GOLD NANODISK ARRAY SURFACE PLASMON RESONANCE SENSOR

by

XUELI TIAN

A THESIS

Submitted in partial fulfillment of the requirements

for the degree of Master of Science in Engineering

in

The Department of Electrical and Computer Engineering

to

The School of Graduate Studies

of

The University of Alabama in Huntsville

HUNTSVILLE, ALABAMA

2015

v

ACKNOWLEDGMENTS

I like to express my gratitude to the people who have helped me in completion of

this degree. First and foremost, I would like to thank my advisor, Dr. Junpeng Guo, who

has been a wise and knowledgeable mentor to me. His passion for the research work

inspired me and his guidance led me to the right direction in my research. Without his

guidance and persistent help, this thesis would not have been possible.

I would like to thank my committee members: Dr. Dashen Shen and Dr. James K.

Baird, for their valuable time and advices for me to complete the thesis. I would like to

thank Dr. Ketan H. Bhatt, Dr. Song Q. Zhao, and Dr. Yi Wang for their help in the

biosensing related experiments. I would also like to thank Ms. Jacqueline Siniard, Ms.

Linda Grubbs, Ms. Jackie Carlson, and Ms. Della West for their administrative support

for this work.

I would like to acknowledge the support from the National Science Foundation

(NSF) EPSCoR RII program and the United States Department of Agriculture (USDA)

National Institute of Food and Agriculture.

Finally, I would like to thank my wife, Mini Zeng, and my parents for their

continuous support and care in my life.

vi

TABLE OF CONTENTS

Page

LIST OF FIGURES ......................................................................................................... viii

LIST OF TABLES............................................................................................................. xi

Chapter

1. INTRODUCTION ......................................................................................................... 1

1.1 History.................................................................................................................. 1

1.2 Motivation ............................................................................................................ 4

1.3 Surface plasmons at a metal-dielectric interface.................................................. 5

1.4 Surface plasmons in metallic nanoparticles ....................................................... 17

1.5 Surface plasmon resonance based sensing ......................................................... 21

2. METHODOLOGY IN THE RESEARCH OF TWO-DIMENSIONAL PERIODIC

METALLIC NANOSTRUCTURES ................................................................................ 24

2.1 Numerical analysis method ................................................................................ 24

2.2 Fabrication method............................................................................................. 29

3. GAP MEDIATED SURFACE PLASMON RESONANCE NANOSTRUCTURES . 34

3.1 Two-dimensional periodic metal nanodisk arrays ............................................. 34

3.2 Fabrication of two-dimensional periodic metal nanodisk arrays ....................... 37

3.3 Transmission and reflection ............................................................................... 38

4. SURFACE PLASMON RESONANCE IN SUPER-PERIODIC NANODISK .......... 42

4.1 Super-period metal nanodisk arrays................................................................... 43

4.2 Gold super-periodic nanodisk arrays device fabrication.................................... 43

4.3 Experiment setup................................................................................................ 44

4.4 Experiment results under different polarizations ............................................... 47

4.5 Simulation results and discussions..................................................................... 51

5. SUMMARY................................................................................................................. 63

5.1 Summary ............................................................................................................ 63

5.2 Suggested future works ...................................................................................... 64

vii

References......................................................................................................................... 66

viii

LIST OF FIGURES

Figure Page

1.1 The growth of the surface plasmon related paper from 1955 to 2015. .................... 3

1.2 Schematic diagram of SPPs at a metal-dielectric interface. The plane wave is

propagating in the x-z plane, with its magnetic field is polarized in the y-direction.......... 8

1.3 The complex permittivities of silver and gold as a function of wavelength. ......... 11

1.4 Dispersion relation of the SPPs at the silver-glass interface and the gold-glass

interface............................................................................................................................. 11

1.5 Propagation range and penetration depth of SPPs along the silver-glass interface

and the gold-glass interface. ............................................................................................. 14

1.6 Dispersion relation of the SPPs at the silver-air interface and the dispersion

relation in the high refractive index glass. ........................................................................ 16

1.7 Schematic of LSPs where the free conduction electrons in the metal nanoparticle

are driven into oscillation due to strong coupling with incident light. The plane wave is

propagating in the x direction, with its electric field in the z-direction. ........................... 18

1.8 Schematic of LSPs in a metal sphere in a dielectric environment. ........................ 19

1.9 Electric field intensity (|𝑬|𝟐) distribution of the gold nanodisk array at the

resonance. (a) The near electric field intensity distribution above the gold-glass interface.

(b) The electric field intensity distribution at the cross-section of the gold nanodisk. ..... 21

3.1 Surface plasmon resonance curve in the gold nanodisk arrays with a period of 480

nm, a disk diameter of 160 nm, and a disk height of 60 nm............................................. 35

3.2 Near electric field intensity (|𝑬|𝟐) distribution of the gold nanodisk array above

the gold-glass interface. (a) 507 nm wavelength; (b) 607 nm wavelength; (c) 707 nm

wavelength; (d) 807 nm wavelength; (e) 907 nm wavelength.......................................... 36

3.3 Electric field intensity (|𝑬|𝟐) distribution of the gold nanodisk array at the cross-

section of the gold nanodisk. (a) 507 nm wavelength; (b) 607 nm wavelength; (c) 707 nm

wavelength; (d) 807 nm wavelength; (e) 907 nm wavelength.......................................... 37

ix

3.4 (a) Schematic of two-dimensional periodic gold nanodisk arrays on a glass

substrate. (b) A SEM picture of the periodic gold nanodisk arrays grating fabricated on a

glass substrate. .................................................................................................................. 38

3.5 Simulation results. (a) Transmittance spectra of different air gap thickness. (b)

Reflectance spectra of different air gap thickness. ........................................................... 40

3.6 Simulation results. (a) Transmittance spectra of different air gap thickness from 0

nm to infinity. (b) Reflectance spectra of different air gap thickness from 0 nm to infinity.

........................................................................................................................................... 40

3.7 Simulation results of the transmittance spectra. (a) Air gap thickness from 0 nm to

40 nm. (b) Air gap thickness from 50 nm to 100 nm........................................................ 41

3.8 Simulation results of the reflectance spectra. (a) Air gap thickness from 0 nm to 40

nm. (b) Air gap thickness from 50 nm to 100 nm............................................................. 41

4.1 (a) Schematic of a super-period gold nanodisk array grating on a glass substrate. (b)

A SEM picture of the super-period gold nanodisk grating fabricated on a glass substrate.

........................................................................................................................................... 44

4.2 Measurement setup for the surface plasmon resonance from the first order

diffraction of the super-period gold nanodisk grating. ..................................................... 45

4.3 The first order diffraction image of the super-period gold nanodisk grating. ....... 46

4.4 Measurement results for the TE polarization incidence. (a) The first order

diffraction CCD image without BSA on the device. (b) The first order diffraction CCD

image with BSA on the device. (c) The first order diffraction spectra with (red) and

without (black) the BSA layer. (d) The zeroth order transmission spectra with (red) and

without (black) the BSA layer on the device surface. ...................................................... 49

4.5 Measurement results for the TM polarization incidence. (a) The CCD image

without the BSA layer on the device. (b) The CCD image with the BSA layer applied on

the device. (c) The first order diffraction spectra with and without BSA layer. (d) The

zeroth order transmission spectra with and without the BSA layer.................................. 51

4.6 Simulation results for the TE polarization incidence. (a) The zeroth order

transmission spectra for different BSA layer thicknesses. (b) The first order diffraction

spectra for different BSA layer thicknesses. (c) The electric field intensity resonance

spectra at the position 10 nm away from the disk 1. (d) The electric field intensity

resonance spectra at the position 10 nm away from the disk 2......................................... 54

x

4.7 The resonance wavelength versus BSA layer thickness for TE polarization. The

resonance wavelengths are the zeroth order transmission, the first order diffraction, the

near electric field intensity of the disk 1, and the near electric field intensity of the disk 2.

........................................................................................................................................... 55

4.8 Simulation results for the TM polarization incidence. (a) The zeroth order

transmission. (b) The first order diffraction. (c) The near electric field intensity at the

position 10 nm to the disk 1. (d) The near electric field intensity at the position 10 nm to

the disk 2. .......................................................................................................................... 57

4.9 The resonance wavelength versus BSA layer thickness for TM polarization. The

resonance wavelengths are of the zeroth order transmission, the first order diffraction, the

near electric field intensity of the disk 1, and the near electric field intensity of the disk 2.

........................................................................................................................................... 58

4.10 Near electric field intensity (|𝑬|𝟐) distributions on the plane of 10 nm above the

nanodisk surface: (a) at the zeroth order transmission resonance dip wavelength of 719.2

nm for TE polarization, (b) at the first order diffraction resonance peak wavelength of

725.7 nm for TE polarization, (c) at the zeroth order transmission resonance dip

wavelength 720.7 nm for TM polarization, and (d) at the first order diffraction resonance

peak wavelength of 722.2 nm for TM polarization. ......................................................... 59

4.11 Comparison of the SPR wavelength for period and super-period structure for

different polarizations in (a) simulation, (b) experiment. ................................................. 60

5.1 (a) Schematic of fiber tip based measurement setup. (b) Schematic of fiber tip

based device. ..................................................................................................................... 65

xi

LIST OF TABLES

Table Page

4.1 Selectivity of the surface plasmon resonance biochemical sensors in the simulation

and experiment for both polarizations. ............................................................................. 61

1

CHAPTER 1

INTRODUCTION

In recent years, a remarkable growth in the research area of surface plasmons has

been observed. Surface plasmons, which are scientifically reported at the beginning of

1900s, are free electron charge oscillation on surface of metals excited by incident light.

The most interesting property of surface plasmons is to circumvent the diffraction limit in

conventional optics and allow the localization of electromagnetic waves into the

nanoscale [1].

Surface plasmons have a potentially wide range of applications such as

information processing, high density data storage, solar energy harvesting, high-

resolution microscopy and spectroscopy, and biosensors. Surface plasmon resonance,

which is sensitive to the refractive index near the metal-dielectric interface, is widely

used for chemical and biological sensors.

1.1 History

The phenomenon of surface plasmons was observed in the ancient glasses. Dating

back to the 4th

century AD, Roman cage cups were decorated by embedding silver-gold

2

alloy nanoparticles in the glass [2]. The Lycurgus cup, a well-known cage cup stored in

British Museum, showed jade green in reflection and ruby red in transmission [3].

The first scientific observation of surface plasmons can be dated back to the

beginning of 20th

century. In 1902, Prof. Robert W. Wood observed an intensity

discontinuous in the spectrum of metallic gratings illuminated by a continuous broadband

light [4]. This phenomenon, which was only present for p-polarized light under certain

conditions, was called “Wood’s anomalies” thereafter. Prof. Wood was also considered

as the initiator of plasmonics because of the observation of the phenomenon [5].

Prof. Wood’s discovery drew considerable attention from scientists in optics. In

1907, the first explanation was proposed by Lord Rayleigh. He claimed that the

anomalies were connected with the “passing off of higher spectra” [6]. However, the

difference between Load Rayleigh’s theory and Prof. Wood’s experiment wasn’t

explained in the next 30 years. In 1941, the first theoretical breakthrough was made by

Prof. Ugo Fano. He explained the difference by using “leaking waves supportable by the

grating” [7]. The modern analysis of Wood’s anomalies began at the beginning of 1970s

due to the revolutions in microlithography, microfabrication [8], and numerical

simulation based on rigorous vector theory of gratings [9]. In 1974, the first successful

comparison [9] was in quantitative agreement with experiment by Dr. Hutley [10].

The first theoretical description of surface plasmons in metal thin films was

published by Dr. Ritchie in 1957 [11]. The properties of surface plasmons were

investigated by using solid-state physics. In 1968, Dr. Ritchie and coworkers described

the Wood’s anomalies by using surface plasmon resonances excited on the gratings [12].

In 1974, the term of surface plasmon polariton (SPP) was first introduced by Dr.

3

Cunningham and coworkers [13]. In the same year, the surface-enhanced Raman

scattering (SERS) spectrum was first observed on roughened silver surface [14].

Along with the breakthrough in theoretical description of surface plasmons, the

revolution in the microfabrication leaded to many surface plasmon resonance (SPR)

based applications, especially the SPR based sensors. In 1983, the first SPR based

biosensors was demonstrated [15]. And the first commercial SPR biosensor product was

launched by Pharmacia Biosensor AB in 1990 [16], which was a major boost to the

research of surface plasmons. The late 1990s was a turning point from laboratory

curiosity to practical applications in this area [17]. In 2007, an estimate of fifty percent of

all publications on this area involved the use of surface plasmons for biodetection [18].

Figure 1.1 shows the annual number of publications containing “surface plasmon” from

1955 to 2015 (the 2015 data is to Oct 28, 2015). The data is obtained from

www.sciencedirect.com.

Figure 1.1 The growth of the surface plasmon related paper from 1955 to 2015.

4

1.2 Motivation

Localized surface plasmons (LSPs) in metal nanoparticles have been investigated

for more than a decade [19]–[22]. This interaction at the metal-dielectric interface

produces electron oscillation with a resonance frequency that strongly depends on

particle materials [23], particle shape [24]–[26], particle size [27], array period [28], and

the dielectric environment [29]. Metal nanoparticle arrays with different geometrics and

compositions have been used for various sensor applications [30]–[33]. The transduction

mechanism of the localized surface plasmon resonance (LSPR) sensor is based on the

resonance shift caused by local refractive index variation [34]. The variation in the

medium near the surface of metal nanostructure is usually used in the biological and

chemical sensing [35]. In this thesis, a gap mediated SPR nanostructure is demonstrated

as a nanometer scale displacement and vibration sensor.

Traditionally, SPR spectra are measured in the zeroth order transmission or

reflection by using optical spectrometers [35]. Recently an SPR spectral measurement

technique without using external optical spectrometer is reported for measuring SPR of

one-dimensional and two-dimensional patterned nanostructures [36]–[40]. In this thesis, a

super-period gold nanodisk array is shown as an SPR spectrometer sensor for protein

bonding. The SPR spectra are measured in the first order diffraction.

This thesis is outlined as follows. An introduction to the surface plasmons is given

in Chapter 1. The fundamentals of SPP and LSPR are introduced in the Section 1.3 and

Section 1.4, respectively. The fabrication and numerical analysis methods to investigate

SPR in two-dimensional nanostructures are described in Chapter 2. The fabrication and

simulation results of gap mediated SPR sensor by using two-dimensional metal nanodisk

5

structure are described in Chapter 3. The experiment and simulation results of the gold

super-period metal nanodisk grating enabled SPR spectrometer sensor in different

polarizations are described in Chapter 4. The summary of previous works and the

suggestions of the future works are given in Chapter 5.

1.3 Surface plasmons at a metal-dielectric interface

As described in [41] and many other books , the surface plasmons can be derived

directly from the classic Maxwell’s equations with material properties and boundary

conditions. In the section, the dispersion relation at a metal-dielectric interface is derived

from a general form of the Maxwell’s equations. Some properties of SPP will be

discussed at the end of this section.

The Maxwell’s equations in differential form are

∇ × 𝑬 = −𝜕𝑩

𝜕𝑡(1.1)

∇ × 𝑯 = 𝐉 +𝜕𝑫

𝜕𝑡(1.2)

∇ ∙ 𝑫 = 𝜌 (1.3)

∇ ∙ 𝑩 = 0 (1.4)

where E is the electric filed, H is the magnetic field, D is the electric displacement, B is

the magnetic flux density, J is current density and ρ is the charge density. Considering a

non-magnetic isotopic material in the absence of external source, the Maxwell’s equation

in equations (1.2) and (1.3) become

∇ ×𝑯 =𝜕𝑫

𝜕𝑡(1.5)

∇ ∙ 𝑫 = 0 (1.6)

where the electric displacement D and magnetic flux density B are expressed by

6

𝐃(t) = 휀0∫ 𝑑𝜏휀(𝑡 − 𝜏)𝑬(𝜏)+∞

−∞

(1.7)

𝑩 = 𝜇0μ𝑯 (1.8)

where ε is the relative permittivity and μ = 1 is the relative permeability of the

nonmagnetic medium.

The Fourier representation of each factor in the equations (1.7)&(1.8) is given by

𝐃(t) =1

2𝜋∫ 𝑑𝜔𝑒𝑖𝜔𝑡�̂�(𝜔)+∞

−∞

(1.9)

𝐄(t) =1

2𝜋∫ 𝑑𝜔𝑒𝑖𝜔𝑡�̂�(𝜔)+∞

−∞

(1.10)

ε(t) =1

2𝜋∫ 𝑑𝜔𝑒𝑖𝜔𝑡휀̂(𝜔)+∞

−∞

(1.11)

𝐇(t) =1

2𝜋∫ 𝑑𝜔𝑒𝑖𝜔𝑡�̂�(𝜔)+∞

−∞

(1.12)

Apply equations (1.10)&(1.11) to equation (1.7) with the consideration of delta

function 𝑓(𝑥′) = ∫ 𝛿(𝑥 − 𝑥′)𝑓(𝑥)𝑑𝑥+∞

−∞, 𝛿(𝜔 − 𝜔′) = 𝛿(𝜔′ − 𝜔) = ∫ 𝑑𝑡

𝑒−𝑖(𝜔−𝜔′)𝑡

2𝜋

+∞

−∞in

Fourier transform,

𝐃(t) = 휀0∫ 𝑑𝑡 [1

2𝜋∫ 𝑑𝜔𝑒𝑖𝜔(𝑡−𝜏)휀̂(𝜔)+∞

−∞

] [1

2𝜋∫ 𝑑𝜔′𝑒𝑖𝜔

′𝜏�̂�(𝜔′)+∞

−∞

]+∞

−∞

= 휀01

2𝜋∫ 𝑑𝜔𝑒𝑖𝜔𝑡휀̂(𝜔) [∫ 𝑑𝜔′ �̂�(𝜔′)

+∞

−∞

] [1

2𝜋∫ 𝑑𝜏𝑒−𝑖(𝜔−𝜔

′)𝜏+∞

−∞

]+∞

−∞

=휀02𝜋

∫ 𝑑𝜔𝑒𝑖𝜔𝑡휀̂(𝜔)+∞

−∞

∫ 𝑑𝜔′ �̂�(𝜔′)+∞

−∞

𝛿(𝜔′ −𝜔)

=휀02𝜋

∫ 𝑑𝜔𝑒𝑖𝜔𝑡휀̂(𝜔)+∞

−∞

�̂�(𝜔)

(1.13)

Combine equations (1.9) and (1.13), the electric displacement D is given by

7

�̂�(𝜔) = 휀0휀̂(𝜔)�̂�(𝜔) (1.14)

𝑫(𝒓, 𝑡) = ∫ 𝑑𝜔+∞

−∞

�̂�(𝒓,𝜔)𝑒𝑖𝜔𝑡 =휀02𝜋

∫ 𝑑𝜔휀̂(𝜔)+∞

−∞

�̂�(𝒓,𝜔)𝑒𝑖𝜔𝑡 (1.15)

And the time derivative of the electric displacement D is given by

𝜕𝑫(𝒓, 𝑡)

𝜕𝑡=휀02𝜋

∫ 𝑑𝜔휀̂(𝜔)+∞

−∞

�̂�(𝒓, 𝜔)𝜕𝑒𝑖𝜔𝑡

𝜕𝑡=휀02𝜋

∫ 𝑑𝜔휀̂(𝜔)+∞

−∞

�̂�(𝒓,𝜔)𝑖𝜔𝑒𝑖𝜔𝑡 (1.16)

Apply curl on both sides of equation (1.12) and consider the magnetic field

change with 𝒓,

𝛁 × 𝐇(𝒓, t) =1

2𝜋∫ 𝑑𝜔𝛁 × �̂�(𝒓,𝜔)𝑒𝑖𝜔𝑡+∞

−∞

(1.17)

Apply equations (1.16)&(1.17) in the equation (1.5),

𝛁 × �̂�(𝒓,ω) = 𝑖𝜔휀0휀̂(𝜔)�̂�(𝒓,𝜔) (1.18)

Apply equations (1.8), (1.10), and (1.12) in the equation (1.1), a similar equation is

derived for the electric field E, which can be written as

𝛁 × �̂�(𝒓,ω) = − 𝑖𝜔𝜇0𝜇�̂�(𝒓,𝜔) (1.19)

Apply curl on both sides of equation (1.18) and use vector cross product ∇ × ∇ ×

�̂� = ∇(∇ ∙ �̂�) − ∇2�̂�, the wave equation is given by

∇2�̂� + 𝑘02휀̂(𝜔)�̂� = 0 (1.20)

where 𝑘0 =𝜔

𝑐is the wave vector in a vacuum，𝑐 =

1

√𝜇0𝜀0is the speed of electromagnetic

waves in a vacuum. Equation (1.20) is the well-known Helmholtz equation. A similar

equation exists for the electric field E, which can be written as

∇2�̂� + 𝑘02휀̂(𝜔)�̂� = 0 (1.21)

We assume that electromagnetic waves propagate along the x-direction on a

Cartesian coordinate system and show no spatial variation in the y-direction, as shown in

8

the Figure 1.2. Then the magnetic field is described as �̂�(𝑥, 𝑦, 𝑧) = �̂�(𝑧)𝑒𝑖𝛽𝑥. 𝛽 = 𝑘𝑥 is

the propagation constant of the wave in the direction of propagation. Inserting the

expression into equation (1.20) yields the desired form of the wave equation

∂2�̂�

∂z2+ [𝑘0

2휀̂(𝜔) − β2]�̂� = 0 (1.22)

The simplest geometry sustaining SPPs is a metal-dielectric interface. A

schematic is shown in Figure 1.2. The dielectric constant of the dielectric at the upper

half space (𝑧 > 0) is a real constant 휀�̂�. The dielectric constant of the metal at the lower

half space (𝑧 < 0) is described by a complex function 휀�̂�(𝜔).

Figure 1.2 Schematic diagram of SPPs at a metal-dielectric interface. The plane wave is

propagating in the x-z plane, with its magnetic field is polarized in the y-direction.

Assuming a TM wave propagates in the x-z plane with the magnetic field H

polarized in the y direction, the magnetic field takes the form

�̂�(𝑥, 𝑦, 𝑧) = 𝐻0𝑒±𝑘𝑧𝑧𝑒𝑖𝛽𝑥�̂� (1.23)

where – for 𝑧 > 0 and + for 𝑧 < 0, 𝑘𝑧 is the component of the wave vector in the z

direction which fulfills

9

𝑘𝑧 = √𝛽2 − 𝑘02휀̂(𝜔) (1.24)

Apply equation (1.23) into equation (1.5) yields

�̂�𝑦(𝑧) = 𝐻𝑑𝑒−𝑘𝑧,𝑑𝑧𝑒𝑖𝛽𝑥 (1.25)

�̂�𝑥(𝑧) = −𝑖𝐻𝑑1

𝜔휀0휀�̂�𝑘𝑧,𝑑𝑒

−𝑘𝑧,𝑑𝑧𝑒𝑖𝛽𝑥 (1.26)

�̂�𝑧(𝑧) = 𝐻𝑑𝛽

𝜔휀0휀�̂�𝑒−𝑘𝑧,𝑑𝑧𝑒𝑖𝛽𝑥 (1.27)

for 𝑧 > 0 and

�̂�𝑦(𝑧) = 𝐻𝑚𝑒𝑘𝑧,𝑚𝑧𝑒𝑖𝛽𝑥 (1.28)

�̂�𝑥(𝑧) = 𝑖𝐻𝑚1

𝜔휀0휀�̂�(𝜔)𝑘𝑧,𝑚𝑒

𝑘𝑧,𝑚𝑧𝑒𝑖𝛽𝑥 (1.29)

�̂�𝑧(𝑧) = 𝐻𝑚𝛽

𝜔휀0휀�̂�(𝜔)𝑒𝑘𝑧,𝑚𝑧𝑒𝑖𝛽𝑥 (1.30)

for 𝑧 < 0. 휀�̂� and 휀�̂�(𝜔) are relative permittivity of dielectric and metal, respectively.

For 𝑧 = 0, continuity of �̂�𝑦 requires

𝐻𝑑 = 𝐻𝑚 (1.31)

And apply equation (1.31) into equations (1.26) and (1.29), the continuity of �̂�𝑥 at 𝑧 = 0

requires

−𝑖𝐻𝑑1

𝜔휀0휀�̂�𝑘𝑧,𝑑𝑒

−𝑘𝑧,𝑑𝑧𝑒𝑖𝛽𝑥 = 𝑖𝐻𝑚1

𝜔휀0휀�̂�(𝜔)𝑘𝑧,𝑚𝑒

𝑘𝑧,𝑚𝑧𝑒𝑖𝛽𝑥 (1.32)

𝑘𝑧,𝑑휀�̂�

+𝑘𝑧,𝑚휀�̂�(𝜔)

= 0 (1.33)

The equation (1.33) can be also rewritten as

𝑘𝑧,𝑑𝑘𝑧,𝑚

= −휀�̂�

휀�̂�(𝜔)(1.34)

10

Apply equation (1.24) for 휀�̂� and 휀�̂�(𝜔) in the equation (1.34),

√𝛽2 − 𝑘02휀�̂�

√𝛽2 − 𝑘02휀�̂�(𝜔)

= −휀�̂�

휀�̂�(𝜔)(1.35)

𝛽2 − 𝑘02휀�̂�

𝛽2 − 𝑘02휀�̂�(𝜔)

=(휀�̂�)

2

(휀�̂�(𝜔))2 (1.36)

𝛽2 = 𝑘02휀�̂�휀�̂�(𝜔)

휀�̂� + 휀�̂�(𝜔)(1.37)

Then the dispersion relation of the SPPs at the metal-dielectric interface is derived as

β = 𝑘0√휀�̂�휀�̂�(𝜔)

휀�̂� + 휀�̂�(𝜔)(1.38)

where the permittivity of metal is described by using complex number,

휀�̂�(𝜔) = 휀�̂�′ (𝜔) + 𝑖휀�̂�

" (𝜔) (1.39)

The real and imaginary parts of the complex permittivity of silver and gold are

shown in Figure 1.3. The data is obtained and derived from Johnson and Christy’s data

[42]. The dispersion relations of the SPPs at the silver-glass interface and the gold-glass

interface are shown in Figure 1.4. It can be seen that the wave vector approach a

maximum at the surface plasmon frequency. The surface plasmon frequency depends on

the permittivity of materials. Generally gold has a lower surface plasmon frequency than

silver. The dashed line shows the wave vector in the glass (n=1.45).

11

Figure 1.3 The complex permittivities of silver and gold as a function of wavelength.

Figure 1.4 Dispersion relation of the SPPs at the silver-glass interface and the gold-glass

interface.

Apply the same equations for the transverse electric (TE) wave, it can be

concluded that no surface modes exist for TE polarization and SPPs only exist for

transverse magnetic (TM) polarization [43].

12

Assuming a real ω and a complex 𝛽 = 𝛽′ + 𝑖𝛽", apply the equation (1.39) in

equation (1.38).

β = 𝑘0√휀�̂�(휀�̂�′ (𝜔) + 𝑖휀�̂�" (𝜔))

휀�̂� + 휀�̂�′ (𝜔) + 𝑖휀�̂�" (𝜔)(1.40)

Under the approximation |휀�̂�′ (𝜔)| ≫ |휀�̂�

" (𝜔)| in the equation (1.40), the second order

terms in �̂�𝑚" (𝜔)

�̂�𝑚′ (𝜔)

can be neglected, obtaining

β = 𝑘0√휀�̂�(휀�̂�′ (𝜔) + 𝑖휀�̂�" (𝜔))[(휀�̂� + 휀�̂�′ (𝜔)) − 𝑖휀�̂�" (𝜔)]

[(휀�̂� + 휀�̂�′ (𝜔)) + 𝑖휀�̂�" (𝜔)][(휀�̂� + 휀�̂�′ (𝜔)) − 𝑖휀�̂�" (𝜔)]

= 𝑘0√휀�̂�

2휀�̂�′ (𝜔) + 휀�̂�휀�̂�′2(𝜔) + 휀�̂�휀�̂�"

2(𝜔) + 𝑖휀�̂�

2휀�̂�" (𝜔)

(휀�̂� + 휀�̂�′ (𝜔))2+ (휀�̂�" (𝜔))

2

= 𝑘0

√ 휀�̂�

2

휀�̂�′ (𝜔)+ 휀�̂� + 휀�̂�

휀�̂�"2(𝜔)

휀�̂�′2(𝜔)

+ 𝑖휀�̂�

2휀�̂�" (𝜔)

휀�̂�′2(𝜔)

(휀�̂� + 휀�̂�′ (𝜔))2

휀�̂�′2(𝜔)

+(휀�̂�" (𝜔))

2

휀�̂�′2(𝜔)

≈ 𝑘0√휀�̂�휀�̂�′ (𝜔)(휀�̂� + 휀�̂�′ (𝜔)) + 𝑖휀�̂�

2휀�̂�" (𝜔)

(휀�̂� + 휀�̂�′ (𝜔))2

= 𝑘0√휀�̂�휀�̂�′ (𝜔)

휀�̂� + 휀�̂�′ (𝜔)√1 + 𝑖

휀�̂�" (𝜔)

휀�̂�′ (𝜔)

휀�̂�휀�̂� + 휀�̂�′ (𝜔)

(1.41)

In order to calculate the square root √𝑧 of a complex number 𝑧 = 𝜌𝑒𝑖𝑡 = 𝜌(cos 𝑡 +

𝑖 sin 𝑡) with 𝜌 = |𝑧|, 𝑐𝑜𝑠𝑡 =𝑅𝑒(𝑧)

|𝑧|, 𝑠𝑖𝑛𝑡 =

𝐼𝑚(𝑧)

|𝑧| . Then

13

√𝑧 = √𝜌𝑒𝑖𝑡2 = √𝜌 (cos

𝑡

2+ 𝑖 sin

𝑡

2) = √𝜌(√

1 + cos 𝑡

2+ 𝑖√

1 − cos 𝑡

2)

= √𝜌 + 𝑅𝑒(𝑧)

2+ 𝑖√

𝜌 − 𝑅𝑒(𝑧)

2

(1.42)

According to the equation (1.41), 𝑧 = 1 + 𝑖�̂�𝑚" (𝜔)

�̂�𝑚′ (𝜔)

�̂�𝑑

�̂�𝑑+�̂�𝑚′ (𝜔)

. Then for the positive term

(�̂�𝑚" (𝜔)

�̂�𝑚′ (𝜔)

�̂�𝑑

�̂�𝑑+�̂�𝑚′ (𝜔)

)2

< 1, 𝑅𝑒(𝑧) = 1 and

𝜌 = √1 + (휀�̂�" (𝜔)

휀�̂�′ (𝜔)

휀�̂�휀�̂� + 휀�̂�′ (𝜔)

)

2

≈ 1 +1

2(휀�̂�" (𝜔)

휀�̂�′ (𝜔)

휀�̂�휀�̂� + 휀�̂�′ (𝜔)

)

2

(1.43)

√𝜌 + 𝑅𝑒(𝑧)

2= √1 +

1

4(휀�̂�" (𝜔)

휀�̂�′ (𝜔)

휀�̂�휀�̂� + 휀�̂�

′ (𝜔))

2

≈ 1 (1.44)

√𝜌 − 𝑅𝑒(𝑧)

2= √

1

4(휀�̂�" (𝜔)

휀�̂�′ (𝜔)

휀�̂�휀�̂� + 휀�̂�′ (𝜔)

)

2

=1

2(휀�̂�" (𝜔)

휀�̂�′ (𝜔)

휀�̂�휀�̂� + 휀�̂�′ (𝜔)

) (1.45)

Apply the equations (1.42), (1.44), and (1.45) to the equation (1.41),

𝛽′ = 𝑘0(휀�̂�휀�̂�

′ (𝜔)

휀�̂� + 휀�̂�′ (𝜔))12 (1.46)

𝛽" = 𝑘0(휀�̂�휀�̂�

′ (𝜔)

휀�̂� + 휀�̂�′ (𝜔))32

휀�̂�" (𝜔)

2(휀�̂�′ (𝜔))2(1.47)

So the propagating length of SPPs, which is defined as the length at which the

intensity of SPPs decreases to 1/𝑒, is given by

𝐿 =1

2𝛽"(1.48)

And the penetration depth, which is also known as skin depth at which the field falls to

1/𝑒, is given by

14

δ =1

|𝑘𝑧|(1.49)

The propagating length and penetration depth of SPPs at the metal-glass

interfaces are shown in Figure 1.5. With the increase of wavelength at the range from 0.5

µm to 2 µm, the propagation length increases and the penetration depth decreases. The

relative permittivities of silver (blue circle) and gold (red circle) are obtained and derived

from Johnson and Christy’s data [42].

Figure 1.5 Propagation range and penetration depth of SPPs along the silver-glass

interface and the gold-glass interface.

The permittivity of metal in SPPs can be described by the famous Drude model

[43] which is given by

휀�̂�′ (ω) = 1 −

𝜔𝑝2𝜏2

1 + 𝜔2𝜏2(1.50)

휀�̂�" (ω) =

𝜔𝑝2𝜏

𝜔(1 + 𝜔2𝜏2)(1.51)

where 𝜏 is the relaxation time of electrons in metal and

𝜔𝑝2 =

𝑛𝑒2

휀0𝑚(1.52)

15

where 𝜔𝑝 is the plasma frequency of metal and 𝑛, 𝑒,𝑚 are the density of the free

electrons, electron charge and electron mass, respectively.

Apply (1.50) into (1.46) under the condition of negligible damping of the free

electrons, 휀�̂�" = 0. Then the surface plasma frequency is defined as

𝜔𝑠𝑝 =𝜔𝑝

√1 + 휀�̂�(1.53)

For a free-electron model with negligible damping based on Drude model, the

SPPs would extend to infinity as it approaches the surface plasmon frequency. However,

Drude model is an idealized material model used for metals. In the simulation of

nanostructures, experiment permittivity data is used and there is no negligible damping.

Thus the SPPs at the surface plasmon frequency are finite, as shown in Figure 1.4.

SPPs at a single smooth metal-dielectric interface cannot be excited directly by

light since the wave vector of light on the dielectric side of the interface is smaller than

the propagating wave vector. At the frequency lower than the surface plasmon frequency,

the incident wave vector in dielectric is always smaller than the SPP wave vector at the

interface, as shown in Figure 1.6. The excitation of SPPs requires enhanced momentum

by using prism coupling[44] or grating coupling [45].

The common and well-known prism coupling method is Kretschmann

configuration [44]. To excite SPPs on smooth surface, a three layer dielectric-metal-

dielectric system was developed. A thin metal film is directly deposited on the base of a

high refractive index prism. Another low refractive index dielectric, usually air, is on the

other side of the metal layer. Incident light shines on the metal film through the prism at a

certain angle. The evanescent fields pass through the thin metal film and excite SPPs at

the metal-air interface. Figure 1.6 shows the dispersion relations of the SPPs at the silver-

16

air interface. The dispersion relation of light in high refractive index glass (n=1.72) is

used to show the concept of Kretschmann configuration. At the surface plasmon

frequency, it can be seen that the wave vector in the glass (red dashed line) is larger than

the wave vector of SPPs at the silver-air interface (blue solid line). For the Kretschmann

configuration, excitation of SPPs can be detected as a minimum in the reflected light by

optimizing the incident angle and the metal thickness.

Figure 1.6 Dispersion relation of the SPPs at the silver-air interface and the dispersion

relation in the high refractive index glass.

The excitation of SPPs by using the grating configuration can be dated back to

Wood’s Anomalies, as discussed in Section 1.1. A grating is required because that the

wave vector β of SPPs is usually larger than free-space wave vector k, as shown in Figure

1.6. Incident light is scattered from the diffraction grating with increasing or decreasing

wave vector. SPPs can be excited at the air-metal interface when the phase-matching

takes place under the condition [43]

β = k sin θ ± 𝜐𝑔 (1.54)

17

where θ is the incident angle to the grating, 𝜐 is the diffraction order, and g is the

reciprocal vector of the grating that 𝑔 =2𝜋

Λand Λ is the grating period. The grating

coupling provides extra momenta to excite SPPs.

1.4 Surface plasmons in metallic nanoparticles

In the previous section I talked about the SPPs in which analytical solutions are

available for both a single interface and dielectric-metal-dielectric layer structures.

However, analytical solution is hard to get for most nanostructures interacted with light

waves. Simulation tools are usually used for analysis.

In this section, a brief review of the LSPR analytical solution for typical

nanoparticles is given. Though it is hard to give a general review of all the metallic

nanoparticles in this rapidly growing area, several common particles are discussed.

LSPs are collective electron charge oscillation confined to metallic nanoparticles

and nanostructures in the dielectric environment. They are excited by incident light near

the resonance wavelength of metallic nanoparticles or nanostructures, as shown in Figure

1.7. Different from the SPPs, the LSPs are non-propagating excitations. The resonance

wavelength highly depends on the geometries, compositions, and dielectric environment

of the nanoparticle.

18

Figure 1.7 Schematic of LSPs where the free conduction electrons in the metal

nanoparticle are driven into oscillation due to strong coupling with incident light. The

plane wave is propagating in the x direction, with its electric field in the z-direction.

Two analytical methods, quasistatic approximation and Mie theory, are used for

typical nanoparticle analysis. In principle, the quasistatic approximation is only

appropriate for particles that are less than one percent of the incidence wavelength [46].

But it is also used for first-order estimations of resonance wavelengths for larger particles

[47]. The most convenient geometry for a quasistatic analysis is a homogeneous,

isotropic metal sphere of radius a surrounded by a homogenous, isotropic dielectric

environment, as shown in Figure 1.8. The sphere is located in a uniform static electric

field 𝑬 = 𝐸0�̂�. The general solution [43] is

Φ(r, θ) =∑[𝐴𝑙𝑟𝑙 + 𝐵𝑙𝑟

−(𝑙+1)]

∞

𝑙=0

𝑃𝑙(cos 𝜃) (1.55)

where 𝑃𝑙(cos 𝜃) is the Legendre Polynomials of order l, and 𝜃 is the angle between the

position vector r at point P and the z-axis, as shown in Figure 1.8. Apply boundary

19

conditions in the equation (1.55) with the consideration of polarizability 𝛼, the resonance

frequency is given by [43]

Re[휀�̂�(𝜔)] = −2휀�̂� (1.56)

This relation is called the Fröhlich condition and associated with the dipole mode (𝑙 = 1).

For gold and silver nanoparticles, this condition is met in the visible region, which makes

there two materials good candidates for numerical applications involving color change. A

general solution to the higher mode is given in [46]. Similar approaches can be used to

calculate the resonance frequency of ellipsoidal particles and spherical nanovoids [47].

Figure 1.8 Schematic of LSPs in a metal sphere in a dielectric environment.

In principle, Mie theory is appropriate for particles that are comparable to the

incidence wavelength [48]. This makes Mie theory is a good candidate for analysis of

such nanoparticles, which provides an exact solution to the scattering problem [49]. It is

used for spherical particles [49], spherical nanovoids [47], ellipsoidal particles [50], and

nanoshells [51], [52]. However, it is complicated and hard to obtain physical meaning

from the results for other nanoparticles [53].

20

For the nanoparticle array structures, the resonance wavelength can be roughly

estimated. In a gold nanodisk array, the resonance wavelength is calculated by [21]

𝜆(𝑖,𝑗) =𝑑 × 𝑛

(𝑖2 + 𝑗2)1/2(1.57)

where d denotes the grating constant, n is the refractive index of the dielectric

environment, and (𝑖, 𝑗) is the grating diffraction order.

Simulation tools like Lumerical are used for detailed simulation of nanoparticle

array structures. The electric field intensity distribution (|𝑬|2) at the resonance

wavelength in a two-dimensional gold nanodisk array is shown in Figure 1.9. Light is

normally incident onto the disk array that is placed on a glass substrate (X-Y Plane).

Light is polarized in the x direction. Figure 1.9(a) shows the near electric field intensity

distribution at the gold-glass interface. At the resonance wavelength, it can be observed

that the electric field emanating from the nanodisk behaves as a radiating electric dipole.

Figure 1.9(b) shows the electric field distribution at the cross-section of the gold nanodisk

(Y=0 Plane). At the resonance wavelength, it can be observed that the electric field is

strongly enhanced at the gold-glass interface.

For other nanoparticles and nanostructures which are not spherical-like,

simulations tools are generally used. The common simulation methods and software are

discussed in the section 2.1.

21

Figure 1.9 Electric field intensity (|𝑬|2) distribution of the gold nanodisk array at the

resonance. (a) The near electric field intensity distribution above the gold-glass interface.

(b) The electric field intensity distribution at the cross-section of the gold nanodisk.

1.5 Surface plasmon resonance based sensing

The area of surface plasmons rapidly grew in the last decades because of the

numerous versatile applications in different disciplines, including bioengineering,

biomedical engineering, chemical engineering, electrical engineering, material science,

mechanical engineering and physics. The SPR based sensing, which is a hot topic in

surface plasmons based applications, is discussed in this section.

22

As discussed in previous sections, the surface plasmons consist of SPPs and LSPs.

The first difference between SPPs and LSPs based devices is the plasmon excitation

method. Sensors based on SPPs require energy and momentum matching of the surface

plasmons at the interface. Prism coupling by using Kretschmann configuration and

grating coupling by using one-dimensional diffraction gratings or two-dimensional

subwavelength arrays [54] are two common excitation methods for SPPs based devices.

On the other hand, LSPs can be excited by illuminating metal nanoparticles or

nanostructures with light at the resonance wavelength. It is usually more convenient to

excite LSPs than SPPs, especially for miniaturized sensing applications like lab-on-chip.

The second difference of SPPs and LSPs based devices is the distance that surface

plasmon field extend into the local environment [55]. SPP fields extend hundreds of

nanometers into the dielectric environment [56], which can be calculated by using

equation (1.49). However, the LSP fields are localized near the surface of the

nanoparticles. Due to the different properties of SPP and LSP, SPP based devices are

used for sensing bulk refractive index change while the LSP based devices are used for

sensing surface refractive index change.

The transduction mechanism of the SPR sensor is based on the local refractive

index change near the vicinity of noble metal nanoparticles [34]. The local refractive

index change is usually modulated into the change of SPR wavelength [57], incident

angle [58], light intensity [59], or polarization [60]. Compared with other modulations,

SPR wavelength modulation generally offers significant improvements in resolution.

As described in section 1.1, a mainstream of the research in surface plasmons is

SPR based biosensor. The SPR based metal nanoparticles can be used as a label-free

23

sensor for the detection of local refractive index change [61]. Several real-time

applications are shown [62]. Selective sensing is desired by immobilizing receptor

molecules to the nanoparticles [63], the transducer.

In this thesis, two SPR based sensors are demonstrated. A gap mediated surface

plasmon resonance nanostructure using a metal nanodisk array device for the detection of

nanometer displacement is shown in the Chapter 3. A surface plasmon resonance

spectrometer sensor technique with the super-period gold nanodisk grating for the

detection of the bonding of BSA proteins on the gold nanodisk surface is demonstrated in

the Chapter 4. Without using external optical spectrometers, the device has potential to

become a miniaturized sensor for biological and chemical applications.

24

CHAPTER 2

METHODOLOGY IN THE RESEARCH OF TWO-DIMENSIONAL

PERIODIC METALLIC NANOSTRUCTURES

Two-dimensional nanostructures form a major part in surface plasmon

nanophotonics due to the ability to tune spectrum. They provide more freedom and

possibilities in design compared with the one-dimensional nanostructures. According to

different goals in research, the SPR spectrum can be tuned by changing the material,

shape, size, period, and the dielectric environment of the subwavelength structure.

The modern micro-nanofabrication technologies, numerical analysis tools on

faster computers, and new optical measurement methods allow for the research in

nanostructure. Different kinds of simulation and fabrication tools are discussed in this

chapter.

2.1 Numerical analysis method

The numerical analysis in electromagnetics has rapidly grown in the last two

decades due to the revolution in the computer capacity and calculation speeds. Dated

back to 30 years ago, the design of electromagnetics devices was based on simple

25

analytical models and experience from trial and error [64]. Now different numerical

analysis methods can provide more reliable and useful results in the analysis,

development and optimization of the designs.

Simulation in surface plasmon is based on computational electromagnetics (CEM),

the numerical approximation of Maxwell’s equations. The techniques in CEM have

grown according to the needs of current radio frequency (RF) and microwave engineering

practice [64]. Many existing techniques are slightly modified and used in the surface

plasmon nanostructure simulation. In this section, I will go over several numerical

analysis methods used in the projects in chapter 3 and chapter 4. Also several common

simulation methods and software will be discussed at the end of this section.

2.1.1 Finite-difference time-domain method

The finite-difference time-domain (FDTD) method approximates the time and

space derivative in the Maxwell’s curl equations by finite-difference expressions [65].

This method, that was first introduced in 1966 by Yee, describes Maxwell’s equation on a

Cartesian grid with structured cells [66].

The FDTD method is improved in the following decades [67]–[69]. Intrinsically,

the FDTD method is limited in the closed space. The introduction of Perfectly Matched

Layer (PML) extends the FDTD method to the structure in the open regions [67]. PML is

then used in the other differential method.

The FDTD method is the only widely used CEM in the time domain, though other

methods described in the following sections can work in the time domain for specialized

applications. Since it is a time domain method, a wideband result can be obtained in just

one run without consideration in accuracy. The main advantage of the FDTD method is

26

simple basic implementation. The theory and implementation is pretty straight forward

which one can implement the basic model in a reasonable time. The main drawback is

inflexible meshing. Flexile meshing can be obtained with the loss of simplicity [70].

Lumerical FDTD Solutions is commercial software implemented by using 3D

FDTD method Maxwell solver to simulate surface plasmon structures in the time domain.

This software used in the simulations shown in chapter 3 and chapter 4. Noncommercial

software like Meep [71] is also available for FDTD simulation.

2.1.2 Finite integration technique

Finite integration technique (FIT) is closely related to the FDTD method [72]. It is

a differential method and the word integration does not imply that it is an integral

equation technique. This method, that was also based on Yee’s method and first

introduced in 1977, describes Maxwell’s equations on a grid space [73]. Thus FIT is

regarded as a generalization of the FDTD method [41].

Some advantages and disadvantages of FIT are similar to those of FDTD method.

FIT is simple to be implemented, especially for the inhomogeneous material. Also

efficient parallel computing can be realized in FIT. The most common drawback is also

because of inflexible meshing, especially on non-orthogonal grids. A comparison

between FDTD and FIT can be found in [74].

A review of FIT shows the numerical treatment of acoustic, electromagnetic, and

electrodynamic waves for different applications [75]. CST Microwave Studio is

commercial software implemented by using FIT Maxwell solver along with the Perfect

Boundary Approximation technique to simulate surface plasmon structures in the time

domain and the frequency domain.

27

2.1.3 Finite element method

The finite element method (FEM) is a numerical technique based on obtaining

approximating solution of partial differential equations. It is widely used to solve

boundary value problems in the electrical, mechanical, fluid flow and chemical

applications. This method is first introduced in 1943 [76] and first used in electrical

problems in 1968 [77].

The basic principle of FEM is to separate a continuous domain described by

unknown functions into numerous sub-domains described by simple interpolation

functions [78]. The major advantage of FEM is straightforward treatment of complex

geometries with dispersive materials. The most common drawback of FEM is the

complexity in implementation, especially in the large three dimensional structures [79].

Fast iterative solvers fail for high frequency Maxwell’s equation in optical range.

Alternative solvers are analyzed and discussed in the framework of FEM [80]. Compared

with FDTD and FIT, FEM generates the simulation data at each frequency point of

interest in one run, while the other two generate a wideband solution per time.

The FEM tools are well investigated and implemented in engineering area.

COMSOL Multiphysics and HFSS are popular commercial software implemented by

using FEM solver to simulate surface plasmon structures in frequency domain.

2.1.4 Rigorous coupled-wave analysis technique

Different from the three full-wave CEM methods described above, the rigorous

coupled-wave analysis (RCWA) is a semi-analytical method that is usually used for the

calculation of the diffraction from 2D and 3D periodic gratings structures [81]–[83]. The

RCWA technique is also called the Fourier modal method (FMM). In the simulation, the

28

grating is separated into rectangles and described by Fourier expansions of the space

periodic part. Thus the question is transformed into a system of ordinary differential

equations and the solution can be written in the form of elementary matrix functions [84].

This method is first used for calculation of dielectric gratings and then expanded to

gratings with metal materials [85].

Though no popular commercial RCWA tools are available in the market, several

different non-commercial implementations are available [86].

2.1.5 Other methods

Transfer matrix method is a simple but useful method to investigate

electromagnetic propagation in layered media. The theory is well described in the Prof.

Yeh’s book [87] and can be implemented in the personal computer. One-dimensional

layered structure can be calculated by using this method with known material permittivity.

Together with Bloch’s theorem, this method can be extended to 2D and 3D photonic

crystal structures [88].

The method of moments (MoM) is probably the most common numerical method

in RF CEM with a long history. Unlike the three differential equation techniques (FDTD

method, FIT, and FEM) described above, MoM is an integral equation technique which

uses Maxwell’s equations in integral form to formulate the electromagnetic problem. The

potential of MoM technique in the simulation of surface plasmon structures has been

shown by using a comparison with Lumerical FDTD method [89].

Benchmarking on the comparison of the simulation methods have been done by

different groups [90]–[92]. Most of the methods or tools described above are tested and

compared in the papers.

29

2.2 Fabrication method

The modern micro-nanofabrication techniques have grown with the development

of semiconductor industry from late 1950s [93]. Thanks to Moore’s law, techniques in

this area evolve and push the size limit from micrometer to nanometer. Now numerous

tools are available in this area for the fabrication of nanometer devices and standard

process procedures are available in the industry.

Several micro-nanofabrication methods are used for the fabrication of surface

plasmon based devices. The two-dimensional periodic metallic nanostructures are usually

made through deposition-patterning-etching or patterning-lift-off-depostion process. In

this section, I will review the two processes and several necessary procedure in the

fabrication of surface plasmon based devices.

2.2.1 Surface preparation

The first step of the fabrication is usually wafer cleaning in the clean room.

Contaminants include organics, chemical residues, and unwanted particles and films. The

wafer need to be cleaned at the beginning of the fabrication and kept clean in the whole

process.

Many different dry and wet wafer cleaning methods are available. RCA clean is

the most famous wet cleaning method. It is developed in 1965 [94] and still widely used

nowadays. It is a four-step procedure: organic contaminants removal, oxide layer strip,

Ionic clean, and rising and drying [95].

For all the fabrication results shown in chapters 3 & 4, an alternative cleaning

method is used. The wafer is first cleaned by acetone, methanol, and isopropyl alcohol

30

(IPA). The wafer is then rinsed by Deionized (DI) water and spun dried at 2500 rpm for 1

minute.

2.2.2 Material deposition

Generally speaking, material deposition is the method to adhere desired materials

to the substrate. The desired materials can be organic this films, metal oxides, metal, and

semiconductors [96]. Physical vapor deposition (PVD), chemical vapor deposition

(CVD), spin coating are three fundamental methods. The selection of the deposition

techniques depends on materials and the following process.

PVD is usually used for the deposition of metal and metal oxides. The general

idea of PVD is material ejection from a solid target to the substrate through the vacuum.

Evaporation and sputtering are two main methods in PVD.

The basic principle of evaporation is pretty straightforward: evaporated atoms

with high vapor pressures are transport to the substrate on top of it. Thus the thin film

made by evaporation is directional but poorly uniform. The directional property is good

for lift-off process. E-beam evaporator is needed for high-melting-point metals, like

tungsten and titanium; while thermal evaporator is good enough for low-melting-point

metals like gold and aluminum.

In sputtering, Argon plasma gas hit the material target and ejects the target atoms

to the substrate at the bottom [96]. The target materials are metal and metal oxides. For

the nonconductive metal oxides, RF power is applied to prevent charging of the target.

Thin film made by sputtering is uniform but non-directional. More parameters are

available in sputtering than in evaporation, which provide more control to tailor film

properties.

31

The CVD processes depend on chemical reactions. It is usually used for the

deposition of different kinds of oxide. Spin coating is used for the deposition of

photoresist and organic thin films.

2.2.3 Patterning

Patterning is the realization of design in micro-nanofabrication. Several

lithography techniques, like photolithography, electron beam (e-beam) lithography, and

focused ion beam lithography, are conventional techniques in patterning. New techniques

like soft lithography, nanoimprint lithography, and nanosphere lithography are developed

to overcome the conventional technique limitations like high cost and low yield [97]–[99].

The e-beam lithography used in the projects shown in chapter 3 & 4 are discussed in this

section.

In the e-beam lithography, e-beam resist is first applied on substrate by using spin

coating. The thickness of the resist depends on the resist material and spin speed. Then

electron beam is focused on the e-beam resist for pattern writing. The pattern is usually

designed by using computer-aided design (CAD) tools. Larger and complicated designs

will cost more time writing. .Developing time and temperature are critical in resist

development [100]. The whole process should be done in the clean room.

2.2.4 Etching and lift-off

Etching and lift-off are two methods to transfer patterning into real structures. The

choice between etching and lift-off depends on the patterning: etching is selected when

the shape of the photoresist pattern is the same as the desired structure; lift-off is selected

when the complementary shape of the photoresist pattern is the same as the desired

structure [96].

32

In general, etching removes the material not protected by the photoresist. Two

kinds of etching are available in micro-nanofabrication: wet etching and dry etching. Wet

etching is usually an isotropic etching in wet bench, which uses an etchant to remove the

desired material with photoresist intact. Dry etching is usually an anisotropic etching,

which uses plasma to remove the desired layer not covered by the photoresist. The

selectivity, which is the etching ratio of desired material over photoresist, is critical.

Reactive ion etching (RIE) is a dry etching method used for anisotropic plasma etching

and the descum method described in the next section. Anisotropic wet etching [101] and

isotropic dry etching [102] are available for special applications.

Lift-off removes the material on the resist layer. The process is similar to resist

strip in etching. The resist is dissolved in solvent thus the materials not in contact with

substrate being removed. The selection of solvent depends of the resist type. Ultrasonic

cleaning may involve for well adherent resist layer.

2.2.5 Other methods

The fabrication process varies highly depending on the material of the desired

structure. Here I will go over several other fabrication concepts and techniques used in

the projects shown in chapters 3 &4.

In the material deposition, adhesion layer is necessary when the substrate and

target materials are not firmly adhered. Gold is widely used in the surface plasmon based

device with glass or silicon substrate. However, the adhesion property between gold layer

and glass or silicon substrate needs to be improved. Thus titanium and chromium are

used as adhesion layer for gold devices. Lots of researches have been done for the

selection and the effects of adhesion layer [103]–[107].

33

Descum is an oxygen plasma treatment to clean the resist residue. It is usually

right before the deposition in the lift-off process. The main goal of descum is to remove

the residue in the resist holes. The residue remained in the development is desired to be

removed in the descum [108].

Annealing is an optional procedure in the end of the process to smooth the

material surface or structure. In the annealing, the material particles are slight modified.

Thus the optical properties are changed and resonance shift can be observed in the

spectrum [109]–[111].

34

CHAPTER 3

GAP MEDIATED SURFACE PLASMON RESONANCE

NANOSTRUCTURES

I investigated a gap mediated surface plasmon resonance nanostructure using a

metal nanodisk array device. The gap mediated surface plasmon resonance nanostructure

is made of gold nanodisk array on thick dielectric layer to detect the thickness of air gap

above the nanodisk array. With the increasing of air gap thickness, blueshift in the

resonance wavelength can be measured in both transmission and reflection.

3.1 Two-dimensional periodic metal nanodisk arrays

Two-dimensional periodic nanostructure has been investigated with the

development of micro-nanofabrication techniques. Different nanostructure, like nanodisk

[112], nanohole [113], nanoring [24], bow tie [114], mushroom [25], are well

investigated over the last decade. Nanodisk and nanohole are two common used

nanostructures for the robust fabrication method and the polarization independent

property. The transmittance, reflectance and absorption spectra of a typical two-

dimensional nanodisk array are shown in Figure 3.1.

35

In the simulation setup, light is normally incident onto the 60 nm disk array that is

placed on a glass substrate. The diameter of the nanodisk is 160 nm and period of the

square lattice array is 480 nm. A SPR resonance wavelength can be observed at around

700 nm in all three spectra, as shown in Figure 3.1. The SPR wavelength of a two-

dimensional nanodisk array can be tuned by changing the period, disk diameter, or disk

height.

Figure 3.1 Surface plasmon resonance curve in the gold nanodisk arrays with a period of

480 nm, a disk diameter of 160 nm, and a disk height of 60 nm.

The near electric field intensity (|𝑬|2) distributions at different frequencies are

shown in Figure 3.2 and Figure 3.3. Figure 3.2 shows the near electric field distribution

of the gold nanodisk array above the gold-glass interface. No obvious electric field

enhancement is observed at 507 nm wavelength, as shown in Figure 3.2(a). At the SPR

wavelength, a strong near electric field is observed, as shown in Figure 3.2(c). Electric

field enhancements are also observed at other wavelength.

36

Figure 3.2 Near electric field intensity (|𝑬|2) distribution of the gold nanodisk array

above the gold-glass interface. (a) 507 nm wavelength; (b) 607 nm wavelength; (c) 707

nm wavelength; (d) 807 nm wavelength; (e) 907 nm wavelength.

Figure 3.3 shows the electric field intensity distribution of the gold nanodisk array

at gold nanodisk cross-section at the y=0 plane. Compared with the results shown in

Figure 3.2(a), Figure 3.3(a) shows a weak enhancement at the gold-air interface on the

top of the gold nanodisk. The resonance wavelength highly depends on the permittivity of

37

the two materials at the interface, as described in equation (1.56). Thus the resonance

wavelength at the gold-glass interface is different from that at the gold-air interface. At

the SPR wavelength, a strong near electric field is observed at both interfaces, as shown

in Figure 3.3(c).

Figure 3.3 Electric field intensity (|𝑬|2) distribution of the gold nanodisk array at the

cross-section of the gold nanodisk. (a) 507 nm wavelength; (b) 607 nm wavelength; (c)

707 nm wavelength; (d) 807 nm wavelength; (e) 907 nm wavelength.

3.2 Fabrication of two-dimensional periodic metal nanodisk arrays

I fabricated two-dimensional periodic gold nanodisk arrays on a glass wafer.

Figure 3.4(a) shows the schematic of the gap mediated structure. The period of the

designed structure is 480 nm. The disk size is 160 nm and the disk height is 50 nm.

The two-dimensional periodic metal nanodisk arrays were fabricated on a glass

wafer substrate by using a standard e-beam lithography and lift-off process. Before the

fabrication, the glass wafer was first cleaned by acetone, methanol, and IPA. Then an e-

38

beam resist layer (495PMMA A4) of 200 nm was spin-coated on the glass substrate at the

speed of 2500 rpm and pre-baked at 180 °C for 90 seconds. Next, a conductive polymer

(AquaSAVE 53za) layer was spin-coated on the photoresist layer to enable e-beam

focusing on the glass substrate. E-beam lithography was used to pattern the 2D nanodisk

array by using an e-beam machine (LEO 1550 SEM) and followed by development in a

1:3 methyl isobutyl ketone (MIBK) to IPA solution. Then an oxygen plasma descum

process was carried out to remove e-beam resist residues. A 1.5 nm thin adhesion layer of

titanium was evaporated on the patterned surface and followed by thermal evaporation of

a 60 nm gold layer on the titanium adhesion layer by using a CVC thermal evaporator.

Finally a lift-off process was carried out in an acetone solution for 12 hours to lift-off the

gold on the e-beam resist. Figure 3.4(b) shows a scanning electron microscope (SEM)

picture of the fabricated gold nanodisk array on a glass substrate. The total patterned

device area is 300 × 300 μm2.

Figure 3.4 (a) Schematic of two-dimensional periodic gold nanodisk arrays on a glass

substrate. (b) A SEM picture of the periodic gold nanodisk arrays grating fabricated on a

glass substrate.

3.3 Transmission and reflection

The transmittance and reflectance from the super-period gold nanodisk grating are

calculated for different air gap thicknesses by using FDTD software developed by

39

Lumerical Solutions, Inc. Since the resonance wavelength is sensitive to the thickness, a

high density mesh with fine mesh near the nanodisk was used in the FDTD simulations.

The FDTD simulation region consists of a unit cell from -0.24 µm to 0.24 µm in the x

direction and from -0.24 µm to 0.24 µm in the y direction with anti-symmetric/symmetric

boundary conditions, and from -1.1 µm to 1.1 µm in the z direction with PML boundary

conditions. A two-dimensional periodic nanodisk array is on a thick glass substrate. The

period, disk diameter, and disk height in the simulation are 480 nm, 160 nm, and 50 nm

respectively. A plane wave source is placed in the glass substrate 1 µm away from the

gold nanodisks. The plane wave is normally incident on the gold nanodisk array and

propagates along the z direction. The electric permittivity of the gold used in simulations

is from the reference [115]. The refractive index of the glass substrate is 1.45.

The transmittance and reflectance spectra for air gap thickness from 0 nm to 100

nm are shown in Figure 3.5. A blue shift is observed with the increase of air gap

thickness, as shown in Figure 3.5(a). The blue shift is significant for smaller air gap. The

shape of the resonance spectra near the SPR wavelength doesn’t change much. Similar

trend is observed in the reflectance spectrum as shown in Figure 3.5(b).

40

Figure 3.5 Simulation results. (a) Transmittance spectra of different air gap thickness. (b)

Reflectance spectra of different air gap thickness.

To show the nonsignificant SPR wavelength blueshift while the air gap thickness

is larger than 100nm, the top glass plate is removed. Thus the air gap can be regarded as

infinity. As shown in Figure 3.6, the spectrum shape and SPR wavelength in the structure

with 100 nm air gap and without air gap are no significant difference. This result matches

the analysis in section 1.5 that the LSP is localized near the surface.

Figure 3.6 Simulation results. (a) Transmittance spectra of different air gap thickness

from 0 nm to infinity. (b) Reflectance spectra of different air gap thickness from 0 nm to

infinity.

Detailed spectra in transmittance and reflectance are shown in Figure 3.7 and

Figure 3.8, respectively. It can be clearly seen that the blueshift is significant when the

41

top glass plate near the gold disk arrays. The SPR wavelength in the setup from 0 nm air

gap to 40 nm SPR is 750.8 nm, 731.2 nm, 723.7 nm, 719.2 nm, and 717.2 nm, as shown

in Figure 3.7(a). The SPR wavelength for 100 nm air gap is 709.7 nm as shown in Figure

3.7(b). Thus when implemented in the experiment, detection of air gap thickness less than

10 nm is possible. Good resolution can be achieved for the air gap thickness less than 40

nm.

Figure 3.7 Simulation results of the transmittance spectra. (a) Air gap thickness from 0

nm to 40 nm. (b) Air gap thickness from 50 nm to 100 nm.

Figure 3.8 Simulation results of the reflectance spectra. (a) Air gap thickness from 0 nm

to 40 nm. (b) Air gap thickness from 50 nm to 100 nm.

42

CHAPTER 4

SURFACE PLASMON RESONANCE IN SUPER-PERIODIC

NANODISK

I experimentally demonstrated a surface plasmon resonance spectrometer sensor

by using an e-beam patterned super-period gold nanodisk grating on a glass substrate.

The super-period gold nanodisk grating has a small subwavelength period and a large

diffraction grating period. The small subwavelength period enhances localized surface

plasmon resonance and the large diffraction grating period diffracts surface plasmon

resonance radiations into different directions corresponding to different wavelengths.

Surface plasmon resonance spectra are measured in the first order diffraction spatial

profiles captured by a charge-coupled device (CCD) in addition to the traditional way of

measurement using an external optical spectrometer in the zeroth order transmission. A

surface plasmon resonance sensor for the bovine serum albumin (BSA) protein nanolayer

bonding is demonstrated by measuring the surface plasmon resonance shift in the first

order diffraction spatial intensity profiles captured by the CCD.

43

4.1 Super-period metal nanodisk arrays

Previously, surface plasmon resonance spectra were measured in the zeroth order

transmission or reflection by using optical spectrometers. Recently, a surface plasmon

resonance spectral measurement technique without using external optical spectrometers

was reported for measuring surface plasmon resonance of metal nanoslit and nanohole

arrays by patterning the metal nanostructures into diffraction gratings. In this work, I

fabricated a super-period gold nanodisk grating and with the super-period gold nanodisk

grating, a surface plasmon resonance spectrometer sensor for BSA protein bonding was

demonstrated.

In this work, I demonstrated a surface plasmon resonance spectrometer sensor

with the super-period gold nanodisk grating for the detection of the bonding of BSA

proteins on the gold nanodisk surface. In our super-period gold nanodisk spectrometer

sensor, surface plasmon resonance was measured in the spatial intensity profile of the

first order diffraction with a CCD. The measured surface plasmon resonance spectra were

compared with the transmission spectra measured in the zeroth order transmission with a

commercial optical spectrometer. Our surface plasmon resonance spectral measurement

technique is similar to the dark field microscope spectroscopy, which measures the

spectrum of scattered light by eliminating the bright background from the incidence.

4.2 Gold super-periodic nanodisk arrays device fabrication

I fabricated a super-period gold nanodisk grating on a glass wafer. Figure 4.1(a)

shows the schematic of a super-period gold nanodisk array grating on a glass substrate.

The small period of the nanodisks is p, which is in the subwavelength regime. The large

period Λ is five times of the small period p, and can be realized by removing one column

44

of nanodisks for every five columns from the 2D square lattice array. The large period Λ

functions as a diffraction grating period. In the device I made, the small period is 480 nm

and the large period is 2400 nm.

The super-period gold nanodisk grating was fabricated on a glass wafer substrate

by using a standard e-beam lithography and lift-off process as shown in section 3.2. After

the lift-off process, the device was annealed on a hot plate at 200 ºC for 5 minutes and

slowly cooled down to the room temperature. Figure 4.1(b) shows an SEM picture of the

fabricated gold nanodisk array on a glass substrate. The diameter of the nanodisks is 170

nm. The thickness of the gold nanodisks is 50 nm, measured by using a surface

profilometer (KLA-Tencor P-10). The total patterned device area is 240 × 240 μm2.

Figure 4.1 (a) Schematic of a super-period gold nanodisk array grating on a glass

substrate. (b) A SEM picture of the super-period gold nanodisk grating fabricated on a

glass substrate.

4.3 Experiment setup

I have measured the surface plasmon resonance from the first order diffraction of

the super-period grating by capturing the spatial intensity profile with a CCD imager

(Sony ICX204AL). In the measurement setup as shown in Figure 4.2, a spatially coherent

white light (NKT Photonics SuperK) was used as the broadband light source. The

spectral range of the white light is from 400 nm to 2400 nm. The broadband white light

45

was first collimated by a 10× microscope objective. The diameter of the collimated beam

was 4 mm. The collimated beam first propagates through a linear polarizer for the control

of the polarization state. The polarization parallel to the diffraction grating lines is TE

polarization. The polarization perpendicular to the diffraction grating lines is TM

polarization. The collimated beam then was focused onto the nanodisk grating device at

the normal incidence by a convex optical lens with 400 mm focal length. The diameter of

the focused beam on the device is about 185 μm. The CCD was placed to capture the

angularly dispersed first order diffraction [39]. A narrow band laser line optical

transmission filter with a center wavelength of 632.8 nm was used to select a single

wavelength for the calibration of the measurement setup.

Figure 4.2 Measurement setup for the surface plasmon resonance from the first order

diffraction of the super-period gold nanodisk grating.

I first captured the spot of 632.8 nm wavelength light of the zeroth order

transmission and the first order diffraction. The distance between the first order

diffraction spot and the zeroth order transmission spot of the 632.8 nm wavelength was

measured with a micrometer and also by counting the number of the CCD pixels between

the centers of two bright spots. Then the distance between the CCD and the device was

then calculated with the diffraction grating equation [116],

46

sin 𝜃 =𝑥

√𝑥2 + 𝑑2=𝜆

Λ(4.1)

where θ is the first order diffraction angle, x is the distance between the first order

diffraction spot and the zeroth order transmission spot on the CCD, d is the distance

between the CCD and the device, λ is the wavelength corresponding to x. The

correspondence between the pixels on the CCD and the diffracted wavelengths in the first

order diffraction was obtained by the diffraction grating equation. After the calibration,

the laser line optical filter was removed. The first order diffraction spectrum can be

obtained by processing the intensity image captured by the CCD. Figure 4.3 shows the

first order diffraction from the super-period gold nanodisk grating when illuminated by

the spatially coherent white light.

Figure 4.3 The first order diffraction image of the super-period gold nanodisk grating.

The spectral range and the resolution of the measurement are determined by the

number of CCD pixels, pixel size, and the distance between the CCD and the nanodisk

grating device. Higher resolution can be obtained by increasing the distance between the

CCD and the nanodisk grating device. For a specified CCD, a larger distance between the

47

CCD and the device provides a higher spectral resolution. In our measurement, the CCD

has 1024×768 pixels with 4.65 μm square pixel size. The CCD was placed at a distance

of 21 mm away from the device. After the diffraction measurement, the zeroth order

transmission from the device was measured with a commercial optical spectrometer

(StellarNet C-SR 50) for comparison.

To demonstrate a surface plasmon resonance spectrometer sensor with the gold

nanodisk grating, about 60 μL BSA solution (BSA in water) with a concentration of 40

μg/mL was applied on the device surface. A thin BSA layer of about 6 nm thick was left

on the surface after the water solvent evaporated. BSA was chosen because it is a 66 kDa

protein and routinely used in biochemical assays to prevent non-specific adsorption of

proteins. BSA also is widely used as stabilizing agent and a biofunctionalized layer for

the gold nanoparticles. Bonding of BSA proteins causes the red-shift of surface plasmon

resonance. Surface plasmon resonance spectra before and after the BSA layer bonding

were measured for the TE and TM polarization incidence respectively.

4.4 Experiment results under different polarizations

I observed a red-shift after a thin BSA layer was applied on the device for both

TE and TM polarizations. Measurement results for the TE polarization were obtained and

shown in Figure 4.4. Figure 4.4(a) shows the color coded first order diffraction image

captured by the CCD for the device exposed to air, corresponding to the wavelength

range from 500 nm to 950 nm. Figure 4.4 (b) shows the color coded first order diffraction

image from the device with a BSA layer bonded. In Figure 4.4(a) and Figure 4.4(b), the

bright spots of CCD images correspond to the surface plasmon resonance modes before

and after the BSA layer was applied. The location of the bright spot on the CCD is

48

determined by the surface plasmon resonance wavelength. Figure 4.4(c) shows the first

order surface plasmon resonance diffraction spectra obtained from the CCD images in

Figure 4.4(a) and Figure 4.4(b) before and after BSA layer was deposited. In Figure

4.4(c), it can be seen that the plasmon resonance peak wavelength in first order

diffraction shifted from 730.2 nm to 747.6 nm after BSA was applied. Figure 4.4(d)

shows the measured zeroth order transmission spectra with a commercial spectrometer

before (black line) and after (red line) the BSA layer was applied. It can be seen that there

is a transmission dip in the zero order transmission while there is resonance peak in the

first order diffraction. This is because the radiation scattering enhanced by LSPR is out of

the phase from the incident light. In the on-axis transmission direction, the transmitted

light intensity is reduced due to the out-of-phase interference at the resonance. In the off-

axis directions, such as the direction of the first order diffraction, the light is the coherent

scattering light from the metal nanodisks. Therefore, there is a resonance peak in the first

diffraction. Because of the angular-wavelength dispersion of the diffraction grating, the

resonance peak in the spectral domain gives a bright spot in the spatial intensity profile

captured by the CCD. When a BSA layer is applied to the device surface, LSPR has a

red-shift, which causes resonance wavelength shift from 710 nm to 721.5 nm in the first

order diffraction. In addition to the red-shift of the resonance wavelength, the bonding of

the BSA layer enhances surface plasmon energy confinement and has increased surface

plasmon energy loss inside gold nanodisks. Therefore, surface plasmon resonance

strength is reduced and the resonance spectral linewidth is broadened after the bonding of

the BSA layer.

49

Figure 4.4 Measurement results for the TE polarization incidence. (a) The first order

diffraction CCD image without BSA on the device. (b) The first order diffraction CCD

image with BSA on the device. (c) The first order diffraction spectra with (red) and

without (black) the BSA layer. (d) The zeroth order transmission spectra with (red) and

without (black) the BSA layer on the device surface.

I repeated the measurement of the first order diffraction and the zeroth order

transmission spectra for the TM polarization by rotating the linear polarizer 90 degree.

The results are shown in Figure 4.5. Figure 4.5(a) is the color coded first order diffraction

image captured by the CCD for the device exposed to air, corresponding to the

wavelength range from 500 nm to 950 nm. Figure 4.5(b) shows the color coded first

50

order diffraction image from the device with a BSA layer on the surface. In Figure 4.5(a)

and Figure 4.5(b), the bright spots of CCD images correspond to the surface plasmon

resonance modes before and after the BSA layer was deposited. The location of the bright

spot on the CCD is determined by the surface plasmon resonance wavelength. Figure

4.5(c) shows measured the first order diffraction spectra with and without the BSA layer.

It can be seen that the resonance peak wavelength measured in the first order diffraction

shifted from 731.5 nm to 744.6 nm after BSA being applied. Figure 4.5(d) shows the

zeroth order transmission spectra from the device with and without BSA on device

surface. It can be seen that the resonance peak wavelength shifts from 717 nm to 728.5

nm after the BSA layer was applied. In addition to the red-shift of the resonance

wavelength, the bonding of BSA layer causes enhanced surface plasmon energy

confinement and has increased energy loss in gold nanodisks. Therefore, the surface

plasmon resonance strength is reduced and the resonance spectral linewidth is broadened

after the bonding of the BSA layer.

51

Figure 4.5 Measurement results for the TM polarization incidence. (a) The CCD image

without the BSA layer on the device. (b) The CCD image with the BSA layer applied on

the device. (c) The first order diffraction spectra with and without BSA layer. (d) The

zeroth order transmission spectra with and without the BSA layer.

4.5 Simulation results and discussions

The zeroth order transmission, the first order diffraction, and the near-field

electric field intensity from the super-period gold nanodisk grating are calculated for

different thicknesses of BSA layers by using FDTD software developed by Lumerical

Solutions, Inc. Since the resonance wavelength is sensitive to the thickness, a high

52

density mesh was used in the FDTD simulations. The FDTD simulation region consists

of a unit cell from -1.2 µm to 1.2 µm in the x direction and from -0.24 µm to 0.24 µm in

the y direction with periodic boundary conditions, and from -2.1 µm to 2.1 µm in the z

direction with PML boundary conditions. A super-period gold nanodisk grating is on a

thick glass substrate. The large grating period, small grating period, disk diameter, and

disk height in the simulation are 2400 nm, 480 nm, 170 nm, and 50 nm respectively. A

thin BSA layer covers on the gold disks and also spaces between the gold disks on the

glass substrate. The thickness of the BSA layer ranges from 0 nm to 20 nm. A plane wave

source is placed in the glass substrate 1.5 µm away from the gold nanodisks. The plane

wave is normally incident on the super-period gold nanodisk grating device and

propagates along the z direction. The polarization along the y direction is TE polarization

and the polarization along the x direction is TM polarization. One 2D power monitors is

placed at z = + 1.5 µm for transmission/diffraction calculation and another 2D monitor is

placed at z = -1.7 µm for reflection calculation. Two point monitors are placed at the

same height of the gold disk top surface and 10 nm away from the edge of the gold disks

along the direction of incident polarization. The electric permittivity of the gold used in

simulations is from the reference [115]. The electric permittivity of the BSA is from the

reference [117]. The refractive index of the glass substrate is 1.45.

I observed that with increasing BSA thickness that the resonance exhibited as red-

shift and broadening in the zeroth order transmission, the first order diffraction, and the

near electric field intensity spectra for TE polarization. Figure 4.6 shows the simulation

results for the TE polarized incidence. Figure 4.6(a) is the zeroth order transmission from

the device with different thicknesses of the BSA layers. In Figure 4.6(a), it can be seen

53

that the resonance wavelength shifts from 710.2 nm to 719.7 nm after 5 nm BSA being

applied. Figure 4.6(b) shows the first order diffraction from the device with a different

thickness of the BSA layer. In Figure 4.6(b), it can be seen that the resonance wavelength

shifts from 715.7 nm to 725.7 nm in the first order diffraction spectrum after 5 nm BSA

being applied. Figure 4.6(c) and Figure 4.6(d) show the near electric field intensity at 10

nm to the outer (disk 1) and inner (disk 2) gold disk along the direction of electric field in

a super-period, respectively. The outer gold disks are next to the gap between two unit

cells in the x direction and the inner gold disks are only next to the disks in the same unit

cell in the x direction. In Figure 4.6(c), it can be seen that the resonance wavelength shifts

from 717.7 nm to 727.2 nm in the near electric field intensity spectrum after 5 nm BSA

being applied. In Figure 4.6(d), it can be seen that the near-field resonance wavelength

shifts from 722.7 nm to 733.2 nm after 5 nm BSA layer being applied.

54

Figure 4.6 Simulation results for the TE polarization incidence. (a) The zeroth order

transmission spectra for different BSA layer thicknesses. (b) The first order diffraction

spectra for different BSA layer thicknesses. (c) The electric field intensity resonance

spectra at the position 10 nm away from the disk 1. (d) The electric field intensity

resonance spectra at the position 10 nm away from the disk 2.

I observed the resonance wavelength in the diffraction is more closely related to

the near field resonance wavelength for the TE polarization. Figure 4.7 shows the

resonance wavelengths versus the BSA thickness for the TE polarization. It can be seen

that the wavelength of the zeroth order transmission resonance minimum is smaller than

the peak wavelengths of the first order diffraction and the near field intensity for TE

polarization. It can be also observed that the first order diffraction resonance wavelength

is approximately the same as the near field intensity resonance wavelength of the disk 1.

55

The red-shift from the zeroth order transmission resonance wavelength to the first order

diffraction resonance wavelength is due to the interference between the surface plasmon

enhanced coherent scattering and the transmitted light through the super-period gold

nanodisk array. Near the metal nanodisk top surface, the LSPR enhanced field is

dominant. Consequently, the near field resonance wavelength is the LSPR wavelength.

The non-zeroth order diffractions from the super-period gold nanodisk grating avoided

the transmission. Therefore, the resonance wavelength in the diffraction is more closely

related to the near field resonance wavelength. The blue-shift from the near field

resonance wavelength to the far-field zeroth order transmission resonance wavelength has

been known and discussed earlier[118]–[121]. Our results for TE polarized incidence are

consistent with previous reports[118]–[121].

Figure 4.7 The resonance wavelength versus BSA layer thickness for TE polarization.

The resonance wavelengths are the zeroth order transmission, the first order diffraction,

the near electric field intensity of the disk 1, and the near electric field intensity of the

disk 2.

I observed that with increasing BSA thickness that the resonance exhibited as red-

shift and broadening in the zeroth order transmission, the first order diffraction, and the

near electric field intensity spectra for TM polarization, which is similar to the trend in

56

the simulation for TE polarization. Figure 4.8 shows the simulation results for the TM

polarized incidence. Figure 4.8(a) shows the zeroth order transmission from the device

with different thicknesses of the BSA layer. In Figure 4.8(a), it can be seen that the

resonance wavelength shifts from 711.7 nm to 720.7nm in simulation after 5 nm BSA

being applied. Figure 4.8(b) shows the first order diffraction from the device with a

different thickness of the BSA layer. In Figure 4.8(b), it can be seen that the resonance

wavelength shifts from 713.2 nm to 722.2 nm in the first order diffraction spectrum after

5 nm BSA being applied. Figure 4.8(c) and Figure 4.8(d) show the near electric field

intensity at 10 nm to the outer (disk 1) and inner (disk 2) gold disk along the direction of

electric field in a super-period, respectively. In Figure 4.8(c), it can be seen that the

resonance wavelength shifts from 718.7 nm to 729.2 nm in the near electric field intensity

spectrum after 5 nm BSA being applied. In Figure 4.8(d), it can be seen that the

resonance wavelength shifts from 718.2 nm to 727.7 nm in the near electric field intensity

spectrum after 5 nm BSA being applied.

57

Figure 4.8 Simulation results for the TM polarization incidence. (a) The zeroth order

transmission. (b) The first order diffraction. (c) The near electric field intensity at the

position 10 nm to the disk 1. (d) The near electric field intensity at the position 10 nm to

the disk 2.

I observed the resonance wavelength in the diffraction is more closely related to

the zeroth order transmission resonance wavelength for the TM polarization. Figure 4.9

shows the resonance wavelengths versus the BSA thickness for TM polarization. In

Figure 4.9, it can be seen that the resonance wavelengths of the first order diffraction and

the zeroth order transmission are approximately the same, especially when the BSA layer

is thick. It can be also observed that the near field intensity resonance wavelength of the

disk 1 is approximately the same as the near field intensity resonance wavelength of the

disk 2 for TM polarization.

58

Figure 4.9 The resonance wavelength versus BSA layer thickness for TM polarization.

The resonance wavelengths are of the zeroth order transmission, the first order diffraction,

the near electric field intensity of the disk 1, and the near electric field intensity of the

disk 2.

I observed near electric field intensity enhancement after BSA being applied on

the device for both polarizations, with a stronger near electric field intensity for TM

polarization than that for TE polarization. Figure 4.10 shows the near electric field

intensity (square of electric field |𝑬|2) distributions on a near field plane of 10 nm above

the metal nanodisk surface. A 5 nm BSA layer was on the top to cover the device in our

simulations. Figure 4.10(a) and Figure 4.10(b) show the near electric field intensity

distributions at the zeroth order transmission resonance wavelength (719.2 nm) and the

first order diffraction resonance wavelength (725.7 nm) of TE polarization, respectively.

It can be seen that the electric field intensity is stronger at 725.7 nm wavelength than the

electric field intensity at 719.2 nm. Figure 4.10(c) and Figure 4.10(d) show the near

electric field intensity at the zeroth order transmission resonance wavelength (720.7 nm)

and at the first order diffraction resonance peak wavelength (722.2 nm) for TM

polarization, respectively. It can be seen that the electric field intensity at 720.7 nm

wavelength and electric field intensity at 722.2 nm are approximately the same. In Figure

59

4.10(a) and Figure 4.10(c), it can be also seen that the near electric field intensity for TM

polarization is stronger than the near electric field intensity for TE polarization.

Figure 4.10 Near electric field intensity (|𝑬|2) distributions on the plane of 10 nm above

the nanodisk surface: (a) at the zeroth order transmission resonance dip wavelength of

719.2 nm for TE polarization, (b) at the first order diffraction resonance peak wavelength

of 725.7 nm for TE polarization, (c) at the zeroth order transmission resonance dip

wavelength 720.7 nm for TM polarization, and (d) at the first order diffraction resonance

peak wavelength of 722.2 nm for TM polarization.

By comparing the SPR wavelength in simulation and measurement, I observed

that the SPR wavelength difference is larger in the experiment than that in the simulation.

To investigate this phenomenon, I simulated and measured the traditional two-

dimensional period structure under same settings, as shown in Figure 4.11(dashed lines).

In the Figure 4.11(a), the SPR wavelengths of the period structure, super-period structure

for TE polarization, and super-period structure for TE polarization are 714.2 nm, 710.2

nm, and 711.2 nm, respectively. 1 nm redshift is observed from SPR wavelength in TE to

that in TM for super-period structure, which is caused by the symmetry breaking in the

super-period structure. In the Figure 4.11(b), the SPR wavelengths of the period structure

for TE polarization, the period structure for TM polarization, super-period structure for

TE polarization, and super-period structure for TE polarization are 724.0 nm, 726.5 nm,

710.0 nm, and 717.0 nm, respectively. 2.5 nm redshift is observed from SPR wavelength

60

in TE to that in TM for period structure, which may be caused by the minor shape

changes in the fabrication. And 7 nm redshift is observed from SPR wavelength in TE to

that in TM for super-period structure, which is due to the super-position of the two

redshifts.

Figure 4.11 Comparison of the SPR wavelength for period and super-period structure for

different polarizations in (a) simulation, (b) experiment.

The sensitivity of surface plasmon resonance biochemical sensors was

traditionally defined as the ratio of the shift of the resonance wavelength Δλ and the

thickness Δd of the biochemical layer bonded on the sensor surface [122]. Since the index

of refraction of the bonding layer affects the resonance wavelength shift significantly,

here I define the sensitivity of our surface plasmon resonance spectrometer sensor Sd as

𝑆𝑑 =∆𝜆

∆𝑑 × (𝑛𝑠 − 𝑛0)(4.2)

where ns is the refractive index of bonding chemical layer and no is the refractive index of

surrounding which is air. The thickness of the BSA layer is approximately 6 nm. The

BSA layer has a refractive index of 1.572 at 632 nm wavelength [117].

According to the experiment results shown in Figure 4.4 and Figure 4.5, the

sensitivity of this spectrometer sensor is calculated at the unit of RIU (refractive index

61

unit) for both polarizations in transmission and diffraction spectra. Also the same

calculations are finished according to the simulation results shown in Figure 4.7 and

Figure 4.9. The calculation results are shown in Table 4.1. As shown in both simulation

and experiment results, the highest sensitivity of surface plasmon resonance biochemical

sensors is observed in the first order diffraction for TE polarization. The difference

between experiment results and simulation results may be caused by the spectrum

resolution.

Table 4.1 Selectivity of the surface plasmon resonance biochemical sensors in the

simulation and experiment for both polarizations.

TE TM

0th

order experiment 3.35/RIU 3.35/RIU

0th

order simulation 3.72/RIU 3.86/RIU

1st

order experiment 5.07/RIU 3.82/RIU

1st

order simulation 4.22/RIU 3.64/RIU

The spectrum resolution of the surface plasmon resonance spectrometer sensor is

defined as the smallest difference dλ in wavelength that can be distinguished at the

wavelength λ. The smallest difference dλ in wavelength and the smallest distance

difference dx at the CCD are defined as

dλ = λ2 − λ1 (4.3)

dx = L × (tan 𝜃2 − tan𝜃1) (4.4)

where θ is the diffracted angle obtained by using the diffraction equation. And dλ is

obtained by calculating the difference between the λ1 and λ2 in the diffraction equation.

Then the spectrum resolution dλ is defined as

dλ = Λ × sin {tan−1 [tan (sin−1𝜆1Λ) +

𝑑𝑥

𝐿]} − 𝜆1 (4.5)

62

where Λ is the grating period 2.4 μm and L is the distance from the fabricated device to

the CCD 21 mm. The smallest difference dx at the CCD is equal to the full width of the

beam at half peak intensity (FWHM). Then we have

𝐼(𝜌, 𝑧) = 𝐼0 × (ω0

𝜔(𝑧))2

× 𝑒𝑥𝑝 (−2𝜌2

𝜔(𝑧)2) = 𝐼0(𝑧) × 𝑒𝑥𝑝 (

−2𝜌2

𝜔(𝑧)2) (4.6)

where 𝐼0(𝑧) is the peak intensity at the position z. Then dx can be obtained as

𝑑𝑥 = 2𝜌 = 2 × √−1

2× 𝑙𝑛

1

2× 𝜔(𝑧) ≈ 1.1774 × 𝜔(𝑧) (4.7)

where 𝜔(𝑧) is the beam width at the position which is defined as

𝜔(𝑧) = 𝜔0 × √1 + (𝑧

𝑧0)2

= 𝜔0 × √1 + (𝑧×𝜆

𝜋×𝜔02)2

= 𝜔0 × √1 + (

𝐿

cos𝜃1 ×𝜆

𝜋×𝜔02 )

2

(4.8)

where 𝜔0 is the beam waist radius which is measured as 70 µm. The spectral resolution

of the spectrometer sensor is 11.3 nm at the wavelength 632 nm.

63

CHAPTER 5

SUMMARY

5.1 Summary

A gap mediated surface plasmon resonance nanostructure using a metal nanodisk

array device was investigated for demonstrating a nanoscale displacement sensor. The

gap mediated surface plasmon resonance nanostructure is made of gold nanodisk array on

the glass substrate to detect the thickness of air gap above the nanodisk array. The air gap

under 100 nm can be shown in transmission and reflection spectrum by the resonance

wavelength shift.

A super-period gold nanodisk grating was fabricated with e-beam lithography for

demonstrating a surface plasmon resonance spectrometer sensor. The super-period

nanodisk grating has two periods: a small subwavelength period for enhancing LSPR and

a large diffraction grating period that directs spatially coherent surface plasmon

radiations into different directions. Surface plasmon resonance scattering radiation

spectra were obtained by capturing the spatial intensity profiles of the first order

diffraction with a CCD. With the surface plasmon resonance spectrometer, a sensor for

64

detecting nanometer scale BSA protein layer bonding on the surface was demonstrated

experimentally. The measurement results of the surface plasmon resonance spectrometer

sensor were compared with the results measured by a traditional optical spectrometer.

The demonstrated surface plasmon resonance spectrometer sensor technique, which

measures the spectrum of off-axis scattering light from nanoparticles by avoiding the

strong transmitted light, has similarity with the dark field microscope technique, but with

additional integrated functions of optical spectral measurement and light signal

enhancement due to the spatial coherence of light scattering from the array of the

nanoparticles.

5.2 Suggested future works

One of the most promising applications in the SPR spectrometer sensor is

biosensing. Now the super-period gold nanodisk grating nanostructure is fabricated on

the glass surface. To claim the device as a biosensor, a receptor molecule is needed to be

immobilized on the structure surface for selectivity. With an appropriate selection of the

receptor molecule and target molecule, the device will show selective response in the first

order diffraction.

A fiber optic spectrometer biosensor can be demonstrated by measuring the

surface plasmon resonance shift in the first order diffraction spatial intensity profiles

captured by the CCD. In addition to the benefits of super-period gold nanodisk grating on

glass discussed above, using optical fiber as a platform has more advantages including

high compactness and immunity to electromagnetic interference [123]. These advantages

have a potential to minimize the size to make a fiber optic spectrometer sensor.

65

Figure 5.1 (a) shows the schematic of the fiber optic based measurement setup.

the fiber tip based surface plasmon resonance spectrometer biosensor, illustrated in

Figure 5.1(b). By fabricating the super-period gold nanodisk grating on a fiber tip instead

of on a glass wafer, measurement setup and the measurement procedure can be simplified

and used for the lab-on-chip applications.

Figure 5.1 (a) Schematic of fiber tip based measurement setup. (b) Schematic of fiber tip

based device.

The concept of super-periodicity can be applied to various other nanostructures.

By diffracting the incident light into non-zeroth orders, the spectrometer can be replaced

by a CCD. Thus super period structure is a candidate solution for the applications that

low cost is desired.

66

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