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i
Design, Fabrication and Analysis of
Photonic Device Nanostructures
By
Muhammad Rizwan Saleem
School of Chemical and Materials Engineering (SCME)
National University of Sciences & Technology (NUST)
17th
September, 2013
ii
Design, Fabrication and Analysis of
Photonic Device Nanostructures
Muhammad Rizwan Saleem 2008-NUST-tfrPhD-MS-E-09
This work is submitted as a PhD thesis in partial fulfillment of the
requirement for the degree of
(PhD in Materials and Surface Engineering)
Supervisor: Prof. Dr. Mohammad Bilal Khan (TI)
Co-supervisor: Prof. Dr. Zaffar Mohammad Khan (SI)
School of Chemical and Materials Engineering (SCME)
National University of Sciences & Technology (NUST), H-12
Islamabad, Pakistan
17th
September, 2013
iii
Certificate
This is to certify that the research work in this thesis has been carried out by
Mr. Muhammad Rizwan Saleem and completed under our supervision in
the Department of Materials Engineering, School of Chemical and Materials
Engineering, National University of Sciences and Technology, Islamabad,
Pakistan.
Supervisor:
Prof. Dr. Mohammad Bilal Khan (TI)
Principal/Director
Centre for Energy Systems (CES)
National University of Sciences & Technology
(NUST), Islamabad
Co-supervisor:
Prof. Dr. Zaffar Mohammad Khan (SI)
Deputy Director General: Advance Engineering and Research Organization (AERO)
Deptt. of Mechanical Engineering
University of Engineering and Technology, Taxila
Submitted through
Prof. Dr. Mohammad Mujahid
Principal/Dean,
School of Chemical & Materials Engineering (SCME)
National University of Sciences & Technology (NUST), Islamabad
iv
In the Name of Allah, the Most Beneficent, the Most Merciful
Dedication
I dedicate my PhD thesis work to my beloved father:
(Muhammad Saleem), mother: Zahida Parveen, wife:
Rabia Rizwan, daughters: Maheen Rizwan, Rameen
Rizwan and Malaika Rizwan.
v
Acknowledgments
I am grateful and offer my most sincere gratitude to my project supervisor, Prof. Dr.
Mohammad Bilal khan and co-supervisor Prof. Dr. Zaffar Mohammad Khan for their
unwavering support, guidance, and extensive discussions throughout this research
endeavor. Special thanks are also extended to Prof. Dr. Amir Azam Khan, Prof. Dr.
Mohammad Mujahid and Prof. Dr. Mohammad Islam for their advices and encouragement
during this work. All of the research work is performed in Finland at the University of
Eastern Finland, Department of Physics and Mathematics under the kind and honorable
supervisions of Prof. Dr. Jari Turunen and Prof. Dr. Pasi Vahimaa, for that the author is
heavily indebted and thankful to them. The author is also thankful to Prof. Dr. Seppo
Honkanen for a great help in Clean room environment to carry out fabrication of optical
sensors over a broad range of materials. I am thankful to all of my colleagues, friends, co-
authors, and co-workers whose efforts have made this research work more valuable as an
International guide for the coming forth researchers and students. I offer my special
thanks to all the faculty and staff of both the National University of Sciences and
Technologies (NUST), School of Chemical and Materials Engineering (SCME) and
University of Eastern Finland, Department of Physics and Mathematics.
Regarding financial fundings author is thankful to Higher Education Commission (HEC),
Pakistan, Academy of Finland, Strategic funding of TAILOR, Tekes, and University of
Eastern Finland, Finland.
vi
Abstract
This thesis provides an insight to resonant waveguide gratings (RWGs) and
thermo-optic coefficients (TOCs) accompanying various organic and inorganic materials.
The RWGs structures were designed by Fourier Modal Method (FMM) based on the
rigorous diffraction theory and fabricated by Atomic Layer Deposition (ALD), Electron-
Beam Lithography (EBL), Nanoimprinting (NIL), Reactive Ion Etching (RIE), and
characterized by Scanning Electron Microscope (SEM), X-Ray Diffraction (XRD), and
Ellipsometer. Categorizing the materials used for RWGs by employing different
fabrication methods in order to facilitate the simplest, cost-effective approach for large-
scale production of aforementioned devices is accomplished. The first type of gratings was
prepared by a simple replication method i.e., Nanoimprinting, where the master stamp was
manufactured by EBL and its subsequent development processes on a silicon wafer
without contribution of an etching process. The subwavelength grating structures are
directly replicated in polymer materials such as Polycarbonate, Cyclic-olefin-copolymer
and UV-curable material Ormocomp® followed by a smooth and conformal cover layer of
high refractive index and amorphous optical material TiO2 by ALD method. This type of
gratings in polymer materials have been demonstrated to exhibit athermal waveguide
operation first time, yielding a net spectral shift of a fraction of a nm over a wide range of
temperatures (25–85 °C). In addition, such gratings depict excellent polarization-
insensitive properties that can be used in optical communications, bio-sensors and
fluorescence-enhancement applications. These demonstrations showed an excellent
agreement between the theoretical and experimental results. The measurement results are
the first experimental demonstration so far on the realization of polarization-insensitive 1D
GMR gratings under normal incidence. The other type of subwavelength grating structures
are explicitly fabricated and demonstrated for polarization-independent properties
containing TiO2 pillars as a waveguide layer on the fused silica substrate. The degeneracy
of both the TE- and TM-modes for second type of non-polarizing grating was further
investigated by studying an over-etch effect into the fused silica substrate. A relatively
vii
good agreement between the theoretical and experimental results was found after
fabrication through a number of processes.
The second research activity contributing this study was to compute TOC of organic and
inorganic materials experimentally. The TOC was obtained from the experimental data as
an ellipsometric measurement followed by using Lorentz-Lorenz relation and optical
Models (Cauchy Model) under a least-square approach. The experimentally calculated
TOC was directly applied extensively for the design/simulation of athermal waveguide in
various photonic applications. This research work includes experimental investigation of
TOCs of Ormocomp®, TiO2 thin films of various thicknesses which are explained on the
basis of a porosity model to the near-surface-region. It was investigated that thin TiO2
films possess a larger negative index-gradient while thicker ones showed positive index-
gradient. The change of signs of TOCs was described on the basis of a surface porosity
model. Furthermore, the proposed porosity model was investigated indirectly by deposition
of diffusion barrier layers of ALD-Al2O3 with different thicknesses on the surface of ALD-
TiO2 films. Interesting results were demonstrated to show a decrease in negative TOCs
with the increase in ALD-Al2O3 film thicknesses which are explained based on the
impermeable properties of ALD-Al2O3 for water molecules. This thesis also reports on
TOCs of ALD-Al2O3 films of different thicknesses for the first time.
viii
Author List of Publications
Peer-reviewed Journals
1. M. R. Saleem, R. Ali, S. Honkanen, and J. Turunen, “Thermal properties of thin
Al2O3 films and their barrier layer effect on thermo-optic properties of TiO2 films
grown by atomic layer deposition,” Thin Solid Films 542, 257-262 (2013).
2. M. R. Saleem, S. Honkanen, and J. Turunen, “Effect of substrate overetching and
heat treatment of titanium oxide waveguide gratings and thin films on their optical
properties,” Appl. Opt. 52 (2013).
3. M. R. Saleem, S. Honkanen, and J. Turunen, “Thermo-optic coefficient of
Ormocomp and comparison of polymer materials in athermal replicated
subwavelength resonant waveguide gratings,” Opt. Commun. 288, 56-65 (2013).
4. T. Kaplas, L. Karvonen, J. Rönn, M. R. Saleem, S. Kujala, S. Honkanen, and Y.
Svirko, “Nonlinear refraction in semitransparent pyrolytic carbon films,” Opt.
Mater. Express, 2, 1822- 1827 (2012).
5. M. R. Saleem, D. Zheng, B. Bai, P. Stenberg, M. Kuittinen, S. Honkanen and J.
Turunen, “Replicable one-dimensional non-polarizing guided mode resonance
gratings under normal incidence,” Opt. Express 20, 16974-16980 (2012).
6. M. R. Saleem, P. Silfsten, S. Honkanen, and J. Turunen, “Thermal properties of
TiO2 films grown by atomic layer deposition,” Thin Solid Films 520, 5442-5446
(2012).
7. M. Erdmanis, L. Karvonen, M. R. Saleem, M. Ruoho, V. Pale, A. Tervonen, S.
Honkanen, and I. Tittonen, “ALD-assisted multiorder dispersion engineering of
nanophotonic strip waveguides,” IEEE; J. Lightwave Technol., 30, 2488-2493
(2012).
8. M. R. Saleem, P. A. Stenberg, M. B. Khan, Z. M. Khan, S. Honkanen, and J.
Turunen, “Hydrogen silsesquioxane resist stamp for replication of nanophotonic
components in polymers,” J. Micro/Nanolith. MEMS MOEMS 11, 013007 (2012).
9. M. R. Saleem, P. Stenberg, T. Alasaarela, P. Silfsten, M. B. Khan, S. Honkanen,
and J. Turunen, “Towards ahtermal organic-inorganic guided mode resonance
filters,” Opt. Express 19, 24241-24251 (2011).
ix
10. M. Islam and M. R. Saleem, “Comparison-property correlation in B2O3-SiO2
preform rods produced using modified chemical vapor deposition technique,” J.
Mater. Eng. and performance 21, 202-207 (2011).
International peer-reviewed Conference Proceedings / Seminars /
Presentations / Abstracts
11. M. R. Saleem, S. Honkanen, and J. Turunen, “Mode-splitting of a non-polarizing
guided mode resonance filter on substrate overetching effect,” Submitted to SPIE
Photonics-West-2014, San Francisco, USA.
12. M. R. Saleem, A. Nisar, Z. M. Khan, M. B. Khan, S. Honkanen, and J. Turunen,
“Effect of waveguide thickness layer on spectral resonance of a Guided Mode
Resonance Filter,” Submitted to IBCAST-2013, Islamabad, Pakistan.
13. M. R. Saleem, A. Nisar, Z. M. Khan, M. B. Khan, S. Honkanen, and J. Turunen,
“Thermal properties of TiO2 films fabricated by atomic layer deposition,”
International Symposium on Advanced Materials ISAM-2013, September 23–
27, 2013.
14. M. R. Saleem, B, Bai, S. Honkanen, and J. Turunen, “1D Non-polarizing resonant
waveguide gratings,” 38th
International Nathiagali Summer College on Physics
and Contemporary Needs, June 24–July 6, 2013, Pakistan.
15. M. R. Saleem, R. Ali, S. Honkanen, and J. Turunen, “Experimental determination
of thermo-optic properties of thin optical films fabricated by atomic layer
deposition,” Optics days; Helsinki, Finland (20–21 May, 2013).
16. M. R. Saleem, S. Honkanen, and J. Turunen, “Non-polarizing single layer
inorganic and double layer organic-inorganic one–dimensional guided mode
resonance filters,” Proc. of the SPIE (2013).
17. M. R. Saleem, S. Honkanen, and J. Turunen, “Partially athermalized waveguide
gratings,” Proc . of SPIE, 8428 842817-1 (2012).
18. M. R. Saleem, S. Honkanen, and J. Turunen, “Temperature independent guided
mode resonance filters,” International Conference on Nanoscience + Technology;
Paris, France, PO3. 10, 23-27 July (2012).
19. M. R. Saleem, M. B. Khan, S. Honkanen, and J. Turunen, “Nearly temperature
independent waveguide gratings,” 8th EOS Topical meeting on diffractive optics;
Delft, Netherlands, ISBN 9783-00-033711-6 (2012).
x
20. M. R. Saleem, P. A. Stenberg, M. B. Khan, Z. M. Khan, S. Honkanen, and J.
Turunen, “HSQ resist for replication stamp in polymers,” Proc. Of SPIE 8249
82490G-1 (2012).
21. P. Stenberg, M. R. Saleem, M. Kuittinen, S. Honkanen, and J. Turunen, “High
accuracy nano scale fabrication techniques in sub-micron patterned polymer
gratings,” Physics days 2012, Joensuu; the 46th annual meeting of the Finnish
Physical Society, 13-15 March 2012.
22. P. Stenberg, M. R. Saleem, and M. Kuitten, “hybrid hot embossing stamp for
replication of polycarbonate,” Optics days; Oulu, Finland (2011).
23. M. R. Saleem, M. B. Khan, P. A. Stenberg, T. Alasaarela, S. Honkanen, B. Bai, J.
Turunen, and P. Vahimaa, “Thermal behavior of waveguide gratings,” Proc. Of
SPIE 8069 80690A-1 (2011).
xi
Contents
Abstract vi
List of Publications viii
List of Figures xv
List of Tables xxiii
Abbreviation xxiv
Chapter 1 Introduction 1
1.1. Background 1
1.2. Importance 8
1.3. Motivation 8
1.4. Main goals 9
1.5. Methods 10
1.6. Outline 11
Chapter 2 Fundamentals of Electromagnetic and Guided mode
Resonance filters theory 12
2.1. Fourier decomposition and the complex representation of
electromagnetic field quantities 12
2.2. Maxwell’s Equations: A microscopic view 14
2.3. Constitutive relations 14
2.4. Boundary Conditions 17
2.5. Wave propagation in homogeneous and isotropic medium 18
2.5. Evanescent waves 18
2.6. Fourier Modal Method (FMM) 20
2.6.1. Principle of FMM 21
2.6.2. Rayleigh expansion and modal field representation
inside1D grating 22
2.6.3. Fourier expansion of permittivity distribution
and eigenvalue equations for transverse electric (TE)
and transverse magnetic (TM) modes 23
2.6.4. Convergence of numerical solutions 26
xii
2.6.5. FMM for multistep profiles 26
2.7. Guided mode resonance filter (GMRF) 26
2.7.1. Structure of a GMRF 28
2.7.2. Principle of operation 29
Chapter 3 Experimental techniques for structure
fabrication, replication and characterization 32
3.1 Electron beam lithography 32
3.1.1. The proximity effect 35
3.2. Electron beam resists 35
3.2.1. PMMA resist 36
3.2.2. ZEP resist 37
3.2.3. HSQ resist 37
3.3. Reactive ion etching techniques (Dry etching) 39
3.3.1. Reactive ion etching of TiO2 material 40
3.4. Micro hot embossing and nanoimprinting 43
3.5. Thin film deposition techniques 46
3.5.1. Physical vapor deposition (PVD) 46
3.5.1.1. Evaporation 46
3.5.1.2. Sputtering 47
3.5.2. Chemical vapor deposition (CVD) 48
3.5.2.1. Atomic layer deposition (ALD) 48
3.6. Spectroscopic Ellipsometry 51
Chapter 4 Theoretical results and Discussion:
Design of Resonant waveguide grating
structures and thin dielectric films 55
4.1. Structure and design of resonant waveguide gratings RWGs 55
4.1.1. Simulation and modeling of athermal behavior 58
4.1.2. Design of athermal behavior of RWGs using
different polymer substrate materials 61
4.1.2.1. Polycarbonate grating (g-I) 61
xiii
4.1.2.2. Cyclic olefin copolymer grating (g-II) 62
4.1.2.3. UV-curable material Ormocomp® grating (g-III) 63
4.2. Structure and design of polarization independent resonant
waveguide gratings 65
4.3. Effect of substrate overetching and heat treatment on
non-polarizing properties of TiO2 RWGs and thin films on their
optical properties 70
4.3.1. Design parameters of TiO2 RWGs on SiO2 substrate 72
4.3.2. Substrate overetching effect on splitting of
TE- and TE- modes 72
4.3.3. Refractive index modeling of amorphous and
crystalline TiO2 films 74
4.4. Thermo-optic coefficient (TOC) of organic and inorganic optical
materials 75
4.4.1. Analysis and computation of thermo-optic
coefficient of Ormocomp® 77
4.4.1.1. Method 1 77
4.4.1.2. Method 2 78
4.4.1.3. Method 3 79
4.4.2. Analysis and computation of thermal properties of
TiO2 films grown by ALD 80
4.4.2.1. Determination of refractive index 82
4.4.2.2. Determination of film density 85
4.4.3. Modeling of thermal properties of
ALD-Al2O3 films 87
4.4.3.1. Temperature dependent refractive index 87
4.4.3.2. Temperature dependent density 89
4.4.4. Thermo-optic coefficient of TiO2 thin films in
presence of thin diffusion barrier layers of ALD-Al2O3 91
Chapter 5 Experimental results and discussion 94
5.1. Fabrication of an etchless master stamp 95
5.1.1. Fabrication and replication process 95
5.1.2. Effect of development and etching time 97
xiv
5.1.3. Optical spectra of grating structures 99
5.2. Athermal measurement of organic-inorganic RWGs 101
5.3. Effect of different polymer substrates on resonance
properties of RWGs 105
5.4. Fabrication and demonstration of one-dimensional
polarization-insensitive RWGs 111
5.4.1. Fabrication of polarization-independent
RWGs of type-I and TiO2 planar thin films 111
5.4.2 Fabrication of polarization-independent
RWGs of type-II 112
5.4.3. Spectral resonance characteristics of
the fabricated non-polarizing RWGs 114
5.5. An over-etching effect in fused silica substrate on
non-polarizing properties of RWGs 116
5.5.1. Structural and optical characterization of
SiO2-TiO2 (type-I) RWGs and TiO2 thin films 116
5.5.2. TiO2 thin films on fused silica substrate 117
5.5.3. TiO2 RWGs on fused silica substrate 119
5.6. Thermo-optic coefficient (TOC) of thin film optical
materials (TiO2 and Al2O3) fabricated by ALD 123
5.6.1. Experimental results of thermo-optic coefficient
of TiO2 thin films 124
5.6.2. Experimental investigation of thermo-optic
coefficient of TiO2 thin films in presence of thin
diffusion barrier layers of ALD-Al2O3 126
5.7. Interpretation 129
Chapter 6 Conclusions 130
References 137
xv
List of Figures
Figure 2.1: Schematic representation of a plane wave propagating
at the interface. 20
Figure 2.2: Schematic of the diffraction grating with various propagating
fields in reflection and transmission orders. 21
Figure 2.3: Schematic of guided mode resonance filter’s structure
with forward and backward diffraction orders. 29
Figure 2.4: Schematic of GMRF with high index TiO2 cover layer
by ALD technique. 30
Figure 3.1: A schematic of a typical e-beam lithographic system with
optical elements (magnetic lenses). 34
Figure 3.2: SEM pictures of top view of grating structures of master
stamps of HSQ resist on Si substrate. 37
Figure 3.3: SEM pictures of front cross-sectional view of binary
grating structures of master stamp using HSQ resist on Si
substrate after heat treatment process. 38
Figure 3.4: Schematics of reactive ion etching (RIE) of TiO2 material. 41
Figure 3.5: SEM picture of a subwavelength TiO2 grating structure
on fused silica substrate. 43
Figure 3.6: SEM pictures of replicated subwavelength grating
structures in (a,b) Polycarbonate (c) Cyclic-olefin-copolymer
(d) UV-curable polymer Ormocomp®. 45
Figure 3.7: SEM pictures of TiO2 thin films on replicated structures
(a) Polycarbonate with t = 80 nm (b) Polycarbonate with t = 60 nm
(c) Cyclic-olefin-copolymer with t = 50 nm (d) UV-curable material
Ormocomp with t = 50 nm. 50
Figure 3.8: Polarization ellipse representing the polarization of an
electric field vector in terms of ellipsometric parameters ψ and phase
shift Δ. 52
Figure 3.9: Schematic illustration of an ellipsometric system configuration
in terms of its optical components. 53
xvi
Figure 4.1: Schematics of an ideal replicated grating profile coated
by a high index amorphous thin TiO2 film by ALD process and placed
on a heat reservoir for thermal measurement. 56
Figure 4.2: Fourier Modal analysis of the effects of parameter
variations in specular reflectance R. (a) Variations of ridge height h
and TiO2 film thickness t. (b) Variations of wavelength λ and
angle of incidence θi. (c) Variations of ridge height h and fill
factor f. (d) Variations of refractive indices ns and nc of the
polycarbonate substrate and TiO2 cover layer, respectively. 57
Figure 4.3: (a) Spectral variations of the specular reflectance R(λ)
with room temperature values of all design parameters. (b) Calculated
spectral reflectance curves at T = 100 °C due to thermal expansion alone
(curve 1-TEC), due to thermo-optic effect alone (curve 2-TOC), and
due to combination of both effects (curve 3-TEC-TOC). 58
Figure 4.4: (a) Simulated room-temperature spectral variation of the
reflectance as a function of TiO2 layer thickness. (b) Spectral lineshapes
of RWGs with TiO2 layer thickness t = 61 nm (blue curve 1) and
t = 71 nm (red curve 2). 58
Figure 4.5: Effect of temperature (T ) change in the spectral shift Δλr of the
resonance peak. (a) Individual TEC and TOC effects of TiO2 and PC.
(b) Combined TEC and TOC effects of TiO2 and PC. 60
Figure 4.6: (a) Specular reflectance R(λ) at room temperature designed
parameter values. (b) Specular reflectance curves calculated at 100 °C
accounting for TEC alone, TOC alone and combined TEC and TOC.
(c) Thermal resonance shift in λr when individual effects of TEC
and TOC of polymer and TiO2 are considered. (d) Thermal shift
in λr when the combined effects of TEC and TOC are considered.
The polymer considered here is Polycarbonate (PC). 61
Figure 4.7: (a) Specular reflectance R(λ) at room temperature designed
parameter values. (b) Specular reflectance curves calculated at 100 °C
accounting for TEC alone, TOC alone and combined TEC and TOC.
(c) Thermal resonance shift in λr when individual effects of TEC and TOC
of polymer and TiO2 are considered. (d) Thermal shift in λr when the
combined effects of TEC and TOC are considered. The polymer
considered here is Cyclic-olefin-Copolymer (COC). 63
Figure 4.8: (a) Specular reflectance R(λ) at room temperature designed
xvii
parameter values. (b) Specular reflectance curves calculated at 100 °C
accounting for TEC alone, TOC alone and combined TEC and TOC.
(c) Thermal resonance shift in λr when individual effects of TEC and
TOC of polymer and TiO2 are considered. (d) Thermal shift in λr
when the combined effects of TEC and TOC are considered. The
polymer considered here is UV-curable OrmoComp®. 64
Figure 4.9: Schematic of the (a) type-I, single layer and (b,c) Type-II,
Double layer 1D non-polarizing RWGs. 65
Figure 4.10: Spectral reflectance at the resonance wavelength λr at
designed linewidth w and structure height h of grating-I (a) TE-Mode
(b) TM-Mode. 67
Figure 4.11: Maximum spectral reflectance at the resonance wavelength
λr = 850 nm (a) Linewidth w and structure height h are evaluated at the
point of intersection of both TE- and TM-Modes (b) TE- and
TM-reflectance spectra at predicted values of w and h. 67
Figure 4.12: Spectral reflectance at the resonance wavelength λr at
designed linewidth w = 200 nm and structure height h = 145 nm of
grating-II for (a) TE-Mode (b) TM-Mode. 68
Figure 4.13: Maximum spectral reflectance at the resonance wavelength
λr = 850 nm for TE- and TM-modes at predicted values of w and h. The
full width at half maximum (FWHM) values for TE = 19.2 nm and
TM = 6.1 nm. 69
Figure 4.14: Maximum spectral reflectance in terms of incident angle
θi and wavelength λ for both (a) TE- and (b) TM-Modes. 69
Figure 4.15: Schematic illustration of a TiO2 RWG. (a) Etched to the
surface of substrate SiO2 and (b) Overetched into substrate SiO2. 70
Figure 4.16: Simulation results of specular reflectance showing
the variation in the resonance wavelength λr with the increase in
overetch depth hs in the fused silica substrate. (a) TE-Mode with
amorphous TiO2 (b) TM-Mode with amorphous TiO2 (c) Both
the TE- and TM-Modes and their effect on the nonpolarizing
property of amorphous TiO2 waveguide gratings and (d) both
the TE- and TM-Modes and their effect on the nonpolarizing
property of crystalline (anatase) TiO2 gratings. 71
Figure 4.17: Simulation results of specular reflectance in terms of
ridge height hc and linewidth w of nonpolarizing RWGs with period
xviii
d = 540 nm, linewidth w = 401.5 nm and the structure height
hc = ~199 nm, showing the propagation mode splitting with an
overetch depth hs = 50 nm into fused silica substrate.(a) TE-Mode
and (b) TM-Mode. 73
Figure 4.18: Measured and fitted ellipsometric data of amorphous and
crystalline (anatase) TiO2 films of thicknesses ~200 nm. (a) ψ, (b) Δ of
amorphous films, (c) ψ, and (d) Δ of crystalline films. 74
Figure 4.19: Simulated spectral shifts in the central resonance wavelength
λr of specular reflectance at normal incidence with a change in refractive
index of TiO2 material, before and after a phase change of TiO2. The RWG
parameters are defined by a period d = 540 nm, a linewidth w = 401.5 nm,
and a structure height hc = ~199 nm. (a) TE-Mode and (b) TM-Mode. 75
Figure 4.20: Linear fit approximation between thermo-optic and volume
thermal expansion coefficients of different polymers in glassy state. 78
Figure 4.21: Measured refractive index of Ormocomp®. (a) Room
temperature measurement and fitted data of n(λ). (b) Temperature
dependent measurement and fitted data of n(T) at a wavelength
of 630 nm. 79
Figure 4.22: Optical design structure of a thin TiO2 film grown by ALD
on a silicon substrate and the geometry of the illumination in
ellipsometric measurements. 81
Figure 4.23: Ellipsometric data of ALD TiO2 films: measured spectral
dependence of the ellipsometric parameters (a) ψ and (b) Δ together with
Cauchy model fits for a film of thickness t = 60 nm. 82
Figure 4.24: Ellipsometric refractive index data n(λ,T) of TiO2 film of
thickness t = 60 nm at various temperatures. 83
Figure 4.25: Experimental and fitted data on TiO2 films of thickness
t = 60 nm. (a) Index variation n(λ,T) and (b) density variation ρ(λ,T) at
λ = 640 nm. 84
Figure 4.26: Experimental data of ALD-Al2O3 films: spectral dependence
of the measured ellipsometric data at T = 20 °C in terms of parameters
(a) ψ and (b) Δ, together with Cauchy model fits for a film of thickness
ta ~ 60 nm. 87
Figure 4.27: Experimental and fitted data of ALD-Al2O3 films: (a) Index
variation n(λ,T) (b) density variation ρ(λ,T) of films of thickness ta ~60 nm
xix
at λ = 640 nm. 88
Figure 4.28: (a) Porosity model on the near surface region of a TiO2 film.
(b) Model for a TiO2 film coated by an Al2O3 barrier layer. 92
Figure 5.1: Process flow for the fabrication and replication of a binary
grating in polycarbonate from HSQ stamp on Si substrate. 96
Figure 5.2: RWG structures with different development times of the
HSQ-resist on silicon substrate after e-beam exposure. (a) ~53 nm
resist-free region. (b) ~68 nm resist-free region. 98
Figure 5.3: Etching profiles in Si with HBr-O2 with different etching
times. (a) After etching 180 s with a depth of ~324 nm. (b) After etching
130 s with a depth of ~244 nm. (c) Top and slightly tilted view with an
etching time of 180 s. 99
Figure 5.4: Calculated spectral reflectance (R) at three incident angles: (a)
d = 425 nm. (b) d = 368 nm. Experimentally measured spectral reflectance
(R) at three incident angles: (c) d = 425 nm. (d) d = 368 nm. Here Y
is the peak reflectance and X is the corresponding wavelength. 100
Figure 5.5: (a) Simulated spectral reflectance variation as a function of
TiO2 film thickness t. (b) Calculated and measured spectral reflectance
R of replicated gratings with TiO2 layer thickness t = 60 nm (blue curves)
and t = 75 nm (brown curves) for the TE-mode at θ = 20° and
d = 425 nm. 101
Figure 5.6: Spectral measurement of RWGs with TiO2 thickness t = 61 nm.
(a) Spectral reflectance curves at temperatures T = 30 °C, 35 °C and 55 °C.
(b) Room-temperature spectral lineshape subjected to thermal measurements
up to T = 85 °C. 103
Figure 5.7: Thermal measurements of RWGs with TiO2 layer thickness
t = 61 nm. (a) Peak thermal spectral shift. (b) Peak resonance
reflectance. 103
Figure 5.8: Spectral measurements of RWGs with TiO2 layer thickness
t = 71 nm. (a) Room-temperature peak resonance lineshape. (b) Peak
thermal spectral shift. (c) Peak resonance reflectance. 104
Figure 5.9: SEM pictures. (a) An HSQ stamp with d = 325 nm, h = 120 nm,
w = 205 nm. (b) A replicated structure in PC with d = 368 nm, h = 120 nm,
w = 232 nm. (c) A replicated structure in COC with d = 325 nm, h = 120 nm,
xx
w = 205 nm. (d) A replicated structure in Ormocomp® with d = 325 nm,
h = 120 nm, w = 205 nm. 106
Figure 5.10: SEM pictures of replicated structures coated by TiO2 cover
Layer of thickness t = 50 nm. (a) Polycarbonate (PC). (b) Cyclic-olefin-
Copolymer (COC). (c) Ormocomp®. 107
Figure 5.11: Measured reflectance spectra of RWGs with various
polymer substrates. (a) Polycarbonate (PC). (b) Cyclic-olefin-Copolymer
(COC). (c) Ormocomp®. 108
Figure 5.12: Experimental measurements of g-I (PC). (a) Measured
Thermal spectral shift as a function of temperature. (b) Measured
spectral reflectance R(λ,T). 109
Figure 5.13: Experimental measurements of g-II (COC). (a) Measured
thermal spectral shift as a function of temperature. (b)Measured
spectral reflectance R(λ,T). 110
Figure 5.14: Experimental measurements of g-III (Ormocomp®).
(a) Measured thermal spectral shift as a function of temperature.
(b) Measured spectral reflectance R(λ,T). 110
Figure 5.15: SEM images of the fabricated TiO2-SiO2 RWGs of Type-I. 113
Figure 5.16: SEM images of the finally fabricated PC-TiO2 non-polarizing
RWGs of Type-II. 113
Figure 5.17: Experimentally measured transmittance spectra: (a) Type-I
and (b) Type-II RWGs. 114
Figure 5.18: XRD patterns of the TiO2 thin films of thicknesses ~200 nm
deposited on fused silica by ALD. (a) As-deposited amorphous phase
and (b) heat-treated crystalline phase (anatase). 116
Figure 5.19: Refractive index of the TiO2 thin films of thicknesses
~200 nm deposited on fused silica by ALD using precursors TiCl4
and H2O with nitrogen as a carrier gas at a deposition temperature
of 120 °C and a growth rate of 0.065 nm per cycle.(a) As-deposited
TiO2 amorphous phase. (b) Heat-treated TiO2 crystalline phase (anatase)
at 300 °C for 7 h. 117
Figure 5.20: SEM pictures of TiO2 films on fused silica substrate.
(a) As-deposited amorphous film. (b) Heat-treated crystalline TiO2 film. 118
xxi
Figure 5.21: Measured transmittance at a wavelength range 380–1800 nm
of TiO2 films deposited on a fused silica substrate by ALD method.
(a) As-deposited TiO2 amorphous phase. (b) Heat-treated TiO2
crystalline phase. 119
Figure 5.22: Scanning electron microscope images of TiO2 RWGs
etched to different depths. (a), (b) Etched to the surface of the
substrate (fused silica). (c) Over-etched 39 nm in the substrate.
(d) Over-etched 73 nm in the substrate. (e) Over-etched 97 nm
in the substrate and (f) over-etched 128 nm in the substrate. 120
Figure 5.23: Measured transmittance, at normal incidence of the
fabricated TiO2 RWGs with a slightly slanted profile with a period
d = 544 nm, a linewidth w = 407 nm and a structure height
hc = 201 nm. (a) TiO2 amorphous phase. (b) Heat-treated TiO2 phase. 121
Figure 5.24: Measured resonance wavelength λr at normal incidence,
with the overetching depth hs in the fused silica substrate of fabricated
RWGs with a period d = 544 nm, a linewidth w = 407 nm and a
structure height hc = 201 nm. (a) Both the TE- and TM-Modes and
their effect on the non-polarizing property of amorphous TiO2gratings.
(b) Both the TE- and TM-Modes and their effect on the non-polarizing
property of the heat-treated TiO2 gratings. 122
Figure 5.25: Scanning electron microscope image of a cleaved
amorphous film of thickness ~200 nm grown by ALD on a Si substrate. 125
Figure 5.26: Thermal and spectral dependence of the material properties
of TiO2 films of variable thicknesses: wavelength (λ) dependence
of the (a) thermo-optic coefficient dn/dT. (b) Density coefficient dρ/dT. 125
Figure 5.27: Variation of the thermal properties of TiO2 films with
thickness t. 126
Figure 5.28: Thermal and spectral dependence of the thermo-optic
coefficient dn/dT of TiO2 films of various thicknesses in presence of
a thin Al2O3 barrier layer of thickness ta ≈ 6 nm. (a) Wavelength (λ)
dependence of the thermo-optic coefficient dn/dT. (b) Variation
of the thermo-optic coefficient with thicknesses tt of TiO2 films at
a wavelength of 640 nm. 127
Figure 5.29: Thermal and spectral dependence of the thermo-optic
coefficient dn/dT of TiO2 films of a fixed thickness tt ≈ 60 nm in
the presence of Al2O3 barrier layers of various thicknesses:
xxii
(a) Wavelength (λ) dependence of the thermo-optic coefficient dn/dT.
(b) Variation of the thermo-optic coefficient with thickness ta of
Al2O3 barrier layers at a wavelength of 640 nm. 129
xxiii
List of Tables
Table 4.1: Thermo-optic and volumetric thermal expansion coefficients
of polymers in a glassy state, dn/dT and γ, respectively. 76
Table 4.2: Measured temperature-dependent refractive index n and
calculated density ρ of an ALD-grown TiO2 film of thickness t = 60 nm
at λ = 640 nm. 86
Table 4.3: Measured and calculated temperature dependent refractive
index (dn/dT × 10-5
) and density (dρ/dT × 10-4
) of ALD-Al2O3 films of
different thicknesses ta = 60–500 nm at T = 20 °C and T = 100 °C for a
wavelength λ = 640 nm. 90
xxiv
Abbreviations
ALD Atomic Layer Deposition
COC Cyclic-Olefin-Copolymer
CVD Chemical Vapor Deposition
GMRFs Guided Mode Resonance Filters
NIL Nanoimprint Lithography
PC Polycarbonate
PVD Physical Vapor Deposition
RIE Reactive Ion Etching
RWGs Resonant Waveguide Gratings
SEM Scanning Electron Microscopy
TE Transverse Electric
TEC Thermal Expansion Coefficient
TM Transverse Magnetic
TOC Thermo-optic coefficient
XRD X-Ray Diffraction
PMMA Poly(methylmethacrylate)
HSQ Hydrogen silsesquioxane
RF Radio frequency
1
Chapter 1: Introduction
1.1 BACKGROUND
In the history, thoughts about the nature of light have been changing with time,
for example, Isaac Newton presented a corpuscular theory of light in his book
Opticks in 1704 in which he stated that light is composed of small particles
propagated in straight lines in some special medium [1]. However, Newton’s
Corpuscular theory of light could not explain the properties of light thoroughly;
for example, it became evident through experiments of Thomas Young that light
possesses wave nature [2]. All of these experimentations led to the conclusion
that some phenomena of light and matter interaction can be explained by wave
nature of light and some by the particle nature of light [3]. This is so called
wave-particle duality. The co-existence of both of the theories was found
necessary to explain all the phenomena of the light. Currently these theories are
used as the fundamental tools to model all the problems relating to the light-
matter interaction.
In 1880’s James Clerk Maxwell [4] unified all of the theories explaining wave
nature of light to the theory of Electromagnetism. Due to electromagnetic nature,
light propagates in straight lines and interacts with the electrically charged
particles of that material medium. The outcome of this interaction in terms of the
external electromagnetic field is described by the optical constants of the
material medium such as refractive index, extinction coefficient, permittivity,
permeability and absorption. Despite their names, optical constants are not real
constants but depend on the frequency of the light, called the dispersion of light.
The dispersion phenomena can be modeled by both the corpuscular [5] and wave
[6] theories successfully and can show mathematical representations for the
frequency dependent optical constant.
The optical constants are used to manifest the interaction of light with the
homogeneous materials while the same interaction with the discontinuous
boundaries (structures) is calculated using rather complicated algorithms based
2
on set of electromagnetic equations. Such interaction give rise to wave
phenomena called diffraction which is the disturbance of light from its rectilinear
propagation at the interfaces of a particular material structure. Diffractive optics
is a phenomena of classical diffraction based on wave nature of light. Diffractive
optical elements (DOEs) are permittivity-modulated microstructures considered
as microrelief profiles
[7,8]. Such profiles may be globally periodic, i.e.,
diffraction gratings or only locally periodic. Thus, diffractive optics has emerged
in micro-optical technology benefited by the wave optical engineering over
geometrical optics that enables the harvesting of light into applications such as
waveguides, holograms, CD-players, high resolution microscopy, diffractive
lenses and optical sensors [7,8].
Such a global or local period d of a DOE can vary from subwavelength to tens of
a wavelength scale. The value of d has a significant effect in the physics and
operation of the device, as well as on the selection of a mathematical method for
its analysis [6,7]. If the size (period d) of a structure is smaller than the
wavelength of light λ, it cannot be resolved by the light, appears as a composite
structure with effective refractive index and regarded as a slab of homogeneous
material, generally an anisotropic medium with an effective permittivity tensor
that depends on the structure. On the other hand if the size (period d) of a
structure is comparable or greater than the wavelength of light, one observes
diffraction phenomena with a number of propagating diffraction orders
depending on the value of d ≥ λ and material may not be regarded as a
homogenous.
The observed number of propagating diffraction orders reduces with the value of
d, but depends also on the angle of incidence and the refractive indices of the
surrounding media. At a particular value of d, there exist only few propagating
orders and the structure (grating) is said to operate in the resonance domain [6].
With a further decrease of d, there exist only zero reflected/transmitted
diffraction order and the structure (grating) acts as a stratified medium composed
of a stack of thin films [9]. In between these two extremes, there is a region
where the size of the structure is smaller than wavelength of light in such a way
3
that no diffraction occurs but the material may not be considered as a
homogenous, this region is called a subwavelength region.
Thin film optical filters employing diffraction theory that are formulated by
Fresnel depend on the amplitude and phase of the light reflected and transmitted
from a material boundary [10]. For example, antireflection coatings are based on
the principle to cancel the reflected light from upper and lower surfaces of thin
films provided the refractive index of the film is kept in between the indices of
incident media (air) and the substrate [11]. Similarly, a stacked structure
composed of an alternate high-low index with a film thickness quarter of a
wavelength that reflects light waves from successive boundaries in the same
phase and recombined by constructive interference, finally gives a strong
reflected signal [12]. Such filters are called reflective filters over a desired
wavelength range that depends on the ratio of high-low indices [13]. Similarly,
thin film optical filters can also be used as short-wave-pass, long-wave-pass, and
stop-band filters and have been applied in a number of different applications
[14].
An analogous narrow-band reflectance characteristic can also be achieved by
subwavelength periodic waveguide gratings based on resonance anomalies
[15,16] with a number of demanding feature characteristics over conventional
multilayered homogeneous thin film filters such as high efficiency, narrow
linewidth and low side-bands [17]. The subwavelength resonant waveguide
gratings in typical dielectric materials give rise to the use of term Guided-Mode
Resonance Filters (GMRFs) [18]. The original demonstration of the working
principle of a GMRF is based on the excitation of leaky waveguide modes [19–
23] and the coupling of these leaky modes to the waveguide modes in narrow-
band and selective reflection filters [24–27] whereas multi-layer thin film filters
work on multi-wave interference along the direction of propagation.
The origin of GMRF came into existence around 1900 when Wood observed
abrupt variations in the intensity of reflectivity of metallic gratings for TM
polarized light with respect to wavelength or angle of incidence of incident light,
these variations were called anomalies [28]. In 1907, Rayleigh presented a
4
detailed theoretical explanation of these anomalies due to appearance of a
particular spectral order at grazing incidence. According to Rayleigh, these
anomalies occurred at a particular wavelength, called Rayleigh wavelength and
correspond closely to Wood anomalies. Therefore, Rayleigh anomalies were
called classical Wood's anomaly [15]. The other type of anomalies is resonance
anomalies that occurred due to excitation of a leaky waveguide mode in periodic
waveguide structures [15].
The spectral variations in diffraction efficiencies of diffraction gratings due to
these anomalies were used in filtering applications [29]. The generation of leaky
modes due to corrugated structure couple with the waveguide modes [22] in
presence of some coupling loss [30]. Typically the resonance effect is
polarization dependent and show reflection peaks at different locations for two
polarizations with the same physical parameters. Such polarization dependent
properties are employed in several applications such as narrow-band filters,
polarization selectors, electro-optic switching, laser cavity-mode selectors,
biosensor devices, tunable filters [19,29,31–33]. While polarization insensitive
diffraction gratings are highly desirable for biochemical sensors [34] e.g., to
enhance fluorescence [35] with the advantage of non-polarized light at normal
and oblique incidence and for optical communications because of the unknown
polarization state of the light emerging from optical fibers in dense-wavelength-
division-multiplexing systems.
Guided Mode Resonance Filters (GMRFs) can be employed as the polarization
insensitive gratings which can couple both TE- and TM-modes with either s- or
p-polarized input optical fields by choosing appropriate grating parameters,
regardless of the input polarization state
[36–41]. Subwavelength, one-
dimensional, high diffraction efficiency, polarization-independent GMRFs at
normal incidence are highly desirable [42]. To realize non-polarizing GMR
filtering effect, several initially proposed designs were either based on 1D GMR
gratings under conical incidence [39,40] or 2D periodic gratings to control both
polarizations [43,44]. In all these previous designs, the structures have certain
5
complexity in either their geometries or incident mountings, imposing additional
difficulty on fabrication and application.
We recently proposed a simple design accompanying single layer 1D GMR
gratings with non-polarizing properties under normal incidence [36]. Initial
prototype fabrication has been performed on a sinusoidal-profile polarization
insensitive 1D GMR grating using photoinduced polymer deformation and
atomic layer deposition (ALD), which presented the potential of cost-effective
fabrication of these devices [36]. In order to enhance the interaction between a
waveguide mode and the grating, the corrugated profile very often is coated by a
high index cover layer [45].
An extensive interest has been directed to thin TiO2 films due to their potential
use and attractive physical, chemical, opto-electronics and optical properties
[46]. A number of deposition techniques are used for TiO2 films such as
chemical vapor deposition (CVD), electron beam evaporation, pulsed bias arc
ion plating, ion-beam assisted deposition, magnetron sputtering [47–53] and
atomic layer deposition (ALD) [54].
Atomic layer deposition is a process by which self limiting, smooth, conformal
coatings can be grown with accurately uniform film thickness on corrugated
surfaces without nanostructure deposition effects such as: line of sight [55].
Generally, deposition proceeds by alternate pulses of precursor gases/vapors
with the help of inert gas flow, followed by purging with inert gas in cycles.
During one cycle, the precursor materials are pulsed in reactor alternatively
which chemisorbs on substrate by surface saturative reactions and grow a
monomolecular layer [56]. In TiO2 waveguides highly uniform films are
required to support coupling effect whereas guided mode phenomena reduces its
coupling power during propagation along the grating due to change of out of
plane coupling effects, mainly caused by thickness changes. The nature of
guided mode, in general, becomes a leaky mode with a corresponding complex
propagation constant [41].
The efficiency of the resonance filter is highly dependent on the optical losses of
the covering material layer and the resulting scattering at the interface [57]. It
6
has been investigated that the coverlayer deposited TiO2 material must be of low
absorbance and surface roughness to reduce scattering effects and enhance
coupling efficiency of leaky excited modes [58]. Furthermore, ALD films are
distinguished to possess distinctive characteristics among other deposition
techniques based on their high optical quality at low growth temperature [59] on
thermoplastic substrates and have been employed in applications such as nano-
optical devices and sensors. Such properties are illustrated in detail in our recent
publications [60–64].
The manufacturing of diffractive optical components is well established at
prototype stage in various applications [8]. In this regard, high precision
manufacturing methods such as lithographic processes are not cost-effective and
could not meet the production requirements [65–67]. Therefore, a large-scale
fabrication method, such as physical copying of microstructures, is a prerequisite
to make and introduce the replication technology at commercial level. The chief
technologies used for micro-optical component’s replication are injection
molding, high pressure stamping by a heating tool. As the requirements for
modern applications are generated to manufacture even more challenging
structures in thermoplastics, keeping in view more stringent resolution
requirements, the conventional manufacturing processes becomes inadequate
[68,69].
Transparent optical polymer materials are potential candidate for nano-optical
devices in thermoplastics since the development of replicable surface relief
microstructures [70,71] around 1990’s and applied directly to GMRFs [72–76].
The replication technological processes such as injection molding, micro-
injection molding and hot embossing have substantially improved the replication
fidelity [77–80]. There remain some technological challenges, for example, how
deep the microstructure can reliably fill and can be possibly separated from the
master stamp or mould without any structure deformation. Thermoplastic
replication technology accompanies heating and cooling cycles over a wide
temperature range, subsequently by a high pressure stamping and finally a de-
molding step. Similarly, such high precision replication techniques by either
7
photo- or heat-curable polymers have been emerged competitive and mature
fabrication technologies. The replication master stamp or mold is filled by a
liquid polymer precursor material and then polymerized by a chemical reaction
that can be initiated by a uv-curing at room temperature or simply heating
[81,82]. This results in a much faster filling process with high replication
fidelity; however, such processes also possess some technical challenges for a
perfect replication. The filling problems in a master stamp occurred due to
trapped residual air in the microstructure mold being employed and the sticking
of the replication material with the master mold due to strong adhesion.
The aim of this study is to design, fabricate and optically characterize resonant
waveguide structures first in thermoplastics, subsequently coated by high index,
amorphous TiO2 cover layer by ALD to give strong coupling effects and other
simple replication processes without recourse dry etching [60,61]. Omitting the
etching process not only brings down the fabrication costs but also limits the
depth inaccuracies in the fabricated profile. The simple etch-free process come
up with fast prototyping of polymeric nano-photonic efficient devices, short
fabrication time, high pattern imprint fidelity, uniform surface-pattern-density,
high quality optical performance, and wide applicability to large scale
production. Such cost-effective fabricated filters are shown to use in
applications, for example, athermal GMRF, polarization-independent devices
and biosensors. Furthermore, athermal properties have been evaluated after
considering various polymer materials that is: thermoplastics, thermosetting and
uv-curable as substrates.
The resonant waveguide structures are also designed, fabricated and
characterized structurally and optically in inorganic materials i.e., in fused silica
substrates, coated with TiO2 layers by employing ALD technique. The final
structures are generated with the aid of conventional reactive ion etching RIE
techniques for both TiO2 and SiO2 etching. A complete analysis of the effect of
substrate over-etching (SiO2) on the performance of polarization independent
resonant waveguide gratings is presented both theoretically and experimentally.
A research work related to the measurement and calculation of thermo-optic
8
coefficient dn/dT and thermal density dρ/dT of thin TiO2 films fabricated by
ALD has been presented with and without thin barrier layers of Al2O3 by ALD
method.
1.2 IMPORTANCE
GMRFs show good filtering performance over a selectable parameter ranges and
has been used in many applications, however, some potential applications require
the use of highly transparent thermoplastic structures for nano-device operation,
while exploiting their properties such as high thermal expansion coefficients,
mechanical toughness (flexibility/ductility). In this research work low-cost
GMRFs are shown to behave actively to get high efficiency sensors covering
athermal operation and non-polarizing effects.
The waveguide is manufactured by coating polymer structures with a high index
and uniform cover layer of TiO2 material that provides strong coupling effects of
leaky excited modes to the waveguide modes. Various polymeric materials are
employed for athermal GMRFs to exploit their best optical properties, taking into
account mechanical properties also. The non-polarizing properties have been
investigated in both inorganic and organic materials used as GMRFs.
Furthermore, the splitting of both TE- and TM-modes is studied after considering
the effect of substrate overetch at various depths both theoretically and
experimentally in SiO2 substrate. The thermo-optic coefficients dn/dT of various
thickness TiO2 films on silicon substrates with and without thin Al2O3 barrier
layers, manufactured by ALD are also studied in detail for their use in sensor
applications.
1.3 MOTIVATION
High accuracy replicated nano-structures with high replication fidelity by nano-
imprint lithography proves a very competitive replication process for the
fabrication of GMRFs. The applied replication process approximately retains the
original profile of structures within the high resolution limit. The fabricated
structures were tested in severe environment and found operational after
successive experiments, which presents both the most economical way of
9
fabrication and demonstrates optical behavior well with known characteristics.
The performance of the fabricated grating structures were tested over a wide
range of temperature and shown to exhibit the original spectral characteristics.
Design and fabrication of resonant waveguide gratings using various polymeric
materials to be applied for athermal filtering devices over a wide temperature
range has been demonstrated both theoretically and experimentally.
Furthermore, the analysis related to the thermo-optic coefficients of organic
(Ormocomp) and inorganic (TiO2) materials that were used in athermal analysis
of the gratings. The evolution of most-economic fabrication methods (etchless
process), superior optical properties (high diffraction efficiency, narrow-band
filtering effect, and non-polarizing effect), a replacement of conventional
multilayer structures, and environment-free operation, provided us the
motivation of this study.
1.4 MAIN GOALS
The fabrication of athermal GMRFs in thermoplastics retaining the stable
position of resonance peak under subjected high temperature environment are
demonstrated for both theoretically and experimentally. Different polymeric
materials i.e., thermoplastic and uv-curable are employed for the nano structure
replication, subsequently coated by a high index TiO2 thin cover layer by ALD.
The spectral positions of the resonance peaks of GMRFs in different polymeric
materials are described in terms of inherent stresses of the materials. The
GMRFs are most often polarization-dependent while the origination of two
resonances TE and TM at the same spectral position by setting the same angle of
incidence, wavelength, and all geometrical parameters i.e., with the use of either
s- or p-polarized light that couple both the TE- and TM-resonances due to same
propagation constant are demonstrated. Such non-polarizing properties are used
in applications: biochemical sensors for fluorescence enhancement and optical
communication systems.
All of the fabrication is achieved by considering low-cost fabrication methods,
without the etching processes in the stamp fabrication using negative e-beam
resist hydrogen silsesquioxane. The application of high index and amorphous
10
thin TiO2 films, fabricated by ALD process as a waveguide on the top of
replicated gratings are much more demanding due to uniform thickness for
extremely thin films, uniform groove coverage and strong coupling effects.
Design, fabrication and characterization of non-polarizing properties are also
demonstrated in TiO2 gratings on fused silica substrate with a result in a perfect
coupling of both TE- and TM-modes at resonance. Furthermore, an overetch
depth in fused silica substrate was demonstrated to investigate the effect of
decoupling of both of the TE- and TM-modes theoretically and experimentally
with a more significant effect for TE-mode.
TiO2 films of different thicknesses 60–500 nm are coated on single crystal Si
wafers to determine their thermo-optic coefficient. It was evaluated that thermo-
optic coefficient of thin films takes negative values while thicker films possess
positive values. The negative values of thermo-optic coefficient were further
investigated by coating TiO2 films with a thin diffusion barrier layer of Al2O3 at
different thicknesses by ALD process.
1.5 METHODS
All of the subwavelength resonant waveguide grating structures presented in this
thesis are designed, simulated and calculated rigorously using home-built codes
of Fourier Modal Method FMM. A number of equipment and techniques are
used for the fabrication of aforementioned grating structures. Spin coater is used
to coat thin layer of resist before e-beam exposure. Electron Beam Lithography
EBL is used for direct writing of the patterns of the considered structures
generated in Autocad, subsequently developed by both manually and through an
auto process. The thickness of the coated resist and structure depth were
measured by Stylo surface profilometer. Material etching to create
nanostructures was performed by Plasmalab 100 and 80 for Cr and TiO2
etchings, respectively. The replication of fabricated nanostructures from master
stamp to various polymers was achieved with Hot-embossing technique and
finally Atomic Layer Deposition (ALD) is used to coat a uniform cover layer of
high index and thin TiO2 film on replicated corrugated surface in polymers and
on planar silicon and fused silica substrates.
11
Scanning electron microscopy (SEM) was used for the structural characterization
of grating structures on silicon, fused silica, and polymer substrates as well as
thin TiO2 films on planar silicon and fused silica substrates. Ellipsometer was
used to characterize all of the reported grating structures optically and to
measure the refractive indices of optical materials (OrmoComp, TiO2 thin films,
Al2O3 thin films, and a stack layer TiO2-Al2O3) are presented in this research
work.
1.6 OUTLINE
This thesis is composed of five further chapters which are outlined shortly from
this research work: Chapter 2 describes the computational methods (FMM) used
to design the grating structures and the theory of GMRFs. Chapter 3 explains the
working principles of the chief technological methods used for this work.
Chapter 4 illustrates the design of GMRFs for various different applications with
the numerical simulations and computations. In addition, a complete analysis to
compute thermo-optic coefficients of Ormocomp, TiO2 films and Al2O3 films of
different thicknesses has been reported. Chapter 5 shows all the experimental
results obtained after this research work and finally conclusion and future plans
are presented in chapter 6.
12
Chapter 2: Fundamentals of
Electromagnetic and Guided Mode
Resonance Filters Theory
The main subject of this thesis is to study the interaction of light with the
subwavelength grating structures (micro- and nanostructured photonic systems). In
this chapter basic principles of electromagnetic theory of light, background of
electromagnetism, and free space propagation of electromagnetic fields are
presented. The construction, working principle and basic theory of aforementioned
nanostructures have also been described.
2.1 FOURIER DECOMPOSITION AND THE COMPLEX REPRESENTATION
OF ELECTROMAGNETIC FIELD QUANTITIES
Real functions of position and time are the measurable field quantities in optics
which are often described by complex mathematics. To explain these quantities, it is
more convenient to use complex representation of electromagnetic fields by
considering a monochromatic stationary time harmonic field of the form
},)({),( ti
re et rUrU (2.1)
Where U(r) represents the complex amplitude of the real valued-function Ure(r,t)
which can be replaced by any of the electromagnetic quantities E(r), H(r), D(r),
B(r), and J(r) are the electric field, magnetic field, electric displacement, magnetic
induction, and current density, respectively. The field represented by Eq. (2.1) has a
limited approach to describe the rigorous behavior of a polychromatic light which
can be avoided by defining a complex counterpart of the real field. For this reason,
any real physical field quantity is supposed to be square integrable with respect to
time, i.e.,
,),(2
dttre rU (2.2)
Ure(r,t) may be represented as a Fourier integral [83]
13
,),(~
),( det ti
rere rUrU (2.3)
where
,),(2
1),(
~dtet ti
rere
rUrU (2.4)
where ),(~
rU re represents spectral amplitude of the real field in space-frequency
domain. Fourier transform pair Eqs. (2.3) and (2.4) shows that any vector field
Ure(r,t) in space-time domain may be represented as a superposition of time
harmonic fields with spectral complex amplitudes ),(~
rU re . Since Ure(r,t) is a real-
valued field with complex amplitude ),(~
rU re that satisfy the following relation
),,(~
),(~ * rUrU rere (2.5)
where * represents complex conjugate. The above relation clearly describes that
negative frequency component (ω < 0) do not contain any information, therefore,
we may define a new spectral function in space-frequency domain
0if),,(~
2
0if,0),(
~
rUrU
re
(2.6)
By using Eq. (2.6) a complex-valued vector field in space-time domain may be
expressed as
0
,),(~
),( det tirUrU (2.7)
Equation (2.7) describes that the positive part of the spectrum is different from that
of original real-valued vector field by a constant factor. Using this property the
complex-valued vector field in space-time domain may be connected to its Fourier
spectrum in space-frequency domain by the relation
dtet ti
),(
2
1),(
~rUrU (2.8)
Equation (2.8) may be applied to physically observable phenomena that have
significance in optics. Similar analysis can be performed to represent scalar field
quantity e.g., electric charge density ρ(r).
14
2.2 MAXWELL’S EQUATIONS: A MICROSCOPIC VIEW
Electromagnetic field quantities introduced in section 2.1 are connected together by
the fundamental laws of electrodynamics are called Maxwell’s equations which
were first introduced by J. C. Maxwell [84]. The complex-valued space-time
domain fields are expressed by four partial differential equations that hold in any
continuous media as well as in vacuum.
),,(),( tt
t rBrE
(2.9a)
),,(),(),( tt
tt rrJrH D
(2.9b)
),,(),( tt rρrD (2.9c)
,0),( trB (2.9d)
Let us assume time-harmonic field quantities in the form of Eq. (2.1), the above
mentioned Maxwell’s equations may be expressed in space-frequency domain as
),,(),( rBrE i (2.10a)
),,(),(),( rDrJrH i (2.10b)
),,(),( rrD (2.10c)
,0),( rB (2.10d)
2.3 CONSTITUTIVE RELATIONS
The Maxwell’s equations described in space-time and space-frequency domains
contain more unknown field quantities than the number of equations. This needs to
introduce some additional relations between the field quantities. A relation between
electric field E(r,t) and electric displacement D(r,t) is defined by introducing a
space-time domain quantity called electric polarization P(r,t).
),,(),(),( 0 ttt rPrErD (2.11)
where ε0 is the electric permittivity of vacuum. Similarly, by introducing the
magnetization M(r,t), a relation between magnetic field H(r,t) and magnetic
induction B(r,t) in space-time domain is given as
15
),,(),(1
),(0
ttt rMrBrH
(2.12)
where μ0 is the magnetic permeability of vacuum. We consider non-magnetic and
linear media; therefore, the magnetic response may be neglected. The relation
between polarization and electric field is linear that is independent on the field
strength. By considering these assumptions the relation between polarization and
electric field may be written as [85]
0
0 ,),(),(2
),( tdtttt rErχrP
(2.13)
where χ(r,t) is the real-valued time-domain dielectric susceptibility tensor. For an
isotropic medium where the relation between electric polarization and electric field
is independent on the direction, the susceptibility tensor simplifies in the form
,),(),( Irrχ tχt (2.14)
where χ(r,t) is the scalar susceptibility and I is the identity matrix. A similar relation
to Eq. (2.13) between electric current density and electric field may be written of
the form
0
,),(),(2
1),( tdtttt rErσrJ
(2.15)
where σ(r,t) is real-valued electric conductivity tensor in space-time domain. For an
isotropic medium the electric conductivity tensor reduces to scalar conductivity
σ(r,t). In analogy to Eqs. (2.13) and (2.15), a relation between electric displacement
and electric field may be expressed as
,),(),(2
),(0
0
tdtttt rErεrD
(2.16)
The set of Maxwell’s Eqs. (2.9) together with Eqs. (2.12), (2.13), (2.15), and (2.16)
show the relation between field quantities. The integration of Eqs. (2.13), (2.15) and
(2.16) in space-time domain is challenging, therefore, an approach towards space-
frequency domain is applied. By using convolution theorem to Eqs. (2.13), the
Fourier transform of electric polarization, may be expressed as
),,(),(),( 0 rErχrP (2.17)
16
Similarly, applying convolution theorem to Eqs. (2.15) and (2.16) gives a set of
equations [86]
),,(),(),( 0 rErεrD (2.18a)
),,(),( 0 rHrB (2.18b)
),,(),(),( rErσrJ (2.18c)
The set of Eqs. (2.18) is called constitutive relations or materials equations.
Substituting Eqs. (2.11) and (2.17) into Eqs. (2.18a) and applying Fourier transform
gives
0
,),(2
11),(1),( dtet ti
rχrχrε (2.19)
Equation (2.19) shows the frequency-dependence of permittivity and is called the
dispersion law of the electric permittivity tensor.
Now consider the relation between current density and electric polarization in
space-time domain
),,(),( tt
t rPrJ
(2.20)
A relation between relative complex permittivity and the electric conductivity is
obtained using Eqs. (2.11), (2.18a) and (2.18c) with Fourier transform
),,(),(),(ˆ0
rσrεrεi
(2.21)
where real and imaginary parts describe the stored energy due to polarization of
dielectric and loss due to conductive nature of the medium, respectively. In general,
the complex refractive index for isotropic media at optical frequencies is defined as
,)()()(ˆ)()()(ˆ iinn (2.22)
where n(ω), κ(ω), ε′(ω), and ε″(ω) are real functions. The attenuation index κ
represents damping or energy loss of a propagating wave through a medium e.g., it
is of much more significance for metallic and almost negligible for dielectric media.
Using the constitutive relations (2.18) and relative complex permittivity from Eq.
(2.21), the Maxwell Eq. (2.10b) may be written of the form
),(),(ˆ),( 0 rErεrH i (2.23)
17
Applying the divergence operator on Eq. (2.23) and using the vector identity
0 V , we obtain
.0),(),(ˆ rErε (2.24)
Maxwell’s equations in space-frequency domain may be written of the form
),,(),( rBrE i (2.25a)
),,(),(ˆ),( 0 rErεrH i (2.25b)
,0),(),(ˆ rErε (2.25c)
,0),( rB (2.25d)
Equations (2.25) are called Maxwell’s equations in space-frequency domain which
will be used in proceedings sections.
2.4 BOUNDARY CONDITIONS
In photonic structures (microstructures) electromagnetic field should be continuous
across all the interfaces adjoining any two materials with different optical
properties. Since Maxwell’s equations that have been derived in section 2.3 are only
valid in continuous media, however, microstructured optical components are based
on the phenomena such as refraction, diffraction or scattering at the boundaries of
discontinuous media that need boundaries conditions to match field components
across these discontinuities. By defining a surface normal unit vector û12 pointing to
the medium of index 2, we may write the boundary conditions in the form
,0)(ˆ1212 BBu (2.26a)
,0)(ˆ1212 DDu (2.26b)
,0)(ˆ1212 EEu (2.26c)
,0)(ˆ1212 HHu (2.26d)
Boundary conditions (2.26) are valid across the discontinuities between any two
dielectric or finite conducting materials. From these equations it is clear that all the
normal magnetic field components and tangential electric field components are
continuous across the interfaces.
18
2.5 WAVE PROPAGATION IN HOMOGENEOUS AND ISOTROPIC MEDIUM
Consider the propagation of electromagnetic field in a homogeneous and isotropic
medium, where Maxwell’s equations (2.25) in space-frequency domain are valid.
Applying operation to both sides of Eq. (2.25a) and using the vector identity
),()()( 2rUrUrU (2.27)
where U(r) is a vector field, Eq. (2.25b) gives
.0),()(ˆ),( 2
0
2 rErE k (2.28)
where 00 ck is the vacuum wave number and 000 1 c is the speed of light
in vacuum. An analogous mathematical treatment with Eq. (2.25b) and using Eq.
(2.25a) gives
.0),()(ˆ),( 2
0
2 rBrB k (2.29)
Equations (2.28) and (2.29) are the general wave propagation equations in
homogeneous and isotropic medium and are called Helmholtz wave equations for
electric field and magnetic induction, respectively. A simple solution of Helmholtz
wave equations is a plane wave for electric field and magnetic induction and may be
written as
,)(),( 0
rkErE
ie (2.30a)
,)(),( 0
rkBrB
ie (2.30b)
where k is the wave vector and defines the normal direction of the planes of
constant phase and therefore the propagation direction of the plane wave.
Electromagnetic plane wave from Eqs. (2.30a) and (2.30b) satisfy Helmholtz
general wave Eqs. (2.28) and (2.29), respectively, under the condition.
,)(ˆ 22
0
2222kkkkk zyx k (2.31)
where )(ˆ)( 0 nkk is the wave number in the material and )(ˆ)(ˆ n is the
complex refractive index of the material.
2.5 EVANESCENT WAVES
Evanescent waves are exponentially decaying waves usually occurred in
subwavelength optical structures and in the study of Surface Plasmon. Let us
19
assume the geometry of considered subwavelength structures where the permittivity
distribution and the field are independent on y-component. Due to this geometry, it
is called y-invariant configuration that is all the derivatives in y-direction vanish in
Maxwell’s equation and the incident field propagates in the xz-plane. Consider a
plane wave propagating in a direction described by the wave vector k and given as
,),()(
00
zkxkii zxeezx EEE
rk (2.32)
A plane wave represents a propagating wave if the exponential is purely imaginary.
Let us assume a planar interface between two homogeneous materials indexed as 1
and 2 with real relative permittivities ε(1)
and ε(2)
with a plane wave propagating to
the interface from material 1 at an angle θ(1)
as shown in Fig. 2.1. According to
Snell’s law
,sinsin )2()2()1()1( nn (2.33)
which implies
,)2()1(
xxx kkk (2.34)
Also consider
.if
if
222222
222222
kkkkkki
kkkkkkk
yxyx
yxyx
z (2.35)
The propagation constant kz has either pure real or imaginary values. The real
values of kz represent homogeneous waves and the imaginary values show
evanescent waves.
Using Eqs. (2.34) and (2.35), we obtain
.sin )1(2
)1(
)2(2
0
)1(2)2(
kk z (2.36)
If we suppose that ε(1)
> ε(2)
, Eq. (2.36) can be solved for angles
)1(
)2(1)1( sin
n
nc (2.37)
For such angles kz(2)
becomes purely imaginary which means that field propagates
parallel to the interface but decaying exponentially along the z-direction in material
2. The 1/e decay distance of the electric field amplitude is then defined by 1/kz(2)
.
20
Figure 2.1: Schematic representation of a plane wave propagating at the interface.
2.6 FOURIER MODAL METHOD (FMM)
Among several modal methods, we used the most popular and efficient method
based on Fourier expansion which is commonly known as the Fourier modal
method (FMM) [87,88] or the coupled-wave method (CWM). This method is used
to determine eigensolutions of Maxwell's equations in a periodic or piecewise
continuous medium by expanding the electromagnetic fields and permittivity
functions into Fourier series, and subsequently applying boundary conditions to
express fields inside the grating by an algebraic eigenvalue problem [89,90].
The method starts by sectioning the modulated region in slabs and finding the
solutions of Maxwell's equations in each individual slab. The result appears in the
form of forward and backward propagating fields consisting of modal fields. These
fields are pseudoperiodic and expressed in the formzie , here β is the eigenvalue
associated with a particular mode. For two polarizations the eigenvalue problem is
expressed in the matrix form which gives a set of allowed values of β and a set of
associated transverse field distributions for each polarization. The fields in all slabs
21
are combined by applying boundary values at each interface. This represents an
overall field inside the modulated region, which is finally matched with fields in
homogeneous regions (Rayleigh expansions). Finally, again the problem is solved
in a matrix form and then the complex transmission and reflection amplitudes are
calculated numerically [91].
Figure 2.2: Schematic of the diffraction grating with various propagating fields in reflection and
transmission orders.
2.6.1 Principle of FMM
To maintain uniform continuity of electromagnetic field components in Maxwell's
equations across the entire permittivity modulated region, the fields are matched
inside grating and homogeneous media. The modulated region of the grating is
defined as 0 < z < h, which is treated as a periodic waveguide as shown in Fig. 2.2.
The field before (z < 0) and after (z > h) the grating region is expressed as a
superposition of plane waves. The z-invariant permittivity distribution ),(ˆ zx inside
the grating region and field components are expanded in Fourier series [8]. The
complex amplitudes of reflected and transmitted fields are determined by matching
the fields inside and outside of the grating region and applying boundary conditions
at the interfaces through S-matrix approach [92,93], as shown in section 2.6.2.
22
2.6.2 Rayleigh expansion and modal field representation inside 1D grating
In order to illustrate the modal field representation inside and outside of a 1D
grating, invariant in y-direction, one needs to find an exact solution of Maxwell's
equations in all media. Such a solution must satisfy boundary conditions inside the
bound region of grating 0 < z < h at each discontinuous interface as shown in Fig.
2.2. Let us suppose that half space media (z < 0) and (z > h) are homogeneous with
refractive indices ni and nt, respectively and indices ni and nt are real and
permittivity distribution ),(ˆ zx inside the grating is z-invariant [8].
The TE polarized incident plane wave with unit amplitude, reflected and transmitted
m:th diffracted orders of electric field component Ey with complex amplitudes rm
and tm are given as
,),()( 00 zkxki
iyzxezxE
(2.38)
,)0,()(
m
zkxki
mryzmxmerzxE (2.39)
,)0,()(
m
i
mty
hzzmkxxmk
etzxE (2.40)
where
0zk ,
zmk and
zmk are the normal components of the wave vectors of the
incident plane wave, reflected and transmitted diffraction orders in the half space z
< 0 and z > h.
ixmixm
ixmxmi
zm
nkknkki
nkkknkk
0
22
0
2
0
222
0
if
if (2.41)
and
txmtxm
txmxmi
zm
nkknkki
nkkknkk
0
22
0
2
0
222
0
if
if (2.42)
Equations (2.41) and (2.42) show the normal components of the wave vectors for
each diffracted order (homogeneous and evanescent) in terms of the tangential wave
vector components kxm, which are given by the grating equation ,2
0d
mkk xxm
23
where d is the grating period and kx0 = k0nisinθi. The field inside the grating region
is represented as a modal expansion [8].
n
hzi
n
zi
nngynn ebeaxXzxE ,)(),(
)( (2.43)
where βn is the modal propagation constant and an and bn are unknown modal
amplitudes. The evaluation of their values gives the field inside the grating and
Xn(x) is defined as
1
,)(m
xik
mnnxmeXxX (2.44)
where Xmn is explained in proceeding section 2.6.3.
2.6.3 Fourier expansion of permittivity distribution and Eigenvalue equations
for Transverse electric (TE) and Transverse magnetic (TM) modes
Let us consider a periodic structure with period d and relative permittivity
distribution εr(x) along x-direction. The periodicity of εr(x) is satisfied by the
condition
),()( xdx rr (2.45)
The Fourier series expansion of εr(x) is given by [91]
,)( 2
t
dtxi
tr ex (2.46)
where the Fourier coefficients are
d
dtxi
rt dxexd
0
2 .)(1 (2.47)
The z-dependent modal solutions of Maxwell's equation which form propagation
invariant fields and x-dependent solutions which satisfy the same periodic
conditions as permittivity are given by
,)( ziezZ (2.48)
and
),()( xXdxX (2.49)
24
Let U(x,z) be the scalar component of a vector field representing the propagation
mode inside the structure of periodicity d. Such fields are called pseudoperiodic
fields and are of the form [8]
.)(),( 0 zixikeexXzxU x (2.50)
By using Eq. (2.49) X(x) may be written in its Fourier form as
,)( 2
q
dqxi
qeXxX (2.51)
where the Fourier coefficient Xq is
d
dqxi
q dxexXd
X0
2 .)(1 (2.52)
Therefore, Eq. (2.50) may be written as
q
zxki
qxqeXzxU ,),(
)( (2.53)
where dqkk xxq 20 and the Eq. (2.53) shows the general propagation invariant
field U(x,z) inside the modulated region of the grating in the form of transverse
pseudo-Fourier expansion.
To derive the eigenvalue equation for TE case, consider the Helmholtz equation
with electric field component Ey
.0),()(),(),( 2
02
2
2
2
zxExkzxE
zzxE
xyryy (2.54)
The electric field component Ey is parallel to discontinuous boundaries in yz-plane
and continuous everywhere inside modulated region, whereas εr(x) is discontinuous
at the boundaries. The product factor εr(x)Ey(x,z) in Eq. (2.54) have no common
discontinuity jumps and requires classic Laurent's rule to expand [92]:
q
lqlqxlql XkXkk .)()( 2
0
2
0 (2.55)
Eq. (2.55) may be expressed in matrix form as [8]
,)()( 2XX 0kβAIAE (2.56)
where E, A, I and X represent the matrices with elements ,ql ,0kkxl lq and ,qX
respectively. Equation (2.56) is called the Eigenvalue equation for TE-polarization.
25
To derive the eigenvalue equation for TM-polarization, the differential equation
with Hy-component may be written as
,0),(),()(),()( 2
0
11
zxHkzxHz
xz
zxHx
xx
yyryr (2.57)
or
.)()()()()( 000 22
0
1 xikxikxik
rrxxx exXexXkexX
xx
xx
(2.58)
The right-hand-side of eq. (2.58) is continuous due to function X(x), whereas before
the curly brackets on the left-hand-side, the function εr(x) is discontinuous. To apply
modified Laurent's rule, the terms inside curly brackets must be discontinuous. The
function )(1 xr
can be expressed in Fourier series as [8],
t
dtxi
tr ex ,)( 21 (2.59)
with Fourier coefficients
d
dtxi
rt dxexd
0
21 .)(1 (2.60)
By associating a matrix S with elements ql to the inverse permittivity function
)(1 xr
and applying modified Laurent's rule with further manipulation, we get a
matrix eigenvalue equation for TM-polarization [8].
.)()( 2
0 XX k AAEIS
11 (2.61)
Eqs. (2.56) and (2.61) give the propagation constants n and Fourier coefficients
qnX for each mode of TE- and TM-polarizations respectively, after using standard
linear algebra algorithms and considering the appropriate convergence of the series.
Equations (2.56) and (2.61) give field expansions in terms of modal coefficients an
and bn inside the grating region 0 < z < h. The fields inside and outside the
modulated region are matched at boundaries z = 0 and z = h by applying
electromagnetic boundary conditions. This gives a pair of infinite system of
equations with unknown modal coefficients an and bn. The system of equations is
solved by e.g., classical Gauss elimination method for modal coefficients an and bn,
26
which gives the reflected and transmitted plane wave amplitudes by means of
rigorous solution of the problem.
2.6.4 Convergence of numerical solutions
Numerically, the convergence of eigenvalue problems leads to confinement of M
modes in the solution. For 1D grating structures, the size of eigenvalue problem
becomes M × M, with M discrete, complex eigenvalues β. The eigenvalue matrix is
transformed to a 2M × 2M simultaneous equations after application of boundary
conditions, which are then solved by classical Gauss elimination method. For 2D
grating structures, where the fields are represented in two-dimensions, the
numerical calculations becomes more difficult with the increase in size of
eigenvalue problem to (2M)2 × (2N)
2, where, M and N are summation indices along
x and y-directions. Generally, for the numerical convergence of a solution, all
propagating diffraction orders with sufficient number of evanescent orders must be
present because evanescent orders contribute significantly inside modulated region
or near-zone. Thus the truncation numbers depend on the grating period and the
nature of gratings such as metallic or dielectric [91].
2.6.5 FMM for multistep profiles
For non-binary profiles, the real profile is divided in a number of small segments in
z-direction such that each small profile is approximated as a z-invariant lamellar
profile. The modal field expansions are executed in each slab and connected to
adjacent slab fields through modal coefficients after applying boundary conditions.
In this staircase method, the accuracy of result can be enhanced by dividing the real
profile in a large number of slices so as to make it as close to actual continuous
profile as necessary at the expense of computational time [91].
2.7 GUIDED MODE RESONANCE FILTER (GMRF)
The dielectric gratings which enhance the resonance anomaly characteristics of a
periodic structure by coupling the incident field to the leaky mode of the waveguide
of the grating for filtering applications are called Guided Mode Resonance Filters
(GMRFs). In other words, a diffraction grating in a dielectric material, in general, is
27
a GMRF, which consists of a periodic modulation of refractive index [94,95]. When
a plane wave is incident on the diffraction grating then it splits into plane waves that
propagate in various directions, i.e., called the diffraction orders as described by the
Rayleigh expansions from Eqs. (2.39) and (2.40) [8,24,96]. At specific wavelength
and angular orientation of the incident illuminated plane wave, the structure
resonates with complete interference and no light is being transmitted [94]. Due to
the nature of the leaky modes, light couples out of the waveguide and propagates to
smaller distances. The out coupling light appears in the form of narrow peaks in
reflectance which then changes from 0 to 100 % over a selectable range of optical
parameters [27,97].
Resonance phenomena were observed by Wood in 1902, when he observed rapid
variations in the efficiencies of metallic reflection gratings in narrow spectral
regions for TM polarized light [28]. Wood observed unexpected bright and dark
narrow bands in the spectrum of a metallic reflection grating, illuminated by a
slowly varying spectral intensity distribution of a light source. He further noted that
these bands weakened by simply rubbing the surface of the gratings and depended
on the polarization of the incident light. These bands appeared only for p-polarized
light, where the electric field vector was perpendicular to the grating lines. Since,
these spectral effects could not be explained by ordinary grating theory; Wood
named them as anomalies.
In 1907, Rayleigh explained these anomalies in terms of outgoing scattered fields.
These scattered fields become singular at particular wavelengths when one spectral
order emerges at grazing incidence. These wavelengths are called Rayleigh
wavelengths and their spectral positions are slightly different than actual resonance
positions [15]. In 1965, Hessel and Oliner [15] demonstrated a theoretical model
with the description that the anomalies in reflection gratings were due to excitation
of surface waves on metallic gratings. In their model they investigated two different
types of variations in efficiencies: a Rayleigh and resonance type.
In Rayleigh anomalies, the earliest theory described the presence of singularities in
the scattered field at Rayleigh wavelength with the appearance of a new spectral
order that correspond to p-polarized light. Rayleigh also explained that the entry of
28
such a new spectral order corresponds to Wood anomalies. Due to appearance of
new spectral order, one could possibly notice rearrangements in the amplitude of
rest of the spectral orders. However, shallow metallic gratings illuminated by s-
polarized light, where electric field vector is parallel to the grating lines behaves in
such a way that the radiation field for a new spectral order is short circuited when it
enters at grazing angle. Therefore, Rayleigh anomalies occur only for p-polarized
light.
When the intensity variations in Wood’s anomalies were investigated carefully, it
was found that the appearance of a new spectral order was not sufficient enough to
describe the rapid intensity variations. There is, in addition, present a resonance
effect that sometimes occur at wavelengths far away from Rayleigh wavelengths.
Such kind of anomalies was called resonance anomalies due to guided complex
waves supported by the structure. Therefore, two kinds of anomalies are:
i. Rapid variation in the amplitudes of the diffracted spectral orders that
correspond to either onset or disappearance of a particular spectral order,
and
ii. A resonance type due to guided complex waves supportable by these
structures.
2.7.1 Structure of a GMRF
The structure of a simple GMRF is shown in the figure 2.3. It consists of a substrate
with an index nt, an overlapping diffraction grating over it with refractive index
distribution n2(x) along x-direction and an incident medium (normally air) with
index ni. The direction of various propagating diffraction orders in 1D-gratings can
be calculated by fundamental grating equation [8].
,sinsin2 dmnn iim (2.62)
where d is grating period, λ is wavelength of incident light, θi is incident angle, θm is
diffracted angle, m = 0, ±1, ±2, ±3.... is the index of diffracted order, ni and n2 are
the refractive indices before and after the interface. For reflection gratings n2 is ni
and for transmission gratings n2 is nt.
29
Figure 2.3: Schematic of guided mode resonance filter’s structure with forward and backward
diffraction orders.
In this thesis one particular type of binary grating is considered, which is fabricated
in thermoplastics by nanoimprint lithography followed by fabrication of a cover
layer of high index amorphous TiO2 film of uniform thickness by atomic layer
deposition. In general, rather more simplified way, the interaction between a
waveguide mode and the grating by means of the waveguide mode field at the
interface can be enhanced by deposition of such high index TiO2 films on
corrugated profile [45]. A schematic of this grating with layered structure in
modulated region is shown in Fig. 2.4.
2.7.2 Principle of Operation
To get narrow reflection or transmission peaks, it is important to understand the
working principle of the GMRF which is based on the excitation of leaky
waveguide modes. Let us consider only the reflecting field by using a grating with
period sufficiently small to allow only zero order diffracted waves. A plane wave is
incident on the grating as shown in Fig. 2.3. The resulting reflected fields above the
grating can be assumed to come up from two separate contributions: a directly
reflected and a scattered field [97]. The direct reflection is the primary reflection
from material boundary as expected from Fresnel’s equations, whereas, the
30
secondary reflection occurs due to excitation and rescattering of leaky waveguide
mode when the following coupling relation holds:
,20 dnkx (2.63)
where kx is the wave vector and γ0 is a propagation constant of fundamental mode.
In the resonance excitation regime, the phase of the secondary field varies rapidly
with the incident field (wave number) and at a particular point becomes completely
in phase with primary reflected field to give a characteristic narrow reflected peak
with wavelength or angle [30]. Figure 2.3 shows the propagation constant γ of leaky
waveguide modes in lateral direction, perpendicular to the direction of grating’s
grooves. Since the modes are leaky and can be represented by the real and the
imaginary parts of propagation constant γ, which in turn form a complex-plane,
called complex γ-plane. The leaky modes are thus represented by a pole in this
complex γ-plane. A planar waveguide supports at least one mode, which is
represented by a single pole on the real γ-axis.
As the periodicity is introduced in the planar waveguide, this single mode splits into
an infinite number of spatial diffracted orders, represented by complex poles with
separation 2π/d on the complex γ-plane. The magnitudes of the real and imaginary
parts of the complex pole represent the range of the modes excited by the input field
(overlapping of the real part with the input field) and the coupling loss, respectively.
Figure 2.4: Schematic of GMRF with high index TiO2 cover layer by ALD technique.
31
Figure 2.4 shows the GMRF considered throughout the presented work; the
replicated grating structures in polymers are coated by high index TiO2 thin films
that form the waveguide layer. The excited modes are couple strongly by this high
index waveguide layer and the excited modes propagates in the lateral direction,
i.e., in the direction normal to the grating’s grooves.
32
Chapter 3: Experimental Techniques for
Structure Fabrication, Replication and
Characterization
3.1 ELECTRON BEAM LITHOGRAPHY
Lithography process employing electron beams to expose resists materials was one
of the earliest processes used for the fabrication of integrated circuits [99]. Today,
all large scale production lithographic structures, even down to 100 nm are
fabricated by optical lithographical techniques because of the advancements in
stepper technology as the bulk manufacturing process [100–101]. In spite of high
throughput, these techniques could not be used for the fabrication of structures with
feature sizes down to 50 nm. The gap is covered by employing electron beam
lithography for even smaller features that covers two main aspects. They can be
used to generate masks [102] which are used in all projection, proximity and contact
exposure systems and to fabricate low-volume manufacturing of ultra-small features
in high performance and functional devices [103] with sufficiently high resolution
[104]. However, in between, a technique so called mix-and-match lithography
where e-beam systems are used to generate especially small features while optical
systems take care of the rest size structures. Therefore, e-beam systems play a
significant role in advanced manufacturing tools despite their throughput limitations
as serial exposure systems. In e-beam systems, electron optics is similar to that
employed in a scanning electron microscope (SEM) [105]. In this thesis e-beam
system Vistec EBPG5000+ES HR was used as a direct writing tool to generate
rectangular patterns at a voltage of 100 kV with a minimum spot size of less than
2.5 nm.
A schematic ray diagram of electron-beam lithography system is shown in Fig. 3.1
where several lenses are considered as thin optical elements. Electron source
consists of an electron gun which can be, for example, a thermionic gun using a
tungsten hairpin, a lanthanum hexaboride source, or a field emission/ thermionic
field emission tungsten gun. The electrons are emitted from the emission source
33
whose cross-over is focused on the substrate surface by means of two magnetic
lenses L1 and L2 for pattern exposure. The beam half angle is controlled by the
beam shaping aperture. To control and minimize the current flowing down the
column, beam shaping aperture must be placed close to the gun or sometimes it
becomes an integral part of the gun. This controlled column current reduces the
electron-electron interactions that might cause an increase in the diameter of the
focused spot on the substrate. Secondly, a lower column current reduces the
insulating contaminating films on the optical elements after controlling the amount
of polymerizing residual hydrocarbons or corresponding siloxane molecules. If
however, contaminating films grow on optical elements, they acquire electric
charge that might result in beam drift and effect pattern resolution.
A magnetic or electrostatic deflector is used to drift the focused beam on the
substrate to be exposed where the deflector is very often placed after the final lens.
The beam can be made off by a beam-blanker assembly consisting of an aperture
and a deflector. In absence of deflector, beam passes through the aperture and hits
the targeted sample; however, in presence of deflector, beam diverts and strikes the
body of the aperture.
Let I be the beam current hitting on the sample at an area A with a charge density
(dose) σ, the total exposure time t is given as
,IAt (3.1)
For short exposure time beam current must be high enough and resist should be as
sensitive as possible. The beam current is given as
))(4
( 22
d
I (3.2)
where α is beam half angle, d is the diameter of the focused spot on the sample and
β is the brightness of the source. Generally, current density in the focused spot is
not uniform and consists of a bell-shaped distribution and corresponds to an
effective diameter d. The current density can be made high if one uses high values
of gun brightness and beam half angle.
Brightness can vary by several orders of magnitude depending on the gun being
used, for example, a value of 105 A cm
-2sr
-1 where numerical aperture is about
34
5×10-3
rad. If one considers a beam spot diameter of 0.5 µm (limited by the source
diameter and magnification by optical elements), a beam current of about 15 nA is
calculated from Eq. (3.2) for typical lithographic system. The exposure time can be
calculated from Eq. (3.1). If one uses a dose of 4800 µC cm-2
, a beam current of 15
nA and a coverage area of 5×5 mm2, a value of about 22.2 hrs of exposure time is
predicted which means that exposure time can be reduced using high beam currents.
Since the resolution of scanned e-beam lithographic systems is not limited by
diffraction, a defocus error Δz may cause to give rise a term called disc of confusion
(Δd) given by the geometrical optics:
,2 zd (3.3)
where α is beam half angle. In e-beam lithographic systems, the depth of focus is
sufficiently large to have minimum effect on resolution.
Figure 3.1: A schematic of a typical e-beam lithographic system with optical elements (magnetic
lenses).
35
3.1.1 The Proximity Effect
During e-beam exposure to the resist materials, the beam probe at the exposed resist
areas is less than that of the region of resist interaction with electrons. In the
exposure process both elastic and inelastic electrons are scattered from the resist
and the substrate. Several models have been proposed for elastic scattering in
submicron- to micron-sized patterns. For example two-Gaussian models to describe
the deposited energy in a resist during exposure from a point source have been
proposed [101]. High amplitude, narrow Gaussian beam describes the incident
beam broadening due to elastic scattering from the resist. Since the atomic number
of the resist materials is generally low and electrons are scattered through smaller
angles that make the exposure area narrow around the incident beam. Substrate
material also gives a secondary Gaussian due to elastic scattering whose amplitude
is about an order of magnitude less than resist Gaussian but it is much broader. The
backscattered electron exposes the resist material to relatively large distances from
the primary electron beam.
The effect of backscatterd electrons on the patterns depends on several parameters
such as electron energy, resist thickness, substrate and the specific pattern. The
scattered electrons from a single excel results in an additional exposure of nearby
excels. This results in a dose dependence on pattern density, feature size and excel
position in the pattern. Due to this backscattering effect the effective dose at the
corners and edges of patterns is less than that at the center.
3.2 ELECTRON-BEAM RESISTS
Resist materials are liquid state polymers dissolved in solvents in proper proportion.
The solubility of the polymer in the solvent is a strongly varying function of its
molecular weight. Resists materials are coated easily on the surface of a variety of
substrates by spin coating process as thin surface films to generate a corresponding
image of exposed writing patterns. Following to spin coating process, the solvent is
driven-off from the substrate surface by pre-baking (soft-baking) that leaves a
durable polymer film on the substrate which becomes ready for exposure and
subsequent desired patterns.
36
Resist materials are sensitive to e-beam exposure that can be modified after having
been energized through exposure in the sense that polymer (resist) chains cross-
linked strongly or loss their cross-linking properties depending on the nature of
resist i.e., negative or positive resists, respectively. The energy deposition process
may results in splitting of polymer chains (chain scission), cross-linking or acid
catalysis. Such modification either appears directly in the development solution or it
requires an intermediate step such as a post-exposure bake (hard-baking).
Thermodynamic properties of polymeric resists play an important role during all the
processes. During the coating, exposure, and development processes of a resist, the
glass transition temperature (Tg) of a polymer influences planarizability, flow, and
diffusion. Although reasonably high Tg values may be desirable, glassy materials
with values above 200 °C are not suitable because of poor mechanical performance.
Resists materials are generally characterized in terms of the properties such as tone,
sensitivity, contrast, resolution, viscosity and dry-etch resistance [106]. Resist
materials are divided into two categories; positive and negative. In a positive resist
exposed regions are more soluble in a developer than that of unexposed areas and
are removed in a development process. On the other hand unexposed areas are more
soluble and clean in a developer solution are regarded as negative resists. In this
thesis both positive and negative e-beam resists are studied and employed to
fabricate subwavelength rectangular (binary) profiles.
3.2.1 PMMA Resist
Poly(methyl methacrylate) (PMMA) is the one of the first positive electron-beam
lithographic resist at low doses which is commonly and extensively used due to its
high resolution. The reported resolution is below 5 nm [107], however, the
limitation is due to secondary electrons generated in the resist, although the role of
molecular size and development is important. The commonly used developer for
PMMA resist is Methyl isobutyl ketone (MIBK) with an appropriate proportion of
Isopropyl alcohol (IPA) to give a reasonable sensitivity and contrast [108]. PMMA
has a poor sensitivity, etch resistance and thermal stability and is available in
various molecular weights from 50 k to 1 M.
37
3.2.2 ZEP Resist
ZEP is a positive electron beam resist which is a copolymer of chlorome-thacrylate
and methylstyrene with a better sensitivity, resolution and etch resistance than
PMMA [109]. It has an excellent etch resistance during plasma etching and acts as a
mask in dry etching of metals [108]. In this research work all of the subwavelength
grating structures are fabricated using ZEP 7000-22 and a developer ethyl 3-
ethoxypropionate (EEP) for a development time of 60 s followed by 30 s in IPA and
rinsing with DI water for a sufficient time.
Figure 3.2: SEM pictures of top view of grating structures of master stamps of HSQ resist on Si
substrate.
3.2.3 HSQ Resist
Hydrogen silsesquioxane (HSQ) is a high resolution, inorganic negative tone resist
and it has been employed for the feature sizes less than 10 nm due to its small
molecular size [110, 111]. It is available from Dow Corning with a code FOX-12,
and the developer we used is MP 351 which contains disodium tetraborate
38
decahydrate and sodium hydroxide. The developer solution is made by mixing MP
351 with water in ratio 1:3 (MP 351:H2O) [112]. Linewidths of 6 nm and 10 nm
have been demonstrated on HSQ layers of thickness 20 nm and 10 nm, respectively
[113]. Dense grating structures have been made on Si and Si3N4 substrates using
HSQ resist [114]. The advantage of HSQ is its etching resistance to O2 which
enables its use as a bilayer resist, for example in etching with Cl2 after O2 plasma
hardening [111]. HSQ has a limited shelf life and because of its high sensitivity, it
cross-links around the lithographic features. In order to minimize these problems, it
is stored in refrigerators and in bottles which are free from contaminations to avoid
cross-linking.
Figure 3.3: SEM pictures of front cross-sectional view of binary grating structures of master stamp
using HSQ resist on Si substrate after heat treatment process.
HSQ can also be used as a direct stamping material after e-beam exposure and
development, for example, in replicating pattern sizes of 30 nm in PMMA,
polycaprolactone (PCL) and polycarbonate by hot embossing [112, 115]. In this
work we used HSQ resist to fabricate a binary grating stamp on a Si substrate
39
without any etching process. The stamp is made by heat treating HSQ at a
temperature of 300 °C for 3–5 hours, which transforms HSQ into SiO2 [116–119]
improves its mechanical properties and makes it suitable to use as a direct
replication stamp in polycarbonate (PC), cyclic-olefin-copolymer (COC) and UV-
curable materials such as OrmoComp [120]. The scanning electron microscope
(SEM) pictures of top view of grating structures of HSQ stamp are shown in Fig.
3.2 and front cross-sectional view in Fig. 3.3. The molecular structure of HSQ
consists of cage structure Si–H at room temperature and is very sensitive to the
curing temperature. The higher Si–H content indicates the presence of a cage
structure that results in a larger free volume of molecular arrangements. The
thermal curing transforms the HSQ from a cage to a network structure with the
formation of dense Si–O–Si molecular arrangements and increases the refractive
index [119], mechanical and dielectric properties [117].
3.3 REACTIVE ION ETCHING TECHNIQUES (DRY ETCHING)
Etching is an important and critical step in microfabrication process. In general, a
lithography step is followed by the selective etching of films or substrates to
produce the desired micro- and nano-patterns and structures. During etching of the
materials, an important factor is the selectivity of the etched material i.e., the
relative removal rate of the target material to that of the masking layer or other
structures (a high selectivity number shows that the difference in etch rates of two
materials is higher). Since the etched profiles can be as deep as several hundred
microns, proper choice of masking materials and their thicknesses is critically
important to avoid unwanted removal of the features on the substrate. The most
commonly used materials for mask layers when etching polysilicon or crystalline
silicon are silicon dioxide and silicon nitride.
Metal films have also been used as masking layers in dry etching processes. If the
etching is aimed without any preferred direction, it is called isotropic etching. If
certain directions are etched at different rates than the others because of the
structure of the substrate or the process variables, the etching is called anisotropic
[121].
40
Highly reactive particles called radicals react with the substrate and results in the
formation of new molecules which are more energetic than the substrate bond
strength. Subsequently, this new molecule removes from the material’s surface and
is called reactive etching. Radicals are isotropic in nature and etch material in all
directions equally, if however, a regular periodic rectangular trench is required
where lateral etching is to be prevented, inhibitors are used. An inhibitor layer is
created when the substrate reacts with the incoming gas and develops a protective
layer so that radicals cannot penetrate through it, this protects the substrate. If one
desires to etch through the substrate by removing the inhibitor which is achieved by
ion bombardment. The incident ions of sufficiently high energy remove the
inhibitor and etch the materials, since the direction and location of ions can be
controlled, material removal is highly accurate.
A mask protects incoming ions from the pre-determined locations to generate the
desired pattern at specifically designed depths due to known etch rates [122]. Thus,
reactive species are generated by the bombardment of injected atoms or molecules
with high energy plasma electrons (which are created by a strong RF field). As a
result of collisions, chemical bonds break and create ions and radicals which
undergo subsequent reactions to create more reactive species. These reactive
species or ions are accelerated towards the sample surface and remove material
through a mask either physically or chemically [123]. In this thesis reactive ion
etching (RIE) is employed to create nanostructures in TiO2 layer deposited on fused
silica substrate in presence of ZEP resist and Cr layer acts as mask.
3.3.1 Reactive ion etching of TiO2 material
Figure 3.4 schematically shows all the process steps performed during TiO2
etching. The fabrication of the TiO2 gratings employed ALD, EBL and RIE
techniques. The fabrication started by cleaning the fused silica substrates with a
diameter of 25 mm and a thickness of 0.5 mm with isopropanol followed by a dry
nitrogen blow. After cleaning the substrates, thin amorphous films of TiO2 with
thicknesses of ~200 nm were coated on the substrates by ALD, using Beneq TFS
200–152 reactor. The commonly known precursor materials TiCl4 and H2O were
used at a low deposition temperature of 120 °C, with chamber and reactor pressures
41
of 6.80 mbar and 1.59 mbar, respectively. Nitrogen was used as the carrier for the
precursor materials and as a purging gas after each precursor pulse during a cycle.
The flow rate of TiCl4 precursor was 200 sccm (standard cubic centimeter per
minute) with a pulse duration of 150 ms, which was followed by a purging for a
duration of 750 ms. For H2O precursor, the flow rate was maintained at 300 sccm
for a pulse duration of 150 ms with a subsequent purging for 1 s. The growth rate of
the deposited films was 0.065 nm per cycle which was measured by the Dektak 150
stylus surface profilometer from Veeco Metrology, and by an ellipsometer.
Figure 3.4: Schematics of reactive ion etching (RIE) of TiO2 material.
The ALD process was followed by the sample coating with a thin Cr layer of
thickness ~30 nm by electron beam evaporation at a vacuum level of 1.5 × 10-6
mbar with a deposition rate of 2 Å/s using the Lebold L560 vacuum evaporator
from Lebold Heraeus. The Cr coated sample was then prepared for a deposition of a
thin layer of positive electron beam resist ZEP 7000 22 by a spin coating process at
42
a spinning speed of 2900 rpm for 60 s using Headway spinner PWM101D from
Headway research Ltd. The resist layer was soft baked at a temperature of 180 °C
for 180 s on a hot plate to evaporate the solvents. The resist was then patterned on
an area of 7 × 7 mm2 by an electron beam writer EBPG5000+ES HR from Vistec
Lithography at a scaled dose of 200 µC/cm2. After e-beam exposure the sample was
developed with 99 % Ethyl 3-ethoxypropionate (EEP) from Aldrich Ltd. for 60 s,
followed by rinsing with isopropanol for 30 s and deionized water, finally dried
with a blow of nitrogen.
After the e-beam exposure and development processes, the sample was etched by
RIE. The Cr mask was dry-etched at a low pressure process (15 mtorr) in the
presence of Cl2 and O2 reactive gases together with inductively coupled plasma
(ICP) at 1500 watt using Plasmalab 100 from Oxford Plasma Technology. A total
flow of ~58 sccm was maintained for a Cr-etching time of ~95 s. The Cr-etching
was followed by a resist removal employing O2 plasma at 100 watt RF power and a
flow rate of 20 sccm for 180 s using March CS-1701 from Microtech-Chemitech
AB. The O2 plasma not only etches the resist layer and the constituent ashes but
also cleans the sample thoroughly for the subsequent TiO2 etching. The TiO2
etching was carried out using the reactive gases SF6 and Ar plasma with a total flow
of 15 sccm at 300 watt RF power, at 20 mtorr process pressure, and with different
etching times by using Plasmalab 80 from Oxford Plasma Technology. After
completion of the TiO2 etching process, the sample was cleaned with O2 plasma
with the same parameters as mentioned above.
The final process step was to remove the Cr layer by wet etching from the entire
sample surface. This step was performed in a mixture of Ammonium cerium (IV)
nitrate from Sigma-Aldrich, acetic acid, and deionized water for sufficient duration
to completely remove the Cr-layer. The Cr wet-etching was followed by rinsing
with deionized water drying with nitrogen blow to complete the fabrication of TiO2
grating structures. The dry etching process is highly anisotropic and directional
etching is achieved in the presence of a mask, whereas, the wet etching is isotropic
and removes the material almost equally in all the directions. The etching process
43
resulted in a positive sidewall slope of TiO2 ridges which may be due to polymer
passivation as shown in Fig 3.5.
Figure 3.5: SEM picture of a subwavelength TiO2 grating structure on fused silica substrate.
3.4 MICRO HOT EMBOSSING AND NANOIMPRINTING
The hot embossing process is divided into four cycles which are given below.
a) Heating of a thin polymer foil to a molding temperature.
b) An isothermal molding process by embossing that is velocity- and force-
controlled.
c) Cooling of molded part to a de-molding temperature with a constant force
during the process.
d) De-molding of the replicated component from the original mold (stamp).
In the beginning of twentieth century the process of hot embossing was matured
commercially for the replication of micro sized features for recordings. The
recording groove was used as a carrier of information for acoustic information
which was replicated on a 12-inch disc defined at large scale hot embossing. The
record developments and its replication started in 1870s when Emil Berliner
developed microphones and telephones. The first stereo cutting process of a shellac
44
record was developed by the engineer Alan Dower Blumlein using two channels.
The left channel was based on the vertical cut (by Edison) and lateral cut (by
Berliner) for the right channel. Both information channels formed a right angle and
the cutting pin traced a spatial curve. In 1982, a new cutting process so called direct
metal mastering (DMM) was introduced for record production at Telefunken-Decca
Company. Thus the history of record development for acoustic applications
illustrates the significance of hot embossing for the development of grooved
structures on a layer so called residual layer as a carrier layer of a stereo long-
playing records. In 1990s the nanoimprint technology was proposed by Chou et al.
[124–126] as a nanofabrication technology for various grating structures. The
Nanoimprint lithography (NIL) was based on the Molded Mask Method which was
first invented by NTT laboratories in Japan in 1970s [127]. Three different
approaches may be considered during nanoimprinting process i.e., nanoimprinting
by micro-contact printing, molding of UV-curable materials and molding of
thermoplastics.
Thermal nanoimprinting and hot embossing processes are similar, as both use
thermoplastics and heating/cooling steps. Hot embossing is a two step compression
molding cycle, where the polymer in the form of a thin sheet or foil is used [128].
The polymer sheet is heated by conduction around glass transition temperature and
a velocity- and force-controlled compression step initiates the flow of a polymer
melt into microcavities of the structure. This process continues for a particular time
called the dwell time at a constant temperature above glass transition temperature,
after that the temperature is decreased gradually. A residual layer of polymer is
formed adjacent to the rough plate surface due to an excess polymer melt flow,
which facilitates the pressure necessary for filling the microcavities [129]. Finally,
cooling occurs down to the de-molding temperature of the polymer and the molded
part is de-molded from the mold by detaching the replicated part in the direction of
grating lines.
The process parameters in terms of temperature, pressure and time depend on the
nature of the polymer [130]; in our case we set the temperature at 165 °C for 120
seconds at a constant pressure of 50 bar and the de-molding occurred at a
45
temperature of 50 °C. The nanoimprinting was performed in polycarbonate, cyclic-
olefin-copolymer and UV-curable material Ormocomp. The SEM pictures of
replicated patterns are shown in Fig. 3.6. In this work we used the Obducat Eitre
imprinter as a hot embossing tool, and the replication process is described in detail
in paper [112].
Figure 3.6: SEM pictures of replicated subwavelength grating structures in (a,b) Polycarbonate (c)
Cyclic-olefin-copolymer (d) UV-curable polymer Ormocomp®.
In this work the replication of microstructures of high aspect ratio are characterized
by microcavities mostly with small cross-sections that are needed to be filled with a
viscous polymer flow. Furthermore, hot embossing is characterized by short flow
distances from the molten semi-finished product into the cavities. If one compares
with the working of injection molding, one finds that the flow distances are much
shorter and the velocity is much lower, which results in a significantly lower shear
stress of the polymer. The final replicated components thus have a lower residual
shear stress due to a reduced shear stress during filling of microcavities. Because of
46
lower residual stress the process is best suited for the replication of microstructured
aeas which are approximately impossible to replicate by micro injection molding
[129].
3.5 THIN FILM DEPOSITION TECHNIQUES
In order to fabricate microstructured surfaces for an optical device, thin films play a
significant role in the performance of an optical component. Thin films can be
deposited by employing various physical and chemical vapor deposition techniques.
Depending on the device application by taking into account various factors and
deposition parameters for the desired film growth such as type of the film (e.g.,
metal, dielectric or semiconductor), mechanical properties (e.g., stresses in the
film), electrical properties, optical properties (refractive index, extinction
coefficient, reflectivity, transmittivity), film quality (e.g., with minimum defects),
film thickness uniformity, film growth rate, and other economical factors for the
film growth. There are various techniques to deposit optical thin films; however, in
this thesis two deposition techniques are reported for the creation of nanostructures.
These are broadly categorized as Physical vapor deposition (PVD) and Chemical
vapor deposition (CVD) [121].
3.5.1 Physical vapor deposition (PVD)
In simple words to force the atoms of a target material to leave a source and
physically adsorb on the surface of a substrate, such techniques are called as
Physical vapor deposition since no chemical reaction is involved in such growth
mechanism. PVD techniques are further divided in evaporation and sputtering
depending on the required film properties [121].
3.5.1.1 Evaporation
This technique is commonly used for the deposition of metallic films
where the target material is evaporated either thermally or by electron-beam and the
emitted target atoms are deposited at a substrate that is held at a given distance from
the target in a vacuum chamber to avoid contaminants in the ambient. The average
47
distance a particle travels between collisions with other particles is called mean free
path and given as [121]:
Pd
TKB
22 (3.4)
where KB is the Boltzmann’s constant (1.381 × 10-23
JK-1
), T is ambient temperature
in Kelvin, P is the pressure and d is the diameter of the gas molecule. In vacuum
evaporation the molecules that left the target material (melt) possess long mean free
paths. This means that molecules can travel a distance of several meters in vacuum
and can be regarded as a point source of target material that travel in straight line
until they hit the substrate surface and deposit there physically [121].
3.5.1.2 Sputtering
In sputtering the surface of the target material is bombarded with a flow
of relatively heavy energetic ions to knock off atoms at the surface of the target
material which then settle down on the surface of the substrate and gradually form a
thin film of the material. The energetic ions are produced with plasma at pressures
on the order of a few mTorrs. Argon is most commonly used gas because of its high
atomic mass and as a noble gas meaning that it does not react with the target or
substrate. Xenon may also use for physical sputtering of materials.
The required plasma can be generated by applying a large DC voltage (from about
500 V to few kilovolts) between two electrodes separated from each other by a
distance of 5–10 cm. For a large enough electric field, the free electrons in the gas
between the electrodes accelerate towards the anode (i.e., the electrode connected to
the higher voltage) and collide with gas molecules on their way, resulting in release
of a large number of species such as excited atoms, high energy electrons, and
positive ions. This is so called as gas breakdown. When the excited atoms return to
their relaxed state, they emit excess energy in form of photons, which generates
plasma with its characteristic glow.
The plasma is sustained by continuous generation of these energized particles. The
plasma color and intensity can be used to calculate and monitor the deposition rate
48
in a sputtering system. The generated positive ions of sufficient high energy
bombard the cathode and transfer part of their momentum to the atoms at the
surface of the cathode that results in to knock atoms out. Some of these atoms
deposit on the surface of the substrate and grow a film [121].
3.5.2 Chemical vapor deposition (CVD)
Chemical vapor deposition (CVD) is a technique to deposit a variety of materials
such as dielectrics, semiconductors, and metals through chemical reactions. In the
beginning the precursor gases are transferred to the surface of a substrate where
they react with each other and form molecules which then adsorb on the solid
surface. In such reactions the surfaces act like a catalysor and molecules result in
the growth of desired film and the reaction byproducts are transported out from the
chamber after desorbing from the surface [121]. CVD technique has been divided
into several processes; however, all of the research work presented in this thesis has
employed Atomic Layer Deposition ALD as a CVD process.
3.5.2.1 Atomic Layer Deposition (ALD)
Thin film electroluminescent (TFEL) displays were required
for better phosphors and dielectric film stacks where ALD was used to fabricate
pin-hole free and high quality films. Since then, the use of ALD in several optical
applications has widened to optical filters and different kinds of optical
nanostructures. Although ALD was invented for making TFEL displays, the late
material research has focused much more on the electrical rather than optical
properties of ALD materials [131]. Thus, it is often quite difficult to find optical
parameters of ALD materials and good processes for different optical or photonics
applications.
The optical properties of crystalline materials are strongly dependent on the crystal
structure of the material. ALD grown TiO2 films can be amorphous or crystalline
depending on the growth temperature with quite different optical properties. The
refractive index can vary from about 2.2 of amorphous TiO2 to 2.65 of
preferentially oriented anatase [132] at a wavelength of 633 nm. Crystalline
materials exhibit high scattering losses, if the crystal size is more than a few
49
nanometers due to material defects e.g., grain boundaries. This can be prevented by
applying thin intermediate layers. Adding intermediate Al2O3 layers to crystalline
TiO2 films increases the specular transmittance and the material behaves optically
amorphous [133]. In waveguide applications, light is usually propagating
centimeters instead of hundreds of nanometers or a few micrometers as in optical
coatings, so the quality requirements are more demanding. The research work
presented in this thesis focuses on low temperature titanium tetrachloride TiCl4 and
H2O process that gives high optical quality amorphous TiO2 films.
ALD is a method in which a gas phase chemical reaction occurs on the solid surface
to deposit thin and uniform films [134]. ALD growth proceeds in cycles and during
one cycle the precursor materials are pulsed in the reactor alternatively, one at a
time, separated by purging with nitrogen gas pulses to remove unnecessary material
or reaction byproducts. Each precursor pulse saturates the surface with a
monomolecular layer which grows the film in a self limiting and conformal manner.
The first precursor pulse when exposed to the surface reacts with the functional
groups of the surface and forms a monomolecular layer or is simply chemisorbed in
case of no functional groups. After the purging step, next precursor pulse is injected
which reacts with the already formed monomolecular layer and produces the
desired solid with the release of some chemical ligands which are then removed
during the next purging pulse [131]. Very often during an ALD growth, the surface
layer is a fraction of a monomolecular layer due to availability of less number of
reactive surface sites or the steric hindrance due to bulky ligands [135]. The
increment in film thickness is digital, which results from the discrete increments
during the ALD process [136].
ALD is a form of chemical vapor deposition (CVD) that can coat intricate shapes of
high aspect ratios with a conformal material layer for waveguide applications [137].
In the ALD chamber, the chemical surface reactions can be driven by several
energy mechanisms, however, thermal activation reactions are the most often used.
At low thermal energy, it is difficult to achieve a complete chemical reaction while
reactions at higher temperatures do not yield higher growth rate because of
50
desorption of species from the surface. Therefore, it is important to maintain the
temperature in the intermediate range called the ALD Window [138].
Figure 3.7: SEM pictures of TiO2 thin films on replicated structures (a) Polycarbonate with t = 80
nm (b) Polycarbonate with t = 60 nm (c) Cyclic-olefin-copolymer with t = 50 nm (d) UV-curable
material Ormocomp with t = 50 nm.
High index amorphous TiO2 films have been widely used in a number of potential
applications [139, 140]. The refractive index and density [141] (in terms of
porosity) of the TiO2 films fabricated by ALD [142] are relatively higher than the
ones of films grown by other methods [143]. A low temperature ALD process
results in films that are amorphous in nature and suitable to use in optical nano-
device applications. In this work we fabricated the TiO2 films by using commonly
known precursors TiCl4 and H2O [144] at a relatively low deposition temperature of
120 °C. High index, amorphous, thin TiO2 films of different thicknesses t were
fabricated by using Beneq TFS 500 and TFS 200-152 ALD reactors on plastic
gratings for operation as GMRFs and are shown in Fig. 3.7. In addition, TiO2 films
51
of different thicknesses (60–500 nm) were fabricated on Si substrates to carry out a
complete analysis of the thermo-optic coefficient (dn/dT) and density of these films.
3.6 SPECTROSCOPIC ELLIPSOMETRY
The polarization of a harmonic light wave is, in general, elliptical which means that
the end points of the electric field vector lies on an ellipse during the propagation of
light. An ellipsometer determines the ellipticity of the polarization state of light, the
optical constants of the materials and the thickness of the thin films. Generally
speaking, spectroscopic ellipsometry measurements are illustrated in terms of two
ellipsometric parameters and which are given by the relation [145, 146].
s
pi
R
Re ~
~
tan~ (3.5)
where pR~
and sR~
are p- (electric field vector in the plane of incidence) and s-
polarized (electric field vector perpendicular to the plane of incidence) Pseudo-
Fresnel reflection coefficients given by
2
,12,01
2
,12,01
~~1
~~~
i
pp
i
pp
perr
errR
(3.6)
2
,12,01
2
,12,01
~~1
~~~
i
ss
i
ss
serr
errR
(3.7)
where pp rr ,12,01~,~ and ss rr ,12,01
~,~ are the Fresnel reflection coefficients from air-film and
film-substrate interfaces for p- and s-polarized lights, respectively. Here it is
assumed that that incident light comes from a residual medium air (layer 0) at an
incident angle 0 and reflected from air-film interface and the other part of the light
transmitted through the film (layer 1) reflected from the film-substrate medium. The
optical thickness (phase thickness) of the light is given by [147]
0
22
0
2
1 sin~~2
nnd
(3.8)
52
where d is film thickness, λ is wavelength and 0 is the angle of incident light, n0
and n1 are the refractive indices of air and film materials, respectively.
Owing to the transverse nature of light, the electric field vector moves along an
elliptic trajectory as shown in Fig. 3.8. At some initial time, the field vector locates
at a position a, with the y-component at maximum and after some other time
(where ω is field frequency), it takes a new position b with the maximum x-
component. The angle between positions a and b is called the relative phase Δ of
the vibrations along x- and y-directions and varies from zero to 2π. The parameter ψ
is defined by YXtan , where X and Y are electric field amplitudes (in p- and s-
directions, respectively) that determine the state of elliptical polarization as shown
in Fig. 3.8.
Figure 3.8: Polarization ellipse representing the polarization of an electric field vector in terms of
ellipsometric parameters ψ and phase shift Δ.
For the dispersion properties of materials, Eq. 3.5 must be satisfied in terms of
measured ψ and Δ values. The spectroscopic scan of a dielectric material over a
53
wavelength range determines the optical constants by applying appropriate
dispersion models, for example, Cauchy's model [148].
.....,)(42
CBAn (3.9)
where A, B and C are constants, whose numerical values change during an iterative
process giving results closer to actual measured results by minimizing the mean
square error (MSE). So while evaluating the optical constants one needs to give
initial estimates for these constants which then converge to the calculated ψ and Δ
values of corresponding measured values, after executing a number of iterative
operations to minimize the root mean square error (RMSE). Figure 3.9 shows the
ellipsometric measurement configuration when a linearly polarized plane wave
illuminates the sample at an incident angle φ with normal to the sample. After light-
matter interaction, the reflected light is measured by a detector to collect the
information about the material optical constants. Ellipsometry is also used to
measure the polarization state of the transmitted light.
Figure 3.9: Schematic illustration of an ellipsometric system configuration in terms of its optical
components.
In this work the refractive indices of TiO2 films were measured by a variable angle
spectroscopic ellipsometer VASE manufactured by J. A. Woollam Co [149]. In
addition, the ellipsometer was also employed to measure the spectral
54
reflectance/transmittance of the resonant gratings under the normal or oblique
illumination of a linearly polarized plane wave whose electric field vector is either
parallel (TE) or perpendicular (TM) to the grating lines. The polarization state (TE
or TM) of the illuminated light is selected by a polarizer stage which transformed
the unpolarized light beam into a linearly polarized light beam. The polarization
stage consisted of a polarizer mounted on a high accuracy continuously rotating
stepper motor. The rotating polarizer modulated the intensity of the light. The phase
and amplitude of the modulation represented the polarization state of the beam
entering the analyzer/detector.
55
Chapter 4: Theoretical Results and
Discussion: Design of Resonant
waveguide grating structures and thin
dielectric films
In this chapter an overview of the design of resonant waveguide grating structures is
presented as athermal dielectric waveguide gratings using various polymer
materials. The demonstration of a non-polarizing waveguide gratings (inorganic and
organic) with the further investigation of an over-etch depth into the inorganic
substrate materials (fused silica) is also presented. The thermo-optic coefficients of
TiO2 films and a combination of TiO2+Al2O3 films have been described to design
with Lorentz-Lorenz relation followed by Cauchy’s model. All of the designs
(grating structures and planar films) are made for dielectric materials (both organic
and inorganic) using Fourier Modal Method (FMM).
4.1 STRUCTURE AND DESIGN OF RESONANT WAVEGUIDE
GRATINGS RWGS
Figure 4.1 illustrates the ideal RWG structure we are aiming at. We first have a
polymer (polycarbonate) substrate with a binary grating profile characterized by
height h, period d and ridge width c so that we can define the fill factor as f = c/d.
This grating is coated by a thin dielectric (TiO2) layer grown by ALD. Owing to the
conformal nature of the ALD process, the thickness t of the high-index layer is
assumed to be the same on all sides of the profile (top and bottom of the grooves as
well as the vertical sidewalls). The superstrate is assumed to be air; the depth of the
final air-filled groove is then h and its width w = d-c-2t is assumed to be greater
than zero. The polymer substrate (with the binary grating profile) has uniform
refractive index ns, and the TiO2 cover layer has a refractive index nc. The RWG is
illuminated from air by a linearly polarized plane wave incident at an angle θi, and
we are primarily interested in the spectral efficiency curve of the specularly
reflected plane wave.
56
Figure 4.1: Schematics of an ideal replicated grating profile coated by a high index amorphous thin
TiO2 film by ALD process and placed on a heat reservoir for thermal measurement.
By appropriate choices of the parameters d, f, h, t, nc, ns, and θi, we can obtain a
guided-mode resonance with 100% reflectance for either TE- or TM-polarized light
at a desired wavelength λr. In our examples we use FMM to design the RWGs
particularly for TE-polarized illumination at center resonance wavelength λr = 853
nm and angle of incidence θi = 20°. Our material choices fix the refractive indices:
we use the room-temperature values ns = 1.570 from Refs. [150–152] and nc =
2.322 obtained by in-house measurement at λr = 853 nm. In the design, d, f, h, and t
are, therefore, treated as variable parameters.
One possible set of experimentally realizable parameters is d = 425 nm, f = 0.63, h
= 120 nm, and t = 61 nm. Figure 4.2 shows the effect of varying different
parameters around the design values, and the spectral shape of the resonance peak
with the parameters listed above is illustrated explicitly in Fig. 4.3a. Figure 4.2a
shows the specular reflectance R of the RWG (index 1 means 100% reflectance)
when the grating ridge height h and the TiO2 film thickness t are varied, and implies
that an error in one parameter can be compensated by changing the other. Hence, if
one finds that the ridge height of the polymer grating is incorrect, one can still
obtain the resonance at the correct spectral position by adjusting t appropriately in
the ALD process, which is the final fabrication step. Figure 4.2b demonstrates the
57
possibility of fine tuning the resonance wavelength by adjusting the angle of
incidence, and Fig. 4.2c shows the reflectance when the ridge height h and the fill
factor f are varied. Thus, for example, an increase in pattern height can be
compensated by reducing the fill factor. Finally, Fig. 4.2d illustrates the (rather
tight) tolerances for variations in the refractive indices of the two materials.
Theoretical results for the effect of TiO2 layer thickness on resonance peak position
for TE-mode are shown in Fig. 4.4. An increase in t from 61 nm to 71 nm leads to a
shift of λr from 853 to 871.6 nm when θ = 20°.
Figure 4.2: Fourier Modal analysis of the effects of parameter variations in specular reflectance R.
(a) Variations of ridge height h and TiO2 film thickness t. (b) Variations of wavelength λ and angle
of incidence θi. (c) Variations of ridge height h and fill factor f. (d) Variations of refractive indices ns
and nc of the polycarbonate substrate and TiO2 cover layer, respectively.
58
Figure 4.3: (a) Spectral variations of the specular reflectance R(λ) with room temperature values of
all design parameters. (b) Calculated spectral reflectance curves at T = 100 °C due to thermal
expansion alone (curve 1-TEC), due to thermo-optic effect alone (curve 2-TOC), and due to
combination of both effects (curve 3-TEC-TOC).
Figure 4.4: (a) Simulated room-temperature spectral variation of the reflectance as a function of TiO2
layer thickness. (b) Spectral lineshapes of RWGs with TiO2 layer thickness t = 61 nm (blue curve 1)
and t = 71 nm (red curve 2).
4.1.1 Simulation and Modeling of thermal behavior
In view of the results shown in Fig. 4.2, the resonance wavelength λr depends
critically on the refractive indices ns and nc of the two materials, which in turn
depend on operating temperature T because of the thermo-optic effect. Furthermore,
λr is affected by modifications of the dimensional parameters of the structure,
caused by thermal expansion of a rectangular/binary grating structure. The latter is a
potentially serious issue since the thermal expansion coefficients of polymers are
known to be nearly ten times larger than those of optical glasses [153]. Complete
modeling of the thermal behavior of RWGs, therefore, requires consideration of
59
both thermo-optic properties of the materials and thermal expansion of the entire
structure.
For polycarbonate, we use the thermal refractive-index data from Refs. [150,154].
Thermal dependence of the refractive index of the TiO2 films is measured by a
homemade heating assembly directly attached with ellipsometry. In modeling,
thermal expansion was taken into account by assuming that the period d and height
h of the polycarbonate grating expand linearly with temperature T while the fill
factor f remains constant. Also the TiO2 layer thickness t was assumed to increase
with T, making the air gap narrower with increasing temperature. The thermal
expansion coefficient of polycarbonate is taken to be 6.55 × 10-5 °
C-1
[150,153,155],
and we used the value 8 × 10-6
°C-1
[150] of crystalline TiO2 to approximate the
thermal expansion coefficient of amorphous TiO2. The small value of thermal
expansion coefficient of amorphous TiO2 results in an advantage to get reasonable
athermal behavior since the thermal expansion coefficients of polymers is an order
of magnitude larger than inorganic materials. Then direct FMM calculations were
applied to the resulting dimensional parameters and refractive indices at each
temperature, ranging from 25 °C to 100 °C in 5 °C steps.
The results of the FMM calculations for TE-mode are presented in Fig. 4.5, where
we consider thermal expansion affects (TEC) and thermo-optic effects (TOC)
separately, as well as the combined effect. All calculated results can be well
approximated by straight lines, also shown in Fig. 4.5. As shown in Fig. 4.5b, since
the TEC fit slope is positive and that of TOC is negative, the combined effects lead
to a partial athermalization of the device, i.e.,
)C25( TMr (4.1)
with a fit slope M ≈ 0.01 nm/°C. The spectral TEC, TOC, and combined effects are
illustrated more explicitly in Fig. 4.5b, where we consider the highest simulated
temperature T = 100 °C. At this temperature the spectral shifts caused by TEC and
TOC are noticeable but the combined effect only leads to a 0.7 nm shift in the
resonance peak position λr for TE-mode.
We also calculated the temperature dependence for the TM-polarized light and the
resulting shift in the resonance wavelength is about the same as for the TE-
60
polarized light. Hence, especially over a somewhat more limited temperature range,
the simulation results predict virtually athermal device operation. The thermo-optic
coefficient for polycarbonate is taken as 14 C1007.1 Tns according to
Refs. [150,154] and self-measured values of nc were used to obtain Tnc (see
section 4.4). The values already given were used for thermal expansion coefficients,
i.e., we chose 16 C108
1
T
t
t and
15 C1055.61
T
d
d. Similar calculations
were performed also for RWGs with t = 71 nm (with other parameters kept
unchanged). The results were virtually identical, the main difference being a 0.1 nm
change in the TOC contribution.
Figure 4.5: Effect of temperature (T) change in the spectral shift Δλr of the resonance peak. (a)
Individual TEC and TOC effects of TiO2 and PC. (b) Combined TEC and TOC effects of TiO2 and
PC.
It is interesting to note from Fig. 4.5 that the negative TOC of TiO2 has a significant
role in athermalization, although its magnitude is an order of magnitude smaller
than that of PC. This is explained by a large overlap of the guided mode with the
TiO2 film. There are ways to further reduce Tr , for example, a plastic material
with a smaller thermal expansion coefficient would do this. On the other hand, one
could change the TiO2 layer thickness t, which would have an effect in the thermal
expansion contribution but also on the thermo-optic contribution since thinner TiO2
films tend to have more negative values of the TOC (see Chap. 5). Changing t
would of course require adjustments of the other structural parameters to retain λr at
the original value.
61
4.1.2 Design of athermal behavior of RWGs using different polymer
substrate materials
In these sections, design of athermal polymer waveguide gratings g-I, g-II, and g-III
are considered by incorporating different polymer materials with different TEC and
TOC values. For such designs, the thermal shifts in the resonance wavelength λr are
calculated over the temperature range 25–100 °C with a temperature step of 5 °C.
The modeling of the effect of TEC and TOC in the physical structure of the RWG
was done in the same way as described in section 4.1.1.
Figure 4.6: (a) Specular reflectance R(λ) at room temperature designed parameter values. (b)
Specular reflectance curves calculated at 100 °C accounting for TEC alone, TOC alone and
combined TEC and TOC. (c) Thermal resonance shift in λr when individual effects of TEC and TOC
of polymer and TiO2 are considered. (d) Thermal shift in λr when the combined effects of TEC and
TOC are considered. The polymer considered here is Polycarbonate (PC).
4.1.2.1 Polycarbonate grating (g-I)
For the design of grating g-I, one possible set of the grating optical
and geometrical parameters at resonance is: period d = 368 nm, linewidth w = 232
nm, structure height h = 120 nm, incident angle θi = 18°. These give a resonance at
62
wavelength λr = 735.10 nm for TE-mode if we take the refractive indices of PC
(substrate) and ALD coated TiO2 film (cover layer) at this wavelength to be ns =
1.575 and nc = 2.391, respectively [151,156]. The TEC values of PC and TiO2 are
6.65 × 10-5
°C-1
and 8.00 × 10-6
°C-1
, while the TOC values of PC and TiO2 are -
1.07 × 10-4
°C-1
and -9.3 × 10-5
°C-1
, respectively [153,154,156].
The calculated room-temperature reflectance spectrum around the peak resonance
wavelength, shown in Fig. 4.6a, has a full width at half maximum (FWHM) of 13
nm. Let us next consider the operation of the RWG at a temperature of 100 °C.
Taking into account the TEC of PC and TiO2 alone shifts the resonance peak to a
longer wavelengths λr = 738.3 nm as shown in Fig.4.6b. On the other hand,
considering only the TOCs this shifts the resonance to λr = 732.8 nm. The
combination of these two spectral shifts in opposite directions leads to a partial
athermalization of the device, depicted by the middle reflectance curve with a
resonance peak at λr = 735.9 nm in Fig. 4.6b. Furthermore, calculations to illustrate
the contribution of each selected material coefficient to the spectral shift are shown
in Fig. 4.6c. The combined effect of TEC and TOC exhibits a net positive slope of
0.0103 with a corresponding spectral redshift of 0.8 nm in the entire temperature
interval, as demonstrated in Fig. 4.6d.
4.1.2.2 Cyclic Olefin Copolymer grating (g-II)
In the design of g-II, we employed a parameter set d = 325 nm, w =
205 nm, h = 120 nm, and θi = 18°; with the TE-mode at λr = 657.80 nm. The room-
temperature refractive indices of COC and ALD coated TiO2 film at λr = 630 nm,
i.e., ns = 1.530 and nc = 2.395, were used [156,157]. The TEC values of COC and
TiO2 are 6.0 × 10-5
°C-1
and 9 × 10-6
°C-1
, while the TOC values are -1.0 × 10-4
°C-1
and -9.3 × 10-5
°C-1
, respectively [153,156,157].
The calculated room-temperature reflectance spectrum around the resonance has a
FWHM of 18.5 nm, as shown in Fig. 4.7a. The spectral shifts in the resonance peak,
by taking into account only the TEC or TOC of COC and TiO2 individually at T =
100 °C, are shown in Fig. 4.7b. Again the shifts are towards longer and shorter
wavelengths, and we have λr = 660.2 nm in case of TEC only, and λr = 655.8 nm in
case of TOC only. The combination of the two spectral shifts still leads to partial
63
athermalization of the device, with the resonance peak at 658.2 nm in Fig. 4.7b. The
calculations performed to illustrate the contribution of each selected material
coefficient are shown in Fig. 4.7c and the combined results in Fig. 4.7d. The
combined results now show a net positive slope of 0.0062 with a corresponding
spectral shift of 0.4 nm towards longer wavelengths, which is smaller by a factor of
~2 than in the case of PC.
Figure 4.7: (a) Specular reflectance R(λ) at room temperature designed parameter values. (b)
Specular reflectance curves calculated at 100 °C accounting for TEC alone, TOC alone and
combined TEC and TOC. (c) Thermal resonance shift in λr when individual effects of TEC and TOC
of polymer and TiO2 are considered. (d) Thermal shift in λr when the combined effects of TEC and
TOC are considered. The polymer considered here is Cyclic-olefin-Copolymer (COC).
4.1.2.3 UV-curable material Ormocomp® grating (g-III)
The design of g-III was based on the parameter set d = 325 nm, w =
205 nm, h = 120 nm, θi = 18°, and λr = 655.40 nm with the TE-mode. The refractive
indices of Ormocomp® and TiO2 at λr = 630 nm are ns = 1.511 and nc = 2.395,
64
respectively [156,158], the TEC of Ormocomp and TiO2 are 6.0 × 10-5
°C-1
and 8 ×
10-6
°C-1
, and finally the TOC of Ormocomp® and TiO2 are -1.27 × 10-4
°C-1
and -
9.3 × 10-5
°C-1
(both are measured in-house), respectively [153,156,158].
Figure 4.8: (a) Specular reflectance R(λ) at room temperature designed parameter values. (b)
Specular reflectance curves calculated at 100 °C accounting for TEC alone, TOC alone and
combined TEC and TOC. (c) Thermal resonance shift in λr when individual effects of TEC and TOC
of polymer and TiO2 are considered. (d) Thermal shift in λr when the combined effects of TEC and
TOC are considered. The polymer considered here is UV-curable OrmoComp®.
For g-III the FWHM width of the resonance peak is 19.4 nm as shown in Fig. 4.8a.
The overall effects of individual contributions of TEC and TOC, as well as the
combined effect, are qualitatively similar to the observations made above for PC
and COC. In case of Ormocomp® substrate the TEC-induced resonance position is
λr = 657.8 nm, TOC alone would shift the resonance to λr = 653.2 nm, and the
combination of both gives λr = 655.6 nm as shown in Fig. 4.8b. Now the combined
net slope is 0.0023 with a corresponding spectral red shift of only 0.2 nm as shown
in Fig.4.8d, which is about one half of the value observed for COC and a quarter of
the shift observed for a PC substrate.
65
As far as the design results are concerned, the use of Ormocomp® yields almost
superior performance amongst the three polymers under consideration, and nearly
athermal operation. When comparing the characteristics slopes of the net effects,
Ormocomp® shows the lowest slope for the thermal spectral shift by employing the
TOC measured experimentally as described in section 4.4.1 (however, the use of
TOC calculated from analytical relations shows the same net effect as for COC).
Figure 4.9: Schematic of the (a) type-I, single layer and (b,c) Type-II, double layer 1D non-
polarizing RWGs.
4.2 STRUCTURE AND DESIGN OF POLARIZATION
INDEPENDENT RESONANT WAVEGUIDE GRATINGS
We investigated two types of RWGs that are schematically depicted in Fig. 4.9. The
Type-I RWG consists of a rectangular-profile TiO2 grating layer on a fused silica
substrate. This design aims to verify the non-polarizing filtering effect with the
simplest single-layer 1D GMR grating geometry, which has not been realized
before. The Type-II grating is a TiO2-coated grating with the polycarbonate
substrate replicated from a rectangular-profile master grating stamp by
nanoimprinting [61]. It aims to demonstrate the replicability of the 1D non-
66
polarizing GMR grating. Without loss of generality, both gratings are designed to
work around a resonance wavelength (λr) of 850 nm under normal incidence. The
gratings at oblique incidence can also be designed easily by the same method. The
electric field vector of the incident field may be parallel (TE) or perpendicular (TM)
to the grating lines.
The optical responses of the RWGs are simulated rigorously with the Fourier Modal
Method [89–91]. The refractive index of the ALD-prepared TiO2 film, which is
sensitive to the deposition method, was measured by ellipsometry and fitted with
the Sellmeier formula:
,1)(2
22
B
An
(4.2)
where A=4.316, B=3.846 × 104 nm
2, and λ is the wavelength in vacuum (in nm).
The refractive indices of the fused silica substrate and polycarbonate are relatively
stable and less dispersive, which were taken as 1.45 and 1.57 in our simulation,
respectively. The small dispersion of TiO2 was taken into account in our
simulations, although its effect on resonance positions is marginal.
The RWGs, for example, Giant reflection to zero order (GIRO) mirrors, are based
on the principle of interference of two propagating modes in the grating region for
both polarizations TE and TM [159]. The resulting outcoupling wave depends on
the phase between the two interfering waves [160]. In the design of non-polarizing
RWGs, an adjustment of the structural parameters can result in a fine tuning of the
dispersion relations of TE and TM excited leaky guided modes in the grating layer.
As a result, there exist a situation where both polarizations have the same
propagation constant at the cross point of the dispersion curves of TE- and TM-
modes at normal incidence [36].
In this design, subwavelength (d < λ) grating structures are employed to allow only
the propagation of zeroth transmitted diffraction order at the resonance. Since the
resonance wavelength λres is related to the grating period d, one can achieve RWG
effect at any desired wavelength by choosing a suitable period d < λres [36]. Thus
the non-polarizing effect is achieved by optimizing the other structural parameters,
by which to engineer the dispersion relations of TE and TM leaky guided modes so
67
that the simultaneous excitation of both can be realized under normal incidence. By
applying the optimization procedure as described in [36] and taking into account the
feasibility of fabrication, we obtained the optimal structural parameters for the
designed RWGs: for the Type-I grating, d = 540 nm, w = 395 nm, h = 195 nm and
θi = 90°. Figure 4.10 shows the simulation at maximum (100 %) diffraction
efficiency in reflection for both TE- and TM-modes in terms of the grating
dimensional parameters linewidth w and structure height h. For such gratings the
non-polarizing geometrical parameters are predicted at the point of intersection of
TE- and TM-Modes, shown in Fig. 4.11a and corresponding reflectance spectra at λr
= 850 nm is shown in Fig. 4.11b.
Figure 4.10: Spectral reflectance at the resonance wavelength λr at designed linewidth w and
structure height h of grating-I (a) TE-Mode (b) TM-Mode.
Figure 4.11: Maximum spectral reflectance at the resonance wavelength λr = 850 nm (a) Linewidth w
and structure height h are evaluated at the point of intersection of both TE- and TM-Modes (b) TE-
and TM-reflectance spectra at predicted values of w and h.
68
For the Type-II grating, d = 540 nm, w = 200 nm, h = 145 nm, and t = 60 nm and θi
= 90°. Figure 4.12 shows the simulation at maximum (100 %) diffraction efficiency
in reflection for both TE- and TM-modes in terms of the grating dimensional
parameters linewidth w and structure height h. For such gratings the non-polarizing
geometrical parameters are predicted at the point of intersection of TE- and TM-
Modes (not shown here) and reflectance spectra of the zeroth orders of RWGs at λr
= 850 nm is shown in Fig. 4.13.
Figure 4.12: Spectral reflectance at the resonance wavelength λr at designed linewidth w = 200 nm
and structure height h = 145 nm of grating-II for (a) TE-Mode (b) TM-Mode.
Polarization tunable operation is obtained by coupling of s- or p-input polarized
field components into either TE- or TM-modes. This is achieved by optimizing the
grating components shown in Fig. 4.12, which results in a high reflectance for both
modes at resonance wavelength, irrespective of the input polarization state. For
resonance to occur, the wavelength is always longer than the corresponding
Rayleigh anomaly [29].
m
ndRAr (4.3)
,nm540 dn
r (4.4)
where λr = 850 nm is the resonance wavelength, n is the refractive index of the
substrate (1.57), m is the diffraction order and d = 540 nm is the grating period.
69
Figure 4.13: Maximum spectral reflectance at the resonance wavelength λr = 850 nm for TE- and
TM-modes at predicted values of w and h. The full width at half maximum (FWHM) values for TE =
19.2 nm and TM = 6.1 nm
Figure 4.14: Maximum spectral reflectance in terms of incident angle θi and wavelength λ for both
(a) TE- and (b) TM-Modes.
Figure 4.13 shows the simultaneous excitation of both TE and TM reflectance
spectral peaks at normal incidence. We investigated the non-polarizing filtering
phenomena for TE- and TM-waveguide modes in terms of dispersion relations. The
reflectance R is plotted as a function of wavelength of incident light λ and incident
angle θi. At resonance, the wave vector of the incident plane wave kx matches with
70
the propagation constant of the leaky guided mode γ through the Eq. (2.63). This is
shown in Fig. 4.14 as a dispersion-curve-plot, where
idP
sin2 (4.5)
Figure 4.14 demonstrates that at normal incidence (θi = 0), resonance phenomena
occurs at λr = 850 nm for both the TE- and TM-Modes of RWGs.
Figure 4.15: Schematic illustration of a TiO2 RWG. (a) Etched to the surface of substrate SiO2 and
(b) Overetched into substrate SiO2.
4.3 EFFECT OF SUBSTRATE OVERETCHING AND HEAT
TREATMENT ON NON-POLARIZING PROPERTIES OF TiO2
RWGS AND THIN FILMS ON THEIR OPTICAL PROPERTIES
. TiO2 RWGs are of very high importance due to the high refractive index and
transparency in the visible and infrared regions. The variations in the thickness of
the waveguide play a significant role, which may result in a change of the nature of
the waveguide modes. To cover all of these aspects, TiO2 RWGs are fabricated by
ALD method to give a precise waveguide thickness control [112]. An important
step in the fabrication of the subwavelength RWG structures is the reactive ion
etching (RIE) or the inductively coupled plasma etching by using various etchants.
Some studies have reported that thin dielectric films prepared by ALD inherently
possess high hardness and chemical inertness, which enable them to be used as
etching masks [161]. Therefore, the selection of the etchant with high etch
71
selectivity of TiO2 over the mask (a resist or a metal such as Cr) is an important
aspect for the fabrication of TiO2 RWGs. In general, the high etch selectivity of
TiO2 over the mask can also influence the substrate layer underneath by etching it.
The subsequent etching of the underlying fused silica substrate (SiO2) is undesired,
as it can change the propagation constants of the TE (field is parallel to the grating
lines) and TM (field is perpendicular to the grating lines) modes of the waveguide
grating.
Figure 4.16: Simulation results of specular reflectance showing the variation in the resonance
wavelength λr with the increase in overetch depth hs in the fused silica substrate. (a) TE-Mode with
amorphous TiO2 (b) TM-Mode with amorphous TiO2 (c) Both the TE- and TM-Modes and their
effect on the nonpolarizing property of amorphous TiO2 waveguide gratings and (d) both the TE-
and TM-Modes and their effect on the nonpolarizing property of crystalline (anatase) TiO2 gratings.
In this section different over-etch depths of the substrate (SiO2) are investigated
theoretically by varying the etching times of the etchant in TiO2 waveguide
gratings. The schematics of TiO2 waveguide gratings etched to and into the
substrate surface are shown in Figs. 4.15a and b. The shift in the resonant
72
wavelength position of both the TE- and TM-modes is studied with an amorphous
phase of the TiO2 films, and then the TiO2 waveguide gratings are heat treated to
change the TiO2 phase (also refractive index) to investigate its effect on the relative
resonance wavelength peak position shift. Furthermore, planar TiO2 films of the
same thicknesses are prepared by ALD in amorphous and crystalline forms and
characterized structurally and optically to investigate their phases and the refractive
indices after a heat treatment process (see Chap. 5).
4.3.1 Design parameters of TiO2 RWGs on SiO2 substrate
The schematics of an ideal RWG under study is shown in Fig. 4.15. The grating
consists of a binary profile in a TiO2 layer of thickness t on a fused silica substrate,
i. e., the grating height hc is equal to the TiO2 thickness t. The superstrate is
assumed to be air with a refractive index na = 1, and the refractive indices of
amorphous TiO2, crystalline (anatase) TiO2 and fused silica are nc = 2.32, 2.43 and
ns = 1.45, respectively. The waveguide grating is illuminated by a linearly polarized
plane wave at an angle θi with the normal to the grating and a specularly
reflected/transmitted plane wave has an angle θ0. The demonstrated waveguide
gratings are designed to work around a resonance wavelength λr = 850 nm at normal
incidence. Gratings operating at oblique incidence can be designed and fabricated
by the same approach. In this design section all the rigorous calculations and
simulations are performed with the Fourier Modal Method [89–91] and grating
parameters are similar to the ones described in section 4.2 for g-I.
4.3.2 Substrate overetching effect on splitting of TE- and TE-Modes
In section 4.2, Figs. 4.10 and 4.11show the simulation results of the optimized
parameters of the designed non-polarizing gratings (g-I) for specular
transmittance/reflectance. In this section we describe the splitting of the degeneracy
of the TE- and TM-modes of the aforementioned RWG structure by calculating and
simulating the effect of an over-etch depth into the fused silica substrate. Note that
an accurate etching of TiO2 layer to the surface of fused silica (substrate) is
challenging achieve to perfection.
73
The effect of over-etching in the fused silica substrate on the non-polarizing
properties of a TiO2 RWG is shown in Fig. 4.16. Figure 4.16a shows the effect of a
variation in hs on the resonance wavelength for the TE-mode. It can be seen that the
rate of change in the resonance wavelength is large in the region of small over-
etching and decreases as the hs depth increases, and the λr vs. hs obeys a parabolic
fit. The change of the resonance wavelength for the TM-mode is relatively smaller
than for the TE-mode as seen in Fig. 4.16b, λr changes linearly with hs. Figure 4.16c
shows the difference of λr between the two propagating modes (TE and TM) with
the overetch depth, illustrating that the dispersion curves for simultaneous
excitation in amorphous TiO2 waveguide gratings are split.
Figure 4.17: Simulation results of specular reflectance in terms of ridge height hc and linewidth w of
nonpolarizing RWGs with period d = 540 nm, linewidth w = 401.5 nm and the structure height hc =
~199 nm, showing the propagation mode splitting with an overetch depth hs = 50 nm into fused silica
substrate. (a) TE-Mode and (b) TM-Mode.
The simulation results also show that the non-polarizing properties are not retrieved
at the same optimized parameters if the phase of the TiO2 material is changed from
amorphous (nc = 2.32) to crystalline (nc = 2.43). Figure 4.16d shows the dispersion
curves of the two propagating modes in a crystalline TiO2 waveguide gratings, i. e.,
the shift in the resonance wavelength as a function of the overetch depth. Although
Figs. 4.16c and 4.16d show similar behavior in the magnitudes of the changes in
individual TE- and TM-dispersion curves, the non-polarizing properties are affected
due to a change of the index of the waveguide layer. Figure 4.17 shows the effect of
an overetch depth hs of 50 nm into the fused silica substrate on the propagation
74
mode splitting of TE- and TM-modes for a non-polarizing RWG. It is evident from
the Fig. 4.17a (representing TE-mode) that, due to an overetch effect to the
substrate material, the deviation from the non-polarizing property is relatively larger
than that of a TM-mode shown in Fig. 4.17b.
Figure 4.18: Measured and fitted ellipsometric data of amorphous and crystalline (anatase) TiO2
films of thicknesses ~200 nm. (a) ψ, (b) Δ of amorphous films, (c) ψ, and (d) Δ of crystalline films.
4.3.3 Refractive index modeling of amorphous and crystalline TiO2 films
The refractive index data of amorphous and crystalline TiO2 thin films of thickness
~200 nm on a fused silica substrate is measured by ellipsometry. The refractive
index n(λ) data from the ellipsometric measurements are retrieved by applying
Wvase software based on the Cauchy model for a two layer planar structure. The
ellipsometric measurements and the model fitting data are expressed in the
ellipsometric parameters ψ and Δ defined by the Eq. (3.5). Figures 4.18a, 4.18b and
75
4.18c, 4.18d show the quality of experimentally predicted and modeled data of
amorphous and crystalline TiO2 thin films in terms of parameters ψ and Δ.
Figure 4.19: Simulated spectral shifts in the central resonance wavelength λr of specular reflectance
at normal incidence with a change in refractive index of TiO2 material, before and after a phase
change of TiO2. The RWG parameters are defined by a period d = 540 nm, a linewidth w = 401.5
nm, and a structure height hc = ~199 nm. (a) TE-Mode and (b) TM-Mode.
The influence of the phase change of the TiO2 material on the spectral positions of
the center resonance wavelength is simulated as a function of refracted index nc(λ)
for both the TE- and TM-modes and the results are shown in Figs. 4.19a and 4.19b.
Here again the variation in the TE-mode is larger than that in the TM-mode and the
center resonance wavelength shifts towards longer wavelengths due to the increase
of the refractive index of TiO2.
4.4 THERMO-OPTIC COEFFICIENT (TOC) OF ORGANIC AND
INORGANIC OPTICAL MATERIALS
Thermo-optic coefficient (dn/dT) is defined as the rate of change of refractive index
of a material with respect to temperature. If index is increasing with increase in
temperature then TOC is said to have a positive value and if index decreases with
increase in temperature, the material possesses negative TOC. Most of the organic
materials (polymers) have negative TOC due to evaporation of solvent content that
may be exploited for various applications in waveguides, for example, athermal
devices that have been described with a significant effect on the spectral behavior
and performance of RWGs [120]. Analogously, TOC of high index inorganic
76
materials vary rapidly and thus influence the resonance peak position of the filtering
device [162]. Thus TOC and thermal expansion coefficient (TEC) of polymer
materials play a vital role in improving the thermal stability [60,120].
The selection of optical polymer materials based on large TEC (approximately 10
times larger than in inorganic materials) are found to enable partial balancing of the
thermal shifts caused by TOCs. In order to analyze TOC of organic and inorganic
dielectric materials, the refractive index is given by the Lorentz-Lorenz equation
[163].
,32
1
0
2
2
M
N
n
n A
(4.6)
where NA is Avogadro's number, ε0 is the permittivity of vacuum, α is molecular
polarizability, M is molecular weight and ρ is the density of the material. In a
homogeneous, single phase material, the density is proportional to refractive index,
which however can be anisotropic due to the polarizability caused by the molecular
chain orientation and residual stresses.
Table 4.1: Thermo-optic and volumetric thermal expansion coefficients of polymers in a glassy state,
dn/dT and γ, respectively.
Polymer dn/dT × 10-4
°C-1
γ × 10-4
°C-1
SAN -1.10 1.95
COC -1.00 1.80
Epoxy -1.00 1.70
PMMA -1.10 2.20
PEMA -1.10 1.90
t B-PEEK -1.00 1.70
Polycarbonate -1.07 1.95
Polystyrene -1.40 2.40
Sol-gel acrylate polymers -2.20 3.40
Sol-gel with diphenysilane -2.30 3.90
In this section we investigate the TOC of optical materials (organic and inorganic)
in narrowband replicated guided mode resonance filters [60–64,112] in terms of
77
thermal spectral shifts as described in section 4.1. In section 4.1 we considered
three polymer materials (polycarbonate, cyclic olefin copolymer, Ormocomp®)
where TEC and TOC of most of the polymers were obtained from the literature,
however, due to non-availability of TOC of Ormocomp®, we need to measure and
compute it by three different approaches, see our recent publication [120].
4.4.1 Analysis and Computation of thermo-optic coefficient of Ormocomp®
For the measurement of the TOC of Ormocomp®, a thin film of an average
thickness of 290 nm was prepared after uv-curing of liquid phase precursor material
that was obtained from Micro resist technology®. For this purpose, two fused silica
circular shaped samples of 2˝ diameter and 0.5 mm thickness were surface treated
with anti-adhesive silane layers using a silanation solution composed of a mixture
of HFE 7100 Engineering solvent with 0.2 % of trimethylhydroxysilane (TMS) in
nitrogen environment.
A small amount of liquid Ormocomp® was spread on the top of a glass surface and
sandwiched between two glass substrates with a small force on the top glass
substrate to spread the liquid evenly. After uniform spreading, the sandwich
structure was placed in a uv chamber SpectrolinkerTM
XL-1000 UV-crosslinker
from Spectronics Corporation under a constant exposure of ultraviolet radiation at
365 nm wavelength for 1 min. Then the solidified material was demolded from the
glass substrate and again placed in uv chamber to consolidate the material further
for 10 min under uv exposure at 365 nm wavelength.
4.4.1.1 Method 1
The thermo-optic coefficient of Ormocomp® is determined with slight
modifications in the method reported by Zhang et al. [164]. In this approach, the
TOCs and TECs of a number of polymers [19,154,157,158] in glassy states, given
in Table 4.1 are plotted to approximate a linear fit as shown in Fig. 4.20. After
plotting and applying the least square fitting, the equation of the linear fit in terms
of plotted parameters is given as,
,1062.0d
d 5 T
n (4.7)
78
where -0.62 is the slope and 10-5
°C-1
is the dn/dT-intercept of the line. By
substituting the volumetric TEC value of Ormocomp®, i.e., 1.8 × 10-4
°C-1
[158] in
Eq. (4.7), the calculated dn/dT value is -1.02 × 10-4
°C-1
.
Figure 4.20: Linear fit approximation between thermo-optic and volume thermal expansion
coefficients of different polymers in glassy state.
4.4.1.2 Method 2
Method 2 is based on the measured refractive indices of Ormocomp® at different
temperatures (20–120 °C with a temperature interval of 10 °C in the wavelength
range 380–1000 nm. The room temperature measured data after applying the
Cauchy model is shown in Fig. 4.21a. We considered a set of index data points at
different temperatures (at a wavelength of 630 nm), which are plotted as (n2 + 2)/(n
2
- 1) as a function of T and fitted by the least squares method in the form of a
quadratic curve, as shown in Fig. 4.21b. The thermo-optic coefficient (dn/dT) is
evaluated from fit equation given below
,35.31085.11051.61
2 426
2
2
TTn
n (4.8)
where the temperature T is expressed in °C and the coefficients of T2 and T in units
°C-2
and °C-1
, respectively. Differentiation of Eq. (4.8) with respect to T gives
79
),1085.11030.1(6
)1(
d
d 4522
Tn
n
T
n (4.9)
where the coefficient of T and the constant are expressed in units °C-2
and °C-1
,
respectively. The use of Eq. (4.9) leads to an average thermo-optic coefficient dn/dT
= -1.27 × 10-4
°C-1
.
Figure 4.21: Measured refractive index of Ormocomp®. (a) Room temperature measurement and
fitted data of n(λ). (b) Temperature dependent measurement and fitted data of n(T) at a wavelength
of 630 nm.
4.4.1.3 Method 3
Method 3 consists of a combination of both experimental and theoretical
approaches. The TOC of a polymer material can be expressed as combinational
effects of density and temperature [165]
T
n
T
n
T
n
Tδ
δ
δ
δ
δ
δ
d
d (4.10)
or
,δ
δ
δ
δ
d
d
T
nnρ
T
n
T
(4.11)
where (ρδn/δρ)T and (δn/δT)ρ are the parts of the TOC influenced by density and
temperature changes, respectively, and γ is the volumetric TEC of Ormocomp®.
One can express the value of (ρδn/δρ)T in terms of the strain polarizability constant
80
Λ0 due to the effect of density changes on the atomic polarizability of polymer
[165], after simplifying Eq. (4.11):
,6
)1)(2()1(
δ
δ 22
0n
nnnρ
T
(4.12)
The value of strain polarizability constant is usually small for polymer materials
(0.15–0.18). The use of constant Λ0 and n at different constant temperatures in Eq.
(4.12) gives values of (ρδn/δρ)T at different constant temperatures. Substitution of
these values in Eq. (4.11), as well as the values of γ and (δn/δT)ρ given by Eq. (4.7)
(method 1), leads to an average value of TOC of Ormocomp® dn/dT = -0.81 × 10-4
°C-1
.
The TOC values calculated by methods 1 and 3 are relatively close to each other in
comparison to the one evaluated by method 2. The methods 1 and 3 are based on
analytical relations [164] while the method 2 describes the TOC through
experimentally measured data. In polymers, the value of TOC depends strongly on
the proportion of voids (density) in the material during uv-curing and thus shows
relatively larger values than predicted directly from analytical relations. On heating,
the slightly higher value of TOC (method 2) may be attributed to relatively larger
expansions than expected due to the proportion of voids being filled initially by the
solvent and strain shrinkage on consolidation during uv-curing [166]. The use of
Eq. (4.11) in method 3 describes that the first term includes density variations at
different constant temperatures. It is significant due to relatively higher TEC of
polymer (~10-4
°C-1
) in comparison to the second term at constant density, which is
directly obtained from the method 1 (~10-5
°C-1
). This explains the need to account
for density variations in, for example, analytical relations to explain the TOC.
4.4.2 Analysis and Computation of thermal properties of TiO2 films grown
by ALD
The use of Atomic Layer Deposition (ALD) shows promise for low cost and large
scale production of TiO2 films with high optical quality. ALD is a unique thin film
deposition method based on saturative surface reactions of alternatively supplied
precursor vapors [131]. Due to the saturative nature of each reaction step, the film
81
growth is self-limiting, providing several practical advantages compared to other
deposition techniques: atomic level control of film composition and thickness,
uniform coverage of corrugated surface profiles or smooth planar surfaces with
large area uniformity.
Figure 4.22: Optical design structure of a thin TiO2 film grown by ALD on a silicon substrate and
the geometry of the illumination in ellipsometric measurements.
The refractive index of TiO2 films deposited by different techniques has been found
to correlate well with the density of the material [167]. Importantly, the films
produced by the same technique but under different growth conditions exhibit
different density and refractive index due to phase changes in their microstructure
[168,169]. The density of the deposited TiO2 films is nearly linearly proportional to
the corresponding mechanical properties (Young's modulus) [170] and refractive
index [171]. For amorphous TiO2 films the density changes at different
temperatures are not caused by the material undergoing a phase change rather these
density changes are attributed to the varying concentration of hydrogen containing
species (H2O, OH, etc.), which adsorb in the voids or residual oxygen vacancies
formed during film growth [167,172].
The refractive index of TiO2 films deposited by different techniques shows a
negative thermo-optic coefficient dn/dT, i.e., the value of refractive index decreases
as temperature increases. The microstructure of TiO2 thin films depends on the
deposition technique and the nature of the substrate. The film properties show
variations in density (porosity), mechanical properties, refractive index, extinction
82
coefficient, etc. For example, thermo-optic coefficients of TiO2 films deposited by
plasma enhanced chemical vapor deposition [173] and electron beam evaporation
deposition [174] exhibit different magnitudes due to the nature of the technique
being employed. In this section we report on thermo-optic coefficients and
temperature dependent density coefficients of TiO2 films grown by ALD. We
deposited amorphous TiO2 films with different thicknesses under the same growth
conditions and measured their temperature-dependent refractive indices over a
broad wavelength range 380 nm < λ < 1800 nm. The coefficients dn/dT and dρ/dT
are evaluated from the experimental results by modeling with the Lorentz-Lorenz
relation.
Figure 4.23: Ellipsometric data of ALD TiO2 films: measured spectral dependence of the
ellipsometric parameters (a) ψ and (b) Δ together with Cauchy model fits for a film of thickness t =
60 nm.
4.4.2.1 Determination of Refractive Index
We applied Wvase 32 software based on the Cauchy model to the three-layer
structure illustrated in Fig. 4.22 to retrieve the refractive-index data n(λ,T) from
measurements of the ellipsometric parameters ψ and Δ. It is worth noting that
inclusion of the oxide and surface-roughness layers in Fig. 4.22 was beneficial for
obtaining a satisfactory fit for the refractive index of the TiO2 film over the entire
wavelength range considered; the exact thicknesses of these nanoscale layers was,
however, not critical. The results shown in Figs. 4.23a and b illustrate the quality of
the Cauchy-model fits, while Fig. 4.24 illustrates the retrieved refractive-index data
for a film of thickness t = 60 nm at several different temperatures.
83
Figure 4.24: Ellipsometric refractive index data n(λ,T) of TiO2 film of thickness t = 60 nm at various
temperatures.
In the scale of Fig. 4.24, the curves at different temperatures appear hard to
distinguish. However, even small variations of refractive index due to
environmental conditions can deteriorate the performance of sensitive optical
devices or, on the other hand, may be employed to advantage in sensor applications.
Before proceeding to further analyze the thermal effects, we point out that the
refractive indices of the TiO2 films fabricated by ALD are comparable to films
fabricated by RF-magnetron sputtering [175], but they are considerably larger than
the refractive indices of films fabricated by, e.g., evaporation techniques [46]. The
refractive index data obtained from the Cauchy model can be further analyzed to
evaluate the thermo-optic coefficient and the density of the TiO2 films. To
accomplish this task, we may rewrite Eq. (4.6), the Lorentz-Lorenz relation in CGS
system [163].
,3
4
2
12
2
M
N
n
n Ae
(4.13)
where eTnn ),,( is the electronic polarizability in units of cm3, ρ is the density
in units g cm-3
, NA = 6.023 × 1023
electrons/mol is the Avogadro number, and M =
84
79.9 g/mol is the molecular weight of the TiO2 molecule. The electronic
polarizabilities of Ti+4
, O-2
and the TiO2 molecule are 0.19 × 10-24
cm3, 2.4 × 10
-24
cm3 and 5 × 10
-24 cm
3, respectively [163]. The electronic polarizability αe connects
the dipole moment p to the applied electric field E by the relation p = αe E [176],
which applies to non-polar molecules at high frequencies so that permanent dipole
moments do not follow the electric field.
Figure 4.25: Experimental and fitted data on TiO2 films of thickness t = 60 nm. (a) Index variation
n(λ,T) and (b) density variation ρ(λ,T) at λ = 640 nm.
To model the thermal properties of the refractive indices of TiO2 films, the left-
hand-side of eq. (4.13) is calculated for temperatures 25–155 °C (interval of 10 °C)
across a wavelength range 380–1800 nm for all TiO2 films that were fabricated and
characterized at a wavelength step of 20 nm. As illustrated in Fig. 4.25a for the case
t = 60 nm at λ = 640 nm, the data points follow well a parabolic curve with a least-
squares fit
,6.1108.1108.51
2 528
2
2
TTn
n (4.14)
where the temperature T is expressed in °C and the coefficients of T2 and T have
units °C-2
and °C-1
, respectively. Differentiation of Eq. (4.14) with respect to T
gives
).108.1106.11(6
)1(
d
d 5822
Tn
n
T
n (4.15)
85
Here, the coefficients of T and T0 have units °C
-2 and °C
-1, respectively. Application
of Eq. (4.15) leads to a thermo-optic coefficient dn/dT = -3.1 × 10-5
°C-1
at room
temperature (T = 25 °C) while dn/dT = -4.5 × 10-5
°C-1
at T = 105 °C.
4.4.2.2 Determination of film density
It has been reported that the refractive index of TiO2 films is linearly proportional to
the density of the material [177]. We calculate the temperature-dependent density
ρ(T) of the TiO2 films from refractive-index values n(T) using eq. (4.13). The
results for film thickness t = 60 nm at λ = 640 nm, plotted in Fig. 4.25b, possess a
good parabolic fit
8.3101.4104.1 527 TT (4.16)
where ρ is expressed in units g cm-3
and the coefficients of T2, T, and T
0 have units
°C-2
g cm-3
, °C-1
g cm-3
and g cm-3
, respectively. Differentiation of Eq. (4.16) with
respect to T leads to
,101.4108.2d 57 TTd
(4.17)
where dρ/dT is expressed in units °C-1
g cm-3
and the coefficients of T and T0 have
units °C-2
g cm-3
and °C-1
g cm-3
, respectively. At room temperature Eq. (4.17)
gives dρ/dT = -4.8 × 10-5
°C-1
g cm-3
, and at T = 105 °C we have dρ/dT = -7.0 × 10-5
°C-1
g cm-3
.
To calculate the temperature dependence of the electronic polarizability dαe/dT, we
differentiate Eq. (4.13) with respect to T:
.d
d
d
d)2(
9
2
d
d 22
TTn
n
m
N
T
n ee
A
(4.18)
Using to the thermal coefficients dn/dT and dρ/dT from Eqs. (4.15) and (4.17),
respectively, in Eq. (4.18) leads to dαe/dT = -1.4 × 10-31
°C-1
cm3. This gradient is
insignificant compared to the density gradient dρ/dT and hence we may conclude
that the latter gives the main contribution to index changes at least at the high
optical frequencies in the visible region.
86
Table 4.2: Measured temperature-dependent refractive index n and calculated density ρ of an ALD-
grown TiO2 film of thickness t = 60 nm at λ = 640 nm.
Temperature T [°C] Refractive Index
of TiO2 film n
Density of TiO2
film ρ [g cm-3
]
25 2.3705 3.8400
35 2.3702 3.8396
45 2.3698 3.8389
55 2.3695 3.8385
65 2.3691 3.8379
75 2.3686 3.8371
85 2.3684 3.8368
95 2.3681 3.8363
105 2.3670 3.8346
115 2.3672 3.8349
125 2.3665 3.8338
135 2.3664 3.8337
145 2.3653 3.8319
155 2.3650 3.8315
Table 4.2 shows the experimentally measured temperature dependence of the
refractive index and the density of an ALD-grown TiO2 film of thickness t = 60 nm
at wavelength λ = 640 nm. The decrease of the refractive index with temperature
corresponds to an average value of dn/dT = -4.2 ± 0.7 × 10-5
C-1
, which is of the
same order of magnitude as reported in Ref. [173] but an order of magnitude
smaller than reported in Ref. [174]. This reflects the dependence of the thermo-optic
coefficient on the deposition technique and the substrate material. The packing
density of TiO2 films is an important parameter contributing to the index values:
denser films fabricated by ALD have a lower index gradient than films with higher
porosity, fabricated by sputtering or vacuum evaporation. This effect has already
been interpreted as resulting from the presence of hydrogenated species in the pores
of TiO2 films: heating causes replacement of water in the pores with air [178]. Due
87
to the atomic-level deposition nature of ALD, the resulting films inherently exhibit
high density (thus being less porous) and therefore, the index gradient is relatively
small. The density values given in the third column of Table 4.2 are slightly above
the highest values obtained by the ion plating method in Ref. [170].
Figure 4.26: Experimental data of ALD-Al2O3 films: spectral dependence of the measured
ellipsometric data at T = 20 °C in terms of parameters (a) ψ and (b) Δ, together with Cauchy model
fits for a film of thickness ta ~ 60 nm.
4.4.3 Modeling of thermal properties of ALD-Al2O3 films
4.4.3.1 Temperature dependent refractive index
In this section we proceed to discuss the modeling of the optical constants of ALD-
Al2O3 films, measured by ellipsometry. For the extraction of accurate optical
properties of thin film materials (optical constants, thicknesses, etc.) from VASE
analysis, it is important to develop an appropriate optical model, which enables
accurate fitting of the experimentally measured data. We consider the simplest
optical model of Al2O3 films on a Si substrate (we call these samples SC(1–6)). The
slight dispersion in refractive index is modeled by using the Cauchy formula to
calculate the refractive index of ALD-Al2O3 films as a function of wavelength and
temperature. The model fit parameters are the thickness of the film and three
Cauchy parameters A, B, and C [see Eq. (3.9)] obtained after a number of iterations
in such a way that the regression algorithm converged to a nearly perfect data fit as
shown in Fig. 4.26. The optical constants used in Eq. (3.9) are A = 1.45, B = 0.01, C
88
= 0. Fitting the measured data of ALD-Al2O3 films of thickness ~60 nm and
temperature T = 20 °C leads to a mean square error (MSE) of 0.8717.
The environmental conditions lead to small variations of refractive index, which
can deteriorate the performance of sensitive optical devices. On the other hand,
such variations may be employed to advantage in sensor applications, for example,
in athermal waveguide devices [60]. The refractive index data retrieved from the
Cauchy model can be further analyzed to evaluate the TOCs and density of
isotropic Al2O3 films by employing the Lorentz-Lorenz relation in CGS unit system
{see Eq. (4.13)} [163].
where n ≡ n(λ,T), αe is the electronic polarizability in units of cm3, ρ is the density
in units g cm-3
, NA = 6.022 × 1023
electrons/mol is the Avogadro number, and M =
101.961 g/mol is the molecular weight of the Al2O3 molecule. The electronic
polarizabilities of Al+3
, O-2
and the Al2O3 molecule are 0.052 × 10-24
cm3, 1.606 ×
10-24
cm3 and 4.922 × 10
-24 cm
3, respectively [179].
Figure 4.27: Experimental and fitted data of ALD-Al2O3 films: (a) Index variation n(λ,T) (b) density
variation ρ(λ,T) of films of thickness ta ~60 nm at λ = 640 nm.
To model the thermal properties of refractive indices of ALD-Al2O3 films, the
reciprocal of the left hand side of Eq. (4.13) is calculated in the temperature range T
= 20–150 °C with a temperature interval of 10 °C for a wavelength λ = 640 nm and
ta = 60 nm for a sample in the set SC(1–6). A least-square fit of a parabolic curve to
the data points in Fig. 4.27a gives
,02.31028.21002.71
2 427
2
2
TTn
n (4.19)
89
where the temperature T is expressed in °C and the coefficients of T2 and T have
units °C-2
and °C-1
, respectively. Differentiation of Eq. (4.19) with respect to T
gives
.1028.21041.16
)1(
d
d 4622
Tn
n
T
n (4.20)
Here, the coefficients of T and T0 have units °C
-2 and °C
-1, respectively. Application
of Eq. (4.20) leads to a thermo-optic coefficient dn/dT = 4.66 ± 1.32 × 10-5
°C-1
at
room temperature (T = 20 °C) while dn/dT = 2.06 ± 1.32 × 10-5
°C-1
T = 100 °C.
4.4.3.2 Temperature dependent density
The temperature dependent density ρ(T) of amorphous ALD-Al2O3 thin films is
directly calculated from the temperature dependent refractive index by using Eq.
(4.13). The calculated density values of ALD-Al2O3 are comparable to those
reported by Groner et. al [180] and consistent with an average density of ~ 2.75 g
cm-3
at a deposition temperature of 120 °C. The refractive index and density of the
ALD-Al2O3 films critically depend on the growth temperature [180]. In this section
we are more interested in the temperature dependent density of amorphous ALD-
Al2O3 films, determined on the basis of refractive index by using Lorentz-Lorenz
relation Eq. (4.13). The calculated values for a film of thickness 60 nm at λ = 640
nm, plotted in Fig. (4.27)b, possess a good parabolic fit
,72.21006.21036.6)( 427 TTT (4.21)
where ρ(T) is expressed in units g cm-3
and the coefficients of T2, T, and T
0 have
units °C-2
g cm-3
, °C-1
g cm-3
and g cm-3
, respectively. Differentiation of Eq. (4.21)
with respect to T leads to
,1006.21027.1d
)(d 46 TT
T (4.22)
where dρ(T)/dT is expressed in units °C-1
g cm-3
and the coefficients of T and T0
have units °C-2
g cm-3
and °C-1
g cm-3
, respectively. At room temperature Eq. (4.22)
gives dρ/dT = 1.81 ± 0.51 × 10-4
°C-1
g cm-3
, and at T = 100 °C we have dρ/dT =
7.88 ± 5.12 × 10-5
°C-1
g cm-3
.
90
Table 4.3: Measured and calculated temperature dependent refractive index (dn/dT × 10-5
) and
density (dρ/dT × 10-4
) of ALD-Al2O3 films of different thicknesses ta = 60–500 nm at T = 20 °C and
T = 100 °C for a wavelength λ = 640 nm.
Sample ID ta [nm] T [°C] dn/dT [°C-1
] dρ/dT [°C-1
g cm-3
]
SC1 60 20 4.66 1.81
SC1 60 100 2.06 0.79
SC2 100 20 8.05 3.10
SC2 100 100 0.49 0.17
SC3 200 20 3.6 1.38
SC3 200 100 1.03 0.27
SC4 300 20 6.98 2.69
SC4 300 100 1.88 0.72
SC5 400 20 4.91 1.89
SC5 400 100 0.61 0.23
SC6 500 20 4.58 1.77
SC6 500 100 1.58 0.61
Table 4.3 shows the values of dn/dT and dρ/dT calculated from the ellipsometric
data for different ALD-Al2O3 film thicknesses at wavelength λ = 640 nm and
temperatures T = 20 °C and T = 100 °C. The dn/dT values for Al2O3 are quite
similar for all the thicknesses, being slightly larger near the room temperature than
at T = 100 °C. The evaluated dn/dT values of ALD-Al2O3 films are similar to the
results already reported by a metal organic plasma enhanced chemical vapor
deposition process [173]. Here we point out that, since the measured refractive
index data at different temperatures follow a parabolic fit, the dn/dT values are
temperature sensitive. The thermal expansion coefficient of alumina is large and
causes the density of thin films to decrease much more slowly than that of the bulk
material. As a result, it favors a large, positive value for the TOC of alumina [173].
The index is related to the increase in density of Al2O3 films and, since ALD- Al2O3
films are inherently dense due to their formation by ALD, they may be considered
almost free from pinhole surface defects [181].
91
4.4.4 Thermo-optic coefficient of TiO2 thin films in presence of thin diffusion
barrier layers of ALD-Al2O3
The high variations of the refractive index in a hot environment or in a relatively
high humidity causes a spectral instability in the central resonance peak of a guided
mode resonance and passband filter applications [60,162]. In high relative humidity
environment water molecules adsorbs on the film during deposition which
evaporate then in a heating environment, leading to a change in the thermo-optic
properties of the optical materials. In order to minimize the evaporation rate of
water molecules or hydrogenated species from the surface of TiO2 films, thin
inorganic gas diffusion barrier layers of Al2O3 are coated on TiO2 surfaces to enable
the stable operation of such optical devices by retaining their thermo-optic
properties in stringent environments.
Regarding these diffusion barrier layers, most of the previous work focuses on the
high water vapor evaporation rates through polymers, since it explains the behavior
of polymer materials to exhibit negative TOC [120]. The water vapor transmission
rates have been reduced by depositing inorganic diffusion barrier layers by atomic
layer deposition (ALD), typically Al2O3 as a single-layer or multilayer stacks on the
polymer [182,183] and Si [184] substrates. Several researchers have reported the
performance of single-layer Al2O3 films as barrier layers to control the water vapor
transmission rate on the polymer substrates [185,186]. In one study, the
permeability of water molecules was controlled by a deposition of Al2O3 followed
by the growth of a SiO2 layer [183]. Similarly, the ALD-Al2O3 layers have been
employed for surface passivation of III-V compound semiconductors to minimize
the electrical leakage current density [187].
In case of TiO2 films the impermeable behavior of Al2O3 films appears in terms of
sealing effects on the TiO2 films or improved nucleation of Al2O3 on porous TiO2
surface due to these defective sites. The measured permeation of H2O molecules
through single-layer inorganic Al2O3 films is attributed to the film defects caused
by the deposition technique being employed or by the substrate imperfections
[188]. The deposition process plays a significant role on the effective nature of the
inorganic gas diffusion barrier layers. The water vapor transmission rate through a
92
barrier layer of Al2O3 deposited by electron beam evaporation on polyethylene
naphthalate substrate is ~500 times larger than that of the Al2O3 barrier films coated
by ALD [189]. Atomic layer deposition is a technique that can produce uniform,
dense, conformal, and nearly pinhole free [190] thin Al2O3 films on the TiO2 films
as gas diffusion barrier layers.
Figure 4.28: (a) Porosity model on the near surface region of a TiO2 film. (b) Model for a TiO2 film
coated by an Al2O3 barrier layer.
In this research work, we report on the perspective of using the ALD-Al2O3
diffusion barrier layers in a slightly different way to investigate the evaporation of
water vapors, qualitatively and quantitatively, from the near surface region of
optical grade thin TiO2 dielectric films in terms of the rate of change of refractive
index with temperature. The idea is to enunciate the surface porosity model
speculated in our recent publication (see Ref. [156] and Fig. 4.28) as being
responsible of the change in refractive index of TiO2 films. The TOC of TiO2 films
is studied after ALD coating of Al2O3 barrier layers with a fixed and a variable
thickness. Furthermore, a study of the TOC of Al2O3 films fabricated by ALD
process is presented for the first time.
93
To this end, three different sets of samples are fabricated by ALD. In the first set the
Al2O3 barrier layer is of constant thickness ta ~6 nm but TiO2 films of different
thicknesses tt ~60−500 nm are considered [named as sample set SA(1–6)], all
fabricated by ALD. In the second set TiO2 films of constant thickness tt ~60 nm are
coated with Al2O3 barrier layers of different thicknesses ta ~6−36 nm [named as
sample set SB(1–6)]. Finally, in the third set we consider only Al2O3 films with
thicknesses ta ~60−500 nm to explicitly study their TOCs [named as sample set
SC(1–6)] that has already been described in section 4.4.3. Measurement of refractive
indices, data fitting and modeling, and TOC of all thin dielectric films was analyzed
and computed in a similar way to that has been described in section 4.4 for TiO2
films only, whereas the experimental results of TiO2 films coated by diffusion
barrier layers of ALD-Al2O3 of different thicknesses are presented in detail in
section 5.6.2, Chap. 5.
94
Chapter 5: Experimental results and discussion
In this chapter all the experimental results of the carried out research work with the
emphasis to explore the most cost-effective and simple fabrication methods for
efficient and functional nano-optical-devices (filters) despite their design with tight
tolerances are presented. The significance of polymeric materials in replicated
RWGs is highlighted by a number of advantages through experimental
investigations over inorganic materials such as flexibility (ductility), high toughness
values, low processing temperatures, accurate nano-processing and nano-imprinting
possibilities, high transparency for waveguide optical materials, high thermal
expansion and thermo-optic coefficients, and for light weight applications etc.
In section 5.1, we describe the technological achievements to fabricate a master
stamp using Hydrogen silsesquioxane (HSQ) e-beam resist on silicon substrate
without going through an etching process. The resist material shows a phase
transformation from HSQ to amorphous SiO2 without changing its amorphous
nature while improves it mechanical properties to be used as a direct stamping
material in nano-replication applications, the details are shown in our publication
[61].
In section 5.2 organic-inorganic RWGs as athermal nano-optical-devices based on
relatively high TEC and TOC of polymeric materials are presented where
experimental results are in relatively good agreement to those calculated
theoretically, for details see our publication [61]. Furthermore, an investigation of
using various polymeric substrate materials in RWGs and their effect on the
experimentally measured resonance properties is described in section 5.3, where
details are presented in our recent publication [120]. Section 5.4 shows the
polarization-independent characteristics of RWGs by fabricating two different types
of gratings. The experimentally measured results show a close agreement with
theoretically calculated results in one-dimensional polarization-insensitive gratings,
see our recent publication [112]. Furthermore, the research work relating to
95
inorganic, single layer RWGs on fused silica substrate is extended to investigate an
over-etch effect in fused silica substrate on the non-polarizing properties that is
shown in section 5.5 and details are described in our recent article [191]. To further
the existing research work on the RWGs, an explicit research study is performed on
thin optical films (TiO2, Al2O3), fabricated by ALD method to investigate their
TOC that is described in section 5.6 and details are presented in our article [156].
5.1 FABRICATION OF AN ETCHLESS MASTER STAMP
In this section we demonstrate high quality replication of grating structures, used as
RWGs, in thermoplastic thin films by using an HSQ stamp on a silicon substrate
with high imprint pattern fidelity. The stamp is made on an HSQ layer directly after
e-beam writing and the development process without employment of any reactive
etching process. The mechanical properties of the resist are improved by a heat
treatment process. The imprinted grating patterns are coated by cover layers of
amorphous TiO2 thin films of different thicknesses to perform the operation of
guided mode resonance filters (RWGs). A high refractive index amorphous material
such as TiO2 can act as a waveguide and couple the reflective diffraction orders
strongly and improve the diffraction efficiency of the structure. The spectral
characteristics of the replicated structures in thermoplastics are also investigated
and are shown to be in agreement with the theoretical calculations. The gratings are
replicated with the following geometric design parameters; periods d = 368 nm and
425 nm, fill factor f = c/d = 0.63, grating depth h = 120 nm, incident angle θ = 18°–
20°, TiO2 thicknesses t = 60 nm and 75 nm.
5.1.1 Fabrication and replication process
The process starts with a 2˝ diameter silicon wafer with <100> crystal orientation.
Using the Headway Spinner PWM101D the wafer is first spin coated with a high
resolution, negative tone resist HSQ (XR-1541) from Dow Corning, having
constituents isobutyl methyl ketone, hydrogen silsesquioxane and toluene. The
rotation speed (2700 rpm) and spinning time (60 s) were adjusted to get a resist
thickness of 120 nm, which is the designed height h of the grating structures. The
HSQ layer thickness was measured by a Dektak 150 stylus surface profilometer
96
manufactured by Veeco Metrology. Three different sets of grating patterns with
periods d = 425 nm, 368 nm and 540 nm and the structure height h ≈ 120 nm and
140 nm were written on the HSQ-resist, covering an exposed area of 5 mm x 5 mm.
A Vistec EBPG5000+ES HR electron beam patterning tool with 100 kV at a scaled
doze of 4800 μC/cm2 was used in the e-beam writing. The exposed patterns were
developed manually with the developer MP 351, which contains disodium
tetraborate decahydrate and sodium hydroxide, mixed with water to give a solution
with the ratio 1:3 (MP 351:H2O), followed by rinsing with isopropanol and water
for 90 and 30 seconds, respectively. After development, the sample was heat treated
for 180 minutes at a temperature of 300 °C in an oven.
Figure 5.1: Process flow for the fabrication and replication of a binary grating in polycarbonate from
HSQ stamp on Si substrate.
A post-treatment process, such as a thermal or a plasma treatment, or their
combination, influences the HSQ properties. For example, the geometry of HSQ
chain structure changes from a cage to a network structure without undergoing any
phase change of non-crystalline HSQ-resist [192]. These treatments transform and
97
improve the properties of the HSQ-resist, such as density, hardness etc. and make it
suitable to be used as a hard stamping material like SiO2.
The heat treated sample was then subjected to a surface treatment in nitrogen
environment to deposit a silane layer with silanization solution composed of a
mixture of HFE 7100 Engineering solvent with 0.2 % of trimethylhydroxysilane
(TMS). It acts as an anti-adhesive layer for stamping in a polycarbonate substrate.
The final patterns were transferred to polycarbonate sheets with a thickness of a few
hundred microns (from Makrofol DE). The replication process was performed by
nano-imprint lithography with Obducat Eitre imprinter shown in Fig. 5.1 as a
process flow. In the replication process the stamp was heated at a temperature of
165 °C, slightly above the glass transition temperature Tg of polycarbonate. After
heating the stamp, a pressure of 50 bar was applied for 120 s, followed by air
cooling at the final processing step. Replication was followed by deposition of high
index amorphous TiO2 films of different thicknesses t, grown by Beneq TFS 500
ALD reactor at the deposition temperature of 120 °C using TiCl4 and H2O as
precursor materials.
5.1.2 Effect of development and etching time
Figure 5.2 shows the grating structure with a period of d = 368 nm and a
corresponding linewidth w = 235 nm obtained with different development times.
The development time has an effect on the complete removal of the resist layer.
Structures in Figs. 5.2a and b were developed with the development times of 90 s
and 120 s, respectively. There appears some residue resist layer after the
development process (see Fig. 5.2a). Figure 5.3 shows the etching profiles of silicon
samples. Etching was performed with inductively coupled plasma + reactive ion
etching (ICP and RIE) sources based on hydrogen bromide (HBr) chemistry, by
using Oxford Instruments Plasmalab 100. The etching times were 180 s and 130 s
with a result of average depths of ~324 nm and ~244 nm in silicon as shown in
Figs. 5.3a and b, respectively. An interesting feature seen in Fig. 5.3 is that the
profile is not identical with the one in Fig. 4.9, rather with sloped sidewalls,
showing more etched area near the top surface of silicon. Such an etching profile is
98
a result caused by an under-developed area of the HSQ-resist layer as shown in Fig.
5.2a.
During etching of silicon, the profile of the under-developed resist mask is
transferred to silicon substrate through etch selectivity and results in an inclined
profile. Although it favors the replication process, it leads to a similar replicated
profile with slope, which finally causes a deviation of the grating response from the
designed one.
Figure 5.2: RWG structures with different development times of the HSQ-resist on silicon
substrate after e-beam exposure. (a) ~53 nm resist-free region. (b) ~68 nm resist-free region.
Figures 3.2 and 3.3 show SEM pictures of the HSQ-resist on top of a silicon
wafer, for a grating structure with d = 425 nm and 325 nm, after the heat
treatment. The shown grating profile is a master stamp (HSQ lines on silicon),
without having gone through a dry reactive ion etching treatment. The HSQ
mold has been used as a nano-replication stamp for more than 20 times and the
measured optical spectra after each replication is found similar to each other. In
addition, no aging effects have been found in the HSQ mold after more than 12
months.
Figure 3.6 shows the replicated grating structures in polycarbonate, Cyclic olefin
copolymer and Ormocomp® using the stamp shown in Fig. 3.3 and a hot
embossing process. However, the profile is not quite of the form assumed in Fig
4.9, mainly because of some rounding of edges of the replicated grating in
polymers that takes place primarily in the hot embossing step and the profile is
close to that with a depth of about 120 nm and 140 nm. The replicated gratings
are coated with a high refractive index layer of amorphous TiO2 grown by
99
atomic layer deposition. Figure 3.7 illustrates the conformal coverage of TiO2 on
the replicated grating profile. This means that the HSQ-resist can be used as a
direct stamping material by eliminating the dry etching process, which not only
reduces the cost and time but also enables replication of the structure very close
to its original stamp.
Figure 5.3: Etching profiles in Si with HBr-O2 with different etching times. (a) After etching 180 s with a
depth of ~324 nm. (b) After etching 130 s with a depth of ~244 nm. (c) Top and slightly tilted view with
an etching time of 180 s.
5.1.3 Optical spectra of grating structures
Grating structures with two different periods, d = 425 nm and 368 nm, were designed
as RWGs for the TE-Mode (Electric field is normal to the incident plane). The
refractive indices of polycarbonate and TiO2 are 1.570, 1.575 and 2.3264, 2.3465 at
wavelengths 855 nm and 740 nm, respectively. The performance of the designed
structures at three different angles of incidence (18–20°) are shown in Figs 5.4a and
b, in terms of spectral reflectance R and wavelength λ with full width half maximum
(FWHM) of ~11 nm. Figures 5.4c and d show the measured spectral reflectance R of
100
the replicated gratings in polycarbonate, with periods d = 425 nm and d = 368 nm,
having FWHMs of 13.5 and 11 nm, respectively. These spectra reveal that not only a
successful replication is achieved using the direct HSQ stamp but also the
experimentally obtained optical responses are in close agreement with the
theoretically designed values.
Figure 5.4: Calculated spectral reflectance (R) at three incident angles: (a) d = 425 nm. (b) d =
368 nm. Experimentally measured spectral reflectance (R) at three incident angles: (c) d = 425
nm. (d) d = 368 nm. Here Y is the peak reflectance and X is the corresponding wavelength.
The wavelength shift of the resonance peak from its designed value may be due
to slight variation of refractive indices of the materials encountered by the light.
The fabrication process itself is composed of a number of steps and parameters
with some limitations, a slight change of any parameter such as the structure
height, exact binary profile, fill factor, TiO2 thickness etc. may cause a shift of
the resonance peak. Additional spectral characteristics of the replicated gratings
with d = 425 nm were obtained by using high index ALD-grown TiO2 cover
layers of different thicknesses t. Figure 5.5a shows the simulated spectral
101
reflectance variation for two different TiO2 thicknesses t = 60 and 75 nm (here
index Y means reflectance). Figure 5.5b shows calculated and experimentally
measured lineshapes of the spectral reflectance for the two thicknesses at the
angle of incidence of 20°. Experimental results are in agreement with the
calculated ones, which is another indication of the high quality of the replicated
structures to be used as RWGs. Regarding the thermal stability of the imprinted
gratings, the performance of a grating was measured after heating it to a
temperature of 140 °C and cooling back to the room temperature shown in Fig.
5.6b. The measured optical spectra were found to be the same as the ones before
the heating with the same diffraction efficiency and profile.
Figure 5.5: (a) Simulated spectral reflectance variation as a function of TiO2 film thickness t. (b)
Calculated and measured spectral reflectance R of replicated gratings with TiO2 layer thickness t =
60 nm (blue curves) and t = 75 nm (brown curves) for the TE-mode at θ = 20° and d = 425 nm.
5.2 ATHERMAL MEASUREMENT OF ORGANIC-INORGANIC RWGs
In this section athermal response of waveguide gratings is investigated
experimentally in relation to the theoretical design and fabrication that have been
described in Sects. 4.1.1 and 5.1.1, respectively. The thermal behavior of the RWG
samples were measured and characterized by a variable angle spectroscopic
ellipsometry as described in section 3.6. The ellipsometer was employed to measure
the spectral reflectance resonance peak for TE-Mode at θ = 20° in the wavelength
range 750–880 nm with a beam spot size of 3 mm by scanning the wavelength with
steps of 0.2 nm. The polycarbonate grating was placed firmly against an aluminum
hot plate built in house whose temperature was controlled and monitored carefully.
102
The heating rate was 0.5 ± 0.1 °C/min during each measurement interval. The
surface temperature of the sample was measured using Convir ST8811 Handheld
Infrared Thermometer by Calex Electronics Limited Company with an accuracy of
± 2 °C. The calibration of both the Aluminum hotplate thermocouple and Convir
was checked by measuring simultaneously the temperature of heated water with a
good quality liquid thermometer. The Infrared thermometer is based on the
principle of detection of emitted thermal radiation from heated samples which
depends on emissivity of source materials. The emissivity of water is found exactly
equal to Convir as well as our polycarbonate substrate material (0.95).
The surface of the aluminum hot plate was rubbed with a fine sand paper to
eliminate any back reflections and it was tested by an initial transmittance and
corresponding reflectance measurement at room temperature without the presence
of hot aluminum plate. The comparison of both measurements at room temperature
(with and without aluminum hot plate) was made and matched prior to the start of
thermal measurements with hot plate. Since each thermal spectral measurement was
performed by a temperature interval of 5 °C, the material may be considered at
thermal equilibrium at each temperature interval. The refractive indices of ALD
coated TiO2 films at various temperatures were measured by ellipsometer and then
employed directly in calculations (section 4.1.2) on the behavior of central
resonance wavelength shift.
Figure 5.6a shows the spectral measurements at temperatures 30 °C, 35 °C and 55
°C. The difference in the peak reflectance is only about 0.4 nm between the spectra
at 35 °C and 55 °C. Figure 5.6a shows the measured shift in resonance wavelength
as a function of temperature, from 25 °C to 85 °C. The shift in the resonance
wavelength is about 1.4 nm for this large temperature range. The experimental
results are in relatively good agreement with the theoretical simulations predicting a
shift of about 0.7 nm for the temperature range from 25 °C to 100 °C (see Fig.
4.5b).
103
Figure 5.6: Spectral measurement of RWGs with TiO2 thickness t = 61 nm. (a) Spectral reflectance
curves at temperatures T = 30 °C, 35 °C and 55 °C. (b) Room-temperature spectral lineshape
subjected to thermal measurements up to T = 85 °C.
Figure 5.7: Thermal measurements of RWGs with TiO2 layer thickness t = 61 nm. (a) Peak thermal
spectral shift. (b) Peak resonance reflectance.
The most noticeable feature in the thermal behavior of the organic-inorganic RWGs
considered here is the reduction of the peak reflectance at high temperatures shown
in Figs. 5.7b and 5.8c. This cannot be attributed to changes of the structural
parameters in a perfectly periodic profile since such changes would only shift the
resonance wavelength, even if the profile is not of the ideal shape assumed in Fig.
4.9. The most plausible explanation for the reduced reflectance is uneven swelling
of the grating in the sense that the grating profile becomes increasingly space-
variant at high temperatures. As a result, the resonance conditions would depend on
position, which would widen the resonance peak and simultaneously decrease the
peak reflectance.
104
The useful temperature range depends on the reflectance value required by the
particular application and can be judged from Fig. 5.7. Importantly, the thermal
reduction of the peak efficiency is reversible: after cooling back down to room
temperature, the resonance peak efficiency returns to the original value and the
spectral line resumes its original shape within the measurement accuracy (see Fig.
5.6b). This is attributed to the recovery of the polymer (PC) within the relaxation
time of the PC.
Figure 5.8: Spectral measurements of RWGs with TiO2 layer thickness t = 71 nm. (a) Room-
temperature peak resonance lineshape. (b) Peak thermal spectral shift. (c) Peak resonance
reflectance.
To further elucidate the good correspondence between theoretical and experimental
results, we fabricated another set of samples with the same polymer grating profile
but a TiO2 layer thickness t = 71 nm. Figure 5.8a shows the measured lineshape of
such a grating, with room-temperature peak at 843.8 nm (at angle of incidence θ =
20°. In view of Fig. 5.8b, a shift of 0.4 nm in peak spectral position takes place at
30 °C. Thereafter, the peak position remains constant (within our measurement
105
accuracy of 0.2 nm), until a final shift of 0.8 nm occurs at 85 °C. The corresponding
peak reflectance values, shown in Fig. 5.8c, exhibit the same trend as for the grating
with 61 nm TiO2 layer thickness. The experimental peak position λr = 843.8 nm is
again some 3 % smaller than the theoretical value λr = 871.6 nm.
5.3 EFFECT OF DIFFERENT POLYMER SUBSTRATES ON RESONANCE
PROPERTIES OF RWGs
In this section we show experimentally measured results of athermal waveguide
gratings using various polymer substrate materials on their respective spectral
characteristics, shown in section 4.1.2 after a complete theoretical analysis. In this
research work, polymer materials PC and COC were obtained from Makrofol® DE
and TOPAS® advanced polymers, respectively, in the form of thin sheets with
thicknesses of a few hundred microns, while Ormocomp® was acquired from
Micro resist technology® in liquid phase. The replication process of PC and COC
gratings was carried out under the same experimental conditions except the
operating temperature of COC was set at 160 °C. The replication of Ormocomp®
was performed after filling the silane treated master grating stamp (mold) with
liquid Ormocomp®, followed by an initial uv-curing for 60 s. Then the molded
Ormocomp® film was solidified enough to allow its demolding without being
constrained by the stamp walls. The final step of the replication process was a
further uv-curing for 10 min. After structure replication, to make the RWGs the
polymer gratings were coated by a high index, amorphous TiO2 film with a
thickness t = 50 nm by an ALD process using Beneq TFS 200-152 reactor with
precursor materials TiCl4 and H2O at a low deposition temperature of 120 °C to
form the final structure shown in SEM Figs. 5.10.
A scanning electron microscope (SEM) picture of an HSQ stamp is illustrated in
Fig. 5.9a, and profiles replicated by hot-embossing and uv-curing processes are
shown in Figs. 5.9b–d. The replicated profiles follow closely the master HSQ
profile fabricated by the etch-free process. Figure 5.10 demonstrates the conformal
growth of the high-index amorphous TiO2 cover layer of thicknesses t = 50 nm. The
measured room temperature reflectance spectra of g-I, g-II, and g-III with
reflectance peaks at 698.6 nm, 631.4 nm, and 630.4 nm and peak reflection
106
efficiencies 0.71, 0.94, and 0.65, respectively, are shown in Fig. 5.11. The peak
resonances occur at different spectral positions and the diffraction efficiencies are
lower than those calculated in section 4.1.2, where we considered the ideal profile
in Fig. 4.9. The spectral shifts are due to errors in the dimensional profile of the
gratings, including the rounding of edges. The reduced peak efficiency is most
likely caused by scattering from surface roughness, slight irregularities in the
straightness of the grating lines, and voids percentage in polymers that cause
refractive-index variations at a microscopic scale.
Figure 5.9: SEM pictures. (a) An HSQ stamp with d = 325 nm, h = 120 nm, w = 205 nm. (b) A
replicated structure in PC with d = 368 nm, h = 120 nm, w = 232 nm. (c) A replicated structure in
COC with d = 325 nm, h = 120 nm, w = 205 nm. (d) A replicated structure in Ormocomp® with d =
325 nm, h = 120 nm, w = 205 nm.
107
Figure 5.10: SEM pictures of replicated structures coated by TiO2 cover layer of thickness t = 50 nm.
(a) Polycarbonate (PC). (b) Cyclic-olefin-Copolymer (COC). (c) Ormocomp®.
The experimentally measured thermal spectral shifts of the polycarbonate grating
(g-I) as a function of temperature are shown in Fig. 5.12a. We find a characteristic
positive slope of 0.010 corresponding to a thermal spectral shift of 0.8 nm in the
interval 25 °C ≤ T ≤ 100 °C. This result is in excellent agreement with the
theoretical calculations performed in section 4.1.2.1 (Fig. 4.6d), which indicated
partially athermalized behavior within the considered temperature range. The
measured data for copolymer grating g-II, shown in Fig. 5.13a, are not in equally
close agreement with the theoretical results in Fig. 4.7d. This is attributed to the
large value of modulus of COC, which makes it rigid and indicates the presence of
stresses in the material [193]. Several researchers have addressed this property
[194] and provide solutions in terms of composite materials made by mixing
flexible particles with the copolymer blends while maintaining its optical
transparency. The onset of heating relaxes such stresses and expands the material,
thus showing a predominance of the TEC effect, which results in a comparatively
larger spectral peak shift towards longer wavelengths in the measured RWGs.
108
Figure 5.11: Measured reflectance spectra of RWGs with various polymer substrates. (a)
Polycarbonate (PC). (b) Cyclic-olefin-Copolymer (COC). (c) Ormocomp®.
The measured thermal spectral shifts of the Ormocomp® grating (g-III), shown in
Fig. 5.14a are also not in complete agreement with calculations in Fig. 4.8d. It is
known that as the uv-induced consolidation process progresses, it results in
continually increasing compressive (shrinkage) strains [166], which also increase
the modulus of the material and ultimately shift the spectral peak towards shorter
wavelengths. Heating the material (in our study) relaxes these strains, which
increases the dimensions of the replicated pattern and thereby strengthens the
predominance of the TEC effect, causing a spectral peak shift towards longer
wavelengths. Hence, although COC and Ormocomp® (g-II and g-III) were found to
be excellent materials for athermal device operation according to the calculations,
the measured spectra show larger spectral shifts (1–2 nm). Therefore, polycarbonate
is in practice the preferable material for athermal devices.
109
Figure 5.12: Experimental measurements of g-I (PC). (a) Measured thermal spectral shift as a
function of temperature. (b) Measured spectral reflectance R(λ,T).
The observed effects may also be explained by means of the molecular orientation
of the polymer chains. The stress generation during mold filling may result in a
partial orientation of polymer chains along the principal stress directions [195]. The
molecular orientations can relax with increasing temperature over a certain time. If,
however, the temperature remains constant and material is uv-cured, the new
molecular orientations can easily be frozen in the glassy state of the polymer. These
new orientations of molecular chains may lead to anisotropy in the refractive index
of the material, and the most important factor is the frozen-in stresses. On placing
the consolidated material in a thermal environment, the stresses relax after
reorientation of the molecular chains. The relaxing phenomena may cause an
increase in the thermal expansion coefficient of the material, which results in larger
spectral shifts than predicted by our calculations. Furthermore, residual stresses can
also be generated due to a misfit of the TEC of the substrate and the coating during
the ALD growth. If the TEC of the thin film is larger than that of the substrate
material, film tends to expand by inducing a compressive stress due to a constraint
imposed by the substrate. Similarly, if the TEC of the thin film is smaller than that
of the substrate, a tensile stress can be generated in the film [196].
110
Figure 5.13: Experimental measurements of g-II (COC). (a) Measured thermal spectral shift as a
function of temperature. (b) Measured spectral reflectance R(λ,T).
The important feature in the thermal analysis of RWGs considered here is the
reduction in peak reflectance at higher temperatures shown in Figs. 5.12b, 5.13b
and 5.14b. This reduction of peak reflectance cannot be related to the variations in
the structural parameters of the periodic profile of the gratings since such changes
can only shift the resonance spectral position. However, the decrease in reflectance
may be caused by uneven swelling of the polymer gratings such that the profile
becomes increasingly space-variant at higher temperatures. Furthermore, this
thermal reduction of peak reflectance is reversible in the sense that after cooling
down the gratings to room temperature, the resonance peak retrieves its original
value and spectral lineshape within the measurement accuracy.
Figure 5.14: Experimental measurements of g-III (Ormocomp®). (a) Measured thermal spectral shift
as a function of temperature. (b) Measured spectral reflectance R(λ,T).
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5.4 FABRICATION AND DEMONSTRATION OF ONE-DIMENSIONAL
POLARIZATION-INSENSTITIVE RWGs
In this section the fabrication and resonance properties of two types of one-
dimensional polarization-insensitive RWGs are demonstrated. The design and
simulations of polarization-insensitive gratings have already been described in
section 4.2.
5.4.1 Fabrication of polarization-independent RWGs of Type-I and TiO2
planar thin films
We employed ALD, EBL, and RIE techniques to fabricate the Type-I RWGs. The
fabrication procedure is schematically presented in Fig. 3.4.The fabrication started
by cleaning the fused silica substrates with a diameter of 25 mm and a thickness of
0.5 mm with isopropanol followed by a dry nitrogen blow. After cleaning the
substrates, thin amorphous films of TiO2 with thicknesses of ~200 nm were coated
on the substrates by ALD, using Beneq TFS 200-152 reactor. The commonly
known precursor materials TiCl4 and H2O were used at a low deposition
temperature of 120 °C, with chamber and reactor pressures of 6.80 mbar and 1.59
mbar, respectively. Nitrogen was used as the carrier for the precursor materials and
as a purging gas after each precursor pulse during a cycle. The flow rate of TiCl4
precursor was 200 sccm (standard cubic centimeter) with a pulse duration of 150
ms, which was followed by a purging for duration of 750 ms. For H2O precursor,
the flow rate was maintained at 300 sccm for a pulse duration of 150 ms with a
subsequent purging for 1 s. The growth rate of the deposited films was 0.065 nm
per cycle which was measured by the Dektak 150 stylus surface profilometer from
Veeco Metrology, and by an ellipsometer.
The ALD process was followed by the sample coating with a thin Cr layer of
thickness ~30 nm by electron beam evaporation at a vacuum level of 1.5 × 10-6
mbar at a deposition rate of 2 Ås-1
using the Lebold L560 vacuum evaporator from
Lebold Heraeus. The Cr coated sample was then prepared for a deposition of a thin
layer of positive electron beam resist ZEP 7000 22 by a spin coating process at a
spinning speed of 2900 rpm for 60 s using Headway spinner PWM101D from
Headway research Ltd. The resist layer was soft baked at a temperature of 180 °C
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for 180 s on a hot plate to evaporate the solvents. The resist was then patterned on
an area of 7 × 7 mm2 by an electron beam writer EBPG5000 + ES HR from Vistec
Lithography at a scaled dose of 200 μC cm-2
. After e-beam exposure the sample was
developed with 99 % Ethyl 3-ethoxypropionate (EEP) from Aldrich Ltd. for 60 s,
followed by rinsing with isopropanol for 30 s and deionized water, finally dried
with a blow of nitrogen. After the e-beam exposure and development processes, the
sample was etched by RIE. The Cr mask was dry-etched at a low pressure process
(15 mtorr) in the presence of Cl2 and O2 reactive gases together with inductively
coupled plasma (ICP) at 1500 watt using Plasmalab 100 from Oxford Plasma
Technology. A total flow of ~58 sccm was maintained for a Cr-etching time of ~95
s. The Cr-etching was followed by a resist removal employing O2 plasma at 100
watt RF power and a flow rate of 20 sccm for 180 s using March CS-1701 from
Microtech-Chemitech AB. The O2 plasma not only etches the resist layer and the
constituent ashes but also cleans the sample thoroughly for the subsequent TiO2
etching.
The TiO2 etching was carried out using the reactive gases SF6 and Ar plasma with a
total flow of 15 sccm at 300 watt RF power, at 20 mtorr process pressures, and with
different etching times by using Plasmalab 80 from Oxford Plasma Technology.
After completion of the TiO2 etching process, the sample was cleaned with O2
plasma with the same parameters as mentioned above. The final process step was to
remove the Cr layer by wet etching from the entire sample surface. This step was
performed in a mixture of Ammonium cerium (IV) nitrate from Sigma-Aldrich,
acetic acid, and deionized water for sufficient duration to completely remove the
Cr-layer. The Cr wet-etching was followed by rinsing with deionized water drying
with nitrogen blow to complete the fabrication of TiO2 RWGs. The SEM images of
finally fabricated RWG structures of type-I are shown in Fig. 5.15.
5.4.2 Fabrication of polarization-independent RWGs of Type-II
The fabrication and replication of the Type-II RWG were performed with the
methods presented in Ref. [61] and schematically illustrated in Fig. 5.1. In brief, the
master stamp grating was fabricated on a Si wafer by EBL with a negative e-beam
binary resist HSQ without any etching process. Then, replication in thermoplastic
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was realized using an Obducat Eitre imprinter at a temperature of 165 °C which is
above the glass transition temperature Tg ~ 150 °C of polycarbonate. After the
nanoimprinting, the polycarbonate substrate was covered by an amorphous TiO2
layer by ALD process at a deposition temperature of 120 °C using commonly
known precursors TiCl4 and H2O. The SEM images of the finally prepared PC-TiO2
RWGs are shown in Fig. 5.16.
Figure 5.15: SEM images of the fabricated TiO2-SiO2 RWGs of Type-I.
Figure 5.16: SEM images of the finally fabricated PC-TiO2 non-polarizing RWGs of Type-II.
114
It is seen from Figs. 5.15 and 5.16 that the fabricated profiles of both types of
RWGs deviate slightly from the theoretical designs, which are slightly circular
domed rather than purely rectangular ones. This is unavoidable in the practical
etching (for the Type-I grating) and master grating fabrication (for the Type-II
grating) processes. Furthermore, the uncertainty of the refractive indices of
materials, especially that of the ALD-prepared TiO2, also sensitively influences the
practical resonance properties of the RWGs. For these reasons, our fabrication
processes, though mainly guided by the theoretical designs, still have to be tuned a
little by reducing temperature interval for example such that material approached
thermodynamic equilibrium so as to get the best structural parameters to
demonstrate the non-polarizing RWGs effect.
5.4.3 Spectral resonance characteristics of the fabricated non-polarizing
RWGs
The optical properties of the fabricated RWG samples were characterized by a
variable angle spectroscopic ellipsometer VASE from J. A. Woollam Co. The
ellipsometer was set to measure the spectral transmittance of the gratings under
normal incidence of TE and TM polarized light. The collimated beam spot diameter
is 3 mm, which is sufficiently smaller than the grating area of 7 × 7 mm2. The
scanning wavelength step is 0.2 nm in measurement in the wavelength range from
700 to 1000 nm.
Figure 5.17: Experimentally measured transmittance spectra: (a) Type-I and (b) Type-II RWGs.
115
The measured zeroth-order transmittance spectra of the two fabricated grating
samples are plotted in Fig. 5.17, both of which show the non-polarizing guided
mode resonance GMR effect around a wavelength of 840 nm. The small shift of the
resonance wavelength (10 nm from the expected 850 nm) is mainly due to the
deviation of the practical grating profiles from the designed ones, as shown above in
Figs. 5.15 and 5.16. In principle, we can tune the resonance wavelength to 850 nm
by further parameter adjustment (for example, by increasing the period d of the
grating or varying linewidth w) in the fabrication process. But the current
fabrication results already demonstrate well the expected non-polarizing GMR
effect at a wavelength very close to the designed one. Furthermore, by comparing
Figs. 5.17a and 5.17b with Figs. 4.11b and 4.13, respectively, we can see very good
correspondence between theory and experiment; the main resonance features such
as the lineshapes, the resonance linewidths, and the diffraction efficiencies are well
reproduced in experiment. These show the reliability of the theoretical design and
the fabrication processes.
The measurement results are also the first experimental demonstration so far on the
realization of polarization-insensitive 1D GMR gratings under normal incidence. By
inspecting the spectra of the Type-I GMR grating in Fig. 5.17a, we can see that the
TE and TM resonance peaks are almost at the same wavelength, with a small
difference of 2.4 nm; the linewidths of the two resonances are also very close to
each other, with a full width at half maximum of 30 nm for TE and 38 nm for TM.
Therefore, the Type-I grating exhibits the non-polarizing GMR effect almost
perfectly. The Type-II grating also demonstrates very good non-polarizing effect
(with only 1.4 nm difference between the TE and TM peak wavelengths), but has a
larger difference between the TE and TM resonance linewidths and the sidebands
are not as well suppressed, as seen in Fig. 5.17b.
The structure needs to be further optimized to improve the filtering property (for
example, by adding underneath alternate layers of different refractive indices to
suppress the sidebands). Nevertheless, owing to the easier fabrication process and
much lower manufacturing cost, the Type-II grating has good perspective for
116
practical applications. We are taking further study to improve its resonance
performance while maintaining the relatively simple geometry.
5.5 AN OVER-ETCHING EFFECT IN FUSED SILICA SUBSTRATE ON NON-
POLARIZING PROPERTIES OF RWGs
In this section the degeneracy of the TE- and TM-modes of non-polarizing SiO2-
TiO2 (Type-I) RWGs that has already been described in section 5.4.3 are
investigated by considering an over-etch effect in fused silica substrate. The
theoretical analysis performed in section 4.3 shows that the non-polarizing
characteristics are split with increasing an ever-etch depth in fused silica (see Fig.
4.16).
Figure 5.18: XRD patterns of the TiO2 thin films of thicknesses ~200 nm deposited on fused silica
by ALD. (a) As-deposited amorphous phase and (b) heat-treated crystalline phase (anatase).
5.5.1 Structural and optical characterization of SiO2-TiO2 (Type-I) RWGs
and TiO2 thin films
The structural characterization of the TiO2 RWGs and thin TiO2 amorphous and
crystalline films were performed by a scanning electron microscope (SEM LEO
1550 Gemini). The samples were sputter coated by a thin ~10 nm conductive layer
of Cu in a sputter coater K675X. The RWGs and thin TiO2 films were heat treated
in an oven at a temperature of 300 °C for 7 hours to change the phase of the TiO2
material. The phase of TiO2 thin films (without plasma treatment) was
characterized by X-ray diffraction (XRD). For the powder diffraction experiment
117
we used Bruker Advance D8 in Bragg-Brentano geometry using a step-scan
technique and Göbel mirror to produce Cu K-alpha radiation (1.54184 Å, 40 kV,
40 mA). The data was collected by a scintillation detector using a continuous
scanning mode in 2θ range of 8–70° with a scan step size of 0.05° and a counting
time of 6 s per step. The spectral characterization of the RWGs (transmission
spectra) and TiO2 thin films (optical constants and transmission spectra) were
characterized by a variable angle spectroscopic ellipsometer. The ellipsometer was
employed to measure the spectral transmittance resonance peak for the TE- and
TM-modes at normal incidence in the wavelength range 700–1000 nm at a
wavelength scan step and a beam spot size of 0.2 nm and 3 mm, respectively. The
refractive indices of amorphous and crystalline TiO2 films prepared by ALD were
measured by an ellipsometer and the optical constants were retrieved after
modeling the measured data as has been discussed in section 4.3.3 (see Fig. 4.18).
5.5.2 TiO2 thin films on fused silica substrate
The XRD patterns of the thin TiO2 films are shown in Fig. 5.18. The as-deposited
films possess amorphous phase (Fig.5.18a) and the ones subjected to a heat
treatment at a temperature of 300 °C for 7 hours clearly show a crystalline phase
with various intensity peaks at anatase positions [197], as seen in Fig. 5.18b.
Figure 5.19: Refractive index of the TiO2 thin films of thicknesses ~200 nm deposited on fused
silica by ALD using precursors TiCl4 and H2O with nitrogen as a carrier gas at a deposition
temperature of 120 °C and a growth rate of 0.065 nm per cycle. (a) As-deposited TiO2 amorphous
phase. (b) Heat-treated TiO2 crystalline phase (anatase) at 300 °C for 7 h.
118
The refractive indices of the as-deposited amorphous and heat treated crystalline
TiO2 films are shown in Fig. 5.19. The measured data from an amorphous film fits
the model as was shown in Figs. 4.18a and 4.18b and reveal a smooth refractive
index change with the wavelength, shown in Fig. 5.19a. On the other hand, the
measured data of a crystalline film have some fluctuations after fitting under the
same conditions as for the amorphous film (Figs. 4.18c and 4.18d) and the
corresponding refractive index data are shown in Fig. 5.19b. This may be
attributed to the fact that after a phase change, some defects are induced to the
TiO2 material which may cause scattering. The indication of these defects is the
increased propagation losses in the films, which have been measured in a
waveguide configuration (not shown here).
Figure 5.20: SEM pictures of TiO2 films on fused silica substrate. (a) As-deposited amorphous
film. (b) Heat-treated crystalline TiO2 film.
Figures 5.20a and 5.20b show the scanning electron microscope pictures of the
amorphous and crystalline films deposited on fused silica, respectively. Figure
5.21 shows the measured transmittance of amorphous and crystalline TiO2 films at
wavelength range 380–1800 nm with a scan step of 2 nm. The spectra show that
TiO2 films are transparent over a wide spectral (visible to infrared) range and the
transmittance of both amorphous and crystalline phases is about the same.
119
Figure 5.21: Measured transmittance at a wavelength range 380–1800 nm of TiO2 films deposited on
a fused silica substrate by ALD method. (a) As-deposited TiO2 amorphous phase. (b) Heat-treated
TiO2 crystalline phase.
5.5.3 TiO2 RWGs on fused silica substrate
Figure 5.22 shows the scanning electron microscope pictures of the fabricated
gratings after etching to and into the fused silica substrate surface at different
depths. Both of the TiO2 and fused silica etchings were performed under the same
experimental conditions using the reactive gases SF6 and Ar. RIE etching is
facilitated by the addition of Argon (Ar) to enhance the ion-assisted removal of etch
products and to provide the ignition of the plasma at lower pressures. Furthermore,
the addition of an inert gas to a discharge is used to stabilize the plasma and to
control the etchant concentration, which affects the etch rate of TiO2. The increase
in TiO2 etch rate at relatively higher Ar partial pressures (keeping overall gas
pressures constant) is most likely due to an increase in ionic bombardment at the
TiO2 surface [198]. Therefore, a strong physical component (Ar) is beneficial in the
etching process for a high bond-strength material like TiO2. Typically, the Ar
etching constitutes the physical component and the presence of SF6 or Cl2 give the
chemical component to the etching process.
Most often the etch rates of TiO2 by SF6/Ar are higher than by Cl2/Ar and the etch
rates of individual chemical components SF6 or Cl2 are higher than that of Ar alone.
In addition, the other parameters such as the dc bias and the chamber pressure have
influence on the etching process. The increase in the dc self-bias will increase the
etch rate in terms of both bond breaking and by removal of the sputtered desorption
120
etch products. Therefore, the average incident ion energy is the sum of the dc self-
bias and the plasma potential [199]. The etch selectivity of TiO2 is strongly affected
by the RF sample power. As the sample bias is increased, the TiO2 etch rate
increases which is most likely attributed to the increase in ion bombardment energy
related to the higher RF sample power [189].
Figure 5.22: Scanning electron microscope images of TiO2 RWGs etched to different depths. (a), (b)
Etched to the surface of the substrate (fused silica). (c) Over-etched 39 nm in the substrate. (d) Over-
etched 73 nm in the substrate. (e) Over-etched 97 nm in the substrate and (f) over-etched 128 nm in
the substrate.
121
The increase in pressure leads to an increase in random collisions among the
particles and results in a decrease in directional etching i.e., the ionic bombardment
is reduced due to an increase in the number of random particle collisions. Hence,
low chamber pressures are preferred in achieving an anisotropic etching profile.
Figure 5.23 shows the transmittance of the TiO2 waveguide gratings with no over-
etching, for both polarizations. The measured spectra of both the TE- and TM-
modes have a center resonance dip around 850 nm which is the same as that of the
theoretically predicted, as was shown in Fig. 4.11b (in terms of reflectance). This
result demonstrates an excellent agreement between the theoretical and
experimental results for a non-polarizing grating.
Figure 5.23: Measured transmittance, at normal incidence of the fabricated TiO2 RWGs with a
slightly slanted profile with a period d = 544 nm, a linewidth w = 407 nm and a structure height hc =
201 nm. (a) TiO2 amorphous phase. (b) Heat-treated TiO2 phase.
The same grating does not show any significant change in the spectra after a heat
treatment process. The theoretical prediction for the heat treated gratings (see Fig.
4.19) was that the resonance peak shifts towards longer wavelengths, from 850 nm
to 877.5 nm for the TE- and to 869 nm for the TM-mode. The prediction was based
on the increase in refractive index of TiO2 from 2.32 to 2.43 (see Fig. 5.19) after a
phase transformation from amorphous to crystalline, as was shown in Fig. 5.18. The
experimentally measured spectra of all the heat treated gratings exhibited a spectral
shift of only 0.6–1.0 nm for the central resonance wavelength. This result may be
attributed to the fact that after RIE and a plasma treatment of TiO2, the surface
chemistry of the grating might be modified due to re-adsorption of the byproducts
122
of the etched material. The chemical component of SF6 may react with the TiO2
surface and re-deposit as titanium fluoride or other byproducts [200] which do not
possess any further change in dielectric constant even after a heat treatment process.
The SEM pictures reveal the presence of byproduct particles on the grating
surfaces; see for example Fig. 5.22c. The investigation on the chemical analyses of
the plasma treated surfaces can be conveniently conducted using Energy Dispersive
Spectroscopy (EDS) that was not available in the current SEM setup.
Figure 5.24: Measured resonance wavelength λr at normal incidence, with the overetching depth hs in
the fused silica substrate of fabricated RWGs with a period d = 544 nm, a linewidth w = 407 nm and
a structure height hc = 201 nm. (a) Both the TE- and TM-Modes and their effect on the non-
polarizing property of amorphous TiO2 gratings. (b) Both the TE- and TM-Modes and their effect on
the non-polarizing property of the heat-treated TiO2 gratings.
The average investigated etching rate of ALD coated amorphous thin TiO2 films on
fused silica using a total flow of 15 sccm of SF6/Ar gases is 49 nm/min, whereas 65
nm/min in fused silica substrate under the same experimental conditions. Each TiO2
waveguide grating was spectrally characterized after an additional over-etched
depth hs approximately 32 nm in the fused silica substrate, corresponding to an
etching time of 30 s. The shift in the resonance wavelength for the waveguide
gratings with an additional 30 s etch is shown in Fig. 5.24, as a plot of λr as a
function of hs. The observed resonance peak shifts both for the TE- and TM-modes
are in agreement with the ones shown in Fig. 4.16c with a parabolic fit for the TE-
and a linear fit for the TM-mode.
The experimental shift in resonance wavelength for the TE-mode is ~3 times more
than that predicted theoretically. This difference might be due to a deviation of the
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grating profile from the ideal one as was shown in Fig. 4.15. During a number of
steps in the entire fabrication process, the grating profile has slanted sidewalls
instead of ideally vertical. The angular variations in the sidewalls have an effect on
the linewidth of the structure and on the propagation constant of the excited leaky
modes by influencing the effective index of the structure. Similarly, the measured
shift in the TM-mode is more than twice the value predicted theoretically. There is
no significant difference in the measured spectral shifts of the heat treated gratings
shown in Fig. 5.24b, which might be attributed to a change in the surface chemistry,
as a result in the various physical and chemical interactions with the dielectric film.
5.6 THERMO-OPTIC COEFFICIENT (TOC) OF THIN FILM OPTICAL
MATERIALS (TiO2 AND Al2O3) FABRICATED BY ALD
In this section experimental investigation of the TOC of TiO2, Al2O3 and
combination of both films is measured and calculated over a wide wavelength region
of 380 ≤ λ ≤ 1800 nm as has already been described in section 4.4 (Chap. 4). The
fabrication of the TiO2 and Al2O3 films on silicon substrates (n-type with
phosphorous dopant) of diameter 50.80 mm, thickness 380 ± 25 μm and crystal
orientation <100> is accompanied by employing ALD. The fabrication process
started with the cleaning of silicon wafers with isopropanol (IPA), followed by a
blow drying with dry N2. Subsequent to substrate cleaning, thin amorphous films of
TiO2 and Al2O3 of different thicknesses were grown on the substrates using Beneq
TFS 200-152 ALD reactor. The commonly known precursor materials used for TiO2
and Al2O3 films were TiCl4/H2O and Al(CH3)3/H2O, respectively. We used a low
deposition temperature of 120 ºC, with chamber and reactor pressures of 6.80 mbar
and 1.59 mbar, respectively. Nitrogen (N2) was used as a carrier gas for all the
precursors and as a purging gas after each precursor pulse during an ALD cycle. The
chamber and process flows for both the TiO2 and Al2O3 films were 200 sccm
(standard cubic centimeter) and 300 sccm, respectively. The pulse durations of TiCl4
and Al(CH3)3 were 150 ms followed by a purging pulse for 750 ms. For H2O
precursor, a pulse duration of 150 ms with a subsequent purging pulse for 1 s was
applied. The growth rates of the deposited TiO2 and Al2O3 films were 0.065 and
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0.12 nm per cycle, as measured by the Dektak 150 stylus surface profilometer
(Veeco Metrology) and by an ellipsometer.
5.6.1 Experimental results of thermo-Optic coefficient of TiO2 thin films
Table 4.2 shows the experimentally measured temperature dependence of the
refractive index and the density of an ALD-grown TiO2 film of thickness t = 60 nm
at wavelength λ = 640 nm. The decrease of the refractive index with temperature
corresponds to an average value of dn/dT = −4.2 ± 0.7×10−5
°C-1
, which is of the
same order of magnitude as reported in Ref. [173] but an order of magnitude smaller
than that reported in Ref. [174]. This reflects the dependence of the thermo-optic
coefficient on the deposition technique and the substrate material. The packing
density of TiO2 films is an important parameter contributing to the index values:
denser films fabricated by ALD have a lower index gradient than films with higher
porosity, fabricated by sputtering or vacuum evaporation. This effect has already
been interpreted as resulting from the presence of hydrogenated species in the pores
of TiO2 films: heating causes replacement of water molecules with air in the pores
[201]. Due to the atomic-level deposition nature of ALD, the resulting films
inherently exhibit high density (thus being less porous) and therefore the index
gradient is relatively small. The density values given in the third column of Table
4.2 are slightly above the highest values obtained by the ion plating method reported
in Ref. [170].
All the films were fabricated at a temperature below 165 °C and thus they possess
amorphous phase characteristics [58]. Figure 5.25 shows a scanning electron
microscope picture of a cleaved amorphous TiO2 film with thickness ~200 nm,
deposited on a silicon substrate. Figure 5.26 shows the temperature-dependent
refractive index and density of all fabricated films as a function of wavelength. The
thermal coefficients dn/dT and dρ/dT are negative for the thinnest films (t = 60 nm
and t = 100 nm) but turn positive and stabilize when t is increased. This behavior is
illustrated in Fig. 5.27, which shows more explicitly the variation of the thermal
coefficients with film thickness.
125
Figure 5.25: Scanning electron microscope image of a cleaved amorphous film of thickness ~200 nm
grown by ALD on a Si substrate.
Figure 5.26: Thermal and spectral dependence of the material properties of TiO2 films of variable
thicknesses: wavelength (λ) dependence of the (a) thermo-optic coefficient dn/dT. (b) Density
coefficient dρ/dT.
To understand qualitatively the thermal properties of thin TiO2 films we recall that
such films have pores close to the surface, which at room temperature are filled with
hydrogen-containing species [51,172]. Such species vaporize on rising temperature,
leaving the pores empty, and therefore the effective refractive index and density in
the porous region decrease. For thin films such a ‘depletion region’ extends through
the entire film. For thicker films (200–500 nm), desorption affects only the region
126
close to the surface and gives rise to a refractive-index gradient. As the film
thickness increases, the desorption has a smaller effect on the average refractive
index and density of the film. As a result, the thermal coefficients dn/dT and dρ/dT
are positive for the film thicknesses larger than ~150 nm.
Figure 5.27: Variation of the thermal properties of TiO2 films with thickness t.
5.6.2 Experimental investigation of thermo-Optic coefficient of TiO2 thin
films in presence of thin diffusion barrier layers of ALD-Al2O3
Thin-layer barrier properties of Al2O3 films of uniform thickness on the TiO2 films
of different thicknesses were investigated by measuring and modeling the TOCs
using the method described in section 4.4.3. Figure 5.28a shows the determined
TOCs of all the films in the sample set SA(1−6). The TOCs of TiO2 films in the
presence of a thin Al2O3 barrier layer show the same behavior as was reported in our
recent publication [156]. The TOC of the thinnest TiO2 film ~60 nm is found to be
the most negative due to higher evaporation rate of H2O molecules near the surface
region. However, the effect decreases with a more positive change in TOC value as
the thickness of TiO2 films increase as shown in Fig. 5.28a. Figure 5.28b shows the
change in the TOCs of the TiO2 films of different thicknesses with a uniform thin
127
barrier layer of ALD-Al2O3 (~6 nm). The thinnest TiO2 films yield an effective
response with temperature, i.e., the presence of a thin Al2O3 barrier layer ~6 nm does
not show effective impermeable properties. It has been suggested that there might
exist some pinhole defects on Al2O3 films, which cause the thermo-optic coefficient
to vary less rapidly at lower barrier layer thicknesses [183, 202]. Thus we need to
evaluate the validity of our proposed model by increasing the ALD-Al2O3 barrier
layer thickness in equal steps. Thereby, we characterized the sample set SB(1−6)
composed of six samples of the same TiO2 thickness (~60 nm) with different
thicknesses of ALD-Al2O3 barrier layers.
Figure 5.28: Thermal and spectral dependence of the thermo-optic coefficient dn/dT of TiO2 films of
various thicknesses in presence of a thin Al2O3 barrier layer of thickness ta ≈ 6 nm. (a) Wavelength
(λ) dependence of the thermo-optic coefficient dn/dT. (b) Variation of the thermo-optic coefficient
with thicknesses tt of TiO2 films at a wavelength of 640 nm.
Figure 5.29a shows the TOCs of TiO2 films of thickness ~ 60 nm coated with barrier
layers of ALD-Al2O3 of various thicknesses ta. The TOCs decrease slightly with the
increase in the Al2O3 thickness over a wide range of wavelengths λ = 380−1800 nm.
Increasing the barrier layer thickness does not change the dn/dT values much. Figure
5.29b shows the dn/dT variation with the thickness of the barrier layers at a
wavelength of 640 nm. We obtain a linear fit of the form
,1035.11044.1d
d 46 atT
n (5.1)
128
where ta is the thickness of Al2O3 barrier layer and the coefficients of ta and ta0 are
expressed in units of ºC-1
nm-1
and ºC-1
, respectively.
The physical interpretation of the slope of Eq. (5.1) describes the activation energy
(per degree rise in temperature per nm) required for the water molecules to permeate
through the ALD-Al2O3 barrier layers. A requirement for higher activation energy
dictates a steep slope, which results in relatively low negative dn/dT for TiO2 films.
An overall 33 % change in the dn/dT values is determined experimentally after
reaching a barrier layer thickness of ~36 nm, which demonstrates well the
impermeable properties of the barrier layers due to impeding the evaporation of
hydrogenated species at the near surface region of TiO2 films. From Fig. 5.29, it is
evident that the barrier layers could not reveal a more significant change in the
reduction of TOCs of TiO2 thin films. This might be attributed to the existence of
some pinhole defects due to the low growth temperature. Also, the Al2O3 films most
often form the hydrate since they are amorphous and have a smaller positive Gibbs
free energy of ΔG = +6 kcal/mol at 100 ºC [183]. These limitations can be improved
by using multi-layers of dielectric materials. One important aspect of depositing thin
and amorphous Al2O3 barrier layers is to preserve the inherent characteristics of high
index optical quality thin TiO2 films used in waveguide applications. Too thick
barrier layers may deteriorate the optical properties of TiO2 thin films in terms of
scattering of the optical signal due to crack formation owing to the fragile nature of
the material [183].
Comparing our results with Al2O3 diffusion barrier layers in terms of TOC with the
already reported results for the water vapor transmission rates [185], both show
almost similar improvement of the impermeable properties of Al2O3 barrier layers.
The reported results showed that the water vapor transmission rate reduces with an
increase of the thickness of Al2O3 films. On the other hand, our results demonstrate
that with the increase of Al2O3 thickness the negative value of TOC of TiO2 film
decreases mainly because of the barrier properties of Al2O3 films and the inherently
positive value of the TOC of the Al2O3 films. On the other hand, the TOC of TiO2
films changes its sign when the thickness of the TiO2 films increases. This might
129
cause instabilities in the performance of optical devices, or it may be an advantage in
filtering applications in integrated optical technology.
Figure 5.29: Thermal and spectral dependence of the thermo-optic coefficient dn/dT of TiO2 films of
a fixed thickness tt ≈ 60 nm in the presence of Al2O3 barrier layers of various thicknesses: (a)
Wavelength (λ) dependence of the thermo-optic coefficient dn/dT. (b) Variation of the thermo-optic
coefficient with thickness ta of Al2O3 barrier layers at a wavelength of 640 nm.
5.7 INTERPRETATION
The simulated and experimentally measured spectra shown in sections 4 and 5 possesses
slightly different spectral peak positions and full width at half maxima (FWHM), primarily
because of the variations in the surface profile shape, dimensions and true refractive indices
of the materials. The fabricated resonant gratings surface profile varies because there are
several fabrication steps involved. The dimensions of the fabricated structures are made as
close to the one assumed in the ideal profile of the design shown in Figs. 4.1, 4.9 and 4.15.
However, the profile is not quite ideal mainly because of rounding of the edges of the
polycarbonate grating that might occur either during the master stamp fabrication or nano-
imprinting. The SEM figures show that the TiO2 growth follows the polycarbonate profile
conformably which is inherent to the ALD process. Secondly, in the measured spectra the
off-resonance points do not cross the zero-line that is present in theoretical curves.
Furthermore, a slight variation in the dimensional parameters of the profile (h,w,t) and
refractive indices of materials might result to a spectral shift. Thirdly, figures 5.7, 5.8, 5.12,
5.13 and 5.14 show the spectral wavelength shift Δλ as a function of temperature T which is
illustrated as discrete steps with a fraction of nanometer step. The spectral shifts in these
discrete steps might arise due to analytical resolution of the measuring equipment.
130
Chapter 6: Conclusions
This thesis provides two-fold optical demonstrations: that is the resonant waveguide
gratings RWGs structures and thermo-optic coefficients of thin films with a new
perspective to employ to nano-optical devices as efficient sensors in a number of
applications. The RWGs with simple geometrical structures have been investigated
in a variety of organic and inorganic materials using the most simple and cost-
effective methods with the impact of atomic layer deposition in these devices.
The fabrication and replication of nanophotonic components with subwavelength
features in polymeric materials is the primary goal and is the most promising
technology to make narrow linewidth resonant filters that are efficient, reliable,
environmentally stable, low-cost and facilitate large scale production. In general,
replication process is an economic process that requires a master stamp (mold) that
is quite often fabricated together by electron-beam lithography (EBL) and reactive
ion etching (RIE) which may raise cost, inaccuracies and reduce efficiency and
performance. In this research work the master stamp is prepared by EBL, employing
a binary negative electron beam resist, Hydrogen silsesquioxane (HSQ) without
carrying out an etch action. The replicated profile of the RWGFs with an appropriate
structure depth is obtained successfully by selecting a suitable spinning speed for the
required coating, development time of resist for the preparation of master stamp on
silicon substrate i.e., the grating patterns were written on the HSQ layer by e-beam
exposure. After a development process, RIE step is replaced by a heat treatment of
the HSQ resist where the mechanical properties of HSQ resist such as density,
hardness were improved. During heat treatment process, the HSQ segmental chain
geometry transforms from a cage to a network without any phase change in the non-
crystalline behavior of the resist. The cage to network transformation shows SiO2
properties which are suitable to be used as a direct master stamp for polymers.
Omitting the etching process not only brings down the fabrication costs but also
reduces the inaccuracies in the depth of the fabricated structures more appropriately.
The reported simple etch free process provides fast prototyping of nano scale optical
devices with a short processing time and high pattern imprint fidelity, high quality
131
optical performance, and wide applicability to large scale production. The fabricated
master stamp is employed to replicate subwavelength grating structures in polymers
with different applications depending on the requirement.
The replicated structures in polymers form a hybrid organic-inorganic resonant
waveguide grating filter with the use of atomic layer deposition to grow a thin layer
of TiO2 as the waveguide layer. This is a low-cost fabrication method, which is
suitable for large-scale production. Both theoretical simulations and experiments
show that nearly athermal operation can be achieved with such filters despite the
large values of thermo-optic and thermal expansion coefficients of the polymer
substrate. The operation of these filters was described with an empirical two-
coefficient-parameter model constituting thermal expansion and thermo-optic
coefficients. This is a result of opposite signs of spectral resonance-peak shifts
caused by the two effects incorporated as two-coefficient-model.
The use of high index dielectric TiO2 films as a superstrate or formation of
multilayered structures that are influenced strongly by environmental factors such as
heat, humidity that results in a spectral shift based on varying refractive index with
temperature. Such environmentally influenced spectral shifts were counter-balanced
by exploiting high thermal expansion (almost 10 times more than that of dielectrics)
optical polymeric materials. Moreover, the obtained results dictate that even more
exact athermalization could be achieved using, e.g., polymers with slightly lower
thermal expansion coefficients. This would be of interest for filter designs with
substantially narrower resonance reflection band (in the 1 nm range or less). The
main thermal limitation of organic substrates is the reduction of resonance-peak
reflectance at high temperatures, but this effect was found to be reversible in the
sense that temporary presence at temperatures up to 85 °C does not destroy the
device permanently.
The proposed approach for athermal organic-inorganic RWGs has applications in
various fields. For each application there are specific issues that need to be taken
into account when designing the device. For example, in medical diagnostics the
analyte is often a liquid, which means that the TOC of the liquid, acting as the
superstrate of the RWGs, has to be included in the design. On the other hand, these
132
types of diagnostic devices are typically used in a laboratory environment, which
means that athermal operation within less than ± 5 °C would be more than enough.
Furthermore, the study of replicated athermal waveguide grating filters was
extended by employing different polymer materials as substrates.
Three resonant grating filters were designed, fabricated and characterized for the
operation as athermal devices using different polymer materials. The thermal
spectral stability of these filters was compared by theoretical calculations and
experimental measurements. For polycarbonate gratings, there is a good agreement
between calculated and measured results with a net spectral shift of 0.8 nm over 75-
degree-wide temperature range. The measured results for gratings with cyclic-olefin-
copolymer (COC) and Ormocomp® substrates showed larger spectral shifts towards
longer wavelengths than predicted by theoretical calculations. The deviation (0–1.5
nm) for the COC grating was explained by high modulus and inherent stresses which
were relaxed during heating and accompanied with the predominance of the thermal
expansion coefficient. The Ormocomp® gratings were subjected to uv-irradiation,
causing the generation of compressive (shrinkage) strains, which were relieved on
heating with a net result of expansion of material, demonstrated by thermal spectral
shifts towards longer wavelengths (0–2.5 nm). The spectral shifts might also be
caused partially by the reorientation of the polymer chains.
RWG filters based on one-dimensional (1D) periodic gratings usually have strong
polarization dependence, which is useful for polarizing filtering applications.
However, in certain applications such as dense wavelength division multiplexing,
polarization-insensitive filters are highly desirable due to the unknown polarization
state of light emerging from optical fibers. In this research, we presented the design
and fabrication of two types of 1D RWGs with simple geometries, which
demonstrate polarization-insensitive resonance gratings phenomena under normal
incidence. The Type-I single-layer rectangular-profile TiO2 grating (TiO2 grating on
fused silica substrate) is fabricated by employing ALD, EBL, and RIE techniques,
which shows almost perfect non-polarizing property. The Type-II double-layer
binary grating (replicated in polycarbonate and coated by TiO2) is a TiO2-coated
polycarbonate grating manufactured by nanoimprinting and ALD, without any
133
etching process. Both types of 1D non-polarizing resonance gratings are realized for
the first time in experiment so far, which show the potential of low-cost mass
production of such functional devices for practical applications, for example, in
enhancing fluorescence in biosensors and many other applications depending on the
requirements. The non-polarizing gratings are designed by tailoring, adjusting and
engineering the grating parameters such that simultaneous excitation of TE- and
TM-modes occur at the same resonance wavelength due to exhibiting similar
propagation constants at resonance. Furthermore, it was observed that degeneracy of
TE- and TM-modes of such non-polarizing properties are strongly dependent on the
effective depth of the substrate material and both modes split due to even a slight
over-etch depth in fused silica.
For such studies, TiO2 subwavelength RWGs and thin TiO2 films of thicknesses
∼200 nm were fabricated on fused silica substrates by ALD. Various TiO2
waveguide gratings were fabricated by dry etching of TiO2 thin films to the substrate
surface and with a subsequent over-etching into the substrate to different depths by
increasing the etching times in equal intervals of 30 s under the same conditions.
The fabricated waveguide gratings and TiO2 thin films were heat treated at 300°C
for 7 h to induce a phase transformation from amorphous (as-deposited) to
crystalline (anatase), which was confirmed by XRD patterns. An excellent
agreement in the theoretical and experimental measurements was shown for the TE-
and TM-modes of the non-polarizing RWGs. Furthermore, an agreement in the
behavior of theoretical and experimental measurements of the spectral shifts in
resonance wavelength due to over-etching in the fused silica substrate was shown to
obey a parabolic fit for TE-modes and a linear fit for TM-modes. The magnitudes of
the measured spectral shifts were, however, ∼2–3 times more than those calculated
theoretically, which might be due to a change in the grating profile after the
fabrication process. Refractive indices of amorphous and crystalline (anatase) phases
of TiO2 films were measured as 2.32 and 2.43, respectively, at a wavelength of 850
nm, and were used in the simulation of the heat-treated TiO2 gratings. The measured
spectra of the heat-treated gratings could not reveal significant spectral shifts, as was
calculated theoretically. This discrepancy might be due to a change in the surface
134
chemistry after RIE and plasma treatment and re-deposition of the reaction
byproducts on the grating surfaces.
The other goal of this study was to investigate the thermo-optic coefficients of the
optical materials such as Ormocomp®, ALD-TiO2, ALD-Al2O3 and ALD-TiO2-
Al2O3 films. The thermo-optic coefficient of uv-curable material Ormocomp® was
investigated in the wavelength range of 380–1000 nm by three methods. Methods 1
and 3 were based on analytical models, gave values of dn/dT = -1.02 × 10-4
°C-1
and
-0.81 × 10-4
°C-1
, respectively. Method 2 was based on experimentally measured
refractive indices of Ormocomp®, followed by modeling. It provided a value of
dn/dT = -1.27 × 10-4
°C-1
, which was used for the athermal analysis of polymeric
RWGs.
ALD provides several advantages in all kinds of filtering applications as a unique
thin film deposition method with atomic level control of film uniformity, thickness,
composition and coverage of corrugated surface profiles. In light guiding devices or
in filter elements, especially at least with a thin cover layer on corrugated surface
profiles, high index and amorphous dielectric materials have stringent requirements
to result in strong coupling effects. In this study, thin TiO2 films as cover layers on
various polymeric materials are deposited with strong adhesion by ALD method and
an exclusive study was performed to measure the thermo-optic coefficient of films
with different thicknesses.
Temperature dependent property i.e., thermo-optic coefficient which vary with film
thickness are explained qualitatively by the porosity in the microstructure during
film growth. The growing films have surface pores which are filled with hydrogen
containing species (H2O, OH). On rising temperature these species de-adsorbed
from the surface leaving behind empty pores, resulting in a decrease in effective
refractive index and film density. This may be attributed to the fact that the porosity
effect is a surface phenomenon, where a depletion region is formed. For thinner
films (t ≤ 150 nm), such depletion region is extended throughout the entire film
thickness, whereas it remains close to the surface regions for thicker films (t ≥ 150
nm). Thus, the desorption effect occurs very close to the surface regions of thick
films (200–500 nm), resulting in a relatively low positive index and density
135
temperature gradients. The thermo-optic coefficients of thin TiO2 films, deposited
by different techniques were different due to dissimilar microstructure and thermal
properties. For example, thin TiO2 films deposited by electron beam evaporation
possess negative values of dn/dT, which was an order of magnitude larger than the
films fabricated by plasma enhanced chemical vapor deposition (PECVD) and ALD,
however, we reported first time the interesting result of variation of dn/dT values
with film thicknesses. The observed porosity model in this study was investigated
one step ahead to cover TiO2 surfaces with diffusion barrier ALD-Al2O3 films to act
as impermeable covers for water molecules.
Thermo-optic coefficients of ALD-TiO2 films on Si substrates, in the presence of
ALD-Al2O3 barrier layers, have been determined to evaluate the porosity model at
the near surface region of TiO2 films. The TOC values of TiO2 films of different
thicknesses with thin ALD-Al2O3 (~ 6 nm) barrier layers were determined after
modeling based on Lorentz-Lorenz relation. The TOCs of TiO2 with different
thicknesses showed different values, particularly the thinnest TiO2 films with the
most effective response due to development of a widespread depletion region
(porosity region) throughout the thickness, despite the presence of thin Al2O3 barrier
layers. Owing to the significantly large negative TOCs of thin TiO2 films (tt ≤ 100
nm), they are further coated by Al2O3 barrier layers with a gradual increase in the
thickness to observe the response of depletion region through impermeable layer.
The negative TOCs of thin TiO2 films decrease gradually with a regular increase in
the thickness of the Al2O3 barrier layers; a linear relation gives a good fit. The
significant reduction in the negative TOC values of the thin TiO2 films could not be
revealed after ALD-Al2O3 barrier layers of thickness ta = ~ 36 nm. However, a 33 %
reduction is determined at this barrier layer thickness. This might be attributed to the
existence of few pinhole defects on ALD-Al2O3 barrier layers or strong dominance
effect of widespread depletion region underneath the barrier layers.
The TOCs of the ALD-Al2O3 films of various thicknesses were determined over a
wide spectral range 380 ≤ λ ≤ 1800 nm and illustrated in detail at a wavelength of
640 nm. The Al2O3 films were demonstrated to exhibit positive TOCs regardless of
the film thickness and significantly depend on the operating temperatures. This
136
might be attributed to the slow decrease in the density of the thin ALD-Al2O3 films
rather than that of the bulk material that results in positive TOCs. The
aforementioned experimental results demonstrated that the TOCs of both the TiO2
and Al2O3 thin films are almost of the same magnitude and opposite in signs. Such
properties depicting the reverse nature of TOCs of both optical grade ALD-TiO2 and
ALD-Al2O3 films are suitable to be implemented in multilayer stacked inorganic or
hybrid organic-inorganic athermal waveguide and narrowband filtering device
applications.
In future, the research on polymeric resonant grating filters could be extended to
medical diagnostics, replacing air by an analyte which most often exists in liquid
form. The TOC of the analyte may provide necessary qualitative information used
for diagnostic purposes in terms of the spectral shift due to change of refractive
index because of variation of composition of constituents. The spectral shifts can
also be accounted for the measurements of residual stresses in the materials. The
residual stresses could be created in the materials intentionally or during
manufacturing which leads to a change of refractive index and finally appears as
spectral shifts. Another interesting application of these filters is to predict the
angular displacements of aerospace vehicles in terms of the spectral shifts since the
polymeric waveguide filters may be impregnated within the composite structure of
aerospace vehicles.
137
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