Jan 28, 2015 - self inductance of thin wire, resorting force have to additional work and ...... of PPR will swell and become more resistant to developer solution ...
Design, Fabrication and Characterization of Metamaterial based THz Filters
A THESIS
submitted by
RAHUL KUMAR
for the award of the degree
of
MASTER OF SCIENCE (by Research)
DEPARTMENT OF ELECTRICAL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY MADRAS. January 2015
THESIS CERTIFICATE
This is to certify that the thesis titled Design, Fabrication and Characterization of Metamaterial based THz filters, submitted by RAHUL KUMAR, to the Indian Institute of Technology, Madras, for the award of the degree of MASTER OF SCIENCE, is a bona fide record of the research work done by him under our supervision. The contents of this thesis, in full or in parts, have not been submitted to any other Institute or University for the award of any degree or diploma.
Dr. ENAKSHI BHATTACHARYA Research Guide Professor Dept. of Electrical Engineering IIT-Madras, 600 036 Place: Chennai Date: 28th January 2015
Dr. ANANTH KRISHNAN Research Guide Assistant Professor Dept. of Electrical Engineering IIT-Madras, 600 036
ACKNOWLEDGEMENTS First and foremost, I dedicate this thesis to Swami Vivekananda, who’s lofty and patriotic ideas have always inspired and motivated me during thick and thin of my journey as MS research scholar. Then, I want to thank my Guides; Prof. Enakshi Bhattacharya and Dr. Ananth Krishnan for giving me opportunity to work in exciting and emerging field of Electromagnetics Metamaterials. Because for their constant guidance and fruitful discussions, I have indeed matured as researcher in both technical and non-technical aspect. I would like to thank Dr. Bala Pesala, Senior Scientist CEERI, for allowing me to use characterization facilities at CSIR campus. In this context, I would also like to acknowledge Shaumik Ray, PhD research scholar, CEERI, for his technical guidance. He went to an extent of rescheduling his work in order to give me characterization slots whenever I needed. I would like to thank Ankit Arora and Suyog Hawal, for technical discussions. In form of Ankit, I got one selfless batch mate and friend. Without his help, I would definitely not have been able to accomplish as much as I have accomplished now. I would like to thanks all staffs of MEMS and micro-electronics lab for helping in fabrication, friends of micro-electronics, optics group and volunteers of Vivekananda Study Circle for making my stay at IITM, a memorable and enriching one. I would also like to take this opportunity to pay my salutations and thanks to Swami Atmashaddhananda, a monk of Ramakrishna Mission, for teaching subtle concepts of Upanishads & Hinduism as whole. Finally, I would like to thank my family for their sacrifices and keep me out of family problems so that I can concentrate on research. In one’s life, there is contribution of lot of persons and it is not possible to mention everyone here. However, I thank them all.
i
ABSTRACT KEYWORDS:
Terahertz (THz), Optical Metamaterials, Split Ring Resonator, Fishnet Metamaterial, Filters
Terahertz waves (0.1 THz to 10 THz) are recently being harnessed in applications like airport security systems, narcotics detection, imaging, sensing, etc. However, these applications are limited due to lack of natural filters as most of polymers and natural dielectrics do not have any characteristics response in THz regime. This bottleneck can be overcome by using artificially designed materials, called metamaterials, where spatial effective relative permittivity (r ) and effective relative permeability (µr ) in the given frequency range can be engineered. In this work, band stop filter based on Square shaped planar THz Split Ring Resonator (SqSRR) and band pass filter based on Fishnet Metamaterial (FM) have been designed, fabricated and characterized for the frequency range of 0.1 THz to 0.3 THz at normal incidence. The experimental results and analysis based on surface current profile of several geometrical modifications of SqSRR structures, highlight the importance of geometrical symmetry and polarization of incident wave on number and position of dips in transmission spectra (resonances). We have further shown that contrary to conventional approximation, the dip in transmission spectra occurring due to electrical resonance shows significant red shift with increase in the arm length perpendicular to the incident E-field. We have attributed these shifts to the dilution of the effective electron density of arm parallel to the incident E-field and proposed a simple modification in existing model to accommodate these shifts. We have designed a novel polarization independent electrically tunable band pass filter showing tunability of ≈ 28 GHz/V around 7 THz, by integrating electrostatic actuation technique to static FM. Fabrication steps carried out for designed tunable filters will also be discussed. Since the response of metamaterials are scalable in THz range, these results will give more insight into working principle of metamaterials and further in designing devices for THz frequency range. ii
TABLE OF CONTENTS ACKNOWLEDGEMENTS
i
ABSTRACT
ii
LIST OF TABLES
vi
LIST OF FIGURES
ix
ABBREVIATIONS
x
NOTATION
xi
1
Introduction
1
1.1
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Motivation, Objective and Scope . . . . . . . . . . . . . . . . . . .
2
1.3
Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
2
3
Fundamentals of Negative Index Metamaterials
4
2.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
2.2
Negative effective permittivity (-ef f ) . . . . . . . . . . . . . . . .
6
2.3
Negative effective permeability (-µef f ) . . . . . . . . . . . . . . . .
8
2.4
Negative Index Material
. . . . . . . . . . . . . . . . . . . . . . .
10
2.5
Retrieval of ef f and µef f from S-parameters . . . . . . . . . . . .
11
2.6
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12
Square shaped Split Ring Resonator (SqSRR) based THz band stop filters
13
3.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
3.2
Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
3.2.1
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
3.2.2
Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . .
15
iii
3.2.3 3.3
Characterization . . . . . . . . . . . . . . . . . . . . . . .
18
Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . .
21
3.3.1
Closed Ring (CR) . . . . . . . . . . . . . . . . . . . . . . .
21
3.3.2
Square shaped Split Ring Resonator (SqSRR) . . . . . . . .
21
3.3.3
Double Slits present on Adjacent Sides (DAS) . . . . . . .
23
3.3.4
Double Slits present on the Opposite Sides (DOS) and Four Slits present on all four sides (FS) . . . . . . . . . . . . . .
24
Effect of the horizontal arms on electrical resonance . . . .
24
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
3.3.5 3.4 4
5
6
Fishnet Metamaterial (FM) based static THz band pass filters
30
4.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
4.2
Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
4.2.1
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
31
4.2.2
Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . .
32
4.2.3
Characterization . . . . . . . . . . . . . . . . . . . . . . .
35
4.3
Results and Discussions . . . . . . . . . . . . . . . . . . . . . . . .
36
4.4
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
Electrically tunable THz band pass filters
40
5.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
40
5.2
Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
5.2.1
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
41
5.2.2
Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . .
43
5.2.3
Characterization . . . . . . . . . . . . . . . . . . . . . . .
48
5.3
Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . .
49
5.4
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
50
Summary and Conclusion
51
6.1
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
52
6.2
Scope of future work . . . . . . . . . . . . . . . . . . . . . . . . .
52
A Matlab code for parameter extraction
54
B Fabrication Chemistry
59 iv
B.1 Photoresist Developer . . . . . . . . . . . . . . . . . . . . . . . . .
59
B.2 Chromium Etchant . . . . . . . . . . . . . . . . . . . . . . . . . .
59
B.3 Gold Etchant . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
B.4 Piranha Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59
LIST OF TABLES 2.1
Bulk plasma frequency (ωp ) of different metals . . . . . . . . . . .
7
3.1
Specifications of the mask plate . . . . . . . . . . . . . . . . . . .
16
3.2
Parameters used for spin-coating PPR . . . . . . . . . . . . . . . .
17
3.3
Parameters used for PPR ashing . . . . . . . . . . . . . . . . . . .
18
4.1
Spin parameters of PPR . . . . . . . . . . . . . . . . . . . . . . . .
34
5.1
Parameters used for spin coating PPR . . . . . . . . . . . . . . . .
43
5.2
PECVD Silicon dioxide deposition parameters . . . . . . . . . . . .
46
5.3
Au electroplating parameters . . . . . . . . . . . . . . . . . . . . .
47
vi
LIST OF FIGURES 2.1
r -µr graph. Taken from (Engheta and Ziolkowski, 2006) . . . . . .
5
2.2
(a) Dispersive profile of r of bulk metal (b) Bulk Metal . . . . . . .
7
2.3
(a) Thin metallic wires embedded in a dielectric. (b) Effective r profile for thin metallic wires. Value of ωp0 can be varied by changing periodicity or thickness of metallic wires or both . . . . . . . . . . . . . .
8
(a) Complementary SRR used by Penday et. al. (Pendry et al., 1999). Inset shows the unit cell along with geometrical parameters. (b) Effective µr profile of complementary SRR. . . . . . . . . . . . . . . . .
9
(a) Image of first NIM realized by Smith. et. al. (Smith et al., 2000). (b) Ray diagram showing negative refraction at RHM-LHM interface (Veselago, 1968). . . . . . . . . . . . . . . . . . . . . . . . . . . .
10
(a) Perspective view of unit cell used in simulation. Geometrical parameters were taken from (Smith et al., 2005) (c) Obtained s-parameters. Extracted (d) Refractive Index (nef f ) (e) Effective relative permittivity (r ) (f) Effective relative permeability (µr ) . . . . . . . . . . . . . .
12
(a) Perspective view of a unit cell of SqSRR along with boundary conditions used in simulation. Polarization of incident wave is shown by arrows. (b) Top view of a unit cell showing obtained geometrical parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14
3.2
Schematic of fabrication steps followed to realize SqSRR arrays . .
15
3.3
Microscopic images of (a) Recalcitrant PPR patches present on sample (b) Same sample after PPR ashing. . . . . . . . . . . . . . . . . . .
18
Microscopic image of fabricated structures: (a) Closed Ring (CR) (b) Split Ring with single silt (SqSRR) (c) Double slits present on Adjacent Sides (DAS) (d) Double slits present on Opposite Sides (DOS) (e) Four Slits placed symmetrically on all four arms (FS). Common scale for all the shown structures is given in panel (e). . . . . . . . . . . . . . .
19
3.5
Schematic of THz Characterization setup . . . . . . . . . . . . . .
20
3.6
(a) Experimental and simulated transmission characteristics of CR. (b) Instantaneous surface current density of CR at frequency of minimum transmission fm . Polarization of incident wave is shown by arrows. (c) Conventional Cut-wire approximation. . . . . . . . . . . . . . . . .
22
(a) Experimental and simulated transmission characteristics of SqSRR in parallel orientation along with instantaneous surface current profile at fm . (b) Experimental transmission characteristics of SqSRR compared with CR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
2.4
2.5
2.6
3.1
3.4
3.7
vii
3.8
(a) Experimental and simulated transmission characteristics of SqSRR in perpendicular orientation along with instantaneous surface current profile at fm of both resonance. (b) Pictorial representation showing the reason of circulating current at EEMR. . . . . . . . . . . . . . .
23
(a) Experimental transmission characteristics of DAS compared with perpendicular orientation of SqSRR. (b) Instantaneous surface current density at fm of both resonance (marked by numbers). . . . . . . .
24
3.10 (a) Experimental transmission characteristics of DOS: (a) Compared with CR when arms without slits are parallel to the incident E-field along with instantaneous surface current profile of DOS at fm . (b) Compared with FS when arms with slits are parallel to the incident E-field. Instantaneous surface current profiles of DOS at fm in both cases are also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
3.11 (a) Microscopic images of fabricated structures with decreasing horizontal arm length (b)Simulated transmission characteristics showing blue shift with decrease in length of horizontal arm.(c) Modified response after taking horizontal arms into consideration. . . . . . . .
26
3.12 (a) Effective metal length in SqSRR after considering horizontal arm. (b) Normalized modified plasma frequency (fpmodif ied ), electrical resonance frequency (f0modif ied ) and the corresponding transmission (fm ) versus length of horizontal arm. These frequencies are normalized with respect to the corresponding cut-wire response. Inset shows position of f0 , fm , fp in typical transmission characteristics. . . . . . . . . . . .
28
3.9
4.1
Evolution of SqSRR to pair of cut-wires. Taken from (Dolling et al., 2005) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
30
(a) Periodic array of pairs of cut-wires (b) Periodic array of continuous wires. (c) Fishnet metamaterials after combining (a) and (b) . . . .
31
(a) Perspective view of unit cell of FM along with boundary conditions used in simulation. Top view of the unit cell. Geometrical parameters for 1 mm period are L = 1 mm, metal arm length l = 0.6 mm , metal width w = 0.6 mm and gap g = 0.2 mm. For 2 mm period, these parameter are: L = 2 mm, metal arm length l = 1 mm , metal width w = 1 mm and gap g = 0.5 mm . . . . . . . . . . . . . . . . . . . . . . . . . .
32
4.4
Schematics of fabrication steps followed to realize FM) . . . . . . .
33
4.5
Microscopic image of fabricated structures having period of : (a) 1 mm (b) 2 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
35
(a)Experimental and simulated transmission characteristics of FM having periodicity of 1 mm. (b) Experimental transmission characteristics of 1mm period compared with 2 mm period. . . . . . . . . . . . . .
36
4.2 4.3
4.6
viii
4.7
(a) Extracted real and imaginary values of effective refractive index (nef f ). Gray area shows real and imaginary values corresponding to 1 peak. (b) Instantaneous surface current and displacement current in top view of upper metallic layer (blue color), top view of lower metallic layer (green color) and side view of dielectric (red color) respectively.
37
(a) Extracted real and imaginary values of effective refractive index (nef f ). Gray area shows real and imaginary values corresponding to 3rd peak. (b) Typical effective r profile for periodic cut-wires pairs, continuous wires and combination of continuous wires and cut-wire pairs. Taken from (Koschny et al., 2004) . . . . . . . . . . . . . . . . . .
38
(a)Simulated transmission characteristics showing effect of sandwiched dielectric’s loss on NI transmission. The NI transmission has been normalized with respect to the PI transmission. . . . . . . . . . . . . .
38
4.10 (a) Schematic view of FM under static E-field test. (b) Experimental transmission characteristics of FM after applying 9 V battery compared with FM without influence of static field. . . . . . . . . . . . . . .
39
4.8
4.9
5.1
(a) Top and Side view of a tunable FM unit cell along with geometrical dimensions. Thickness of air tair = 0 - 2 µm. (b) Microscopic image of repeating unit of membrane with dimensions. Boxes show the supporting pillars. . . . . . . . . . . . . . . . . . . . . . . . . . . .
42
5.2
Microscopic image of static FM fabricated using micromirror mask.
42
5.3
Normalized transmission characteristics of various substrates. These transmissions are normalized with respect to transmission of free space/atmosphere. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.4
Schematics showing the fabrication steps of tunable FM . . . . . . .
44
5.5
(a) Mask-1 (b) Mask-2. Not drawn to scale. . . . . . . . . . . . . .
45
5.6
Microscopic image showing formation of bubbles in underlying PPR.
47
5.7
Microscopic image of static FM with PECVD SiO2 as sandwiched dielectric layer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
48
(a) Transmission characteristics of the tunable FM showing shift in the negative peak with variation in the air gap thickness.(b) Displacement versus Voltage graph showing pull-in voltage ≈ 9 V and cross-sectional view of deformed top metallic layer at pull-in voltage. . . . . . . .
49
(a) Transmission characteristics of two similar fabricated static FM. (b) Microscopic image showing non-uniform etching before optimization and uniform etching after optimization. . . . . . . . . . . . . . . .
50
5.8
5.9
ix
ABBREVIATIONS
CR
Closed Ring
DAS
Double slits on Adjacent Sides
DI water
De-Ionized Water
DNM
Doubly Negative Medium
DOS
Double slits on Opposite Sides
EEMR
Electrical Excitation to Magnetic Resonance
EM wave
Electromagnetic Wave
FS
Four Slits
IPA
IsoPropyl Alcohol
LH
Left Handed
LHM
Left Handed Material
MEMS
Micro Electro Mechanical System
NI
Negative Index
NIM
Negative Index Material
PBC
Periodic Boundary Conductor
PDMS
Periodic Boundary Conductor
PEC
Perfect Electric Conductor
PECVD
Plasma Enhanced Chemical Vapor Deposition
PI
Positive Index
PMC
Perfect Magnetic Conductor
SRR
Split Ring Resonator
SqSRR
Square shaped Split Ring Resonator
TCE
TrichloroEthylene
THz waves
Electromagnetic waves having frequency between 0.1 - 10 THz
UHV
Ultra High Vacuum
x
NOTATION
µr µef f r ef f ef f
α λ ω ωp
Relative Permeability Effective Relative Permeability Relative Permittivity Effective Relative Permittivity Effective Refractive Index Attenuation constant Free space wavelength Frequency Plasma Frequency
xi
CHAPTER 1
Introduction
1.1
Overview
Electromagnetic Metamaterials (metamaterials) are a special class of functional composite materials that exhibit tailor made electromagnetic properties at a desired frequency range. Doubly Negative Metamaterials (DNM) or Negative Index Metamaterials (NIM) comprising of periodic arrangement of sub-wavelength structures, exhibit effective negative relative permittivity (r ) and effective negative relative permeability(µr ) simultaneously at a desired frequency range. The propagation of electromagnetic waves in a homogeneous NIM was theoretically predicted in 1968 (Veselago, 1968). However, the first experimental demonstration of a NIM was performed in 2000 at microwave frequencies using a periodic array of Split Ring Resonators (SRRs) to provide effective negative µr in combination with a periodic thin metallic wires for effective negative r (Smith et al., 2000). The presence of simultaneous negative r and µr results in various interesting physical phenomena like left-handed propagation, negative refraction, reversed Doppler shift and reversed Cerenkov radiation (Veselago, 1968). These extraordinary phenomena and demonstration of their practical realizability resulted in the exponential increase in the research of this field. These intriguing properties of metamaterials have led to the invention of new devices and/or to the improvement in the performance of existing devices like couplers, routers, switches, modulator, filters, lenses and are being used in plethora of applications ranging from Telecommunication, energy harvesting, THz and biological imaging, stealth technology, and the most attractive being the invisibility cloak (Ziolkowski and Kipple, 2003; Islam et al., 2004; Caloz et al., 2004; Chen et al., 2006; Grzegorczyk and Kong, 2006; Schurig et al., 2006; Thomas et al., 2006; Chin et al., 2008; Yao et al., 2009; Ergin et al., 2010; Hawkes et al., 2013).
In this thesis, usage of metamaterials as static and dynamic THz Filters have been investigated.
1.2
Motivation, Objective and Scope
Terahertz waves (0.1 THz to 10 THz) are non-ionizing radiations with high penetration capacity through most of non-metallic optically opaque objects and posses characteristics absorption lines of many explosives, narcotics, proteins and bio-molecules (Zhu et al., 2009). In past two decades, with the advent of high power broadband and pulsed sources and sensitive detectors in the THz regime, due to above mentioned properties, these waves are being harnessed in applications like non-destructive testing, airport security systems, narcotics detection, short distance wireless communications, imaging, sensing, etc. (Fitzgerald et al., 2002; Yen et al., 2004; Federici et al., 2005). However, these applications are limited due to the lack of natural filters as most of polymers and natural dielectrics do not have any characteristics response in THz regime. This bottleneck can be overcome by designing artificial THz filters using metamaterials. The objective of this work is to explore the feasibility of metamaterials within the available fabrication and characterization constraints in demonstration of static THz band stop and THz band pass filters working at normal incidence. Further, it extends into designing of novel electrically tunable THz band pass filters using MEMS actuation technique. The response of metamaterials are scalable in THz range, therefore, the results obtained from this research work will give more insight into their working principle and in designing various metamaterial based THz devices.
1.3
Thesis Outline
Chapter 2 gives a brief discussion of fundamentals of negative index metamaterials. Realization of negative r and µr and their engineered combination to achieve negative index materials have been discussed. Chapter 3 discuss about Square shaped Split Ring Resonators (SqSRRs) and their response at normal incidence. These SqSRRs have
2
been demonstrated as THz band stop filter. Inadequacy of SqSRR to exhibit negative µr at normal incidence led to invention of Fishnet Metamaterial (FM). In chapter 4 FM has been demonstrated to exhibit negative index response and further utilized as THz band pass filter. Designing and fabrication of electrical tunability achieved in FM by incorporating MEMS actuation technique is the subject of chapter 5. Thesis ends with summary, conclusion and scope of future work, given in chapter 6.
3
CHAPTER 2
Fundamentals of Negative Index Metamaterials
2.1
Introduction
The solution to Maxwell’s equation for plane EM wave travelling in z direction in source-free, isotropic and homogeneous medium is given by, E = E0 exp (αz − i(
2π √ r µr z)), λ
(2.1)
where E0 is the amplitude of E-field, α is the attenuation constant, λ is free space wavelength, r and µr are relative permittivity and relative permeability respectively of the medium in which wave is propagating. The real and imaginary nature of the factor
√
r µr (refractive index) in Equ. 2.1
governs the nature of propagation of wave in the given medium which in turn depends on the algebraic sign of r and µr . All possible combinations of algebraic signs of r √ and µr are shown in Fig. 2.1. In the first quadrant, when r and µr are positive, r µr will be real, therefore, wave will propagate in such a medium. Also, positive value of r and µr will allow triplet of vectors E, H, k to follow the Right Hand (RH) coordinate system as per Eq. 2.2. Majorities of dielectrics belong to this quadrant. k × E = ωµH, k × H = −ωE,
(2.2)
where k is the wave propagation vector. In the second and forth quadrants, the factor
√ r µr will be imaginary as either r
or µr is negative. Therefore, the waves will have evanescent nature. All metals below plasma frequency exhibit negative r whereas few magnetic materials exhibit negative µr in MHz frequencies. In the third quadrant, due to simultaneous occurrence of negative r and negative µr ,
r
r r 0 & imag
Electric plasma
r r 0 & real
Dielectrics
E
E
H
z
k S
Evanescent wave
Propagating wave
Propagating wave
Evanescent wave
Electric plasma
k
E H
r
E
S
z
NI Metamaterials Magnetic plasma r r 0 & real
r r 0 & imag
Figure 2.1: r -µr graph. Taken from (Engheta and Ziolkowski, 2006) √
r µr will be real, thus resulting in propagating nature of wave (Veselago, 1968). How-
ever, the nature of propagation of the wave in materials belonging to this quadrant will be different from materials belonging of first quadrant. The first and foremost difference can be seen from Eq. 2.2, where, due to simultaneous negative r and negative µr , the three vectors E, H, k satisfy Left Hand (LH) coordinate system, thus known as Left Handed Material (LHM). However, the energy flow will be in the direction opposite to that of k which can be inferred from Eq. 2.3. Also, to satisfy certain causality condi√ tions r µr should be negative (Veselago, 1968). Thus, these materials are also known as Negative-Index (NI) materials. These materials are called metamaterials because no natural materials exhibit negative r and negative µr simultaneously. Therefore, in subsequent sections, engineered ways to achieve negative r and negative µr in a desired frequency range will be discussed.
S = E × H, where S is poynting vector.
5
(2.3)
2.2
Negative effective permittivity (-ef f )
Negative r is naturally found in metals for all incident EM wave frequencies below the plasma frequency (ωp ). ωp for given metal can be derived from the Drude model (Kittel and McEuen, 1976). This model considers electrons as non-interacting particles, therefore after neglecting damping and restoring forces, response of free electron to the time varying sinusoidal incident E-field can be given by Newton’s second law of motion as
me
∂ 2x = qe Ex , ∂t2
(2.4)
where me is the mass of electron, x is the displacement for its mean position and qe is the charge of electron. Due to the sinusoidal nature of the incident E-field , x is also sinusoidal in nature, therefore the Eq. (2.4) reduces to −me ω 2 x = qe Ex , qe Ex ⇒x=− 2 . ω me
(2.5)
The Dipole moment(p) created between the displaced electron and the underlying ionic core is given by, p = −qe x =
qe2 Ex . ω 2 me
(2.6)
Therefore, overall Polarization density (P) of the metal becomes P = Np =
N qe2 Ex , ω 2 me
(2.7)
where the N is the number of free electrons per unit volume. In terms of susceptibility (χ), P can be defined as P = 0 χEx = 0 (r − 1)Ex ,
(2.8)
where 0 is permittivity of vacuum and r is relative permittivity. From equation (2.7) and equation (2.8) r can be written as, r = 1 −
6
ωp2 , ω
(2.9)
where ωp2 =
N qe2 . 0 me
(2.10)
It can be seen from Eq. (2.9), also plotted in Fig. 2.2(a), that r is negative for all ω less than ωp . From Eq. (2.10) it is evident that for a given bulk metal, as shown in Fig. 2.2(b), the number of free electrons per unit volume (N ), is a characteristic property, therefore ωp is a constant. Typical value of N and ωp for few metals are given in Table (2.1)(Murata and Tanaka, 2010). (a)
(b)
Figure 2.2: (a) Dispersive profile of r of bulk metal (b) Bulk Metal
Table 2.1: Bulk plasma frequency (ωp ) of different metals M etal N (m−3 ) Gold 5.90×1028 Silver 5.8×1028 Aluminium 2.1×1029
ωp (T Hz) 2183 2180 3570
However, in 1996 Pendry et. al. (Pendry et al., 1996), showed that ωp of a medium can be varied by periodically embedding thin metallic wires in a dielectric, as shown in Fig. 2.3(a). The incident EM wave having the direction of the E-field parallel to the axis of the wires and wavelength longer than periodicity of metallic wires, will not be able to distinguish between two consecutive wires. Therefore, it will see the medium having effective free electron density (Nef f ) as Nef f = N
πr2 , a2
(2.11)
where r is the radius of wire and a the length of cubic unit cell. Also due to the large self inductance of thin wire, resorting force have to additional work and this effect can 7
be seen as increase in the rest mass of the electron. The new effective mass will be, mef f =
µ0 πr2 qe2 N a ln( ). 2π r
(2.12)
Substituting for Nef f and mef f in Eq. (2.10), the reduced plasma frequency (ωp0 ) will be, ωp02 =
Nef f qe 2πc2 = 2 0a , 0 mef f a ln( r )
(2.13)
where c0 is the speed of light in vacuum. It can be seen from Eq. 2.13 that ωp0 is not a constant but depends on the geometrical parameters. Hence, ωp0 , as shown in Fig. 2.3(b), can be tuned to the desired frequency by varying the periodicity (a) or the thickness of wire (r) or both.
Figure 2.3: (a) Thin metallic wires embedded in a dielectric. (b) Effective r profile for thin metallic wires. Value of ωp0 can be varied by changing periodicity or thickness of metallic wires or both
2.3
Negative effective permeability (-µef f )
Natural materials showing negative permeability at high frequency are almost nonexistent as magnetic resonant phenomena, analogous to dipole oscillation, tend to occur at sub-GHz frequencies (Engheta and Ziolkowski, 2006). However, in 1999, Pendry et. al. proposed an artificial way to achieve negative µef f using thin nonmagnetic metallic rings of sub-wavelength size, popularly known as Split Ring Resonators (SRR), in micro-wave frequencies, as shown in Fig. 2.4(a) (Pendry et al., 1999). For the incident H- field perpendicular to the plane of the SRR, a current will be 8
Figure 2.4: (a) Complementary SRR used by Penday et. al. (Pendry et al., 1999). Inset shows the unit cell along with geometrical parameters. (b) Effective µr profile of complementary SRR.
induced in the metallic-ring following Lenz’s law, thus creating an induced H-field parallel and opposite to the incident H- field. Due to this induced current, SRR has inherent resonance which can be modelled as a series RLC circuit, where R accounts for the losses, C is the capacitance at the slits and L accounts for the inductance due to the induced surface current in the ring. Due to its sub-wavelength nature, the medium will be effectively homogeneous, with individual SRR acting as a "magnetic atom". Therefore, µef f of these periodic structures can be given by Eq. 2.14. At the resonance frequency (ωm ), the induced current and hence the opposing (induced) H-field will be maximum (as impedance will be minimum) to an extent that the resultant H-field will be opposite to the incident field, resulting in negative µef f for a narrow band of frequencies above ωm , as shown in Fig. 2.4(b). Since, ωm and Γm (damping factor) depends on geometrical parameters, as given by Eq. 2.14, the resonance frequency can be tuned to the desired frequencies by changing the geometrical parameters.
µef f = 1 −
Aω 2 , 2 + iωΓ ω 2 − ωm m
where, 3ac20 ωm = , πln( 2w )r3 d 2aσ Γm = , rµ0 πr2 A = . a2 9
(2.14)
2.4
Negative Index Material
The method to achieve negative r and negative µr in a desired frequency range, as discussed above, can be utilized to realize simultaneous negative r and µr . The first demonstration of the propagation of a wave through a medium with simultaneous negative r and µr using a periodic array of metallic post and SRRs as shown in Fig. 2.5(a), is shown by Smith et al. (Smith et al., 2000). Later, it was experimentally confirmed that such materials indeed have negative index of refraction, as predicted by Veselago (Shelby et al., 2001; Parazzoli et al., 2003). Snell’s law for negative index materials is given in Eq. 2.15 and the ray diagram at the LHM-RHM interface is shown in Fig. 2.5(b). It can be seen that contrary to the RHM, incident waves and refracted waves are on the same side ofthe normal, accounting for the negative angle of refraction. √ − 2 µ2 sin(θ) n2 = = √ , sin(φ) n1 2 µ2
(2.15)
where θ is the angle of incidence, φ is the angle of refraction, n2 , 2 and µ2 are the refractive index, effective permittivity and effective permeability of the LHM whereas n1 , 1 and µ1 are the corresponding values for the RHM.
1
2
Figure 2.5: (a) Image of first NIM realized by Smith. et. al. (Smith et al., 2000). (b) Ray diagram showing negative refraction at RHM-LHM interface (Veselago, 1968).
10
2.5
Retrieval of ef f and µef f from S-parameters
In electromagnetic analysis of any structure, reflection (S11) and transmission (S21) are two directly measurable quantities. However, in order to get a physical insight to the response, knowledge of effective material properties (ef f and µef f ) is important. Therefore, this section discuss about the retrieval method for ef f and µef f using the S-parameters (Smith et al., 2005). Impedance (ηn ) from the magnitude and phase of S-parameters can be calculated as, s ηn = ±
2 (1 + S11 )2 − S21 . 2 (1 − S11 )2 − S21
(2.16)
Algebraic sign of ηn is decided in such a way that its real part should always be positive. Dependence of the imaginary and real part of effective refractive index on S-parameters is given in Eq. 2.17. Since metamaterial is a passive medium, the imaginary part of refractive index is taken as positive. Im(nef f ) = ±Im( Re(nef f ) = ±Re(
2 2 )]) − S21 cos−1 ( 2S121 [1 − (S11
k0 d 1 −1 2 2 cos ( 2S21 [1 − (S11 − S21 )]) k0 d
),
)+
2πm , k0 d
(2.17)
where m is an unknown integer corresponding to the number of cycles a wave goes through in the slab, k0 is the wave number and d is the distance between the transmitter and the receiver port. After extracting ηn and nef f , ef f and µef f can be calculated as, n , ηn = nηn .
ef f = µef f
(2.18)
Simulation parameter extraction methodology used in the rest of thesis is validated using the structure as reported in (Smith et al., 2005). The perspective and top view of the unit cell are shown Fig. 2.6(a) and Fig. 2.6(b) respectively. Geometrical parameters are: Thickness of dielectric tdi = 0.25 mm, unit cell length L = 2.5 mm, slit gap g = 0.3 mm, width of SRR wSRR = 0.2 mm, width of wire wwire = 0.14 mm, gap between inner and outer ring d = 0.15 mm. The obtained S-parameters and the extracted values of nef f , ef f and µef f is shown in Fig. 2.6(d-f). It can be seen that for a certain band of 11
frequencies, negative nef f is obtained and for these frequencies the retrieved ef f and µef f are simultaneously negative.
k
L
(b)
|S |
wSRR
11
d
E
H
(c)
g
L
g
wwire
tdi
S parameter
(a)
l
1
0.5
5
0
-5 7
8 9 10 11 Frequency (GHz)
5
real imag
0
-5
-10 7
8 9 10 11 Frequency (GHz)
Effective Permeability ( r)
real imag
8 9 10 11 Frequency (GHz)
(f)
(e) Effective Permittivity ( r)
Refractive Index (n)
10
21
wSRR 0 7
(d)
|S |
10
real imag
0
-10 7
8 9 10 11 Frequency (GHz)
Figure 2.6: (a) Perspective view of unit cell used in simulation. Geometrical parameters were taken from (Smith et al., 2005) (c) Obtained s-parameters. Extracted (d) Refractive Index (nef f ) (e) Effective relative permittivity (r ) (f) Effective relative permeability (µr )
2.6
Summary
In this chapter, all possible combinations of algebraic sign of r and µr and their consequence on wave propagation in respective media have been discussed. Wave will have propagating nature in case of simultaneous existence of positive or negative r and µr . Since, materials with simultaneous negative r and µr do not exist in nature, prevalent method to achieve negative r using periodic thin metallic wires and negative µr using periodic SRRs at desired frequency range have been presented. These methods were combined to achieve negative index metamaterials. Finally, retrieval methods to extract effective material parameters from reflection (S11) and transmission (S21) coefficients have been elucidated.
12
CHAPTER 3
Square shaped Split Ring Resonator (SqSRR) based THz band stop filters
3.1
Introduction
Earlier demonstrations of SRR at microwave frequencies, exhibited effective negative µr , when the incident wave was polarized such that the incident H-field was perpendicular to the plane of SRR arrays (grazing incident angles). Until recently, there have been several efforts to increase the operating frequency of the SRR to the optical regime by the reduction in size or by the modification of shapes of the SRR (Linden et al., 2004; Dolling et al., 2007; Shalaev, 2007; Azad et al., 2008). One of the popular geometries among them is a Square shaped SRR (SqSRR), due to the ease of micro and nanoscale fabrication of Cartesian structures. At higher frequencies, due to the planar nature of the fabricated structure and the small thickness of the dielectric on which the SqSRR array is patterned, it is tedious to couple incident wave at grazing angle. Hence, at higher frequencies, normal incidence on SqSRR has gained popularity (Linden et al., 2004; Shalaev, 2007; Azad et al., 2008) and production of circulating currents in this polarization configuration is referred to as Electrical Excitation to Magnetic Resonance (EEMR) even though in this configuration, only effective negative r is obtained (Linden et al., 2004; Katsarakis et al., 2004). Apart from the magnetic resonance, there also exists a much less analyzed electrical resonance wherein the currents are oscillatory in nature, giving rise to effective negative r at all orientations. In the first section (3.2) of this chapter, design, fabrication and characterization methodologies of planar SqSRR structures and its various geometrical modifications operating in 0.05 - 0.35 THz will be discussed. In the second section (3.3), based on the experimental and simulated transmission characteristics and analysis of instantaneous surface current density profile, effect of geometrical orientations, number of slits and
the arms perpendicular to the incident E-field (horizontal arms) on various resonances will be elucidated. Since, these resonances will give rise to a dip in the transmission characteristic, the analysis presented will help in the efficient and precise design of SqSRR based THz band stop filters.
3.2
Methodology
3.2.1
Design
The geometrical parameters of SqSRR arrays exhibiting dips in transmission characteristic due to various resonances in 0.05 - 0.35 THz were determined using a commercial full wave Maxwell’s equation solver (Ansoft, 2013). The perspective view of a unit cell along with the boundary conditions is given in Fig. 3.1(a). Wave ports were used at the top and the bottom of the unit cell for exciting and receiving electromagnetic waves at normal incidence. Perfect Electric Conductor (PEC) and Perfect Magnetic Conductor (PMC) boundary conditions were used on sides, perpendicular to the E-field and Hfield respectively, to maintain the incident wave polarization, as shown by red arrows in Fig. 3.1(a). SqSRR was defined using a 150 nm thick gold layer with a conductivity of 58 × 106 S/m. The glass of thickness 180 µm and refractive index 2.45 was considered as the substrate (Naftaly and Miles, 2007). The optimized geometrical parameters obtained through simulation are shown in Fig. 3.1(b). (a)
(b)
288 μm
E
k
36 μm
H
8 μm
288 μm 280 μm
Figure 3.1: (a) Perspective view of a unit cell of SqSRR along with boundary conditions used in simulation. Polarization of incident wave is shown by arrows. (b) Top view of a unit cell showing obtained geometrical parameters.
14
The azimuthal orientation of the structures, where the side without the slit is parallel to the incident E-field, will be referred to as parallel orientation in the rest of the chapter and the azimuthal orientation where the side without the slit is perpendicular to the incident E-field will be referred to as perpendicular orientation.
3.2.2
Fabrication
Structures corresponding to the optimized geometrical dimensions were fabricated indigenously on a borosilicate glass (BK7; ≈ 18 mm × 18 mm × 180 µm). The schematic representation of the complete fabrication steps are shown in Fig. 3.2 and following sub-sections elaborate them in details.
(a) Glass Substrate
(b) Cr/Au deposition (20/150 nm)
(c) PPR Coating U V
(f) Cr/Au etching
(e) PPR Development
(d) UV exposure using mask
(g) PPR removal
Figure 3.2: Schematic of fabrication steps followed to realize SqSRR arrays
Substrate Cleaning Glass substrates were sonicated in Acetone for 2 minutes using ultrasonic agitator to remove organic impurities followed by Iso-Proply Alcohol (IPA) and De-ionized (DI) water for another 2 minutes each. After sonicating in DI water, substrate was quickly dried with N2 to prevent forming of DI water stain.
15
Metallization Approximately 20 nm Chromium (Cr) and 150 nm Gold (Au) were deposited on cleaned substrates using Ultra High Vacuum (UHV) e-beam evaporation unit 1 at elevated temperature of 100◦ C and pressure 2.13 × 10−6 mbar. The thickness of the deposited layers were measured using an in-built quartz crystal oscillator. A Cr layer was deposited to have imposed adhesion of Au with the substrate.
Photolithography The mask layouts of optimized geometry were created using L-EDIT 15
TM
CAD
tool. The layouts were converted to the standard photomask writer compatible format, Graphic Database System 2 (GDSII). The patterns were then transferred to the Positive Photoresist (PPR) coated the mask plate using DWL66 writer 2 . Specifications of the mask plate are given in Table. 3.1. After direct writing of the pattern, PPR was developed using NaOH solution. Exposed Cr was developed using the Cr etchant (APPENDIX B.2) and finally the remaining PPR was removed by boiling in acetone. Table 3.1: Specifications of the mask plate Transparent layer
:
Fused Silica
Absorbing layer
:
Chromium (≈ 50 nm)
Photoresist
:
AZP-1350 (≈ 500 nm)
Au coated samples were cleaned in DI water and dried with N2 . These samples were then kept in hot air oven at 120◦ C for 5 min for dehydration bake to ensure complete removal for moisture for proper adhesion of positive photoresist (PPR)- MicropositT M S1813 G2 3 with samples. Optimized spin parameters used for PPR coating are given in Table. 3.2. PPR coated samples were baked in hot air oven at 80◦ C for 20 minutes to harden the PPR. 1
HHV 5000; Manufacturer: HHV technologies Manufacturer: Heidelberg Instruments GmbHT M ; laser source: He-Cd laser of λ = 442 nm 3 Manufacturer: Shipley Company 2
16
Table 3.2: Parameters used for spin-coating PPR Spin Speed
:
4000 RPM
Acceleration
:
400 RPM/sec
Time
:
40 second
The PPR coated samples were then aligned with the photomask using MA6/BA6 mask aligner 4 and exposed to UV( λ =365 nm (i-line); intensity ≈ 3.7 mW/cm2 ) for 10 seconds. The exposed PPR was dissolved by gently shaking the samples in 0.1 M solution of NaOH. After few iterations, the optimized time for best results was found to be ≈ 10 seconds. Before doing wet etching of deposited Cr/Au layers, the developed samples were baked in oven at 120◦ C for 20 minutes to further hardened the remaining PPR.
Wet Etching The wet etching of deposited Cr/Au were performed at room temperature using Cr and Au etchant respectively. The techniques for preparing these etchants are elaborated in APPENDIX B.2. The optimized etching time of Cr and Au using these etchants were ≈ 32 seconds and ≈ 25 seconds respectively.
PPR removal The PPR present on the samples was removed by boiling them in acetone for ≈ 10 minutes. In few cases, recalcitrant PPR patches were present even after boiling in acetone, as shown in Fig. 3.3(a). In order to remove these patches of PPR, PPR ashing using Reactive Ion Etching (RIE)5 was used. The parameters used for PPR ashing is given in Table. 3.3 and microscopic image of sample after this treatment is shown in Fig. 3.3 (b). 4 5
Manufacturer: Suss MicroTec / Karl Suss Plasma; manufacturer: Oxford Instruments
17
(b)
(a)
100 μm
100 μm
Figure 3.3: Microscopic images of (a) Recalcitrant PPR patches present on sample (b) Same sample after PPR ashing.
Table 3.3: Parameters used for PPR ashing Gas used
:
O2
Gas flow rate
:
50 sccm
Temperature
:
20 ◦ C
Pressure
:
0.4 mbar
DC bias
:
214-215 V
Time
:
10 minutes
Color of plasma
:
Whitish
Microscopic images of the final fabricated square shaped Closed Ring (CR), Split Ring with one slit (SqSRR), Double slits present on Adjacent Sides (DAS), Double slits present on Opposite Sides (DOS) and Four Slits places symmetrically on all four sides (FS) are shown in Fig. 3.4.
3.2.3
Characterization
Transmission characteristics of the fabricated structures from 0.05-0.35 THz with a frequency step of 5 MHz were obtained using a coherent Continuous-Wave (CW) THz transmitter/receiver system (range: 0.05 THz -1.2 THz)6 , present at Central Electronics Engineering Research Institute, Chennai. The key components of this system consist of a pair of thermally tunable Distributed Feedback (DFB) Lasers, a photodiode based 6
Manufacturer: Toptica Photonics
18
Figure 3.4: Microscopic image of fabricated structures: (a) Closed Ring (CR) (b) Split Ring with single silt (SqSRR) (c) Double slits present on Adjacent Sides (DAS) (d) Double slits present on Opposite Sides (DOS) (e) Four Slits placed symmetrically on all four arms (FS). Common scale for all the shown structures is given in panel (e).
THz emitter, photoconductive coherent receiver, focusing arrangement and precision stage along with a stepper motor. The detailed schematic of the characterization setup is shown in Fig. 3.5 and various components are elucidated in following subsections.
THz Generation CW THz waves are obtained by irradiating two near infra-red (operating around 1550 nm) DFB lasers 7 , having adjacent frequencies, on InGaAs based photodiode. The bias voltage applied to the photodiode generates a photocurrent that oscillates at beat frequency. These oscillating photocurrent are translated into THz waves by a bow-tie antenna structure surrounding the photodiode. Since, the generated THz wave has the frequency exactly at the difference of these two lasers, the output frequency can be varied by thermally tuning their frequencies (Lang et al., 2012; Deninger et al., 2008). For example, in order to generate a wave having frequency of 50 GHz, the difference in temperature between the two DFB lasers is around 38◦ C. The output THz waves of the transmitter were made parallel to the axis of a low loss 7
TeraSource 1500
19
AC Bias
Transmitter
Off-axis Parabolic Mirror
DFB Laser 1 Terahertz Waves 50:50 Splitter/Combiner
Plano-Convex Lens Stepper Motor
Sample
Lock-in Detection
DFB Laser 2
Terahertz Waves Receiver
Plano-Convex Lens
Off-axis Parabolic Mirror
Figure 3.5: Schematic of THz Characterization setup
plano-convex teflon lens using an off-axis parabolic mirror. These parallel waves were focused on fabricated structure with a spot of diameter ≈ 5 mm. The stepper motor is used to position the sample with accuracy of 40 nm. To capture the effect of azimuthal orientation on the transmission characteristics, the fabricated structures were rotated by 90o along the axis perpendicular to their surface (as shown in the inset of Fig. 3.5). The transmitted waves from structures were collected using a similar arrangement of lens and mirror.
THz Detection The THz waves coming from the mounted structures along with original laser beat are allowed to impinge on another InGaAs photomixer acting as a receiver. The incoming THz waves generate a voltage in the antenna while laser beats modulate the conductivity of the photomixer. The resulting photocurrent is proportional to amplitude of incident THz electric field, therefore this photocurrent is used to measure the characteristic peaks or dips of the mounted sample. Since the resulting photocurrent is typically in nanoampere range, lock-in detection 8 is used to amplify this weak signal. The ob8
TeraControl 110
20
tained photocurrent was normalized with respect to the photocurrent of a bare glass wafer of the same thickness to remove the effect of the substrate.
3.3 3.3.1
Results and Discussions Closed Ring (CR)
Simulated and experimental transmission characteristics of the CR, as shown in Fig. 3.6(a), exhibit a dip in the transmission for a band of frequencies. The frequency of minimum transmission (fm ) was ≈ 0.155 THz in simulation and ≈ 0.163 THz in experiment. The difference between the simulated and the experimental fm was attributed to fabrication tolerances and differences in material constants. In order to establish the exact mechanism of the dip (resonance), the instantaneous surface current density of the CR was calculated at fm (shown in Fig. 3.6(b)). It can be seen that the surface current density in the arms parallel to the incident E-field (vertical arms) are oscillatory in nature, going from the bottom to the top as shown (or top to bottom depending on the phase of the incident E-field, not shown in Figure). In literature, this current has been attributed to the dipole oscillation of free electrons in the vertical arms, in the presence of the incident E-field. The corresponding resonance is termed as the electrical resonance, as this resonance is due to the coupling of the incident E-field with the structure under study. The concentration of surface current at the inner periphery of the vertical arms was attributed to the diamagnetic behaviour of the CR which has been earlier reported for SRR structures (Economou et al., 2008) . In earlier reports, only the vertical arms were considered to be participating in the electrical resonance. Therefore the electrical response of the CR was approximated to be equivalent to a cut-wire geometry as shown in Fig. 3.6(c). This approximation is referred as Cut-wire approximation (Linden et al., 2004; Koschny et al., 2004).
3.3.2
Square shaped Split Ring Resonator (SqSRR)
Simulation and experimental transmission characteristics of the SqSRR in the parallel orientation , shown in Fig. 3.7(a), exhibits a single resonance similar to that observed in the CR. The analysis of instantaneous surface current density at fm , shown in Fig. 21
Transmission [dB]
(a)
(b)
0
(c) +δQ
+δQ
-δQ
-δQ
-10 1
-20
-30 -40
E Simulation 1 Experiment 0.1 0.2 0.3 Frequency (THz)
k
H
Polarization Current
Figure 3.6: (a) Experimental and simulated transmission characteristics of CR. (b) Instantaneous surface current density of CR at frequency of minimum transmission fm . Polarization of incident wave is shown by arrows. (c) Conventional Cut-wire approximation.
3.7(a), revealed the origin of this resonance to be the dipole oscillations of the free electrons present in the vertical arms in response to the incident E-field. In current orientation, SqSRR is not only symmetric about the incident E-field but has vertical arms identical to CR. Therefore, the position of fm is almost same in the both cases. This can been observed by comparing the experimental response of SqSRR with that of CR, as shown in Fig. 3.7(b). 0
(b)
-10 1
-20
E
-30
1
-40
Simulation k Experiment
H
Transmission [dB]
Transmission [dB]
(a)
-10
-20
-30 0.1
0.1 0.2 0.3 Frequency (THz)
CR SqSRR 0.2 0.3 Frequency (THz)
Figure 3.7: (a) Experimental and simulated transmission characteristics of SqSRR in parallel orientation along with instantaneous surface current profile at fm . (b) Experimental transmission characteristics of SqSRR compared with CR.
In the perpendicular orientation, SqSRR exhibits two dips in the transmission characteristics, as shown in Fig. 3.8(a). The instantaneous surface current density at fm (≈ 0.63 THz), shown in 3.8(a) (marked as 1), is circulating in nature. At this resonance frequency (occurring at a series RLC resonance), due to the spatial asymmetry present 22
in the structure with respect to the incident E-field, the charge gradient in one of vertical arm dominates over the other, thus giving rise to circulating currents (shown in Fig. 3.8(b). In literature, this resonance is called as EEMR (Katsarakis et al., 2004). However, the induced H-field rising due to this circulating current is not opposing the incident H-field (as both are orthogonal), and therefore the effective µr is not negative. The dip at higher frequency (≈ 0.229 THz) is attributed to the electrical resonance as surface current density, shown in Fig. 3.8 (marked as 2), and is oscillatory in nature.
Transmission [dB]
(a)
(b)
0 1
-10
E
-20
k
1
-30 -40
Simulation Experiment
2
H 2
0.1 0.2 0.3 Frequency (THz)
Figure 3.8: (a) Experimental and simulated transmission characteristics of SqSRR in perpendicular orientation along with instantaneous surface current profile at fm of both resonance. (b) Pictorial representation showing the reason of circulating current at EEMR.
3.3.3
Double Slits present on Adjacent Sides (DAS)
The DAS is asymmetric in both azimuthal orientations. Therefore, like asymmetric orientation of SqSRR, two dips in the transmission characteristics were observed, as shown in Fig. 3.9(a). However, there is a distinct blue shift in both dips in comparison to SqSRR. The instantaneous surface current density at fm , shown in Fig 3.9(b), shows circulating current profile for the first dip (marked as 1) and oscillating current profile for the second dip (marked as 2). Hence, the first (≈ 0.123 THz) and the second dip (≈ 0.301 THz) are attributed to EEMR and electrical resonance respectively. The EEMR was shifted by ≈ 1.54 times that of SqSRR due to the presence of an additional series capacitance (slit) of almost equal value. There was a decrease in the strength of the attenuation at the transmission dip because of increased dielectric loss in these capacitors (due to the fringing fields). The shift in the electrical resonance frequency is also due to 23
the presence of extra capacitance in the horizontal arm. The role of the horizontal arms in determining the electrical resonance will be discussed in more details in subsequent section.
Transmission [dB]
(a)
(b)
0
-10
-20
1
2
E
k
H
DAS SqSRR 0.1 0.2 0.3 Frequency (THz)
Figure 3.9: (a) Experimental transmission characteristics of DAS compared with perpendicular orientation of SqSRR. (b) Instantaneous surface current density at fm of both resonance (marked by numbers).
3.3.4
Double Slits present on the Opposite Sides (DOS) and Four Slits present on all four sides (FS)
Both DOS and FS have spatial symmetry with respect to the incident E-field in both azimuthal orientations and hence only one dip corresponding to the electrical resonance was observed. In azimuthal orientation, where the vertical arms of the DOS are identical to that of CR, the transmission characteristics are similar, as shown in Fig. 3.10(a). On rotating the structure by 90o , the vertical arms of DOS is similar to that of FS. Therefore, the transmission characteristics of these two cases are almost identical, as shown in Fig. 3.10(b)
3.3.5
Effect of the horizontal arms on electrical resonance
The discussed results till now seem to support the conventional cut-wire approximation (ref. Fig 3.6). However, on meticulously analysing the instantaneous surface current density of all the discussed structures at electrical resonance, the surface current can be
24
0
(b)
Transmission [dB]
Transmission [dB]
(a)
-10
-20
-30
DOS CR 0.1 0.2 0.3 Frequency (THz)
DOS FS
0
-10
-20
0.1 0.2 0.3 Frequency (THz)
E DOS
k
H
DOS
Figure 3.10: (a) Experimental transmission characteristics of DOS: (a) Compared with CR when arms without slits are parallel to the incident E-field along with instantaneous surface current profile of DOS at fm . (b) Compared with FS when arms with slits are parallel to the incident E-field. Instantaneous surface current profiles of DOS at fm in both cases are also shown.
seen flowing into horizontal arms from the top extreme of the vertical arms and out of it at the bottom extreme of the vertical arms. Also, the simulated transmission characteristics of symmetric SqSRR structures with decreasing horizontal arms length, i.e moving from the closed ring to the vertical stripes (ref. Fig. 3.11(a)), shows a significant blue shift in the transmission characteristics, as shown in Fig. 3.11(b). These blue shifts further strengthen the fact that, contrary to cut-wire approximation, horizontal arms also play a role in determining the electrical resonance. With a decrease in the horizontal arm length, blue shift in ωp indicates that the horizontal arms, instead of providing free electrons in dipole oscillation, are reducing it. This also proves that, free electrons present in the vertical arms are the only ones participating in the dipole oscillation. The dipole oscillation will momentarily create charge accumulation at the top and the bottom of the vertical arms. In the presence of the horizontal arms, these accumulated charges will lead to a potential gradient, thus leading to a surface current in the horizontal arms (termed as the compensating current), as shown with blue arrows in Fig. 3.11(c). This compensating current reduces the free electrons present in the vertical arms. To model the net reduction of free electrons in the vertical arm as a function of 25
(b)
(c)
Normalized Transmission
(a)
+Q
+Q
-Q +Q`
-Q +Q`
Decreasing arm length
1
0.5
Q` < Q
0 0.1
0.2 Frequency (THz)
0.3
-Q`
-Q`
Figure 3.11: (a) Microscopic images of fabricated structures with decreasing horizontal arm length (b)Simulated transmission characteristics showing blue shift with decrease in length of horizontal arm.(c) Modified response after taking horizontal arms into consideration.
the horizontal arms length, the expression for plasma frequency (ωp ) for the periodic structures of thin wires given in (Pendry et al., 1996) by Eq. (3.1) was taken as a starting point (ref. section Fundamentals of Metamaterial for more detail). ωp2 =
Nef f e2 0 mef f
(3.1)
where Nef f is the effective electron density in a unit cell, e is the charge of electron, mef f is the effective mass of electron and 0 is the permittivity of free space. In case of SqSRR, if the effect of the horizontal arms are neglected, the effective electron density Nef f can be given as, Nef f = 2 × n
lw L2
(3.2)
where N is the electron density in the bulk medium, l is the length, w is the width and L is the lattice constant (refer to Fig. 1(a)). The factor of the 2 comes in the equation due to the presence of 2 vertical arms that are symmetric about the vertical axis. In this study, all SqSRR structures considered were symmetric about the vertical axis and asymmetric modifications, even though possible, are not considered for simplicity. If the effect of the horizontal arms are considered, Nef f will decrease due to the flow of accumulated charges from the vertical into the horizontal arms. In Eq. (3.1), mef f is assumed to be a constant for all variations of horizontal arms, as in all the cases, the surface current densities in the vertical arms were of the same order. Due to the vertical symmetry, assuming uniform distribution of electrons over the entire length of metal in 26
the left half of the unit cell (as electron will quickly redistribute along the horizontal arm to nullify the potential gradient), the effective metal length on the left half of unit cell can be rewritten as (ref. Fig. 4(a)) Effective Metal Length = Vertical Arm length + Top Horizontal Arm Extension + Bottom Horizontal Arm Extension Each horizontal arm extension =
l g −w− 2 2
Effective Metal Length = 2l − 2w − g Now, the effective electron density (Nef fmodif ied ) will be reduced and can be written as Nef fmodif ied = Nef f ×
l (2l − 2w − g)
(3.3)
where g is the gap width. In the case of vertical stripes (cut-wire), the above modification will reduce to Eq. (3.2). On substituting Eq. (3.3) in Eq. (3.1) and representing it in terms of cut-wire plasma frequency we get, 2 ωp2modif ied = ωcutwire
l (2l − 2w − g)
(3.4)
where, 2 ωcutwire =
Nef f e2 . 0 mef f
(3.5)
Also due to the finite length of the vertical arm, r is negative between f0 and fp . This lower cut-off frequency (f0 ) has been empirically derived in (Koschny et al., 2003) as, √ f0 = [clight / 2πl] × [a0 ln(l/∆) + a1 ]−1/2
(3.6)
where clight is the speed of light in vacuum, ∆ is the separation between the vertical arms of adjacent unit cells, a0 and a1 are model fitting parameters. Since, we have assumed uniform distribution of electrons over the entire length of the metal l, the expression can be modified as, √ f0modif ied = [clight / 2π(2l − 2w − g)] × [a0 ln((2l − 2w − g)/∆) + a1 ]−1/2
(3.7)
The blue shift in the transmission characteristics were experimentally validated by 27
1
l/2-w
w
0.5 g/2
0 0
1 0.5
fo
fp
f
p
modified
fm
Frequency
0 0
Normalized frequency
l
(b)
Transmission
l/2-w-g/2
Normalized frequency
Normalized frequency
(a)
f
f
01
modified
p
f modified
Sim. f
m
Sim. f
0
modified
Exp. f
m
0.5
100 0 Length 0 of Horizontal 100 arm (m) 200 100 200(m) Length of Horizontal arm Length of Horizontal arm (m)
fabricating and characterizing, several SqSRR structures with varying horizontal arm length. The variation of the modified plasma frequency (fpmodif ied = ωpmodif ied /2π), the modified resonant frequency(f0modif ied ) and the fm after normalizing with respect to their cut-wire response as a function of the horizontal arm length are plotted in Fig. 3.12(b). It can be seen that they are in good agreement.
Summary
In this chapter, a THz band stop filters based on SqSRR were designed, fabricated and characterized for 0.05 THz - 0.35 THz. Various geometrical modifications of SqSRR were investigated to know the effect of the azimuthal orientation and the position/number of slits on the number of dips occurring in transmission characteristics due to various resonances. Using full wave Maxwell simulations, the origin of the multiple resonances were attributed to oscillatory or circulating currents. It was shown that in structures symmetric about the incident E-field, only one dip in transmission characteristics due to oscillatory surface current in the vertical arms (electrical resonance) occurred, whereas in structures asymmetric about the incident E-field, an additional dip in the transmission characteristics due to circulating surface current (EEMR) was observed. The azimuthal orientation of SqSRR, was used to turn on/off the EEMR, while the electrical
28
Exp. f
m
Figure 3.12: (a) Effective metal length in SqSRR after considering horizontal arm. (b) Normalized modified plasma frequency (fpmodif ied ), electrical resonance frequency (f0modif ied ) and the corresponding transmission (fm ) versus length of horizontal arm. These frequencies are normalized with respect to the corresponding cut-wire response. Inset shows position of f0 , fm , fp in typical transmission characteristics.
3.4
m
200
resonance shifted in frequency. The presented results show the importance of analyzing the nature of resonances in both symmetric and asymmetric structures in order to distinguish clearly between EEMR and electrical resonance. Also, it was shown that, contrary to conventional cut-wire approximation, the horizontal arms play a significant role in determining the electrical resonance by providing a path for the redistribution of momentarily accumulated charges at the ends of the vertical arm. This effect was modelled, assuming uniform distribution of electrons over the entire length of metal and was found to give good agreement with simulated and experimental results.
29
CHAPTER 4
Fishnet Metamaterial (FM) based static THz band pass filters
4.1
Introduction
The combination of periodic arrays of continuous wires and SRRs cannot be used to achieve Negative Index (NI) condition at normal incidence, as in this polarization, the induced H-field arising due to the circulating current of SRR is orthogonal to the incident H-field. Therefore, SRR loses its ability to provide an effective negative µr . However, this impediment has been overcome by gradually reducing the SqSRR to cutwire pairs and rotating them by 90o in order to make the induced H-field parallel to the incident H-field, as shown in Fig. 4.1 (Dolling et al., 2005). These cut-wire pairs are compatible to CMOS fabrication technique and have higher LC resonance frequency than SRR of same dimensions due to overall smaller capacitance.
Figure 4.1: Evolution of SqSRR to pair of cut-wires. Taken from (Dolling et al., 2005)
The periodic arrays of cut-wire pairs (shown in Fig. 4.2(a)) are combined with continuous wires (shown in Fig. 4.2(b)) to obtain the planar structure as shown in Fig 4.2(c), for NI response at normal incidence. This planar structure, consisting of a stack of perforated metal layers separated by a dielectric medium, is called as Fishnet Metamaterial (FM) (Kafesaki et al., 2007). Since their inception, FMs have been extensively used to achieve NI at optical frequencies (Shalaev, 2007; Valentine et al., 2008).
In this chapter, the fist section will be dedicated to the discussion of design, fabrication and characterization methodologies of FM based band pass THz filters whereas the second section expounds the analysis of the obtained experimental and simulated transmission characteristics and various methods for identifying the observed transmission as due to Positive Index (PI) or NI.
(a)
(b)
(c)
E
k
H
Figure 4.2: (a) Periodic array of pairs of cut-wires (b) Periodic array of continuous wires. (c) Fishnet metamaterials after combining (a) and (b)
4.2 4.2.1
Methodology Design
The geometrical parameters of FM showing band pass characteristics in 0.05 - 0.25 THz were determined by a commercial full wave Maxwell’s equation solver (Ansoft, 2013). Perspective view of the unit cell showing the boundary conditions used in the simulation, is given in Fig. 4.3(a). Wave ports were used at the top and the bottom of the unit cell for exciting and receiving the electromagnetic waves at normal incidence. Unlike SqSRR, designed FMs were polarization insensitive, therefore, Periodic Boundary Condition (PBC) were used on the remaining four sides. Top and bottom metallic layers of FM were defined using 200 nm thick Aluminium (Al) layer with a conductivity of 38 × 106 S/m. The dielectric medium separating the top and bottom metallic layers was defined using a 180 µm thick glass having refractive index of 2.45 + 0.0597i (Naftaly and Miles, 2007). Top view of a unit cell showing the optimized geometrical parameters for 1 mm and 2 mm period are shown in Fig. 4.3(b).
31
(a)
(b) Excitation Port l w PBC g
g Receiver Port
L
Figure 4.3: (a) Perspective view of unit cell of FM along with boundary conditions used in simulation. Top view of the unit cell. Geometrical parameters for 1 mm period are L = 1 mm, metal arm length l = 0.6 mm , metal width w = 0.6 mm and gap g = 0.2 mm. For 2 mm period, these parameter are: L = 2 mm, metal arm length l = 1 mm , metal width w = 1 mm and gap g = 0.5 mm
4.2.2
Fabrication
Perforated metallic layers corresponding to the optimized geometrical dimensions were fabricated indigenously on either side of borosilicate glass (BK7; ≈ 18 mm × 18 mm × 180 µm), acting as dielectric layer. Instead of wet etching, lift-off technique was used for easy alignment of the top PPR pattern with the bottom metallic layer. The schematic representation of complete fabrication steps are shown in Fig. 4.4 and following subsections elaborate them in details.
32
U V
(a) Glass Substrate (side 1)
(f) PPR removal
(b) PPR coating
(e) Al deposition
(c) UV exposure using mask
(d) PPR development U V
(g) Glass Substrate (side 2)
(l) PPR removal
(h) PPR coating
(i) UV exposure using mask
(k) Al deposition
(j) PPR development
Figure 4.4: Schematics of fabrication steps followed to realize FM)
Substrate Cleaning Borosilicate glass substrates were sonicated in Acetone for 2 minutes using ultrasonic agitator to remove organic impurities followed by IPA and DI water for another 2 minutes each. After sonicating in DI water, substrate was quickly dried with N2 to prevent forming of DI water stain.
Photolithography The mask layouts of optimized geometry were created using L-EDITT M 15 CAD tool. The layouts were converted to the standard photomask writer compatible format, Graphic Database System 2 (GDSII). Since, the minimum feature size of patterns was more than 200 µm, Printed Circuit Board (PCB) mask was preferred as low cost alternative. The
33
complementary patterns, suitable for lift-off, were printed on Cellulose films and then pasted on fused silica glass plate using transparent glue. The cleaned samples were kept in oven at 120◦ C for 5 minutes for dehydration bake to ensure complete removal of moisture for proper adhesion of PPR. The spin parameters used for PPR coating were optimized to obtain the thickness at least thrice the thickness of the metal layer to ensure proper lift-off. The optimized parameters are given in Table 4.1. PPR coated samples were baked in hot air oven at 80◦ C for 20 minutes to harden the PPR. Table 4.1: Spin parameters of PPR Spin Rate
:
3000 RPM
Acceleration
:
600 RPM/sec
Time
:
40 sec
The PPR coated samples were then aligned with the photomask using MA6/BA6 mask aligner and exposed to UV( λ =365 nm (i-line); intensity ≈ 3.7 mW/cm2 ) for 10 seconds. The samples after exposure were soaked in Chlorobenze for ≈ 1 minute to create oblique side walls in PPR after development for easier lift-off as the top surface of PPR will swell and become more resistant to developer solution after treating with chlorobenzene. Samples were not rinsed with DI water after this process. Then the samples were gently shaken in 0.1 M NaOH solution for ≈ 18 seconds to develop the pattern. High temperature processes including post baking were avoided to prevent hardening of PPR, which will result in unsuccessful lift-off.
Metallization Approximately 200 nm Al was deposited on patterned substrates using UHV thermal evaporation unit 1 at room temperature and pressure 4.6 × 10−6 mbar. 1
HPVT-305G; manufacturer: HPV technology
34
PPR removal The samples were dipped in acetone for ≈ 10 minutes to dissolve the underneath PPR. In few cases, when PPR was not dissolved completely even after heating in acetone, ultrasonic agitation was tried. However, ultrasonic agitation was found to create uneven edges, therefore it was not used in further runs. As an alternative, disposable syringe was used to create acetone jet flow striking the sample’s surface resulting in successful lift-off. Glass substrates were flipped and processes from photolithography to PPR removal were repeated to obtained second metal pattern. The microscopic images of the fabricated structure with 1 mm and 2 mm period are shown in Fig. 4.5. (a)
(b)
400 μm
400 μm
Figure 4.5: Microscopic image of fabricated structures having period of : (a) 1 mm (b) 2 mm.
4.2.3
Characterization
The fabricated structures were characterized using the same setup as described in section (3.2.3). However, in this case the obtained photocurrents were first normalized with respect to air and then with itself, as the glass substrate used the sandwiched dielectric was an integral part of the structure.
35
4.3
Results and Discussions
The simulated and experimental transmission characteristics of the FM having period of 1 mm, as shown in Fig. 4.6(a), exhibits a high transmission for band of frequencies centered around 0.193 THz (marked as 3). In order to confirm this pass band as a structural property, transmission characteristics of the FM with 1 mm period was compared with the FM of 2 mm period. Pass band was found to be shifted from 0.193 THz to
(b)
0.8
Experimental Simulation
0.4
3
2 1
0
0.1 0.2 Frequency (THz)
Normalized Transmission
(a)
Normalized Transmission
0.100 THz, as shown in Fig. 4.6(b).
0.8
2 mm 1 mm
0.4
0
0.1 0.2 Frequency (THz)
Figure 4.6: (a)Experimental and simulated transmission characteristics of FM having periodicity of 1 mm. (b) Experimental transmission characteristics of 1mm period compared with 2 mm period.
In Fig. 4.6(a), apart from transmission peak marked as 3, two more small peaks in experimental transmission characteristics marked as 1 (also present in simulation) and 2 are present. The transmission peak marked as 2 is present only in experiment and not consistent. Therefore, it is attributed to the manual tilt present in the mounted sample (Alici and Ozbay, 2008) The transmission peak marked as 1 (occurring at ≈ 0.123 THz) is present in both simulation and experimental transmission characteristics. The exact physical mechanism behind this transmission peak were established by extracting the effective refractive index (nef f ) using simulated transmission (S21) and reflection (S11) parameters (ref section for more details). The real part of nef f , as shown in Fig. 4.7(a), is negative for same band of frequencies (marked as gray). Therefore, this transmission is attributed to NI condition. The occurrence of NI condition can also be verified by analyzing instantaneous surface current density at frequency of maximum transmission 36
(fN I ). At this frequency, surface current density in the top view of upper metallic layer, in the top view of lower metallic layer and displacement current in the side view of dielectric, as shown in Fig. 4.7(b), constitute a circulating current (i.e. moving from upper metallic layer - dielectric layer - lower metallic layer - dielectric layer - upper metallic layer). This circulating give rise to the induced H-field opposite to the incident H-field (shown in Fig. 4.7(b)). (a)
(b) Upper Metal (Top View)
Lower Metal (Top View)
H
k
E
Dielectric (Side View)
Figure 4.7: (a) Extracted real and imaginary values of effective refractive index (nef f ). Gray area shows real and imaginary values corresponding to 1 peak. (b) Instantaneous surface current and displacement current in top view of upper metallic layer (blue color), top view of lower metallic layer (green color) and side view of dielectric (red color) respectively.
Transmission peak marked as 3 (occurring at ≈ 0.193 THz) is due to Positive Index (PI) condition (simultaneous occurrence of positive µef f and positive ef f ) as the real part of nef f , shown in Fig. 4.8(a), is positive (marked as gray). Also, the imaginary part of nef f is seen to be minimum for these band of frequencies, hence, transmission is maximum. The occurrence of PI is due to coupled response of cut-wire pairs (ref. Fig. 4.2(a)) and continuous wires (ref. Fig. 4.2(b)) to incident E-field. The effective permittivity of cut-wire pairs follows lorenzian model whereas effective permittivity of continuous wires follows drude model, as shown in Fig. 4.8(b). However, due to their coupling the resultant effective permittivity will modify as shown in Fig. 4.8(b) (Koschny et al., 2004). On analyzing the resultant effective permittivity, it can be seen that for band of frequencies (ωp0 to ω0 ) it goes to positive. Since, effective permeability is always positive except at NI transmission, occurrence of this positive permittivity will give rise to PI transmission. 37
(a)
(b)
()
()
r
r
0
p
Cut-Wire pairs
p
Wires () '
p
0
p
Wires +Cut-Wire pairs
Figure 4.8: (a) Extracted real and imaginary values of effective refractive index (nef f ). Gray area shows real and imaginary values corresponding to 3rd peak. (b) Typical effective r profile for periodic cut-wires pairs, continuous wires and combination of continuous wires and cut-wire pairs. Taken from (Koschny et al., 2004)
NI transmission is lower than PI transmission mainly due to high loss in the sandwiched dielectric medium. This was concluded by analyzing simulated NI transmission for different dielectric losses. Fig. 4.9 shows significant improvement in transmission amplitude and quality factor of NI peak with decrease in loss in dielectric layer. Slight
Normalized Transmission
shift in fN I may be due to increase in overall mutual inductance.
Actual loss 50% loss No loss
0.4
0.2
0
0.12 0.14 Frequency (THz)
Figure 4.9: (a)Simulated transmission characteristics showing effect of sandwiched dielectric’s loss on NI transmission. The NI transmission has been normalized with respect to the PI transmission.
The effect of static E-field on the transmission characteristics of FM was studied by applying 9 V battery to top and bottom metallic layers, as shown in Fig. 4.10. 38
The transmission characteristics of FM under influence of static E-field was found to be identical with that of FM without its influence, as shown in Fig. 4.10(b). This experiment was performed to validate the idea of electrical tunablility in FM, which
(a)
(b)
9V
Normalized Transmission
will be discussed in detail in next chapter.
0.8
0V 9V
0.4
0
0.1 0.2 Frequency (THz)
Figure 4.10: (a) Schematic view of FM under static E-field test. (b) Experimental transmission characteristics of FM after applying 9 V battery compared with FM without influence of static field.
4.4
Summary
In this chapter, Static band pass filter in the THz frequencies, utilizing FM were designed, fabricated and characterized. The occurrence of peaks in transmission characteristics and their identification as PI or NI peak with help of extracted effective refractive index and calculated surface current density were discussed. Further, it was shown that NI peak is more susceptible to losses in sandwiched dielectric layer. Lastly, the presence of static electric field was found to have no effect on transmission characteristics of FM.
39
CHAPTER 5
Electrically tunable THz band pass filters
5.1
Introduction
In the previous chapter, it was shown that NI transmission is less than PI transmission. Despite this fact, NI transmission is of interest because the frequency of NI transmission (fN I ) is independent of the thickness of the sandwiched dielectric but depends inversely on the square root of its permittivity, as shown in Eq. 5.1) (Kafesaki et al., 2007). 1 1 fN I = √ × . π µ L
(5.1)
where L is the length of the unit cell, is the permittivity and µ the permeability of the sandwiched dielectric layer. This inverse dependence of fN I on the permittivity of the dielectric medium had been utilized to design a novel electrically tunable THz band pass filter. To achieve tunability, an air gap as a dielectric medium of variable thickness was introduced between the top metallic layer an the dielectric medium. The variation in the thickness of the air gap with the application of electrostatic force between the top and bottom metallic layers changes the overall permittivity of the sandwiched layers, which in turn changes fN I . In literature, there have been few demonstrations of structural tunability in metamaterials. However, these structures required complex fabrication techniques and tuning methods. Some of the prevalent tuning methods are cantilevers, thermal gradient, liquid crystals, mechanical stress, etc. (Minovich et al., 2010; Li and Wang, 2010; Tao et al., 2011; Ou et al., 2011; Liu et al., 2012). The proof of concept device was designed for higher fN I (8 THz) as increasing fN I reduces the length of the unit cell (ref. Eq. 5.1). The miniaturized unit cell had several advantages like - reduction in thickness of dielectric medium required to have good quality factor, low loss in dielectric medium, low voltage requirement for actuation of
the upper membrane and reduction in complexity of the fabrication steps to achieve the air gap comparable to the thickness of the static dielectric medium. In first section of this chapter, designing and fabrication aspects of tunable filters have been discussed. Fabrication and characterization methods of static FM of same geometrical parameters is also presented. The second section deals with analysis of change in electromagnetic response with electrostatic actuation of tunable structure. This section culminates with discussion of experimental results of the static FM and fabrication difficulties of a large area membrane release.
5.2 5.2.1
Methodology Design
The geometrical parameters of a tunable FM having fN I around 8 THz were determined by commercial full wave Maxwell’s equation solver (Ansoft, 2013). The top and bottom metallic layers were defined using 2 µm and 150 nm thick Au layers respectively. Top membrane was made thicker so that it would have enough mechanical strength to sustain the actuation. Static sandwiched dielectric layer was defined using 3 µm thick PDMS having refractive index 1.533 + 0.013i (Khodasevych et al., 2012) and variable dielectric layer was defined by 2 µm air gap. The top and cross sectional view of unit cell along with optimized dimensions are shown in Fig. 5.1(a). The beam spot size in the characterization setup is ≈ 1 cm and to get a response of the FM, the complete beam should interact with the structure. This was inferred by studying the response of static fishnet structures of dimension 1 mm × 1mm, fabricated using existing micromirror mask (shown in Fig. 5.2), used in (Prakash et al., 2011). In this case we were unable to extract the response of the structure possibly due to low interaction area resulting in poor signal-to-noise ratio. Therefore, the optimized dimensions of unit cell obtained from electromagnetic simulation were repeated across 1.5 cm X 1.5 cm in lateral directions. However, such large membranes pose a serious problem of sagging. To avoid unwanted sagging of the top membrane, supportive pillars (75 µm × 75 µm) were provided at regular interval of 500 µm. Microscopic image showing the top view is shown in Fig. 5.1(b). Supporting pillars are shown by red 41
boxes. The pull-in voltage (the minimum voltage at which top membrane will snap as the electrostatic force at and above this voltage dominates the restoring force) of this repeating unit was calculated using commercial MEMS based simulator (IntelliSense, 2013). (a)
(b)
575 μm
L
A
l
Top View
A’ 575 μm
g
g 75 μm
tair
75 μm
Side View (AA’)
Figure 5.1: (a) Top and Side view of a tunable FM unit cell along with geometrical dimensions. Thickness of air tair = 0 - 2 µm. (b) Microscopic image of repeating unit of membrane with dimensions. Boxes show the supporting pillars.
Figure 5.2: Microscopic image of static FM fabricated using micromirror mask.
42
5.2.2
Fabrication
Structures with optimized geometrical parameters were fabricated on silicon (Si) substrate. Specification of substrate is given in Table. 5.1. Table 5.1: Parameters used for spin coating PPR Doping
:
P-type
Resistivity
:
1-10 Ω-cm
Crystal Orientation
:
Thickness
:
200 µm
The careful selection of substrate was made after analyzing the transmission characteristics of available options. The least absorption in frequency range around 8 THz was observed in 200 µm thick Si substrate, as shown in Fig. 5.3. Schematic of fabrication
Normalized Transmission
steps is shown in Fig. 5.4 and corresponding details are given in following subsections.
0.6
0.4
0.2
0
Si (200 m) BK7 (180 m) Si (500 m) 3 6 9 Frequency (THz)
Figure 5.3: Normalized transmission characteristics of various substrates. These transmissions are normalized with respect to transmission of free space/atmosphere.
Substrate Cleaning Silicon substrates were boiled in Trichloroethylene (TCE) followed by Acetone for 2 minutes each to remove organic contamination. The substrates were then quickly rinsed 43
(a) Silicon Substrate (≈ 200 μm thick)
(b) Cr/Au deposition for bottom layer
(c) Patterning of Cr/Au
(f) Deposition of Cr/Au as seed layer
(e) Coating and Pattering of PPR as sacrificial layer
(d) Deposition of PECVD SiO2 dielectric layer
(g) Electroplating + Patterning of Cr/Au
(h) Removal of sacrificial layer
Figure 5.4: Schematics showing the fabrication steps of tunable FM
in DI water to remove Acetone and dried with N2 . To remove inorganic contamination these substrates were further boiled in nitric acid (HNO3 ) till white fumes were observed. The substrates were rinsed in DI water and dried with N2 . This treatment formed a thin oxide film on the surface which was confirmed by its hydrophyllic nature. Then these substrates were dipped in 10 percentage v/v Hydroflouric acid (HF) for 30 seconds, rinsed in DI water and dried with N2 . This treatment removed the oxide layer, thus exposing fresh silicon surface, which was confirmed by its hydrophobic nature.
Bottom layer Metallization Approximately 20 nm Chromium (Cr) and 150 nm Gold (Au) were deposited on cleaned substrates using UHV e-beam evaporation unit as described in section 3.2.2
Photolithography of bottom layer The mask layouts of optimized geometry of FM (Mask-1) and supporting pillars (Mask2) were created using L-EDIT 15 CAD tool. Fig. 5.5 shows section of these two masks. For easy alignment, plus shaped alignment markers of Mask-1 were designed comple-
44
mentary to that of Mask-2, as shown in Fig. 5.5. These layouts were then transferred to the PPR coated mask plate using DWL66 writer by following the procedures elaborated in section 3.2.2.
Figure 5.5: (a) Mask-1 (b) Mask-2. Not drawn to scale.
Au coated samples were cleaned in DI water and dried with N2 . These samples were then kept in oven at 120◦ C for 5 min for dehydration bake. Spin parameters used for PPR coating were same as given in Table 3.2. PPR coated samples were baked in oven at 80◦ C for 20 minutes to harden the PPR. The PPR coated samples were then aligned with the Mask-1 using MA6/BA6 mask aligner and exposed to UV( λ =365 nm (i-line); intensity ≈ 3.7 mW/cm2 ) for 10 seconds. The exposed PPR was dissolved by gently shaking the samples in 0.1 M solution of NaOH for ≈ 10 seconds. Before doing wet etching of deposited Cr/Au layers, the developed samples were baked in oven at 120◦ C for 20 minutes to further hardened the remaining PPR.
Wet Etching The wet etching of deposited Cr/Au were performed at room temperature using Cr and Au etchant respectively as described in section . The optimized etching time of Cr and Au using these etchants were ≈ 32 seconds and ≈ 25 seconds respectively.
PPR removal The PPR present on the samples was removed by boiling them in acetone for ≈ 10 min. If PPR patches were present even after boiling in acetone, PPR ashing was carried out 45
with the parameters given in Table 3.3.
Deposition of Dielectric layer Silicon dioxide (SiO2 ), acting as dielectric layer, was deposited using PECVD system. The optimized parameters used for deposition are summarized in Table 5.2. The thickness of the deposited oxide layer was measured using spectroscopic ellipsometer 1 . Table 5.2: PECVD Silicon dioxide deposition parameters Temperature
:
300◦ C
Pressure
:
0.2 mbar
Silane
:
6 sccm
N2 O
:
160 sccm
RF power
:
10 Watts
Deposition rate
:
35±5 nm/min
Deposition time
: ≈ 55 minutes
Coating and photolithography of sacrificial layer PPR, acting as sacrificial layer, was spin coated using parameters given in Table 3.2. The sacrificial layer coated samples were then aligned with the Mask-2 using MA6/BA6 mask aligner and exposed to UV( λ =365 nm (i-line); intensity ≈ 3.7 mW/cm2 ) for 10 seconds to create pits for supporting pillars. The exposed samples were developed using same procedure as mentioned in above photolithographic step. Post baking at 80◦ C for 20 minutes was done to remove moisture and trapped remaining solvents before top layer metallization. This was to prevent any damage to top metallic layer due to bubbles formation in sacrificial layer (as shown in Fig. 5.6) during further high temperature processes. 1
M-2000; manufacturer: J.A. Wollam
46
300 μm
Figure 5.6: Microscopic image showing formation of bubbles in underlying PPR.
Top layer metallization Approximately 40 nm Chromium (Cr) and 100 nm Gold (Au) were deposited on patterned sacrificial layer using UHV e-beam evaporation unit at room temperature and pressure 2.1 × 10−6 mbar. This was used as seed layer for further thicking of Au by electroplating. The parameters used for electroplating are given in Table 5.3. Table 5.3: Au electroplating parameters Electrolyte
:
Sulphite based gold solution
Temperature
:
62◦ C (Constant temperature water bath)
Current density
:
0.25 mA/cm2
Deposition Rate
: ≈ 16 nm/min
Photolithography & wet etching of top layer Same procedure as that for bottom layer was used to pattern the top layer. However, due to higher thickness of Cr and Au etching time was increase to 3 minutes and 2 minutes respectively.
Removal of top PPR and sacrificial layer To remove top PPR and sacrificial layer procedure given in (Sharma and DasGupta, 2008) was followed. As per the procedure, samples were first dipped in Acetone twice for 15 minutes each to remove major portion of PPR. Then samples were treated with 47
Piranha (Appendix B.3) for 15 minutes to remove residual PPR. The treated samples were again dipped in Acetone twice for 15 minutes each to completely remove traces Piranha. To prevent stiction, samples were transferred from Acetone to Carbinol and kept for 15 minutes twice to ensure complete replacement of Acetone. From Carbinol samples were then transferred to IPA and kept for 15 minutes twice to ensure complete replacement of Carbinol. The samples were taken out of IPA and kept tilted in oven at 80◦ C for 30 minutes. This sequence was followed keeping in mind the lowest surface tension and boiling point of IPA among the three solvents. Before fabricating the tunable filters, static filters with same dimensions were fabricated following the above procedure except for the deposition of the sacrificial layer and electroplating, as these two processes were not used. Microscopic image of fabricated structure is shown in Fig. 5.7.
Figure 5.7: Microscopic image of static FM with PECVD SiO2 as sandwiched dielectric layer.
5.2.3
Characterization
Characterization of fabricated static structures were performed on Fourier Transform InfraRed (FT-IR) spectrometer
2
at normal incidence. The system consists of broad-
band incoherent electronically temperature controlled IR source having spectral range of 700-50 (cm−1 ) and DTGS (PE) receiver. Since, the measurement chamber was not completely free from atmospheric water vapor, average of several measurements were taken to cancel its effect. The obtained transmission characteristics were normalized with respect to a transmission of bare silicon substrate of same thickness to remove the 2
NICOLET 6700
48
effect of the substrate.
5.3
Results and Discussion
Fig. 5.8(a) shows blue shift in fN I with increase in air gap where as there is no shift in PI peak. fN I shifted from 7.85 THz to 9.25 THz as the air gap was varied from 0 µm to 2 µm. fN I is increasing with increase in air gap due to the decrease in the average permittivity of the dielectric medium present between metallic layers. Fig. 5.8(b) shows the displacement of the top membrane as function of applied voltage across the top and bottom metallic layers and the cross-sectional view of the deformed top metallic layer at pull-in voltage. Pull-in voltage was calculated to be ≈ 9V. (a)
Displacement (m)
Normalized Transmission
(b)
1
0 m 1.5 m 2 m
0.5
0 7
8 9 10 11 Frequency (THz)
2
1
0 0
5 Voltage (V)
10
Air gap
Figure 5.8: (a) Transmission characteristics of the tunable FM showing shift in the negative peak with variation in the air gap thickness.(b) Displacement versus Voltage graph showing pull-in voltage ≈ 9 V and cross-sectional view of deformed top metallic layer at pull-in voltage.
The experimental transmission characteristics of two fabricated static samples after normalizing with respect to the transmission characteristics of a bare substrate are shown in Fig. 5.9(a). The transmission characteristics show the NI peak at 3.5 THz and PI peak at 4.5 THz. First and second microscopic image of Fig. 5.9(b) shows respectively unoptimized and optimized etching of top metallic layer. Due to the requirement of large and thick top metallic layer, release of entire membrane was a challenge due to improper etching of etch-holes, mostly due to thickness fluctuations in the electroplating process. The problem was partially mitigated using a lower current density for electroplating of top 49
Normalized Transmission
(a)
(b)
1 0.8
Sample 1 Sample 2
0.6 0.4 25 μm
25 μm
0.2 0
2
3 4 Frequency (THz)
5
Figure 5.9: (a) Transmission characteristics of two similar fabricated static FM. (b) Microscopic image showing non-uniform etching before optimization and uniform etching after optimization.
layer to ensure more uniformity and by decreasing the thickness of the top layer to ≈ 700 nm to reduce under-cuts. Also releasing using wet release process described above resulted in poor yield because the vigorous reaction of piranha tore the top membrane and also severely affect the underlying dielectric layer. Therefore, dry release using O2 plasma has to be optimized.
5.4
Summary
Electrically tunable THz band pass filter showing tunability of ≈ 28 GHz/V around 8 THz was designed by electrostatically changing the thickness of air gap introduced between top metallic layer and sandwiched dielectric layer. The fabrication and characterization of static FM with miniaturized designed parameters were discussed. Further, few fabrication difficulties in proper release of large membrane and possible ways to circumvent these difficulties were expounded.
50
CHAPTER 6
Summary and Conclusion
In this thesis, concepts of optical metamaterials have been utilized to demonstrated static band stop filters and band pass filters in THz frequency regime. This concept was further extended to design novel electrically tunable band pass filter by concatenation of metamaterial and MEMS. No natural materials, till now have been reported to have simultaneous occurrence negative r and negative µr . Therefore, in chapter 2, artificial ways to engineer negative r using continuous wire and negative µr using SRR in desired frequency range have been discussed. Thoughtful combination of these two structures was shown to exhibit NI properties. In chapter 3, Square Shaped SRR and its several geometrical modifications, operating in 0.05- 0.35 THz, was designed, fabricated and characterized. The experimental results and analysis based on surface current profile, highlighted the importance of geometrical symmetry on number and position of dips in transmission characteristics. For asymmetric orientation with respect to the incident E-field, two dips corresponding to EEMR and electric resonance were observed whereas in symmetric orientation EEMR completely vanished, thus giving raise to only one dip corresponding to electrical resonance. It was further shown that contrary to conventional approximation, the dip in transmission characteristics occurring due to electrical resonance shows significant blue shift with decrease horizontal arm length. These shifts were attributed to the dilution of the effective electron density (Nef f ) of vertical arms and a modification in existing models were proposed to accommodate these shifts. Inability of SqSRR to yield negative mu at normal incident led to invention of planar Fishnet Metamaterial (FM). In chapter 4, response of the FM was used to demonstrate band pass filters in 0.1- 0.25 THz. The occurrence pass bands in the experimental and simulated transmission characteristics were identified as NI and PI transmission with the help of retrieved effective refractive index and surface current density. Low
transmission at the NI pass band with respect to the PI pass band was mainly due to losses in sandwiched dielectric. In chapter 5, using the inverse dependence of frequency of NI transmission on permittivity of sandwiched dielectric medium, a novel polarization independent electrically tunable band pass filter showing tunability of ≈ 28 GHz/V around 8 THz was designed by integrating electrostatic actuation technique to static FM. Before fabrication of tunable structure, the optimized dimensions were used to demonstrate static FM. However, to satisfy characterization constraint, tunable structure was made 1.5 cm X 1.5 cm in lateral direction. This large area membrane lead to various fabrication difficulties. The chapter concludes with elucidation of problems related to release of large membrane and their possible mitigation.
6.1
Conclusions
• A periodic array of Square Shaped Split Ring Resonator (SqSRR) has been designed to exhibit band stop characteristics in THz regime. However, in the case of the symmetric structures, only one dip in transmission characteristics corresponding to electrical resonance (dipole oscillation of electrons in vertical arms) is present whereas in the case of asymmetric structure apart from electrical resonance one more dip due to circulating current, known as EEMR, is present. • Contrary to the conventional cut-wire approximation, horizontal arms also play a significant role in the electrical resonance as the presence of horizontal arms dilute the effective electron density of vertical arms. • Fishnet Metamaterial (FM) with proper dimensions can be used as THz band pass filters. However, two pass bands, one due to Negative Index (NI) transmission and other due to Positive Index (PI) transmission are present. • Effective refractive index extracted using magnitude and phase of obtained Sparameters, can be used to identify given transmission as NI or PI. • NI transmission is more susceptible to permittivity and losses of medium separating two metallic layers. • A novel polarization independent electrically tunable band pass filter utilizing inverse dependence of frequency of NI transmission on the permittivity of underlying dielectric has been proposed.
6.2
Scope of future work
Future works include, 52
a) Optimization of dry release process using O2 plasma to successfully release the top membrane. b) Increasing the transmission efficiency of NI peak by using less lossy dielectric medium like Polyimide or PDMS. c) Demonstration of tunability in range of 1-2 THz where signature absorption of most of explosives and narcotics are present. d) Develop these filters into commercial product.
53
APPENDIX A
Matlab code for parameter extraction
close all ; clc ; filename =’ S11_real ’ ; f i l e n a m e =[ f i l e n a m e
’. txt ’ ] ;
data=load ( filename ) ; S11_real=data ( : , 2 ) ;
f i l e n a m e = ’ S11_imag ’ ; f i l e n a m e =[ f i l e n a m e
’. txt ’ ] ;
data=load ( filename ) ; S11_imag= d a t a ( : , 2 ) ;
filename =’ S21_real ’ ; f i l e n a m e =[ f i l e n a m e
’. txt ’ ] ;
data=load ( filename ) ; S21_real=data ( : , 2 ) ;
f i l e n a m e = ’ S21_imag ’ ; f i l e n a m e =[ f i l e n a m e
’. txt ’ ] ;
data=load ( filename ) ; S21_imag= d a t a ( : , 2 ) ;
filename =’ S12_real ’ ; f i l e n a m e =[ f i l e n a m e
’. txt ’ ] ;
data=load ( filename ) ; S12_real=data ( : , 2 ) ;
f i l e n a m e = ’ S12_imag ’ ; f i l e n a m e =[ f i l e n a m e
’. txt ’ ] ;
data=load ( filename ) ; S12_imag= d a t a ( : , 2 ) ;
f i l e n a m e = ’ S22_imag ’ ; f i l e n a m e =[ f i l e n a m e
’. txt ’ ] ;
data=load ( filename ) ; S22_real=data ( : , 2 ) ;
f i l e n a m e = ’ S22_imag ’ ; f i l e n a m e =[ f i l e n a m e
’. txt ’ ] ;
data=load ( filename ) ; S22_imag= d a t a ( : , 2 ) ;
f r e q = d a t a ( : , 1 ) . ∗ 1 e9 ; K0= (2 ∗ p i / 3 e8 ) . ∗ f r e q ; d =1000 e −6; S11= S 1 1 _ r e a l +1 i ∗ S11_imag ; S21= S 2 1 _ r e a l +1 i ∗ S21_imag ; S12= S 1 2 _ r e a l +1 i ∗ S12_imag ; S22= S 2 2 _ r e a l +1 i ∗ S22_imag ;
figure (); p l o t ( f r e q . / 1 e9 , a b s ( S11 ) , f r e q . / 1 e9 , a b s ( S22 ) , ’ L i n e w i d t h ’ , 6 ) ; s e t ( gca , ’ F o n t S i z e ’ , 3 0 , ’ f o n t w e i g h t ’ , ’ b ’ , . . . ’ FontName ’ , ’ Times New Roman ’ ) ; x l a b e l ( ’ F r e q u e n c y ( GHz ) ’ , ’ F o n t S i z e ’ , 3 0 , ’ f o n t w e i g h t ’ , ’ b ’ , . . . ’ FontName ’ , ’ Times New Roman ’ ) ; y l a b e l ( ’ Magnitude of S parameter ’ , ’ FontSize ’ , 3 0 , ’ f o n t w e i g h t ’ , ’ b ’ , . . . ’ FontName ’ , ’ Times New Roman ’ ) ; l e g e n d ( ’ | S_ { 1 1 } | ’ , ’ | S_ { 2 1 } | ’ ) ; xlim ( [ 7 1 1 . 5 ] ) T11 = ( ( 1 + S11 ) . ∗ ( 1 − S22 ) + ( S21 . ∗ S12 ) . / ( 2 . ∗ S21 ) ) ; T12 = ( ( 1 + S11 ) . ∗ ( 1 + S22 ) −( S21 . ∗ S12 ) . / ( 2 . ∗ S21 ) ) ;
55
T21 =((1 − S11 ) . ∗ ( 1 − S22 ) −( S21 . ∗ S12 ) . / ( 2 . ∗ S21 ) ) ; T22 =((1 − S11 ) . ∗ ( 1 + S22 ) + ( S21 . ∗ S12 ) . / ( 2 . ∗ S21 ) ) ;
% i m p e d a n c e _ n u m e r a t o r = ( T22−T11 ) + s q r t ( ( T22−T11 ) . ^ 2 + 4 . ∗ T12 . ∗ T21 ) ; i m p e d a n c e _ d e n o m e n a t o r = 2 . ∗ T21 ;
Sav= s q r t ( S11 . ∗ S22 ) ; i m p _ n u m e r a t o r =(1+ Sav ).^2 − S21 . ^ 2 ; i m p _ d e n o m e n a t o r =(1− Sav ).^2 − S21 . ^ 2 ; impedance= s q r t ( imp_numerator . / imp_denomenator ) ;
f o r i =1: l e n g t h ( impedance ) i f ( r e a l ( impedance ( i ))
