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

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 MAJOR: NANOTECHNOLOGY CODE: PILOT RESEARCH SUPERVISOR: Ph.D PHAM TIEN THANH HANOI, 2019 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 i TABLE OF CONTENTS Acknowledgement i LIST OF FIGURES, SCHEMES iv LIST OF ABBREVIATIONS vi CHAPTER 1: INTRODUCTION .1 1.1 Metamaterial 1.2 Optical material relate to refractive index CHAPTER 2: FUNDAMENTAL THEORY 2.1 Effective Medium Theory 2.1.1 Effective medium 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 ii 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) Fig 2.1: A material model of UEM 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 iv 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 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 vi 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 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 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 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 ϵ𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 = ϵ𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 = 𝑑𝑑 + 𝑑𝑚 𝑑𝑚 𝑑𝑑 + 𝜖𝑚 𝜖𝑑 𝑑𝑚 𝜖𝑚 + 𝑑𝑑 𝜖𝑑 𝑑𝑑 + 𝑑 𝑚 with ϵ𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 and ϵ𝑝𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟 are dielectric function following directions those are parallel and perpendicular with surface of multilayer structure; dd and dm are thickness; 𝜖𝑚 and 𝜖𝑑 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 inclusion also contribute to the metamaterials Most of the researches about the b a c 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 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 38 Fig 4.20: SEM image of self-synthesis silver nanoparticles Transmittance (unit) 105 100 95 90 x mg/ml self-synthesis 2x mg/ml self-synthesis 3x mg/ml self-synthesis 1.43E-6 mg/ml standard 3E-6 mg/ml standard 85 80 75 300 400 500 600 Wavelength (nm) 700 800 Fig 4.21: Transmittance spectrum of self-synthesis and commercial silver nanoparticles solution 39 4.2.2 Properties of thin films 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 PVP PVA 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 40 Transmittance (unit) 0.95 0.9 PVA solution 0.85 PVA_Ag3% solution 0.8 PVP solution 0.75 PVP_Ag3% solution 0.7 0.3 0.4 0.5 0.6 Wavelength (m) 0.7 0.8 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 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 41 drop-casting method) The explanation demands more experiments that I could not complete on this research 1.02 1.01 Transmittance (unit) 0.99 0.98 0.97 0.96 PVA_Ag3%_drop coating PVP_Ag3%_drop coating PVA_Ag0%_ drop coating PVP_Ag0%_ drop coating Ag_drop 0.95 0.94 0.93 0.92 0.3 0.4 0.5 0.6 Wavelength (m) 0.7 0.8 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 PVPbased 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 42 Transmittance (unit) 1.005 PVP_Ag3%_spin PVP_Ag4%_spin 0.995 PVP_Ag5%_spin 0.99 0.3 0.4 0.5 0.6 Wavelength (m) 0.7 0.8 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 from them The existence of silver nanoparticles decreases index of 43 refraction Then this decrease makes blue shift of LSPR signal For consider this phenomena, the range of particles fill fraction will be expanded later 1.02 PVA_Ag3%_spin Transmittance (unit) 1.015 1.01 PVP_Ag4%_spin 1.005 PVA_Ag5%_spin 0.995 0.99 0.985 0.98 0.975 0.3 0.4 0.5 0.6 Wavelength (m) 0.7 0.8 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 PVAbased 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 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 44 CONCLUSION 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 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 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