LUẬN văn THẠC sĩ study of low refractive index homogeneous thin film for application on metamaterial

INTRODUCTION

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 ϵ 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 =𝑑 𝑑 + 𝑑 𝑚

𝑑 𝑑 + 𝑑 𝑚 withϵ 𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 and ϵ𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟are dielectric function following directions those are parallel and perpendicular with surface of multilayer structure; dd and dm are thickness; 𝜖 𝑚 and 𝜖 𝑑 are 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 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.

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

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

- Calculation transmittance of thin films based on calculated materials

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

FUNDAMENTAL THEORY

Effective Medium Theory

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 (𝜖 ℎ ) and inclusion dielectric constant (𝜖 𝑖 ), can be replaced by a Uniform Effective Medium (UEM) with a dielectric constant (𝜖 𝑒𝑓𝑓 ) [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

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 in diameter is chosen

Then, it’s necessary to consider the limitation of volume fill fraction that relates to distance between particles For theoretically and very simple consideration, we can consider a following model Fig 2.3

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, f =𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒𝑠

For predictable by Maxwell Garnett Topology (MGT), the fill fraction of metal nanoparticles on material should be less than 0.0335 The size and fill fraction 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

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

With N atoms in a lattice that has volume V, the local field correction can be estimated as − −

3 𝑝𝑉/𝑁 Now, the polarizability is written as: p = α [E − −

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

Meanwhile, there is a relation between dipole moment per unit 𝑃, electrical field E and dielectric constant 𝜖 following:

So, we can derive an equation describing relation of dielectric constant 𝜖 and polarizability α, which is as known as Claudius – Mossotti relation: ϵ−1 ϵ+2= 4π

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 p 𝑖 of the inclusion sphere within the host medium is: p 𝑖 = a 3 ϵ 𝑖 −ϵ ℎ ϵ 𝑖 +2ϵ ℎ 𝐸 0 (2.1.7)

Where a is the radius of sphere, ϵ 𝑖 is the dielectric constant of inclusion, ϵ ℎ is the dielectric constant of host medium and 𝐸 0 is the electrical field applied far from inclusion Thus, we can identify an effective polarizability as: α = a 3 ϵ 𝑖 −ϵ ℎ ϵ 𝑖 +2ϵ ℎ (2.1.8)

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: ϵ 𝑒𝑓𝑓 −ϵ ℎ ϵ 𝑒𝑓𝑓 +2ϵ ℎ= 4𝜋

The dielectric constant of effective medium ϵ 𝑒𝑓𝑓 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 in Chapter 4.

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 optical element representing by 2x2 matrices called Jones matrices [14] The matrix multiplication of light presenting vector and Jones Matrices results a new vector that describe behavior of light after propagate through mediums described by Jones Matrices This method is very convenient for consider thin films, multilayer, crystal according to reflection, transmittance and extinction of material [1-3, 39-42] The Transfer Matrix Method (TMM) is suitable to predict transmittance, reflectance of thin films discussed on this study The detail discussion about TMM is showed on

[19] Here, we just introduce parameters and formulas that are used for the problem 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 real measurement of samples We consider the propagation of incident light from air medium (medium 1) through material (medium 2) and glass (medium 3) to air medium (medium 4) The complex dielectric constants of air, glass and material are 𝜖 𝑎𝑖𝑟 = 1, 𝜖 𝑔𝑙𝑎𝑠𝑠 = 1.5 and 𝜖 𝑚𝑎𝑡𝑒𝑟𝑖𝑎𝑙 , respectively The dielectric constants of air and glass are almost unchanged following the wavelength Meanwhile, dielectric constant of material is considered as a function of wavelength due to dependence of dielectric constant of medium on dielectric constant of nanoparticles inclusion The used constants is taken from the available database [24] The thickness of air is assumed as infinity because it’s external medium The thickness of glass can be determined but it not very 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 considering forward and backward propagating electric fields through mediums The E-field in medium 1 E 1 is represented by two-component vector:

With 𝐸 1 + is forward-propagating E-field and 𝐸 1 − is backward-propagating E- field in medium 1 By the same way, the E-field in medium 4 is represented by:

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:

We can assume that 𝐸 4 − = 0 because it has no incident light from medium 4

Then, if divide both 2 side to 𝐸 1 + we have:

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

𝐸 1 + is the overall transmission amplitude t So, the reflectance R and transmittance Tr can be evaluated following:

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:

With 𝑡 𝑖𝑗 and 𝑟 𝑖𝑗 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 𝜖 𝑖 and 𝜖 𝑗 are complex dielectric constant of medium i and medium j The reflection and transmission amplitudes for s-polarized light are following [9]:

And the corresponding expressions for p-polarized light are:

The second ingredient of propagation of light on our problem is the propagation on each medium The propagation matrix Pi of medium i is expressed following:

With 𝑝 𝑖 = exp (𝑖𝑁 𝑖 𝑘 0 𝑑 𝑖 ) and 𝑝 𝑖 = 𝑝̅ 𝑖 −1 (k0 is vacuum wave vector 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:

By this way, the transmittance Tr13 can be calculated with determined complex dielectric constant and thickness of thin film Following Fressnel’s equation [14] the transmittance Tr glass of light propagating from glass to To compare with experiment results, the final calculated transmittance is evaluated by:

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

Finite Difference Time Domain (FDTD)

The Finite-Difference Time-Domain (FDTD) method is the simplest full- wave techniques used to solve problems in electromagnetics The FDTD method can solve complicated problems, but it consumes a lot of computation resource

Solutions may demand a large amount of memory and computation time The FDTD 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 on the order of a wavelength in size If an object is very small compared to a wavelength, quasi-static approximations generally provide more efficient solutions

Alternatively, if the wavelength is exceedingly small compared to the physical features of interest, ray-based methods or other techniques may provide a much more 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 x0 with an offset of ± 𝛼

2) 2 f ′′ (x 0 ) − ⋯ (2.3.2) where the primes indicate differentiation Subtracting the equation (2.3.1) to the equation (2.3.2), we have: f (x 0 + 𝛼

Here, we see that with 𝛼 is very small, the parts including high derivative of f(x) are neglect able So, we have an approximation following: df(x) dx x=x 0

This is the central-difference approximation Since the lowest power of 𝛼 being ignored is the second order, the central difference is said to have second-order accuracy or second-order behavior This implies that if 𝛼 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 𝛼 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 express the (unknown) future fields in terms of (known) past fields

3 Evaluate the magnetic fields one time-step into the future so they are now known (effectively they become past fields)

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: μ 𝜕𝐻 𝑦

𝜕𝑥 (2.3.7) 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:

H 𝑦 (x, t) = H 𝑦 (m∆x, q∆t) = H 𝑦 𝑞 [m] (2.3.9) 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 (2.3.6): μ 𝜕𝐻 𝑦

𝜕𝑥 (𝑚 + 𝟏/𝟐)∆𝑥,𝑞∆𝑡 (2.3.10) Using the central approximation, we can see that it possible to derive unknown value H 𝑦 𝑞+1/2 [m + 1/2] from available values H 𝑦 𝑞−1/2 [m + 1/2] ,

𝜇∆𝑥E 𝑧 𝑞 [m + 1] − E 𝑧 𝑞 [m] (2.3.12) 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 the electric-field node in the grid, the dividing line between what is known and what are unknown moves forward another one-half temporal step They would be updated again, 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 in terms of the ratio of how far energy can propagate in a single temporal step to the spatial step The maximum speed electromagnetic energy can travel is the speed of light in free space c = 1/√ϵ 0 𝜇 0 and hence the maximum distance energy can travel in one time step is c∆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 to process 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 is optimizing grid, boundary condition and domain arrangement to archive good prediction for optical properties of research object.

EXPERIMENTS

Silver nanoparticles synthesis

Silver nitrate: AgNO3 (Sigma Aldrich) Poly Vinyl Pyrrolidone (PVP) powder Sodium borohydride: NaBH4 (Sigma Aldrich) Distilled water

Step 1: Take 0.51 g Poly Vinyl Pyrrolidone and dissolve in 20 mg distilled water, stirring in 60 minutes (solution M2)

Step 2: Take 0.05 mg NaBH4 and dissolve in 50 ml distilled water, stirring in

Step 3: Take 0.01 g AgNO3 and dissolve in 10 ml distilled water, stirring in

Step 4: After all the solutes are completely dissolved, Add solution M1 to solution M2, string in 15 minutes (Mixture M)

Step 5: After that, drop slowly solution M3 to mixture M The drop flow is less than 1l/second

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.

Thin films fabrication

Poly Vinyl Pyrrolidone (PVP) powder Poly Vinyl Alcohol (PVA) powder Silver nanoparticles solution (Sigma Aldrich) Distilled water

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

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

 Solutions made by PVA and silver nanoparticles were prepared by add nanoparticles solution into prepared PVA 10%w.t solution with water as solvent The mass ratios of nanoparticles solution and PVA correspond to 3%, 4% and 5% fill fraction of silver nanoparticles on thin films

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

 Drop coating: 10l prepared solution were dropped into 1 side of glass substrates Then, samples were dried on vacuum at 60 o C 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 rpm on 10 seconds Then, samples were dried on vacuum at 60 o C for more than 3 hours.

Optical properties determination

The optical property of thin films is determined by UV – VIS spectrophotometer The measurement investigates transmittance of thin films and solutions on wavelength region from 300nm to 800nm The glass substrates which have thin films are placed directly into measuring chamber The solutions are packaged in cuvettes The reference is glass substrate in case of thin films or distilled water in case of solution The scan speed is 40nm/minute.

Thin films thickness determination

The thickness of thin films is determined by the Alpha-step profiler It investigates the height difference of area with and without thin film to derive thickness of thin films The scan mode is 2D on region 10000m The resolution is approximate 1 scan point/m The thickness deviation of this system is around 30nm The thickness of each film is sampled four times then took average.

RESULTS AND DISCUSSION

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 as constants because they are stable over visible wavelength The considered inclusions are by copper, gold and main object – silver The complex dielectric constants of these elements are functions of wavelength The dielectric constants used for calculations are taken from the available database [30]

The calculated index of refraction and index of extinction of 3 types of material based on PVP as host medium following UEM are described in Figure 4.1 and Figure 4.2, respectively The calculation is processed using Maxwell Garnett expression for effective dielectric constant ϵ 𝑒𝑓𝑓 The host is PVP with index of refraction 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

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 the most suitable element for low refractive index material It shows the index of refraction 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 also can decrease index of refraction But, the purpose is fabricating a material which has index of refraction approximate refractive index of air So, silver nanoparticle is chosen as inclusion of material Just composite materials including polymer and silver nanoparticles are considered on later part of thesis

The other considered host medium is PVA We also calculated refractive index 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 by wavelength are illustrated on Fig 4.3 and Fig 4.4 Actually, both index of refraction and index of extinction of PVA based materials are quite similar as case of PVP

The index 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

PVP_Cu3% 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

For both PVP and PVA cases, the main challenge is shown in Fig 4.2 and Fig 4.4 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 to both index of extinction and thickness of thin film For application for metamaterial, the thickness of thin film should much less than working wavelength that about 40nm 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 of material but also relate to fill fraction of inclusion on material The wavelength depend index of refraction for PVP-based and PVA-based material in number of fill fraction are shown in Fig 4.5 and Fig 4.6

Fig 4.5: The index of refraction of PVP including 2%, 3%, 4% and 5% volume fill fraction of silver

Fig 4.6: The index of refraction of PVA including 2%, 3%, 4% and 5% volume fill fraction of silver

The fill fraction approximate 1 is achieved in case fill fraction of silver about 3% and higher for both case PVP-based and PVA-based materials Consistent with results in the previous section, the deep of index of refraction spectrum of PVP- based material appears at longer wavelengths than PVA’s The trend of results for PVP-based materials are similar as available results that confirmed by experiment in

[33] However, the confirmed results are just limited for wavelength over 500nm

The reliability of prediction should be considered by comparison with experiments

Fig 4.7: The index of extinction of silver and PVP including 2%, 3%, 4% and 5% volume fill fraction of silver

Fig 4.8: The index of extinction of silver and PVA including 2%, 3%, 4% and 5% volume fill fraction of silver

The dependence of index of extinction on fill fraction is described in Fig 4.7 and Fig 4.8 corresponding to PVP-based and PVA-based materials The position of peak on index of extinction spectrum is quite similar as confirmed result in [15] As

PVA_Ag5% the unnatural point that the indexes of extinction in case about 5% fill fraction or more are higher than silver’s This problem is being considered and will be discuss more detail in other research

4.1.3 Calculation for thin film following EMT using TMM

Applying Maxwell Garnett equation, the dielectric constant of material can be calculated in case of known fill fraction and host and inclusion material Using these data, the transmittance of thin films can be calculated using TMM Fig 4.9 and Fig 4.10 illustrate transmittance spectrum of different silver fill fraction thin film films that thick 30nm corresponding to PVP-based and PVA-based materials The glass substrate is though as reference The incident light is Transverse Electric and comes perpendicular to the surface of thin film The calculation is processed following section 2.2

Fig 4.9: Transmittance spectrum of 30 nm PVP-based films corresponding to different Ag fill fraction

PVP_3%_30nmPVP_4%_30nmPVP_5%_30nm

Fig 4.10: Transmittance spectrum of 30 nm PVA-based films corresponding to different Ag fill fraction

For both two cases, the trends of spectrum are similar The deeps of spectrum of PVP-based material are red-shift (approximate 5nm in case of 5% fill fraction) compare with PVA-based material’s There is a point that the transmittance is higher than 100% in some region The reason is that the calculated indexes of refraction in those regions are higher than 1 (assumed index of refraction of air) and lower than 1.5 (assumed index of refraction of glass substrate) In this case, the transmittance of system air/material/glass/air should be higher than the transmittance of system air/glass/air that considered as reference Here, the problem is that the regions of wavelength where material has low index of refraction (lower than 1) are in extinction region Although these regions do not include deep of spectrum (the strongest extinction region), there is an obstacle for index of refraction determination The very common method for refractive index determination is determining the Brewster angle [14] using reflectometer In this case, the extinction can make the Brewster angle determination become inaccurate

Because of the lack of tool, the comparison between calculated transmittance spectrum and experimental results might be only way to preconceive the index of

PVA_3%_30nmPVA_4%_30nmPVA_5%_30nm refraction of material To compare with transmittance of fabricated film that will be discussed later, the transmittance spectrum of 200nm film were calculated and shown in Fig 4.11 and Fig 4.12 The overall trend of calculated transmittance spectrum of 200nm films is quite similar as in case of 30nm films However, the role of extinction becomes clearer There are some variations of calculated transmittance due to the variation of predicted index of extinction

Fig 4.11: The calculated transmittance spectrum of 200 nm PVP-based films corresponding to different Ag fill fraction using TMM

PVP_Ag3%_TMMPVP_Ag4%_TMMPVP_Ag5%_TMM

Fig 4.12: The calculated transmittance spectrum of 200 nm PVA-based films corresponding to different Ag fill fraction using TMM

4.1.4 Calculation for thin film using FDTD method

To predict transmittance spectrum of films, the FDTD method is used to calculate the transmittance of 200 nm film for both PVP-based and PVA-based material including 20 nm silver nanoparticles The description of domain is shown in Fig 4.13 The length of domain correspond to x, y, z direction are 200 nm, 200 nm and 600nm, respectively The grid size for all direction is 1.5nm The boundary condition for x and y direction is periodic and for z direction is 25nm thick PML

The host material dielectric constants are defined following [20,31] The inclusions are spheres which are sized 20 nm diameter They dielectric constants are defined as

Ag that following [30] Each sphere is distributed randomly and spacing the other at least 2 nm The launch field is typed plane wave and expose incident light that is Transverse Electric and comes perpendicular to the surface of thin film Time step is auto optimized following Courant condition [34] The monitor is sized 200x200 nm 2 The output is the power of light depends on wavelength in region from 300 nm to 800 nm The estimated memory is about 133.1 megabytes The calculation processes are stable This model is different compare with real samples The

PVA_Ag3%_TMMPVA_Ag4%_TMMPVA_Ag5%_TMM disappearance of glass substrate on the calculation model could be a factor that affect to accuracy of calculation The more accurate model will be considered on later research because limitation of time and calculation condition

Fig 4.13: The FDTD domain for calculation of 200nm film by x, y, z direction and

Fig 4.14: The calculated transmittance spectrum of 200 nm PVP-based films corresponding to different Ag fill fraction using FDTD method

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

The calculate transmittance spectrum of 200 nm films using FDTD method are shown in Fig 4.14 and Fig 4.15 It can be seen that the main deeps of

PVP_Ag3%_FDTD PVP_Ag4%_FDTD PVP_Ag5%_FDTD PVP only_FDTD

Experiment results

The solution of silver nanoparticles has dark brown color that is shown in Fig 4.19 This figure also shows images of silver nanoparticles solution in three steps on cleaning process It can be seen that the concentration of nanoparticles solution is decreased a lot due to cleaning The good point is that it has a large amount of particles which are should have smaller size than participate particles, still in leachate after centrifugation It means that the synthesis is successful But, the bad point is that the centrifugation speed looks not very effective for cleaning process

The lost still continue in case using very low concentration solution Maybe, the higher centrifugation speed should be better if it possible

Fig 4.19: The images of silver nanoparticles solution after synthesis(a), after centrifugation(b) and after re-disperse on water(c)

The SEM image in Fig 4.20 confirmed that particles size is approximate 20nm Besides that, the transmittance spectrum of solution in Fig 4.21 also shows that the size of self-synthesis silver nanoparticles is comparable with commercial sample used as standard sample The concentration of self-synthesis samples should be evaluated through comparing amplitude of deep that due to LSPR of silver nanoparticles in spectrum of very low concentration self-synthesis samples and commercial sample which has known concentration There is a point that the commercial sample has one more deep which do not appear in case of self-synthesis samples It could be due to the existence of a family of particles that bigger than 20nm diameter It suggests a problem that may be the self-synthesis solution has less participate because of the remaining of PVP on solution This problem will cause errors for fill fraction of nanoparticles in materials So, this section is just for introduce a promise able synthesis process and general quality of products The optimization will be considered later In this study, the commercial Ag nanoparticle is used for all the other experiments a b c

Fig 4.20: SEM image of self-synthesis silver nanoparticles

Fig 4.21: Transmittance spectrum of self-synthesis and commercial silver nanoparticles solution

Wavelength (nm) x mg/ml self-synthesis2x mg/ml self-synthesis3x mg/ml self-synthesis1.43E-6 mg/ml standard3E-6 mg/ml standard

Two polymers used as the host material are PVP and PVA which have molecular formula shown in Fig 4.22 On visible region, the index of refraction of PVP gradually decreases from 1.5606 to 1.5207 and the index of extinction decrease from 0.0045 to 0.0014 [24] The index of refraction of PVA also decreases from 1.5338 to 1.4702 on 300 to 800nm wavelength region Assumed that the extinction of polymers can be neglected, the transmittance of polymers can be evaluated using Fresnel’s equation In glass substrate, the transmittance of PVP film is about 0.9077 to 0.9127 and PVA film’s is about 0.9111 to 0.9182 compare with vacuum Meanwhile, transmittance of glass is about 0.9091 Theoretically, the transmittance of substrate with film is higher than glass substrate in some regions of wavelength In some cases, the results of real samples can be different due to scattering of ununiformed surfaces of film

Fig 4.22: Molecular formula of PVP and PVA

To confirm the existence of silver nanoparticles in solutions which are used to fabricate thin films, the transmittance spectra of them is measured by UV-VIS spectrophotometer These spectra of PVP and PVA with and without existence of silver nanoparticles are showed in Fig 4.23 The spectra of solution of polymer without silver haven’t any deep, while it including Ag particles show two deep that similar as solution of commercial silver nanoparticles solution

Fig 4.23: Transmittance spectrum of PVA, PVP solution with and without existence of silver nanoparticles

The fabricated thin films by drop-coating method are light brown and transparent Fig 4.24 shows transmittance depending on wavelength of 3% silver nanoparticles fill fraction PVP-based and PVA-based films compare with the transmittance of PVP, PVA without silver and silver sample in glass substrate The spectra of PVP and PVA without silver don’t show any deep while spectra of polymer including silver show the deeps in wavelength about 400nm corresponding extinction Those deep are due to LSPR of silver nanoparticles that also exist in spectrum of dropped silver sample The red shift of LSPR signal in PVP and PVA host compare with dropped silver particles is related to index of refraction of host medium In case of dropped silver particle, the host medium can be assumed as the air which has refractive index equals 1 It is smaller than refractive index of both PVP and PVA in considered region of wavelength The spectra have many fluctuations in region 300 – 400nm because of used device The thickness of films made by drop-casting method is almost could not determine by Alpha step profile because of non-uniform surface There is unnatural point that transmittance of the films is much higher than the solution used in above case although the concentration of silver in films should much higher than in solution (at least in case of applying

PVA solution PVA_Ag3% solution PVP solution

PVP_Ag3% solution drop-casting method) The explanation demands more experiments that I could not complete on this research

Fig 4.24: Transmittance spectrum of drop-coating PVP, PVA films corresponding

3% fill fraction of silver nanoparticles

As showed in Fig 4.25, the transmittance spectrum of spin-coating PVP- based thin film with different fill fraction of silver nanoparticles has no signal of extinction due to silver nanoparticles The explanation could be that the viscosity of PVP solution is too low When sample is rotated, almost the amount of solution is almost wiped out The remaining solution is just enough for a thin film with a mount of silver particles too little to make a signal in spectra To avoid this problem,

I tried decrease rotation speed But, the results are not good The fabricated films are as thick as drop coating and non-uniform

PVA_Ag3%_drop coatingPVP_Ag3%_drop coatingPVA_Ag0%_ drop coatingPVP_Ag0%_ drop coatingAg_drop

Fig 4.25: Transmittance spectrum of PVP-based films different fill fraction of silver nanoparticles

The transmittance spectra of PVA-based films are showed in Fig 4.26 The thicknesses of films are approximate 164nm, 132nm and 136nm corresponding to 3%, 4% and 5% fill fraction of silver particles, respectively Here, we can expect the deeps to be LSPR signals, especially the deep in case of 3% silver fill fraction

Now, it has two issue of this case

 The first issue is the huge difference between the extinction occurring in real samples and calculation Actually, this problem was already reported in [10]

The actual index of extinction is usually lower than calculated by Maxwell Garnett’s equation It has some people have developed different model than MGT to get more accurate approximation, such as [39] This work also will be processed on continuing research

 The second issue is the blue shifts of deep from 3% fill fraction case to 5% fill fraction case It has a supposition that the LSPR signal of each particle is affected by the decreasing dielectric constant of overall medium due to effect

PVP_Ag3%_spinPVP_Ag4%_spinPVP_Ag5%_spin refraction Then this decrease makes blue shift of LSPR signal For consider this phenomena, the range of particles fill fraction will be expanded later

Fig 4.26: Transmittance spectrum of PVA-based films different fill fraction of silver nanoparticles

On wavelength region about 310nm to 400nm, the transmittance of PVA- based films with silver particles (≥ 98.5%) is higher than calculated transmittance of films without particles ( ≥96%) It suggests that the index of refraction of PVA including silver is lower than bare PVA’s and higher than 1 in this wavelength region of light This trend of index of refraction is quite similar as predicted index by EMT So, the decrease of index of extinction due to the nanoparticles is confirmed for PVA thin film As an initial research, this research phase can be considered as completed The next phase will focus to optimize the calculation approximation and to determine precisely both of index of refraction and index of extinction of material

PVA_Ag3%_spinPVP_Ag4%_spinPVA_Ag5%_spin

In conclusion, the initial study about the low refractive index and low loss material based on PVP and PVA including silver nanoparticles has conducted The numerical calculation was run using Wolfram Mathematica software and FullWAVE software Applying the approximation following Maxwell Garnett topology for uniform effective medium, the index of refraction and index of extinction of materials was calculated The silver is predicted to be a better element of inclusion for object material compare with gold and copper The suitable size of using silver particles is 20 nm diameter The suitable fill fraction of silver nanoparticles is about 3% to less than 5% Theoretically, the indexes of refraction of those materials are lower than 1 in region of wavelength about 380 to 400 nm The transmittance of thin films based on two types of material was calculated using two methods those are TMM apply refractive index predicted by EMT and FDTD method They verify the existence of LSPR signal at wavelength about 400 nm The predicted extinction is stronger than in real samples The FDTD method also introduces the problem of neighbor-particles interaction affect to transmittance of films It illustrates the picture that should be nearly similar as in real films

The experiments focused on determining transmittance of real thin films The PVP-based material is easy to prepare but hard to fabricate and maintain The PVA- based material is harder to prepare but more stable The signal of LSPR of silver nanoparticles is investigated for case of PVA-based films The decrease of index of refraction is also confirmed through transmittance of PVA including silver nanoparticles thin films Here, it is possible to conclude that PVA and silver nanoparticle are promising host and inclusion to fabricate low index of refraction and low loss material The future research will focus to optimize the approximation for prediction and investigate precisely optical properties of materials

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