Study Of Low Refractive Index Homogeneous Thin Film For Application On Metamaterial.pdf

VIETNAM NATIONAL UNIVERSITY OF HANOI VIETNAM JAPAN UNIVERSITY PHAM DINH DAT STUDY OF LOW REFRACTIVE INDEX HOMOGENEOUS THIN FILM FOR APPLICATION ON METAMATERIAL MASTER’S THESIS HANOI, 2019 VIETNAM NATI[.]

VIETNAM NATIONAL UNIVERSITY OF HANOI

VIETNAM JAPAN UNIVERSITY

PHAM DINH DAT

STUDY OF LOW REFRACTIVE INDEX HOMOGENEOUS THIN FILM FOR APPLICATION ON METAMATERIAL

MASTER’S THESIS

HANOI, 2019

VIETNAM NATIONAL UNIVERSITY OF HANOI

VIETNAM JAPAN UNIVERSITY

PHAM DINH DAT

STUDY OF LOW REFRACTIVE INDEX HOMOGENEOUS THIN FILM FOR APPLICATION ON METAMATERIAL

Acknowledgement

First and foremost, I want to express my appreciation to my supervisor, Pham Tien Thanh Ph.D for his patient guidance and encouragement during my study and research at Vietnam Japan University

I would like to thank Prof Kajikawa Kotaro and his students at Kajikawa Lab, Faculty of Electrical and Electronics Engineering, Tokyo Institute of Technology who helped us facilities to perform calculation, experiments and measurements

I also would like to send my sincere thanks to the lecturers of Nanotechnology Program, Vietnam Japan University, who have taught and interested me over the past two years

Besides, I am grateful to my family and my friends who are always there to share their experiences that help me overcome the obstacles of student’s life

Hanoi, 17 June, 2019

Author Pham Dinh Dat

TABLE OF CONTENTS

Acknowledgement i

LIST OF FIGURES, SCHEMES iv

LIST OF ABBREVIATIONS vi

CHAPTER 1: INTRODUCTION 1

1.1 Metamaterial 1

1.2 Optical material relate to refractive index 3

CHAPTER 2: FUNDAMENTAL THEORY 5

2.1 Effective Medium Theory 5

2.1.1 Effective medium 5

2.1.2 Permittivity calculation 8

2.2 Transfer Matrix for multilayer optics 10

2.3 Finite Difference Time Domain (FDTD) 14

CHAPTER 3: EXPERIMENTS 19

3.1 Silver nanoparticles synthesis 19

3.1.1 Chemicals 19

3.1.2 Process 19

3.2 Thin films fabrication 20

3.2.1 Chemicals 20

3.2.2 Process 20

3.3 Optical properties determination 21

3.4 Thin films thickness determination 21

CHAPTER 4: RESULTS AND DISCUSSION 22

4.1 Calculation results 22

4.1.1 Index of refraction and index of extinction depend on element of particles

22

4.1.2 Index of refraction and index of extinction depend on volume fill fraction of silver nanoparticles on polymer matrix 25

4.1.3 Calculation for thin film following EMT using TMM 28

4.1.4 Calculation for thin film using FDTD method 31

4.1.5 Neighbor particles interaction 34

4.2 Experiment results 37

4.2.1 Properties of silver nanoparticles 37

4.2.2 Properties of thin films 40

CONCLUSION 45

LIST OF FIGURES, SCHEMES

Fig 1.1: Multilayer structure and nanowires embedded structure metamaterial (A: metal-dielectric layered, B: wires in dielectric host) 2 Fig 2.1: A material model of UEM 5 Fig 2.2:Three simple model of UEM material classified following topology _ 6 Fig 2.3: A simple model for assumption limitation of volume fill fraction _ 7 Fig 2.4: Considered system of TMM problem 11 Fig 2.5: The arrangement of electric- and magnetic-field nodes in space and time 17 Fig 4.1: The index of refraction of PVP including 3% volume fill fraction of silver, gold and copper 22 Fig 4.2: The index of extinction of PVP including 3% volume fill fraction of silver, gold and copper 23 Fig 4.3: The index of refraction of PVA including 3% volume fill fraction of silver, gold and copper 24 Fig 4.4: The index of extinction of PVA including 3% volume fill fraction of silver, gold and copper 24 Fig 4.5: The index of refraction of PVP including 2%, 3%, 4% and 5% volume fill fraction of silver _ 25 Fig 4.6: The index of refraction of PVA including 2%, 3%, 4% and 5% volume fill fraction of silver _ 26 Fig 4.7: The index of extinction of silver and PVP including 2%, 3%, 4% and 5% volume fill fraction of silver 27 Fig 4.8: The index of extinction of silver and PVA including 2%, 3%, 4% and 5% volume fill fraction of silver 27 Fig 4.9: Transmittance spectrum of 30 nm PVP-based films corresponding to

different Ag fill fraction _ 28 Fig 4.10: Transmittance spectrum of 30 nm PVA-based films corresponding to different Ag fill fraction _ 29 Fig 4.11: The calculated transmittance spectrum of 200 nm PVP-based films

corresponding to different Ag fill fraction using TMM _ 30

Fig 4.12: The calculated transmittance spectrum of 200 nm PVA-based films

corresponding to different Ag fill fraction using TMM _ 31 Fig 4.13: The FDTD domain for calculation of 200nm film by x, y, z direction and 3D visions 32 Fig 4.14: The calculated transmittance spectrum of 200 nm PVP-based films

corresponding to different Ag fill fraction using FDTD method 33 Fig 4.15: The calculated transmittance spectrum of 200 nm PVA-based films

corresponding different Ag fill fraction using FDTD method 33 Fig 4.16: The simple model for consider neighbor-particles interaction 35 Fig 4.17: Calculated extinction spectra of two neighbor-particles with distance equal 3nm in medium that has refractive index equal 1.5 using FDTD 36 Fig 4.18: Calculated extinction spectra of neighbor-particles with distance equal 3nm in medium that has refractive index equal 1.5 using DDA _ 37 Fig 4.19: The images of silver nanoparticles solution after synthesis(a), after

centrifugation(b) and after re-disperse on water(c) _ 38 Fig 4.20: SEM image of self-synthesis silver nanoparticles 39 Fig 4.21: Transmittance spectrum of self-synthesis and commercial silver

nanoparticles solution _ 39 Fig 4.22: Molecular formula of PVP and PVA 40 Fig 4.23: Transmittance spectrum of PVA, PVP solution with and without existence

of silver nanoparticles _ 41 Fig 4.24: Transmittance spectrum of drop-coating PVP, PVA films corresponding 3% fill fraction of silver nanoparticles 42 Fig 4.25: Transmittance spectrum of PVP-based films different fill fraction of silver nanoparticles 43 Fig 4.26: Transmittance spectrum of PVA-based films different fill fraction of silver nanoparticles 44

LIST OF ABBREVIATIONS

DDA: Discrete Dipole Approximation

EMT: Effective Medium Theory

EM: Effective Medium

E-field: Electric field

LSPR: Localized Surface Plasmon Resonance

MGG: Maxwell Garnet geometry

MGT: Maxwell Garnett theory

FDTD: Finite Different Time Domain

H-field: Magnetic field

PVP: Poly Vinyl Pyrrolydone

PVA: Poly Vinyl Alcohol

PML: Perfect Match Layer

SPR: Surface Plasmon Resonance

TMM: Transfer Matrix Method

UEM: Uniform Effective Medium

CHAPTER 1: INTRODUCTION

1.1 Metamaterial

Electromagnetic metamaterial is a class of material using for engineering electromagnetic space and controlling light propagation Metamaterials have shown their promise for the next generation optical materials with electromagnetic behaviors almost can’t be obtained in any conventional materials They have a plenty of application including cloaking [11,15,26], imagining [12,29,41], sensing [18,23,36], wave guiding [13,22,38], absorber [5], etc

The metamaterial is fabricated based on the composite structures including inclusions that have sub-wavelength structures The inclusions have designed structure They can be totally artifact or emulate based on nature structure The inclusions are arranged on a host medium that is normally dielectric Due to the small size and distance of inclusion, the metamaterials can be considered as the homogeneous mediums The properties of material are represented through permittivity and permeability By changing shape and size of inclusion, permittivity and permeability of metamaterial can be adjusted to very high or low (even negative) value Under the consideration for permittivity and permeability, the material can be classified into 4 groups [31] They are epsilon-negative material (ENG), mu-negative material (MNG), double positive material (DPS) and double negative material (DNG) The metamaterial is in class of ENG, MNG and DNG materials Besides that, the metamaterial includes band gap material but it will not

be considered in this research

The three classes ENG, MNG and DNG of metamaterial show the noticeable

of negative permittivity and permeability For example, the index of refraction of materials can become small than 0 with structure like in Fig 1.1 It makes the refraction of light becomes very different when comparing with the original materials

Fig 1.1: Multilayer structure and nanowires embedded structure metamaterial (A:

metal-dielectric layered, B: wires in dielectric host)

The metamaterials structuring as in Fig 1 are called as hyperbolic metamaterial In this class of metamaterial, the refractive indexes and arrangement

of components play a significant role to properties of metamaterial The below equations is used to calculate the anisotropic dielectric function of layered metamaterial

are thickness; 𝜖𝑚 and 𝜖𝑑are dielectric function of dielectric material and metal Following it, the very low refractive index n = √𝜖 can be achieved by this way [38] The problem is that the fabrication is very complex and expensive The distance between wires, the thickness of each layer must be very precise

Here, we can see some issues of the metamaterial Firstly, the properties of metamaterial depend on not only structures but also nature of hosts and inclusions

It suggests that along with structural changes, developing materials as host or inclusion also contribute to the metamaterials Most of the researches about the

metamaterial focus on optimizing structure So, it is lacking in the studies which develop the constituent material of metamaterial The second is the difficulty in fabrication that mentioned above As an impact of the second, the limitation of working wave length also is an issue The most common topic about metamaterial relates to terahertz region that corresponds to long wavelengths where demand inclusion in micrometer level We need more research about metamaterial that works in shorter wavelength region So, it is necessary to study a material which is easy to fabricate and can be applied to metamaterial working in visible wavelength

1.2 Optical material relate to refractive index

The refractive index is very important parameter describing optical material properties It relate to all optical phenomena such as refraction, reflection, transmission By changing the refractive index of material, we can create new materials that can be to various fields There has been many researches related to high refractive index material and negative refractive index material The high refractive index materials are very useful for application of solar cell due to anti-reflection property of them [1,6,7] The negative index material is new class of material that is promising for many applications [11-13] However, it has a lack of research for low refractive index material They play a significant role in application relate to the reflection materials and metamaterials It has some types of low refractive index including metal nano-rod or metamaterial used nano-wires as inclusion [11,12] They are hard to fabricate and only work in IR wavelength region

I want to make a material that is easy to fabricate and work in visible region It is possible based on the effective medium theory

Following J Sipe et al, it has a number of topology of materials which show theirs behaviors as effective medium [41] Without layered metamaterial, it has two other topology having this properties are Maxwell Garnett topology and Bruggman topology The Maxwell Garnet composite geometry, including well-defined spherical inclusions in host background [1] The next topology is disordered where the constituent materials are more or less than inclusion They will be considered in

detail later The point is that both of these topology demand simpler than the layered structure It suggests a composite material that can achieves properties as like as layered metamaterial but easier to fabricate This material can be based on a polymer host material with metal nanoparticles as inclusion It can be used for thin films, metamaterial application

In this study, my purpose is making a type of nano-composite material that has low index of refraction and low index of extinction Based on the idea of hyperbolic metamaterial, it is able to create the low refractive index and low loss medium by the combination of low refractive index but loss material as metals and low loss but high refractive index as polymers I fabricated the nanocomposite based on nano silver particles embedded on polymers This type of material was considered in about absorption [49], high refractive index region [33], etc In this study, I used calculation to orient and predict about object material and experiment

to verify my prediction

The research contents include:

- Calculation refractive index of PVP-based and PVA-based material with

Ag nanoparticles as inclusion

- Calculation transmittance of thin films based on calculated materials

- Fabricate the thin films using object materials and compare with calculation

CHAPTER 2: FUNDAMENTAL THEORY 2.1 Effective Medium Theory

2.1.1 Effective medium

Consider a type of material that is presented in Fig 2.1, it has some length scales which are presented (a and b), are well-defined and all much less than the wavelength of light This condition means that the scattering cause by the inhomogeneity resulting from the composite natural can be negligible In this case, the real composite material, with host dielectric constant (𝜖ℎ) and inclusion dielectric constant (𝜖𝑖), can be replaced by a Uniform Effective Medium (UEM) with a dielectric constant (𝜖𝑒𝑓𝑓) [41]

Fig 2.1: A material model of UEM

Fig 2.2 shows three simple models of this type of material that are classified based on their topology The first that is called the Maxwell Garnet composite geometry, including well-defined spherical inclusions in host background [1] The next topology is disordered where the constituent materials are more or less than inclusion The last is the ordered, layered composite geometry [41]

a

2b

Fig 2.2: Three simple model of UEM material classified following topology.

The object of research is the material that following the Maxwell Garnet composite geometry for applying to metamaterial as the third type of geometry introduced above For predictable by Effective Medium Theory (EMT), the material should considered following some conditions At first, the scattering should be neglect able, at least with theoretical view It means that the size of metal particles must be much smaller than the working wavelength This study mostly consider characteristic of material on the visible wavelength region of light that around 300 –

800 nm So, the particles radius should be smaller than about 30nm (about tenth times compare with the shortest wavelength) In this study, the nanoparticle 20nm

Fig 2.3: A simple model for assumption limitation of volume fill fraction

In this model, the medium can be divided to cube cells which include a part

of space that is occupied by one particle (8 pieces x 8) If we call that the mean

distance between each particle and the nearest approximately is a, the volume fill fraction f of 20 nm diameter particles on polymer matrix should be limited depend

on a The distance b should much less than wavelength of light As the size of particles condition, the distance a should be less than 30nm Hence,

of nanoparticles which will be used for fabricate material could be roughly considered and limited following above There is an upper limitation of fill fraction related to index of extinction but we will consider it later

20 nm

a

2.1.2 Permittivity calculation

The index of refraction and extinction of material following MGT can be predicted through calculation There are two approaches to deriving the calculation ways The first is to examine, at some level of approximation, the nature of mesoscopic fields in material and perform spatial averages over them to identify the values of the macroscopic fields [7,34] The second is based on the expression for internal energy of the material and comparing it with expression for an effective medium [8] For easy to understanding, the first way will be used to introduce the calculation method

At first, we can refer to the particles as “molecules” in a region which include amount of particles much more than one [29] So, we can consider

“particles” as an atom which is characterized by polarizability (α) In a space

consisting of atoms that are arranged in defined lattice, the atomic polarizability links to the dipole moment p by the local field that due to Maxwell electrical field (E) and dipole respond field that can be expressed by local field corrections Hence:

p = α(E + local field corrections) (2.1.1)

We assume that the integral of the microscopic electric field e over a sphere around a charge distribution with a dipole moment p is given in electrostatic limit

[16,24] This condition is represented by the below equation This assumption means that the electromagnetic interaction between dipoles (particles or atom in this consideration) should be neglected The reason is that the averages of the fields due

to dipoles come to zero in case of medium contain a large amount of dipole

p = α [E − −

4𝜋

3 𝑝

𝑉 𝑁

The above equation is derived in case the “atoms” are in vacuum In our case,

we consider the inclusion as sphere not atom Under effective of electrical field, there is an internal electrical field inside the sphere that occurred by external field and depolarization field So, we have the dipole moment p𝑖 of the inclusion sphere within the host medium is:

p𝑖 = a3 ϵ𝑖−ϵℎ

Where a is the radius of sphere, ϵ𝑖 is the dielectric constant of inclusion, ϵℎ is the dielectric constant of host medium and 𝐸0 is the electrical field applied far from inclusion Thus, we can identify an effective polarizability as:

α = a3 ϵ 𝑖 −ϵℎ

Here, we can apply this expression for Claudius Mossotti relation that is derived above for inclusion sphere in a host material to get as known as Maxwell Garnett equation: