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Active integrated photonic devices in single crystal LiNbO₃ micro-platelets and a hybrid Si-LiNbO₃ platform
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Active integrated photonic devices in single crystal LiNbO₃ micro-platelets and a hybrid Si-LiNbO₃ platform
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Content
ACTIVE INTEGRATED PHOTONIC DEVICES
IN SINGLE CRYSTAL LiNbO
3
MICRO-PLATELETS
AND A HYBRID Si-LiNbO
3
PLATFORM
by
Yoo Seung Lee
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)
August 2011
Copyright 2011 Yoo Seung Lee
ii
Dedication
This Thesis is dedicated to my beloved family:
Wife : Hye Shin Song
Father : Yong Ji Lee
Mother : Soon Jai Cho
iii
Acknowledgements
It is a pleasure to thank the many people. This thesis could not have
been accomplished without their consistent help and support.
First and foremost I would like to express my sincerely appreciation to my
advisor, Prof. William H. Steier, for his guidance, encouragement and support.
During my PhD in his group at University of Southern California, he gave me a lot
of knowledge, insight, and advice and provided a great environment to conduct my
thesis.
I would like to thank the members of my thesis committee Prof. Daniel
Dapkus and Prof. Andrea M. Armani, and the members of my qualification
committee Prof. Robert W. Hellwarth and Prof. Aluizio Prata Jr. for their insight and
advice.
I am really thankful to all past and present members of my research group.
They are Dr. Bipin Bhola, Dr. Greeshma Gupta, Dr. Andrew Yick, Satsuki Takahashi,
Hari Mahalingam, and Nutthamon Suwanmonkha. They gave me knowledge, help
and encouragement.
I must thank my collaborators. Special thanks to Prof. Sang-Shin Lee who is
a professor in the Department of Electronic Engineering at Kwangwoon University,
Seoul, Korea for encouragement and advice. Many thanks to his group members for
their hard work. I also thank Dr. Hyung-Joon Chu, Ting-Wei Yeh and Eric Jaquay for
their help.
iv
I also want to thank to all my friends for their support and encouragement.
Finally, I give my greatest thanks to my wife; father; mother; brothers;
parents-in-law for their constant support, encouragement, advice, prayers, and love.
Thank you for that and everything else blessed and unsaid.
v
Table of Contents
Dedication ii
Acknowledgements iii
List of Tables vii
List of Figures viii
Abstract xiii
Chapter 1: Introduction 1
1.1 Background and Motivation 1
1.2 References 4
Chapter 2: Single crystal LiNbO
3
ultra thin films 6
2.1 Introduction 6
2.2 LiNbO
3
properties and its applications 8
2.3 Crystal ion slicing 10
2.4 Fabrication of single crystal LiNbO
3
ultra thin films 12
2.5 Single crystal LiNbO
3
ultra thin films and its properties 18
2.6 Applications of single crystal LiNbO
3
thin films 21
2.7 Conclusion 22
2.8 References 24
Chapter 3: Free standing single crystal LiNbO
3
micro-platelets 26
3.1 Introduction 26
3.2 Fabrication of free standing single crystal LiNbO
3
micro-platelets 28
3.3 Crystal structure and micro-platelet formation 29
3.4 LiNbO
3
micro-platelet integration to various substrates 31
3.4.1 SiO
2
/LiNbO
3
Substrate 31
3.4.2 SiO
2
/Si Substrate 32
3.4.3 Si/SiO
2
/Si Substrate 34
3.4 Conclusion 35
3.5 References 36
Chapter 4: Hybrid Si-LiNbO
3
nanophotonics 37
4.1 Introduction 37
4.2 One-dimensional slab optical waveguide 38
4.3 Modeling of hybrid Si-LiNbO
3
structure 42
vi
4.4 Modeling of hybrid Si-LiNbO
3
Micro-ring Resonator 46
4.5 Fabrication of hybrid Si-LiNbO
3
Micro-Ring Tunable Resonator 48
4.6 Experimental Results 54
4.7 Conclusion 61
4.8 References 63
Chapter 5: LiNbO
3
photonic slab 65
5.1 Introduction 65
5.2 Modeling of LiNbO
3
photonic slab 68
5.3 Fabrication of LiNbO
3
photonic slab 71
5.3 Conclusion 74
5.4 References 75
Chapter 6: Hybrid Si-LiNbO
3
Active Photonic Slab 77
6.1 Introduction 77
6.2 Modeling of Hybrid Si-LiNbO
3
photonic slab 78
6.3 Fabrication of LiNbO
3
photonic slab 82
6.3 Conclusion 86
6.4 References 87
Chapter 7: Electro-optic resonant FSR modulators based on a dual-disc
resonator for increasing the sensitivity-bandwidth product 89
7.1 Introduction 89
7.2 Device modeling 93
7.2.1 Transmission properties of dual-disc structures 93
7.2.2 Characteristics of the FSR RF-optic modulation 101
7.2.3 Analysis of RF output power and sensitivity 107
7.2.3.1 Modulation frequency equals the FSR 107
7.2.3.2 Modulation frequency slightly off the FSR 109
7.2.3.3 Optimum laser tuning 110
7.3 Results and discussion 114
7.3.1 Sensitivity and RF bandwidth 114
7.3.2 Fabrication errors and its theoretical results 118
7.4 Conclusion 122
7.5 References 124
Chapter 8: Conclusion and future work 126
6.1 Summary 126
6.2 Future Work 128
6.3 References 130
Bibliography 131
vii
List of Tables
Table 2.1: Properties of LiNbO
3
9
Table 5.1: Dimensions of the LiNbO
3
photonic slab 71
viii
List of Figures
Figure 2.1: The structure of LiNbO
3
. (a) vertical view. (b) viewed down z-
axis. 7
Figure 2.2: A general diagram of crystal ion-slicing process. 10
Figure 2.3: Process of a single crystal LiNbO
3
ultra thin film fabrication. 13
Figure 2.4: Implantation depth as a function of implantation energy. 14
Figure 2.5: A calculated He
+
ion distribution in LiNbO
3
after the
implantation process. 15
Figure 2.6: A Schematic of ion implantation with various doping doses. 16
Figure 2.7: Optical micrograph of the integrated single crystal LiNbO
3
ultra thin film on SiO
2
/LiNbO
3
substrate. 17
Figure 2.8: AFM image of fabricated single crystal LiNbO
3
film (a) 3D
image. (b) 2D image. RMS (root mean square) roughness is
~6 nm. 19
Figure 2.9: XRD profile (intensity vs angle of diffracted X-Ray) of bulk
LiNbO
3
wafer (left) and LiNbO
3
thin film (right). 20
Figure 2.10: Types of LiNbO
3
waveguides on a LiNbO
3
on SiO
2
platform
and their applications. 22
Figure 3.1: The procedure for obtaining single crystal LiNbO
3
micro-
platelets and transferring and integrating them on Si-on-
insulator substrate. 27
Figure 3.2: Optical micrograph of free standing single crystal LiNbO
3
micro-platelets on SiO
2
/Si substrate. 29
Figure 3.3: (a) Unit cell of the hexagonal LiNbO
3
crystal structure with c-
axis down view. (b) Free standing LiNbO
3
micro-platelets
with crack directions indicated. (c) Schematic of free standing
single crystal LiNbO
3
micro-platelets. (d) A mm long LiNbO
3
micro-platelet. 30
ix
Figure 3.4: Optical micrograph of LiNbO
3
micro-platelet integrated on
SiO
2
/LiNbO
3
. 32
Figure 3.5: Optical micrograph of the micro-platelet integrated on SiO
2
/Si
at (a) 1000
o
C and (b) 600
o
C. (c) FESEM micrograph of the
micro-platelet integrated on SiO
2
/Si. 33
Figure 3.6: Optical micrograph of the micro-platelet integrated on
Si/SiO
2
/Si. 34
Figure 4.1: A Schematic of the three layer slab optical waveguide. 38
Figure 4.2: Effective index curves of 1D slab waveguide as a function of
the Si thickness for TE
0
and TM
0
modes. 41
Figure 4.3: Field distributions of 1D slab waveguide for TE
0
and TM
0
modes. 42
Figure 4.4: A hybrid structure of Si waveguide and LiNbO
3
thin film for
electro-optic active devices. 43
Figure 4.5: Electric field distribution for the TM mode of the hybrid Si-
LiNbO
3
micro-ring resonator with (a) a 300 nm width
waveguide and (b) a 500 nm waveguide. 44
Figure 4.6: The effective index difference of the Si waveguide as a
function of the index difference of LiNbO
3
. 46
Figure 4.7: (a) Schematic of a Si micro-ring resonator. (b) SEM
micrograph of a Si micro-ring resonator (top view). 49
Figure 4.8: SEM micrograph of the cross section of a Si micro-ring
resonator (45
o
angle view) 50
Figure 4.9: (a) The integration procedure for the hybrid structure LiNbO
3
micro-platelet and Si micro-ring waveguide. (b) Optical
micrograph (left) and FESEM micrograph (right) of the
fabricated structure. 51
Figure 4.10: Optical micrograph of the hybrid Si-LiNbO3 micro-ring
resonators. 53
x
Figure 4.11: (a) An optical micrograph of a hybrid Si-LiNbO
3
micro-ring
resonator (b) Electric field distribution for the TE mode of the
hybrid Si-LiNbO
3
micro-ring resonator.
55
Figure 4.12: (a) Experimental setup and (b) optical micrograph of device
under test setup. 56
Figure 4.13: Transmission spectra for a Si micro-ring resonator and a
hybrid Si-LiNbO
3
micro-ring resonator. 57
Figure 4.14: Transmission spectra of (a) a Si micro-ring resonator and (b) a
hybrid micro-ring resonator. 59
Figure 4.15: Transmission spectrum of a hybrid Si-LiNbO
3
resonator for
the different values of V
LN
. 61
Figure 5.1: The photonic band diagram of a triangular array air hole in
LiNbO
3
for (a) TE polarization and (b) TM polarization.
Normalized frequency ( a/2 c =a/ ) are plotted as a function
of normalized wave vector (ka/2 ). 67
Figure 5.2: (a) Proposed design of the LiNbO
3
photonic slab and (b) The
photonic band diagram of the structure. 70
Figure 5.3: Process of LiNbO
3
photonic slab fabrication. 71
Figure 5.4: FESEM micrograph of a photonic crystal structure (a) on a Cr
layer and (b) on a LiNbO
3
substrate. 73
Figure 6.1: The photonic band diagram of the structure. (a) h=0.6a and
r=0.2a (b) h=0.6a and r=0.25a (c) h=0.7a and r=0.2a (d)
h=0.7a and r=0.25a. 79
Figure 6.2: The photonic band diagram of the structure. (a) h=0.7a and
r=0.18 (b) h=0.7a and r=0.19a (c) h=0.7a and r=0.21a (d)
h=0.7a and r=0.22a. 80
Figure 6.3: The photonic band diagram of the structure for the different
values of the radius. 81
Figure 6.4: Process of LiNbO
3
photonic slab fabrication. 82
xi
Figure 6.5: Optical micrograph and SEM image of hybrid Si-LiNbO
3
photonic slab. 83
Figure 6.6: Schematic illustration of the hybrid Si-LiNbO
3
photonic slab
with 3 m wide stripe waveguides. 84
Figure 6.7 SEM image of the hybrid Si-LiNbO
3
photonic slab with a
stripe waveguide 85
Figure 7.1
(a) Transmission of the dual resonator when the ratio of the
diameter is 2:1. The position of the laser frequency and the
modulation sidebands are shown. (b) The dual resonant EO
modulator with the RF field applied to disc 2. The electrode
only covers one half the modulated disc as required for a
lumped circuit electrode when the RF frequency is equal to the
FSR of disc 2.
91
Figure 7.2 Light coupling in a dual-disc resonator.
92
Figure 7.3 Through transmission with the r
2
and the r
1
(a) at θ
1
= π(2n+1)
(one disc resonant)) and (b) at θ
1
= 2 πn (both discs resonant).
95
Figure 7.4 (a) Transmission as a function of the r
2
for the different values
of θ
1
and (b) reflectivity r
2
as a function of r
1
for three cases
(a
1
= 0.993 and a
2
= 0.985).
97
Figure 7.5 Through transmission around θ
1
= π(2n+1) and θ
1
= 2n π for r
1
= 0, 0.2, 0.4, and 0.6. For (a) case1, (b) case2, and (c) case3.
98
Figure 7.6 (a) Sideband mode linewidth and (b) laser mode finesse as
function of r
1
for each case. The values are normalized to
those of the single disc resonator.
100
Figure 7.7 | τ
5
|
2
spectrum (top) and phase shift (bottom) as a function of
θ
1
for the case 1 (r
1
= 0.2, r
2
= 0.978, a
1
= 0.993, and a
2
=
0.985).
102
Figure 7.8 Analysis of dual-disc resonator at the upper sideband
frequency, ω
sb
+
= ω + ω
m
. All primed fields are at ω
sb
+
.
104
xii
Figure 7.9 | τ
sb
|
2
spectrum (top) and phase shift (bottom) as a function of
θ
1
for the case 1 (r
1
= 0.2, r
2
= 0.978, a
1
= 0.993, and a
2
=
0.985).
106
Figure 7.10 Transmission spectrum of the dual-disc resonator and the FSR
modulation with double sidebands.
110
Figure 7.11 Normalized detected RF current versus displacement of the
laser wavelength from the peak of the laser mode in phase,
Δ/2 , with various values of r
1
for case 1.
111
Figure 7.12 For the three cases, (a) optimum Δ for maximum detected
current and (b) normalized detected current at optimum Δ as a
function of r
1
.
113
Figure 7.13 Normalized sensitivity as a function of r
1
in all three cases. In
this analysis, Figure 7.4(b) and Figure 7.5(a) were used for
optimum r
2
and Δ.
114
Figure 7.14 Scheme of the non FSR modulation. 115
Figure 7.15 Detected RF output power vs Δ
m
with various values of r
1
with
(a) case 1, (b) case 2, and (c) case 3.
116
Figure 7.16 (a) Normalized RF modulation bandwidth and (b) normalized
sensitivity-RF bandwidth product. The three cases are
defined in Section 2.1 and have to do with the coupling at
resonance for the laser and the sideband modes. For each
value of r
1
, the optimum offset between the laser frequency
and the peak of the laser mode.
117
Figure 7.17 Transmission spectrum of the sideband frequency as a
function of the round trip phase θ
1
with different value of r
1
for (a) 1.9 : 1 ratio of two discs and 2.1 : 1 ratio of two discs.
120
Figure 7.18 Impact of fabrication error (a) Normalized sideband linewidth
and (b) RF bandwidth and (c) sensitivity as a function of r
1
with 5% radius errors.
121
xiii
Abstract
This work addresses new ultra fast (over 40 Ghz) electro-optic device platforms and
their applications using single crystal LiNbO
3
ultra thin films (~1 m) and Si nano-
photonics for compact size photonic integrated circuits, optical networks and optical
interconnects.
It is divided into two parts: the fabrication of active electro-optic device
platforms and the integrations of active electro-optic devices based on these
platforms. In the first part, the new fabrication technologies of single crystal LiNbO
3
films, free standing LiNbO
3
micro-platelets, and hybrid Si-LiNbO
3
device platforms
were demonstrated and discussed. The second part of this work discusses simulation
and experimental work for electro-optically tunable waveguide, micro-ring resonator
modulators, active photonic bandgap crystal slab waveguides, and dual-disc
resonator for increasing the sensitivity-bandwidth product.
LiNbO
3
thin films have been integrated on SiO
2
/LiNbO
3
by He
+
ions
implantation and direct bonding through careful control of the thermal expansion and
stress of the implanted wafer and substrate. After slicing the films, their single crystal
property and comparable surface roughness (rms ~6 nm) has been presented by XRD
and AFM measurements.
Free standing single crystal LiNbO
3
micro-platelets (mm long and 1 m
thick) have been obtained from a z-cut LiNbO
3
wafer by He
+
ions implantation and
thermal treatment. They have been first invented by using a different slicing method.
They have been transferred, positioned and bonded to SiO
2
/LiNbO
3
, SiO
2
/Si, and Si-
on-insulator (SOI: Si/SiO
2
/Si) by direct bonding method with optimum annealing
conditions.
Hybrid Si-LiNbO
3
electro-optic tunable ring resonators have been proposed
and demonstrated as a path to achieving ultra compact and high speed electro-optic
devices. The platelets were transferred and thermally bonded on top of Si resonators
that were fabricated in an SOI platform by a 0.18 m standard CMOS process. For
xiv
the hybrid micro-ring resonator, a FSR of 16.5 nm, a finesse F of ~1.67 10
2
, a Q-
factor of ~1.68 10
4
, and an effective r coefficient of ~1.7 pm/V were achieved for
the TE mode. These values are in good agreement with the calculated results.
Photonic crystal structures based on LiNbO
3
-on-insulator (LOI) platform
have been proposed and discussed for active photonic devices. 3D FDTD method has
been used in order to design LiNbO
3
photonic slab more precisely. In the E-Beam
lithography, electron doses and sizes of the hole have been varied to fine optimum
values. Etching methods with various equipments and recipes have been investigated
since they were the most important issue to fabricate the real structure. Further work
is to fabricate photonic slab waveguide in a LOI structure.
Hybrid Si-LiNbO
3
active photonic slab have been proposed and discussed in
order to employ second order nonlinear effect to the Si photonic slab. Bonding
between a LiNbO
3
micro-platelet and a Si photonic slab has been demonstrated. In
order to optimize hybrid photonic slab, the dimensions of the Si slab have been
carefully designed by using PWE method. For this design, ± 10 % error in the
radius of the holes appears acceptable. Further work is to integrate the hybrid Si-
LiNbO
3
photonic slab waveguide with coplanar electrodes for EO fast tunable filters
and EO modulators.
Resonant free spectral range (FSR) RF-optic modulators using dual disc
resonators with 2:1 ratio of the radii of the discs have been proposed and
theoretically analyzed to increase the sensitivity-bandwidth product compared to a
single resonator modulator. The transmission of the coupled resonator structure is
analyzed for various coupling parameters. The sensitivity and modulation bandwidth
can be increased by factors of 1.9 and 6.4, respectively, for the different cases. The
sensitivity-bandwidth product can be increased up to a factor of 3.3 in one design.
For 5% error of the ratio of the radius of each disc, errors of the sensitivity and
modulation bandwidth were acceptable.
１
Chapter 1
Introduction
1.1 Background and Motivation
As the volume of internet and mobile contents explosively increased, demand for
broadband internet access is rapidly getting increase. Thus, network traffic is also
continuously and dramatically increasing. Current cooper-based network solutions
are not sufficient anymore to meet these demands. For this reason, optical network
solutions are replacing the current network solutions. It is therefore highly desirable
to have integration techniques of optical devices and systems [1-2].
Over the last decade, photonic integrated circuit (PIC) technology has been
widely investigated in order to develop high-performance and low-power-
consumption optical network equipments because of its compact size. Most optical
components such as laser diodes, electro-optic modulators, filters, photo detectors,
etc are made individually and then assembled by optical fiber to produce an optical
device. Thus, optical devices are relatively bigger than electronic devices. In the PIC
２
technology, however, all optical components can be integrated in one chip and
connected by optical waveguide. Then, the size of the optical device can be reduced
similar to an electronic chip and the power consumption and optical loss can be
significantly decreased. In addition, fabrication cost can be reduced by removing the
fiber connection.
This technology is important not only for optical network solutions, but also
for optical computing systems since there are many limitations to improve the speed
of microprocessors such as CPU using electronic technology. In addition, optical
interconnects is one of the most interesting field to apply PIC technology since
electrical interconnect is insufficient to carrier the data flow of the microprocessors.
Moreover, recently, biomedical devices such as label free optical biosensors have
been demonstrated by using various PIC technologies. Thus, PIC technology has
many applications which can overcome the limitations of current electronic
techniques.
There are several materials to fabricate PIC devices such as a LiNbO
3
, an
electro-optic polymer, a Si-on-insulator (SOI), etc. Each material has advantages and
disadvantages. SOI technology is the most interesting approach to realize PIC
devices since Si fabrication technique is currently well developed and this technique
can be applied to SOI waveguide fabrication [1-2]. In addition, it has low optical
propagation loss and low optical bending loss due to the strongly confined modes.
However, Si lacks the second order NLO effect [3]. Thus, additional structures such
３
as a MOS capacitor [4-7], a p-i-n diode carrier injection [8-12], and a pn diode
carrier depletion [13-17] structures are fabricated on SOI waveguide. Unfortunately,
in these structures, there are additional optical loss and power consumption. In
addition, more complex fabrication process is required.
In this paper, fabrication of single crystal LiNbO
3
ultra thin films is
presented. Their crystal structure and properties are discussed. Using these films,
LiNbO
3
-on-insulator (LOI) platform like SOI is demonstrated and its applications
are discussed. Fabrication of free standing single crystal LiNbO
3
micro-platelets and
its integration to various Si-based substrates are first presented. Using this micro-
platelet, hybrid structure of LiNbO
3
-Si, one of the most interesting applications of
the micro-platelet, is proposed and demonstrated in order to develop high-
performance and compact size PIC devices. Finally, a LiNbO
3
photonic slab on a
LOI platform is proposed and its fabrication issues are discussed. Then, current
experimental results are presented.
４
1.2 References
[1] G. T. Reed and A. P. Knights, Silicon photonics : an introduction, John Wiley
& Sons, 2004.
[2] G. T. Reed, Silicon Photonics: the state of the art, John Wiley & Sons, 2008.
[3] R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J.
Quantum Electron., vol. QE-23, no. 1, pp. 123-129, 1987.
[4] A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu,
and M. Paniccia, “A high-speed silicon optical modulator based on a metal-
oxide-semiconductor capacitor,” Nature, vol. 427, pp. 615–618, 2004.
[5] D. Samara-Rubio, L. Liao, A. Liu, R. Jones, M. Paniccia, D. Rubin, and O.
Cohen, “A gigahertz silicon-oninsulator Mach-Zehnder modulator,” in Optical
Fiber Communication Conference, Vol. 2 of OSA Proceeding Series (Optical
Society of America, Washington, D.C.), pp. 3-5, 2004
[6] L. Liao, D. S. Rubio, M. Morse, A. Liu, D. Hodge, “High speed silicon Mach-
Zehender modulator,” Opt. Express 13, pp. 3139, 2005.
[7] C. T. Shih, Z. W. Zeng, and S. Chao, “Design and Analysis of Metal-Oxide-
Semiconductor–Capacitor Microring Optical Modulator With Solid-Phase-
Crystallization Poly-Silicon Gate,” Journal of Lightwave Technology, Vol. 27,
Issue 17, pp. 3861, 2009.
[8] Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon
electro-optic modulator,” Nature, vol. 435, pp. 325–327, May 2005.
[9] Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, “12.5 Gbit/s
carrier-injection-based silicon micro-ring silicon modulators,” Opt. Express, 15,
(2), pp. 430–436, 2007.
[10] S. Manipatruni, X. Qianfan, B. Schmidt, J. Shakya, and M. Lipson, “High speed
carrier injection 18 Gb/s silicon micro-ring electro-optic modulator,” in Proc.
20th Lasers Electro-Opt. Soc. Meeting (LEOS), Oct. 21–25, 2007.
[11] W. M. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra compact, low
RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express, vol. 15, no.
25, pp. 17 106–17 113, 2007.
５
[12] W. M. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low
RF power, 10 Gb/s silicon Mach-Zehnder modulator,” in Proceedings of the
20th Annual Meeting of the IEEE Lasers & Electro-Optics Society (Institute of
Electrical and Electronics Engineers, New York), Postdeadline paper PD1.2,
2007.
[13] A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and
M. Paniccia, “High-speed optical modulation based on carrier depletion in a
silicon waveguide,” Opt. Express, 15, (2), pp. 660–668, 2007.
[14] L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky,
and M. Paniccia “40 Gbit/s silicon optical modulator for highspeed
applications,” Electronics Letters,. 43, (22), 2007.
[15] B. Analui, D. Guckenberger, D. Kucharski, and A. Narasimha, “A fully
integrated 20-Gb/s optoelectronic transceiver implemented in a standard 0.13-
um CMOS SOI technology,” IEEE J. Solid-State Circuits 41, 2945-2955, 2006.
[16] T. Pinguet, V. Sadagopan, A. Mekis, B. Analui, D. Kucharski, S. Gloeckner, “A
1550 nm, 10 Gbps optical modulator with integrated driver in 130 nm CMOS,”
in Proc. 4th Conf. Group IV Photon., Tokyo, Japan, Sep. 19–21, 2007.
[17] D. Marris-Morini, L. Vivien, J. M. Fédéli, E. Cassan, P. Lyan, S. Laval, “Low
loss and high speed silicon optical modulator based on a lateral carrier depletion
structure,” Opt. Express, vol. 16, no. 1, pp. 334–339, 2008.
６
Chapter 2
Single crystal LiNbO
3
ultra thin film
2.1 Introduction
LiNbO
3
has remarkable properties as both optical material and electro-optic material
since it has low loss at optical communication wavelength of 1.55 um and the large
electro-optic coefficient. Graded-index waveguides such as Ti-diffused or proton
exchange waveguides have been widely used for LiNbO
3
material. However, it is
unacceptable for the compact size integration since these waveguides have high
bending loss due to the weakly confined modes. Thus, a ridge waveguide structure is
required in order to fabricate compact size devices [1-2]. It is therefore necessary to
have LiNbO
3
thin film in order to fabricate the ridge waveguide. There are two main
methods used for fabrication of LiNbO
3
thin films; they are deposition or growth
method [3-4] and ion slicing method [5-6]. LiNbO
3
thin films obtained by the first
method are not single crystal structure; these films have multi-crystalline which
７
means material properties are worse than that of bulk single crystal LiNbO
3
. In the
second case, however, LiNbO
3
films are sliced from bulk single crystal wafer.
Therefore, these thin films have material properties like bulk LiNbO
3
wafer [5].
Figure 2.1. The structure of LiNbO
3
. (a) vertical view. (b) viewed
down z-axis.
With crystal ion slicing (CIS) method, single crystal LiNbO
3
thin films (0.6
~ 10 um thick) have been fabricated for last 10 years [5-6]. In addition, ridge
waveguides with single crystal LiNbO
3
thin films have been demonstrated and it has
low bending loss due to the tightly confined modes [1-2]. It is, however, difficult to
obtain large size of the films for less than 1 um thick films. Particularly, etching
selectivity is very low for both wet and dry etching and etched surface has relatively
poor roughness compared with polymer and Si ridge waveguide. It is therefore
８
necessary to determine optimum fabrication conditions such as implantation
conditions, bonding conditions, and etching conditions.
2.2 LiNbO
3
properties and its applications
LiNbO
3
which is a human-made dielectric material has ferroelectric phase at
temperatures below the Curie temperature (1210
0
C) while it is in paraelectric phase
above the Curie temperature. In this ferroelectric phase, LiNbO
3
is a member of the
trigonal crystal system (R3c) and classified as a member of 3m point group. It has
conventional hexagonal cell which exhibits three-fold rotation symmetry [8-9].
Figure 2.1 shows the structure of LiNbO
3
in the ferroelectric phase.
LiNbO
3
is an interesting and important ferroelectric material since it has
excellent electro-optic, piezoelectric, pyroelectric, photo-elastic, and nonlinear optic
properties [9-10] as shown in Table 2.1. With these properties, LiNbO
3
has been
widely used in high speed electro-optic modulators, waveguide nonlinear optical
devices, surface acoustic wave (SAW) devices and other photonics devices.
９
Table 2.1. Properties of LiNbO
3
Property Value Notes
Point Group 3m
Space group R3c
Congruent melting point 1250
o
C
Ordinary index of refraction 2.21 = 1.55 um
Extraordinary index of refraction 2.14 = 1.55 um
Electrical conductivity 110
-18
( -cm)
-1
at DC
Thermal conductivity 5.6 W/m
o
C
Thermal expansion coefficient (z-cut) 15.410
-6
o
C
-1
Thermal expansion coefficient (x-cut) 7.510
-6
o
C
-1
Electro-optic coefficients r
33
= 30.8 pm/V
r
22
= 3.4 pm/V
r
13
= 8.6 pm/V
r
51
= 28.0 pm/V
Density 4.635 g/cm
3
Longitudinal Sound velocity 7500 m/s
Transverse Sound velocity 3700 m/s
１０
2.3 Crystal ion slicing
Crystal Ion Slicing technology to obtain single crystal thin films for metal oxide
materials is basically similar to Smart-Cut technology which is used to fabricate Si-
on-insulator (SOI) wafer. In this technique, single crystal thin films are exfoliated
from bulk crystal by high dose ion implantation and annealing or chemical etching
methods. These films have bulk-comparable material properties [11] while thin films
fabricated by deposition or growth have much less material properties than that of
bulk crystal. Generally, this technique has four processes; they are ion implantation,
pre-slicing processing, slicing, and post-slicing processing as shown in Figure 2.2.
Optimum conditions and parameters of the processes are very dependent on the
material to be sliced.
Figure 2.2. A general diagram of crystal ion-slicing process.
１１
In order to prepare ion implantation process, three main parameters
(implantation ions, implantation energy, and ion dose) should be determined. Either
H
+
or He
+
which are the lightest ions can be selected by its reactivity with the target
material. For example, He
+
ions are implanted into LiNbO
3
while H
+
ions are
implanted into Si. While the ions penetrate to the target material, they lose their
energy and finally stop. Depth of stop position can be estimated by using a Monte
Carlo simulation program which call TRIM (Transport-of-ions-in-matter) [12-13]. In
order to obtain large films and good surface roughness, doses of the implantation ion
can be optimized by varying the doses.
Pre-slicing processing includes RTA (rapid thermal annealing), polishing,
cleaning, and bonding. Sacrificial layer can be damaged more by RTA. Thus crystal
films can be obtain easily since etching speed is increased and less thermal annealing
is required. However, if film thickness is less than 1 um, film might be cracked by
RTA. Temperature and annealing time of RTA are dependent on the material.
Unimplanted area at the sample edges can be removed by polishing. Cleaning is very
important in order to obtain large film without crack for less than 1 um thick film due
to the improvement of the bonding strength. Implanted surface of the material is
bonded to the supporting material to avoid crack. Bonding process has two methods
[14]; they are direct wafer bonding and anodic bonding. Direct bonding can be
applied for all materials. In contrast, anodic bonding can be applied for the materials
which have high ion conductivity because strong electric field applied to form the
１２
oxide bonding. Anodic bonding has much simple step compared with direct wafer
bonding.
Slicing process has two methods: wet etching method and thermal slicing
method. Ion implanted sacrificial layer has high etching selectivity in HF acid or a
mixture of HNO
3
and HF. This selectivity can be enhanced about 100 times by RTA
which is one of pre-slicing processes [15]. Using etching method without bonding
process, freestanding single crystal films can be obtained. In the thermal slicing
method, high temperature is applied in order to separate the thin films from the bulk
material. Size of micro voids in the sacrificial layer is increased by increasing the
temperature [16]. The voids can join together when their size increased enough. Then
thin film can be sliced abruptly from the bulk material.
The post-slicing process is required in order to recover slightly damaged
structure on the implanted side surface of the film. For using etching method, there is
additional damage. However this degradation is not critical. Thus, by annealing at
the high temperature for several hours, crystal structure and material properties can
be recovered [11].
2.4 Fabrication of single crystal LiNbO
3
ultra thin films
The process of the fabrication of single crystal LiNO
3
ultra thin films is divided into
four steps as shown in Figure 2.3. In the first step, He
+
ions are implanted onto a
LiNbO
3
sample and SiO
2
is deposited onto other supporting LiNbO
3
sample. The
１３
second step is cleaning both LiNbO
3
samples and applying the direct wafer bonding
process. In the next step, additional direct wafer bonding is applied for a bonded
LiNO
3
sample and a Si sample to achieve large thermal stress. The final step is
slicing thin film by annealing.
Figure 2.3. Process of a single crystal LiNbO
3
ultra thin film
fabrication.
In order to obtain high quality single crystal LiNbO
3
films, all implantation
parameters such as ion, energy, and dose should be carefully determined. He
+
ion is
selected as an implantation ion instead of H
+
ion because of its reactivity with
LiNbO
3
. During the annealing procedure, distribution of the implanted He
+
ions is
１４
stable at the original position while implanted H
+
ions are diffused from the original
position. Thus He
+
ions are implanted into a LiNbO
3
bulk wafer in order to obtain a
stable sacrificial layer.
0 200 400 600 800 1000
0.0
0.5
1.0
1.5
2.0
2.5
Implantation Depth (um)
Implantation Energy (keV)
Figure 2.4 Implantation depth as a function of implantation energy.
Figure 2.4. represents implantation depth predicted by TRIM simulation as a
function of implantation energy of He
+
ions [13]. Using this simulation, implantation
energy of 380 keV has been selected in order to obtain the implantation depth of ~1
um. Implanted He
+
ions profile has been calculated as shown in Figure 2.5.
１５
Figure 2.5 A calculated He
+
ion distribution in LiNbO
3
after the
implantation process.
We have varied the ion doses over the range of (3-4.5) 10
-6
cm
-2
to find an
optimum value. To vary He
+
ions doses, two inch mounting wafer (Si) has been used
and divided by four areas. Then, three LiNbO
3
samples (1 cm 1 cm) have been
mounted by thermal tape on each area as shown in Figure 2.6. He
+
ions have been
implanted three times onto LiNbO
3
samples. Each implantation had different doses
(310
-6
cm
-2
, 110
-6
cm
-2
, and 0.5 10
-6
cm
-2
) and Al foil has been used to block He
+
ions. Then, we have obtained optimum values near 4.5 10
-6
cm
-2
after slicing
LiNbO
3
films.
A SiO
2
deposited (2 um thick) LiNbO
3
wafer has been used as a supporting
material for wafer bonding since LiNbO
3
slab waveguide structure could be
demonstrated by integration of LiNbO
3
ultra thin film to this SiO
2
layer. CVD
(chemical vapor deposition) equipment has been used to deposit SiO
2
on LiNbO
3
.
１６
Then, the top surface of SiO
2
layer has been polished to reduce surface roughness in
order to enhance bonding strength.
Figure 2.6 A Schematic of ion implantation with various doping
doses.
Direct wafer bonding [14] has been widely used since it requires no
additional adhesive layer and bonding strength is very strong. Ultra cleaning and
hydrophilic treatment for both samples are required to obtain strong bonding strength
before the direct wafer bonding process. Oxygen plasma ashing treatment may help
to remove residual contaminations after chemical cleaning. Hydrophilic surface can
be obtained by RCA1 (H
2
O
2
-NH
4
OH-H
2
O) solution. Initial bonding is preformed by
hydrogen bonding with water cluster after contacting two samples in the DI water
and drying in the air. Then, during the annealing, covalent bonds via oxygen bridges
１７
are performed by removing Hydrogen. Bonding strength can be improved by
increasing the temperature due to more covalent bonds [17]. In this experiment,
annealing temperature has been applied up to 210
o
C to prevent breaking of the
surface of the He
+
implanted side before bonding is performed. Then, the samples
have been annealed for 3~4 hours at this temperature.
Figure 2.7 Optical micrograph of the integrated single crystal
LiNbO
3
ultra thin film on SiO
2
/LiNbO
3
substrate.
In general, thin films can be separated from the bulk wafer by increasing the
temperature after bonding. It is because micro voids of implanted He
+
ions at the
sacrificial layer is expanded by increasing the temperature and the layer is finally
１８
separated when voids can join together [18]. For general slicing technique, pre-
annealing treatment such as RTA (rapid thermal annealing) before bonding helps to
improve slicing the film. Less than 1 um thick films, however, can break during the
RTA since it couldn’t stand vertical pressure of micro voids [16]. In addition, without
pre-annealing, thin films might not be obtained easily by bonding and increase
temperature [15].
Thus, we proposed the second direct bonding with Si as shown in Figure (c)
to obtain more thermal stress since the TCE (thermal coefficient of expansion) of z-
cut LiNbO
3
is about 6 times bigger than that of Si; the TCE of z-cut LiNbO
3
and Si
are 15.4 10
-6
/
o
C and 2.6 10
-6
/
o
C, respectively. Then, LiNbO
3
thin films have been
integrated on SiO
2
/LiNbO
3
substrate during the direct wafer bonding at 230
o
C by the
large thermal mismatch between LiNbO
3
and Si as shown in Figure 2.7.
2.5 Single crystal LiNbO
3
ultra thin films and its properties
It has been previously reported that the quality and properties of single crystal thin
films obtained by ion implantation and slicing using the thermal shock or the etching
method are generally close to the bulk wafer except for the implanted region [5, 18-
19]. In addition, the quality of the implanted region can be recovered by high
temperature annealing at over 800
o
C [11]. In Figure 2.8, the surface roughness of the
implanted side of the LiNbO
3
thin film has been measured by atomic force
microscope (AFM) measurement (Digital Instruments Dimension 3100) after
１９
bonding to a substrate. A surface roughness of ~6 nm was measured which is close to
the previous report [1, 6].
Generally this roughness can be improved up to 0.3 nm by
polishing [1]. The surface roughness of the other side of the film is the same as the
polished surface of the bulk wafer.
Figure 2.8 AFM image of fabricated single crystal LiNbO
3
film (a)
3D image. (b) 2D image. RMS (root mean square) roughness is ~6
nm.
２０
Figure 2.9 XRD profile (intensity vs angle of diffracted X-Ray)
of bulk LiNbO
3
wafer (left) and LiNbO
3
thin film (right).
In order to show that the LiNbO
3
thin films are single crystal, X-Ray
Diffraction (XRD) measurement (Rigaku Ultima IV) has been used. The
measurement was done on slightly larger platelets (~0.5 0.5 mm
2
) bonded to a
２１
SiO
2
/LiNbO
3
. This was necessary because of the X-ray beam size. Figure 2.9 shows
Cu K ( = 1.54406 Å) peak of the XRD measurement for the bulk LiNbO
3
sample
and for the LiNbO
3
thin film on SiO
2
/LiNbO
3
. Peak angle corresponds to the (006)
plane space of LiNbO
3
unit cell. The peak line-width of the thin LiNbO
3
films was
very close to that of the bulk LiNbO
3
, which indicates these thin films are single
crystal. Deposited poly-crystal LiNbO
3
films have much broad peak linewidth [3-4].
In the Figure 2.9 (right), there is a slight shift in the peak angle of the thin LiNbO
3
because there was residual strain due to the thermal mismatch between LiNbO
3
and
SiO
2
. The structure on the right side of the thin film peak could be due to various
stresses in the large film.
2.6 Applications of single crystal LiNbO
3
thin films
With the excellent second order NLO effect and low optical loss, a number of active
devices can be demonstrated by using LiNbO
3
single crystal thin films: a tunable
filter, an electro-optical modulator, an electric field sensor, etc. In general, three
types of waveguides are possible as shown in Figure 2.10. LiNbO
3
ridge waveguide
and buried waveguide can be demonstrated by direct etching the LiNbO
3
film. In
these waveguide, sidewall roughness is the biggest issue because of the propagation
loss [1, 6]. SiO
2
cladding could help to reduce the propagation loss since it has less
scattering than air cladding. On the other hand, to improve the bending loss, air
cladding is better than SiO
2
cladding because of the strongly confined modes. These
２２
waveguides is acceptable to demonstrate micro-ring resonator devices because of the
low bending loss due to the high index contrast between waveguide region and other
regions. Other method is the fabrication of a polymer strip on LiNbO
3
films. Because
of the difference of the effective index between polymer cladding region and other
region, modes can be confined below the polymer strip. It can improve the
propagation loss problem by reducing the side wall roughness. However, it has high
bending loss compared with etching-based waveguide. This waveguide is therefore
not sufficient to demonstrate a compact size micro-ring resonator.
Figure 2.10 Types of LiNbO
3
waveguides on a LiNbO
3
on SiO
2
platform and their applications.
2.7 Conclusion
The fabrication of ~1 um thick single-crystal LiNbO
3
ultra thin films on
SiO
2
/LiNbO
3
substrates have been demonstrated by using direct bonding and ion
２３
exfoliation from a bulk, single-crystal wafer. The films have been obtained through
careful control of the thermal expansion and stress of the implanted wafer and
substrate. The surface roughness of the separated side of the film has been measured
using AFM measurement. The crystal structure of the full-sample film has been also
investigated using XRD measurement. It shows the films are single crystal. Then,
applications of the LiNbO
3
thin films have been discussed.
２４
2.8 References
[1] P. Rabiei, W. H. Steier, “Lithium niobate ridge waveguides and modulators
fabricated using smart guide,” Appl. Phys. Lett., 86, 161115-1, 2005.
[2] A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, P. Günter, “Electro-
optically tunable microring resonators in lithium niobate,” Nature Photonics, 1,
407, 2007.
[3] T. A. Rost, H. Lin, T. A. Rabson, R. C. Baumann, D. L. Callahan, “Deposition
and analysis of lithium niobate and other lithium niobium oxides by rf
magnetron sputtering,” J. Appl. Phys., 72, 4336, 1992.
[4] V. Srikant, J. S. Speck, D. R. Clarke, “Mosaic structure in epitaxial thin films
having large lattice mismatch,” J. Appl. Phys., 82, 4286, 1997.
[5] M. Levy, R. M. Osgood Jr., R. Liu, L.E. Cross, G. S. Cargill III, A. Kumar, H.
Bakhru, “Fabrication of single-crystal lithium niobate films by crystal ion
slicing,” Appl Phys Lett., 73, 2293, 1998.
[6] P. Rabiei and P. Günter, “Optical and electro-optical properties of
submicrometer lithium niobate slab waveguides prepared by crystal ion slicing
and wafer bonding, ” Appl. Phys. Lett., 85, 4603, 2004.
[7] R. M. Roth, D. Djukic, Y. S. Lee; R. M. Osgood, S. Bakhru, B. Laulicht, K.
Dunn, Bakhru, H. W. Liqi, and H. Mengbing, “Compositional and structural
changes in LiNbO
3
following deep He+ ion implantation for film exfoliation,”
Appl Phys Lett., 89, 112906-1, 2006.
[8] S. C. Abrahams, J. M. Reddy and J. L. Bernstein, “Ferroelectric lithium niobate.
3. Single crystal X-ray diffraction study at 24°C,” J. Phys. Chem. Solids 27, p.
997, 1966.
[9] R. S. Weis and T. K. Gaylord, “Lithium Niobate: Summary of Physical
Properties and Crystal Structure,” Applied Physics A 37, pp. 191-203, 1985.
[10] K. K. Wong, Properties of lithium niobate, INSPEC, Institution of Electrical
Engineers, London, 1989.
[11] T. A. Ramadan, M. Levy, and Jr Osgood, R. M. “Electro-optic modulation in
crystal-ion-sliced z-cut LiNbO
3
thin films,” Applied Physics Letters, 76, 1407-9,
2000.
２５
[12] J. F. Ziegler, J. P. Biersack, and U. Littmark. The Stopping and Range of Ions in
Solids, Pergamon Press, 1985.
[13] J. F. Ziegler, computer code SRIM2006 (freely available at www.srim.org).
[14] Q.-Y. Tong and U. Gösele (eds.), Semiconductor Wafer Bonding, Wiley & Sons,
Inc., New York, 1999.
[15] A. M. Radojevic, M. Levy, Jr. Osgood, R. M., A. Kumar, H. Bakhru, C. Tian,
and C. Evans. “Large etch-selectivity enhancement in the epitaxial liftoff of
single-crystal LiNbO
3
films,” Applied Physics Letters, 74, 3197-9, 1999.
[16] C. M. Varma, “Hydrogen-implant induced exfoliation of silicon and other
crystals,” Appl. Phys. Lett. 71, 3519, 1997.
[17] K. Eda, T. Ogura, and Y. Tomita, “One-Chip Quartz Crystal Oscillator Using a
Direct-. Bonding Technique of Quartz Crystal onto Silicon,” Proc. IEEE-US
symp., pp1045-1049, 1994.
[18] R. M. Roth, D. Djukic, Y. S. Lee, R. M. Osgood, S. Bakhru, B. Laulicht, K.
Dunn, Bakhru, H.; W. Liqi, H. Mengbing, “Compositional and structural changes
in LiNbO
3
following deep He+ ion implantation for film exfoliation,” Appl Phys
Lett., 89, 112906-1, 2006.
[19] Y. S. Lee, D. Djukic, R.M. Roth, R. Laibowitz, T. Izuhara, R. M. Osgood, S.
Bakhru, H. Bakhru, S. Weidong, and D. Welch, “Fabrication of patterned
single-crystal SrTiO
3
thin films by ion slicing and anodic bonding,” Appl Phys
Lett., 89, 122902, 2006.
２６
Chapter 3
Free standing single crystal LiNbO
3
micro-
platelets
3.1 Introduction
In crystal ion slicing method, LiNbO
3
single crystal ultra thin films less than 1 um
thick have been integrated only on LiNbO
3
based substrates (SiO
2
/LiNbO
3
and
BCB/LiNbO
3
) without crack because of its large thermal expansion coefficient
(15.4 10
-6
/
o
C for z-cut and 7.5 10
-6
/
o
C for z-cut). This films have difficulty in
bonding on Si based substrates (Si, SiO
2
/Si, and Si/SiO
2
/Si) since thermal expansion
coefficient (2.6 10
-6
/
o
C) of Si is much smaller than that of LiNbO
3
. Thus, LiNbO
3
films can be shattered during the bonding due the large thermal mismatch between Si
and LiNbO
3
. Fortunately, free standing LiNbO
3
ultra thin films, however, can be
bonded on Si based substrates without crack since ultra thin film is much more
flexible and stretchable than thick LiNbO
3
. Thus, free standing LiNbO
3
single crystal
２７
film is particularly useful for transferring and bonding on other materials which have
different thermal expansion coefficient and require material properties of LiNbO
3
. In
general, free standing LiNbO
3
films (~10 um thick) have been fabricated by chemical
etching in the ion slicing method [1, 2]. Even though large size films can be obtained
by this method, 10 um thick films are insufficient to overcome large thermal
mismatch between Si and LiNbO
3
. In addition, it is very expensive to achieve 10 um
depth implantation since high implantation energy (3.8 MeV) is required. In this
chapter, the fabrication of 1 um thick freestanding LiNbO
3
micro-platelets and its
integration to various Si based substrates without crack are presented.
Figure 3.1. The procedure for obtaining single crystal LiNbO
3
micro-platelets and transferring and integrating them on Si-on-
insulator substrate.
２８
3.2 Fabrication of free standing single crystal LiNbO
3
micro-platelets
Figure 3.1 shows the fabrication process of the free standing LiNbO
3
micro-platelets.
He
+
ions were implanted into a bulk single crystal LiNbO
3
wafer (z-cut). The
implantation energy of 380 keV was selected by using the Stopping and Range of
Ions in Matter (SRIM) calculation [3] in order to obtain implantation depth of 1.1 um.
Implantation current of 20 uA, implantation angle of 7
o
, and doping dose of 4.5x10
16
cm
-2
were used. Applying these conditions, a structural defect layer was formed at a
depth of 1.1 um. The implanted sample was pressed onto a SiO
2
coated Si wafer and
heated to 170
o
C in air. The thermal coefficients of expansion of z-cut LiNbO
3
and Si
are 15.4 10
-6
m/
o
C and 2.6 10
-6
m/
o
C, respectively. Because of this difference in
thermal expansion and because the bonding strength of direct bonding is very weak
at 170
o
C, single crystal LiNbO
3
films are separated from bulk LiNbO
3
wafer and are
not bonded to the substrate. The free standing single crystal platelets are ~1 um thick
and they have various widths (15~100 um) and lengths (0.4~2 mm). As shown in
Figure 3.2, many of them are not flat but curved at radii between 230 um and 260 um
in the long direction with the implanted side on the inside of the curvature. The
curvature can be removed by thermal annealing, and we believe the curvature is due
to stress caused by the crystal damage in the implanted layer. Individual micro-
platelets can be picked up from the surface by the electro-static attraction between an
optical fiber tip and the micro-platelet, moved to another substrate, positioned, and
２９
subsequently bonded to the new substrate.
Figure 3.2 Optical micrograph of free standing single crystal
LiNbO
3
micro-platelets on SiO
2
/Si substrate.
3.3 Crystal structure and micro-platelet formation
The micro-platelets were from z-cut LiNbO
3
wafers and the optic axis of the micro-
platelets is perpendicular to their surface. The edges of the micro-platelets appear
consistent with the direction of the three hexagonal axes (a
1
, a
2
, a
3
). Figure 3.3a
shows the oxygen array idealized one unit cell of LiNbO
3
structure viewed down the
c-axis [4, 5]. It represents a trigonal crystal system (3m point group) and the
hexagonal unit cell with a three-fold symmetry about its c-axis. Figure 3.3b is an
３０
optical photograph of free standing LiNbO
3
micro-platelets and shows that the crack
angles correspond well with the three hexagonal axes. The index of refraction in the
plane of the micro-platelets is the ordinary index.
Figure 3.3. (a) Unit cell of the hexagonal LiNbO
3
crystal structure
with c-axis down view. (b) Free standing LiNbO
3
micro-platelets
with crack directions indicated. (c) Schematic of free standing
single crystal LiNbO
3
micro-platelets. (d) A mm long LiNbO
3
micro-platelet.
As shown in Figure 3.3c and 3.3d, many of the micro-platelets were curled
up due to the large stress created by the residual He
+
ions on one surface. This
bending was previously observed at LiNbO
3
films obtained by ion slicing method [6].
３１
A tighter bend radius occurs in these thinner films since the residual thickness of He
+
ion implanted layer is relatively larger for thinner films. The micro-platelets can be
flattened by annealing at temperatures in the range of 600-1000
o
C.
3.4 LiNbO
3
micro-platelet integration to various substrates
The LiNbO
3
micro-platelets were picked up and transferred onto other substrates
including SiO
2
/LiNbO
3
, SiO
2
/Si and Si/SiO
2
/Si by an optical fiber tip. Then, they
were integrated on these substrates by direct bonding under selected conditions. We
could not directly measure the bonding strength since the width of the micro-platelet
is very small but we have done the widely used scotch tape test to measure bonding
quality [7]. After scotch tape test, micro-platelets were still bonded on the all
substrates (SiO
2
/LiNbO
3
, SiO
2
/Si, and Si/SiO
2
/Si).
3.4.1 SiO
2
/LiNbO
3
Substrate
Figure 3.4 represents the fabrication of a LiNbO
3
micro-platelet onto a SiO
2
/LiNbO
3
substrate by direct bonding at 1000
o
C for 3 hours. For the substrate, 2 um thick SiO
2
was deposited on 500 um thick LiNbO
3
wafer. No pre-annealing or flattening of the
curved micro-platelet was required; the flattening and the bonding occur in the same
step. Even though there is large thermal mismatch between LiNbO
3
and SiO
2
, the
LiNbO
3
micro-platelets do not crack during the 1000
o
C bonding apparently because
the deposited SiO
2
layer and ultra thin LiNbO
3
micro-platelet can accommodate the
３２
strain.
Figure 3.4 Optical micrograph of LiNbO
3
micro-platelet integrated
on SiO
2
/LiNbO
3
.
3.4.2 SiO
2
/Si Substrate
Direct bonding of the micro-platelets on an SiO
2
/Si substrate at 1000
o
C was not
successful as shown in Figure 3.5a; several cracks occurred due to the large thermal
mismatch between LiNbO
3
micro-platelet and Si substrate during the bonding.
However, as shown in Figure 3.5b, a lower temperature bond at 600
o
C was
successful without cracking. Again the bonding and flattening were done
simultaneously at 600
o
C. Figure 3.5c shows a Field Emission Scanning Electron
Microscope (FESEM) picture with 45
o
tilted view and the inset represents magnified
３３
edge area. Hitachi S-4800 FESEM has been used for this measurement. In this figure,
we can see that the micro-platelets are cleaved cleanly along the one direction and
attached to the substrate. The substrates were 1 um thick SiO
2
deposited on a 330 um
thick Si wafer.
Figure 3.5 Optical micrograph of the micro-platelet integrated on
SiO
2
/Si at (a) 1000
o
C and (b) 600
o
C. (c) FESEM micrograph of the
micro-platelet integrated on SiO
2
/Si.
３４
Figure 3.6 Optical micrograph of the micro-platelet integrated on
Si/SiO
2
/Si.
3.4.3 Si/SiO
2
/Si Substrate
The hybrid structure of a LiNbO
3
micro-platelet and an SOI wafer is the most
interesting case because this can provide second order NLO effect to Si photonics
technology. The Si/SiO
2
/Si substrate, which consisted of a 300 nm thick top Si layer,
a 2 um thick intermediate fused SiO
2
layer, and 500 um thick bottom Si layer. In this
case a lower temperature bond and a pre-flattening were required to prevent cracking
of the LiNbO
3
. The free standing LiNbO
3
micro-platelets were flattened on an un-
polished quartz surface by annealing at 1000
o
C for 3 hours. The micro-platelets do
not bond to the unpolished surface and do not crack during the annealing. We note
that flattening occurs at lower temperatures when both flattening and bonding are
３５
occurring simultaneously as in the case of SiO
2
/Si substrate. The flattened micro-
platelets were transferred on the SOI substrate and bonded by direct bonding at
300
o
C for 4 hours. In Figure 3.6, LiNbO
3
micro-platelet was bonded on the Si
surface between Si ridge waveguides.
3.4 Conclusion
Free standing single crystal LiNbO
3
micro-platelets have been proposed and
discussed to integrate on different materials. These micro-platelets have been
fabricated by ion implantation and thermal shock. The edges of the micro-platelets
correspond to the crystalline planes of LiNbO
3
with the optic axis perpendicular to
the platelets. These free standing micro-platelets are flexible and transferable to other
substrates. The micro-platelets have been bonded on SiO
2
/LiNbO
3
, SiO
2
/Si, and SOI
substrates by the direct bonding at temperatures sufficient to provide a good bonding
strength.
３６
3.5 References
[1] M. Levy, R. M. Osgood Jr., R. Liu, L.E. Cross, G. S. Cargill III, A. Kumar, H.
Bakhru, “Fabrication of single-crystal lithium niobate films by crystal ion
slicing,” Appl Phys Lett., 73, 2293, 1998.
[2] T. A. Ramadan, M. Levy, and Jr Osgood, R. M. “Electro-optic modulation in
crystal-ion-sliced z-cut LiNbO
3
thin films,” Applied Physics Letters, 76, 1407-9,
2000.
[3] J. F. Ziegler, computer code SRIM2006 (freely available at www.srim.org).
[4] S. C. Abrahams, J. M. Reddy and J. L. Bernstein, “Ferroelectric lithium niobate.
3. Single crystal X-ray diffraction study at 24°C,” J. Phys. Chem. Solids 27, p.
997, 1966.
[5] R. S. Weis and T. K. Gaylord, “Lithium Niobate: Summary of Physical
Properties and Crystal Structure,” Applied Physics A 37, pp. 191-203, 1985.
[6] O. Gaathon, A. Ofan, J. Dadap, A. Wirthmüller, L. Vanamurthy, S. Bakhru, H.
Bakhru, R. M. Osgood Jr., “Femtosecond laser milling of ultrathin films of
LiNbO
3
,” Proc. SPIE - The International Society for Optical Engineering: High-
Power Laser Ablation VII 2008, 7005, 70052Y, 2008
[7] G. S. Frankel, S. Purushothaman, T. A. Petersen, S. Farooq, S. N. Reddy, and V.
Brusic, “Corrosion and Adhesion of Multilayer Pad Structures for Packaging
Applications,” IEEE Trans. Comp.: Packaging, and Manufact. Tech.–Part B, 18,
709, 1995.
３７
Chapter 4
Hybrid Si-LiNbO
3
nanophotonics
4.1 Introduction
There is considerable interest in integrated electro-optic and non-linear
optical devices with small footprints and this requires small bending radii and
therefore tighter mode confinement. LiNbO
3
and similar crystals are the premier
electro-optic (EO) and nonlinear optical (NLO) materials for integrated optics at the
telecommunication wavelengths. Most waveguides in these materials are based on Ti
in-diffusion or proton exchange which results in very low index contrast waveguides
and most devices have a relatively large footprint, for example Mach Zehnder optical
modulators. To achieve tight confinement, thin films of LiNbO
3
and ridge
waveguides have been demonstrated but they have not as yet demonstrated low loss
[1, 2]. Another approach is to bond LiNbO
3
onto a tight confinement waveguide
materials system such as Si-on-insulator (SOI). Unfortunately, because of the large
３８
difference in thermal expansion, it has proven very difficult to achieve an effective
bond. In this work we have investigated a method to overcome this limitation by first
fabricating small (100 um 2 mm) thin (~1 um) single crystal micro-platelets of
LiNbO
3
, transferring and positioning these micro-platelets to a pre-fabricated SOI
optical circuit, and bonding at a modest temperature. These smaller platelets can
handle the thermal stress without fracture and remain bonded to the optical circuit.
The LiNbO
3
interacts with the optical wave by evanescent coupling. Since Si has no
second order NLO effect [3-17], the goal is to bring a very good EO and NLO
material (LiNbO
3
) into the well developed SOI system.
Figure 4.1 A Schematic of the three layer slab optical waveguide.
4.2 One-dimensional slab optical waveguide
In this section, an analysis of a three layer slab optical waveguide with a
３９
one-dimensional (1D) structure is discussed for TE and TM modes as shown in
Figure 4.1. This analysis is important to understand design parameters of an actual
2D optical waveguide structure.
First, TE mode consists of the field components E
y
, H
y
and H
z
. E
y
field
solutions can be expressed by
d x d k A
x k A
d x d k A
x E
c x
x
c x
y
exp cos
cos
exp cos
d x
d x d
d x
where
0
2 2
0
2 2
0
2
2 2
0
2 2
0
2
2 2
0
2 2 2
0
k N
n N k n k
n N k n k
N n k n k k
eff
s eff s s
c eff c c
eff f f x
;
A is constant; n
c
, n
f
and n
s
are refractive index of upper cladding, core and lower
cladding materials, respectively; N
eff
is effective index; is propagation constant; k
x
is phase constant in the x direction;
c
and
s
are attenuation constants in upper
cladding and lower cladding regions, respectively.
At the interface between the core layer and the upper or lower cladding layer,
the tangential field components E
y
and H
z
are continuous. Using these boundary
conditions, we can obtain the eigenvalue equation as
x
c
x
s
x
c
x
s
x
k k
m
k k
m
d k
1 1
1 1
tan
2
1
tan
2
1
2
tan
2
1
tan
2
1
2
(m = 0, 1, 2, 3, …).
４０
Finally, we can obtain the relation between core thickness (T) and effective
index (N
eff
).
b
a b
b
b
m
k
d T
x
1
tan
1
tan
1
2
1 1
where
2 2
2 2
s f
c s
n n
n n
a
and
2 2
2 2
s f
s eff
n n
n N
b
For TM mode, similarly, the H
y
field solutions can be expressed by
d x d k A
x k A
d x d k A
x H
c x
x
c x
y
exp cos
cos
exp cos
d x
d x d
d x
Then, E
x
field can be written by
d x d k n
x k n
d x d k n
A
x E
c x s
x f
c x c
x
exp cos
cos
exp cos
2
2
2
0
d x
d x d
d x
Using boundary conditions, we can obtain the eigenvalue equation as
x
c
c
f
x
s
s
f
x
c
c
f
x
s
s
f
x
k n
n
k n
n
m
k n
n
k n
n
m
d k
2
2
1
2
2
1
2
2
1
2
2
1
tan
2
1
tan
2
1
2
tan
2
1
tan
2
1
2
(m = 0, 1, 2, 3, …).
Then, we can obtain the relation between core thickness (T) and effective
index (N
eff
).
b
a b
n
n
b
b
n
n
m
k
d T
c
f
s
f
x
1
tan
1
tan
1
2
2
2
1
2
2
1
４１
Figure 4.2 represents effective index as a function of the Si thickness for TE
0
and TM
0
modes. In addition, this relation is also dependent on the wavelength of the
propagation light. For general Si-on-insulator (SOI) structure, the thickness of the Si
layer is about 250 nm. Thus, the effective index (2.99) of TE
0
mode is very different
that (2.56) of TM
0
mode at this thickness.
Figure 4.2 Effective index curves of 1D slab waveguide as a
function of the Si thickness for TE
0
and TM
0
modes.
Figure 4.3 shows electric field distributions in the 1D slab waveguide for
TE
0
and TM
0
. In Figure 4 (a) and (c), TM
0
mode has about twice more evanescent
0 100 200 300 400 500 600 700 800 900 1000
2.2
2.4
2.6
2.8
3.0
3.2
3.4
LiNbO
3
Si
SiO
2
Wavelength 1.55 um
n
SiO
2
= 1.45
n
Si
= 3.48
n
LiNbO
3
= 2.21 (TE), 2.14 (TM)
TE
TM
Effective Index
Si thickness (nm)
４２
field to the both cladding layers compared with TE
0
mode. In addition, more electric
field escapes to the cladding when the thickness of the core layer (Si) decreases. For
this structure, the refractive index of the upper cladding layer (LiNbO
3
) can be
modulated. Thus, using TM mode is more effective to demonstrate an electro-optic
modulator in this structure.
Figure 4.3 Field distributions of 1D slab waveguide for TE
0
and
TM
0
modes.
4.3 Modeling of hybrid Si-LiNbO
3
structure
Figure 4.4 represents hybrid structure of Si and LiNbO
3
. LiNbO
3
micro-
４３
platelet is integrated to the Si waveguide and micro-ring structure on a Si-on-
insulator platform. In order to improve bonding area and strength, supporting Si
ridge structures can be fabricated on either side of the waveguides. Then LiNbO
3
micro-platelet can be bonded onto both the waveguide upper surface and onto the
side structures. Electrodes are then integrated on the top of the LiNbO
3
micro-
platelet.
Figure 4.4 A hybrid structure of Si waveguide and LiNbO
3
thin film
for electro-optic active devices.
Using the finite difference method (OlympIOs), the TM Mode Field
distribution of the actual 2D Si ridge waveguide has been calculated as shown in
Figure 4.5. The solid curve corresponds to the vertical cross section for the TM field.
The height of the Si waveguide and the etching depth between the ridges are same as
stated above and the top LiNbO
3
film is 1 m thick. The refractive indices of Si and
４４
SiO
2
are 3.48 and 1.45, respectively. LiNbO
3
is a uniaxial crystal: The ordinary
refractive index n
o
and the extraordinary refractive index n
e
for LiNbO
3
are 2.212
and 2.141, respectively. And n
e
is used for the TM mode since the film is made up of
a z-cut LiNbO
3
. The field distribution has been analyzed at 1550 nm wavelength.
Figure 4.5. Electric field distribution for the TM mode of the hybrid
Si-LiNbO
3
micro-ring resonator with (a) a 300 nm width
waveguide and (b) a 500 nm waveguide.
４５
In this analysis, two different width waveguides (300 nm and 500 nm) were
used as shown in Figure 4.5(a) and 4.5(b). In this polarization, the large volume of
the field is located above and below the Si ridge waveguide and extends widely into
the cladding. Thus, in this hybrid structure, the effective index of the Si waveguide
can be varied by the modulation of the refractive index of the LiNbO
3
cladding layer.
For these devices, the TM mode is more effective than the TE mode because more of
the modal power is traveling in the upper cladding. The evanescent field in the
LiNbO
3
region strengthens when the width and height of the Si waveguide are
decreased, which reduces its effective index and mode confinement as shown in
Figure 4.5(a) and 4.5(b). Thus, the sensitivity of the Si waveguide to the LiNbO
3
cladding layer is inversely proportional to its dimension.
As shown in Figure 4.6, the effective index difference of the Si waveguide
Si
eff
n has been calculated as a function of the index difference of the LiNbO
3
LN
e
n
by finite difference method. The ratio between these two index differences
n
R is
about 0.31, which means
Si
eff
n corresponds to 31% of
LN
e
n . Reducing the
thickness of the Si waveguide, the ratio is getting increased. In addition, the effective
index difference of the Si waveguide can be achieved about value of 1.0 10
-4
by
applying few voltages in this hybrid structure. It is considerable value compared with
current active Si waveguides which are demonstrated by the free-carrier dispersion
effect such as carrier-injection and carrier-depletion methods.
４６
0.0
2.0x10
-4
4.0x10
-4
6.0x10
-4
0.0
5.0x10
-5
1.0x10
-4
1.5x10
-4
2.0x10
-4
n
eff
of Si waveguide
n
e
of LiNbO
3
Figure 4.6 The effective index difference of the Si waveguide as a
function of the index difference of LiNbO
3
.
4.4 Modeling of hybrid Si-LiNbO
3
Micro-ring Resonator
Using the ratio
n
R between
LN
e
n and
Si
eff
n , we can simply obtain effective
r
(electro-optic) coefficient of the Si waveguide
Si
eff
r .
V pm r
n
n
R r
Si
eff
LN
e
n
Si
eff
/ 2 . 7
33
3
(1)
where E r n n
LN
e
LN
e 33
3
2
1
, (2)
E r n n
Si
eff
Si
eff
Si
eff
3
2
1
, (3)
４７
and
LN
e n
Si
eff
n R n (4)
where
33
r (=30 pm/V) is a r coefficient of the LiNbO
3
for z-axis, E is applied
field for z-axis.
Phase shift is expressed by
L
0
(5)
where
V r
g
n
eff
Si
Si
eff
3
(6)
where is propagation constant, L is perimeter of a ring, is the free space
optical wavelength, V is applied voltage to a ring, is the electrical-optical
overlap integral, and g is the electrode gap.
Electro optic (EO) tuning efficiency of resonance frequencies
EO
is given by
g
r n c
g
r n
n
f
dV
dn
dn
df
dV
df
eff
Si
eff
Si
eff
Si
eff
Si
eff
Si
EO
2 2
2 3
(7)
When
eff
Si
n = 2.3511 for TM mode, g = 1.5 m, = 1, and = 1.55 m, Electro
optic (EO) tuning efficiency of resonance frequencies is 2.55 GHz/V .
The voltage to tune the FWHM of the resonance
f
V
is given by
EO
f
f
V
(8)
where f is FWHM of the resonance.
Thus, if the hybrid micro-ring resonator has higher Q factor, it has higher
４８
sensitivity because of the higher modulation depth from sharp slop near the
resonance in the transmission spectrum.
4.5 Fabrication of hybrid Si-LiNbO
3
Micro-Ring Tunable
Resonator
Si micro-ring resonator has been fabricated on a Si-on-insulator (SOI)
platform (from SOITEC) as shown in Figure 4.7. In order to fabricate the submicron
size of Si waveguide structures, a 0.18 m standard CMOS process have been used.
The height of the Si waveguide is 250 nm, the etching depth between the ridges is
200 nm, the width of Si waveguide is 500 nm, the thickness of the buried SiO
2
layer
is 2 m, and the thickness of the bottom Si layer is 700 m. Figure 4.8 shows SEM
images of the cross section of the Si waveguide on SiO
2
/Si. To couple to an optical
fiber, vertical grating couplers have been fabricated by the same CMOS process at
both ends of the Si waveguide.
４９
(a)
(b)
Figure 4.7 (a) Schematic of a Si micro-ring resonator. (b) SEM
micrograph of a Si micro-ring resonator (top view).
５０
(a)
(b)
Figure 4.8 SEM micrograph of the cross section of a Si micro-ring
resonator (45
o
angle view).
５１
Individual single crystal LiNbO
3
micro-platelets can be picked up from the
surface by the electro-static attraction between an optical fiber tip and the micro-
platelet, moved to another substrate, positioned, and subsequently bonded to the new
substrate. The micro-platelets were transferred and bonded to the Si micro-ring
resonator via a direct bonding at 300
o
C. The bonding temperature was lower than the
general direct bonding temperature to prevent crack caused by the large thermal
stress between Si waveguides and LiNbO
3
films.
Figure 4.9 (a) The integration procedure for the hybrid structure
LiNbO
3
micro-platelet and Si micro-ring waveguide. (b) Optical
micrograph (left) and FESEM micrograph (right) of the fabricated
structure.
５２
We bonded the micro-platelets directly on the Si ridge waveguides and on
micro-ring structures by direct bonding at 500
o
C for 4 hours. Pre-annealing and
flattening were required. Figure 4.9(a) represents the process of the fabrication. In
Figure 4.9(b) (left), an optical microscope picture shows a transparent LiNbO
3
micro-platelet on Si micro-ring waveguide structure. An FESEM picture with tilted
angle view (10 degrees) clearly shows the LiNbO
3
micro-platelet film fabricated on
the Si waveguide in Figure 4.9(b) (right). Thus, the top cladding of the Si ridge
waveguide has been changed from air to LiNbO
3
film. This is the structure that can
lead to electro-optic modulation and NLO effects due to the evanescent fields
extending into the LiNbO
3
.
In the fabrication, the bonding area is very small since the LiNbO
3
is bonded
only to the top of the Si waveguide. Height of Si waveguide is 300 nm and etching
depth between the ridges is 250 nm. Because of the small area, we could not confirm
the bonding by the scotch tape test but there are no optical fringes seen and the
FESEM image of the edge of the LiNbO
3
, Figure 4.9(b), appears to show a bonded
interface. Figure 4.10 show the optical micrograph of various hybrid micro-ring
resonators. In Figure 4.10(d) and (f), fringe pattern represents that there is air gap
between a LiNbO
3
micro-platelet and Si waveguide. Thus, the LiNbO
3
micro-platelet
was not bonded onto the Si waveguide. But, except these two devices, they were well
bonded. The bonding area and strength could be improved by using supporting Si
ridge structures on either side of the waveguides and bonding to both the waveguide
５３
upper surface and to the side structures.
Figure 4.10. Optical micrograph of the hybrid Si-LiNbO3 micro-
ring resonators.
In addition, polishing the surface of LiNbO
3
micro-platelet is not necessary
to improve the surface roughness in this hybrid structure. It is because a surface
５４
roughness of 6 nm measured by AFM (in chapter 2) should not be an issue for the
hybrid waveguiding structure since the polished surface of the micro-platelet was
bonded onto the SOI structure. In these hybrid structures, only the exponential tail of
the optical mode is in the LiNbO
3
and since optical field is very low at the implanted
separated surface, the surface roughness of ~6 nm is acceptable for the hybrid
structure.
4.6 Experimental Results
Figure 4.11(a) represents the optical micrograph of a hybrid Si-LiNbO
3
micro-ring resonator, and the inset shows the cross section of the hybrid structure.
Figure 4.11(b) displays the cross-section of the hybrid Si-LiNbO
3
waveguide and
shows the guided TE mode calculated by using a finite-difference tool, OlympIOs.
The solid curve corresponds to the vertical cross section for the TE field. For this
calculation it was assumed that the Si waveguide was fabricated using the design
parameters and the top LiNbO
3
film was 1 m thick. The refractive index of Si and
SiO
2
is 3.48 and 1.45, respectively. LiNbO
3
is a uniaxial crystal: The ordinary
refractive index n
o
and the extraordinary refractive index n
e
for LiNbO
3
are 2.212
and 2.141, respectively. The ordinary index is used for the TE mode since the film is
made up of a z-cut LiNbO
3
. The field distribution has been analyzed at 1550 nm
wavelength. A large volume of the evanescent field is found to reside in the LiNbO
3
region above the Si waveguide for the guided TE mode. The evanescent field in the
５５
LiNbO
3
region increases when the width and height of the Si waveguide is decreased,
which reduces its effective index and mode confinement. Thus, the sensitivity of the
Si waveguide to the LiNbO
3
cladding layer is inversely proportional to its dimension.
Figure 4.11 (a) An optical micrograph of a hybrid Si-LiNbO
3
micro-ring resonator (b) Electric field distribution for the TE mode
of the hybrid Si-LiNbO
3
micro-ring resonator.
５６
Figure 4.12. (a) Experimental setup and (b) optical micrograph of
device under test setup.
５７
In order to couple light more efficiently between optical fibers and a Si
waveguide, an one dimensional vertical grating coupler has been fabricated by the
same CMOS process at both ends of the Si waveguide. Figure 4.12(a) shows
experimental setup for transmission spectrum measurement. A tunable laser source
(Agilent 8164B), a polarization controller, a device under test setup and an optical
power meter were used. For device under test setup, high precision 3-axis translation
stages were used to control input and output fiber and both fibers were mounted at a
10
o
C angle with respect to the vertical direction as shown in Figure 4.12(b).
Figure 4.13. Transmission spectra for a Si micro-ring resonator and
a hybrid Si-LiNbO
3
micro-ring resonator.
５８
For the hybrid Si-LiNbO
3
tunable ring resonator, the radius of the micro-ring
is 6 m and the gap between the waveguide and the micro-ring is 220 nm. Figure
4.13 shows the TE mode transmission spectra for a Si micro-ring resonator prior to
the LiNbO
3
film bonding and for a hybrid Si-LiNbO
3
resonator after the bonding.
The observed free spectral ranges (FSRs) of the two devices were 15.65 nm and
16.50 nm for the TE mode, respectively, leading to a difference of 0.85 nm (5.4%
increment). For both Si and Si-LiNbO
3
resonators, the FSR for the TM mode has not
been measured due to its high bending loss [18].
To obtain a theoretical FSR, the group index n
g
of the two structures has
been estimated by means of the film mode matching (FMM) method available from
OlympIOs. Here the FSR is given by
2
/n
g
L, where L is the circumference of the ring.
For the TE mode, the theoretical effective index n
eff
and the group index n
g
for the
hybrid Si-LiNbO
3
waveguide were 2.617 and of 3.849 respectively, while they were
2.532 and 4.056 for the Si waveguide. It is noted that the hybrid waveguide exhibits
a higher effective index because of the high refractive of the cladding LiNbO
3
(n
o
=
2.21). For the group index, however, it has a lower value. The calculated FSR for the
hybrid and the Si resonator was 16.12 nm and 16.99 nm respectively, as a result the
difference between them becomes 0.87 nm, which corresponds to an FSR increase of
5.4%. Thus, the experimental FSRs and their difference were in good agreement with
the theoretical values and this provides good assurance that the LiNbO
3
is optically
bonded to the Si.
５９
(a)
(b)
Figure 4.14. Transmission spectra of (a) a Si micro-ring resonator
and (b) a hybrid micro-ring resonator.
The finesse F and the quality factor Q have been considered for the two
devices. For the Si resonator, F and Q were ~3.30 10
2
and ~3.31 10
4
, respectively.
1569.9 1570.0 1570.1 1570.2 1570.3 1570.4 1570.5
-12
-10
-8
-6
-4
-2
0
Normalized Transmission Power [dBm]
Wavelength [nm]
Experiment
Fit
= 0.99561
= 0.99213
n
eff
= 2.624
1569.0 1569.1 1569.2 1569.3
-12
-10
-8
-6
-4
-2
0
Normalized Transmission Power [dBm]
Wavelength [nm]
Experiment
Fit
= 0.99806
= 0.99657
n
eff
= 2.539
６０
For the hybrid device, they were reduced by 50% to provide F of ~1.67 10
2
and Q of
~1.68 10
4
due to the increase of the coupling and the bending loss.
In order to find an effective index n
eff
, a loss factor per round trip and a
self-coupling coefficient , the analytical transfer function [19] was fitted by trial and
error to the measured transmission spectra as shown in Figure 4.14. For the Si ring
resonator, we found n
eff
of ~2.539, of ~0.9966, and of ~0.9981. For the
hybrid case, n
eff
was ~2.6240, ~0.9921, and ~0.9956. For the hybrid structure, the
effective index of the gap region between the waveguide and the ring resonator
increases due to the LiNbO
3
cladding layer. Thus, the cross-coupling coefficient
was increased and decreased. Q and decreased because the evanescent field in the
LiNbO
3
upper cladding increased the bending loss.
To observe the EO effect, an electric field was applied between the top of the
LiNbO
3
film and the bottom of the SOI wafer by applying a voltage V
a
. For V
a
=100
V, the voltage across the LiNbO
3
film V
LN
is ~7.2 V with most of the voltage
dropped across the 2 m thick SiO
2
layer in the hybrid structure. Figure 4.15 shows
the transmission spectra for different applied voltages, while the inset displays the
resonance shift as a function of V
LN
. For V
LN
=8.6 V (V
a
=120 V), the resonance
shifted by ~0.07 nm corresponding to n
eff
of 1.2 10
-4
. The effective EO coefficient
r
eff
of 1.7 pm/V was calculated from n
eff
=(n
eff
)
3
·r
eff
·E, where E is the electric field in
the LiNbO
3
. In this structure, z-cut LiNbO
3
was used and r
13
(8.6 pm/V) is the
coefficient for the TE mode. Hence, the effective EO effect for the hybrid structure is
６１
equivalent to ~20% of that of the LiNbO
3
. This is consistent with the overlap of the
applied E field and the optical field in the upper cladding. Equivalent V
L and EO
tuning efficiency of the resonance frequency df/dV were 0.22 V/cm and 0.75 GHz/V,
respectively. They could be improved by increasing Q and optimum design of the
electrodes.
Figure 4.15 Transmission spectrum of a hybrid Si-LiNbO
3
resonator for the different values of V
LN
.
4.7 Conclusion
A hybrid structure of LiNbO
3
and Si photonic has been proposed. This is a
promising approach to integrating a second order NLO material, LiNbO
3
, into the Si-
６２
on-insulator (SOI) photonics technology. An 1D Si slab waveguide with a LiNbO
3
cladding layer has been analyzed for the TM and TE mode in order to characterize
various parameters related to evanescent field profile. Then, an actual 2D Si ridge
waveguide with a LiNbO
3
cladding layer has been investigated. Theoretical
calculation proved that considerable effective index difference of the Si waveguide
could be achieved by changing the index of the LiNbO
3
cladding layer.
Finally, a hybrid Si-LiNbO
3
micro-ring electro-optic tunable resonator has
been demonstrated based on direct bonding for TE mode. Free standing single crystal
LiNbO
3
micro-platelets have been obtained, transferred, and bonded on the Si micro-
ring resonator. An effective r coefficient of 1.7 pm/V for the TE hybrid micro-ring
tunable resonator has been measured. For high Q-factor micro-ring modulators, sub-
nanometer wavelength tuning is enough to achieve a high modulation depth [1]. We
note several avenues to improve the modulator. For the TE mode, coplanar electrodes
on the top of the LiNbO
3
would be a more efficient since, with the proper design, a
larger E field in the LiNbO
3
could be achieved for a given applied voltage. The TM
mode would be a better modulator because of the increased optical power in the
upper cladding and the appropriate coefficient would be the larger r
33
coefficient
(~30.8 pm/V). Unfortunately the TM mode in Si ring resonators typically has a
significantly lower and a waveguide design to decrease the loss of the TM mode
would be necessary.
６３
4.8 References
[1] P. Rabiei, W. H. Steier, “Lithium niobate ridge waveguides and modulators
fabricated using smart guide,” Appl. Phys. Lett., 86, 161115-1, 2005.
[2] A. Guarino, G. Poberaj, D. Rezzonico, R. Degl’Innocenti, P. Günter, “Electro-
optically tunable microring resonators in lithium niobate,” Nature Photonics, 1,
407, 2007.
[3] R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J.
Quantum Electron., vol. QE-23, no. 1, pp. 123-129, 1987.
[4] A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu,
and M. Paniccia, “A high-speed silicon optical modulator based on a metal-
oxide-semiconductor capacitor,” Nature, vol. 427, pp. 615–618, 2004.
[5] D. Samara-Rubio, L. Liao, A. Liu, R. Jones, M. Paniccia, D. Rubin, and O.
Cohen, “A gigahertz silicon-oninsulator Mach-Zehnder modulator,” in Optical
Fiber Communication Conference, Vol. 2 of OSA Proceeding Series (Optical
Society of America, Washington, D.C.), pp. 3-5, 2004
[6] L. Liao, D. S. Rubio, M. Morse, A. Liu, D. Hodge, “High speed silicon Mach-
Zehender modulator,” Opt. Express 13, pp. 3139, 2005.
[7] C. T. Shih, Z. W. Zeng, and S. Chao, “Design and Analysis of Metal-Oxide-
Semiconductor–Capacitor Microring Optical Modulator With Solid-Phase-
Crystallization Poly-Silicon Gate,” Journal of Lightwave Technology, Vol. 27,
Issue 17, pp. 3861, 2009.
[8] Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon
electro-optic modulator,” Nature, vol. 435, pp. 325–327, May 2005.
[9] Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, “12.5 Gbit/s
carrier-injection-based silicon micro-ring silicon modulators,” Opt. Express, 15,
(2), pp. 430–436, 2007.
[10] S. Manipatruni, X. Qianfan, B. Schmidt, J. Shakya, and M. Lipson, “High speed
carrier injection 18 Gb/s silicon micro-ring electro-optic modulator,” in Proc.
20th Lasers Electro-Opt. Soc. Meeting (LEOS), Oct. 21–25, 2007.
６４
[11] W M. Green, M J. Rooks, L Sekaric, and Y A. Vlasov, “Ultra compact, low RF
power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express, vol. 15, no. 25,
pp. 17 106–17 113, 2007.
[12] W. M. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low
RF power, 10 Gb/s silicon Mach-Zehnder modulator,” in Proceedings of the
20th Annual Meeting of the IEEE Lasers & Electro-Optics Society (Institute of
Electrical and Electronics Engineers, New York), Postdeadline paper PD1.2,
2007.
[13] A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and
M. Paniccia, “High-speed optical modulation based on carrier depletion in a
silicon waveguide,” Opt. Express, 15, (2), pp. 660–668, 2007.
[14] L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky,
and M. Paniccia “40 Gbit/s silicon optical modulator for highspeed
applications,” Electronics Letters,. 43, (22), 2007.
[15] B. Analui, D. Guckenberger, D. Kucharski, and A. Narasimha, “A fully
integrated 20-Gb/s optoelectronic transceiver implemented in a standard 0.13-
um CMOS SOI technology,” IEEE J. Solid-State Circuits 41, 2945-2955, 2006.
[16] T. Pinguet, V. Sadagopan, A. Mekis, B. Analui, D. Kucharski, S. Gloeckner, “A
1550 nm, 10 Gbps optical modulator with integrated driver in 130 nm CMOS,”
in Proc. 4th Conf. Group IV Photon., Tokyo, Japan, Sep. 19–21, 2007.
[17] D. Marris-Morini, L. Vivien, J. M. Fédéli, E. Cassan, P. Lyan, S. Laval, “Low
loss and high speed silicon optical modulator based on a lateral carrier depletion
structure,” Opt. Express, vol. 16, no. 1, pp. 334–339, 2008.
[18] B. E. Little, J. S. Foresi, G. Steinmeyer, E. R. Thoen, S. T. Chu, H. A. Haus, E.
P. Ippen, L. C. Kimerling, and W. Greene, “Ultra-compact Si-SiO
2
microring
resonator optical channel dropping filters,” Photon. Technol. Lett. 10, 549, 1998.
[19] J. Niehusmann, A. Vörckel, P. Haring Bolivar, T. Wahlbrink, W. Henschel, and
H. Kurz, “Ultrahigh-quality-factor silicon-on-insulator microring resonator,”
Opt. Lett. 29, 2861, 2004.
６５
Chapter 5
LiNbO
3
photonic slab
5.1 Introduction
Photonic crystals which can control flow of the light are interesting structure since it
has a large number of applications in photonic integrated circuit [1]. It is an artificial
periodic structure of dielectric materials which might introduce photonic band gaps
similar to electronic band gap in semiconductor materials. The photonic band gap
prevents light propagation in certain direction with specified energies. Thus, light can
be controlled by varying the band gap with the defect structure in the photonic
crystal.
There are three types of photonic crystal structures; they are 1D, 2D, and 3D
photonic crystals. In 1D photonic crystals, a periodic dielectric structure is along one
direction. For example, a multi-layer dielectric film [2] is the well-known application
ranging from low and high reflection coatings on lenses and mirrors. A photonic
６６
crystal fiber [3] is typical application of 2D photonic crystal which variation is along
two directions. In case of a 3D photonic crystal [4-9], there are some examples, but
they have difficulty in fabrication actual devices. Thus, an 1D and a 2D photonic slab
structure have been widely studied because they are more acceptable than other
structure [1]. These structures have 1D or 2D periodicity, but 3D light propagation
might be considered since they are physically 3D structures. A large number of
practical applications such as a waveguide, a coupler, a splitter, a resonator, a filter,
etc., can be demonstrated in these photonic slab structures [10-15].
As a photonic crystal material, high refractive index and low optical loss are
required. Previously, Si and GaAs have been used to demonstrate photonic slab
devices. Recently, LiNbO
3
has been studied and partially demonstrated for an active
photonic crystal device [16-19] since LiNbO
3
has strong electro-optic coefficient as
well as high refractive index and low optical loss. In these demonstrations, however,
an annealed proton-exchanged (APE) gradient-index LiNbO
3
waveguide was used
and depth (1-1.5 um) of air holes is much smaller than width (8 um) of guided mode.
Thus, holes do not reach the center (2.5 um) of the optical mode. Thus, light can
propagate for all wavelengths even in band gap region, although there is low
transmission in band gap region compared with other region. In order to fabricate
actual photonic slab structure, it might be fabricated on thin film structure such as
LiNbO
3
thin films.
６７
Figure 5.1 The photonic band diagram of a triangular array air hole in
LiNbO
3
for (a) TE polarization and (b) TM polarization. Normalized frequency
( a/2 c =a/ ) are plotted as a function of normalized wave vector (ka/2 ).
６８
In this chapter, an active photonic slab in a LiNbO
3
thin film-on-insulator is
proposed and discussed. Theoretical calculation shows photonic band gap in this
structure and gives optimum parameters. Fabrication techniques and its major issues
are discussed and current progress and future work are presented.
5.2 Modeling of LiNbO
3
photonic slab
Photonic band gap in photonic slab structure heavily is dependent on various
parameters such as hole array, light polarization mode, radius of hole, period of hole,
slab thickness, wavelength, refractive index, etc. The fabrication limit of the actual
device should be also considered to design ratio between the radius and the period of
the hole. First, 2D photonic crystal structure has been analyzed by plane wave
expansion (PWE) method because the photonic crystal properties can be estimated
roughly with minimal computation. Then, an actual 2D photonic slab has been
investigated by 3D FDTD simulation.
An air columns 2D periodic structure has been investigated since the
manufacturing of this structure is easier than that of a LiNbO
3
columns 2D periodic
structure. A triangular array structure has been used since it has a large band gap
compared with a squire lattice structure. Figure 5.1 represents band diagrams of a
triangular structure for TE and TM modes. In this calculation, PWE method has been
used and the extraordinary and ordinary indices of the z-cut LiNbO
3
have been
applied to TM and TE modes, respectively. At 1.55 um wavelength, n
e
and n
o
are
６９
2.141 and 2.215, respectively. The radius of the hole was 0.25a, where a is period of
the lattice. In this Figure, TM modes have no band gap while TE modes have a band
gap in the triangular array structure. The right inset shows a cross-sectional view of
the triangular array structure and the left inset shows the Brillouin zone with the
irreducible zone shaded light blue. Normalized frequency ( a/2 c =a/ ) in the gap
varies from 0.3395 to 0.3112 for the TE polarized light. At 1.55 um wavelength, the
lattice constant in the photonic crystal and the diameter of air hole can be selected to
be 504 nm and 126 nm, respectively. The corresponding bad gap is in the range of
1.4845–1.6195 um.
To design actual devices, a 2D photonic slab structure of the LiNbO
3
thin film
has been analyzed by FDTD method. Figure 5.2a illustrates the triangular array
lattice of photonic slab of the LiNbO
3
thin film on SiO
2
substrate. Upper cladding
and holes are air. In the 2D photonic crystal structure, if periodic array is in the x-y
plane, k
z
is zero for both TE and TM mode. However, in the photonic slab, k
z
is not
zero. Thus, the modes can no longer be characterized as pure TE or TM modes. They
are kind of hybrid modes and called predominantly TE- or TM-like modes. Figure
5.2b shows the photonic band diagram (normalized frequency versus normalized
wave vector). In this structure, band gap exists only TE like modes like a 2D
photonic crystal structure. Because of the slab structure, the modes above the SiO
2
light cone are radiated to the cladding of the slab. Thus, only modes below the SiO
2
light cone can be guided to the photonic slab. Band gap frequency was shifted to the
７０
high normalized frequency (0.3565- 0.3922). Table 5.1 represents design parameters
and actual structure dimensions.
Figure 5.2 (a) Proposed design of the LiNbO
3
photonic slab and (b)
The photonic band diagram of the structure.
７１
Table 5.1 Dimensions of the LiNbO
3
photonic slab
Wavelength a r=0.29a h=0.9a Band Gap
1550 nm 580 nm 168 nm 522 nm 1478.84~1626.93 nm
1300 nm 487 nm 141 nm 438 nm 1241.71~1366.06 nm
Figure 5.3 Process of LiNbO
3
photonic slab fabrication.
5.3 Fabrication of LiNbO
3
photonic slab
Before we fabricate the LiNbO
3
photonic slab structure, the LiNbO
3
etching method
should be determined because the material and the thickness of the etching mask are
dependent on the etching equipment and its recipe. LiNbO
3
has strong resistance to
standard etching methods both for the wet and dry etching [20]. In addition, it has
７２
poor etching roughness compared with III-V materials or polymer materials. Thus,
the etching method is currently the biggest issue. Cr was mainly used for deep
etching [58]. Annealed proton-exchanged (APE) LiNbO
3
has much higher etching
selectivity than bulk LiNbO
3
. A Focused Ion Beam (FIB) etching equipment doesn’t
require the etching mask since a focused ion beam etches LiNbO
3
directly. However,
it requires much higher cost and longer etching time than other methods [16].
Considering the previous methods [21], possible etching methods have been
investigated. Then, a sufficient etching selectivity (LiNbO
3
/Cr ~ 4) has been
achieved by using the STS ICP RIE equipment. In this method, the chamber pressure
of 94 mTorr, RF power of 700 W and C
4
F
8
/Ar/CHF
3
Gases of 7/10/33 sccm have
been used.
Figure 5.3 shows the fabrication process of a LiNbO
3
photonic slab. A Cr
layer of 130 nm is deposited by using a E-beam evaporator. After fabrication of the
PMMA photonic slab structure, Cr is etched by using a CR7 solution, a Cr etchant.
Then, LiNbO
3
film is etched by the STS ICP RIE equipment. In order to optimize
fabrication parameters of each process, photonic structures have been demonstrated
on bulk LiNbO
3
samples before we fabricate a LiNbO
3
photonic slab structure. From
the previous section (chapter 5.2), hole radius of 168 nm and period of 580 nm has
been selected. The radius of the hole over the range of 128-168 nm and electron
doses of E-beam has been varied to find an optimum value of each parameter.
７３
Figure 5.4 FESEM micrograph of a photonic crystal structure (a)
on a Cr layer and (b) on a LiNbO
3
substrate.
In Figure 5.4a, the FESEM image shows Cr photonic slab structure after wet
etching for 40 secs. Because of the over etching, hole size was little bigger than the
PMMA hole size. There were residual Cr particles inside the hole. Figure 5.4b shows
a FESEM image of the photonic crystal pattern on bulk LiNbO
3
after dry etching for
15 mins. It shows additional etched lines to the triangular directions since the Cr
７４
layer between holes might be etched faster than other area. Thus, band gap might be
smaller than the expected values since fabricated hole size is smaller than designed
value. However, in the analysis, this structure has large band gap (around 150 nm).
Thus, experimental structure could have enough a band gap even though it is smaller
than the design value.
5.4 Conclusion
Active photonic crystal devices using a LiNbO
3
film on SiO
2
substrate have been
proposed because of useful properties of LiNbO
3
such as high electro-optic
coefficient and low optical loss. To estimate the design values roughly, 2D LiNbO
3
photonic crystal structure has been analyzed by PWE method because of its short
simulation time. Then, 3D FDTD method has been used in order to design LiNbO
3
photonic slab more precisely. Etching methods with various equipments and recipes
have been investigated since they were the most important issue to fabricate the real
structure. The STS ICP RIE equipment has been selected for the etching method after
the investigation of available etching methods. In the E-Beam lithography, electron
doses and sizes of the hole have been varied to fine optimum values. Cr photonic
crystal pattern has been achieved by wet etching with a CR7 Solution. Finally,
LiNbO
3
photonic crystal structure has been demonstrated in a bulk LiNbO
3
sample.
Further work is to fabricate photonic slab waveguide in a LiNbO
3
thin film-on-
insulator structure.
７５
5.5 References
[1] J. D. Joannopoulos, S. G. Johnson, Photonic Crystals: Molding the Flow of
Light (2nd ed.), Princeton NJ: Princeton University Press. ISBN 978-0-691-
12456-8, 2008.
[2] J. W. S. Rayleigh, “On the remarkable phenomenon of crystalline reflexion
described by Prof. Stokes,” Phil. Mag 26: 256–265, 1888.
[3] P. St. J. Russell, “Photonic crystal fibers,” Science 299, 358-362, 2003.
[4] K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in
periodic dielectric structures,” Phys. Rev. Lett., Vol. 65, 3152, 1990.
[5] E. Yablonovitch and T. J. Gmitter, and K. M. Leung, “Photonics Band
Structure: The Face-Centered-Cubic Case Employing Nonspherical Atoms,”
Phys. Rev. Lett., Vol. 67, 2295, 1991.
[6] S. Noda, N. Yamamoto, and A. Sasaki, “New Realization Method for Three-
Dimensional Photonic Crystal in Optical Wavelength Region,” Jpn. J. Appl.
Phys. Vol. 35, Part 2, L909, 1996.
[7] A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C.
Lopez, F. Meseguer, H. Miguez, J. P. Mondia, G. A. Ozin, O. Toader and H. M.
van Driel “Large-scale synthesis of a silicon photonic crystal with a complete
three-dimensional bandgap near 1.5 micrometres,” Nature, Vol. 405, 437, 2000.
[8] S. G. Johnson and J. D. Joannopoulos, “Three-dimensionally periodic dielectric
layered structure with omnidirectional photonic band gap,” Appl. Phys. Lett.,
Vol. 77, 3490, 2000.
[9] O. Toader and S. John, “Proposed Square Spiral Microfabrication Architecture
for Large Three-Dimensional Photonic Band Gap Crystals,” Science Magazine
Vol. 292, 1133, 2001.
[10] H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S.
Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58,
R10096–R10099, 1998.
７６
[11] T. Baba and M. Nakamura, “Photonic crystal light deflection devices using the
superprism effect,” IEEE J. Quantum Electron. 38, 909–914, 2002.
[12] R. W. Ziolkowski and T. Liang, “Design and characterization of a grating–
assisted coupler enhanced by a photonic–band–gap structure for effective
wavelength–division demultiplexing,” Opt. Lett. 22, 1033–1035, 1997.
[13] S. H. Fan, P. R. Villeneuve, J. D. Joannopoulos, and H. A. Haus, “Channel drop
filters in photonic crystals,” Opt. Express 3, 4–11, 1998.
[14] A. Yariv, Y. Xu, R. K. Lee, and A. Scherer, “Coupled–resonator optical
waveguide: a proposal and analysis,” Opt. Lett. 24, 711–713, 1999.
[15] M. Notomi, K. Yamada, A. Shinya, J. Takahashi, C. Takahashi, and I.
Yokohama, “Extremely large group–velocity dispersion of line–defect
waveguides in photonic crystal slabs,” Phys. Rev. Lett. 87, 253902, 2001.
[16] F. Lacour, N. Courjal, M. P. Bernal, A. Sabac, C. Bainier, and M. Spajer,
“Nanostructuring lithium niobate substrates by focused ion beam milling,” Opt.
Mater. 27, 1421–1425, 2005.
[17] M. Roussey, M.-P. Bernal, N. Courjal, D. Van Labeke, and F. Baida, “Electro–
optic effect exaltation on lithium niobate photonic crystals due to slow
photons,” Appl. Phys. Lett. 89, 241110, 2006.
[18] M. Roussey, F. I. Baida, and M.-P. Bernal, “Experimental and theoretical
observation of the slow light effect on a tunable photonic crystal,” J. Opt. Soc.
Am. B 24, 1416–1422, 2007.
[19] G. W. Burr, S. Diziain, and M.-P. Bernal, “The impact of finite-depth
cylindrical and conical holes in lithium niobate photonic crystals” Optics
Express, Vol. 16, Issue 9, pp. 6302-6316, 2008.
[20] EMISData Reviews Series No. 5, Properties of Lithium Niobate (IN-SPEC,
London and New York, 1989).
[21] H. Hu, A. P. Milenin, and R. B. wehrspohn “Plasma etching of proton-
exchanged lithium niobate,” J. Vac. Sci. Technol. A Volume 24, Issue 4, pp.
1012-1015, July 2006.
７７
Chapter 6
Hybrid Si-LiNbO
3
Active Photonic Slab
6.1 Introduction
As stated in chapter 4, Si photonics based on Si-on-insulator (SOI) are being widely
investigated for next generation photonic networks and opto-electronic integrated
circuits [1-2]. It is because they enable compact size integration due to low bending
loss with tight optical confinement. Their fabrication technologies are compatible
with the well-developed complementary metal-oxide-semiconductor (CMOS)
technology. For this reason, Si photonic slabs based on SOI are the most promising
Photonic Crystal (PhC) structure. Since Si photonic slab is two dimensional PhC
structures, fabrication is much easier than three dimension photonic crystal.
Particularly, Si photonic slab and Si ridge waveguide could be integrated together in
the same chip since they are fabricated on same SOI device platform.
７８
For active devices, Si photonic slab uses plasma dispersion effects or
thermal effect since Si doesn’t have second order nonlinear effect [3-17]. Operation
speed of these devices is limited (~10 Gbps) by carrier life time and they require
additional complex fabrication process.
In this chapter, I propose and discuss hybrid Si-LiNbO
3
photonic slab device
platform and devices. In this structure, free standing LiNbO
3
micro-platelets are
bonded on Si photonic slab. Then, the effective index of Si photonic slab is changed
by the refractive index of upper cladding LiNbO
3
layer which can be varied by
applied electric field.
6.2 Modeling of Hybrid Si-LiNbO
3
photonic slab
In order to design the Hybrid Si-LiNbO
3
photonic slab, three parameters and three
conditions have been considered. Three parameters are the period of the holes or
lattice constant (a), the radius of the holes (r), and the height of the slab (h) and these
values should be optimized. But, for actual simulation, only two parameters (r and h)
are considered since normalized values are used; a is a unit value; r and h are
expressed r/a and h/a, respectively. Three conditions are about band gap, wavelength
and the height of the slab (h). Band gap should be below the light cone for LiNbO
3
.
Mid gap should be around 1.55 m wavelength for optical communication and
network applications. For general SOI wafer, the thickness of the Si slab layer is 250
nm. Thus, h should be around this value.
７９
Figure 6.1 shows band diagrams for the different values of r/a and h/a. A
triangular array structure has been used since it has a large band gap compared with a
squire lattice structure. PWE method has been used and the extraordinary and
ordinary indices of the z-cut LiNbO
3
have been applied to TM and TE modes,
respectively. At 1.55 um wavelength, n
e
and n
o
are 2.141 and 2.215, respectively.
(a) (b)
(c) (d)
Figure 6.1 The photonic band diagram of the structure. (a) h=0.6a
and r=0.2a (b) h=0.6a and r=0.25a (c) h=0.7a and r=0.2a (d) h=0.7a
and r=0.25a.
８０
(a) (b)
(c) (d)
Figure 6.2 The photonic band diagram of the structure. (a) h=0.7a
and r=0.18 (b) h=0.7a and r=0.19a (c) h=0.7a and r=0.21a (d)
h=0.7a and r=0.22a.
For r/a > 0.25, the light cone for LiNbO
3
exists within or below the band gap
region. On the other hand, for r/a < 0.2, band gap is too small. Then, optimized
values of r/a and h/a are 0.2 and 0.7 as shown in Figure 6.1(c). In this design, the
normalized frequency (a/ ) of the mid gap is 0.2349. Then, corresponding value of a
is 364 nm since we fixed mid gap wavelength is 1.55 m. Corresponding values of r
８１
and h are 73 nm and 255 nm, respectively. Band gap region is between 1504 nm (a/
= 0.2420) and 1598 nm (a/ = 0.2278).
Figure 6.3 The photonic band diagram of the structure for the
different values of the radius.
In the fabrication of the hybrid photonic slab structure, there could be no
fabrication error for the height of the slab (h) since the SOI wafer which has 250 nm
thick Si layer is commercially available. But, the radius of the holes (r) deviate from
the optimum value of 0.2 during the e-beam lithography and etching. Thus, we have
investigated up to ± 10% error for the r/a. Figure 6.2 represents band diagrams for
８２
± 5% error and ± 10% error. The highest frequency of the TE-like mode 1 and the
lowest frequency of the TE-like mode 2 are at position K and M of the wavevector,
respectively. The band gap region is between these two values. Figure 6.3 illustrates
the change of TE-like mode 1 and TE-like mode 2 for the different values of r/a.
Inset shows band gap as a function of r/a. Thus fabrication errors for the radius of
the holes are acceptable up to around 10%.
Figure 6.4 Process of LiNbO
3
photonic slab fabrication.
6.3 Fabrication of LiNbO
3
photonic slab
Figure 6.4 shows the fabrication process of a hybrid Si-LiNbO
3
photonic slab. For E-
beam lithography, PMMA has been spun on top of the SOI substrate. Then, PMMA
is used as a etching mask for Si. Using the PMMA pattern, Si is etched by Oxford
８３
ICP-RIE (Inductively Coupled Plasma Reactive Ion Etching). After removing
PMMA pattern, Si photonic slab is obtained. Then, the free standing single crystal
LiNbO
3
micro-platelet is integrated on the Si photonic slab by direct bonding at
around 200
0
C.
Figure 6.5 Optical micrograph and SEM image of hybrid Si-
LiNbO
3
photonic slab.
In order to verify bonding between the LiNbO
3
micro-platelet and the Si
photonic slab, we tried to bond the LiNbO
3
micro-platelet on general Si photonic
slab structure which is different from our design. Figure 6.5 shows optical
micrograph and SEM images of the hybrid Si-LiNbO
3
photonic slab. Bonding
８４
between the LiNbO
3
micro-platelet and Si photonic slab was performed well since
there was no fringe pattern in the optical micrograph. SEM images represent two
dimensional Si photonic crystal structures.
Figure 6.6 Schematic illustration of the hybrid Si-LiNbO
3
photonic
slab with 3 m wide stripe waveguides.
In order to measure the transmission spectrum of the hybrid Si-LiNbO
3
photonic slab, stripe waveguides (3 m width) are used for the input and output of
optical signals as shown in Figure 6.6 [18]. Fabry–Pérot resonance spectrum may
exist as a back ground noise in this waveguide and photonic crystal structure. In
order to remove this background noise spectrum, other waveguide without photonic
crystal is used as shown in Figure 6.6. Incident light propagates along the -
direction. The photonic crystal structure between the waveguides has fifteen lines of
air holes which are enough to measure the band gap transmission spectrum. Using
８５
this device design, the Si photonic slab has been fabricated as shown in Figure 6.7
This SEM image clearly shows photonic crystal structure with input and output
waveguides.
Figure 6.7 SEM image of the hybrid Si-LiNbO
3
photonic slab with
a stripe waveguide.
Transmission spectrum of the Si photonic slab should be measured before
bonding of a free standing LiNbO
3
micro-platelet in order to compare the
transmission spectrum of the hybrid Si-LiNbO
3
photonic slab. Band gap region of
the transmission spectrum is shifted by LiNbO
3
upper cladding layer since the
effective refractive index of the Si photonic slab is changed. Furthermore, this hybrid
structure promises tunable photonic crystal devices such as electro-optic tunable
filter and modulator by applying electric field in the LiNbO
3
layer.
８６
6.4 Conclusion
Hybrid Si-LiNbO
3
photonic slab have been proposed and discussed for active
photonic devices in order to employ second order nonlinear effect to the Si photonic
slab. The lattice constant, the radius of the holes, and the height of the Si slab have
been carefully designed by using PWE method. For this design, ± 10 % error in the
radius of the holes appears acceptable. By using the direct bonding method, a free
standing single crystal LiNbO
3
micro-platelet has been bonded on the Si photonic
slab which was optimized for air cladding case to prove integration of the hybrid
structure. Then, Si photonic slab structures using optimum values for hybrid
structure have been fabricated by E-beam lithography and ICP-RIE. To measure
transmission spectrum, input and output strip waveguides have been employed at the
end of the Si photonic crystal. Further work is to integrate the hybrid Si-LiNbO
3
photonic slab waveguide with coplanar electrodes for EO fast tunable filters and EO
modulators.
８７
6.5 References
[1] G. T. Reed and A. P. Knights, Silicon photonics : an introduction, John Wiley
& Sons, 2004.
[2] G. T. Reed, Silicon Photonics: the state of the art, John Wiley & Sons, 2008.
[3] R. A. Soref and B. R. Bennett, “Electrooptical effects in silicon,” IEEE J.
Quantum Electron., vol. QE-23, no. 1, pp. 123-129, 1987.
[4] A. Liu, R. Jones, L. Liao, D. Samara-Rubio, D. Rubin, O. Cohen, R. Nicolaescu,
and M. Paniccia, “A high-speed silicon optical modulator based on a metal-
oxide-semiconductor capacitor,” Nature, vol. 427, pp. 615–618, 2004.
[5] D. Samara-Rubio, L. Liao, A. Liu, R. Jones, M. Paniccia, D. Rubin, and O.
Cohen, “A gigahertz silicon-oninsulator Mach-Zehnder modulator,” in Optical
Fiber Communication Conference, Vol. 2 of OSA Proceeding Series (Optical
Society of America, Washington, D.C.), pp. 3-5, 2004
[6] L. Liao, D. S. Rubio, M. Morse, A. Liu, D. Hodge, “High speed silicon Mach-
Zehender modulator,” Opt. Express 13, pp. 3139, 2005.
[7] C. T. Shih, Z. W. Zeng, and S. Chao, “Design and Analysis of Metal-Oxide-
Semiconductor–Capacitor Microring Optical Modulator With Solid-Phase-
Crystallization Poly-Silicon Gate,” Journal of Lightwave Technology, Vol. 27,
Issue 17, pp. 3861, 2009.
[8] Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon
electro-optic modulator,” Nature, vol. 435, pp. 325–327, May 2005.
[9] Q. Xu, S. Manipatruni, B. Schmidt, J. Shakya, and M. Lipson, “12.5 Gbit/s
carrier-injection-based silicon micro-ring silicon modulators,” Opt. Express, 15,
(2), pp. 430–436, 2007.
[10] S. Manipatruni, X. Qianfan, B. Schmidt, J. Shakya, and M. Lipson, “High speed
carrier injection 18 Gb/s silicon micro-ring electro-optic modulator,” in Proc.
20th Lasers Electro-Opt. Soc. Meeting (LEOS), Oct. 21–25, 2007.
[11] W. M. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra compact, low
RF power, 10 Gb/s silicon Mach-Zehnder modulator,” Opt. Express, vol. 15, no.
25, pp. 17 106–17 113, 2007.
８８
[12] W. M. Green, M. J. Rooks, L. Sekaric, and Y. A. Vlasov, “Ultra-compact, low
RF power, 10 Gb/s silicon Mach-Zehnder modulator,” in Proceedings of the
20th Annual Meeting of the IEEE Lasers & Electro-Optics Society (Institute of
Electrical and Electronics Engineers, New York), Postdeadline paper PD1.2,
2007.
[13] A. Liu, L. Liao, D. Rubin, H. Nguyen, B. Ciftcioglu, Y. Chetrit, N. Izhaky, and
M. Paniccia, “High-speed optical modulation based on carrier depletion in a
silicon waveguide,” Opt. Express, 15, (2), pp. 660–668, 2007.
[14] L. Liao, A. Liu, D. Rubin, J. Basak, Y. Chetrit, H. Nguyen, R. Cohen, N. Izhaky,
and M. Paniccia “40 Gbit/s silicon optical modulator for highspeed
applications,” Electronics Letters,. 43, (22), 2007.
[15] B. Analui, D. Guckenberger, D. Kucharski, and A. Narasimha, “A fully
integrated 20-Gb/s optoelectronic transceiver implemented in a standard 0.13-
um CMOS SOI technology,” IEEE J. Solid-State Circuits 41, 2945-2955, 2006.
[16] T. Pinguet, V. Sadagopan, A. Mekis, B. Analui, D. Kucharski, S. Gloeckner, “A
1550 nm, 10 Gbps optical modulator with integrated driver in 130 nm CMOS,”
in Proc. 4th Conf. Group IV Photon., Tokyo, Japan, Sep. 19–21, 2007.
[17] D. Marris-Morini, L. Vivien, J. M. Fédéli, E. Cassan, P. Lyan, S. Laval, “Low
loss and high speed silicon optical modulator based on a lateral carrier depletion
structure,” Opt. Express, vol. 16, no. 1, pp. 334–339, 2008.
[18] Y. Sugimoto, N. Ikeda, N. Carlsson, K. Asakawa, N. Kawai, and K.
Inoue,"Fabrication and characterization of different types of two-dimensional
AlGaAs photonic crystal slabs," J. Appl. Phys. 91, 922, 2002
８９
Chapter 7
Electro-optic resonant FSR modulators based
on a dual-disc resonator for increasing the
sensitivity-bandwidth product
7.1 Introduction
Resonant electro-optical modulators have been demon- strated as relatively low V
modulators with their RF bandwidth limited by the linewidth of the optical resonance
[1]-[6]. In these modulators there is always a sensitivity- bandwidth trade-off since
high Q means higher sensitivity but narrower linewidth [7].
Resonant RF-optical modulators can be used in a system employing a sub-
carrier whose frequency matches the free spectral range (FSR) of the resonator and
they have been proposed and demonstrated for applications in RF-subcarrier links,
wireless communications, RF receiver and cable TV [8]-[13]. In this case the optical
wavelength is set at the point of highest slope of one of the resonator modes and the
９０
optical sidebands fall in the two adjacent modes which are separated by the FSR. The
bandwidth of the system around the subcarrier frequency is then limited by the
linewidth of the resonant modes and the sensitivity-bandwidth trade-off remains the
same [7].
In a single disc resonator, in order to obtain maximum sensitivity, the
frequency of an incident laser is adjusted to the maximum slope of the resonance
spectrum where the transmission is 25% [3]. Generated optical sidebands are then
within the closest two resonances when sub-carrier frequency equals the FSR. The
sensitivity of the modulator depends on the resonance linewidth of the mode near the
laser frequency. On the other hand, the modulation bandwidth relies on the resonance
linewidth of the mode near the sidebands. In this single resonator, however, both
laser and sidebands have the same resonance linewidth and we have to trade off
between the sensitivity and bandwidth.
We demonstrate here that a dual coupled resonator modulator, shown as two
coupled disc resonators in Figure 7.1, can have a significantly larger sensitivity-
bandwidth product than a single resonator modulator. The RF field is applied to the
larger disc by electrodes while the smaller disc has no RF field applied. If the ratio of
the diameter of discs is 2:1, the ratio of the FSR of the two is 1:2. The coupling
between the bus waveguide and the coupled resonators can be different on adjacent
FSR modes [14]. By adjusting the coupling between the resonators and the coupling
to the bus, alternate modes can be critically coupled with high loaded Q while the
９１
other alternate modes are over-coupled with lower loaded Q. The optical wavelength
is set within the narrow linewidth mode and the sidebands are aligned within the
broad linewidth modes on either side. The sensitivity can be high while the RF
bandwidth is increased. Figure 7.1(b) shows a dual-disc RF-optical modulator.
(a)
(b)
Figure 7.1. (a) Transmission of the dual resonator when the ratio of
the diameter is 2:1. The position of the laser frequency and the
modulation sidebands are shown. (b) The dual resonant EO
modulator with the RF field applied to disc 2. The electrode only
covers one half the modulated disc as required for a lumped circuit
electrode when the RF frequency is equal to the FSR of disc 2.
９２
The larger disc (disc 2 in Figure 7.1(b)) is resonant at every mode shown in
Figure 7.1(a) while the smaller disc (disc 1) is resonant at every other mode. Since
the coupling from the bus waveguide to disc 2 is through disc 1, the coupling is
higher when disc 1 is resonant. Thus when only disc 2 is resonant the coupling is low
and reflection coefficient r
1
and r
2
are set for critical coupling to disc 2. When both
disc 1 and disc 2 are resonant the coupling is higher and disc 2 is over-coupled.
Figure 7.2. Light coupling in a dual-disc resonator.
First, we calculate the through transmission for the dual resonators for various
values of r
1
and r
2
. Three cases are considered which will then be used in the
９３
modulator analysis. In the modulator analysis we assume phase modulation in disc 2
with modulation depth m. We then calculate the detected RF power, the sensitivity,
the linewidth of the sidebands, and the 3dB RF bandwidth around the sub-carrier.
The sensitivity- bandwidth product is compared to that of the single disc modulator.
The optimum position of the laser wavelength relative to the resonant wavelength of
disc 2 is also calculated. Finally, we consider the effects of fabrication errors (the
ratio of radii is slightly off 2:1) on the sensitivity-bandwidth product.
7.2 Device modeling
7.2.1 Transmission properties of dual-disc structures
In this section, we will analyze the transmission and phase shift of the dual-
disc resonator without RF modulation. The geometry of a dual-disc resonator is
shown in Figure 7.2. The E field reflection and coupling coefficients between the
disc 1 and the bus waveguide are r
1
and t
1
and between the resonators r
2
and t
2
. The
loss factors of two discs are a
1
and a
2
, respectively. The disc 2 has twice larger radius
than the disc 1. Considering the field transfer between the two discs and between
disc 1 and the waveguide, two matrix forms can be expressed by
5
2
2 2
2 2
6
3
E
E
r it
it r
E
E
(1)
９４
4 1 1
1 1
1
E
E
r it
it r
E
E
in out
(2)
where ) exp( t i E E
in in
and 1
2 2
k k
t r ) 2 , 1 ( k
Considering the loss factor and the phase shift term, we can express
6 2 6 2 2 5
) exp( E E i a E (3)
1 1 1 1 1 2
) 2 / exp( E E i a E (4)
3 1 3 1 1 4
) 2 / exp( E E i a E (5)
where
k
a
k
exp(-i θ
k
) (k = 1,2); θ
k
T
k
is the round trip optical phase parameter; T
k
n
eff
L
k
/c is the round trip time; L
k
is the cavity length, n
eff
is the effective index, and
k represents the k
th
disc. We assume the resonators are made of the same material so
that θ
2
= 2 θ
1
.
Using equations (1) through (5), we finally obtained
in out out
E E ) (
1
(6)
where
1
1
1 1
1
) exp( ) (
r
r
i
out out out
(7)
) 2 exp( 1
) 2 exp(
) exp(
1
1 2 2
1 2 2
1 1 1
2 2
2 2
i a r
i a r
i a
r
r
(8)
Then we can express
) ( exp ) (
1 out out in out
t i E E
(9)
９５
(a)
(b)
Figure 7.3. Through transmission with the r
2
and the r
1
(a) at θ
1
=
π(2n+1) (one disc resonant)) and (b) at θ
1
= 2 πn (both discs
resonant).
９６
Using Eq. (9), we obtained the transmission T of the dual-disc resonator as a
function of θ
1
.
2
1
2
) ( /
out in out
E E T (10)
Using Eq. (10), we have analyzed the transmission properties of a dual-disc
resonator. The disc 1 is resonant at θ
1
= 2n (n = integer) while the disc 2 is resonant
at θ
1
= n due to the fact that θ
2
is 2 θ
1
. Thus, both discs are resonant at θ
1
= 2n
while only disc 2 is resonant at θ
1
= (2n+1) . The frequency of the incident laser is
then tuned near θ
1
= (2n+1) and we will call these the laser modes. The frequencies
of the generated optical sidebands are near θ
1
= 2n and we will call these the side-
band modes. Figure 7.3(a) and 7.3(b) represent the transmission properties as a
function of r
1
and r
2
for θ
1
= (2n+1) (the laser mode) and θ
1
= 2n (the sideband
mode), respectively. In all calculations, we assume the loss factors were a
1
= 0.993
and a
2
= 0.985, respectively. These correspond to 0.05dB/cm optical loss which is
appropriate for LiNbO
3
and FSR = 10 GHz.
In order to get significant power coupled into the dual resonator (low T) at
both sets of modes, r
2
should be larger than 0.9 as shown in Figure 7.3(a) and 7.3(b).
We consider three cases of coupling conditions and how r
1
relates to r
2
for each case.
In the first case, the values of r
1
and r
2
are selected for critical coupling (T = 0) for
the laser mode. In the second case, the condition is that the transmission at the laser
mode and the sideband mode are identical. Finally, the third case is for a critical
coupling at the sideband mode.
９７
(a)
0.80 0.85 0.90 0.95 1
0.0
0.2
0.4
0.6
0.8
1.0
(Laser mode)
(Sideband mode)
r
1
= 0.4
(2) (3) (1)
1
= (2n+1)
1
= 2n
Transmission
r
2
(b)
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.90
0.92
0.94
0.96
0.98
1.00
Case 1
Case 2
Case 3
r
2
r
1
Figure 7.4. (a) Transmission as a function of the r
2
for the different
values of θ
1
and (b) reflectivity r
2
as a function of r
1
for three cases
(a
1
= 0.993 and a
2
= 0.985).
９８
(a)
0.0
0.5
1.0
r
2
= 0.978
r
2
= 0.985
r
1
= 0.4
r
1
= 0.6
r
1
= 0.2
r
1
= 0
2n (2n+1)
Through Transmission
1
r
2
= 0.941
r
2
= 0.965
(b)
0.0
0.5
1.0
r
2
= 0.985
r
2
= 0.985
r
1
= 0.4
r
1
= 0.6
r
1
= 0.2
r
1
= 0
2n (2n+1)
Through Transmission
1
r
2
= 0.985
r
2
= 0.985
(c)
0.0
0.5
1.0
r
2
= 0.990
r
2
= 0.985
r
1
= 0.4
r
1
= 0.6
r
1
= 0.2
r
1
= 0
2n (2n+1)
Through Transmission
1
r
2
= 0.996
r
2
= 0.994
Figure 7.5. Through transmission around θ
1
= π(2n+1) and θ
1
= 2n
π for r
1
= 0, 0.2, 0.4, and 0.6. For (a) case1, (b) case2, and (c) case3.
９９
To illustrate the three cases, for r
1
= 0.4, Figure 7.4(a) shows the transmission
as a function of r
2
for different value of θ
1
( θ
1
= 2n and θ
1
= (2n+1) ). Symbols (1),
(2) and (3) in Figure 7.4(a) indicate case 1, 2 and 3, respectively, and corresponding
values of r
2
are 0.965, 0.985, and 0.994, respectively. For the various values of r
1
, we
have obtained corresponding values of r
2
for the three cases as shown in Figure
7.4(b). In the case 1, if the value of r
1
is larger than 0.6, the resonance profile does
not exist around θ
1
= 2n . When r
1
= 0 this is the case of a single large diameter disc.
Figure 7.5(a), 7.5(b), and 7.5(c) represent through transmission spectrum as a
function of the phase θ
1
for various values of r
1
and r
2
for the three cases,
respectively. In the first case, the laser mode remains critically coupled and the
linewidth is little changed. The linewidth of the sideband mode increases with the
value of r
1
. This will be the case of most interest for the modulator. At r
1
= 0, the
modes are identical since this is the case of a single large disc.
In the second case, the transmission of both modes is the same for each
combination of r
1
, r
2
. The linewidth of the sideband mode increases with the value of
r
1
but, the coupling at resonance decreases. In the third case, the sideband mode
remains critically coupled. The linewidth and coupling of the laser mode decreases
with the value of r
1
while the linewidth of sideband mode changes little.
１００
(a)
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0
2
4
6
8
10
12
14
16
18
Case 1
Case 2
Case 3
SB Linewidth (2 discs)
SB Linewidth(1 disc)
r
1
(b)
0.00.1 0.20.3 0.40.5 0.6
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Case 1
Case 2
Case 3
Finesse(2 Discs)
Finesse(1 Disc)
r
1
Figure 7.6. (a) Sideband mode linewidth and (b) laser mode finesse
as function of r
1
for each case. The values are normalized to those
of the single disc resonator.
The modulation bandwidth is related to the linewidth of the sideband mode.
On the other hand, the sensitivity depends on the finesse of the laser mode. Figure
7.6(a) and 7.6(b) represent the normalized linewidth of the sideband mode and the
normalized finesse of the laser mode, respectively, as a function of r
1
with optimum
r
2
for all three cases. They are normalized by the values of single disc resonator (r
1
=
１０１
0 and r
2
= 0.985). For the case 1, the linewidth of the sideband mode increases
rapidly with r
1
while there is little change in the finesse of the laser mode. The
linewidth of the sidebands is 16 times larger than that of the single disc resonator (r
1
= 0). For other cases, the finesse increases with the value of r
1
even though the
bandwidth increases less compared to the first case
7.2.2 Characteristics of the FSR RF-optic modulation
In the proposed modulator, the discs are made of an electro-optic material such
as LiNbO
3
or electro-optic polymers. Electrodes are fabricated on the top and bottom
of disc 2 and the circulating field is phase modulated. The detected power at the
modulation frequency is calculated as follows. From the given E
in
, the output, E
out
,
and the circulating field in disc 2, E
5
, are calculated, where is the laser frequency.
The circulating field is phase modulated at
m
and the sidebands at ±
m
are
generated. Even though there is some small optical loss in disc 2, we assume E
5
is
constant throughout the phase modulator. This phase modulation now becomes the
source for ±
m
and the output E
out
± m
is calculated assuming E
in
± m
= 0. From
E
out
and E
out
± m
the detector current at
m
can be calculated.
Using equations (1) through (5), we obtain
in
E E ) (
1 5 5
(12)
where
１０２
) exp( ) (
1 1
) (
5 1 5
1 2 2
2 1 2 1
1 5
i
r r
t t
(13)
-2
2
0
4
2n 2(n+2) (2n+1)
Phase Shift
Phase
1
0
10
20
30
|
5
|
2
Figure 7.7. | τ
5
|
2
spectrum (top) and phase shift (bottom) as a
function of θ
1
for the case 1 (r
1
= 0.2, r
2
= 0.978, a
1
= 0.993, and a
2
= 0.985).
Figure 7.7 indicates the transmission magnitude and phase shift for the E
5
from
the input to the disc 2.
After the phase modulation
t m t i E
t i E t m i a E
m
m
sin exp
) exp( sin exp
~
5
6 2 2 5
(14)
The round trip phase θ
2
of the disc 2 is given by θ
2
+ msin
m
t by the phase
１０３
modulation.
The depth of modulation, m [15], is
c
d E r n
m
m eff
2
33
3
sinc
c
d n
eff m
2
where
m
is the applied RF frequency, n
eff
the effective index of the electro-optic
material, r
33
the electro-optic coefficient of the material, and d the length of the
electrode. For a lumped circuit electrode when
m
= FSR of disc 2, d is limited to
R
2
, half the circumference of disc 2. For a traveling wave electrode, the modulation
signal is a traveling wave on the electrode and d can be the full circumference of disc
2.
This phase term can be expanded by Jacobi–Anger expansion:
n
t n t i
n in
m
e m J E E
) ( ) (
~
1 5 5
(15)
Assuming m << 1, higher orders of m can be neglected. Then,
sb sb
m
m in
E E E t t i
m
t t i
m
t i E E
5
1 5 5
exp
2
exp
2
) exp( ) (
~
(16)
where
t t i E
m
E
m in
sb
exp ) (
2
1 5
(17)
t t i E
m
E
m in
sb
exp ) (
2
1 5
(18)
１０４
Thus, the phase modulation becomes the source of the two dominant sideband
waves at ω
sb
+
= ω + ω
m
and ω
sb
-
= ω - ω
m
.
Figure 7.8. Analysis of dual-disc resonator at the upper sideband
frequency, ω
sb
+
= ω + ω
m
. All primed fields are at ω
sb
+
.
The sidebands are coupled to the output by assuming no input at the sideband
frequency and a source of sideband power in disc 2. First, we consider the upper
sideband frequency ω
sb
+
= ω + ω
m
as shown in Figure 7.8.
Similarly to our earlier analysis we obtain
/
5
/
2
2 2
2 2
/
6
/
3
E
E
r it
it r
E
E
(19)
１０５
/
4
/
1 1
1 1
/
1
E
E
r it
it r
E
E
in
sb
out
(20)
E
5
sb+
consists of the E
6
sb+
term after one round trip plus the phase modulation
generated E
sb+
term. E
in
sb+
is zero because of no incident sideband wave.
sb sb
E E E E i a E
/
6
/
2
/
6
/
2 2
/
5
) exp( (21)
/
1
/
1
/
1
/
1 1
/
2
) 2 / exp( E E i a E (22)
/
3
/
1
/
3
/
1 1
/
4
) 2 / exp( E E i a E (23)
where ) exp(
/ /
i i i
i a ,
i sb i
T
/
,
/
1
/
2
2 and all primed quantities are at
the upper sideband frequency.
The sidebands are coupled to the output bus waveguide using Eq. (19) through
(23), we obtain
sb
sb sb
sb
sb
sb
out
E i E E ) exp( ) ( ) (
/
1
/
1
(24)
where
/
2
/
1 1
/
1 2 1
/
2 2
/
1 2 1 /
1
1
) (
r r r r
t t
sb
(25)
Figure 7.9 shows the transmission magnitude and phase shift for the generated
sideband from disc 2 to the output.
For the lower sideband frequency ω
sb
-
= ω - ω
m
, we similarly obtain
１０６
sb
sb sb
sb
sb
sb
out
E i E E ) exp( ) ( ) (
//
1
//
1
(26)
where
//
2
//
1 1
//
1 2 1
//
2 2
//
1 2 1 //
1
1
) (
r r r r
t t
sb
(27)
where the double prime represents ω
sb
-
wave.
0
3
2
2n 2(n+2) (2n+1)
Phase Shift
Phase
1
0
10
20
30
|
sb
|
2
Figure 7.9. | τ
sb
|
2
spectrum (top) and phase shift (bottom) as a
function of θ
1
for the case 1 (r
1
= 0.2, r
2
= 0.978, a
1
= 0.993, and a
2
= 0.985).
１０７
7.2.3 Analysis of RF output power and sensitivity
7.2.3.1 Modulation frequency equals the FSR
From the calculated E
out
, E
out
sb+
, and E
out
sb-
, we can calculate the detected
power at the modulation frequency. If the RF modulation is equal to the FSR of disc
2,
1
/
1
and
1
//
1
(28)
Using Eq. (6), (24), and (26), total optical output is given by
sb
sb
sb
sb in out
sb
out
sb
out out
Total
out
E E E
E E E E
) ( ) ( ) (
//
1
/
1 1
(29)
Then we can express
) exp( ) ( ) ( ) 2 / (
) exp( ) ( ) ( ) 2 / ( ) ( ) exp(
1 5
//
1
1 5
/
1 1
t i m
t i m t i E E
m sb
m sb out
o
in
Total
out
(30)
The optical input and output power
2
0 *
) 2 / (
in in in
optical
in
E E E P (31)
*
Total
out
Total
out
optical
out
E E P (32)
where
) / ( /
0 0
n Area Area
The detected current at
m
is given
１０８
t i i
i P m
E E E E i
m sb out sb
sb out sb out
optical
in
sb
out out
sb
out out
rf
D
exp ) ( exp ) (
) ( exp ) ( Re ) ( ) (
Re 2
5
//
1
5
/
1 1 5 1
* *
(33)
where
) /( ) (
e
e and
e
is quantum efficiency.
Since the RF modulation equals the FSR,
1
/
1
and
1
//
1
.
sb sb
(34)
) ( ) (
/
1
//
1
sb sb
(35)
These lead to
) ( ) (
//
1
/
1
sb sb
(36)
Substituting Eq. (33) into (36), the detected current is simplified
t P m i
m sb out
optical
in
rf
D
cos ) ( ) ( ) ( 2 Re
*
1 5
* /
1 1
(37)
Zero-to-peak value of detected current can be written as
*
1 5
* /
1 1
) ( ) ( ) ( 2 Re
sb out
optical
in
rf
peak D
P m i
(38)
And the detected RF output power is
2 /
2
D
rf
peak D
rf
D
R i P
(39)
where R
D
is the detector resistor.
Finally, the detected RF output power is normalized to that for single disc structure
(r
1
= 0)
１０９
) 0 ( ) 0 (
~
1
2
1
2
1
1
r K
r K
r P
r P
P
rf
D
rf
D rf
D
(40)
where
*
1 5
* /
1 1 1
) ( ) ( ) ( 2 Re
sb out
r K (41)
7.2.3.2 Modulation frequency slightly off the FSR
If the RF modulation frequency is not equal to the FSR,
m
1
/
1
and
m
1
//
1
(
m
is offset from the FSR).
Then (33) gives
t B t A P m i
m m out
optical
in
rf
D
sin cos ) ( ) (
1 5 1
(42)
where
5
//
1 5
/
1
cos ) ( cos ) (
sb out sb sb out sb
A
5
//
1 5
/
1
sin ) ( sin ) (
sb out sb sb out sb
B
Then detected current can be written as
t B A P m i
m out
optical
in
rf
D
cos ) ( ) (
2 2
1 5 1
(43)
where
) / ( tan
1
A B
Then amplitude of detected current (zero to peak value) is written by
2 2
1 5 1
) ( ) ( B A P m i
out
optical
in
rf
peak D
(44)
１１０
Then, normalized RF output power
) 0 ( ) 0 (
~
1
2
1
2
1
1
r K
r K
r P
r P
P
rf
D
rf
D rf
D
(45)
where
2 2
1 5 1 1
) ( ) ( B A r K
out
(46)
Figure 7.10. Transmission spectrum of the dual-disc resonator and
the FSR modulation with double sidebands.
7.2.3.3 Optimum laser tuning
The laser wavelength should be set to obtain the maximum detected RF
current. We define Δ as the displacement of the laser frequency from the resonance
peak (2n+1) as shown in Figure 7.10. The FSR RF modulation is then applied and
both sidebands are aligned at θ
1
= 2n + Δ and θ
1
= 2(n+1) + Δ, respectively. In the
１１１
round trip phase domain, FSR RF modulation is equal to .
01 23 4
0
5
10
15
20
25
r
1
=0.4
r
1
=0.5
r
1
=0.6
Detected Current (i
rf
D-peak
/ mP
in
)
/2 (x10
-3
)
r
1
=0
r
1
=0.1
r
1
=0.2
r
1
=0.3
Figure 7.11. Normalized detected RF current versus displacement
of the laser wavelength from the peak of the laser mode in phase,
Δ/2 , with various values of r
1
for case 1.
c L n
eff m
m
/
1
where ω
m
is RF modulation frequency.
In a single disc resonator, the optimum Δ to obtain the maximum current is
achieved where transmission spectrum has the highest slope (at T = 0.25) [3].
However, for a dual-disc structure with different radius discs, optimum Δ is not
achieved at the highest slope of the transmission spectrum because the resonance
depth of the laser and the sideband modes are different. To determine the optimum Δ,
１１２
the detected current as a function of Δ has been calculated for different values of r
1
for the case 1 as shown in Figure 7.11. The detected current is normalized for a fixed
depth of modulation and a fixed laser power. For r
1
= 0 (single disc) we obtain the
optimum Δ = 0.0014 2 from Figure 7.11. This corresponds to a transmission of
0.25 where the slope of the transmission curve is maximum as expected for the
single disc. But, for r
1
0, the optimum value of Δ is not at the maximum slope
transmission. In Figure 7.11, the optimum value of Δ increases with r
1
since the
resonance depth of the sideband modes decreases.
In Figure 7.12(a) we have plotted the optimum values of Δ as a function of r
1
for all three of the cases defined in Section 2.1. The optimum Δ is determined by
both the finesse of the laser mode and the coupling for both the laser and the
sideband modes and therefore is different for the three cases. The detected current at
the optimum Δ has been analyzed for all three cases as shown in Figure 7.12(b). For
the three cases, the detected current has a maximum value at different values of r
1
. In
all cases the maxima of the detected current is larger than that for single disc
modulator (r
1
= 0). For example, in the case 1, detected current is maximum at r
1
=
0.23. It is interesting that, in case 1, the current is larger than that of the single disc
resonator (r
1
= 0) although the finesse of the laser mode does not change with r
1
.
Furthermore, from Figure 7.6(a), the linewidth of the sideband mode is also larger
than that for the single disc resonator. Thus, for case 1 and values of r
1
between 0
and 0.42, sensitivity and linewidth are both larger than the single disc resonator.
１１３
(a)
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Case 1
Case 2
Case 3
/2 for Maximum i
rf
D-peak
(x10
-3
)
r
1
(b)
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0
5
10
15
20
25
30
Case 1
Case 2
Case 3
Detected Current (i
rf
D-peak
/ mP
in
)
r
1
Figure 7.12. For the three cases, (a) optimum Δ for maximum
detected current and (b) normalized detected current at optimum Δ
as a function of r
1
.
１１４
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Case 1
Case 2
Case 3
Sensitivity (2 discs)
Sensitivity (1 disc)
r
1
Figure 7.13. Normalized sensitivity as a function of r
1
in all three
cases. In this analysis, Figure 7.4(b) and Figure 7.5(a) were used
for optimum r
2
and Δ.
7.3 Results and discussion
7.3.1 Sensitivity and RF bandwidth
The resonator sensitivity is proportional to the detected RF output power.
Using Eq. (40), the normalized sensitivity has been analyzed as a function of r
1
as
shown in Figure 7.13. The bandwidth of the resonator is proportional to the linewidth
of the sidebands transmission spectrum as shown in Figure 7.6(a). In all three cases
the peak sensitivity is larger than the sensitivity of a single disc but the peak occurs
at a different value of r
1
.
１１５
The 3dBe RF modulation bandwidth is proportional to the linewidth of the
sideband transmission spectrum but is not equal to the linewidth. To calculate the 3
dBe bandwidth we use Eq. (45) which gives the normalized RF power as a function
of Δ
m
, the detuning of the modulation frequency from the FSR. This is shown in
Figure 7.14. The optimum detuning of the laser frequency from the peak of the laser
mode, Δ, is chosen for each value of r
1
. Due to difference between the modulation
frequency and the FSR of the resonator, the transmission of the two sidebands is
different as shown in Figure 7.14 and, in addition, the phase shifts of the two
sidebands are not equal to as shown in Figure 7.9(b). For the three cases, Figure
7.15(a), 7.15(b), and 7.15(c) show the detected output RF power normalized for
constant optical power and depth of modulation, as a function of Δ
m
with different
values of r
1
. Again the optimum value of Δ was chosen for each value of r
1
and r
1
= 0
corresponds to a single disc modulator.
Figure 7.14. Scheme of the non FSR modulation.
１１６
(a)
-0.02 -0.01 0.00 0.01 0.02
0
100
200
300
400
500
600
r
1
= 0
r
1
= 0.1
r
1
= 0.2
r
1
= 0.3
r
1
= 0.4
r
1
= 0.5
r
1
= 0.6
Detected Power
P
D
rf
/(
2
m
2
P
in
2
R
D
/2)
m
/2
(b)
-0.02 -0.01 0.00 0.01 0.02
0
100
200
300
400
500
600
700
800
900
r
1
= 0
r
1
= 0.1
r
1
= 0.2
r
1
= 0.3
r
1
= 0.4
r
1
= 0.5
r
1
= 0.6
Detected Power
P
D
rf
/(
2
m
2
P
in
2
R
D
/2)
m
/2
(c)
-0.02 -0.01 0.00 0.01 0.02
0
100
200
300
400
500
600
700
800
900
r
1
= 0
r
1
= 0.1
r
1
= 0.2
r
1
= 0.3
r
1
= 0.4
r
1
= 0.5
r
1
= 0.6
Detected Power
P
D
rf
/(
2
m
2
P
in
2
R
D
/2)
m
/2
Figure 7.15. Detected RF output power vs Δ
m
with various values
of r
1
with (a) case 1, (b) case 2, and (c) case 3.
１１７
(a)
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0
1
2
3
4
5
6
7
Case 1
Case 2
Case 3
RF Bandwidth (2 discs)
RF Bandwidth (1 disc)
r
1
(b)
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Case 1
Case 2
Case 3
Sensitivity X RF Bandwidth (2 discs)
Sensitivity X RF Bandwidth (1 disc)
r
1
Figure 7.16. (a) Normalized RF modulation bandwidth and (b)
normalized sensitivity-RF bandwidth product. The three cases are
defined in Section 2.1 and have to do with the coupling at
resonance for the laser and the sideband modes. For each value of
r
1
, the optimum offset between the laser frequency and the peak of
the laser mode.
１１８
The 3 dBe bandwidth corresponds to the point where the detected power
falls by 3 dB from the peak. Figure 7.16(a) illustrates the normalized RF 3 dBe
bandwidth as a function of r
1
with different cases. For r
1
= 0, the calculated 3 dBe
RF modulation bandwidth is 0.0082 2 / T
1
while the linewidth of the sideband
mode is 0.0048 2 / T
1
. Thus, RF modulation band is larger than the linewidth of
the sideband for r
1
= 0 as noted in earlier publications [16]. In the case 1, the 3 dBe
bandwidth can be significantly larger than that of a single disc as expected from
Figure 7.6(a). The 3 dBe bandwidth for cases 2 and 3 does not change significantly.
The most important criterion is the product of the sensitivity and the
bandwidth. Figure 7.16(b) represents the normalized sensitivity-3 dBe bandwidth
product as a function of r
1
. In the case 1, it increases monotonically with r
1
and
can
be three times larger than that for a single disc modulator. On the other hand, for the
other two cases, there is a maximum for a specific value of r
1
. For the three cases,
maximum sensitivity-RF bandwidth products are 3.3, 1.9, and 1.3 times increased,
respectively.
7.3.2 Fabrication errors and its theoretical results
In the fabrication of the dual-disc resonator, the ratio of the disc radii may
deviate from the optimum 2:1. Thus, we have investigated up to 5% error in the
radius ratio between the two discs. Figure 7.17(a) and 7.17(b) indicate the
transmission spectrum of the sideband mode as a function of r
1
in the case 1 with
１１９
1.9 : 1 and 2.1 : 1 ratio of radii of two discs, respectively. The error causes the
resonant frequency to shift with r
1
but the linewidth of the sideband mode shows
little change from the ideal 2:1 ratio shown in Figure 7.6(a). For the case 2 and 3, the
resonant frequencies also shift with r
1
but we will consider only case 1 since that is
the most promising design.
Next we have analyzed the change in the linewidth of the sideband mode, in the 3
dBe bandwidth, and in the sensitivity for the 5% radius error. Figure 7.18(a),
7.18(b) and 7.18(c) show normalized sideband linewidth, normalized RF bandwidth
and normalized sensitivity as a function of r
1
in the case 1. In this simulation, we
assumed the RF modulation frequency always matches the frequency spacing
between carrier and sidebands resonance frequencies at each value of r
1
. We assume
this would be the likely case where the modulation frequency used with a given
modulator would be tuned to the spacing between the laser and the sideband modes.
For up to r
1
= 0.4, errors of bandwidth and sensitivity are less than 3% and 1%.
Furthermore, bandwidth and sensitivity of + 5% error and – 5% error are the same.
We have investigated for the case 2 and case 3 and the change in the sensitivity and
bandwidth are less than those for case 1. Thus, for all three cases, a 5% error in the
ratio of the disc radii appears acceptable.
１２０
(a)
0.0
0.2
0.4
0.6
0.8
1.0
2n (2n+0.01) (2n-0.01)
r
1
= 0
r
1
= 0.1
r
1
= 0.2
r
1
= 0.3
r
1
= 0.4
r
1
= 0.5
r
1
= 0.6
Transmission
Sideband
(b)
0.0
0.2
0.4
0.6
0.8
1.0
(2n-0.01) (2n+0.01) 2n
r
1
= 0
r
1
= 0.1
r
1
= 0.2
r
1
= 0.3
r
1
= 0.4
r
1
= 0.5
r
1
= 0.6
Transmission
Sideband
Figure 7.17. Transmission spectrum of the sideband frequency as a
function of the round trip phase θ
1
with different value of r
1
for (a)
1.9 : 1 ratio of two discs and 2.1 : 1 ratio of two discs.
１２１
(a)
0.00.1 0.20.3 0.40.5 0.6
0
2
4
6
8
10
12
14
16
18
Ratio of radii of two discs
2 : 1
1.9 : 1 or 2.1 : 1 (5 % error)
SB linewidth (two discs)
SB linewidth (one disc)
r
1
(b)
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0
1
2
3
4
5
6
7
Ratio of radii of two discs
2 : 1
1.9 : 1 or 2.1 : 1 (5 % error)
RF BW (two discs)
RF BW (one disc)
r
1
(c)
0.0 0.1 0.2 0.3 0.4 0.5 0.6
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Ratio of radii of two discs
2 : 1
1.9 : 1 or 2.1 : 1 (5 % error)
Sensitivity (two discs)
Sensitivity (one disc)
r
1
Figure 7.18. Impact of fabrication error (a) Normalized sideband
linewidth and (b) RF bandwidth and (c) sensitivity as a function of
r
1
with 5% radius errors.
１２２
7.4 Conclusion
Based on our analysis, the dual-disc RF-optic modulator for FSR modulation can
significantly increase the sensitivity- bandwidth product when compared to a single
disc modulator. There are several trade-offs possible depending on the design and
whether a premium is placed on high sensitivity, large bandwidth, or some
compromise of the two. For example, the case 2 design, at r
1
= 0.3, has a large
increase in the sensitivity (1.8) and only a small change in the RF bandwidth. For the
case 1 design at r
1
= 0.3, the sensitivity increase is smaller (1.3) but the bandwidth
increase is significantly increased by a factor of 1.7. The largest increase in the
sensitivity-bandwidth product, 3.3, is in the case 1 design at r
1
~ 0.6. In this case the
bandwidth increases significantly while the sensitivity falls to ~50% of the single
disc value.
Our calculations are based on the optical loss typical of LiNbO
3
and in these cases
the coupling between the two discs is small. The coupling reflection coefficient, r
2
,
ranges from 0.97 to 0.99 which corresponds to a power coupling of 6% to 2%. This
modest coupling appears achievable between whispering gallery mode (WGM) discs
or between waveguide ring resonators. On the other hand, the coupling reflection
coefficient between the bus waveguide and the smaller disc, r
1
, should be in the
range of 0.3-0.6. This corresponds to a power coupling of 90% to 75%. This large
coupling may be difficult using WGM discs and waveguides but can be achieved
between waveguide ring resonators and bus waveguides.
１２３
Based on our results, the fabrication tolerances required to achieve a significant
increase in either or both the sensitivity and bandwidth are feasible. The accuracy of
the coupling, r
1
and r
2
, is not critical as long as it is in the desired range of values.
We have shown that a deviation of ±5% from the desired value of 2 for the ratio of
the disc diameters has little effect on the properties of the modulator.
１２４
7.5 References
[1] E. I. Gordon and J. D. Rigden, “The Fabry-Perot electo-optic modulator,” Bell
System Tech. J., vol. 42, pp. 155-179, Jan. 1963.
[2] P. Rabiei, W. H. Steier, C. Zhang, and L. R. Dalton, “Polymer micro-ring filters
and modulators,” IEEE J. Lightw. Technol., vol. 20, no. 11, pp. 1968-1974, Nov.
2002.
[3] H. Tazawa, Y . H. Kuo, I. Dunayevskiy, J. Luo, A. K.-Y . Jen, H. R. Fetterman, and
W. H. Steier, “Ring resonator-based electro-optic polymer traveling-wave
modulator,” IEEE J. Lightw. Technol., vol. 24, no. 9, pp. 3507-3514, Sep. 2006.
[4] T. Sadagopan, S. J. Choi, S. J. Choi, P. D. Dapkus, and A. E. Bond, “Optical
modulators based on depletion width translation in semiconductor microdisk
resonators,” IEEE Photon. Technol. Lett., vol. 17, no. 3, pp. 567–569, Mar. 2005.
[5] D. A. Cohen, M. Hossein-Zadeh, and A. F. J. Levi, “High-Q microphotonic
electro-optic modulator,” Solid-State Electron., vol. 45, no. 9, pp. 1577-1589,
Sep. 2001
[6] Q. Xu, B. Schmidt, S. Pradhan, and M. Lipson, “Micrometre-scale silicon
electro-optic modulator,” Nature, vol. 435, no. 7040, pp. 325–327, 2005.
[7] R. C. Williamson, “Sensitivity-bandwidth product for electro-optics modulators,”
Opt. Lett., vol. 26, no. 17, pp. 1362-1363, Sep. 2001.
[8] J. Oreilly and P. Lane, “Remote delivery of video services using mm-waves and
optics,” IEEE J. Lightw. Technol., vol 12, no 2, pp. 369-375, Feb. 1994.
[9] H. Ogava, D. Polifko, and S. Banba, “Milimeter-wave fiber optic systems for
personal radio communication,” IEEE Trans. Microw. Theory Tech., vol. 40, no.
12, pp. 2285-2293, Dec. 1992.
[10] V . S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Sub-microwatt
photonic microwave receiver,” IEEE Photon. Technol. Lett., vol. 14, no. 11, Nov.
2002.
[11] M. Hossein-Zadeh and A. F. J. Levi, “Mb/s data transmission over a RF fiber-
Optic link using a LiNbO
3
microdisk optical modulator,” Solid-State Electron.,
vol. 46, no. 12, pp. 2173-2178, Dec. 2002.
１２５
[12] M. Hoessein-Zadeh and A. F. J. Levi, “Self-homodyne RF-optical LiNbO
3
microdisk receiver,” Solid-State Electron., vol. 49, no. 8, pp. 1428-1434, Aug.
2005.
[13] R. C. J. Hsu, A. Ayazi, B. Houshmand, and B. Jalali, “All-dielectric photonic-
assisted radio front-end technology,” Nature Photon., vol. 1, pp. 535-538, Sep.
2007.
[14] L. Y. Tobing, P. Dumon, R. Baets, D. C. Lim, and M. Chin, “The transmission
properties of one-bus two-ring devices,” IEICE Trans. Electron., vol. E91-C, no.
2, pp. 167-172, Feb. 2008.
[15] A. Yariv, and P. Yeh, Optical Waves in Crystals, Hoboken, NJ: John Wiley &
Son, 2003, pp. 243-251.
[16] H. Tazawa, and W. H. Steier, “Analysis of ring resonator-based traveling-wave
modulators,” IEEE Photon. Technol. Lett., vol. 18, no. 1, pp. 211-213, Jan. 2006.
１２６
Chapter 8
Conclusion and future work
8.1 Summary
LiNbO
3
has remarkable properties as both optical material and electro-optic material
since it has low loss at optical communication wavelength of 1.55 um and the large
electro-optic coefficient [1, 2]. For single crystal LiNbO
3
thin film, electro-optic
effect is drastically enhanced due to the strong mode confinement [3]. Free standing
LiNbO
3
micro-platelets are enabling to integrate other material such as Si which
lacks second order nonlinear effect [4, 5]. These single crystal thin film technologies
are very important for next generation active device platforms and devices.
In chapter 2, general crystal ion slicing method to obtain single crystal thin
films has been introduced [6, 7]. Single crystal LiNbO
3
ultra thin films have been
obtained by the modified crystal ion slicing method. XRD and AFM measurement
proved their single crystal structure and high quality surface roughness [4, 5]. Most
of all, various applications based on LiNbO
3
-on-insulator platform and their
１２７
advantages compared with applications of LiNbO
3
bulk wafer have been discussed.
Chapter 3 discussed fabrication of free standing single crystal LiNbO
3
micro-platelets [4, 5]. Micro-platelet formation depends on its crystal structure; they
were achieved along the three hexagonal axes. 1 m thick micro-platelets with
various widths (15~100 m) and lengths (0.4~2 mm) were achieved from the bulk
wafer. Integration of the micro-platelets to various substrates such as SiO
2
/LiNbO
3
,
SiO
2
/Si, Si/SiO
2
/Si Substrates has been demonstrated. Then, its applications for
active photonic devices have been discussed.
In chapter 4, the hybrid structure of Si-LiNbO
3
promising approach for
bringing LiNbO
3
into the SOI technology has been proposed and discussed [8, 9].
The analysis of the one-dimensional and two-dimensional slab optical waveguides
proved the electro-optic effect of the hybrid structure form LiNbO
3
film cladding
layer. Hybrid Si-LiNbO
3
electro-optic tunable micro-ring resonators have been
fabricated and its electro-optic properties have been measured by applied electric
field.
In chapter 5, LiNbO
3
photonic slab waveguides on a LiNbO
3
-on-insulator
(LOI) platform has been proposed and discussed. Dimension of the structure has
been selected by 3-dimensional FDTD method. Various etching methods have been
discussed and investigated in order to find high etching selectivity between LiNbO
3
and Cr mask layer since it is the most important issue to fabricate LiNbO
3
photonic
slab. Using the slow light region, the electro-optical effect can be increased.
１２８
Chapter 6 describes the hybrid Si-LiNbO
3
photonic slab waveguides on a
LiNbO
3
-Si-on-insulator (LSOI) platform. Similarly with hybrid Si-LiNbO
3
micro-
ring resonators, this hybrid photonic slab has second order nonlinear effect from
LiNbO
3
film. Using plane wave expension (PWE) method, the structure of the
photonic slab has been designed and ± 10% fabrication error was acceptable. This
structure was integrated by bonding a LiNbO
3
micro-plate on the Si photonic slab.
Finally, chapter 7 proposed and discussed resonant free spectral range (FSR)
RF-optic modulators using dual disc resonators in order to improve increase the
sensitivity-bandwidth product [10, 11]. If the ratio of the diameter of discs is 2:1, the
coupling between the bus waveguide and the coupled resonators can be different on
adjacent FSR modes. Theoretical calculation proved that the sensitivity and
modulation bandwidth could be increased by factors of 1.9 and 6.4, respectively; the
sensitivity-bandwidth product could be increased up to a factor of 3.3. For 5%
fabrication error were acceptable.
8.2 Future work
For LOI device platform, large size samples can be obtained by optimizing
ion slicing conditions. Waveguide fabrication technology based on LOI can be
improved to obtain better etching selectivity and the sidewall roughness of the
waveguide. Using the device platform, we could develop more efficient electro-optic
devices.
１２９
It is important to investigate handling and bonding techniques of free
standing single crystal LiNbO
3
micro-platelet. Using patterned ion implantation or
patterned bonding-substrate, the size and orientation of the micro-platelets could be
controlled.
In order to improve bonding strength between LiNbO
3
micro-platelet and Si
waveguide, fabrication of the supporting Si ridge structures on either side of the Si
waveguides is required. Finally, an electro optical modulator can be demonstrated
after integrating co-planer electrodes on the LiNbO
3
micro-platelet.
For LOI active photonic slab, we can investigate and develop more effective
etching methods using various etching equipments and conditions. For LSOI active
photonic slab, bonding technique can be improved by obtaining optimum
temperature conditions. To enhance the efficiency of the electro-optic effect, devices
structures such as line defect waveguides, resonator, MZ interferometer can be
theoretically analyzed.
Dual-ring resonator modulators are theoretically similar to the dual-disc
resonator modulator. Using the LOI or LSOI device platform, high sensitive and
large bandwidth RF-FSR modulators can be demonstrated.
１３０
8.3 References
[1] R. S. Weis and T. K. Gaylord, “Lithium Niobate: Summary of Physical
Properties and Crystal Structure,” Applied Physics A 37, pp. 191-203, 1985.
[2] K. K. Wong, Properties of lithium niobate, INSPEC, Institution of Electrical
Engineers, London, 1989.
[3] P. Rabiei, W. H. Steier, “Lithium niobate ridge waveguides and modulators
fabricated using smart guide,” Appl. Phys. Lett., 86, 161115-1, 2005.
[4] Y. S. Lee, S.-S. Lee and W. H. Steier, “Free Standing Single Crystal LiNbO
3
Micro-wires Fabricated by Ion Slicing, Transferred and Bonded to SiO
2
/Si,”
OSA Optics & Photonics Congress / ASSP 2010, ATuA21, Jan., 2010.
[5] Y. S. Lee, S.-S. Lee, W.-G. Lee, and W. H. Steier, “Fabrication of Free
Standing LiNbO
3
Single Crystal Micro-Platelets and Their Integration to Si-on-
Insulator Platforms,” Thin Solid Films, 519, 4271, 2011.
[6] M. Levy, R. M. Osgood Jr., R. Liu, L.E. Cross, G. S. Cargill III, A. Kumar, H.
Bakhru, “Fabrication of single-crystal lithium niobate films by crystal ion
slicing,” Appl Phys Lett., 73, 2293, 1998.
[7] P. Rabiei and P. Günter, “Optical and electro-optical properties of
submicrometer lithium niobate slab waveguides prepared by crystal ion slicing
and wafer bonding, ” Appl. Phys. Lett., 85, 4603, 2004.
[8] Y. S. Lee, G.-D. Kim, S.-S. Lee, W.-G. Lee, and W. H. Steier, “Hybrid Si-
LiNbO
3
micro-ring resonators for active microphotonic devices,” Proc. SPIE
Photonics West, San Francisco, paper 7934-18, Jan., 2011
[9] Y. S. Lee, G.-D. Kim, W.-J. Kim, S.-S. Lee, W.-G. Lee, and W. H. Steier,
“Hybrid Si-LiNbO
3
micro-ring tunable resonators for active photonic devices ,”
Opt. Lett., 36, 1119, 2011.
[10] Y. S. Lee, S.-S. Lee and W. H. Steier, “Increasing the sensitivity-bandwidth
product of resonant FSR optical modulators using coupled resonators,” OSA
Annual Meeting / FiO 2009, FMD7, 2009
[11] Y. S. Lee, S.-S. Lee and W. H. Steier, “Electro-optic resonant FSR modulators
based on a dual-disc resonator for increasing the sensitivity-bandwidth
product,” IEEE J. Lightw. Technol., 28, 725, 2010
１３１
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Abstract (if available)
Abstract
This work addresses new ultra fast (over 40 Ghz) electro-optic device platforms and their applications using single crystal LiNbO₃ ultra thin films (~1 micrometer) and Si nano-photonics for compact size photonic integrated circuits, optical networks and optical interconnects. ❧ It is divided into two parts: the fabrication of active electro-optic device platforms and the integrations of active electro-optic devices based on these platforms. In the first part, the new fabrication technologies of single crystal LiNbO₃ films, free standing LiNbO₃ micro-platelets, and hybrid Si-LiNbO₃ device platforms were demonstrated and discussed. The second part of this work discusses simulation and experimental work for electro-optically tunable waveguide, micro-ring resonator modulators, active photonic bandgap crystal slab waveguides, and dual-disc resonator for increasing the sensitivity-bandwidth product. ❧ LiNbO₃ thin films have been integrated on SiO₂/LiNbO₃ by He⁺ ions implantation and direct bonding through careful control of the thermal expansion and stress of the implanted wafer and substrate. After slicing the films, their single crystal property and comparable surface roughness (rms ~6 nm) has been presented by XRD and AFM measurements. ❧ Free standing single crystal LiNbO₃ micro-platelets (mm long and 1 micrometer thick) have been obtained from a z-cut LiNbO₃ wafer by He⁺ ions implantation and thermal treatment. They have been first invented by using a different slicing method. They have been transferred, positioned and bonded to SiO₂/LiNbO₃, SiO₂/Si, and Si-on-insulator (SOI: Si/SiO₂/Si) by direct bonding method with optimum annealing conditions. ❧ Hybrid Si-LiNbO₃ electro-optic tunable ring resonators have been proposed and demonstrated as a path to achieving ultra compact and high speed electro-optic devices. The platelets were transferred and thermally bonded on top of Si resonators that were fabricated in an SOI platform by a 0.18 µm standard CMOS process. For the hybrid micro-ring resonator, a FSR of 16.5 nm, a finesse F of ~1.67×10², a Q-factor of ~1.68×10⁴, and an effective r coefficient of ~1.7 pm/V were achieved for the TE mode. These values are in good agreement with the calculated results. ❧ Photonic crystal structures based on LiNbO₃-on-insulator (LOI) platform have been proposed and discussed for active photonic devices. 3D FDTD method has been used in order to design LiNbO₃ photonic slab more precisely. In the E-Beam lithography, electron doses and sizes of the hole have been varied to fine optimum values. Etching methods with various equipments and recipes have been investigated since they were the most important issue to fabricate the real structure. Further work is to fabricate photonic slab waveguide in a LOI structure. ❧ Hybrid Si-LiNbO₃ active photonic slab have been proposed and discussed in order to employ second order nonlinear effect to the Si photonic slab. Bonding between a LiNbO₃ micro-platelet and a Si photonic slab has been demonstrated. In order to optimize hybrid photonic slab, the dimensions of the Si slab have been carefully designed by using PWE method. For this design, ± 10 % error in the radius of the holes appears acceptable. Further work is to integrate the hybrid Si-LiNbO₃ photonic slab waveguide with coplanar electrodes for EO fast tunable filters and EO modulators. ❧ Resonant free spectral range (FSR) RF-optic modulators using dual disc resonators with 2:1 ratio of the radii of the discs have been proposed and theoretically analyzed to increase the sensitivity-bandwidth product compared to a single resonator modulator. The transmission of the coupled resonator structure is analyzed for various coupling parameters. The sensitivity and modulation bandwidth can be increased by factors of 1.9 and 6.4, respectively, for the different cases. The sensitivity-bandwidth product can be increased up to a factor of 3.3 in one design. For 5% error of the ratio of the radius of each disc, errors of the sensitivity and modulation bandwidth were acceptable.
Linked assets
University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Lee, Yoo Seung
(author)
Core Title
Active integrated photonic devices in single crystal LiNbO₃ micro-platelets and a hybrid Si-LiNbO₃ platform
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Electrical Engineering
Publication Date
07/18/2011
Defense Date
05/03/2011
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
Electro-Optic Device,Electro-Optic Material,Electro-Optic Modulator,LiNbO3,Micro-Ring Resonator,Nonlinear Material,OAI-PMH Harvest,optical interconnects,photonic crystal,photonic devices,RF-Photonics
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Steier, William H. (
committee chair
), Armani, Andrea M. (
committee member
), Dapkus, P. Daniel (
committee member
)
Creator Email
2useung@gmail.com,yooseunl@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c127-630192
Unique identifier
UC1355207
Identifier
usctheses-c127-630192 (legacy record id)
Legacy Identifier
etd-LeeYooSeun-108-0.pdf
Dmrecord
630192
Document Type
Dissertation
Rights
Lee, Yoo Seung
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Access Conditions
The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Repository Email
cisadmin@lib.usc.edu
Tags
Electro-Optic Device
Electro-Optic Material
Electro-Optic Modulator
LiNbO3
Micro-Ring Resonator
Nonlinear Material
optical interconnects
photonic crystal
photonic devices
RF-Photonics