Study of low refractive index homogeneous thin film for application on metamaterial

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 nanoparticl

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

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

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

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

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

Hanoi, 17 June, 2019Author

Pham Dinh Dat

i

TABLE OF CONTENTS

Acknowledgement

LIST OF FIGURES, SCHEMES

LIST OF ABBREVIATIONS

CHAPTER 1: INTRODUCTION

1.1Metamaterial

1.2Optical material relate to refractive index

CHAPTER 2: FUNDAMENTAL THEORY

2.1Effective Medium Theory

2.1.1Effective medium

2.1.2Permittivity calculation

2.2Transfer Matrix for multilayer optics

2.3Finite Difference Time Domain (FDTD)

CHAPTER 3: EXPERIMENTS

3.1Silver nanoparticles synthesis

3.1.1Chemicals

3.1.2Process

3.2Thin films fabrication

3.2.1Chemicals

3.2.2Process

3.3Optical properties determination

3.4Thin films thickness determination

CHAPTER 4: RESULTS AND DISCUSSION

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

iii

LIST OF FIGURES, SCHEMES

Fig 1.1: Multilayer structure and nanowires embedded structure metamaterial (A:metal-dielectric layered, B: wires in dielectric host) 2Fig 2.1: A material model of UEM 5Fig 2.2:Three simple model of UEM material classified following topology _ 6Fig 2.3: A simple model for assumption limitation of volume fill fraction _ 7Fig 2.4: Considered system of TMM problem 11

Fig 2.5: The arrangement of electric- and magnetic-field nodes in space and time 17Fig 4.1: The index of refraction of PVP including 3% volume fill fraction of silver,gold and copper 22Fig 4.2: The index of extinction of PVP including 3% volume fill fraction of silver,gold and copper 23Fig 4.3: The index of refraction of PVA including 3% volume fill fraction of silver,gold and copper 24Fig 4.4: The index of extinction of PVA including 3% volume fill fraction of silver,gold and copper 24Fig 4.5: The index of refraction of PVP including 2%, 3%, 4% and 5% volume fillfraction of silver _ 25Fig 4.6: The index of refraction of PVA including 2%, 3%, 4% and 5% volume fillfraction of silver _ 26Fig 4.7: The index of extinction of silver and PVP including 2%, 3%, 4% and 5%volume fill fraction of silver 27Fig 4.8: The index of extinction of silver and PVA including 2%, 3%, 4% and 5%volume fill fraction of silver 27

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

corresponding to different Ag fill fraction using TMM _ 31

visions 32Fig 4.14: The calculated transmittance spectrum of 200 nm PVP-based films

corresponding to different Ag fill fraction using FDTD method 33Fig 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 equal3nm in medium that has refractive index equal 1.5 using FDTD 36

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

solution _ 39

Fig 4.22: Molecular formula of PVP and PVA 40

silver nanoparticles _ 41

fill fraction of silver nanoparticles 42

Fig 4.25: Transmittance spectrum of PVP-based films different fill fraction of silvernanoparticles 43Fig 4.26: Transmittance spectrum of PVA-based films different fill fraction of silvernanoparticles 44

v

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: INTRODUCTION1.1 Metamaterial

Electromagnetic metamaterial is a class of material using for engineeringelectromagnetic space and controlling light propagation Metamaterials have showntheir promise for the next generation optical materials with electromagneticbehaviors almost can’t be obtained in any conventional materials They have aplenty 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 includinginclusions that have sub-wavelength structures The inclusions have designedstructure They can be totally artifact or emulate based on nature structure Theinclusions are arranged on a host medium that is normally dielectric Due to thesmall size and distance of inclusion, the metamaterials can be considered as thehomogeneous mediums The properties of material are represented throughpermittivity and permeability By changing shape and size of inclusion, permittivityand permeability of metamaterial can be adjusted to very high or low (evennegative) value Under the consideration for permittivity and permeability, thematerial can be classified into 4 groups [31] They are epsilon-negative material(ENG), mu-negative material (MNG), double positive material (DPS) and doublenegative material (DNG) The metamaterial is in class of ENG, MNG and DNGmaterials 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 ofmaterials can become small than 0 with structure like in Fig 1.1 It makes therefraction of light becomes very different when comparing with the originalmaterials

1

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 hyperbolicmetamaterial In this class of metamaterial, the refractive indexes and arrangement

of components play a significant role to properties of metamaterial The belowequations is used to calculate the anisotropic dielectric function of layeredmetamaterial

ϵ

ϵ

with ϵ and ϵ are dielectric function following directions those are parallel and perpendicular with surface of multilayer structure; d d and d m are thickness; and are dielectric function of dielectric material and metal Following it, the very low refractive index n = √ 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 ofmetamaterial depend on not only structures but also nature of hosts and inclusions

It suggests that along with structural changes, developing materials as host or

metamaterial focus on optimizing structure So, it is lacking in the studies whichdevelop the constituent material of metamaterial The second is the difficulty infabrication that mentioned above As an impact of the second, the limitation ofworking wave length also is an issue The most common topic about metamaterialrelates to terahertz region that corresponds to long wavelengths where demandinclusion in micrometer level We need more research about metamaterial thatworks in shorter wavelength region So, it is necessary to study a material which iseasy 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 materialproperties It relate to all optical phenomena such as refraction, reflection,transmission By changing the refractive index of material, we can create newmaterials that can be to various fields There has been many researches related tohigh refractive index material and negative refractive index material The highrefractive 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 ofmaterial that is promising for many applications [11-13] However, it has a lack ofresearch for low refractive index material They play a significant role in applicationrelate to the reflection materials and metamaterials It has some types of lowrefractive index including metal nano-rod or metamaterial used nano-wires asinclusion [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 ispossible based on the effective medium theory

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

3

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

In this study, my purpose is making a type of nano-composite material thathas low index of refraction and low index of extinction Based on the idea ofhyperbolic metamaterial, it is able to create the low refractive index and low lossmedium by the combination of low refractive index but loss material as metals andlow loss but high refractive index as polymers I fabricated the nanocompositebased on nano silver particles embedded on polymers This type of material wasconsidered in about absorption [49], high refractive index region [33], etc In thisstudy, 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 lengthscales which are presented (a and b), are well-defined and all much less than thewavelength of light This condition means that the scattering cause by theinhomogeneity resulting from the composite natural can be negligible In this case,the real composite material, with host dielectric constant ( ℎ ) and inclusiondielectric constant ( ), can be replaced by a Uniform Effective Medium (UEM) with

a dielectric constant ( ) [41]

a

2b

Fig 2.1: A material model of UEM

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

5

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

The object of research is the material that following the Maxwell Garnetcomposite geometry for applying to metamaterial as the third type of geometryintroduced above For predictable by Effective Medium Theory (EMT), the materialshould considered following some conditions At first, the scattering should beneglect able, at least with theoretical view It means that the size of metal particlesmust be much smaller than the working wavelength This study mostly considercharacteristic 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 tenthtimes compare with the shortest wavelength) In this study, the nanoparticle 20nm indiameter is chosen

Then, it’s necessary to consider the limitation of volume fill fraction thatrelates to distance between particles For theoretically and very simple consideration,

we can consider a following model Fig 2.3

20 nm

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,

7

2.1.2 Permittivity calculation

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

At first, we can refer to the particles as “molecules” in a region whichinclude 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 polarizabilitylinks 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)

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 assumptionmeans that the electromagnetic interaction between dipoles (particles or atom in thisconsideration) 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 − −

Then, the dipole moment per unit volume P is given following:

Meanwhile, there is a relation between dipole moment per unit , electrical

field E and dielectric constant following:

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 fieldand depolarization field So, we have the dipole moment p of the inclusion spherewithin the host medium is:

the electrical field applied far from inclusion Thus, we can identify an effective polarizability as:

ϵ −ϵ ℎ

ϵ +2ϵ

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

9

ϵ −ϵ

ℎ

ℎThe dielectric constant of effective medium ϵ can be calculated from

dielectric constant of constituents and fill fraction of inclusion f Here, we can see

that the dielectric constant which is calculated following Maxwell Garnett equation

is just depend on material of host, inclusion and fill fraction of inclusion However,the properties of real thin film depend on some other factors, i.e size of particles,distance and distribution of them, etc More detail consideration will be given inChapter 4

2.2 Transfer Matrix for multilayer optics

The matrix representation is very useful technique to consider the behaviors

of polarized light In general, this method presents the polarized light as two –component vector (2x1 matrix) and the effect of medium to the light as the opticalelement representing by 2x2 matrices called Jones matrices [14] The matrixmultiplication of light presenting vector and Jones Matrices results a new vector thatdescribe behavior of light after propagate through mediums described by JonesMatrices This method is very convenient for consider thin films, multilayer, crystalaccording to reflection, transmittance and extinction of material [1-3, 39-42] TheTransfer Matrix Method (TMM) is suitable to predict transmittance, reflectance ofthin films discussed on this study The detail discussion about TMM is showed on

of this study

Fig 2.4: Considered system of TMM problem.

Our problem is illustrated in Fig 2.4 It is designed to simulate the realmeasurement of samples We consider the propagation of incident light from airmedium (medium 1) through material (medium 2) and glass (medium 3) to airmedium (medium 4) The complex dielectric constants of air, glass and material are

= 1, = 1.5 and , respectively The dielectric constants of air and glass are almostunchanged following the wavelength Meanwhile, dielectric constant of material isconsidered as a function of wavelength due to dependence of dielectric constant ofmedium on dielectric constant of nanoparticles inclusion The used constants istaken from the available database [24] The thickness of air is assumed as infinitybecause it’s external medium The thickness of glass can be determined but it notvery necessary because the neglected extinction on glass The thickness of material

is important to calculate so it must be known for calculation

The consideration about propagation of light is processed by consideringforward and backward propagating electric fields through mediums The E-field in

medium 1 E 1 is represented by two-component vector:

11

Following matrix representation of for polarized light, the relation between

E-field in medium 1 and medium 4 is showed by matrix multiplication:

With T is 2x2 matrix The matrix T is the overall transfer matrix that describe

the effect of medium to incident light as an operator that change vector of E-field

from incident medium to measuring medium Call that:

Then, we have expression of multiplication:

It’s easily to see that 1−/ 1+ is the overall reflection amplitude r and 4+/ 1+is the overall

transmission amplitude t So, the reflectance R and transmittance Tr can be evaluated following:

R = r 2 = (

12

= t2 = ( 11 + 12 )2

Now, the problem is finding the overall transfer matrix The propagation of

light through mediums includes two ingredients The first is the propagation at the

interface of medium i and medium j those have different refractive index For

isotropic media, the transfer matrix for interface is a 2x2 matrix defined by:

1

Mij =

With and are the transmission and reflection amplitudes for light come from

medium i to medium j Call that Ni and Nj is the reduced wave vector on

propagation direction and and are complex dielectric constant of medium i and

medium j The reflection and transmission amplitudes for s-polarized light are

The second ingredient of propagation of light

propagation on each medium The propagation matrix Pi

magnitude and di is thickness of material) Now, we can evaluate overall transfer

matrix from two ingredients applying for propagation of light from medium 1 to 3:

13

By this way, the transmittance Tr13 can be calculated with determinedcomplex dielectric constant and thickness of thin film Following Fressnel’s

equation [14] the transmittance Tr glass of light propagating from glass to .Tocompare with experiment results, the final calculated transmittance is evaluated by:

Tr =

This result correspond to measured transmittance of thin film on glasssubstrate with reference is glass

2.3 Finite Difference Time Domain (FDTD)

The Finite-Difference Time-Domain (FDTD) method is the simplest wave techniques used to solve problems in electromagnetics The FDTD methodcan solve complicated problems, but it consumes a lot of computation resource.Solutions may demand a large amount of memory and computation time TheFDTD method loosely fits into the category of “resonance region” techniques, i.e.,ones in which the characteristic dimensions of the domain of interest are somewhere

full-on the order of a wavelength in size If an object is very small compared to awavelength, quasi-static approximations generally provide more efficient solutions.Alternatively, if the wavelength is exceedingly small compared to the physicalfeatures of interest, ray-based methods or other techniques may provide a muchmore efficient way to solve the problem [36]

The FDTD method is mainly based on the central-difference approximation This approximation can be applied to both the spatial and temporal derivative in Maxwell’s equation Now,

we consider the Taylor series expansions of the function f(x) expanded about the point x 0 with an offset

of ± 2 :

2

14

f (x0 − ) = f(x0) −

2

where the primes indicate differentiation Subtracting the equation (2.3.1) to

the equation (2.3.2), we have:

Here, we see that with is very small, the parts including high derivative of

f(x) are neglect able So, we have an approximation following:

df(x)

=

This is the central-difference approximation Since the lowest power of being

ignored is the second order, the central difference is said to have second-order

accuracy or second-order behavior This implies that if is reduced by a factor of 10,

the error in the approximation should be reduced by a factor of 100 (at least

approximately) In the limit as goes to zero, the approximation becomes exact

The FDTD algorithm as first proposed by Kane Yee in 1966 employs

second-order central differences The algorithm can be summarized as follows [36]:

1 Replace all the derivatives in Ampere’s and Faraday’s laws with finite

differences Discretize space and time so that the electric and magnetic fields are

staggered in both space and time

2 Solve the resulting difference equations to obtain “update equations” that

15

4 Evaluate the electric fields one time-step into the future so they are now

known (effectively they become past fields)

5 Repeat the previous two steps until the fields have been obtained over the

desired duration

Here, let’s consider 1 dimension problem of FDTD method We assumed that

the E-field only has a z component and there are only variations in x direction

Following Maxwell’s equation, we can derive two scalar equations corresponding to

Faraday’s law and Ampere’s:

where μ and ϵ are permeability and permittivity of medium, respectively Then, we

could replace the derivatives in (2.3.6) and (2.3.7) with finite differences To convenient,

the below notation will be used to indicate the location in space and time that the fields are

considered:

where ∆x is the spatial offset between sample points and ∆t is the temporal

offset The index m corresponds to the spatial step, effectively the spatial location,

while the index q corresponds to the temporal step Time and x direction can be

considered as two independence dimension So, the arrangement of electric- and

magnetic-field nodes in space and time is showed in Fig 2.5 Assume that all the

fields below the dashed line are known—they are considered to be in the past—

while the fields above the dashed line are future fields and hence unknown The

FDTD algorithm provides a way to obtain the future fields from the past fields

Fig 2.5: The arrangement of electric- and magnetic-field nodes in space and time.

Now, let consider the space-time point ((m + 1/2)∆x, q∆t) by equation

This is known as an update equation, specifically the update equation for the

Hy field And by the same way applying for equation (2.3.7), we can derive theupdate equation for the Ez field After these update equation applying to every

17

electric-field node in the grid, the dividing line between what is known and what areunknown moves forward another one-half temporal step They would be updatedagain, then the electric fields would be updated, and so on.

It is often convenient to represent the update coefficients ∆t/ϵ∆x and ∆t/μ∆x interms of the ratio of how far energy can propagate in a single temporal step to the spatialstep The maximum speed electromagnetic energy can travel is the speed of light in freespace c = 1/√ϵ0 0 and hence the maximum distance energy can travel in one time step isc∆t (in all the remaining discussions the symbol c will be reserved for the speed of light in

free space) The ratio c∆t/∆x is often called the Courant number which we label Sc It plays

an important role in determining the stability of a simulation

The more detail consideration about 3D problem and the boundary condition

is important to understand clearly about FDTD method but it’s not suitable to discus

in here The deeper discussions are provide in many the other relation document[8,17,21,28,30,37]

In this study, I use the FullWAVE software by RSOFT design group toprocess the calculation for materials It allows me to simulate the material in form

of thin film or particles to predict optical properties of object The purpose isoptimizing grid, boundary condition and domain arrangement to archive goodprediction for optical properties of research object

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CHAPTER 3: EXPERIMENTS 3.1 Silver nanoparticles synthesis

3.1.1 Chemicals

Silver nitrate: AgNO3 (Sigma Aldrich)

Poly Vinyl Pyrrolidone (PVP) powder

Sodium borohydride: NaBH4 (Sigma Aldrich)

Step 6: After that, keep the string in 1 hour or more

Step 7: Purification by centrifugation at 11000 rounds per minutes The centrifugation is repeated 3 times with 20 minutes each time

Step 8: The cleaned samples is redistributed into distilled water

3.2 Thin films fabrication

3.2.1 Chemicals

Poly Vinyl Pyrrolidone (PVP) powder

Poly Vinyl Alcohol (PVA) powder

Silver nanoparticles solution (Sigma Aldrich)

Distilled water

3.2.2 Process

Step 1: The solution used to film fabricate is prepared from 20nm diameter silvernanoparticles solution (Sigma Aldrich) with sodium citrate is used as stabilizer andwater as solvent It has two types of solution:

Solutions made by PVP and silver nanoparticles were prepared by addingnanoparticles solution to PVP powder The mass ratios of nanoparticlessolution and PVP powder correspond to 3%, 4% and 5% fill fraction of silvernanoparticles on thin films

Solutions made by PVA and silver nanoparticles were prepared by addnanoparticles solution into prepared PVA 10%w.t solution with water assolvent The mass ratios of nanoparticles solution and PVA correspond to3%, 4% and 5% fill fraction of silver nanoparticles on thin films

Step 2: Before film making, the solutions are sonicated for 30 minutes usingultrasonicator bath The thin film was fabricated on glass substrate following 2methods:

Drop coating: 10l prepared solution were dropped into 1 side of glasssubstrates Then, samples were dried on vacuum at 60oC for more than 3 hours

Spin coating: 10l prepared solution were dropped into 1 side of glass

substrates The spin program is following: 1500rpm on 60 seconds  500

20

rpm on 10 seconds Then, samples were dried on vacuum at 60oC for more than 3 hours.

3.3 Optical properties determination

The optical property of thin films is determined by UV – VISspectrophotometer The measurement investigates transmittance of thin films andsolutions on wavelength region from 300nm to 800nm The glass substrates whichhave thin films are placed directly into measuring chamber The solutions arepackaged in cuvettes The reference is glass substrate in case of thin films ordistilled water in case of solution The scan speed is 40nm/minute

3.4 Thin films thickness determination

The thickness of thin films is determined by the Alpha-step profiler Itinvestigates the height difference of area with and without thin film to derivethickness of thin films The scan mode is 2D on region 10000m The resolution isapproximate 1 scan point/m The thickness deviation of this system is around30nm The thickness of each film is sampled four times then took average

CHAPTER 4: RESULTS AND DISCUSSION 4.1 Calculation results

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

In this study, it has two host materials which are Poly Vinyl Pyrrolidone(PVP) and Poly Vinyl Alcohol (PVA) Their dielectric functions are considered asconstants because they are stable over visible wavelength The consideredinclusions are by copper, gold and main object – silver The complex dielectricconstants of these elements are functions of wavelength The dielectric constantsused for calculations are taken from the available database [30]

The calculated index of refraction and index of extinction of 3 types ofmaterial based on PVP as host medium following UEM are described in Figure 4.1and Figure 4.2, respectively The calculation is processed using Maxwell Garnettexpression for effective dielectric constant ϵ The host is PVP with index ofrefraction as 1.5523 and neglected index of extinction [24] The inclusions are gold,copper and silver with volume fill fraction 3%

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

Following Fig 4.1, it’s easily to see that silver nanoparticles should be themost suitable element for low refractive index material It shows the index ofrefraction about 1 on wavelength region from 390 to 410 nm Comparing with index

of refraction of PVP (approximate 1.55), the existence of silver, gold or copper alsocan decrease index of refraction But, the purpose is fabricating a material whichhas index of refraction approximate refractive index of air So, silver nanoparticle ischosen as inclusion of material Just composite materials including polymer andsilver nanoparticles are considered on later part of thesis

The other considered host medium is PVA We also calculated refractiveindex for material with PVA as host material and inclusion as like as in case of PVP(material and fill fraction) The index of refraction and index of extinction bywavelength are illustrated on Fig 4.3 and Fig 4.4 Actually, both index of refractionand index of extinction of PVA based materials are quite similar as case of PVP Theindex of refraction of PVA – silver material is about 1 on wavelength region from

385 to 400 nm However, the confirmation that PVP based and PVA based

material has similar indexes of refraction is necessary The experimental discussion

about two types of material will be showed in more detail later

Fig 4.3: The index of refraction of PVA including 3% volume fill fraction of

silver, gold and copper

Fig 4.4: The index of extinction of PVA including 3% volume fill fraction of

silver, gold and copper

24

For both PVP and PVA cases, the main challenge is shown in Fig 4.2 and Fig4.4 Although material including silver could have low index of refraction, the index

of extinction of it is much higher than the others However, the extinction relate toboth index of extinction and thickness of thin film For application for metamaterial,the thickness of thin film should much less than working wavelength that about40nm in case of silver based material In this case, the extinction is acceptable

4.1.2 Index of refraction and index of extinction depend on volume fill fraction

of silver nanoparticles on polymer matrix

The index of refraction and index of extinction not only depend on type ofmaterial but also relate to fill fraction of inclusion on material The wavelengthdepend index of refraction for PVP-based and PVA-based material in number of fillfraction are shown in Fig 4.5 and Fig 4.6

1.81.30.80.3

Wavelength ( m)

The reliability of prediction should be considered by comparison with experiments