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A study of semiconductor microresonators in chip-scale wavelength division multiplexing (CS-WDM) systems

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A study of semiconductor microresonators in chip-scale wavelength division multiplexing (CS-WDM) systems

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Content
A STUDY OF SEMICONDUCTOR MICRORESONATORS IN CHIP-SCALE
WAVELENGTH DIVISION MULTIPLEXING (CS-WDM) SYSTEMS

by

Qi Yang

A Dissertation Presented to the
FACULTY OF THE GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(ELECTRICAL ENGINEERING)

May 2008

Copyright 2008 Qi Yang

ii
Acknowledgements
First of all, I would like to express my deepest gratitude to my advisor, Prof.
P. Daniel Dapkus. I would like to thank him for giving me the opportunity to work in
his group and supporting me throughout my Ph.D. study at USC. I am always
amazed by his endless enthusiasm for science and technology. I truly thank him for
his great encouragement and valuable advices.
I would also like to thank all of the thesis committee members, Prof. O’Brien,
Prof. Steier, Prof. Kim, and Prof. Goo, for their kind attention to my work and
precious advices on my research.
I would like to thank my colleague, Dr. Seung June Choi for teaching me
processing and leading me in the microresonator project. I thank Dr. Zhen Peng for
numerous discussions on the project and tremendous help in the lab. I thank Dr. Sang
Jun Choi and Eui Hyun Hwang for taking the time to grow the material for this work.
I am also grateful to Dr. Wei Zhou for the TEM measurement, and Dr. Dawei Ren
for the CL measurement in this work.
I would like to thank all my colleagues in CSL: Dr. Thiruvikraman
Sadagopan, Dr. Ryan Stevenson, Dr. Yuanming Deng, Dr. Zhijian Wei, Hyung-Joon
Chu, Lawrence Stewart, Suzana Sburlan, Tingwei Yeh, and Loring Smith, who have
created the wonderful atmosphere to work in. I wish all of them the very best.
Last but not least, I would like to thank my family for their unconditional
love and support throughout my life.

iii
Table of Contents
Acknowledgements ...................................................................................................... ii

List of Tables ............................................................................................................... v

List of Figures ............................................................................................................. vi

Abstract ...................................................................................................................... xii

Chapter 1: Introduction to micro-resonators ................................................................ 1
1.1 Role of micro-resonators in CSWDM ......................................................... 1
1.2 Basic theories and functionalities of micro-resonators ................................ 4
1.3 Available platform technologies and brief review of earlier works ............. 7
1.4 Thesis outline ............................................................................................. 14
Chapter 1 References ............................................................................................. 15

Chapter 2: Goal of this work – a multi-pole DEMUX ............................................... 18
2.1 System response requirement ..................................................................... 18
2.2 Existing single-pole DEMUX .................................................................... 19
2.3 Proposed multi-pole DEMUX ................................................................... 23
Chapter 2 References ............................................................................................. 24

Chapter 3: Loss-related analysis and experiment....................................................... 25
3.1 Calculations of loss in resonators ............................................................... 25
3.1.1 Material loss ....................................................................................... 25
3.1.2 Scattering loss .................................................................................... 27
3.1.3 Modal loss .......................................................................................... 29
3.1.3.1 Bending loss ................................................................................... 30
3.1.3.2 Substrate leakage loss .................................................................... 33
3.1.3.3 Total modal loss ............................................................................. 36
3.1.4 Summary ............................................................................................ 38
3.2 Experiments aiming at reducing resonator loss ......................................... 39
3.2.1 a-Si
x
N
y
:H deposition for balanced scattering and bending loss ......... 39
3.2.2 Oxidation of InAlAs for isolating substrate leakage .......................... 47
3.2.2.1 Design and simulations .................................................................. 47
3.2.2.2 Oxidation tests ................................................................................ 51
3.2.2.3 Possible degradation in QW layer by CL measurement ................ 58
3.2.2.4 Summary ........................................................................................ 61
3.2.3 New design: bi-level etching .............................................................. 62
3.3 Loss in bus waveguides .............................................................................. 63
3.3.1 Calculated bus loss ............................................................................. 65
3.3.2 New design: reserving the top cladding layer .................................... 67

iv
3.3.3 Measured loss of bus waveguides ...................................................... 69
3.4 Conclusions ................................................................................................ 69
Chapter 3 References ............................................................................................. 71

Chapter 4: Coupling-related analysis ......................................................................... 74
4.1 Apodization for target values of coupling coefficients .............................. 74
4.1.1 z-transform for filter synthesis ........................................................... 74
4.1.2 Error-tolerance analysis ...................................................................... 81
4.2 Physical realization of the coupling ........................................................... 85
4.2.1 Vertical coupling controlled by epitaxial growth ............................... 85
4.2.2 Lateral coupling by evanescently decaying fields .............................. 86
4.2.3 Assisted lateral coupling by racetrack, overgrowth window and
MMI ................................................................................................... 91
4.2.3.1 Coupling through racetrack-shaped resonators .............................. 91
4.2.3.2 Coupling through InP overgrowth windows .................................. 93
4.2.3.3 Coupling through ridge waveguides .............................................. 99
4.2.3.4 Coupling through an MMI coupler .............................................. 102
4.3 Conclusions .............................................................................................. 103
Chapter 4 References ........................................................................................... 105

Chapter 5: Design and fabrication of a multi-pole DEMUX ................................... 106
5.1 Finalized device design ............................................................................ 106
5.2 Fabrication development .......................................................................... 108
5.2.1 E-beam lithography .......................................................................... 108
5.2.1.1 Resolution of EBL ....................................................................... 110
5.2.1.2 Alignment in EBL ........................................................................ 114
5.2.1.3 Plasma etching with PMMA ........................................................ 117
5.2.1.4 Summary of e-beam process for disk formation .......................... 122
5.2.2 Double/Triple masking technique .................................................... 125
5.2.3 Problems and challenges .................................................................. 129
5.3 Preliminary results and discussions ......................................................... 131
Chapter 5 References ........................................................................................... 133

Chapter 6: Summary and future works .................................................................... 134
6.1 Summary .................................................................................................. 134
6.2 Future works – Resonators in other material systems .............................. 135
6.2.1 Resonators in SOI ............................................................................. 135
6.2.2 Resonators in GaAs .......................................................................... 136
Chapter 6 References ........................................................................................... 139

Bibliography ............................................................................................................. 140

Appendix: Definition of gold alignment mark in Leica system ............................... 146

v
List of Tables
Table 1.1: A comparison of available platform technologies for coupled
microresonators. ..................................................................................................13
Table 2.1: (Courtesy of [1]) Parameters of 8-channel DEMUX .................................21
Table 3.1: A summary of different loss sources with respect to different
parameters. ..........................................................................................................38
Table 3.2: Summary of a-Si
x
N
y
:H deposition tests by PECVD. .................................42
Table 3.3: Summary of surface oxidation tests with thickness and refractive
index of the oxide measured by ellipsometry. ....................................................52
Table 4.1: Summary of calculated modal indices and needed lateral separation
distances. .............................................................................................................90
Table 4.2: Summary of dimensions needed to achieve target coupling and the
corresponding loss of each design. ......................................................................98
Table 4.3: Summary of dimensions required to achieve the target coupling
coefficients and the corresponding loss of the ridge-waveguide design. ..........101
Table 5.1: List of EBL exposure conditions in Leica EBL-100. (Note: The
dosages may vary from time to time and should be re-calibrated on a
regular basis.) ....................................................................................................114

vi
List of Figures
Figure 1.1: Schematic drawing of a simple WDM system. ..........................................1
Figure 1.2: Basic principle of microresonator as a channel-dropping filter with
spectra plots of dropped port and transmitted port. ...............................................2
Figure 1.3: Illustrations of (a) gain tuning and (b) resonant wavelength tuning in
microresonators. ....................................................................................................3
Figure 1.4: Calculation model in coupled mode theory. ...............................................4
Figure 1.5: System response of a single-ring resonator ................................................6
Figure 1.6: Schematic drawings of platform technologies for microresonator
coupled to bus waveguides. ...................................................................................8
Figure 1.7: Cross-sectional view of air-guided micro-resonator vertically
coupled to (a) air-guided and (b) BH bus waveguides. .......................................10
Figure 1.8: (Courtesy of [19]) SEM pictures of (a) cross-section of planar
vertically stacked resonator layers on top of BH bus; (b) etched micro-ring
resonator vertically coupled to BH bus waveguides. ..........................................11
Figure 1.9: (Courtesy of [20]) (a) SEM cross-section view of a buried
waveguide; (b) Calculated and measured transmission spectra of a 200 μm-
radii buried ring resonator. ..................................................................................12
Figure 2.1: (a) Schematic drawing of a single-pole 8-channel DEMUX; (b)
Calculated system response of the DEMUX (R
1
~R
8
=10, 10.1, 10.2, 10.6,
10.7, 10.8, 10.9, 11.1µm, κ
in
= κ
out
=4% and α=3cm
-1
for all resonators are
assumed). .............................................................................................................19
Figure 2.2: (Courtesy of [1]) (a) Top view of fabricated 8-channel DEMUX; (b)
Schematic drawing of an active microdisk resonator vertically coupled to
I/O bus lines. .......................................................................................................20
Figure 2.3: (Courtesy of [1]) (a) Measured throughput (open circles) and drop-
port (closed circles) spectra of channel 2 at 1506.2nm; (b) A complete set
of DEMUX output spectra with 1.6nm channel spacing. The channel
wavelengths and applied currents are listed in Table 2.1. ...................................22
Figure 3.1: Schematic drawing of a waveguide sidewall with random roughness. ....28

vii
Figure 3.2: Calculated scattering loss as a function of refractive index of the
cladding material. ................................................................................................29
Figure 3.3: Schematic drawing of a curved waveguide. .............................................30
Figure 3.4: Bending loss as a function of the radius of the curvature calculated
by (a) Marcatili’s method and (b) WKB method. ..............................................31
Figure 3.5: Scattering and bending combined loss as a function of refractive
index of the cladding, with the bending loss derived by both (a) Marcatili’s
and (b) WKB methods. .......................................................................................33
Figure 3.6: (a) Cross-sectional view of a straight waveguide; ....................................35
Figure 3.7: Modal loss calculated by OlympIOs as functions of (a) refractive
index of the lateral cladding; (b) etching depth of the InP coupling layer;
and (c) radius. (d) is the cross-sectional view of a typical modal field
generated by the solver (n
eff
=3.08, α=13.7cm
-1
, for parameters R=10 μm,
n
clad
=1, t
etch
=0.7 μm). ...........................................................................................37
Figure 3.8: SEM pictures of waveguides (a) before a-Si
x
N
y
:H deposition and ..........40
Figure 3.9: Plot of refractive index of the a-Si
x
N
y
:H film as a function of gas
flow ratio of SiH
4
and NH
3
. ................................................................................44
Figure 3.10: SEM pictures showing the incomplete gap-filling of the deposition. ....45
Figure 3.11: a-Si
x
N
y
:H deposited at lower rate still could not completely fill the
gap .......................................................................................................................46
Figure 3.12: Cross-sectional view of the simulated structure (distances are in
μm). .....................................................................................................................49
Figure 3.13: Calculated modal loss as a function of: (a) oxide thickness; (b)
oxide width. .........................................................................................................50
Figure 3.14: Calculated modal fields of (a) old design without oxide and (b)
new design with oxide. ........................................................................................51
Figure 3.15: Plot of refractive indices of the oxide at different oxidation
temperatures measured by ellipsometry. .............................................................53
Figure 3.16: Schematic drawing of the cross-section view of the tested structure. ....54

viii
Figure 3.17: Example SEM pictures of partially oxidized InAlAs layers. .................55
Figure 3.18: Estimated lateral oxidation rate of 0.4 μm thick InAlAs layer. ...............56
Figure 3.19: (a) Illustration of measured spots; (b) Spatial CL measurement on
those spots. ..........................................................................................................58
Figure 3.20: Line-scan CL measurement across the mesa top before and after
oxidation. (a) is plotted using one scale; (b) is the same data re-scaled to
have the same peak intensities. ...........................................................................59
Figure 3.21: Line-scan CL results of QW-only samples before and after furnace
treatment. The waveguides were formed by (a) wet etching and (b) dry
etching, respectively. ...........................................................................................61
Figure 3.22: Schematic drawing and cross-section view of a bi-level etched
micro-ring resonator vertically coupled with a buried bus waveguide. ..............63
Figure 3.23: Calculated modal loss of air-guided and buried bus waveguides as
functions of (a), (c) thickness and (b), (d) width of the top cladding layer. ......65
Figure 3.24: Examples of modal fields of an air-guided bus waveguide solved
by OlympIOs: (a) w
top
=0; (b) w
top
=0.8μm; (c) w
top
=1.8 μm; (b) w
top
=2.8 μm. ....66
Figure 3.25: Process flow of utilizing coupling layer as bus top cladding: (a)
forming ring mesa and bus cladding taper at the same time; (b) opening on
top of bus by optical lithography; (c) wet etching off disk cladding and
core layers. ..........................................................................................................67
Figure 4.1: Schematic drawings of z-transforms of (a) a single-stage ring filter;
(b) a multi-stage ring filter coupled in series; (c) a multi-stage ring filter
coupled in parallel. ..............................................................................................76
Figure 4.2: A comparison of single-stage and multi-stage ring filter response for
(a) serial coupled and (b) parallel coupled configurations. Two adjacent
channels are plotted together to indicate different channel isolations. The
insert plots are magnified spectra showing details of the filter passband. ..........79
Figure 4.3: Calculated filter responses with loss and coupling coefficients
different than design parameters. ........................................................................83
Figure 4.4: Calculated vertical coupling coefficient between disk and bus
waveguide. ..........................................................................................................86

ix
Figure 4.5: Schematic drawings of (a) ring-bus lateral coupling and (b) ring-ring
mutual coupling. ..................................................................................................87
Figure 4.6: Calculated total power coupling coefficient as a function of
minimum lateral separation distance for (a) disk-bus, (b) ring-bus lateral
coupling and (c) disk-disk, (d) ring-ring mutual coupling. .................................89
Figure 4.7: (a) Schematic drawing of racetrack resonators; (b) BPM simulated
coupling coefficient as a function of coupling length of the racetrack. ..............92
Figure 4.8: Schematic drawings of InP-assisted mutual coupling for the
racetrack resonators: (a) asymmetric rectangular growth window; (b)
symmetric rectangular growth window; (c) asymmetric tapered growth
window; (d) symmetric tapered growth window; (e) fabrication-limited
symmetric tapered growth window. ....................................................................94
Figure 4.9: BPM simulation results on various designs of InP-overgrowth
windows: (a, b) symmetric and asymmetric rectangular windows; (c, d)
asymmetrically tapered windows; (e, f) symmetrically tapered windows; (g,
h) fabrication-limited symmetrically tapered windows. .....................................95
Figure 4.10: Calculated relation between single-pass power loss and distributed
loss. ......................................................................................................................97
Figure 4.11: Schematic drawings of (a) a ridge-type waveguide and (b) two
ridge-type waveguides coupled with each other. ................................................99
Figure 4.12: OlympIOs-calculated whispering gallery modes of 10 μm-radii (a)
rib-type and (b) ridge-type ring resonators. ......................................................100
Figure 4.13: BPM simulation results of (a) coupling coefficient and (b) loss of
two straight ridge-type waveguides with parameters defined in Figure 4.11. ..101
Figure 4.14: Schematic drawing of an MMI coupler: top view and cross-
sectional view. ...................................................................................................102
Figure 5.1: Block-diagram illustration of the design rules. ......................................106
Figure 5.2: Schematic drawings of (a) an 8-channel multi-pole DEMUX with
each channel consisting of three micro-resonators coupled with (b) air-
guided and (c) BH bus waveguides. ..................................................................107

x
Figure 5.3: Mix-and-match approach for disk-pattern formation: (a) Disk
pattern and taper ends of bus top-cladding defined by e-beam lithography,
transferred to SiN
x
; (b) Bus top-cladding taper completed by optical
lithography, transferred to SiN
x
a second time; (c) Final SiN
x
mask, ready
for disk formation etch. .....................................................................................109
Figure 5.4: SEM pictures of developed PMMA exposed at different
acceleration voltages. ........................................................................................111
Figure 5.5: Monte Carlo simulated trajectories of 100 electrons in PMMA resist
on silicon. ..........................................................................................................112
Figure 5.6: Separated EBL masks for different dosages: (a) fine gaps; (b)
remaining areas. ................................................................................................113
Figure 5.7: SEM pictures of developed PMMA with different thicknesses: (a)
~1μm; (b) ~0.3 μm. ............................................................................................114
Figure 5.8: Alignment scheme in Leica EBL100.....................................................115
Figure 5.9: Mutually coupled disks patterned by E-beam lithography. ....................116
Figure 5.10: Etching residue problem with PMMA..................................................119
Figure 5.11: SEM pictures of SiN
x
mask (60min CVD) etched by
CF
4
/H
2
=27/18sccm for 1100sec, and cleaned by 40min Acryl warm bath
and 6min O
2
plasma. .........................................................................................120
Figure 5.12: Comparison of post-baking effect on sidewall smoothness. ................121
Figure 5.13: SEM pictures of fabricated (a) disk mask by a combination of EBL
and optical photolithography; and (b) the resulting disk mesas dry-etched
by BCl
3
. .............................................................................................................124
Figure 5.14: Scheme of two-step etching to achieve different etching depths. ........125
Figure 5.15: Scheme of double-masking process to realize bi-level etching. ...........126
Figure 5.16: Scheme of triple-masking process to remove disk layers on bus
automatically. ....................................................................................................128
Figure 5.17: SEM pictures of single resonator vertically coupled to BH bus
waveguides fabricated with the triple-masking process by Zhen Peng.
(Pictures courtesy of Zhen Peng) ......................................................................128

xi
Figure 5.18: Last fabricated multi-pole filter with buried bus waveguides using
planarization overgrowth technique (gaps between disks were merged; the
process stopped after that). ................................................................................130
Figure 5.19: Last fabricated multi-pole filter with air-guided bus waveguides
using wafer-bonding technique (bus waveguides were attacked during
disk-layer removal step; process stopped after that). ........................................131
Figure 5.20: (Courtesy of Zhen Peng) Measured transmission spectra of a single
resonator vertically coupled to a single BH bus waveguides. ...........................132
Figure 6.1: Schematic drawing of an SOI-based microresonator. ............................135
Figure 6.2: Cross-sectional view of a partially oxidized ring resonator in a
GaAs/AlGaAs material system. (Distances are in µm) .....................................137

xii
Abstract

Micro-cavity devices such as micro-ring resonators are frequency selective
elements that can perform a variety of functions such as add/drop filtering, switching,
and modulating in chip-scale wavelength-division-multiplexing (CS-WDM) systems.
Their compact size and low-power-consuming property have enabled them to
become a strong candidate as building blocks in the future photonic integrated
circuits (PICs). In this dissertation, InP/InGaAsP-based micro-ring (or micro-disk)
resonators vertically coupled with bus waveguides were investigated mainly as
active bandpass filters serving as multiplexer/demultiplexers (MUX/DEMUXs) in
the WDM communication system.
After a brief review of the existing 8-channel single-pole (first order)
DEMUX, theoretical analysis suggested that the filter response could be improved
by increasing the order of the filter from first to third, and with reduced losses from
the microresonator and the bus waveguides. Device parameters were designed and
optimized to meet the required system specifications. Experiments and progresses on
the proposed 8-channel multi-pole (third order) DEMUX were presented.
Preliminary results indicated an encouraging potential in the new design.

1
Chapter 1 Introduction to micro-resonators
1.1 Role of micro-resonators in CSWDM
Ever since the explosive growth of information technology, there has been an
enormous demand for larger bandwidth in data transmission. Given the fact that a
single-mode fiber’s potential bandwidth is nearly 50Tb/s, which is almost four orders
of magnitude higher than electronic data rates of a few Gb/s, optical communication
technology such as wavelength division multiplexing (WDM) systems is one of the
most effective solutions to meeting the ever-growing need. Not only does it have the
potential to provide huge bandwidth, but it is also capable of providing low signal
attenuation, low signal distortion, low power consumption, and greatly enhanced
security [1]. WDM is the process by which a few wavelengths of individual light
signals, each of which carries a separate data stream, are assembled on a single
optical fiber at the transmitting end, and then the multiplexed signal is separated into
its respective channels at the receiving end (Figure 1.1).

Figure 1.1 Schematic drawing of a simple WDM system.

A key component for controlling the optical signals in the integrated chip-
scale WDM (CS-WDM) system is the wavelength selective element. Arrayed
MUX
λ
1

λ
2
λ
N
Amplifier
Fiber
Local
add/drop
DEMUX
λ
1

λ
2
λ
N
Fiber
Amplifier

2
wavelength gratings (AWGs), fiber Bragg gratings (FBGs), and thin film filters
(TFFs) are among the most widely used optical filtering elements. Nevertheless, this
dissertation investigates a relatively new but highly attractive technology for optical
filtering – semiconductor bus-coupled microresonators. Their excellent wavelength
selectivity, compact size, and versatile functionalities have enabled them to be
considered as potential building blocks in the future photonic integrated circuit (PIC).
As a circular resonant cavity, a microdisk or microring resonator works as a
channel add/drop filter in the way that only the wavelength equal to its own
resonance can be picked up from the input signal, and then coupled out to the output
bus waveguide. The dropped and transmitted spectra can be viewed as those of band-
pass and band-stop filters (Figure 1.2). A rigorous analysis of the system response is
presented in the next section.

Figure 1.2 Basic principle of microresonator as a channel-dropping filter with spectra plots of
dropped port and transmitted port.

The microresonator was firstly proposed by Marcatili in 1969 [2], but only
recently have fabrication advances allowed the realization of micrometer-sized
structures with sufficiently high quality. Since then they have received considerable
λ
λ
i

Transmitted
λ
λ
i

Dropped
Input
( λ
1
λ
2
… λ
i
...)
Transmitted
( λ
1
λ
2
… λ
i-1
λ
i+1
...)
λ
resonance
= λ
i

Dropped ( λ
i
)
Coupled
( λ
i
)

3
attention for optical signal processing applications. The uniqueness of microring
resonators is that they can provide various functionalities in PICs while being
compact and consuming little power. Reserchers have demonstrated resonator-based
tunable add/drop filters [3], switches [4], modulators [5], lasers [6], detectors, and
optical amplifiers [7] in various material systems such as InP/InGaAsP [3-7],
GaAs/AlGaAs [8], Si/SiO
2
[9] and polymers [10]. Thus, there is no doubt that they
are one of the strongest candidates as building blocks for very large scale integrated
(VLSI) photonic circuits.
Among all material systems, one of the attractive advantages of III-V
compound semiconductor micro-resonators is that quantum wells can be easily
incorporated into the cavity to provide gain, absorption, electro-absorption and
electro-refraction (Figure 1.3(a)) [4]. Moreover, the resonant wavelength can be
tuned by injecting minority free carriers into or depleting majority carriers from a p-n
(or p-i-n) heterostructure (Figure 1.3(b)) [3]. Those active properties make micro-
resonators even more flexible in terms of external control and more forgiving in
regards to compensating optical losses and fabrication imperfections.

(a) (b)
Figure 1.3 Illustrations of (a) gain tuning and (b) resonant wavelength tuning in microresonators.

λ
λ
0
’

T
λ
0

Index
tuning
λ
T
λ
0

Gain
tuning

4
1.2 Basic theories and functionalities of micro-resonators
There are several methods of calculating the response of a micro-ring
resonator. Below is one example that uses the widely accepted coupled mode theory
in time domain (CMT) [11]. Another method involving the z-transform method will
be introduced later in Chapter 4. CMT utilizes the direct correspondence between
circulating power and cavity energy. It links the coupling of modes in time with the
coupling of modes in space by relating the energy decay rate to the common power
coupling coefficient between waveguides. For example, consider a single ring
resonator coupled to two bus waveguides as illustrated in Figure 1.4.

Figure 1.4 Calculation model in coupled mode theory.

The ring can be viewed as a lumped oscillator with energy amplitude a(t),
normalized so that |a(t)|
2
represents the total energy stored in the resonator.
Correspondingly,
R
v
t a
g
π 2
) (
2
, where v
g
is the group velocity of the mode and R is
the radius of the ring, gives the total power flowing through any cross section of the
ring waveguide at time t. The power amplitude of input, transmitted, added, and
( κ
in,
κ
out
are unitless
power coupling
coefficients of input and
output bus waveguides,
respectively.)
Input s
i
(t)
Dropped s
d
(t)
R
ω
0
Transmitted s
t
(t)
Added s
a
(t)
κ
out
κ
in
a(t)

5
dropped waves propagating in the bus waveguides can be denoted as s
i
(t), s
t
(t), s
a
(t)
and s
d
(t), respectively, all having sinusoidal frequency dependency exp(j ωt) so that
d/dt=j ω. The resonator has a resonant frequency of ω
0
and an amplitude decay time
constant of 1/τ, which is the result of three contributions – the power coupled into
the resonator 1/τ_
in
, the power coupled out of the resonator 1/τ_
out
, and the intrinsic
loss of the resonator itself 1/τ_
loss
. The time rate of change of the ring energy can
then be derived from:

⎪
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎪
⎨
⎧
a(t)
τ
(t)-j (t)=s s
a(t)
τ
(t)-j (t)=s s
(t) s
τ
(t)-j s
τ
a(t)-j )
τ
- a(t)=(j ω
dt
d
out
a d
in
i t
a
out
i
in
2
2
2 2 1
0
(1.1)
where
loss out in
τ
+
τ
+
τ
=
τ
1 1 1 1
, and
2
1
2
2
/
/
g
loss
g out in
out in
v α
=
τ
,
πR
v κ
=
τ
, α is the distributed
power loss of the resonator in [m
-1
]. Considering no added signal on the output
waveguide, s
a
(t)=0, the transmitted and the dropped functions are then

()
()
⎪
⎪
⎩
⎪
⎪
⎨
⎧
+ −
+ −
+ − −
− − −
− − −
− − −
2
1 1 1
0
2
2
1 1 1
0
1 1 1
0
2
2
loss out in
out in
i
d
loss out in
loss out in
i
t
τ + τ )+ τ ω j( ω
τ τ
=
s
s
= D
τ + τ )+ τ ω j( ω
τ + τ τ ) ω j( ω
=
s
s
= T
ω
ω
(1.2)
The quality factor Q (defined as the time averaged stored energy divided by
the power lost per optical cycle either through coupling or intrinsic loss) is related to

6
the time constant τ through the relation Q
-1
=2/ωτ. Hence the transmission function
can be rewritten as

⎪
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎪
⎨
⎧
−
=
−
−
−
=
− − −
− −
− − −
− − −
2
1 1 1
0
1 1
2
1 1 1
0
1 1 1
0
2
1
)
2
1
2
1
)
) +Q +Q (Q )+
ω ω
j(
Q Q
D( ω
) +Q +Q (Q )+
ω ω
j(
) +Q +Q Q ( )+
ω ω
j(
T( ω
loss out in
out in
loss out in
loss out in
ω
ω
ω
(1.3)
where
0 0
2
2 4
αλ
πn
= Q ,
λ κ
Rn π
= Q
eff
loss
in/out
eff
in/out
. Figure 1.5 below is an example of the
calculated transmission function of a single micro-ring resonator coupled to two bus
waveguides.
1544 1545 1546 1547 1548
0
0.2
0.4
0.6
0.8
1
Wavelength [nm]
Transmitted power
1544 1545 1546 1547 1548
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Wavelength [nm]
Dropped power

Figure 1.5 System response of a single-ring resonator
(assuming R=10µm, κ
in
= κ
out
=4%, and α=3cm
-1
).

The resonant wavelength is determined by the resonant condition
2 πRn
eff
=m λ
0
where m is an integer known as the mode number. The free spectral

7
range (FSR) of the filter is given by
1
0
2
0
1
2
−
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
+ =
λ
λ
π
λ
d
dn
n Rn
FSR
eff
eff eff
which takes the
material dispersion into account. The filter bandwidth Δλ, or the full-width-half-
maxima (FWHM), of a single microresonator is determined by the sum of the
coupling and the loss:
( )
eff
out in
loss out in
n R
R
c
2
2
0
2
0
4
2 1 1 1
π
λ α π κ κ
π
λ
τ τ τ
λ
+ +
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+ + = Δ . Critical
coupling occurs when α π κ κ R
out in
2 + = leading to a complete power extraction at
the resonant frequency, i.e. T( ω
0
)=0.

1.3 Available platform technologies and brief review of earlier
works
The available platform technologies for microresonators are commonly
categorized into four different types based on their physical geometries and coupling
configurations. They are, as shown in Figure 1.6, (a) air-guided microresonator
laterally coupled to air-guided bus waveguides; (b) air-guided microresonator
vertically coupled to air-guided bus waveguides; (c) air-guided microresonator
vertically coupled to buried heterostructure (BH) bus waveguides; and (d) BH
microresonator laterally coupled to BH bus waveguides.

8

Figure 1.6 Schematic drawings of platform technologies for microresonator coupled to bus
waveguides.

An air-guided microresonator laterally coupled to air-guided bus waveguides
(Figure 1.6(a)) is the most classical configuration of bus-coupled microresonators
[12,8]. With a high index-contrast at the air-semiconductor interface, it has the
advantage of strong optical confinement for both the resonator and the bus so that
both waveguides can be built sufficiently small while maintaining relatively low loss.
On the other hand, the strong confinement can make the coupling between the two
waveguides extremely difficult. The lateral separation distances must usually be in
the range of one to two hundred nanometers. Therefore, high resolution lithography
is needed to make this type of devices. In addition to these fabrication challenges, the
lateral geometry also requires that the materials of the resonator and the bus be the
same. This serves to restrict the choice of materials in designing active devices.
(a) (b)
(c) (d)

9
In the second type of configuration (Figure 1.6(b)), an air-guided
microresonator is vertically coupled to air-guided bus waveguides. A wafer-bonding
technique has successfully been developed to realize this configuration [13,14]. The
fabrication procedure begins with the formation of input/output bus waveguides by
optical lithography and dry etching. The entire sample is then flipped over and
thermally bonded to another InP transfer wafer. After mechanical polishing the
wafer-bonded sample, the remaining InP from the original substrate is completely
removed by selective wet etching. The disk mesas are then formed by CH
4
/H
2
/Ar
plasma etching in ECR under reactive ion etching (RIE) condition. Lastly, polyimide
is used to planarize the device surface and electrodes are formed on the disks.
The coupling between the upper resonator and the lower bus is mainly
determined by the thickness of the coupling layer in between, which can be precisely
controlled through epitaxial growth. We also have the freedom to choose different
materials for resonator and bus core layers. So far, our group has demonstrated a
series of active bus-coupled microresonators with this platform technology,
including wavelength tunable filters [3], electro-absorption and gain tuning
modulators [4,15], high-speed modulators [16,17], and single mode continuous-wave
(CW) lasers [6] and laser arrays [18]. The disadvantages of this platform, however,
are the poor heat sink and poor electrical conduction through the substrate (Figure
1.7(a)). The relatively high loss in the bus waveguide is another drawback. Refer to
section 3.3 for further discussion on bus loss.

10

Figure 1.7 Cross-sectional view of air-guided micro-resonator vertically coupled to (a) air-guided
and (b) BH bus waveguides.

In the third configuration (Figure 1.6(c)), the air-guided microresonator is
vertically coupled to buried bus waveguides. A novel planarization overgrowth
technique is developed to provide a planar surface for the resonators on top of the
BH buses [19]. To fabricate this device, bus waveguides are formed first and the
SiN
x
mask is left on the mesa so that InP can be selectively grown to fill up the areas
between the mesas. A planar surface is obtained by carefully choosing the V/III ratio
during the MOCVD growth. After the first overgrowth, SiN
x
is removed by BOE and
the upper disk layers are grown continuously. The remaining process of disk and
contact formation is similar to the devices with air-guided buses. SEM pictures of a
fabricated device are shown in Figure 1.8.
This approach takes full advantage of vertically coupled microresonators
without the wafer-bonding process. When choosing materials for the bus waveguides,
we have the freedom of choosing a different material than the disk layer, which can
also be undoped thus eliminating carrier-induced material loss. Other benefits of this
design include good heat sink and the excellent electrical conduction path through
the substrate (Figure 1.7(b)). One of the main limitations of this configuration,
however, is the substrate leakage loss due to the low effective index of the resonator
(a) (b)
p-InP
i-InGaAsP
n-InP
n-InGaAsP
n-InP
Disk core
Bus core
p-InP
i-InGaAsP
i-InGaAsP
n-InP
Current path

11
mode and the close distance from the mode to the substrate. The measured loss
coefficient of this device is about 20cm
-1
, which we believe is mainly due to power
leakage into the substrate. Detailed analysis and discussions can be found in section
3.1.3.2.

(a) (b)
Figure 1.8 (Courtesy of [19]) SEM pictures of (a) cross-section of planar vertically stacked resonator
layers on top of BH bus; (b) etched micro-ring resonator vertically coupled to BH bus waveguides.

In the last platform technology (Figure 1.6(d)), both resonators and buses are
buried and they are laterally coupled to each other. The fabrication of this device is
probably the easiest of all. All patterns are formed at one time and a thick layer of
InP is grown on top to cover them. No planarization is needed during the growth.
The main difference of this scheme is that it requires a much larger resonator radius
than the other three platforms. Due to the low index-contrast between the core and
the cladding materials of the buried waveguide, the radius of the resonator must be
larger than 100 μm to avoid the huge bending loss. Also, due to the lateral coupling
configuration, there is not much freedom in choosing the material of the bus

12
waveguide. Active devices also suffer from poor electrical confinement if there are
no current blocking structures. The advantages of all-buried devices include low
scattering loss, high coupling efficiency achieved by normal optical lithography,
good heat sink through the substrate, and very narrow linewidth in the response
spectrum. Our group has demonstrated Qs of 10
5
or higher from 200 μm-radii
InP/InGaAsP single mode ring resonators with loss coefficient as low as 0.4cm
-1

(Figure 1.9 [20]). To compensate the reduced FSR of large devices, the Vernier
effect can be utilized by cascading multiple resonators [21].

Figure 1.9 (Courtesy of [20]) (a) SEM cross-section view of a buried waveguide; (b) Calculated and
measured transmission spectra of a 200 μm-radii buried ring resonator.

As a summary, a comparison of different platform technologies is given in
Table 1.1. It is important to understand the characteristics of each scheme and select
the most suitable approach to realize the desired functionality.

Buried waveguide
1554.0 1554.1 1554.2
0.0
0.2
0.4
0.6
0.8
1.0
1554.0 1554.1 1554.2
κ
in
= 4.0 %
κ
out
= 4.0 %
α = 0.4cm
-1
Calculated

Normalized Transmission
Wavelength [nm]
Δλ = 0.0137 nm
Q
total
= 1.1x10
5
Measured

(a) (b)

13
Table 1.1 A comparison of available platform technologies for coupled microresonators.
Advantages Disadvantages
Air-guided resonator;
Air-guided bus;
Laterally coupled.
Small size (large FSR);
Low-loss possible.
Same material for both
resonator and bus;
Weak coupling (difficult
fabrication).
Air-guided resonator;
Air-guided bus;
Vertically coupled.
Small size (large FSR);
Low-loss resonator;
Free to choose materials;
Coupling strength controlled
by epi-growth.
Wafer-bonding needed;
High-loss doped bus;
Poor heat sink;
Poor electrical conduction.
Air-guided resonator;
BH bus;
Vertically coupled.
Small size (large FSR);
Free to choose materials;
Coupling strength controlled
by epi-growth;
Low-loss undoped bus;
Good heat sink;
Good electrical conduction.
Planarization overgrowth
needed;
Substrate leakage loss.
BH resonator;
BH bus;
Laterally coupled.
Low scattering loss;
Strong coupling (easy
fabrication);
High Q;
Good heat sink.

Large size (small FSR);
Same material for both
resonator and bus;
Poor electrical
confinement without
current blocking
structures.

14
1.4 Thesis outline
This dissertation is organized as follows. Chapter 2 states the overall goal of
the work. System specifications are given as a guide for designing new devices.
Fabrication and measurement results of existing devices are briefly introduced. A
proposed new design with improved characteristics is then followed. In order to
choose the appropriate platform technology to realize the new device, two key issues
in bus-coupled microresonators are addressed in detail in the next two chapters –
namely loss and coupling. Chapter 3 discusses the loss of the resonators as well as
the loss of the bus waveguides. Theoretical analysis and experiments aiming at
reducing loss are presented. A novel design of low-loss bus waveguide is also
included. Chapter 4 focuses on coupling-related analysis. The required coupling
coefficients are first derived and simulations of how to realize them follow. After
this analysis, a finalized design of the new device is described in Chapter 5.
Development and challenges in device fabrication, such as e-beam lithography and
multi-masking processes, are presented. Promising preliminary results are shown at
the end. Chapter 6 summarizes this dissertation and takes a look at future
microresonators in other material systems.

15
Chapter 1 References

[1] B.Mukherjee, “WDM optical communication networks: progress and challenges”,
IEEE Journal of Selected Areas Communications, vol.18, no.10, pp.1810-1824,
Oct 2000.

[2] E.A.Marcatili, “Bends in optical dielectric waveguides”, The Bell System
Technical Journal, vol. 48, pp.2103-32, 1969.

[3] K.D.Djordjev, S.J.Choi, S.J.Choi, and P.D.Dapkus, “Microdisk tunable resonant
filters and switches”, IEEE Photonics Technology Letters, vol.14, no.6, pp.828-
830, Jun 2002.

[4] K.D.Djordjev, S.J.Choi, S.J.Choi, and P.D.Dapkus, “Vertically coupled InP
microdisk switching devices with electro-absorptive active regions”, IEEE
Photonics Technology Letters, vol. 14, no. 8, pp.1115-1117, Aug 2002.

[5] 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 Photonics Technology Letters, vol.17, no.17, pp.567-569, Aug
2002.

[6] S.J.Choi, K.D.Djordjev, S.J.Choi, and P.D.Dapkus, “Microdisk lasers vertically
coupled to output waveguides”, IEEE Photonics Technology Letters, vol.15,
no.10, pp.1330-1332, Oct 2003.

[7] K.D.Djordjev, S.J.Choi, S.J.Choi, and P.D.Dapkus, “Active semiconductor
microdisk devices”, IEEE Journal of Lightwave Technology, vol.20, no.1,
pp.105-113, Jan 2002.

[8] D.Rafizadeh, J.P.Zhang, S.C.Hagness, A.Taflove, K.A.Stair, S.T.Ho, and
R.C.Tiberio, “Waveguide-coupled AlGaAs/GaAs microcavity ring and disk
resonators with high finess and 21.6 nm free spectral range”, Optics Letters,
vol.22, no.16, pp.1244-1246, Aug 1997.

[9] 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”, IEEE Photonics Technology Letters, vol.10,
no.4, pp.549-551, Apr 1998.

16

[10] P. Rabiei, “Electro-optic and thermo-optic polymer microring resonators and
their applications”, Ph.D. dissertation, University of Southern California, USA,
2002.

[11] H. A. Haus, Waves and Fields in Optoelectronics, Chapter 7, New Jersey:
Prentice Hall, 1984.

[12] B.E.Little, S.T.Chu, H.A.Haus, J.Foresi, and J.P.Laine, “Microring resonator
channel dropping filters”, IEEE Journal of Lightwave Technology, vol.15, no.6,
pp.998-1005, Jun 1997.

[13] D.V.Tishinin, I.Kim, C.Lin, A.E.Bond, and P.D.Dapkus, “Novel fabrication
process for vertical resonant coupler with precise coupling efficiency”, Proc.
IEEE 11
th
Annual LEOS Meeting, San Francisco, TuK5, pp.93-94, Oct 1998.

[14] K.D.Djordjev, S.J.Choi, S.J.Choi, and P.D.Dapkus, “High-Q vertically coupled
InP microdisk resonators”, IEEE Photonics Technology Letters, vol.14, no.3,
pp.331-333, Mar 2002.

[15] K.D.Djordjev, S.J.Choi, S.J.Choi, and P.D.Dapkus, “Gain trimming of the
resonant characteristics in vertically coupled InP microdisk switches”, Applied
Physics Letters, vol.80, pp.3467-3469, May 2002.

[16] T.Sadagopan, S.J.Choi, S.J.Choi, P.D.Dapkus and A.E.Bond, “Carrier induced
refractive index changes in circular microresonators for low-voltage high-speed
modulation”, IEEE Photonics Technology Letters, vol.17, no.2, pp.414-416, Feb
2005.

[17] T.Sadagopan, S.J.Choi, S.J.Choi, P.D.Dapkus and A.E.Bond, “Modulators
based depletion width translation in semiconductor microdisk resonators”, IEEE
Photonics Technology Letters, vol.17, no.3, pp.567-569, Mar 2005.

[18] S.J.Choi, Z.Peng, Q.Yang, S.J.Choi, and P.D.Dapkus, “Eight-channel microdisk
CW laser arrays vertically coupled to common bus waveguides”, IEEE Photonics
Technology Letters, vol.16, no.2, pp.356-358, Feb 2004.

[19] S.J.Choi, K.D.Djordjev, S.J.Choi, P.D.Dapkus, W.Lin, G.Griffel, R.Menna, and
J.Connolly, “Microring resonators vertically coupled to buried heterostructure
bus waveguides”, IEEE Photonics Technology Letters, vol.16, no.3, pp.828-830,
Mar 2004.

17

[20] S.J.Choi, K.D.Djordjev, Z.Peng, Q.Yang, S.J.Choi, and P.D.Dapkus, “Laterally
coupled, buried heterostructure high-Q ring resonators”, IEEE Photonics
Technology Letters, vol.16, no.10, pp.2266-2268, Oct 2004.

[21] S.J.Choi, Z.Peng, Q.Yang, S.J.Choi, and P.D.Dapkus, “Tunable, narrow
linewidth, all-buried heterostructure ring resonator filters using Vernier effects”,
IEEE Photonics Technology Letters, vol.17, no.1, pp.106-108, Jan 2005.

18
Chapter 2 Goal of this work – a multi-pole DEMUX
2.1 System response requirement
We know that the performance of a single resonator can be viewed as a filter
picking up equally spaced wavelengths corresponding to its own resonances. This
function can be utilized as a demultiplexer in the WDM system where different
signals are assigned to channels with different frequencies. The goal of this
dissertation is to demonstrate such a microresonator-based eight-channel
demultiplexer with the following system specifications:
(1) Wavelength range: C
α
-band (1532~1555nm);
(2) Channel spacing: 100GHz, or 0.8nm in wavelength;
(3) Channel isolation: greater than 30dB;
(4) Filter bandwidth: 20GHz, or 0.16nm, for each channel.

In order to filter out eight channels of signals, a set of eight-resonator filter
arrays are required with each one assigned to one specific channel, as illustrated in
Figure 2.1(a). To ensure that the interference between adjacent channels is
minimized, the minimum FSR of all resonators is chosen to be larger than the
channel spacing. Figure 2.1(b) shows an example of the calculated performance of
an 8-channel DEMUX using the CMT method described in the previous chapter. The
radii of the resonators are chosen so as to fulfill the 0.8nm channel spacing
requirement.

19

(a)
1544 1546 1548 1550 1552
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Wavelength [nm]
Dropped power
1544 1546 1548 1550 1552
0
0.2
0.4
0.6
0.8
1
Wavelength [nm]
Transmitted power

(b)
Figure 2.1 (a) Schematic drawing of a single-pole 8-channel DEMUX; (b) Calculated system
response of the DEMUX (R
1
~R
8
=10, 10.1, 10.2, 10.6, 10.7, 10.8, 10.9, 11.1µm,
κ
in
= κ
out
=4% and α=3cm
-1
for all resonators are assumed).

2.2 Existing single-pole DEMUX
An eight-channel demultiplexer using vertically coupled active microdisk
resonators was demonstrated in 2004 by Dr. Seung-June Choi et al. [1] in our group.
The reason why vertical-coupling geometry is chosen over lateral-coupling is
because the material compositions and physical separation of the bus and resonator
waveguides can be independently designed and precisely controlled. Quantum wells
(QWs) are incorporated into the disk core layer so that current can be injected into
the active region to compensate optical loss. Meanwhile, by controlling the injection
Input
Dropped
R
1
, λ
1

Transmitted
R
2
, λ
2
R
3
, λ
3
R
8
, λ
8

λ
2
λ
3
λ
8

λ
1

20
levels, the resonant wavelength of each microdisk can be tuned either with the free
carrier plasma effect or thermal effect to meet the target spectral specifications in
case of an offset due to fabrication imperfections.

Figure 2.2 (Courtesy of [1]) (a) Top view of fabricated 8-channel DEMUX; (b) Schematic drawing of
an active microdisk resonator vertically coupled to I/O bus lines.

The epitaxial structure of the device starts from a highly p-doped InGaAs
contact layer on the InP substrate, followed by the disk p-cladding layer that has
decreasing doping levels to reduce free carrier absorption in the resonator. Two
vertically stacked waveguides are formed after that – the disk core layer, which
incorporates active QW’s, and the bus waveguide layer, which are separated by a
0.8µm-thick InP coupling layer. The disk core, with a total thickness of 0.4µm,
consists of two separate confinement heterostructure (SCH) layers ( λ
SCH
=1.25µm,
n
disk
=3.36) and four QWs (0.5% compressively strained, λ
QW
=1.51µm). The bus core
layer is also 0.4µm thick, with wavelength λ
bus
=1.1µm (n
bus
=3.29). Finally, an n-
doped InP layer is grown as the lower cladding of the bus waveguides. Device
Common
Input / throughput
Drop-port
Output
Polyimid
Disk
resonator
Electrode
Probe
Input
fiber
Output
fiber
Common
throughput
Common
input
Drop-port
output
50μm
(a)
(b)

21
fabrication is essentially the same as for a single-microdisk resonator [2]. The top
view of the fabricated device and a schematic drawing of a single microdisk
resonator are shown in Figure 2.3 [1].
Table 2.1 (Courtesy of [1]) Parameters of 8-channel DEMUX
Disk
R
[μm]
FSR [nm]
λ
0
at I = 6 ± 0.4
mA [nm]
Channel adjustment [nm]
1 9.6 11.5 1504.6 1504.6 → Ch. 1
2 9.6 11.5 1516.1 1515.5 (I = 7 mA) → Ch. 8
3 10.7 10.0 1506.2 1506.2 → Ch. 2
4 10.7 10.0 1516.2 1513.9 (I = 9 mA) → Ch. 7
5 12.3 8.4 1507.8 1507.8 → Ch. 3
6 12.3 8.4 1507.8 1509.4 (I = 10.5mA)→ Ch. 4
7 12.9 8.0 1510.9 1512.4 (I = 11 mA) → Ch. 6
8 12.9 8.0 1510.9 1510.9 → Ch. 5

The eight microdisks are designed to have four different radii, with every two
disks having the same radii. Each microdisk is turned on by injecting currents at
about 6mA to reduce optical loss from 55cm
-1
to 1.5cm
-1
. The measured individual
resonant wavelengths can be found in Table 2.1 [1]. Next, the current injection level
is carefully adjusted in order to tune the resonant wavelength toward the target
spectral position. Free carrier injection into QW’s causes band-filling and free carrier
plasma effects, which affects the absorption coefficients of QW’s and reduces the
refractive index in the spectral range of interest. As a result, the resonant wavelength
blue-shifts with injected current [2]. At the same time, the temperature of the device
rises with increasing current until finally the thermal effect becomes dominant. This
causes the resonant wavelength to red-shift, thus limiting the tuning efficiency [3].

22
For the given devices, the maximum tuning capability is -4nm at 9.5mA and +3nm at
12mA, which sufficiently corrects all the detuned characteristics that are due to
fabrication imperfections.
Figure 2.3(a) shows the measured throughput and drop-port spectra of one of
the channels ( λ
2
=1506.2nm) at 5.8mA pumping current. Note that the rest of the
disks are unpumped and remain absorptive so that only the resonant wavelength of
this particular channel appears in the common throughput spectrum, while others are
effectively off. Plot (b) gives a complete set of demultiplexed output spectra for the
eight-channel microdisk array. The achieved channel spacing is 1.6nm with a typical
linewidth of 0.15nm or less. The measured channel isolation is 15~20dB.

1504 1505 1506 1507 1508
0.0
0.2
0.4
0.6
0.8
1.0
Ch. 2
1506.2 nm
Ch. 3
1507.8 nm
Ch. 1
1504.6 nm

Normalized Intensity
Wavelength [ nm ]
1504 1506 1508 1510 1512 1514 1516
Ch. 1
Wavelength [ nm ]
Ch. 2
Ch. 3
Ch. 4
Ch. 5
Dropped Intensity [ a.u. ]
Ch. 6
Ch. 7
Ch. 8

(a) (b)
Figure 2.3 (Courtesy of [1]) (a) Measured throughput (open circles) and drop-port (closed
circles) spectra of channel 2 at 1506.2nm; (b) A complete set of DEMUX output spectra
with 1.6nm channel spacing. The channel wavelengths and applied currents are listed in
Table 2.1.

23
2.3 Proposed multi-pole DEMUX
It can be seen from equation (1.3) that the response of a micro-resonator filter
has a Lorentzian-shape which is not ideal for a practical WDM system. Its lineshape
lacks passband flatness and has a large wing in the stopband leading to high cross
talk and poor channel isolation. To improve its performance and meet the system
specifications, a higher-order filter is required to realize the sharp roll-off from
passband to stopband as well as the large out-of-band rejection.
Furthermore, the loss in resonators also limits the overall filter performance.
There are several sources of loss including material loss, scattering loss and modal
loss. Each source of loss has its own determining parameters, such as carrier
concentration, radius of the disk, refractive index of the cladding material, etching
depth, and so on. By thoroughly analyzing the loss dependencies on every parameter,
it is possible to gain an understanding of how to optimize those parameters in order
to reduce the overall loss. Meanwhile, the relatively high loss in the bus waveguide
puts another constraint on the integrated circuit where passive and active components
are connected via common bus lines on the same chip. To improve the efficiency of
light transmission throughout the chip, a different design of bus waveguide with
reduced loss should also be included in the new device.
The following three chapters address the above issues and put forth possible
solutions for optimizing our devices. Due to the required FSR, most analysis will be
focused on small-size resonators.

24
Chapter 2 References

[1] S.J.Choi, Z.Peng, Q.Yang, S.J.Choi, and P.D.Dapkus, “An eight-channel
demultiplexing switch array using vertically coupled active semiconductor
microdisk resonators”, IEEE Photonics Technology Letters, vol.16, no.11,
pp.2517-2519, 2004.

[2] K.D.Djordjev, S.J.Choi, S.J.Choi, P.D.Dapkus, “Microdisk tunable resonant
filters and switches”, IEEE Photonics Technology Letters, vol.14, no.6, pp.828-
830, 2002.

[3] S.J.Choi, K.D.Djordjev, S.J.Choi, and P.D.Dapkus, “Microdisk lasers vertically
coupled to output waveguides”, IEEE Photonics Technology Letters, vol.15,
no.10, pp.1330-1332, 2003.

25
Chapter 3 Loss-related analysis and experiment
In this chapter, the first key issue of the resonator system, loss, is discussed in
detail. We consider the loss within the resonator as well as the loss in the bus
waveguides. Different loss mechanisms are categorized and calculated according to
theory. Experiments and new designs aiming to reduce the loss are then presented.

3.1 Calculations of loss in resonators
Generally, the total loss in resonators is categorized into three different
mechanisms – material loss, scattering loss, and modal loss. We analyze each of
these loss mechanisms separately in the following sections.

3.1.1 Material loss
Since InP is almost transparent at wavelength 1.55 μm, the material loss of an
undoped passive device can be safely neglected. Once the material is doped, or
injected with free carriers by electrical or optical means, both the loss coefficient and
the refractive index are altered as the carrier concentration changes. This change is
generally categorized into three effects: bandfilling, bandgap shrinkage, and free-
carrier absorption [1]. The first two effects change interband absorptions and are
usually less important than the third intraband effect. In the Drude model, the free-
carrier absorption, or free-carrier plasma effect, is estimated as being directly
proportional to the concentration of electrons and holes [2].

26
32
23 *2 *2
0
4
ce e ch h
eN P
cn m m
λ
α
πεμ μ
⎛⎞ ΔΔ
Δ= +
⎜⎟
⎝⎠

where Δα is the change in loss coefficient, ΔN is the change in electron concentration,
ΔP is the change in hole concentration; e is the electronic charge, λ is the wavelength,
ε
o
is the permittivity of free space, n is the refractive index, m
ce
*
is the conductivity
effective mass of electrons, m
ch
*
is the conductivity effective mass of holes, μ
e
is the
electron mobility, and μ
h
is the hole mobility.
For InP at 1.55 μm wavelength (n=3.17, m
ce
*
=0.08m
o
, m
ch
*
=0.42m
o
,
μ
e
=5400cm
2
V
-1
s
-1
, μ
h
=200cm
2
V
-1
s
-1
[3]), the equation becomes
P N Δ × + Δ × ≈ Δ
− − 18 18
10 1 . 1 10 1 . 1 α , with Δα having units of cm
-1
and ΔN , ΔP having
units of cm
-3
. For InGaAsP of ~1eV bandgap (n=3.36, m
ce
*
=0.06m
o
, m
ch
*
=0.56m
o

[4], μ
e
=5200cm
2
V
-1
s
-1
, μ
h
=80cm
2
V
-1
s
-1
[5]), the relation is
P N Δ × + Δ × ≈ Δ
− − 18 18
10 5 . 1 10 0 . 2 α with the same units.
According to our MOCVD growth conditions, the undoped InP or InGaAsP
has a carrier concentration of less than 10
16
cm
-3
, corresponding to a negligible loss of
less than 0.01cm
-1
. The n- or p-type InP has 3~5×10
17
cm
-3
carrier concentration
leading to a loss on the order of 0.1cm
-1
. When a tuning current is applied to the
material, the loss will continue to increase with increasing number of carriers. Since
it is determined by the intrinsic properties of the semiconductor itself, the carrier-
induced material loss is always inevitable. The only controllable way to improve our
system is to minimize the background doping level during the MOCVD growth.

27
3.1.2 Scattering loss
Scattering loss mainly results from rough interfaces between the
semiconductor and the cladding material. Surface roughness can be generated
through lithography or dry etching during fabrication. Imperfection on the walls of
the waveguides or surface roughness results in energy being scattered out of the
resonant cavity and into the radiation field. This is often considered the major loss
mechanism in high-index-contrast optical waveguides. There have been several
approaches to theoretically analyze the problem. One of the most commonly used
model was devised by Marcuse [6], and is based on the coupling between guided and
radiation modes of the waveguide. Little et al. applied the volume current method to
account for both the scattering into the radiation modes and the back-reflections into
the counter-propagating mode [7]. Here, another simpler approach is exploited, with
the waveguide treated as a radiating antenna and the random wall imperfections as an
equivalent current source. Details of the modeling and derivation can be found in
reference [8]. The general loss coefficient is given by
()
3
22 22 0
0
0
() cos
4
scattering edge core clad clad
core
k
En n R kn d
n
π
α βθθ
π
=− −
∫
%

where E
edge
is the normalized optical field at the waveguide core/cladding interface
or the edge of the disk plane, n
core
, n
clad
are the refractive indices of the core and the
cladding materials respectively, k
o
=2π/ λ, β is the propagation constant, and ( ) R θ
%
is
the Fourier transform of R(u), where () ( ) ( ) Rufzfzu =+ is the autocorrelation
function of the random roughness function f(z) (see Figure 3.1 as an example).

28

Figure 3.1 Schematic drawing of a waveguide sidewall with random roughness.

If we characterize the waveguide roughness as having a Gaussian
autocorrelation function, then
2
2
2
( ) exp( )
u
Ru
L
σ
−
= , where σ
2
is the mean square
roughness and L is the correlation length. The corresponding loss coefficient is then
()
3
2
22 22 2 2 0
0
0
() exp cos 4
4
scattering edge core clad clad
core
k
En n L kn L d
n
π
α σπ β θ θ
π
⎡ ⎤
=− −−
⎣ ⎦
∫

Clearly the loss coefficient is proportional to the depth of roughness as
measured by σ
2
. It is also proportional to the index difference squared (n
core
2
-n
clad
2
)
2
.
Therefore, besides improving the fabrication quality, the scattering loss can also be
reduced by decreasing the index-contrast of the waveguide, e.g. using a higher index
cladding material. We also note that the dependence on the radius of the resonator is
mainly due to the optical field at the edge of the disk E
edge
. For smaller radii the
mode would be pushed further towards the edge of the waveguide, causing a higher
E
edge
and hence higher loss. Figure 3.2 shows the calculated loss coefficient as a
function of refractive index of the cladding material. The sidewall roughness and the
correlation length were both assumed to be 10nm so that the calculated values
corresponded reasonably well with our measured results, i.e. a conventional wafer-
bonded microdisk resonator with 10 μm radii had a total loss of 3~4cm
-1
, which we
believed to be mainly due to the scattering loss.
n
core
(waveguide layer)
z
f(z)
n
clad
(cladding layer)

29
1.01.5 2.02.5 3.0
0.1
1
10
σ = 10nm
L
c
= 10nm
Disk scattering loss, n
core
= 3.36, t=0.4um
[cm
-1
]
α
scatter
n
clad
R=1
R=3
R=5
R=8
R=10
R=15
R=20

Figure 3.2 Calculated scattering loss as a function of refractive index of the cladding
material.

3.1.3 Modal loss
An optical mode propagating inside a micro-resonator is referred to as a
whispering gallery mode. It corresponds to light traveling close to the inner
perimeter of the disk or ring, impinging on its edge with angles larger than the
critical angle of refraction. It is a leaky mode which radiates mostly in the lateral
direction. In the buried bus waveguide configuration there will be extra radiation in
the vertical direction. These two types of radiation are treated separately in the next
two sections. To verify the calculated loss coefficients, a commercially available
software, OlympIOs
*
, was also used to solve for the optical modes. The advantage of
this solver is that it can analyze bended waveguides and the modal index it gives is

*
“OlympIOs” is a product of C2V Corp. of the Netherlands.

30
complex, with the real part being the effective index of the propagation mode and the
imaginary part directly linked to the power loss coefficient α by { }
eff
n k Im 2
0
= α .

3.1.3.1 Bending loss
Bending loss is the most often considered loss mechanism in curved
waveguides. It originates from the lateral radiation of the whispering gallery mode.
Based on the classic Marcatili’s method [9], the wave equations are first solved in
the vertical direction as in slab waveguides, then in the transverse direction counting
in the curvature, ignoring a small percentage of the total power that flows through
the shaded areas as shown in Figure 3.3.

Figure 3.3 Schematic drawing of a curved waveguide.

The power attenuation due to the curvature, α
bend
, is then derived by
matching the field outside the guide, which is represented by a Hankel function of
complex order, to the fields inside the guide that are assumed unperturbed from a
straight guide. The final form of α
bend
is
z
x
y
w
n
core
n
clad
n
clad

R

31
2 / 1
2
0
2
2 2
0
4
4
2 / 3
2
0
0
2
0
2 / 1
2
0
3
2
0
2 / 1
2
2
1 2 1 1
2
1 1
3
exp
1 1
1
−
−
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
− + ⎟
⎠
⎞
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
− −
⎪
⎭
⎪
⎬
⎫
⎪
⎩
⎪
⎨
⎧
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+ ⎟
⎠
⎞
⎜
⎝
⎛
−
ℜ
− ⋅ ℜ
×
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎠
⎞
⎜
⎝
⎛
−
⎟
⎠
⎞
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
− =
π π
π
π π
α
W k
w n
W n W k
n
n
wk
c W k
W k
w
W
n
w k n
n
n
R
x
core
clad x
core
clad
x
x
x
core
x clad
core
clad
bend

where
()
2 / 1
2 2
0
2
clad core
n n
W
−
=
λ
,
()
3 2 2
0
2 2
0
3
2
W k k n k
R
y x core
− −
= ℜ
π
,
3
0
0
2
1
⎟
⎠
⎞
⎜
⎝
⎛
ℜ
=
W
w
w k
c
x
π
.
R is the outer radius of the curvature, w is the width of the waveguide, k
xo
is the
propagation constant in the x direction without curvature, and k
y
is the transverse
propagation constant in the y direction which does not depend on the curvature. The
calculated loss coefficient is plotted in Figure 3.4 (a).
0 102030 40506070
1E-10
1E-8
1E-6
1E-4
0.01
1
100
10000
0 102030 40506070
1E-10
1E-8
1E-6
1E-4
0.01
1
100
10000
Bending loss (WKB)
Radius [um]
Bending loss (Marcatili)
n_core=3.36
t = 0.4μm

α
bend
[cm
-1
]
Radius [um]
n_clad=1
n_clad=1.5
n_clad=2
n_clad=2.5
n_clad=3
n_core=3.36
t = 0.4μm
n_clad=1
n_clad=1.5
n_clad=2
n_clad=2.5
n_clad=3

(a) (b)
Figure 3.4 Bending loss as a function of the radius of the curvature calculated by
(a) Marcatili’s method and (b) WKB method.

32
As a comparison, an alternative method involving Wentzel-Kramers-
Brillouin (WKB) approximations was also considered [10]. It employs a conformal
transformation to the wave equations and then divides the structure into multilayers
where boundary conditions are matched among the layers. Detailed explanations and
derivations can be found in [10]. The results are plotted in Figure 3.4 (b).
Although there is a considerable difference in results calculated by the two
approaches, the overall trend is the same, i.e. the bending loss coefficient is
exponentially dependent on the radius,
R
bend
e
−
∝ α . Therefore, the most effective
way to reduce α
bend
is to increase the radius or the size of the resonator. Moreover,
the loss is also implicitly dependent on the core/cladding index-contrast. It tends to
decrease at a higher index-contrast – simply because the higher the index-contrast,
the more the light is confined inside the waveguide, and thus the less radiation there
will be. For an air-cladded microdisk the radius can be well below 10 μm and still
have negligible bending loss.
We notice an opposite dependence of the bending loss on the core/cladding
index-contrast as compared with the scattering loss mentioned earlier. It turns out
that a high index-contrast causes a higher scattering loss but lowers the bending loss
at the same time, and vice versa. In order to see the combined effects and find a
proper compromise between the two loss mechanisms, the sum of the two loss
coefficients was calculated and plotted in Figure 3.5. The combined loss decreased at
first for small n
clad
, or high index-contrasts, when bending loss was negligible and
scattering loss was dominant. After reaching a minimum it started to increase rapidly

33
with n
clad
, when bending loss overpowered scattering loss at lower and lower index-
contrasts. The optimal index-contrast for each minimal loss differed with the radii of
the resonators. Smaller radii required high index-contrasts to sustain the loss while
larger radii could tolerate much lower index-contrasts. As an example, when
R=10 μm, the optimal cladding material had a refractive index of 2.5~2.7 depending
on different methodologies used in the bending loss analysis.
1.0 1.5 2.0 2.5 3.0
0.1
1
10
100
1000
1.0 1.5 2.0 2.5 3.0
0.1
1
10
100
1000
R= 1um
R= 3um
R= 5um
R= 8um
R=10um
R=15um
R=20um

α
scatter
+ α
bend (WKB)
n
clad
n
clad
[cm
-1
]
[cm
-1
]
R= 1um
R= 3um
R= 5um
R= 8um
R=10um
R=15um
R=20um
α
scatter
+ α
bend (Marcatili)

(a) (b)
Figure 3.5 Scattering and bending combined loss as a function of refractive index of the
cladding, with the bending loss derived by both (a) Marcatili’s and (b) WKB methods.

3.1.3.2 Substrate leakage loss
Substrate leakage loss, also recognized as radiation loss in the vertical
direction, is often observed in SOI or GaAs-based devices where the substrate
material has the same highest refractive index as the guiding layer. In our
InP/InGaAsP waveguide configuration, although the guiding material itself has

34
slightly higher index than the substrate (n
core
=3.36 vs. n
sub
=3.17), the effective index
of the propagating whispering gallery mode is usually less than 3.1, lower than the
index of the substrate. As a result, light will be gradually attracted towards the
higher-index substrate when propagating close to it, which eventually leads to
additional power loss. In the wafer-bonded structure, no leakage is present because
the resonator mode is effectively blocked off from the substrate by air (n=1). In the
buried-bus structure, on the other hand, the guided mode is only 0.7~0.8µm above
the substrate (corresponding to the thickness of the coupling layer), thus light cannot
be effectively confined in the guiding layer.
A simplified model was employed to estimate the leakage loss of a straight
waveguide. When we only consider the field in the vertical direction, the fact that the
evanescent tail of the field intensity at the substrate level begins to propagate
downwards is analogous to the tunneling of light through a lossy barrier. In the WKB
approximation, the transmission coefficient (T) through the barrier is given by [11]
( )
etch y
y
y
y
t k exp dy k exp T 2 2
2
1
− = ⎟
⎠
⎞
⎜
⎝
⎛
− =
∫

where
2 2
0 eff InP y
n n k k − = is the propagation constant in the vertical direction, n
eff

is the effective modal index (a typical value of 3.08 was used in the calculation) and
t
etch
is the etching depth of the InP coupling layer into the substrate (Figure 3.6 (a)).
Since this “transmission” is actually a loss to the resonator, the distributed loss
coefficient, α
sub
, is related by ( ) T R exp
sub
− = ⋅ − 1 2π α , leading to the final expression

35
⎟
⎠
⎞
⎜
⎝
⎛
− − −
=
−
=
2 2
0
2 1
1
2
1
1
1
2
1
eff InP etch
sub
n n t k exp
ln
R T
ln
R π π
α .
Calculated results are plotted in Figure 3.6 (b).

Figure 3.6 (a) Cross-sectional view of a straight waveguide;
(b) Estimated substrate leakage loss by WKB method.

We can clearly see that the leakage loss was exponentially dependent on the
etching depth. Meanwhile, as the radius increased, n
eff
also increased substantially so
that the term
2 2
eff InP
n n − in the exponential began to dominate the 1/R term,
leading to a higher loss. However, this was only valid for such small-size resonators,
where a small amount of change in radius could cause a big shift in the effective
index. For larger resonators, on the other hand, the effective index varied much more
InP
InGaAs
1
t
etch

0.4
1.0
In
y
1

y
2

Vertical
field
(a) (b)
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0.01
0.1
1
10
100
R=5μm, n
eff
~3.01
R=10μm, n
eff
~3.08
R=15μm, n
eff
~3.12
R=20μm, n
eff
~3.14
Estimated substrate leakage loss

α
sub
[cm
-1
]
Etching depth of lower InP cladding t
etch
[μm]

36
slowly with the radius. We would then expect the substrate leakage loss to decrease
at larger radii with the same amount of etching depth.
We had also ignored the effect of lateral cladding material. In fact, higher
cladding index would lead to weaker confinement in the lateral direction but possibly
a higher modal index. The closer n
eff
was to the index of the substrate n
InP
, the less
leakage there would be in the vertical direction.

3.1.3.3 Total modal loss
The calculations discussed above assumed the bending loss and substrate
leakage were independent. To verify our conclusions, OlympIOs was then used to
directly solve for the whispering gallery mode. Figure 3.7 includes plots of modal
losses as functions of the refractive index of the lateral cladding material, the etching
depth of the InP coupling layer, and the radius of the resonator. The modal loss
shown here did not take material loss or scattering loss into account. Therefore, it
should represent the combined effect of bending and substrate leakage. We see from
plot (a) that the dependence on n
clad
became significant only when it had increased
above a certain value where bending loss became dominant. This critical value
depended on the radius – it increased with a larger radius indicating a growing
tolerance in the core/cladding index-contrast. In plot (b) the loss coefficient showed
an exponential dependence on the etching depth, which agreed with our earlier
calculations. The larger the disk, the less etching that was required to achieve the
same amount of loss as in smaller disks. Figure 3.7(c) shows the combined effect of

37
several variables. By looking at curves having the same etching depth but different
index-contrast, we can see that t
etch
was more influential than n
clad
for larger-sized
resonators. As the radius decreased, n
clad
became crucial. Figure 3.7(d) is an example
of a typical modal field generated by the mode solver, OlympIOs.
1.01.5 2.02.5 3.0
0.1
1
10
100
1000
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
0.01
0.1
1
10
100
1000
Loss of a micro-disk, R=10μm

Modal loss [cm
-1
]
n
clad
t_etch=0.7μm
t_etch=1.0μm
t_etch=1.3μm
Loss of a micro-disk, n
clad
=1
Modal loss [cm
-1
]
t
etch
[μm]
R= 5μm
R=10μm
R=15μm
R=20μm

(a) (b)

(c) (d)
Figure 3.7 Modal loss calculated by OlympIOs as functions of (a) refractive index of the
lateral cladding; (b) etching depth of the InP coupling layer; and (c) radius.
(d) is the cross-sectional view of a typical modal field generated by the solver
(n
eff
=3.08, α=13.7cm
-1
, for parameters R=10 μm, n
clad
=1, t
etch
=0.7 μm).

0 5 10 15 20 25 30
0.1
1
10
100
1000
n_clad=1, t_etch=0.7μm
n_clad=1, t_etch=1.3μm
n_clad=2.5, t_etch=0.7μm
n_clad=2.5, t_etch=1.3μm
Loss of a micro-disk

Modal loss [cm
-1
]
Radius [μm]

38
3.1.4 Summary
The dependence of different loss mechanisms on various parameters is listed
in Table 3.1. The effects on the total loss, α
total
, are also included. Overall, we would
want low carrier concentration, large radius, large etching depth and a compromised
cladding index to reduce the total loss. Exactly which values are to be used will
depend on other requirements such as system specifications.
Table 3.1 A summary of different loss sources with respect to different parameters.
α
material
α
scatter
α
bend
α
sub_leak
α
total

ΔN
( ΔP)
ΔN( ΔP) ↓
Î α
material
↓
() [] P N Δ Δ ∝
No effect. No effect. No effect.
ΔN( ΔP) ↓
Î α
total
↓
( ) [] P N Δ Δ ∝
R No effect. R ↑ Î α
scatter
↓
R ↑ Î α
bend
↓
( ) [ ] R exp − ∝
R ↑ Î α
sub_leak
↑
for small disks;
R ↑ Î α
sub_leak
↓
for large disks.
Most likely
R ↑ Î α
total
↓
n
clad
No effect.
n
clad
↑ Î α
scatter
↓
[
()
2
2 2
clad core
n n − ∝
]
n
clad
↓ Î α
bend
↓ n
clad
↑ Î α
sub_leak
↓
Depends.
(optimal value
exists)
t
etch
No effect. No effect. No effect.
t
etch
↑ Î α
sub_leakl
↓
( ) [ ]
etch
t exp − ∝
t
etch
↑ Î α
total
↓
() []
etch
t exp − ∝

We here emphasize that in our theoretical analysis, the absolute values of the
results should be treated with less attention than the general trends and dependence
on the variables. Hence, the fact that the calculated results vary with the applied
methodologies or approaches should not be a hindering factor. The simulated results
would only serve as a guideline when designing real devices.

39
3.2 Experiments aiming at reducing resonator loss
After analyzing different sources of resonator loss, efforts have been made to
reduce each individual loss. To balance scattering loss and bending loss, we searched
for cladding materials having a refractive index of around 2.5. An amorphous silicon
nitride dielectric film was explored for this purpose. A partially oxidized indium
aluminum oxide was also considered. On the other hand, to reduce the substrate
leakage loss in BH-bus devices, we investigated an approach which involved
inserting a layer of low-index material such as oxide underneath the resonator mode.
An alternative solution of bi-level etching was also proposed.

3.2.1 a-Si
x
N
y
:H deposition for balanced scattering and bending loss
Silicon nitride films deposited by a variety of chemical vapor deposition
(CVD) techniques, including plasma-enhanced CVD (PECVD), have a wide range of
applications in microelectronics as passivation layers, diffusion barriers, and
insulators. In most cases, the plasma deposited films are non-stoichiometric as Si
3
N
4
,
but generally referred to as hydrogenated amorphous silicon nitride, a-Si
x
N
y
:H or a-
Si
x
N
y
H
z
. Studies have shown that the physical, electrical, and optical properties of
the a-Si
x
N
y
:H are strongly dependent on the film composition, i.e. the [Si]/[N]
atomic ratio and the hydrogen content [12], which is determined by the deposition
parameters and the geometric configuration of the plasma reactor. With respect to the
refractive index of the film, the one property that we are interested in, a wide
variation from 1.5 to 3.5 at 1500nm has been reported in [13]. It is believed that

40
higher [Si]/[N] ratio leads to a lower bandgap and a higher refractive index in the
film. The behavior is mostly explained in terms of different concentrations of N-H
and Si-H bonds, where hydrogen atoms are not intentionally added, but are
introduced as decomposition products from the source gases, usually silane (SiH
4
)
and ammonia (NH
3
). The specific relationship between the refractive index and the
[Si]/[N] ratio differs according to source in the literature (e.g. [12, 14, 15, 16]), but
the underlying interpretation is always intuitively the same – by varying the
deposition conditions, it is possible to continuously change the Si content of silicon
nitrides from a-Si, having a refractive index of 3.4, to the stoichiometric Si
3
N
4
,
having a refractive index of 1.9.
In our own experiment, a-Si
x
N
y
:H film was deposited in a PECVD system
with SiH
4
/NH
3
/N
2
gas sources. Figure 3.8 shows several examples of optical
waveguides before and after deposition.

(a)
Figure 3.8 SEM pictures of waveguides (a) before a-Si
x
N
y
:H deposition and
(b) after 20min deposition.

41
(Figure 3.8, Continued)

(b)

Different values for the flow rates, pressure, temperature, and RF power were
tested. The refractive indices were extracted from ellipsometry measurements and
data fitted with the Cauchy model
*
. The results ranged from 1.9 to 2.8 at 1550nm
wavelength. However, in some cases the mean squared error (MSE), an estimator of
quantifying the difference between the measured curve and the fitted curve, was
greater than 10 indicating a poor fit. The highly amorphous characteristic of the film
could be one of the reasons. The detailed results are listed in Table 3.2. Some

*
Cauchy model:
4 2
λ λ C B A n + + = . A, B and C are parameters to be fitted; λ is the wavelength.

42
conditions were tested more than once to verify the reproducibility. The conditions
that produced the targeted results are highlighted. Note that the actual flow rates
were estimated from the scales of the MFCs and the compositions of the gas sources,
i.e. SiH
4
source was 2%, NH
3
5%, N
2
100%; the full scales of their MFCs were
400sccm, 100sccm, and 500sccm respectively. The targeted 2.5 refractive index
could be achieved repeatedly at 220°C, 600mTorr, 30W RF power, with
SiH
4
/NH
3
/N
2
=77/2/0 which was the highest possible SiH
4
/NH
3
flow rate setting in
our PECVD system. The deposition rate was around 55nm/min.
Table 3.2 Summary of a-Si
x
N
y
:H deposition tests by PECVD.
Run
#
Temperature
[°C]
Pressure
[mTorr]
RF
power
[W]
SiH
4
/NH
3
/N
2
flow rate
settings
SiH
4
/NH
3
/N
2
actual flow
rate [sccm]
Deposition
rate
[nm/min]
Fitted
refractive
index
MSE
1 275 440 30 40/20/60 3.2/1.0/476 9 1.93 1.8
2 275 440 30 60/30/0 4.8/1.5/0 17.5 1.95 10
3 220 600 30 60/30/0 4.8/1.5/0 44.5 1.91 13.5
4 220 600 30 77/10/0 6.2/0.5/0 44.5 2.17 19.1
5 220 600 30 77/5/0 6.2/0.25/0 44 2.18 21.6
6 220 600 30 77/2/0 6.2/0.1/0 56 2.54 10.9
7 275 600 30 77/2/0 6.2/0.1/0 92 2.51 12
8 220 600 30 77/2/0 6.2/0.1/0 57 2.50 10.4
9 220 330 30 77/2/0 6.2/0.1/0 88 2.52 8.9
10 220 800 30 77/2/0 6.2/0.1/0 55 2.73 5.5
11 220 600 30 77/3/0 6.2/0.15/0 64 2.31 12.6
12 220 600 30 77/4/0 6.2/0.2/0 59 2.38 7.1
13 220 400 30 77/2/0 6.2/0.1/0 63 2.46 10.4
14 220 500 30 77/2/0 6.2/0.1/0 73 2.43 3.9

43
(Table 3.2, Continued)
Run
#
Temperature
[°C]
Pressure
[mTorr]
RF
power
[W]
SiH
4
/NH
3
/N
2
flow rate
settings
SiH
4
/NH
3
/N
2
actual flow
rate [sccm]
Deposition
rate
[nm/min]
Fitted
refractive
index
MSE
15 220 600 20 77/2/0 6.2/0.1/0 67 2.22 12.5
16 220 600 40 77/2/0 6.2/0.1/0 54 2.81 5.1
17 220 600 30 77/2/0 6.2/0.1/0 55 2.49 9.3
18 220 600 30 77/2/0 6.2/0.1/0 70 2.26 14.7
19 220 600 30 77/2/0 6.2/0.1/0 52.7 2.19 11.3
20 220 600 30 77/2/0 6.2/0.1/0 55 2.51 4.7
21 220 600 40 77/2/0 6.2/0.1/0 89 2.69 7.5
22 220 600 50 77/2/0 6.2/0.1/0 85 2.19 5.2
23 220 600 40 77/2/0 6.2/0.1/0 56 2.32 12
24 220 600 30 77/2/0 6.2/0.1/0 59 2.39 3.4
25 220 700 30 77/2/0 6.2/0.1/0 64 2.45 11
26 220 800 30 77/2/0 6.2/0.1/0 65 2.42 3.7
27 220 600 30 77/2/0 6.2/0.1/0 46 2.71 4
28 220 600 30 77/2/0 6.2/0.1/0 48 2.54 3.9
29 220 600 30 77/5/0 6.2/0.25/0 54 2.44 5.4
30 220 600 30 77/10/0 6.2/0.5/0 60 2.27 9.3

The experiment indicates that the SiH
4
/NH
3
flow rate ratio was indeed the
dominant factor in influencing the refractive index of the deposited film. Also, the
higher the process pressure, the higher the growth rate. Figure 3.9 plots the refractive
index as a function of SiH
4
/NH
3
flow rate ratio without taking into account the other
parameters in the depositions. The following linear fit gives a relation

44
[ ]
[]
3
4
008 . 0 019 . 2
NH
SiH
n × + =
Thus, to get a refractive index of 2.5, the SiH
4
/NH
3
flow rate ratio has to be greater
than 60. Note that this number is only valid for the specific PECVD system in use.
As stated earlier, the properties of the film depend strongly on the configuration of
the plasma reactor. In addition, the flow rate ratio in the above expression is related,
but not necessarily equal, to the atomic ratio of Si and N. To determine the absolute
value of [Si]/[N] in the film, Rutherford backscattering spectroscopy (RBS) or Auger
electron spectroscopy (AES) can be used. The [Si-H]/[N-H] bond density ratio,
which is a function of [Si]/[N], is usually found by infrared absorption spectroscopy.
0 10 2030 4050 6070
1.8
2.0
2.2
2.4
2.6
2.8

Refractive index of a-SiN:H
Flow rate ratio [SiH
4
] / [NH
3
]
Measured
Linear fit
n = 2.019 + 0.008 * [SiH
4
]/[NH
3
]

Figure 3.9 Plot of refractive index of the a-Si
x
N
y
:H film as a function of gas flow ratio of
SiH
4
and NH
3
.

As we can see from the plot, the results were not perfectly consistent from run
to run, partly because the PECVD system in use did not have a high vacuum (base

45
pressure around 40mTorr) and each time the chamber was opened the system could
be contaminated. There was no plasma cleaning process available and the alternative
manual cleaning could not guarantee the remove of all the deposition residues.
Apart from the refractive index, we must also ensure that the material can be
deposited inside the narrow gaps that exist in our system between the laterally
coupled ring and bus waveguides, or between mutually coupled rings. After many
test runs with various deposition conditions, we concluded that this was the main
challenge of this technique. The deposition favored the top as apposed to the
sidewalls of the mesas. Therefore, there was always a void formed in the middle of
the gap, as shown in the Figure 3.10 below. Even gaps with depth-to-width ratios
lower than 1 could not be filled completely.

Figure 3.10 SEM pictures showing the incomplete gap-filling of the deposition.

We also used slower growth rates in an effort to minimize the disparity in the
growth on different planes, but this approach did not solve the problem (Figure 3.11).

46

Figure 3.11 a-Si
x
N
y
:H deposited at lower rate still could not completely fill the gap
(220°C, 330mTorr, 60W, SiH
4
/NH
3
=77/2, 30min).

In the literature it has been demonstrated that a combined deposition/etchback
process with high density plasma was successful in producing good quality materials
with excellent trench filling abilities [17]. This is essentially a PECVD process with
a high ion density in the discharge such that a high quality dielectric can be deposited
at high deposition rates. During the deposition, the high density, high energy ions
bombard the substrate providing a sputtering effect such that the deposition profile
can be modified to reduce the chance of void formation. Various reactors, such as
ECR or ICP, can be used for this process. The gas chemistries are also different than
simple PECVD processes. Detailed explanations and discussions can be found in
[17].
Another concern for the deposited a-Si
x
N
y
:H film is its robustness. Since
amorphous materials are meta-stable, they can degrade if operated at high current
densities and at high temperatures. It was later proved that our film could not stand
high heat due to thermal stress. It cracked at 430°C which was the temperature of our
annealing process for the Ohmic contact formation.

47
In conclusion, the a-Si
x
N
y
:H thin film with the desired refractive index, 2.5,
could be reproducibly deposited with our PECVD system. However, the dielectric
material was unable to completely fill high depth-to-width ratio trenches or gaps thus
leaving trapped voids inside the gaps. The unstable nature of the amorphous film
also rendered it impractical for micro-resonator applications.

3.2.2 Oxidation of InAlAs for isolating substrate leakage
3.2.2.1 Design and simulations
Following the discussions in 3.1.3.2, one of the ways to reduce the substrate
leakage loss is to embed a low-refractive index material under the whispering gallery
mode to isolate it from leaking into the substrate. Since most III-V semiconductors
tend to have high refractive indices, we turned to low-index dielectrics such as
oxides. We also focused on native oxides because of their easy integration. In the
InP-based material system, efforts have been to find good insulators for current
confinement in edge-emitting lasers as well as FET gates. In
0.52
Al
0.48
As or InAlAs
*
,
with an aluminum content of 48% when lattice matched to InP, is a viable material
for native oxidation.
The probable mechanism for the oxidation is that the group V arsenic atoms
in InAlAs are predominantly diffused out in the form of AsH
3
. Various arsenic
oxides (e.g. As
2
O
3
) may form at the same time, probably to a lesser extent, but are

*
“InAlAs” will be used henceforth in place of “In
0.52
Al
0.48
As” for simplicity.

48
also quickly diffused out due to their high vapor pressures. Aluminum has a strong
affinity for oxygen thus forming the dominant oxide, Al
2
O
3
. The indium in InAlAs
remains in the films as excess atoms or indium oxides, which form with much lower
probability than aluminum oxide because of their lower enthalpies and lower
oxidation potentials [18]. It is generally believed that the oxidation is a diffusion-
limited process in which a dense oxide inhibits the diffusion of the oxidizing species,
causing the oxidation rate to follow a square-root-of-time dependence [19,20].
Having chosen the material, we conducted a comprehensive set of simulations
on the disk mode with the purpose of assessing the optimal configuration of the
InAlAs and the corresponding oxide. We proposed to have a layer of InAlAs
embedded in the substrate, either above or below the bus core layer, selectively
oxidizing it in order to achieve a certain amount of low-index oxide underneath the
disk core layer. The closer this oxide is to the disk core, the more effective the mode
isolation will be. If the InAlAs is below the bus core layer, the oxide is at least 1.2 μm
away from the disk core (0.8 μm coupling layer + 0.4 μm bus core layer). Simulations
showed it was too far away to affect the disk mode. If we move the InAlAs upward
so that it overlaps with the bus core layer to some extent, meaning that the bus
waveguides are formed first and then buried in InAlAs, we must use planarization
overgrowth to form the upper disk layers. So far, we have limited experience in
planarizing InP and do not know how difficult it would be to planarize InAlAs. (We
do not have the ability to grow InAlAs by ourselves at the moment.)

49
A third alternative is to place the InAlAs above the bus core, i.e. inside the
coupling layer. Since the refractive index of InAlAs is 3.2, close to that of InP – 3.17,
it could be used as the coupling material replacing part of the InP. However, the
thickness of InAlAs is then predetermined to be less than 0.8 μm – the thickness of
the coupling layer, which might limit its ability to isolate the mode. The simulation
model on such a design is shown in Figure 3.12. A 0.1 μm thin InP layer was left
above the oxide to protect the InAlAs in the center from vertical oxidation. An extra
step of lithography and etching was required to expose the InAlAs from the side.

Figure 3.12 Cross-sectional view of the simulated structure (distances are in μm).

There were mainly two parameters to be determined – the thickness and the
effective width of the oxide, depicted in the figure as t and w respectively. Other
parameters and dimensions were set to the typical values of a conventional micro-
0.4
InP
1
1
InP substrate
Air
R=12
t
w
InP
InGaAsP
2
0.8-t
(bus core)
InAlAs
Oxide
0.1

50
ring resonator. The position of the bus waveguide is shown in dashed lines. It was
not included in the simulation. The modal loss calculated by OlympIOs as functions
of t and w is shown in Figure 3.13.
0.10.2 0.30.4 0.5 0.6
0.01
0.1
1
10
0.2 0.4 0.6 0.8 1.0
1E-3
0.01
0.1
1
10
Modal loss [1/cm]
InP thickness (0.8μm-t)
0.7 0.6 0.5 0.4 0.3 0.2
InAlAs/oxide thickness (t) [μm]

Modal loss [1/cm]
w=0.1um
w=0.2um
w=0.3um
w=0.4um
w=0.5um
t=0.2um
t=0.3um
t=0.4um
t=0.5um
Effective oxide width (w) [μm]

(a) (b)
Figure 3.13 Calculated modal loss as a function of: (a) oxide thickness; (b) oxide width.

As expected, larger t or w led to lower loss. However, when taking the tuning
mechanism into consideration, more oxide equals less current-flow path, which
poses a series of problems for active devices. What we were looking for then, was a
compromised solution with both lower modal loss and reasonably wide current path.
Following such a design rule, t=0.4 μm and w=0.4 μm were chosen for the ring-only
regions. The loss was 0.22cm
-1
, about 50 times lower than the original design
without any oxide (12.7cm
-1
). Figure 3.14 shows the calculated disk mode at such
configurations, along with the mode without oxide for comparison.

51

(a) (b)
Figure 3.14 Calculated modal fields of (a) old design without oxide and (b) new design
with oxide.

As for the bus-ring coupling region, w=0 was required to ensure the bus-to-
ring coupling was not affected by the presence of the oxide. The oxidation mask had
to be carefully designed to allow different w at different locations. A precise control
of the oxidation depth was also crucial in fabricating these devices.

3.2.2.2 Oxidation tests
(a) Surface oxidation
To achieve selective formation of oxide underneath the disk core layer,
several oxidation tests of InAlAs were performed. As a first step, surface or vertical
oxidation was tested on samples with a 0.145 μm thick InAlAs layer grown on an InP
substrate
*
. Wet oxidation was carried out in a horizontal quartz tube in a three-zone

*
All InAlAs-related growth was done by the former T-NETWORKS INC.
Without oxide: α=12.7cm
-1
With oxide, t=w=0.4 μm: α=0.22cm
-1

52
furnace. Nitrogen gas passed through a water bubbler maintained at 88°C and carried
the water vapor into the furnace. The N
2
flow was regulated at 3400sccm. The
oxidation temperatures were chosen to be around 500°C to allow for an acceptable
oxidation rate while limiting the thermal degradation of the materials involved. Later
experiment showed it should be lower than 500°C to avoid phosphorus-dissociation.
(This will be discussed later in this section.) The thickness and refractive index of the
oxidized film were then measured by ellipsometry. Table 3.3 is a summary of the test
results. It should be noted that the fully oxidized layer was thinner than the original
0.145 μm due to the well-known oxidation-induced layer shrinkage effect. The
vertical oxidation rate was roughly estimated to be 0.2 μm/hr at 525°C, 0.08 μm/hr at
500°C, and 0.025 μm/hr at 475°C, which were quite low as a result of low Al-
concentration in the InAlAs.
Table 3.3 Summary of surface oxidation tests with thickness and refractive index of the
oxide measured by ellipsometry.
Temperature
[°C]
Time
[hour]
Thickness of
oxide [ μm]
Refractive index
of the oxide
Notes
525
2 0.138 1.75 Completely oxidized.
1 0.131 1.81 Somewhere in between.
0.5 0.105 2.06 Partially oxidized.
500
3 0.132 1.80 Completely oxidized.
2 0.126 1.89 Somewhere in between.
1 0.082 2.09 Partially oxidized.
475
6 0.130 1.95 Completely oxidized.
3 0.076 2.10 Partially oxidized.

53
Judging from the measured refractive indices of fully oxidized samples, we
confirmed that the main composition of the films was Al
2
O
3
, which had an index of
around 1.7. We also took the incompletely oxidized samples into account because we
hoped to find materials having refractive index close to 2.5 for the application of the
lateral cladding materials of the micro-resonators (see 3.1.3.1 for details). In a
previous work, one group has demonstrated the oxidized InAlAs having a 2.43 index
of refraction [21]. Another group claimed that the index can be as high as 2.5 if the
InAlAs layer is incompletely oxidized [18]. They also stated that, “if the entire
InAlAs epitaxial layer is not completely consumed by the oxidation process, the
resulting oxide film will be of poor electrical and optical quality”. In our case
however, the highest index of refraction we could achieve experimentally was only
2.1 (Figure 3.15).
01 23 45 6
1.7
1.8
1.9
2.0
2.1
2.2
Measured refractive index of the oxide

n (oxide)
Surface oxidation time [hour]
525C
500C
475C

Figure 3.15 Plot of refractive indices of the oxide at different oxidation temperatures
measured by ellipsometry.

54
Our results agreed reasonably well with reference [20], in which the authors
analyzed the exact composition of the oxide with techniques such as Auger electron
spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS). According to their
results, “the oxide produced on InAlAs is composed mainly of In
2
O
3
and Al
2
O
3
, with
the amount of Al
2
O
3
tending to increase with increasing temperature”. Knowing that
the refractive index of In
2
O
3
is ~2.0, higher than that of Al
2
O
3
, their observation
suggests that the refractive index of the oxide should decrease with increasing
temperature. This is consistent with what we observed in Figure 3.15.

(b) Lateral oxidation
Since the process of completely oxidizing InAlAs was unreliable, this
material was no longer considered as a candidate for the ideal cladding material of
the micro-resonators. We would therefore limit our interest to its oxide properties for
the purpose of blocking substrate leakage of the whispering gallery mode.

Figure 3.16 Schematic drawing of the cross-section view of the tested structure.

InP
QW’s 0.4 μm
InP 0.4 μm
InAlAs 0.4 μm
7 μm
Wet oxidation
InAlAs oxide oxide
Oxidation
depth
QW’s 0.4 μm
InP 0.4 μm
7 μm
Oxidation
depth

55

(a) 1hr at 450°C (b) 1hr at 475°C

(c) 4hr at 450°C (d) 4hr at 475°C
Figure 3.17 Example SEM pictures of partially oxidized InAlAs layers.

To calibrate the oxidation behavior according to the design, we prepared
samples with quantum well (QW) layers on top of InAlAs and patterned straight
waveguides (Figure 3.16) simulating the microdisk configuration as designed in the
previous section. Examples of partially oxidized InAlAs layers are shown in Figure
3.17. The samples were stain-etched to reveal the oxidation fronts. At shorter
oxidation times such as 1 or 2 hours, the oxide/semiconductor interfaces looked quite
clear. As time went by only a few samples appeared to have abrupt oxidation fronts
as in Figure 3.17 (d) while most others had tapered fronts as shown in Figure 3.17 (c).
If this could not be attributed to bad cleaving, then it would seem that the oxidation

56
became harder and harder as the interface moved deeper into the un-oxidized
material. The tapered shape might be an indication of non-uniform or incomplete
oxidation at the oxide/semiconductor interface. Longer time or proper adjustment of
oxidation conditions might be helpful to ensure the oxidation is complete for the
length of interest according to design.
Due to the low concentration of Al in InAlAs and limited amount of material
available for oxidation (0.4 μm thick), the oxidation rate was relatively low (Figure
3.18). At 475°C the oxidation rate was about 0.48 μm/hr while at the lower 450°C it
was only 0.16 μm/hr. (Nevertheless, the numbers remained comparable to the results
in [20].) Therefore, if we were to keep the design value for the oxidation depth of
2.4 μm, the real sample would need to be oxidized for almost 5 hours at 475°C.
123 4
0.0
0.5
1.0
1.5
2.0
475
o
C (~0.48μm/hr)
450
o
C (~0.16μm/hr)
Oxidation rate of InAlAs (0.4μm-thick )

Oxidation depth [ μm ]
Oxidation time [hour]

Figure 3.18 Estimated lateral oxidation rate of 0.4 μm thick InAlAs layer.

It is worth mentioning that, during the lateral oxidation test, a phosphorus-
dissociation phenomenon was observed. At first we found some test samples that
suffered a hazy-surface problem after the oxidation. In the SEM we saw needle-

57
shaped microstructures densely distributed both on top of the waveguide mesas and
on the surface of the wafer. Since the patterned samples had most of the InP
substrate exposed to the wet N
2
during oxidation, we believed this was the result of
phosphorus dissociation. It is known that at temperatures higher than 350°C, InP
begins to decompose and phosphorus atoms start to leave the surface. The remaining
indium atoms become “droplets” on the surface and they tend to migrate at high
temperatures to form “islands”. The indium is then oxidized into In
2
O
3
, which has a
pseudo-periodic crystal structure, and the “islands” finally grow into “needles”. In
the literature, there are several ways to suppress the phosphorus dissociation, such as
creating an excess phosphorus ambient [22], sulfurizing the InP surface [22], or
capping the samples with an InP wafer [23].
In our own experiment, we noted that this phenomenon only occurred in
samples that we had soaked in BOE in an attempt to remove the SiN
x
mask before
the oxidation, while others without pre-BOE treatment remained shiny throughout
the oxidation. We concluded that BOE had removed a thin protection layer off the
InP surface. Further experiment suggested that the protection layer was most likely
the native oxide of InP formed during the O
2
plasma cleaning process. Consequently,
we could still use BOE-treatment as long as an O
2
plasma step was added
immediately before the oxidation. We found that 5min standard oxygen cleaning in
RIE was sufficient for this purpose.

58
3.2.2.3 Possible degradation in QW layer by CL measurement
Due to the long time and high temperature oxidation process, concerns about
the possible damages to the QW layer above the InAlAs arose. To analyze this
problem quantitatively, cathodoluminescence (CL) method was applied. Both
“spatial CL”, which measures the light intensity of a fixed spot on the sample at
different wavelengths, and “line-scan CL”, which measures the light intensity along
a line on the sample (e.g. across the mesa top) at a fixed wavelength, were performed
on samples before and after the oxidation.

Figure 3.19 (a) Illustration of measured spots; (b) Spatial CL measurement on those spots.

1460 1480 1500 1520 1540
0
200
400
600
0
200
400
600
800
center
1μm off
2μm off
3μm off

after oxidation
(4hr, 475
o
C)
Wavelength [nm]
CL Intensity (a.u.)
center
1μm off
2μm off
3μm off
before oxidation

Spatial CL on mesa top
CL Intensity (a.u.)
center
1 μm off-center
2 μm off-center
3 μm off-center
Mesa
7 μm
(a)
(b)

59
The spatial CL result is shown in Figure 3.19. We see that even without any
furnace treatment the intensity profile could not follow the rectangular shape of the
mesa very well, i.e. the light intensity was always lower at the edges than at the
center. This is partly because the carriers are depleted at the air/semiconductor
interface. Meanwhile, the prior dry etching process can also cause surface defects
that form trap levels leading to non-radiative recombination. In both these cases, the
difference in CL intensity before and after oxidation indicates that there was indeed
degradation in the QW light intensity after the oxidation process. This degradation
was especially significant at the edge of the mesa where the oxidation actually
occurred.
02468 10 12
0
200
400
600
800
0
100
200
300
400
500
02468 10 12
0
200
400
600
800
Position [μm]
CL Intensity (a.u.)
Approx.
oxidation
front
Line-scan CL at 1500nm

Intensity after oxidation (a.u.)
Intensity before oxidation (a.u.)
Position [ μm ]
Ideal
mesa
profile

Approx.
oxidation
front
Before
After
Ideal
mesa
profile
Line-scan CL at 1500nm

(a) (b)
Figure 3.20 Line-scan CL measurement across the mesa top before and after oxidation. (a)
is plotted using one scale; (b) is the same data re-scaled to have the same peak intensities.

The line-scan CL measured across the mesa top as illustrated in Figure 3.20(a)
shows the same intensity drop after the oxidation. To minimize the measurement-
induced error (e.g. different waveguides used in the measurement before and after

60
oxidation, or signal noise), we could assume there was no intensity degradation and
re-scaled the data to show the same peak intensity as in Figure 3.20(b). By doing so
we observed a lateral shrinkage in the profile. The intensity almost dropped to zero at
the edge of the mesa. This implied that the quality of the QW material right above
the oxide was significantly degraded.
Our explanation was that, during the oxidation, the thickness of the InAlAs
layer decreased inducing a stress in the upper QW layer. We then took a few TEM
measurements on the cross-section of the sample but did not find any dislocations
[24]. Hence, the degradation could be due to non-radiative carrier recombination at
the interface of the InP and the oxide layer. As a comparison, we did the same
experiment on two samples with the same QW structure but without the InAlAs layer.
In this way we were able to see the pure effect that heating in the furnace had on the
material. The results are shown in Figure 3.21. One sample was wet etched to form
the waveguide mesas. The other was dry etched by BCl
3
plasma, just like all the
other samples in the previous oxidation tests. The plots reveal a lateral shrinkage in
the intensity profile similar to the previous results. This then suggested that the long-
time heating step had caused the problem, regardless of the presence of the oxide.

61
02 46 8 10 12
0
200
400
600
800
1000
0
50
100
150
200
0 246 8 10 12
0
200
400
600
800
1000
0
50
100
150
200
1535 1527 CL Linescan at / nm (Dry etching)
Intensity before heating (a.u.)
Intensity after heating (a.u.)
Position [μm]
1530 1535 CL Linescan at / nm (Wet etching)
Position [μm]
Intensity after heating (a.u.)
Intensity before heating (a.u.)
width of
mesa top
~ 6μm

width of
mesa top
~ 7μm

(a) (b)
Figure 3.21 Line-scan CL results of QW-only samples before and after furnace treatment.
The waveguides were formed by (a) wet etching and (b) dry etching, respectively.

Hence, we would have to find a way to reduce the oxidation time in order for
this approach to become practical for our purposes. Of course, we should not rely on
just one type of measurement. There were also many uncertainties in the experiment
that prevented us from reaching a decisive conclusion. Other methods of testing the
quality of the material should be carried out as well. Furthermore, it would be much
more straightforward to build edge-emitting lasers on similar structures. This would
make it possible for us to directly assess the performance of the laser in order to
determine whether the oxidation process really contributed to the degradation.

3.2.2.4 Summary
In order to reduce substrate leakage loss, we proposed embedding a low-
index oxide layer underneath the disk mode. InAlAs could be a strong candidate

62
because of its ready integration within the InP system and the native oxide it could
provide. Simulations showed that significant reduction in modal loss could be
achieved when a 0.4 μm thick oxide was placed right above the bus waveguide layer.
However, the design required precise control over the lateral oxidation process,
which later proved to be non-trivial. Meanwhile, the low Al-content in the InAlAs
demanded a long-time, high-temperature process in the furnace. Evidence of QW
degradation after the oxidation was observed in CL measurement. If indeed we do
have degradation in the QW layer, it would introduce a significant drawback in our
approach.

3.2.3 New design: bi-level etching
Since the method of inserting a low-index material underneath the resonator
introduced many difficulties during fabrication, we considered other approaches that
would reduce the substrate leakage loss. Earlier calculations have indicated that the
leakage loss can be reduced considerably by increasing the distance between the
propagating optical mode and the substrate. Theoretically, we could essentially
eliminate the leakage by deeply etching the disk mesas. However, the vertical-
coupling geometry pre-determines the etching depth to be just above the bus core
layer. It is then desired to develop a bi-level etching process in which the etching
depth in the bus-ring coupling region is shallow while the rest is deep, as illustrated
in Figure 3.22.

63

Figure 3.22 Schematic drawing and cross-section view of a bi-level etched micro-ring
resonator vertically coupled with a buried bus waveguide.

To achieve this, we could deposit another SiN
x
mask layer after the first etch,
align and define a second mask covering the bus waveguide as well as the ring in the
non-coupling region, then etch again. Obviously the required alignment is critical
and difficult because we don’t want any physical steps on the sidewall of resonators
due to misalignment. One possible solution would be to preserve the original ring
mask after the first etch, define the second mask on top and etch again. Alternatively,
we could use double masks to define different patterns in advance so that the mesa
etching could be done just once. More explanation on these techniques is provided in
Chapter 5.

3.3 Loss in bus waveguides
Aside from resonator losses, loss from the bus waveguides also adds to the
insertion loss of the device, affecting the overall performance of the optical filter. In
a broader point of view, the concept of CS-WDM is to integrate various
functionalities onto the same chip. Passive and active components have to be
t
etch1

Micro-ring
Buried bus
t
etch2

64
connected via common bus lines. It is crucial that those bus lines have low loss to
efficiently deliver signals throughout the chip.
Despite all the advantages of the vertically coupled micro-resonator structure,
there are several constraints imposed on the design of air-guided bus waveguides.
First of all, there is a highly asymmetrical distribution of refractive indices. In the
vertical coupling geometry, the coupling layer also serves as the lower cladding of
the resonator which has to be etched through in order to form the disk mesa. Hence
there is hardly any top cladding left for the bus waveguide. The poor shape causes
the bus mode to leak toward the substrate. Secondly, the material of the bus core
layer is chosen to have lower refractive index than the disk core layer, n
bus
=3.29
(Q1.1) vs. n
disk
=3.36 (Q1.25), so that better phase-match can be achieved between
bus mode and disk mode for efficient vertical coupling. The tradeoff is that the low
index provides less confinement for the bus mode serving to increase substrate
leakage. Meanwhile, since the bus and the post underneath the disk are on the same
layer, this layer must be n-doped in order to complete the overall p-i-n diode
structure for tuning applications. The n-type free carriers in the bus waveguide thus
induce additional loss.
On the other hand, the completed buried heterostructure (BH) waveguides
could have much lower loss. Although it also presents the same asymmetrical
problem as the wafer-bonded waveguides, the BH bus built with the planarization
overgrowth technique does not have to be doped as in the wafer-bonded case. Thus
the undoped waveguide could avoid the extra material loss due to the carriers. More

65
importantly, the low core/cladding index-contrast lowers the scattering loss
significantly comparing with the air-guided bus waveguides. Recall that the
scattering loss is proportional to (n
core
2
-n
clad
2
)
2
. By burying the bus core in InP, this
term can be reduced by almost two orders of magnitude. As a result, the requirement
of device fabrication can be relaxed accordingly.

3.3.1 Calculated bus loss
0.0 0.5 1.0 1.5 2.0 2.5 3.0
0.1
1
10
100
0.0 0.2 0.4 0.6 0.8 1.0
20
40
60
80
100
n
core
=3.29
n
clad
=1
Thickness of top cladding t
top
[μm]
α
bus
[cm
-1
]
Modal loss of air-guided bus waveguide
0.8μm
0.8μm
1.2μm
0.4μm
w
top
Modal loss of air-guided bus waveguide

α
bus
[cm
-1
]
Width of top cladding w
top
[μm]
n
core
=3.29
n
clad
=1
1.2μm

0.8μm
0.4μm
t
top

(a) (b)
0.0 0.5 1.0 1.5 2.0
10
100
0.0 0.2 0.4 0.6 0.8 1.0
1
10
100
n
core
=3.29
n
clad
=3.17
Thickness of top cladding t
top
[μm]
α
bus
[cm
-1
]
Modal loss of BH bus waveguide Modal loss of BH bus waveguide

α
bus
[cm
-1
]
Width of top cladding w
top
[μm]
0.7μm
0.8μm
0.4μm
w
top
n
core
=3.29
n
clad
=3.17

0.8μm
0.4μm
t
top

(c) (d)
Figure 3.23 Calculated modal loss of air-guided and buried bus waveguides as functions of
(a), (c) thickness and (b), (d) width of the top cladding layer.

66
The modal loss of both types of bus waveguides having different dimensions
was simulated in OlympIOs. Figure 3.23 shows the influence of the top cladding layer
on the bus mode. Both the air-guided and the buried waveguides showed similar
dependence on the thickness and the width of the top cladding. In order to minimize
the loss we should make the top cladding as thick and as wide as possible. Figure
3.24 gives several examples of the modal fields of the air-guided bus waveguides at
different top-cladding widths. As w
top
increased from 0 to 2.8 μm, the modal loss
decreased from 100 to 0.14cm
-1
– a reduction of almost 3 orders of magnitude.

(a) (b)

(c) (d)
Figure 3.24 Examples of modal fields of an air-guided bus waveguide solved by OlympIOs:
(a) w
top
=0; (b) w
top
=0.8 μm; (c) w
top
=1.8 μm; (b) w
top
=2.8 μm.

67
3.3.2 New design: reserving the top cladding layer
The simulation results guided us towards a new approach for future devices –
preserving the bus top cladding layer. As we already know, the coupling layer in the
vertical-coupling geometry serves three functions – besides providing the coupling
medium between resonator and bus waveguides, it also serves as the lower cladding
of the resonator, and the upper cladding of the bus waveguide simultaneously. To
solve the problem of an asymmetric bus waveguide as discussed in the previous
section, we propose a way of building the waveguides with intact top claddings in
the non-disk-bus-interaction, or non-coupling, region.

(a) (b) (c)
Figure 3.25 Process flow of utilizing coupling layer as bus top cladding: (a) forming ring
mesa and bus cladding taper at the same time; (b) opening on top of bus by optical
lithography; (c) wet etching off disk cladding and core layers.

Taking the buried bus waveguide as an example, first the tapered bus
cladding is patterned together with ring resonators. It is then etched through the disk
core layer and most of the coupling layer as shown in Figure 3.25 (a). Now the “bus”
waveguide has a double layer structure. Another cover mask is applied to expose just
the top of the bus waveguide while covering the disk mesas and the rest of the

68
surfaces (b). The disk cladding (top InP) and core (InGaAsP, Q1.35) layers on the
bus waveguide can then be removed by selective wet etching (c). This way the
coupling layer could serve as the top cladding for most part of the bus waveguide.
The concern with this method is the abrupt physical step from one waveguide
with top cladding to one without. Due to the vertical coupling geometry, it is pre-
determined that the bus waveguides should have no top cladding in the vicinity of
micro-ring mesas. Thus in vertical coupling configuration, the transition between
symmetric and asymmetric waveguide is inevitable. One possible way to ameliorate
this problem is to create a gradual change instead of an abrupt change. First, we
could leave a thicker portion of coupling layer behind during the disk etch, so that
the transition will be from a 0.8µm cladding (assuming the total thickness of
coupling layer is 0.8µm) to a 0.1 or 0.2µm cladding instead of zero cladding.
Furthermore, we could use a taper design for the top cladding whereby it gradually
decreases from full width to zero over a fairly long distance so that the transition
approaches an adiabatic process. A simulation using beam propagation method
(BPM) shows that by leaving a 0.1µm coupling layer on top of the bus core, the
power loss per pass (which includes transitions from symmetric to asymmetric and
back to symmetric waveguides sections) is about 20%. It also shows that by
increasing the length of the taper, the loss can be reduced even further.

69
3.3.3 Measured loss of bus waveguides
The loss of bus waveguide can be measured using a Fabry-Perot resonance
method [25]. Assuming perfectly coherent monochromatic light, the transmitted
optical power through a Fabry-Perot cavity formed by cleaved end facets is given by:
2 2 2 2
2 2
4
sin exp
4
cos exp 1
exp 1
]
λ
πnL
αL) ( +[r ]
λ
πnL
αL) ( r [
αL) ( ) r (
)= T(
⋅ − ⋅ ⋅ − ⋅ −
− −
λ
where r
2
is the intensity reflection coefficient of the facets, L is the waveguide length,
n is the waveguide effective index, and α is the distributed loss coefficient. The data
is fitted to the measured FP spectrum to find the corresponding loss coefficient. The
result for a conventional n-doped, air-guided bus waveguide like the one in the
vertical coupled micro-resonator structure is 3~5cm
-1
, while for a fully buried bus it
is only 0.4cm
-1
of loss [26].

3.4 Conclusions
A thorough analysis of loss mechanisms in microresonators as well as bus
waveguides is presented in this chapter. The loss in microresonators is divided into
material loss, scattering loss, and modal loss. Material loss, usually carrier-induced,
can be minimized by lowering the background doping level during material growth.
Scattering loss can be reduced by improving etching quality or decreasing the
contrast of refractive indices between the waveguide core and cladding materials.
Modal loss, mainly bending loss, is lowered with larger radii or high core/cladding
index-contrast. To account for the opposite effect of index contrast on the scattering

70
and bending loss, optimal values of index-contrast are derived for different sizes of
the resonators. For the size of interest (R=10 μm), a cladding index of 2.5 is desirable.
However, experiments to obtain for such materials (e.g. a-Si
x
N
y
:H) have not been
successful. In the BH-bus configuration, there is an additional substrate leakage loss,
which can be suppressed by inserting a low-index material underneath the resonator
mode, or by deeply etching the resonator in the non-coupling region. Experiments on
the former approach involved long-time high-temperature oxidation process, which
was not favorable due to the possible damages to the QW active layers. Hence, the
latter approach is chosen in the new design to minimize the substrate leakage.
Different levels of etching are needed to achieve this goal.
The loss in the bus waveguide is primarily due to its asymmetric shape in the
vertical direction. By preserving the top cladding layer of the bus, we believe this
loss can be reduced substantially.

71
Chapter 3 References

[1] B.R.Bennett, R.A.Soref, and J.A.D.Alamo, “Carrier-induced change in refractive
index of InP, GaAs, And InGaAsP”, IEEE Journal of Quantum Electronics,
Vol.26, No.1, pp.113-122, 1990.

[2] R.A.Soref, B.R.Bennett, “Electrooptical effects in silicon”, IEEE Journal of
Quantum Electronics, Vol.QE-23, No.1, pp.123-129, 1987.

[3] http://www.ioffe.ru/SVA/NSM/Semicond/InP/electric.html#Hall

[4] S.Adachi, “Material parameters of InGaAsP and related binaries”, Journal of
Applied Physics, Vol.53, No.12, pp.8775-8792, 1982.

[5] http://www.ioffe.ru/SVA/NSM/Semicond/GaInAsP/electric.html#Hall

[6] D.Marcuse, “Mode conversion caused by surface imperfections of a dielectric
slab waveguide”, The Bell System Technical Journal, Vol.48, pp.3187-3215,
1969.

[7] B.E.Little, J.P.Laine, S.T.Chu, “Surface-roughness-induced contradirectional
coupling in ring and disk resonators”, Optics Letters, Vol.22, No.1, pp.4-6, 1997.

[8] J.P.R.Lacey, F.P.Payne, “Radiation loss from planar waveguides with random
wall imperfections”, IEE Proceedings, Vol.137, Pt. J, No.4, pp.282-288, 1990.

[9] E.A.J.Marcatili, “Bends in optical dielectric guides”, The Bell System Technical
Journal, Vol.48, No.7, pp.2103-2132, 1969.

[10] M.Heiblum, J.H.Harris, “Analysis of curved optical waveguides by conformal
transformation”, IEEE Journal of Quantum Electronics, Vol. QE-11, No.2,
pp.75-83, 1975.

[11] R.L.Liboff, Introductory Quantum Mechanics, New York: Holden-Day, pp.269,
1980.

[12] W.A.P.Claassen, W.G.J.N.Valkenburg, F.H.P.M.Habraken, and Y.Tamminga,
“Characterization of plasma silicon nitride layers”, J. Electrochem. Soc., vol.130,
No.12, pp.2419-2423, 1983.

72

[13] F.Giorgis, C.F.Pirri, and E.Tresso, “Structural properties of a-SiN:H films
grown by plasma enhanced chemical vapor deposition by SiH
4
+NH
3
+H
2
gas
mixtures”, Thin Solid Films, 307, pp.298-305, 1997.

[14] T.Makino, “Composition and structure control by source gas ratio in LPCVD
SiN
x
”, J. Electrochem. Soc., Vol.130, No.2, pp.450-455, 1983.

[15] E.Bustarret, M.Bensouda, M.C.Habrard, J.C.Bruyere, S.Poulin, and
S.C.Gujrathi, “Configurational statistics in a-Si
x
N
y
H
z
alloys: A quantitative
bonding analysis”, Physical Review B, Vol.38, No.12, pp.8171-8184, 1988.

[16] B.G.Budaguan, D.A.Stryahioev, A.A.Aivazov, “Optical properties, statistics of
bond angle deformations and density of states in Si-rich a-SiN
x
:H alloys”,
Journal of Non-Crystalline Solids, 210, pp.267-274, 1997.

[17] C.S.Pai, “High quality voids free oxide deposition”, Materials Chemistry and
Physics, 44, pp.1-8, 1996.

[18] P.A.Grudowski, R.V.Chelakara, and R.D.Dupuis, “An InAlAs/InGaAs metal-
oxide-semiconductor field effect transistor using the native oxide of InAlAs as a
gate insulation layer”, Applied Physics Letters, Vol.69, No.3, pp.388-390, 1996.

[19] H.Gebretsadik, K.Kamath, W.Zhou, P.Bhattacharya, C.Caneau, and R.Bhat,
“Lateral oxidation of InAlAs in InP-based heterostructures for long wavelength
vertical cavity surface emitting laser applications”, Applied Physics Letters,
Vol.72, No.2, pp.135-137, 1998.

[20] R.J.Hussey, G.I.Sproule, J.P.McCaffrey, and M.J.Graham, “Characterization of
oxides formed on InP, InGaAs, InAlAs, And InGaAs/InAlAs heterostructures at
300-500°C”, Oxidation of Metals, Vol.57, Nos.5/6, pp.427-447, 2002.

[21] H.Takenouchi, T.Kagawa, Y.Ohiso, T.Tadokoro and T.Kurokawa, “Laterally
oxidized InAlAs-oxide/InP distributed Bragg reflectors”, Electronics Letters,
Vol.32, No.18, pp.1671-1673, 1996.

[22] R.Iyer, R.R.Chang, A.Dubey, and D.L.Lile, “The effect of phosphorous and
sulfur treatment on the surface properties of InP”, Journal of Vacuum Science
Technology B, Vol.6, No.4, pp.1174-1179, 1988

[23] J.Zhang, D.Crouse, Z.H.Zhu, and Y.H.Lo, “Improved lateral wet-oxidation of
InAlAs”, LEOS 1-4 Dec. 1998, IEEE Vol. 2, pp. 114-115, 1998.

73

[24] Wei Zhou, “III-V Compound Semiconductor Material Characterization of
Microstructures and Nanostructures on Various Optoelectronic Devices with
Analytical Transmission Electron Microscopy and High Resolution Electron
Microscopy”, Ph.D. Thesis, Chap.5, 2004.

[25] L.S.Yu, Q.Z.Liu, S.A.Pappert, and S.S.Lau, “Laser spectral linewidth
dependence on waveguide loss measurements using the Fabry-Perot method”,
Applied Physics Letters, vol.64, no.5, pp.536-538, Jan 1994.

[26] S.J.Choi, “Semiconductor microresonators for chip-scale wavelength division
multiplexing (CSWDM) applications”, Ph.D. dissertation, University of
Southern California, USA, 2005.

74
Chapter 4 Coupling-related analysis
In this chapter, the second important issue of the resonator system, coupling,
is analyzed. The coupling between resonator and bus waveguides, and the coupling
among resonators themselves is considered. A digital signal processing technique is
employed to synthesize the filter characteristics and derive the needed coupling
coefficients. A beam propagation method is then applied to simulate the physical
realization of those coefficients.

4.1 Apodization for target values of coupling coefficients
4.1.1 z-transform for filter synthesis
Instead of the conventional coupled mode theory in the time domain, an
alternative approach – digital signal processing – was applied to the design and
analysis of our optical filters in this section. In particular, the commonly used z-
transform concept for discrete signals was employed to describe and eventually
optimize the performance of the filter [1].
The z-transform is defined for a discrete signal by substituting z for e
jω
in the
transfer function:
∑
−
−
∞
∞ n=
n
h(n)z H(z)=
where h(n) is the impulse response of a filter. The
filter functions arise from the interference of two or more waves that are delayed
relative to one another. When the signals are recombined, their relative phases
determine whether they interfere constructively or destructively. The phase for each
path is the product of the distance traveled L and the propagation constant β=2 πn
eff
/ λ.

75
The key to using the z-tranform method to analyze optical filters is that each delay
must be an integer multiple of a unit delay length L
u
. The phase for each path is then
expressed as a multiple of βL
u
so that the total electric field at the output is the sum
over each optical path given by E
out
= E
0
+ E
1
e
-j βL
u
+ E
2
e
-j2 βL
u

+ …+ E
N
e
-jN βL
u
.
Substituting in z
-1
= e
-jωT
u

= e
-jω ( L
u
• n
eff
/c)
= e
-j βL
u
(T
u
being the unit delay time =
1/FSR), we have the corresponding z-transform: E
out
= E
0
+ E
1
z
-1
+ E
2
z
-2
+ …+ E
N
z
-N
.
A single ring resonator with two waveguides, as shown in Figure 4.1 (a), is
the simplest optical filter with a single-pole response. An expression for the sum
over all optical paths is found to be:
(z) +...}X z ) κ )( κ ( + { z κ κ (z)= X
in out in out in drop
1 1
1 1 1
− −
− − −
where z
-1
=exp[(- α/2-j β)•2 πR] includes the optical loss. The common term,
1 −
− z κ κ
out in
, is the transmission from the input to the output without the
feedback path connected. Propagation once around the feedback path is given by
1
1 1
−
− − z ) κ )( κ (
out in
. The infinite sum simplifies to the following expression for the
ring’s transfer function in terms of square magnitude response:
2
1
1
2
1 1 1
−
−
− − −
−
z ) κ )( κ (
z κ κ
=
X
X
D=
out in
out in
in
drop
. Similarly, we can get
2
1
1
2
1 1 1
1 1
−
−
− − −
− − −
z ) κ )( κ (
z κ κ
=
X
X
T=
out in
out in
in
tran
. The results agree very well with those
calculated with coupled mode theory in Chapter 2.

76

Figure 4.1 Schematic drawings of z-transforms of (a) a single-stage ring filter; (b) a multi-
stage ring filter coupled in series; (c) a multi-stage ring filter coupled in parallel.
(b)
z
-1

X
in
(z)
X
tran
(z)
X
add
(z)
X
drop
κ
1
κ
2
κ
3
κ
N+1

z
-1
M
1

M
2 M
3
M
N+1

M
delay
M
delay
(c)
z
B
-1
X
in
(z)
X
tran
(z)
X
add
(z) X
drop
(z)
κ
11
κ
21
κ
N1

z
-1

M
1
M
2 M
N
M
delay
κ
12
z
B
-1
κ
22
z
-1
z
-1

κ
N2

(a)
z
-1/2

z
-1/2

in
j - κ

out
j - κ

out
- 1 κ

out
- 1 κ

in
- 1 κ

in
- 1 κ

X
in
(z)
X
tran
(z) X
add
(z)
X
drop
(z)

77
There are normally two ways of cascading multiple rings into one filter. One
is a serial-coupled arrangement as illustrated in Figure 4.1 (b) where resonators are
mutually coupled with one another and a signal has to pass sequentially through each
resonator to reach the drop port. The other is a parallel-coupled arrangement as in
Figure 4.1 (c), where all resonators are coupled to both input and output bus
waveguides but not directly to one another. An optical signal goes through all
resonators simultaneously.
To simulate a multi-stage filter, a transfer matrix method is introduced to
simplify the problem. In the serial-coupled scheme, the structure of N ring resonators
can be broken down into N+1 coupling blocks, described by matrices M
1
to M
N+1
,
and N delay blocks, M
delay
. Here, identical resonators are assumed. The final output
can then be derived from the product of all transfer matrices:
⎥
⎦
⎤
⎢
⎣
⎡
⋅ ⋅ ⋅
⎥
⎦
⎤
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
+
tran
in
delay delay delay N
tran
in
drop
add
X
X
M M M M M =M
X
X
=M
X
X
1 2 1
, in which
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
− −
− −
i
i
i
i
κ
κ
κ j
= M
1 1
1 1 1
(i=1,…, N+1),
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−
0
0
1
z
z
= M
delay
. And by
assuming X
add
=0, we get
2
12
11 22
21
2
M
M M
M =
X
X
D=
in
drop
− , and
2
12
11
2
M
M
=
X
X
T=
in
tran
−
(M
ij
, i,j =1,2, denotes the matrix element of M). Similarly, in the parallel-coupled
scheme the system is composed of N resonator blocks, described by M
1
to M
N
, and
N-1 bus delay blocks, M
delay
. The matrix equation is then

78
⎥
⎦
⎤
⎢
⎣
⎡
⋅ ⋅ ⋅
⎥
⎦
⎤
⎢
⎣
⎡
⎥
⎦
⎤
⎢
⎣
⎡
−
add
tran
N delay N delay delay
add
tran
drop
in
X
X
M M M M M M =M
X
X
=M
X
X
1 2 1

where
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
− − − −
− − −
− − −
− −
− −
− 1
2 1
1
2 1
1
2 1
1
2 1
1
2 1
1 1
1 1 1
1 1
1
z ) κ )( κ ( z κ κ
z κ κ )z κ )( κ (
z κ κ
= M
i i i i
i i i i
i i
i

(i=1,…, N) and
⎥
⎦
⎤
⎢
⎣
⎡
−
B
B
delay
z
z
= M
0
0
1
,
B B
B
)L j β
α
(
B
=e z
− −
−
2
1
is the delay caused by bus
waveguides assuming L
B
, the distance between each stage, is identical. The overall
transfer functions are:
2
11
21
2
M
M
=
X
X
D=
in
drop
and
2
11
2
1
M
=
X
X
T=
in
tran
.
The goal of using this multi-stage filter structure is that its response will
approximate a perfect box-shaped filter. The ideal bandpass filter has a rectangular
magnitude response and a linear-phase response. Three regions are specified, the
passband, transition band, and the stopband. Ideally, the passband has a magnitude of
one, the stopband has magnitude of zero, and the transition band occurs over the
smallest possible frequency range. The linear-phase response is important only over
the passband. Since the ideal rectangular response cannot be realized with a causal
filter, approximation has to be applied. From the design perspective, the filter order
can always be increased to reduce the error in the approximation. However,
indefinitely increasing the filter order is unwise for optical filters because more
stages lead to added components and sensitivity to fabrication errors, in addition to
the extra insertion losses. For these reasons, the filter order should be minimized as
long as the desired performance is achieved.

79

(a)

(b)
Figure 4.2 A comparison of single-stage and multi-stage ring filter response for (a) serial
coupled and (b) parallel coupled configurations. Two adjacent channels are plotted together
to indicate different channel isolations. The insert plots are magnified spectra showing
details of the filter passband.

From the well-developed filter theory used in circuit design, we know that
the poles and zeros of the transfer function can be manipulated to synthesize a
1534 1534.5 1535 1535.5 1536
-30
-25
-20
-15
-10
-5
0
R
1
=10um, R
2
=10.9um, κ
in/out
= 10% , lossless
Dropped power [dB]
Wavelength [nm]
N=1
N=3
N=5
1534.6 1534.8 1535 1535.2 1535.4
-3
-2
-1
0
1546.5 1547 1547.5 1548 1548.5 1549
-100
-80
-60
-40
-20
0
N=5
Dropped power [dB]
R
1
=10um, R
2
=10.9um, κ
in/out
= 10% , lossless
Wavelength [nm]
N=3
N=1
1547.05 1547.15 1547.25 1547.35 1547.45
-3
-2
-1
0

80
specific filter response, which in our case is preferably a maximally flat response.
Since the poles and zeros are functions of coupling coefficients κ
i
(i=1, 2, … , N+1),
the desired coupling can be derived accordingly. This method of optimizing the filter
parameters is called apodization. For an N=3 multi-stage filter, the bus-ring and ring-
ring coupling coefficients have to satisfy the relation: κ
2
= κ
3
= 0.125, κ
1
2
= 0.125 κ
4
2

to achieve maximally a flat response [2], where κ
1
and κ
4
are the input and output
coupling coefficients, respectively. For N=5, the relations are: κ
2
= κ
5
= 0.0955 κ
1
2
,
κ
3
= κ
4
= 0.0295 κ
1
2
, and κ
6
= κ
1
for equal input and output coupling. The calculated
results using the above coupling coefficients are presented in Figure 4.2. Two
adjacent channels, about 0.8nm apart, are plotted together to show the improvement
of channel isolation by using higher ordered filters. The resonators in each channel
all had the same radii and they were assumed lossless.
It can be seen that the serial-coupled filter response is approaching the ideal
box shape with flatter passband and sharper roll-off as the number of stages increases.
The 3dB bandwidths are 0.36nm, 0.16nm, and 0.1nm for single-ring, three-ring, and
five-ring filters respectively, and the channel isolations are 15dB, 60dB, and >100dB
for single, three, and five rings. If loss is included in the calculation, the bandwidth
will broaden and channel isolation will decrease accordingly but the overall
performance could still meet the system specifications with a three-ring filter. In the
parallel-coupled resonators however, although flat passband can be achieved by
increasing filter orders, the bandwidth also simultaneously increases and the channel
isolation worsens. During the calculation it was also noticed that the response was

81
quite sensitive to the phase shift induced by the bus waveguide in between each
resonator. With the inevitable uncertainty of device fabrication, we would then have
to install tuning units on those parts of the bus waveguides to finely control the phase
shifts. This would introduce extra complexity into the already crowded circuit.
Based on all the above observations, we concluded that the serial-coupled
scheme was preferable and a third-order resonator-based filter was chosen in the
final design of the new multi-pole MUX/DEMUX. The coupling coefficients were
determined by the apodization relation κ
μ
= 0.125 κ
in
2
= 0.125 κ
out
2
in order to create
maximal flatness in the filter passband ( κ
in
= κ
1
, κ
out
= κ
N+1,
,as in Figure 4.1 (b),

are
the main coupling coefficients between resonators and buses; κ
μ
= κ
2
= κ
3
are the
mutual coupling coefficient among the resonators). Given the bandwidth requirement
(0.16nm) and the assumption that the bandwidth was solely dependent on coupling
(lossless), we decided to target the main coupling coefficients at 10% and hence the
mutual coupling coefficient 0.125%.

4.1.2 Error-tolerance analysis
Once we chose the scheme and the order of the filter with target values κ
in
=
κ
out
=10%, κ
μ
=0.125%, the error tolerance due to fabrication imperfections was
investigated. In particular, the loss of the resonator (α) and the coupling coefficients
( κ
in
, κ
out
, κ
μ
) were the most likely parameters to cause adverse effects in our system
response in the presence of fabrication defects. To see their effects on the filter
performance, the following three situations were considered.

82
First, assuming the loss of the resonator is larger than expected, the resulting
responses with different levels of loss are plotted in Figure 4.3(a). When the loss is
increased, the insertion loss also increases and the bandwidth broadens. At the same
time, the filter shape moves farther away from the ideal. Therefore, a low-loss
resonator is always beneficial from every perspective. To quantify the maximal
tolerable loss, a plot of bandwidth and insertion loss as a function of loss coefficient
α is shown in Figure 4.3(b). To satisfy the 30dB channel isolation requirement,
further calculations show that the loss coefficient cannot exceed 5cm
-1
. (In the
lossless case, the passband response is 0dB and the channel isolation is 40dB with
the apodized parameters. The added loss will cause an insertion loss and thus a
response lower than 0dB at the passband. However, the response at 0.4nm away
from the center wavelength where two adjacent channels overlap, does not change
significantly with the loss – always around -40dB. As a result, the channel isolation
will drop to 30dB when the passband response drops from 0dB to −10dB,
corresponding to a loss coefficient of 5cm
-1
for each single resonator.)

83

(c) (d)

(e) (f)
Figure 4.3 Calculated filter responses with loss and coupling coefficients different than design
parameters.
1545.6 1545.8 1546 1546.2 1546.4 1546.6 1546.8
-50
-40
-30
-20
-10
0
Wavelength [nm]
Dropped power [dB]
R=10μm, α =0, κ
in
=κ
out
=10%

κ
μ
=0.125%
κ
μ
=0.625%
κ
μ
=0.025%
0.0 0.2 0.4 0.6 0.8 1.0
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
1k
10k
100k
R
1
=R
2
=R
3
=10μm
κ
main
=10%, α=0
Effect of κ
μ
on filter performance
Filter bandwidth [nm]
Mutual coupling coefficient κ
μ
[%]
Quality factor Q
1546.1 1546.2 1546.3 1546.4
-12
-10
-8
-6
-4
-2
0
Wavelength [nm]
Dropped power [dB]
R=10μm, κ
μ
=0.125%

α=0, κ
in
=10%,κ
out
=10%
α=0, κ
in
=15%,κ
out
=5%
α=1/cm, κ
in
=10%,κ
out
=10%
α=1/cm, κ
in
=15%,κ
out
=5%
0 5 10 15 20
0.168
0.170
0.172
0.174
0.176
0.178
0 5 10 15 20
-10.0
-8.0
-6.0
-4.0
-2.0
0.0
3dB bandwidth
R
1
=R
2
=R
3
=10μm
κ
μ
=0.125%, α=0
κ
out
=20% - κ
in
Effect of κ
main
on filter performance
Filter bandwidth [nm]
Main coupling coefficient κ
in
[%]
Insertion loss
ripple amplitude

Insertion loss; ripple amplitude [dB]
0 246 8 10
0.16
0.18
0.20
0.22
-20.0
-15.0
-10.0
-5.0
0.0
R
1
=R
2
=R
3
=10μm
κ
main
=10% , κ
μ
=0.125%
Effect of loss on filter perform ance
Filter bandwidth [nm]
Loss coefficient α [1/cm ]

Insertion loss [dB]
1545.9 1546.1 1546.3 1546.5 1546.7
-40
-35
-30
-25
-20
-15
-10
-5
0
Wavelength [nm]
Dropped power [dB]
R=10μm, κ
in
=κ
out
=10%, κ
μ
=0.125%

α=0
α=3cm
-1
α=6cm
-1
α=10cm
-1
1546 1546.2 1546.4
-20
-15
-10
-5
0
(normed
(a)
(b)

84
Secondly, if the main coupling coefficients are not equal to each other, which
could occur due to a misalignment of the resonators to the underlying bus
waveguides in the lithography step, the apodization relation no longer holds. The
asymmetry will generate small ripples in the filter passband as shown in Figure
4.3(c). The sum of κ
in
and κ
out
was assumed to be fixed at 20%. From plot (d) we see
that the bandwidth and insertion loss do not vary significantly with the shifted main
coupling. The amplitude of the ripple exceeds 3dB when the main coupling is lower
than 5% or higher than 15%. Thus, as long as the misalignment is within ±5%, the
filter performance is still acceptable.
Thirdly, if the mutual coupling coefficients are off target with respect to the
main coupling, corresponding to the case where gaps between the resonators have
different sizes than designed, the impact on the filter response could be detrimental.
As shown in Figure 4.3(e) and (f), if the mutual coupling is much stronger (i.e. gaps
are narrower) than desired, not only is the apodization relation violated, but also the
photon lifetime in the resonator system starts to increase, inducing a lower quality
factor or a broadened bandwidth. Even with corrected main coupling coefficients to
reestablish the apodization relation and recover the flat top, the passband width could
never shrink back to the target values. On the other hand, if the mutual coupling is
much weaker (i.e. gaps are wider) than designed, fewer photons are coupled into the
cavity and thus the quality factor increases corresponding to a narrowed filter
passband. In this case, our system no longer meets the design requirement.

85
In summary, among the three parameters (α, κ
in/out
, and κ
μ
), κ
μ
seemed to be
the most sensitive factor in determining the filter response. Therefore, it is crucial to
have good control over this particular parameter.

4.2 Physical realization of the coupling
4.2.1 Vertical coupling controlled by epitaxial growth
In the configuration of micro-resonator vertically coupled to air-guided or
BH bus waveguides, the main coupling between resonators and buses are precisely
controlled by epitaxial growth. From the earlier mode calculations, we see that the
effective index of the bus mode is always higher than that of the resonator mode. Our
conventional wafer-bonded device has a disk core layer of 0.4 μm thick and
n
core
=3.36 (Q1.25). Through a 0.8 μm-thick coupling layer, the coupling coefficient is
measured to be ~4% (R=10 μm). In the BH-bus configuration, the effective index of
the buried bus is even higher, resulting in more phase mismatch and weaker coupling.
To enhance the coupling efficiency, the disk core layer can be chosen as Q1.35
which has a refractive index of 3.4. The thickness should also be increased to 0.6 μm
to provide a higher modal index in the disk which more closely matches the bus
mode. By doing so, the coupling can be strengthened by nearly a factor of 2, as
shown in Figure 4.4. Methods of calculating the vertical coupling coefficient can be
found in [3]. To achieve 10% main coupling, the vertical separation has to be around
0.6 μm.

86

Figure 4.4 Calculated vertical coupling coefficient between disk and bus waveguide.

4.2.2 Lateral coupling by evanescently decaying fields
In the case of lateral coupling, one of the most common or straightforward
schemes is natural coupling through the cladding material that surrounds the two
waveguides. This coupling depends on the intensity of the evanescently decaying
optical field once the two waveguides are in close vicinity to each other. The strength
of the coupling is then determined by the physical distance between the waveguides
and the type of material that surrounds them.
The evaluation of power coupling coefficients is based on the widely
accepted coupled-mode theory (CMT) [4]. Considering only the fundamental modes
of the two waveguides with amplitudes A
1
(z) and A
2
(z) propagating in the same
direction, the so-called codirectional coupling equations are
2 4 6 8 10
x 10
-7
0.1
1
10
100
Lateral separation distance [m]
K
total
[%]
Disk (R=10um) vertically coupled to bus waveguides

Disk: Q1.25, t=0.4um; Bus: air-guided
Disk: Q1.25, t=0.4um; Bus: BH
Disk: Q1.35, t=0.6um; Bus: BH
Vertical separation distance
(thickness of the coupling layer) [m]

87
() () () () ()()
() ()() () () ()
⎭
⎬
⎫
⎩
⎨
⎧
⎥
⎦
⎤
⎢
⎣
⎡
Δ ⋅
Δ
+ Δ ⋅ + Δ ⋅ − =
⎭
⎬
⎫
⎩
⎨
⎧
Δ ⋅ −
⎥
⎦
⎤
⎢
⎣
⎡
Δ ⋅
Δ
− Δ ⋅ =
Δ
−
Δ
0
2
0
0 0
2
2 1
*
12 2
2
2
12
1
2
1
A z S sin
S
i z S cos A z S sin
S
i e z A
A z S sin
S
i A z S sin
S
i z S cos e z A
z i
z i
β κ
κ β
β
β

where Δβ= β
1
- β
2
(phase mismatch), ()
2
2
12
2 β κ Δ + = S and κ
12
is a measure of the
magnitude of coupling between the two modes per length. It can be calculated from
the overlap integral of the two unperturbed modal fields, E
1
(x, y) and E
2
(x,y), when
the two waveguides have no interaction with each other and thus have separate
refractive indices n
1
(x, y) and n
2
(x,y):
() () () () [ ]
∫∫
− =
+
∗
dxdy y x n y x n y x E y x E , , , ,
4
2
1
2
2 1 2 1
0
12
ωε
κ . Here, n
1+2
(x,y) is the profile
of index of refraction when the waveguides are brought together as in the coupling
picture under investigation. The term ( ) ( ) [ ] y x n y x n , ,
2
1
2
2 1
−
+
represents the dielectric
perturbation in one waveguide due to the presence of the other waveguide.

Figure 4.5 Schematic drawings of (a) ring-bus lateral coupling and (b) ring-ring mutual coupling.

We applied this approach directly to the analysis of coupling between
resonator and bus waveguides. Schematic drawings of ring-bus lateral coupling and
d
sep

R
d
sep
β
bus

z
(a)
… z
-l
… 0 … z
l
…
β
disk

β
disk

z
(b)
… z
-l
… 0 … z
l
…

88
ring-ring mutual coupling are shown in Figure 4.5. After solving the disk and the bus
modal fields respectively, the local coupling magnitude κ
l
(l=integer) [1/m] was
calculated at different positions (z
l
) along the z-axis. The two modes were then
coupled as they propagated by finite distance propagation steps Δz via a transmission
matrix method.
()
()
() () ()
() () ()
()
()
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⋅
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
Δ ⋅
Δ
+ Δ ⋅ Δ ⋅ −
Δ ⋅ − Δ ⋅
Δ
− Δ ⋅
=
⎥
⎦
⎤
⎢
⎣
⎡
Δ
Δ
−
−
Δ
Δ
−
z i
l bus
z i
l disk
l
l
l
l l
l
l
l
l
l
l
l
l
l
l bus
l disk
l
l
e z A
e z A
z S sin
S
i z S cos z S sin
S
i
z S sin
S
i z S sin
S
i z S cos
z A
z A
2
1
2
1
2
,
,
2
β
β
β κ
κ β

where ()
2
1 R z
l disk bus l
− − = Δ β β β (taking into account the propagation direction
of the disk mode), ()
2 2
2
l l l
S β κ Δ + = , z z z
l l
Δ + =
−1
. The initial values were set
to A
disk
(z
- ∞
)=0, A
bus
(z
- ∞
)=1. The percent total power coupling coefficient was derived
from the final values of the two amplitudes A
disk
(z
+ ∞
) and A
bus
(z
+ ∞
):
()
()
2
∞ +
∞ +
=
z A
z A
bus
disk
total
κ . The symbol d
sep
denotes the minimum separation distance
between the two waveguides. The total percentage of coupled power was calculated
as a function of d
sep
for various lateral cladding materials. Mutual coupling
coefficients between the resonators were calculated in a similar way. The results are
shown in Figure 4.6.

89
0.0 0.1 0.2 0.3 0.4 0.5
1E-3
0.01
0.1
1
10
100
0.0 0.1 0.2 0.3 0.4 0.5
1E-3
0.01
0.1
1
10
100
n_clad=1
n_clad=1.5
n_clad=2
n_clad=2.5
n_clad=3
Ring-Bus lateral coupling
Lateral separation distance d
sep
[μm]
R=10μm, n_core=3.36,
t=0.4μm, w_bus=0.8μm
Disk-Bus lateral coupling
d
sep

Total power coupled [%]
Lateral separation distance d
sep
[μm]
n_clad=1
n_clad=1.5
n_clad=2
n_clad=2.5
n_clad=3
R=10μm, n_core=3.36,
t=0.4μm,w_ring=1μm,w_bus=0.8μm

d
sep

(a) (b)
0.00.1 0.20.3 0.40.5
1E-3
0.01
0.1
1
10
100
0.00.1 0.20.3 0.40.5
1E-3
0.01
0.1
1
10
100
n_clad=1
n_clad=1.5
n_clad=2
n_clad=2.5
n_clad=3
Ring-Ring mutual coupling
Lateral separation distance d
sep
[μm]
R=10μm,n_core=3.36,t=0.4μm
Disk-Disk mutual coupling
d
sep

Total power coupled [%]
Lateral separation distance d
sep
[μm]
n_clad=1
n_clad=1.5
n_clad=2
n_clad=2.5
n_clad=3
R=10μm, n_core=3.36
t=0.4μm,w_ring=1μm

d
sep

(c) (d)
Figure 4.6 Calculated total power coupling coefficient as a function of minimum lateral separation
distance for (a) disk-bus, (b) ring-bus lateral coupling and (c) disk-disk, (d) ring-ring mutual coupling.

It can be clearly seen that the coupling coefficient is exponentially dependent
on the separation distance. This is simply due to the fact that the modal fields are
exponentially decaying into the other waveguides causing an overlap with the local
unperturbed fields and hence the coupling resulted. Having a higher refractive index
in the cladding could ease the coupling because the optical fields become broader at

90
lower core/cladding contrast levels. The difference in the calculated coupling
coefficients between disk and ring is trivial since most of the light is confined at the
edge of the waveguide. The disk-bus coupling is weaker than the disk-disk mutual
coupling at the same separation distances. This is partly because the curvature of the
resonator induced a phase mismatch between the two waveguides, whereas in the
disk-disk mutual coupling case, the two fields are exactly the same and therefore the
phases are perfectly matched. Another factor contributing to this effect is that the
modal field of the bus being well confined inside the waveguide, thus contributing
less in the overlap integral. In contrast, both fields tend to leak toward each other in
the case of disk-disk coupling . As a result, the overlap integral for disk-disk
coupling is always higher than disk-bus coupling.
Table 4.1 Summary of calculated modal indices and needed lateral separation distances.
(R=10 μm, n
core
=3.36, t
core
=0.4 μm, w
ring
=1 μm, w
bus
=0.8 μm).
n
clad
=1 n
clad
=1.5 n
clad
=2 n
clad
=2.5 n
clad
=3
n
eff bus
3.1508 3.1534 3.1576 3.1657 3.1875
n
eff disk
3.0416 3.0438 3.0476 3.0560 3.0985
n
eff ring
3.0391 3.0414 3.0456 3.0547 3.0984
Δβ/ β
bus
~3.5% ~3.5% ~3.5% ~3.5% ~2.8%
d
sep
needed
for κ
in,out
=10%
<10nm 13nm 28nm 77nm 240nm
d
sep
needed
for κ
μ
=0.125%
200nm 230nm 290nm 480nm 1130nm

Table 4.1 is a summary of the calculated modal indices and the separation
distances that are required to achieve the target coupling coefficients. These results
suggest that the main coupling would be almost impossible to achieve if the
waveguides are positioned laterally. Thus, vertical configuration is the only choice

91
for the disk-bus coupling. The disk-disk mutual coupling requires much less strength,
and can be achieved using high-resolution lithography, such as deep-UV, projection,
or electron-beam lithography.

4.2.3 Assisted lateral coupling by racetrack, overgrowth window
and MMI
4.2.3.1 Coupling through racetrack-shaped resonators
Given the difficulty of evanescent coupling, other geometries could be
employed to assist or enhance the coupling strength. We can think of two intuitive
way of achieving this – having a longer coupling length and a lower core/cladding
index contrast. In the first approach, a racetrack-shaped resonator (illustrated in
Figure 4.7(a)) could be an alternative to the conventional circular resonator with the
advantage of longer coupling distance as well as less phase mismatch. In particular,
if the two waveguides are exactly the same, there will be zero mismatch, which
means the coupled power can reach 100% given a long-enough coupling length.
However, the lengthened cavity would cause a longer round trip time and a
decreased FSR, which might fail the system specifications. What we were looking
for was a solution that did not require high-resolution lithography but still satisfied
the requirements of system response.

92

Figure 4.7 (a) Schematic drawing of racetrack resonators; (b) BPM simulated coupling coefficient as
a function of coupling length of the racetrack.

The coupling between the straight waveguide portions of the racetracks was
more straightforward and reliable than curved waveguide portions. Here we
introduced the commonly used beam-propagation method (BPM) to calculate the
percentage of power coupled from one straight waveguide to the other straight
waveguide. The dimensions of the waveguides are noted in Figure 4.7(a). In order to
allow normal optical lithography in the fabrication process, the lateral separation
distance between the waveguides was set to 0.8 μm. Figure 4.7(b) shows the coupling
coefficients as a function of the length of the racetrack with different cladding
materials. The power drop for low-index claddings (see the inserted magnified plot)
was probably due to numerical errors in the simulation. Since the coupling was
already quite weak (~0.036%), a 0.003% drop did not make any difference. It
L
(a)
(b)
0 2040 6080 100
0
1
2
3
4
5
6
7
8
9
10
020 40 60 80 100
0.032
0.034
0.036
0.038
0.040
0.042
0.044
n
clad
=3 n
clad
=3.17
n
core
=3.36
d
sep
=0.8μm
t=0.4μm
w=1μm

Coupling between two straight waveguides by BPM
Total power coupled [%]
Coupling length L [μm]
n
clad
=2.5
n_clad=1
n_clad=1.5
n_clad=2
n_clad=2.5
d
sep

t
w
n
clad

n
core

93
seemed that for 0.8 μm separation distance and a reasonably short racetrack (<20 μm),
a 0.1% coupling could only be achieved with cladding materials that have indices of
refraction higher than 2.5. The 10% coupling would have to require the highest-
index cladding available, which was that of InP - 3.17.

4.2.3.2 Coupling through InP overgrowth windows
These results implied that we would probably need very high-index materials
in the straight region to achieve the desired coupling. However, the curved part of
the racetrack could not have the same cladding due to the sensitive bending loss at
such small radii. One possible solution would be to define a window just exposing
the coupling region, where high-index materials, such as InP, could be grown or
deposited, while leaving other areas unchanged. Several configurations of the
overgrowth windows were investigated. The shape of the window was basically
rectangular, and it could be placed in between the two straight waveguides
(asymmetric window, see Figure 4.8(a)), or covering the outer sides of both
waveguides (symmetric window, Figure 4.8(b)). The BPM simulation on these two
designs (Figure 4.9(a,b)) showed that although the target coupling coefficient could
be achieved with a fairly short window, there was always a non-negligible power
loss after the light exited the window which was a result of the abrupt discontinuity
at the edge of the rectangular window. The symmetric window provided weaker
coupling but lower loss than the asymmetric window.

94

Figure 4.8 Schematic drawings of InP-assisted mutual coupling for the racetrack resonators: (a)
asymmetric rectangular growth window; (b) symmetric rectangular growth window; (c) asymmetric
tapered growth window; (d) symmetric tapered growth window; (e) fabrication-limited symmetric
tapered growth window.

To suppress the transition loss, tapers were added to the window, both
asymmetric (Figure 4.8(c)) and symmetric (Figure 4.8(d)). We could see from Figure
4.9(c,d,e,f) that by this reduced the single-pass loss to well below 5%. It should be
noted that all the tapers in the simulation had sharp ends, which were unlikely to
form during processing. To account for this fabrication limitation, another design
with more realistic dimensions was considered (Figure 4.8(e)). Its BPM simulation
results are plotted in Figure 4.9 (g,h).
d
sep

d
sep
/2
L
taper

L
taper

L
InP

d
sep
d
sep

0.8 μm
d
sep

(b)
(c) (d) (a)
d
sep

(e)
d
sep
/2
w
taper

95
1.0 1.5 2.0 2.5
0.0
0.1
0.2
0.3
0.4
0.5
0.6
1.0 1.5 2.0 2.5
5
10
15
20
25
30
InP window length L
InP
[μm]
Single-pass loss [%]

Coupling coefficient & single-pass loss of rectangular InP regrowth window
Total power coupled [%]
InP window length L
InP
[μm]
Asymmetric window: d
sep
=1μm; d
sep
=1.2μm; d
sep
=1.5μm
Symmetric window: d
sep
=1μm; d
sep
=1.5μm; d
sep
=2μm

(a) (b)
0 5 10 15 20 25 30
0
5
10
15
20
0 5 10 15 20 25 30
0
1
2
3
4
5
6
123
0.0
0.2
0.4
0.6
0.8
1.0
123
0.0
0.2
0.4
0.6
0.8
1.0
1.2
InP window length L
InP
[μm]
Single-pass loss [%]
Coupling coefficient & single-pass loss of asymmetricly tapered InP window
Total power coupled [%]
InP window length L
InP
[μm]
d
sep
=1μm; d
sep
=1.5μm; d
sep
=2μm

(c) (d)
Figure 4.9 BPM simulation results on various designs of InP-overgrowth windows: (a, b) symmetric
and asymmetric rectangular windows; (c, d) asymmetrically tapered windows; (e, f) symmetrically
tapered windows; (g, h) fabrication-limited symmetrically tapered windows.

96
(Figure 4.9, Continued)

0 5 10 15 20 25 30
0
1
2
3
4
5
0 5 10 15 20 25 30
0
1
2
3
4
12 3
0.0
0.2
0.4
0.6
0.8
1.0
123
0.0
0.2
0.4
0.6
0.8
1.0
InP window length L
InP
[μm]
Single-pass loss [%]
Coupling coefficient & single-pass loss of symmetricly tapered InP window
Total power coupled [%]
InP window length L
InP
[μm]
d
sep
=1μm; d
sep
=1.5μm; d
sep
=2μm

(e) (f)
12 345
0.0
0.5
1.0
1.5
2.0
2.5
12 345
0
1
2
3
4
5
6
7
8
12 34 5
0.0
0.1
0.2
0.3
InP window length L
InP
[μm]
Single-pass loss [%]
Coupling coefficient & single-pass loss of fabrication-limited tapered InP window
Total power coupled [%]
InP window length L
InP
[μm]
L
taper
=10μm, L
taper
=7μm, L
taper
=5μm, L
taper
=3μm, L
taper
=2μm

(g) (h)

To translate the single-pass power loss into a distributed loss coefficient, we
can use the following equation: ( ) K L exp
RT
− = − 1
κ
α , where α
κ
denotes the
coupling-induced loss coefficient, L
RT
is the round-trip length of the cavity (e.g.
L
RT
=2πR+2L
straight
for a racetrack) and K is the fracture of power lost after each time

97
passing the coupling region. Consequently,
⎟
⎠
⎞
⎜
⎝
⎛
−
=
K L
RT
1
1
ln
1
κ
α . Figure 4.10 gives
an example of the distributed coupling-induced losses of a 10 μm-radii circular
resonator and a racetrack resonator with a 10 μm-long straight section and two 10 μm-
radii curved sections. Learning from the plot, a 6~8% single-pass loss would
translate into 10cm
-1
distributed loss. Given all the other loss mechanisms in the
resonator itself, we probably cannot afford a loss higher than that. In fact, it would be
much safer if we could minimize this coupling-induced loss as much as possible.
110 100
1
10
100
1000

R=10μm,L_straight=0
R=10μm,L_straight=10μm
Translation of coupling-induced loss
Distributed loss [1/cm]
Single-pass power loss [%]

Figure 4.10 Calculated relation between single-pass power loss and distributed loss.

Table 4.2 summarizes the dimensions needed to realize the target coupling
level and the corresponding power loss of each design. For the weak mutual coupling,
the length of the InP window was relatively short, and thus the change in FSR was
not considered. On the other hand, to achieve the 10% main coupling, the size of the
racetrack needed to be increased significantly. The new FSR that results in this case
as compared to the original 10 μm-radii circular resonator is listed in the table

98
(FSR
disk
≈λ
o
2
/(2 πRn
eff
)=12.3nm, FSR
racetrack
≈ λ
o
2
/[(2 πR+2L
InP
+2L
taper
)n
eff
] ).
According to the system requirement, the channel spacing is 0.8nm for 8 channels.
Therefore the FSR of each filter should be at least 0.8×8=6.4nm to avoid crosstalk
noise. With this consideration, only the racetracks with rectangular windows were
able to meet the requirement. However, the corresponding power losses of 35% and
25% were entirely too high, which means none of the racetrack designs was suitable
for the main coupling.
Table 4.2 Summary of dimensions needed to achieve target coupling and the corresponding loss of
each design.

Asymmetric
rectangular
window
Symmetric
rectangular
window
Asymmetric
tapered
window
Symmetric
tapered
window
Fabrication limited
symmetric tapered
window
For
κ
μ
=
0.125%
d
sep
1.2 μm 1.5 μm1.5 μm2 μm 2 μm 2 μm 2 μm
L
InP
1.5 μm 2.1 μm1.4 μm1.8 μm2 μm 1 μm 4.5 μm (L
taper
=5 μm)
loss 6.4% 10% 13% 20% 1% 0.5% 2.4%
For
κ
in,out
=
10%
d
sep
0.8 μm 0.8 μm 1 μm 1 μm 2 μm
L
InP
7.1 μm 28 μm 22 μm 65 μm > 100 μm
loss 35% 25% 1.5% 13% /
FSR 10.1nm 6.5nm 6.1nm 3.6nm <2.8nm

In conclusion, although mutual coupling could be readily achieved by
racetracks coupled with tapered InP regrowth windows, an even stronger coupling
mechanism was desired for the main bus-to-resonator coupling.

99
4.2.3.3 Coupling through ridge waveguides
To further enhance the coupling, ridge-type waveguides can be used instead
of the conventional rib-type waveguides, as shown in Figure 4.11. The basic idea is
that the two waveguides in the coupling area have shared core layers, but unlike an
MMI (discussed in the next section), they are still individually guided by the top
ridge. Just like the InP overgrowth windows, such configurations can only be applied
to the straight part of the resonator, while the curved part should remain rib type in
order to guide the whispering gallery mode. The calculated modal field of a ridge-
type ring resonator was not only lossy but also prone to multi-mode operation, as
illustrated in Figure 4.12. For this reason, we return to the racetrack shape for our
resonator, with alternating ridge-waveguides in the straight section and rib-
waveguides in the curved section.

(a) (b)
Figure 4.11 Schematic drawings of (a) a ridge-type waveguide and (b) two ridge-type waveguides
coupled with each other.

1.2 μm
1.2 μm
0.4 μm
w
ridge

0.1 μm
n = 1
n = 3.17
n = 3.36
d
sep

d
sep

d
sep

100

(a) (b)
Figure 4.12 OlympIOs-calculated whispering gallery modes of 10 μm-radii (a) rib-type and (b) ridge-
type ring resonators.

BPM simulation shows the coupling was much more efficient than normal
rib-type waveguides (Figure 4.13). A summary of specific values needed to meet the
target coupling coefficients as well as the corresponding power loss are listed in
Table 4.3. As with the previously discussed InP overgrowth windows, the weak
mutual coupling was easy to achieve while the main coupling could be a potential
problem due to the loss and the reduced FSR. In addition, this design showed a
serious problem of ridge-to-rib transition loss, which had not been included in the
simulations above. The physical discontinuity was even more abrupt than the
overgrowth windows. Neglecting the backward reflection at the ridge/rib interfaces
(BPM normally cannot simulate backward propagations), and the modal mismatch
between a straight waveguide and a bending waveguide, neither of which was trivial,
a simple BPM simulation of light propagating from 100 μm-long ridge to 100 μm
straight rib, then back to 100 μm ridge again along straight waveguides, introduced a
power loss of more than 70%. Such detrimental loss would require an extremely

101
large amount of gain to offset it. Alternatively, a taper was introduced to soften the
abrupt step. However, tapers were found to be inefficient at reducing the loss, and
their sharp-tipped ends were extremely difficult to fabricate.

0 1020 3040
0.0
2.5
5.0
7.5
10.0
12.5
15.0
024
0.00
0.05
0.10
0.15
0.20
0 10203040
0
5
10
15
024
0
1
2
3
1.6μm
2.0μm
1.2μm
0.8μm
Coupling coefficient and loss of two straight ridge waveguides
Single-pass power loss [%]

Total power coupled [%]
Coupling length [μm]
d
sep
=0.8μm, d
sep
=1.2μm, d
sep
=1.6μm, d
sep
=2.0μm

1.6μm
2.0μm 1.2μm
0.8μm
Coupling length [μm]

(a) (b)
Figure 4.13 BPM simulation results of (a) coupling coefficient and (b) loss of two straight ridge-type
waveguides with parameters defined in Figure 4.11.

Table 4.3 Summary of dimensions required to achieve the target coupling coefficients and the
corresponding loss of the ridge-waveguide design.
d
sep
0.8 μm 1.2 μm 1.6 μm 2.0 μm
For
κ
μ
=
0.125%
L
straight
0.8 μm 1.4 μm 2.4 μm 4.0 μm
loss 0.3% 2.1% 1.0% 0.6%
For
κ
in,out
=
10%
L
straight
15 μm 17 μm 41 μm 35 μm
loss 7.0% 11% 2.6% 9.6%
FSR 8.3nm 8.0nm 5.4nm 5.8nm

102
4.2.3.4 Coupling through an MMI coupler
Multimode interference (MMI) probably provides the most effective coupling
method. An MMI coupler (Figure 4.14) consists of a broad center waveguide which
supports several modes depending on the width and the layer structure of the
waveguide. This type of waveguide has the property of self-imaging, which means
that an arbitrary input field launched at the input port is periodically reproduced in
the transmission direction of the center waveguide. Between those positions, the
input filed is reproduced with only a fraction of the input intensity, divided
symmetrically in the multimode section [5].

Figure 4.14 Schematic drawing of an MMI coupler: top view and cross-sectional view.

We considered various designs of MMIs, including an MMI between two
straight sections of a racetrack resonator, an MMI between two circular bending
waveguides, an MMI between one straight and one bending waveguide, etc. The end
results always yielded a considerable power loss at the interface between MMI and
non-MMI regions, or the end facet of the MMI coupler. We also considered using
d
sep
w
MMI
L
MMI

Input
ports
Output
ports
Multimode
section
d
sep w
MMI

103
tapers to soften the discontinuity. The tapers were able to decrease the loss to some
extent but not sufficiently to warrant their use in real devices given all other
limitations. Another concern about the MMI is its high sensitivity to the phases of
the input fields.
Rabus et al. [6] have used MMI for their racetrack resonators, but in that case
the resonators are quite large, with L
straight
~150 μm and R~100 μm. Their design and
fabrication tolerance was not as strict as ours. Kostadin et al. [7] also demonstrated
ridge-type rectangular resonators. They avoided the ridge-rib transition loss by
introducing a deeply etched corner mirror, achieving a right-angle reflection of light
in the resonators. This idea could be an interesting approach to be investigated
further in the future.

4.3 Conclusions
Theoretical analysis of coupling is discussed in this chapter. By means of
apodization via z-transform, the required relations of coupling coefficients are found
to synthesize the flat-top filter response. Based on system specifications, the target
values of the coefficients are fixed at κ
in,out
= 10%, κ
μ
= 0.125% for a 3-pole filter. To
physically realize those coefficients, various lateral coupling schemes are
investigated, including evanescent coupling, racetrack coupling, assisted coupling
through overgrowth window, coupling between ridge waveguides, and MMI
couplers. Although some of them show potential in achieving the target coupling
strength, the single-pass loss appears to be a common problem. Considering the

104
affordable amount of loss in the resonators, it is safe to choose the natural way of
coupling - evanescent coupling through air - to minimize the coupling-induced loss.
Because of the weak coupling level of this scheme, high resolution lithography is
needed to achieve mutual coupling. As far as the main coupling, we continue to use
the vertical coupling scheme controlled by epitaxial growth.

105
Chapter 4 References

[1] C.K.Madsen, J.H.Zhao, Optical filter design and analysis: A signal processing
approach, New York: John Wiley & Sons, 1999.

[2] B.E.Little, S.T.Chu, H.A.Haus, J.Foresi, and J.P.Laine, “Microring resonator
channel dropping filters”, IEEE Journal of Lightwave Technology, vol.15, no.6,
pp.105-113, 1997.

[3] K.D.Djordjev, “Active microdisk resonant devices and semiconductor optical
equalizers as building blocks for future photonic circuitry”, Ph.D. dissertation,
University of Southern California, USA, 2002.

[4] A.Yariv, P.Yeh, Optical waves in crystals: Propagation and control of laser
radiation, Chapter 6, New York: John Wiley & Sons, 1984.

[5] L.B.Soldano, E.C.M.Pennings, “Optical multi-mode interference devices based
on self-imaging: Principles and applications”, IEEE J. Lightwave Technology,
Vol.13, No.4, pp.615-627, Apr. 1995.

[6] D.G.Rabus, “Realization of optical filters using ring resonators with integrated
semiconductor optical amplifiers in GaInAsP/InP”, Ph.D. dissertation, Heinrich-
Hertz-Institut für Nachrichtentechnik, Berlin, 2002.

[7] K.D.Djordjev, J.Zhu, D.Bour, C.K.Lin, M.Tan, “Demonstration of a low-voltage
resonant modulator based on the folded cavity design”, LEOS 2005. The 18th
Annual Meeting of the IEEE, pp.420–421, Oct. 2005.

106
Chapter 5 Design and fabrication of a multi-pole DEMUX
In this chapter, the final design of the new device is presented and the
proposed fabrication methods are discussed in detail. The development and
challenges in e-beam lithography are stressed in particular. Novel fabrication
techniques such as double- and triple-masking processes are introduced. From the
promising results of a single-resonator coupled to buried bus waveguides, we expect
the newly-developed processing scheme to work equally well on multi-pole
resonator filter devices in the future.

5.1 Finalized device design

Figure 5.1 Block-diagram illustration of the design rules.

Starting from the system specifications, the design rules for the 8-channel
demultiplexer can be illustrated in Figure 5.1. The 0.8nm channel-spacing requires
the FSR of the filter to be at least 8×0.8nm=6.4nm. As a result, small sized
microresonators are favorable. We had chosen R=10 μm for the new devices. To
From specified
channel spacing
(0.8nm)
From desired
flat-top filter
response
Find proper FSR
(~ spacing ×No.
of channels)
Find ring radii:
R~10 µm
Design
multi-pole
filter
Find No. of poles and
apodization relation:
N=3, κ
mutual
=0.125 κ
in,out
2
From specified filter bandwidth
(0.16nm)
Find κ’s :
κ
in,out
~10%, κ
mutual
~0.1%
Choosing
platform
to realize
the filter

107
achieve the flat-top filter response, we decided to pursue a third order serially-
cascaded microresonator filter with coupling coefficients satisfying the apodization
relation. The required bandwidth led us to the specific values of the coupling
coefficients, i.e. κ
in/out
=10%, κ
μ
=0.125%.

Figure 5.2 Schematic drawings of (a) an 8-channel multi-pole DEMUX with each channel consisting
of three micro-resonators coupled with (b) air-guided and (c) BH bus waveguides.

Combining all the requirements and all the calculation results, we finally
chose the configuration with an air-guided microdisk resonator vertically coupled to
air-guided or BH bus waveguides, with the three resonators laterally coupled with
one another through air. High resolution lithography is needed to define the narrow
separation gaps between adjacent disks. In the case of air-guided bus waveguides,
the conventional wafer-bonding technique is applied and most fabrication steps are
(b)
(c)
Input
Dropped
R
1

Transmitted
R
2
R
3
R
8

λ
2
λ
3
λ
8
λ
1

R
1

R
1

R
2

R
2

R
3

R
3

R
8

R
8

(a)

108
similar to the steps used for fabricating the single microdisk resonator [1]. In the case
of BH bus waveguides, the planarization overgrowth technique is employed to bury
the bus waveguides and form planar disk layers upwards [2]. To minimize the
substrate leakage loss, the resonators are deeply etched outside the bus-disk coupling
region. Newly designed bus waveguides with reserved top cladding layers are also
included. The schematic of the final device is shown in Figure 5.2.

5.2 Fabrication development
5.2.1 E-beam lithography
In order to realize the 0.125% mutual coupling, the lateral separation between
two air-guided micro-resonators is around 200nm according to previous calculations
(section 4.2.1). Such small dimensions are beyond the limit of optical lithography.
Therefore, we have adopted a high-resolution method, electron beam lithography
(EBL), to pattern the narrow gaps. PMMA was chosen as the e-beam resist. Since it
is a positive resist, the exposed area will be developed and removed later. The e-
beam needs to write in areas surrounding the real patterns (e.g. disks and bus
waveguides). To save writing time and ease electron dosage control, only the
resonator part was defined by e-beam lithography while the rest of the bus top
cladding was defined by a subsequent optical lithography step. The entire disk-
pattern formation is a referred to as a mix-and-match process. The mask definition
steps are illustrated in Figure 5.3.

109

Figure 5.3 Mix-and-match approach for disk-pattern formation: (a) Disk pattern and taper ends of bus
top-cladding defined by e-beam lithography, transferred to SiN
x
; (b) Bus top-cladding taper
completed by optical lithography, transferred to SiN
x
a second time; (c) Final SiN
x
mask, ready for
disk formation etch.

The e-beam system in use is Leica EBL-100
*
. It is a computer controlled
EBL system which includes features of a converted SEM as well as a full e-beam
system. It features a lanthanum hexaboride (LaB
6
) thermal emission cathode, with
10kV to 100kV acceleration voltage, beam current adjustable from 5pA to 10nA, and
a motorized stage with laser positional-error feedback. The field size can be adjusted
from 50 μm to 1mm. The laser stage allows stitching of patterns with less than 50nm
error. Alignment of several layers can be made with accuracy of 30nm. Its software
is also capable of mark recognition for automatic alignment of many dies across the
wafer.

*
The Leica EBL100 system in use is a property of UCLA Nanoelectronics Research Laboratory.
Patterned by
optical
lithography
Underneath
bus
waveguides
Patterned by
e-beam
lithography
(a) (b)
(c)

110
5.2.1.1 Resolution of EBL
The resolution of EBL is mainly limited by the electron scattering effect.
When an electron enters a polymer film, it loses energy via elastic and inelastic
collisions known collectively as electron scattering. Elastic collisions result only in a
change of direction of the electrons while inelastic collisions result in energy loss.
These scattering processes lead to a broadening of the beam, i.e., the electrons spread
out as they penetrate the solid producing a lateral flux normal to the incident beam
direction. This then causes exposure of the resist at points remote from the point of
initial electron incidence, which in turn results in developed resist images larger than
expected.
There are two major types of scattering – forward and backward scattering.
Forward scattering refers to the small angle (<90°) scattering of electrons in the
resist layer. Because of forward scattering, the incident beam broadens more so at the
bottom of the resist than at the top. The increase in effective beam diameter due to
forward scattering is given empirically by d
f
=0.9(R
t
/V
b
)
1.5
, where d
f
is the increase in
beam diameter in nanometers, R
t
is the resist thickness in nanometers, and V
b
is beam
voltage in kilovolts. Forward scattering is minimized by using the thinnest possible
resist and the highest available acceleration voltage. Figure 5.4 shows an example of
developed resist profiles at different acceleration voltages. We can clearly see the
beam broadening effect towards the bottom of the resist at 15kV, whereas the 71kV
acceleration voltage produced much steeper sidewalls.

111

Figure 5.4 SEM pictures of developed PMMA exposed at different acceleration voltages.
(The pattern exposed at 15kV was done by an SEM-converted system, Philips XL30, at USC.)

On the other hand, backscattering refers to large-angle (~180°)-scattering as
the electrons continue to penetrate through the resist into the substrate. These
electrons may scatter back through the resist at a significant distance from the
incident beam, causing additional resist exposure. Backscattering is the main cause
of the proximity effect, i.e. the undesired exposure of resist in areas not directly
addressed by the electron beam. It is commonly observed that linewidth varies with
different patterns, e.g. a narrow line between two large exposed areas may receive so
many scattered electrons that it can actually develop away. Conversely, a small
isolated feature may lose so much of its dose due to scattering that it develops
incompletely. Backscattering depends on both the energy of the primary electrons
and the type of substrate. Usually, the lower the beam voltage, the less
backscattering occurs. A substrate whose atoms have lower atomic number also has
less backscattering.
15kV 71kV

112
This situation is depicted in Figure 5.5 which shows the Monte Carlo
simulated trajectories for 100 electrons projected onto the x-z plane for a 10kV and
20kV point source [3]. The figure qualitatively shows the degree of forward and
backscattering. The forward scattered electrons are difficult to identify because of
their high density and small lateral spread. On the other hand, the backscattered
electrons are clearly evident being spread out over distances on the order of 1 μm for
10kV while at 20kV the distance is 3~4 μm.

Figure 5.5 Monte Carlo simulated trajectories of 100 electrons in PMMA resist on silicon.

There are several ways to correct the proximity effect. The most common
technique is dose modulation, where each individual shape in the pattern is assigned
a dose such that the shape prints at its intended size. More specifically, a lower dose
is applied to large or dense features whereas a higher dose is applied to small or
isolated features. A similar approach to dose modulation is pattern biasing, in which
the size of dense patterns is intentionally reduced to compensate for the extra dose

113
they receive. There are also commercially available softwares that simulate
corrections for the proximity effect.

(a) (b)
Figure 5.6 Separated EBL masks for different dosages: (a) fine gaps; (b) remaining areas.

In our own case, the e-beam pattern is mainly mutually coupled disks. The
critical feature is the narrow gaps in between. Compared with the rest of the features
which have larger exposure areas, the gaps would require more dosage.
Consequently, the e-beam mask was broken down into two parts (shown in Figure
5.6) – the gaps (including the outer edges of each disk i.e. three connected thin rings)
and the remaining areas. After performing frequent dose tests, the correct dosage for
the gaps was found to be almost two times that of the rest. The detailed exposure
condition is listed in Table 5.1. SEM pictures of small features achieved with these
dosages are presented in Figure 5.7. Different PMMA thicknesses were tested in
order to address different thicknesses of the dielectric layers to which the pattern
would be transferred. In (a) the 1 μm-thick PMMA was spin-coated at 1500rpm three
times with 5min hot-plate baking at 180°C between each coating and 10min baking

114
after the last coating. In (b) the 0.3 μm-thick PMMA was coated at 1500rpm just once
and baked for 15min. The original EBL mask for both patterns had a gap size of
200nm. The exposure dosages were as shown in Table 5.1, and the measured gap
sizes after development were 230nm and 160nm respectively.
Table 5.1 List of EBL exposure conditions in Leica EBL-100. (Note: The dosages may vary from
time to time and should be re-calibrated on a regular basis.)
Acceleration
voltage
Beam
current
Field size
Beam
step
PMMA
thickness
Dosage [ μC/cm
2
]
Gaps
Remaing
areas
71kV 40pA (102.4μm)
2
6.25nm
~0.3 μm 800~1000 375~450
~1 μm 1000~1100 500~600

(a) (b)
Figure 5.7 SEM pictures of developed PMMA with different thicknesses: (a) ~1 μm; (b) ~0.3 μm.

5.2.1.2 Alignment in EBL
It is necessary to employ the alignment function because the bus waveguides
and micro-resonators are not formed at the same time. As a result, the disk patterns
need be aligned with the underlying bus waveguides. In the vertical-coupled
PMMA
SiN
x
SiN
x

PMMA

115
configuration, the quality of alignment directly determines the input/output coupling
strengths.

Figure 5.8 Alignment scheme in Leica EBL100.

There are two levels of alignment available in Leica, global and in-field die-
by-die, illustrated in Figure 5.8. In the global alignment, the system registers three
alignment marks on the sample. The marks are usually several millimeters apart but
they can be as far apart as the whole of the stage run (72mm). Based on their relative
distances input beforehand, the system then establishes a new coordinate system on
the sample and writes on particular positions relative to this coordinate system. The
in-field die-by-die alignment is an extra level of alignment to global alignment.
Besides the global alignment marks, it uses another set of four local marks per die to
Global mark pitch (x)
Pitch
(y) of
die
array
Global
mark
pitch
(y)
Global
alignment
mark
Pitch (x) of
die array
Die mark
pitch (y)
Die mark
pitch (x)
Center of die-
array layout
Center of
pattern
Die-by-die
alignment
mark

116
accurately place patterns inside. Since the sizes of our typical samples were small
(1~2cm
2
), only global alignment was performed, and it was proved that global
alignment alone was sufficient for our applications.
An additional optical lithography step was required to pattern the alignment
marks, which were 50nm-thick 5 μm×5 μm gold squares placed near the desired disk
pattern positions (see Figure 5.9). To enhance the adhesion of gold to the dielectric
layer, a thin layer of Cr, 2.5nm, was evaporated onto the surface beforehand. A
complete definition of the mark for Leica recognition is listed in Appendix. Since the
e-beam alignment was solely dependent on those marks, their correct placement
with respect to the underlying bus waveguides was crucial. A set of comb-shaped
marks were placed on the sample at the same time to measure the exact amount of
misalignment between the gold squares and the bus waveguides. This error was then
corrected manually in the EBL jobfile setup, where the relative coordinates of the
disk patterns were shifted accordingly.

Figure 5.9 Mutually coupled disks patterned by E-beam lithography.

Gold
alignment
marks
SiN
x
mask
InP surface

117
It was later discovered that in the wafer-bonded bus waveguides, although the
underlying bus waveguides were invisible from the top in both the optical
microscope and a secondary-electron SEM, they were readily captured by the
backscattering-electron (BSE) detector in Leica. This is because the BSE signal
depends strongly on the atomic number of the material to be scanned. The patterns in
the underlying bus layers had voids everywhere, which provided enough contrast
with respect to the semiconductors that the BSE detector was able to recognize them.
This interesting phenomenon can be utilized in future designs where no additional
gold squares are needed for e-beam alignment. Instead, we could include square
holes or mesas at the same time that we are forming the bus waveguides, and use
these to align the disks directly. This way, not only do we avoid the extra processing
steps, but even more advantageously we can align the e-beam marks perfectly to the
bus waveguides.

5.2.1.3 Plasma etching with PMMA
(a) CF
4
/H
2
chemistry for enhanced etch resistance
Although PMMA is well-known for its high resolution and high contrast as
an e-beam resist, when transferring such high-resolution profiles into hard dielectric
masks, it suffers from poor etch-resistance in plasma processes compared to novolac-
based photoresists. Theoretically, we could use a thicker PMMA to compensate its
high etch rate. However, thicker resist leads to poor resolution due to the elevated
forward scattering effect. More importantly, the depth-to-width ratio of fine features

118
such as narrow gaps would increase accordingly, creating a difficulty in etching them
through into the dielectric layer. To solve this problem, we developed a new etching
chemistry with H
2
added to the original CF
4
plasma.
It has been observed the PMMA etch rate decreases with increasing hydrogen
concentration [4]. At high hydrogen concentrations (above 25%), silicon dioxide or
nitride etches faster than PMMA. The high selectivity between the dielectrics and
PMMA obtained here is due to the fluorine deficiency produced by the addition of
hydrogen to CF
4
. It is believed that hydrogen can scavenge some of the fluorine into
HF, and HF is considered a stable product and believed to have little participation in
the plasma chemistry for etching dielectrics. At very high hydrogen concentrations
of ~40%, or extremely fluorine-deficient conditions, polymerization rather than
etching can occur. The boundary between polymerization and etching is a function of
the amount of ion activity on the surface which retards the formation of polymers.
The reaction for plasma polymerization is probably not due to rapid deposition of
carbon but rather radical reduction to stable CF
2
. Under such conditions, polymer
deposition dominates the process instead of the etching of PMMA. Therefore,
PMMA becomes a suitable mask near the region of polymerization due to its low
etch rate.
To test this idea, we started from our regular CF
4
etching recipe in ECR: CF
4

flow rate=27sccm, RF power=500W, and pressure=10mT. Different amounts of H
2

were added to the plasma while all other parameters were kept unchanged. It was
proven that the PMMA resistance was enhanced considerably with the help of H
2
.

119
The etch rate of PMMA in CF
4
alone was estimated to be higher than 15nm/min (the
etch rate of SiN
x
was ~20nm/min). With gas flow rate setting CF
4
/H
2
=27/18sccm
(actual flow: 25.6/14.2sccm), the etch rate of PMMA dropped to below 5nm/min.
The minimum amount of H
2
for etching 60min CVD-deposited SiN
x
(~460nm) was
found to be 8sccm. Thinner SiN
x
may require less H
2
than this, and thicker may
require more. For H
2
flow rates higher than 18sccm there was no observable
improvement in terms of etching selectivity.
In the meantime, however, more H
2
had indeed produced more polymers on
top of the PMMA, especially at the edges of the patterns (Figure 5.10(a)). Those
etching byproducts turned out to be extremely difficult to remove. Normal solvents
did not work well on them, neither did the standard 5min O
2
plasma cleaning, which
was routinely performed on photoresists after plasma dry etching. Sometimes the
residues were redeposited onto the semiconductor surface (Figure 5.10(b)) and acted
as micro-masks that led to micro-pillars on the surface after the mesa etching (Figure
5.10(c)).
(a) (b) (c)
Figure 5.10 Etching residue problem with PMMA.

SiN
x

Etching residues SiN
x
mask
Etching residues
Disk mesa
Pillars formed by
micro-masking

120
Various methods had been tried to remove those residues, including sulfuric
acid, long-time O
2
plasma, ultrasonic cleaning, etc., but none of them was efficient or
reproducible. Some sources stated that after plasma etching with CF
4
, a thin veil of
“Teflon”-type polymer may be generated [5]. That would explain why they were so
difficult to remove. It was later found that only a specially-made solvent, Acryl, by
Microchem Corp., was able to clear out most of the residues. The etched sample was
put in the solvent inside a 70°C water bath for 20min then switched to a second bath
of fresh Acryl for another 20min, and rinsed with acetone, methanol, and DI water.
(It should be noted that this method did not work every time. Sometimes, an
ultrasonic bath had to be performed to mechanically shake off the residues.) Even so,
an additional O
2
plasma was still needed to ensure the surface was completely clean.
SEM pictures of Acryl-treated SiN
x
masks are shown in Figure 5.11.

Figure 5.11 SEM pictures of SiN
x
mask (60min CVD) etched by CF
4
/H
2
=27/18sccm for 1100sec, and
cleaned by 40min Acryl warm bath and 6min O
2
plasma.

(b) Post-develop bake for smooth sidewall
After improving the selectivity of PMMA, we found that the quality of the
etched SiN
x
was not as good as that patterned by normal photoresists. To improve
SiN
x

InP

121
the smoothness of the dielectric mask, an additional baking step was suggested after
the PMMA was developed. The baking temperature was tested to be 110°C, which
was the highest temperature possible without any pattern distortion. (According to
the manufacturer’s data sheet, PMMA images will round/flow above 125°C) The
baking time should be longer than 3min for 0.3 μm-thick PMMA and might be even
longer for thicker resists. Figure 5.12 gives an example of the resulting SiN
x
mask
and InP disk mesa with and without post-baking treatment.

Without post-bake With post-bake: 3min@110°C
SiN
x
mask etched by CF
4
/H
2

SiN
x
mask etched by CF
4
/H
2

InP mesa etched by BCl
3
InP mesa etched by BCl
3

Figure 5.12 Comparison of post-baking effect on sidewall smoothness.

122
Unfortunately, not all samples had smooth sidewalls after the post-bake. The
results shown in the figure was not reliably reproducible. It became more and more
difficult to achieve smooth sidewalls as the dielectric layer became thicker. It was
hypothesized that due to the reaction between PMMA and CF
4
plasma, plenty of
polymers were generated and possibly re-deposited on the previously-exposed SiN
x

sidewalls. Thicker SiN
x
required longer CF
4
etching thus more polymer deposition.
As mentioned earlier, those etching byproducts were Teflon-like and thus difficult to
remove. It would be possible for them to stick to the SiN
x
sidewall and become part
of the mask, causing the roughness on the subsequently formed disk sidewalls. It
might also be due to limitations of the etching tools or the etching chemistry. Some
researchers use CHF
3
or SF
6
instead of CF
4
to transfer patterns from PMMA. Some
even add a small amount of O
2
to etch off the excess polymers. We had the options
of trying one of these ourselves, or modifying the existing etching recipe.

5.2.1.4 Summary of e-beam process for disk formation
The detailed processing steps of disk mask formation for a BH-bus
configuration are listed below. It is assumed the alignment marks are already formed
on the SiN
x
layer.
(1) PMMA coating: 1500rpm, 45sec (~0.3µm), hot-plate baking for 15min at 180°C;
(If thicker PMMA is needed, use multiple coating with 5min baking after each
coating and a 10min baking in the end);

123
(2) E-beam exposure: Leica100EBL, EHT=71KV, beam current=40pA, field
size=102.4×102.4µm
2
, dosage=800µC/cm
2
(gaps), 450µC/cm
2
(remaining areas),
automatic global alignment;
(3) Develop: MIBK:IPA=1:3 for 35~45sec, rinse with IPA for ~1min;
(4) Post-bake: 3min at 110°C;
(5) Pattern transfer from PMMA to SiN
x
mask by CF
4
/H
2
plasma etching in ECR;
(6) Residue clean-up: prepare 2 beakers of Acryl (or Remover PG) in a 70°C water
bath; soak sample in each beaker for 20min successively; rinse thoroughly with
ACE (or IPA); 6min O
2
plasma (120W/150mT);
(7) Additional patterning on the existing SiN
x
by optical lithography (resist: S1813
or AZ5214);
(8) Pattern transfer from photoresist to SiN
x
mask by CF
4
plasma in ECR or RIE;
(9) Residue clean-up: rinse thoroughly in ACE, methanol, and DI water; 5min O
2

plasma (120W/150mT).

SEM pictures of the final disk mask fabricated by the mix-and-match method
are shown in Figure 5.13(a). Pictures in (b) show the resulting disk mesas dry-etched
by BCl
3
in ICP system.

124

(a)

(b)
Figure 5.13 SEM pictures of fabricated (a) disk mask by a combination of EBL and optical
photolithography; and (b) the resulting disk mesas dry-etched by BCl
3
.

SiN
x

InP
SiN
x

InP

125
5.2.2 Double/Triple masking technique
To realize bi-level etching, one possible solution was to preserve the
dielectric mask after the first etch, deposit a second layer of dielectric on top of it,
define a pattern covering up the bus-ring coupling region, and etch again. This way
the previous disk mask on top of the mesa was preserved and later deep etching
would follow the original mask in defining the resonator. Figure 5.14 illustrates this
process for a single resonator. The last step of removing the excess disk-core layers
on top of the bus waveguides required a separate lithography step, described earlier
in section 3.3.2, Figure 3.25.

Figure 5.14 Scheme of two-step etching to achieve different etching depths.

Since SiN
x
was used for both masking materials, the second cover mask was
defined by wet etching in BOE. Dry etching was not suitable here because of the
vertical directionality of the etching and having to ensure that the second SiN
x

Defining
cover mask
Second
etch:
Removing
excess layers
on bus
1
st
SiN
x

First etch:
2
nd
SiN
x

2
nd
mask
deposition

126
deposited on mesa sidewalls was completely removed. The problem, however, was
the lateral corrosion of the first SiN
x
mask during the wet etching process. As a result,
the twice etched disk did not look smooth. There was always a physical step on the
sidewall marking the interface between the two etches.

Figure 5.15 Scheme of double-masking process to realize bi-level etching.

To solve this problem, a novel double-masking technique was developed in
which both masks were patterned prior to mesa etching and the disks were etched in
one single run. The bi-level etching was realized automatically because of the fact
that the second mask wore off naturally in the middle of the BCl
3
dry etching. The
coupling region was then exposed to the plasma without any mask on top. The depth
of the shallow etching in this area was determined by the thickness of the second
mask and the well-controlled total etching time. Different dielectric materials were
Etching
continued
One-time
BCl
3
etch:
After removing
disk layers on bus
2
nd
SiN
x
1
st
SiO
2

(when 2
nd
SiN
x
is
etched away)

127
required so that the second mask could be selectively removed over the first mask.
Zhen Peng in our group had successfully developed a CF
4
/N
2
/O
2
-based dry etching
recipe which could etch SiN
x
on top of SiO
2
with a selectivity higher than 40 [6].
Consequently, we chose SiO
2
as the first disk mask and SiN
x
as the second cover
mask (Figure 5.15).
Through this process, the discontinuity on the deeply-etched disk sidewall
was eliminated. However, another physical step, though much smaller, was found at
the coupling region where the two masks overlapped. Unlike the one mentioned
earlier, it was a vertical discontinuity at the interface of the shallow- and deep-etched
areas. The radius of the disk at the shallow-etch region (the coupling region) was
slightly larger than that at the deep-etch region. This could be a result of different
etch rates for SiO
2
and SiN
x
in BCl
3
. A reversed masking process, i.e. patterning the
cover mask first followed by the disk mask, was applied and showed considerable
improvement [6].
An even more novel triple-masking technique was developed by Zhen Peng
[6], in which the excess layers on top of the bus waveguides could be removed
automatically by carefully designing the thicknesses of each mask layer. The scheme
is illustrated in Figure 5.16. The first taper mask was 70nm-thick SiN
x
. Then a
200nm SiO
2
bus cover mask was defined on top. The third SiN
x
disk mask was at
last formed by CF
4
/N
2
/O
2
plasma and was made to be the thickest – 600nm – in
order to survive the entire BCl
3
dry etching. SEM pictures of single resonators after
the triple-masking process are shown in Figure 5.17.

128

Figure 5.16 Scheme of triple-masking process to remove disk layers on bus automatically.

Figure 5.17 SEM pictures of single resonator vertically coupled to BH bus waveguides fabricated
with the triple-masking process by Zhen Peng. (Pictures courtesy of Zhen Peng)

1
st
SiN
x

2
nd
SiO
2
3
rd
SiN
x

One-time
BCl
3
etch
(when 3
rd
SiN
x
is
almost etched away)
Etching
continued
Etching
continued
(when 1
st
SiN
x

is etched away)
(when 2
nd
SiO
2

is etched away)

129
5.2.3 Problems and challenges
We have not been able to fabricate multi-pole resonators vertically coupled to
BH bus waveguides using either the double-masking or triple-masking technique. On
the one hand, we do not have the proper masks for the 3-pole devices. (Even the
single-pole resonator did not have the designated masks for double- or triple-
masking process. The device shown in Figure 5.17 was fabricated by mixing and
matching some of our existing masks, with several very tough alignments.) On the
other hand, we face the major challenge of pattern transfer from PMMA to the thick
dielectric layer. As mentioned earlier, the quality of the dielectric mask was not
always consistent due to the PMMA-related etching byproducts. In our attempts at
real device fabrications, we found that either the etched surface was rough, or the
small gaps were merged due to unsuccessful pattern-transfer from PMMA to SiN
x

(Figure 5.18). In the last attempt to fabricate wafer-bonded 3-pole filters, we found
the disk etching to be acceptable, but the bus waveguide was attacked in the
following disk-layer removal step probably due to misalignment when defining the
cover mask (Figure 5.19). In the future, the triple-masking approach should be used
instead to avoid this problem.

130

Figure 5.18 Last fabricated multi-pole filter with buried bus waveguides using planarization
overgrowth technique (gaps between disks were merged; the process stopped after that).

Disk
sidewall

131

Figure 5.19 Last fabricated multi-pole filter with air-guided bus waveguides using wafer-bonding
technique (bus waveguides were attacked during disk-layer removal step; process stopped after that).

5.3 Preliminary results and discussions
A single-resonator vertically coupled to BH bus waveguides was fabricated
by Zhen Peng using the triple-masking technique. The measured transmission
spectrum is shown in Figure 5.20. The loss of the resonator was fitted to be 2.8cm
-1
–
significant reduction compared to the old design (loss of 20cm
-1
[7]). The quality
factor had increased from 2500 to 9000. This promising improvement led us to
Disk
sidewall

132
expect that given the proper masks the novel processing technique should work
equally well on multiple-resonator devices.
1550 1555 1560 1565 1570
20
30
40
50
60
70
Data fitting:
α=2.8cm
-1

κ
in/out
=8.4%
Microdisk (R=12μm) vertically coupled to
single BH bus WG w/ non-tapered top cladding
Q ~ 9000

Transmission (μW)
Wavelength (nm)

Figure 5.20 (Courtesy of Zhen Peng) Measured transmission spectra of a single resonator vertically
coupled to a single BH bus waveguides.

133
Chapter 5 References

[1] K.D.Djordjev, “Active microdisk resonant devices and semiconductor optical
equalizers as building blocks for future photonic circuitry”, Ph.D. dissertation,
University of Southern California, USA, 2002.

[2] S.J.Choi, “Semiconductor microresonators for chip-scale wavelength division
multiplexing (CSWDM) applications”, Ph.D. dissertation, University of Southern
California, USA, 2005.

[3] L.F.Thompson, C.G.Willson, and M.J.Bowden, Introduction to microlithography:
theory, materials, and processing, American Chemical Society, Washington D.C.,
1994.

[4] J.D.Chinn, I.Adesida, E.D.Wolf, and R.C.Tiberio, “Reactive ion etching for
submicron structures”, Journal of Vacuum Science and Technology, Vol.19,
No.4, pp.1418-1422, 1981.

[5] W.M.Moreau, Semiconductor lithography: principles, practices, and materials,
pp.808, Plenum Press, New York, 1988.

[6] Z.Peng, “Coupled multiple micro-resonators design and active semiconductor
micro-resonator fabrication”, Ph.D. dissertation, University of Southern
California, USA, 2007.

[7] S.J.Choi, K.Djordjev, S.J.Choi, P.D.Dapkus, W.Lin, G.Griffel, R.Menna, and
J.Connolly, “Microring resonators vertically coupled to buried heterostructure
bus waveguides”, IEEE Photonics Technology Letters, Vol.16, No.3, pp.828-830,
2004.

134
Chapter 6 Summary and future works
6.1 Summary
The goal of this dissertation was to demonstrate an 8-channel multi-pole filter
array as a DEMUX in the CS-WDM system. Starting from the existing single-pole
DEMUX, we thoroughly analyzed the loss and the coupling coefficients. Attempts of
reducing resonator losses were made, such as finding the optimal cladding materials
and applying low-index materials between the resonator and the substrate. The final
device was not successfully fabricated due to limited resources and tools, but we
gained invaluable insights into the fabrication techniques necessary to achieve such a
structure. Simulations on various coupling schemes were also presented. Some of
them provided the desired coupling coefficients but the resulting power loss was not
affordable. After examining all the requirements and calculations, we decided to
pursue a third order microresonator filter vertically-coupled to air-guided or BH bus
waveguides, with the resonators mutually-coupled with one another through air. In
fabricating the new devices, e-beam lithography was employed to define the narrow
gaps between the resonators. Multi-masking processes were developed in order to
achieve the bi-level etching and to preserve the top cladding of the bus waveguide.
Preliminary results from the single-pole resonators coupled to BH-bus waveguides
showed considerable reduction in the loss coefficient. With proper masks it seems
promising to apply the novel processing techniques in the fabrication of the multi-
pole microresonator filter in the future.

135
6.2 Future works – Resonators in other material systems
6.2.1 Resonators in SOI
As an expansion of platform technologies, we also considered building
micro-ring resonators in other material systems such as silicon-on-insulator (SOI).
SOI-based waveguides have high-index-contrast on both horizontal and vertical
directions, enabling light to be well confined in a fairly small rectangular cross-
section – typically 300nm × 500nm. The devices are thus quite compact. The buried
oxide layer, usually 1~3µm thick, readily functions as the isolation layer blocking
mode leakage to the high-index Si-substrate. Meanwhile, since it is based on Si
technology it is fully compatible with the already mature CMOS fabrication
processes. Researchers have demonstrated various SOI components with all kinds of
functionalities including filters, modulators, gratings, and photonic crystal
waveguides. Among them, micro-ring resonators in SOI (Figure 6.1) have always
been a rapidly developing topic attracting widespread interest. The radius of an SOI
ring resonator can be as small as 5µm without incurring considerable bending loss.

Figure 6.1 Schematic drawing of an SOI-based microresonator.
Si substrate
SiO
2
: 1~3 μm
Si waveguide
(typical size:
0.5x0.3 μm
2
)

136
The biggest drawback of SOI is, of course, its tuning ability because the
electro-optical effect in silicon is much weaker than in III-V materials. Nevertheless,
it has been reported that various mechanisms, mostly based on free carrier injection
or charge re-distribution, can be introduced to alter the refractive index of silicon and
hence the resonant wavelength [1,2]. It has been demonstrated that resonator-based
modulators could have up to 5GHz of modulation speed [3].
In order to achieve our 3-pole ring filter, the bus-ring coupling has to be
lateral as well, since the vertical-coupling geometry is not applicable in the SOI
configuration. The evanescent coupling is in air again, but an improvement is gained
in the fact that the waveguides are only half a micron thin, which makes it much
easier to perform the dry etching step. Our calculation suggested that to achieve
~10% main coupling and ~0.1% mutual coupling, the separation gaps should be
0.2µm between bus and ring, and 0.4µm between each pair of rings (assuming
waveguide width = 0.5µm, thickness = 0.2µm). Thus, e-beam lithography is still
necessary in the fabrication.

6.2.2 Resonators in GaAs
Besides SOI, the GaAs material system is also a strong candidate for micro-
ring resonators. Normally, GaAs/AlGaAs-based micro-resonators are fabricated in a
similar fashion as the InP/InGaAsP system, i.e. GaAs is used for the waveguide core
and AlGaAs for the upper and lower cladding. Here instead, we considered quite a
different approach. Recall that in section 3.2.2 we proposed inserting an InAlAs

137
layer and partially oxidizing it to form low-index oxide underneath the resonator
mode to reduce substrate leakage loss, but the oxidation turned out to be difficult to
carry out due to the low aluminum composition. Now, with the high Al composition
in AlGaAs, it should be much easier to form the isolation oxide.
Because of the oxidation process, we would not able to have an AlGaAs top
cladding layer for the resonator – any cladding AlGaAs will also be oxidized and we
would not be able to have any electrical path. Meanwhile, since the ring/bus
waveguide has high index contrast in all four directions, its dimensions would have
to be reduced in order to maintain single-mode operation. This is quite similar to SOI
configurations. Also, if we only partially etch the GaAs waveguide layer in the
center of the ring then current can still pass through the substrate which would
provide a benefit for tuning applications in an active device. Below is a suggested
GaAs-based resonator (Figure 6.2).

Figure 6.2 Cross-sectional view of a partially oxidized ring resonator in a GaAs/AlGaAs
material system. (Distances are in µm)

The challenges of this design are first, the tuning efficiency. As seen from the
sketch, the electric path is narrow. Carriers have to travel 1 μm in the lateral direction
1
0.5
AlGaAs
GaAs
AlO
x

R=10µm
1
0.1
0.3

138
inside a 0.1 μm thin layer. Also the surface recombination velocity of GaAs is about
10 times higher than that of InP, which means the tuning efficiency of GaAs will be
a lot lower than InP. Surface passivation is one possible option to suppress the
recombination. It is indicated in the literature that a sulfide solution can be applied
onto the GaAs surface for this purpose. On the other hand, if we could use a lateral
instead of a vertical p-i-n configuration, current would flow laterally from the p-
contact through ring waveguide to the n-contact, and thus avoiding the issue of
surface recombination.
Secondly, we have to achieve efficient lateral coupling. To meet the system
specifications of a 3-pole filter, the calculated lateral separation distances should be
~0.15 μm between bus and ring and 0.3 μm between each pair of rings. This again
requires a high resolution lithography process such as e-beam.
In conclusion, this design incorporates the advantages of both SOI and InP
technologies. It provides good optical confinement in a compact size as in SOI. It
also exhibits the efficient electro-optical tuning typical of most III-V devices. Thus,
it would be beneficial to design a device based on this material system in the future.

139
Chapter 6 References

[1] V.R.Almeida, C.A.Barrios, R.R.Panepucci, and M.Lipson, “All-optical control of
light on a silicon chip”, Nature, vol.431, pp.1081-1084, Oct. 2004.

[2] Q.Xu, B.Schmidt, S.Pradhan, and M.Lipson, “Micrometre-scale electro-optic
modulator”, Nature, vol.435, pp.325-327, May 2005.

[3] S.F.Preble, Q.Xu, B.Schmidt, and M.Lipson., “Ultrafast all-optical modulation on
a silicon chip” , Optics Letters, Vol.30, No.21, pp.2891-2893, Nov 2005.

140
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146
Appendix: Definition of gold alignment mark in Leica
system

Geometry
Mark size tolerance 15%
Fine scan extent (Height) 1 μm
Fine scan extent (Width) 1 μm
Mark height 5 μm
Mark width 5 μm
Scan
Video samples/point 128
Line averaging 2
Exel step interval 15
Coarse scan size 15μm
N fine scans/edge 3
Fine scan length 2 μm
Signal
Edge slope length 1.5 μm
Minimum contrast 10%
Bright on dark 9
*

*
Use “Dark on bright” instead if the alignment mark is an etched hole.

Abstract (if available)

Abstract Micro-cavity devices such as micro-ring resonators are frequency selective elements that can perform a variety of functions such as add/drop filtering, switching, and modulating in chip-scale wavelength-division-multiplexing (CS-WDM) systems. Their compact size and low-power-consuming property have enabled them to become a strong candidate as building blocks in the future photonic integrated circuits (PICs). In this dissertation, InP/InGaAsP-based micro-ring (or micro-disk) resonators vertically coupled with bus waveguides were investigated mainly as active bandpass filters serving as multiplexer/demultiplexers (MUX/DEMUXs) in the WDM communication system.

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Asset Metadata

Creator Yang, Qi (author)

Core Title A study of semiconductor microresonators in chip-scale wavelength division multiplexing (CS-WDM) systems

School Andrew and Erna Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Electrical Engineering

Publication Date 03/25/2008

Defense Date 12/06/2007

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag CS-WDM,high-order optical filter,micro-resonator,MUX/DEMUX,OAI-PMH Harvest,PIC

Language English

Advisor Dapkus, P. Daniel (committee chair), Goo, Edward K. (committee member), O'Brien, John D. (committee member)

Creator Email qyang@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-m1004

Unique identifier UC1230226

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Document Type Dissertation

Rights Yang, Qi

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Repository Name Libraries, University of Southern California

Repository Location Los Angeles, California

Repository Email cisadmin@lib.usc.edu