal-enhanced fluorescence (MEF) due to silver colloids on a

planar surface: potential applications of indocyanine green to in vivo

imaging,” The Journal of Physical Chemistry A 107, 3443-3449 (2003).

[44] P. Cheng, D. Li, Z. Yuan, P. Chen, and D. Yang, “Enhancement of ZnO

light emission via coupling with localized surface plasmon of Ag island

film,” Applied Physics Letters 92, 041119 (2008).

[45] E. L. Moal, S. Leveque-Fort, M.-C. Potier, and E. Fort, “Nanoroughened

plasmonic films for enhanced biosensing detection,” Nanotechnology 20,

225502 (2009).

[46] Y. Wang, M. Becker, L. Wang, J. Liu, R. Scholz, J. Peng, U. Gsele, S.

Christiansen, D. H. Kim, and M. Steinhart, “Nanostructured gold films for

SERS by block copolymer-templated galvanic displacement reactions,”

Nano Letters 9, 2384-2389 (2009).

[47] S. M. Tabakman, L. Lau, J. T. Robinson, J. Price, S. P. Sherlock, H. Wang,

B. Zhang, Z. Chen, S. Tangsombatvisit, J. A. Jarrell, P. J. Utz, and H. Dai,

“Plasmonic substrates for multiplexed protein microarrays with femtomolar

56

sensitivity and broad dynamic range,” Nature Communications 2, 466

(2011).

[48] U. Bhanu, M. R. Islam, L. Tetard, and S. I. Khondaker, “Photoluminescence

quenching in gold - MoS2 hybrid nanoflakes,” Scientific Reports 4, 5575

(2014).

[49] D.-M. Yeh, C.-F. Huang, C.-Y. Chen, Y.-C. Lu, and C. C. Yang, “Localized

surface plasmon-induced emission enhancement of a green light-emitting

diode,” Nanotechnology 19, 345201 (2008).

[50] R. Santbergen, T. L. Temple, R. Liang, A. H. M. Smets, R. A. C. M. M. van

Swaaij, and M. Zeman, “Application of plasmonic silver island films in

thin-film silicon solar cells,” Journal of Optics 14, 024010 (2012).

[51] S.-P. Ng, X. Q. Lu, N. Ding, C.-M. L. Wu, and C.-S. Lee, “Plasmonic

enhanced dye-sensitized solar cells with self-assembly gold-

TiO2@core?shell nanoislands,” Solar Energy 99, 115-125 (2014).

[52] I. M. Soganci, S. Nizamoglu, E. Mutlugun, O. Akin, and H. V. Demir,

“Localized plasmon-engineered spontaneous emission of CdSe/ZnS

nanocrystals closely-packed in the proximity of Ag nanoisland films for

controlling emission linewidth, peak, and intensity,” Optics Express 15,

14289-14298 (2007).

[53] T. R. Jensen, L. Kelley, A. Lazarides, and G. C. Schatz, “Electrodynamics

of noble metal nanoparticles and nanoparticle clusters,” Journal of Cluster

Science 10, 295-317 (1999).

[54] Y. Kanamori, K. Hane, H. Sai, and H. Yugami, “100 nm period silicon

antireflection structures fabricated using a porous alumina membrane mask,”

Applied Physics Letters 78, 142-143 (2001).

[55] S. Park, G. Lee, S. H. Song, C. H. Oh, and P. S. Kim, “Resonant coupling

of surface plasmons to radiation modes by use of dielectric gratings,”

Optics Letters 28, 1870-1872 (2003).

57

[56] J. Cesario, R. Quidant, G. Badenes, and S. Enoch, “Electromagnetic

coupling between a metal nanoparticles grating and a metallic surface,”

Optics Letters 30, 3404-3406 (2005).

[57] D. Kim, “Effect of resonant localized plasmon coupling on the sensitivity

enhancement of nanowire-based surface plasmon resonance biosensors,”

Journal of the Optical Society of America A 23, 2307-2314 (2006).

[58] K. M. Byun, S. J. Yoon, D. Kim, and S. J. Kim, “Sensitivity analysis of a

nanowire-based surface plasmon resonance biosensor in the presence of

surface roughness,” Journal of the Optical Society of America A 24, 522-

529 (2007).

[59] D. Stoyan, W. S. Kendall, and J. Mecke, 2nd Ed., Stochastic Geometry and

Its Applications (Wiley, 1996).

[60] F. A. Haight., Handbook of the Poisson Distribution (John Wiley & Sons,

1967).

[61] A. Hassibi, H. Vikalo, and A. Hajimiri, “On noise processes and limits of

performance in biosensors,” Journal of Applied Physics 102, 014909 (2007).

[62] S. Das, H. Vikalo, and A. Hassibi, “On scaling laws of biosensors; a

stochastic approach,” Journal of Applied Physics 105, 102021 (2009).

[63] E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, 1985).

[64] R. D. Yates and D. J. Goodman, 2nd Ed., Probability and Stochastic

Processes (Wiley, 2005).

[65] M. R. Foreman, W.-L. Jin, and F. Vollmer, “Optimizing detection limits in

whispering gallery mode biosensing,” Optics Express 22, 5491-5511 (2014).

58

국문요약

표면 플라즈몬 공명 바이오 센서의 검출 특성에 관한 확률적

추정과 플라즈몬 식각을 이용한 동시국소화 구현

표면 향상 표면 플라즈몬 공명 바이오 센서의 검출 특성이

연구되었다. 나노섬 구조에서 만들어지는 근접장 패턴은 무작위적으로

분포하기 때문에 확률적 해석의 접근을 요한다. 검출 특성 분석을 위해

확률적으로 해석된 비선택적, 비동시국소화 그리고 동시국소화 검출

모형에서 중첩 적분을 계산하였다. 공통적으로 나타난 특징으로, 중첩

적분 크기는 표적 분자 농도에 비례하며 증가하는 경향을 보였고 표적

분자 크기의 영향도 컸다. 한편, 센싱 신호의 신뢰성은 표적 분자

크기의 영향보다 표적 분자 농도의 영향을 받았다. 동시국소화 모형은

가장 큰 값의 중첩 적분과 가장 신뢰할 만한 신뢰성을 보여주었다.

비선택적 모형과 비교 시, 동시국소화 모형은 검출 한계를 10000 배

향상 시킬 수 있는 것으로 계산되었다.

.

핵심 용어: 바이오 센서, 표면 플라즈몬 공명, 표면 플라즈몬 공명

바이오 센서, 준연속 나노구조, 나노섬 구조, 확률 이론