On-Chip Photonic Devices for Coupling to

On-Chip Photonic Devices for Coupling to Color Centers in Silicon Carbide - CaltechTHESIS
CaltechTHESIS
A Caltech Library Service
About
Browse
Deposit an Item
Instructions for Students
On-Chip Photonic Devices for Coupling to Color Centers in Silicon Carbide
Citation
Wang, Chuting
(2020)
On-Chip Photonic Devices for Coupling to Color Centers in Silicon Carbide.
Dissertation (Ph.D.), California Institute of Technology.
doi:10.7907/m2p0-6t37.
Abstract
Optical quantum networks are important for global use of quantum computers, and secure quantum communication. Those networks require storage devices for synchronizing or making queues of processing transferred quantum information. Practical quantum information networks should minimize loss of transmitted data (photons) and have high efficiency mapping when writing data on memories (solid state qubits). This requires strong light-matter interaction that is enabled by coupling qubits to optical cavities.
The first half of the thesis focuses on emerging candidates for promising qubits in silicon carbide (SiC). The optical and quantum properties of these color centers are discussed with focus on divacancies in 4H-SiC due to their long spin coherence time. Optically detected magnetic resonance of divacancies is shown, an essential technique for reading out the qubit state using the intensity of optical emission.
The second half of the thesis focuses on hybrid photonic devices for coupling to silicon carbide qubits. Hybrid devices are made of another layer of high refractive index material other than the qubit hosting material. Evanescent coupling to qubits close to the surface can be achieved without damaging the host material. Mainly the silicon (Si) on 4H-SiC hybrid ring resonator architecture is discussed starting from design, simulation to fabrication. The fabrication includes Si membrane transfer that is an important step to create a light confining layer on 4H-SiC. The final ring resonator device shows quality factors as high as 23000.
Item Type:
Thesis (Dissertation (Ph.D.))
Subject Keywords:
Silicon carbide, quantum information, ring resonator, divacancy
Degree Grantor:
California Institute of Technology
Division:
Engineering and Applied Science
Major Option:
Applied Physics
Thesis Availability:
Public (worldwide access)
Research Advisor(s):
Faraon, Andrei
Thesis Committee:
Vahala, Kerry J. (chair)
Painter, Oskar J.
Minnich, Austin J.
Faraon, Andrei
Defense Date:
16 December 2019
Record Number:
CaltechTHESIS:04122020-055837611
Persistent URL:
DOI:
10.7907/m2p0-6t37
ORCID:
Author
ORCID
Wang, Chuting
0000-0002-3711-682X
Default Usage Policy:
No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:
13673
Collection:
CaltechTHESIS
Deposited By:
Chuting Wang
Deposited On:
17 Apr 2020 00:14
Last Modified:
17 Jun 2020 20:08
Thesis Files
Preview
PDF (Full thesis)
- Final Version
See Usage Policy.
175MB
Preview
PDF (Front matter)
- Final Version
See Usage Policy.
123kB
Preview
PDF (Chapter 1)
- Final Version
See Usage Policy.
10MB
Preview
PDF (Chapter 2)
- Final Version
See Usage Policy.
28MB
Preview
PDF (Chapter 3)
- Final Version
See Usage Policy.
19MB
Preview
PDF (Chapter 4)
- Final Version
See Usage Policy.
24MB
Preview
PDF (Chapter 5)
- Final Version
See Usage Policy.
49MB
Preview
PDF (Chapter 6 and conclusion)
- Final Version
See Usage Policy.
27MB
Preview
PDF (References)
- Final Version
See Usage Policy.
92kB
Preview
PDF (Appendix)
- Final Version
See Usage Policy.
17MB
Repository Staff Only:
item control page
CaltechTHESIS is powered by
EPrints 3.3
which is developed by the
School of Electronics and Computer Science
at the University of Southampton.
More information and software credits
On-chip Photonic Devices for Coupling to Color Centers
in Silicon Carbide

Thesis by

Chuting Wang

In Partial Fulfillment of the Requirements for the
Degree of
Doctor of Philosophy

CALIFORNIA INSTITUTE OF TECHNOLOGY
Pasadena, California

2020
Defended December 16, 2019

Chuting Wang
ORCID: 0000-0002-3711-682X

iii

ACKNOWLEDGEMENTS
Andrei, thank you so much for the opportunity of joining your lab and working on
this research project. I learned a lot that I could not learn in my undergraduate
studies. This project effectively pushed my limit to become more independent
researcher. I deeply appreciate your patient attitude regarding my research and
coursework, allowing myself to have enough time for reflection and planning.
I thank my thesis committee members professor Painter, professor Vahala and professor Minnich for reading my thesis and providing insightful feedback during my
defense.
I am very grateful to KNI staff members for maintaining tools to make cutting edge
science happen. Many thanks to Guy, Matt, Nathan, Alex, Bert and Melissa for
training me to operate various tools safely and efficiently.
Thank you to Faraon group members for inspiring talks and discussions in group
meetings. Thank you Ioana for a lot of discussions not only related to work but
also to general interests. Thank you for putting up with me when I talked too
much. Thank you Evan for your help to catch up with the lab and KNI work in the
beginning. Thank you Yu for your help with simulations on servers and fabrication.
Thank you Tian Z. and John for asking good questions and help in the lab. Thank
you Mahsa and Ehsan for many observations and operational runs in KNI. Thank
you Jon for your help with the laser and the single photon detector setup. Thank
you Jake for your help with fabrication and communicating with people at Montana
Instruments. Thank you Mi for your strong curiosity and for convincing me to go
to the gym again. Thanks again to Ioana, Mahsa, Ehsan and Jon for help with
coursework.
I am thankful to my previous advisors during my undergraduate studies, professor
Kai-Mei Fu and professor Kohei Itoh for introducing me into the world of quantum
applications.
I am thankful to my parents for exposing me to different environments when I was
kid, and for allowing me to have a good education. Thank you for the support
through the years. I am thankful to my grandparents for teaching me the importance
of education and how a person should live.

ABSTRACT
Optical quantum networks are important for global use of quantum computers,
and secure quantum communication. Those networks require storage devices for
synchronizing or making queues of processing transferred quantum information.
Practical quantum information networks should minimize loss of transmitted data
(photons) and have high efficiency mapping when writing data on memories (solid
state qubits). This requires strong light-matter interaction that is enabled by coupling
qubits to optical cavities.
The first half of the thesis focuses on emerging candidates for promising qubits in
silicon carbide (SiC). The optical and quantum properties of these color centers are
discussed with focus on divacancies in 4H-SiC due to their long spin coherence
time. Optically detected magnetic resonance of divacancies is shown, an essential
technique for reading out the qubit state using the intensity of optical emission.
The second half of the thesis focuses on hybrid photonic devices for coupling to
silicon carbide qubits. Hybrid devices are made of another layer of high refractive
index material other than the qubit hosting material. Evanescent coupling to qubits
close to the surface can be achieved without damaging the host material. Mainly the
silicon (Si) on 4H-SiC hybrid ring resonator architecture is discussed starting from
design, simulation to fabrication. The fabrication includes Si membrane transfer
that is an important step to create a light confining layer on 4H-SiC. The final ring
resonator device shows quality factors as high as 23000.

PUBLISHED CONTENT AND CONTRIBUTIONS

[1] Chuting Wang et al. “Hybrid silicon on silicon carbide integrated photonics
platform”. In: Applied Physics Letters 115.14 (2019), p. 141105.
DOI:10.1063/1.5116201
W.C participated in the conception of the project, fabricated and characterized
the device, gathered and analyzed the data, and wrote the manuscript with
F.A.
[2] Chuting Wang et al. “Silicon on Silicon Carbide Ring Resonators for Coupling
to Color Centers”. In: 2018 Conference on Lasers and Electro-Optics (CLEO).
IEEE. 2018, pp. 1–2.
W.C participated in the conception of the project, fabricated and characterized
the device, gathered and analyzed the data, and wrote the manuscript with
F.A.

TABLE OF CONTENTS

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Published Content and Contributions . . . . . . . . . . . . . . . . . . . . . . v
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Illustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
Chapter I: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Optical defects and their applications in quantum information technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Silicon Carbide (SiC) material background . . . . . . . . . . . . . . 4
1.3 Polytypes of SiC and 4H-SiC crystal structure . . . . . . . . . . . . 4
1.4 Divacancies (VC VSi ) in SiC as promising qubits . . . . . . . . . . . 5
1.5 Coupling optical defects to cavities . . . . . . . . . . . . . . . . . . 6
Chapter II: Photoluminescense of defects and impurities in SiC . . . . . . . . 9
2.1 Divacancies in 4H-SiC . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Cr4+ ions in 4H, 6H-SiC . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Other color centers . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Chapter III: Optically detected magnetic resonance of defects in 4H-SiC . . . 22
3.1 Principles of ODMR . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.2 ODMR setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 ODMR results on ensemble divacancies and on Cr ions . . . . . . . 24
Chapter IV: Design and simulations of photonic resonators . . . . . . . . . . 29
4.1 Silicon photonic devices for near IR wavelength . . . . . . . . . . . 29
4.2 Principles of finite-difference time-domain (FDTD) method . . . . . 30
4.3 Comparison with other EM simulation method . . . . . . . . . . . . 33
4.4 MEEP simulation of c-Si on SiC ring resonator devices . . . . . . . 34
Chapter V: Fabrication of on-chip photonic devices for coupling to defects in
SiC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
5.1 Qubits generation in 4H-SiC . . . . . . . . . . . . . . . . . . . . . . 42
5.2 4H-SiC transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.3 a-Si:H Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
5.4 c-Si Membrane Transfer . . . . . . . . . . . . . . . . . . . . . . . . 45
5.5 c-Si on SiC device patterning and fabrication . . . . . . . . . . . . . 50
Chapter VI: Photonic device characterization . . . . . . . . . . . . . . . . . 56
6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Chapter VII: Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . 63
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Appendix A: GaAs photonic crystals . . . . . . . . . . . . . . . . . . . . . . 72
A.1 GaAs photonic crystal fabrication . . . . . . . . . . . . . . . . . . . 72

vii
Appendix B: Related codes . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
B.1 MEEP codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

viii

LIST OF ILLUSTRATIONS

Number
Page
1.1 An optical quantum network consists of three components: Quantum
channels (black or green lines), quantum processors (laptop icons)
and quantum repeaters (star icons) . . . . . . . . . . . . . . . . . . . 3
1.2 Left: the smallest periodic component of the SiC unit cell. The
center black sphere shows a Si (C) atom and the white spheres show
C (Si) atom. Right: The SiC ideal tetrahedral component viewed in
the plane that is parallel to connected straight line connecting two
nearest atoms of same kind (1120 plane). . . . . . . . . . . . . . . . 6
1.3 2H, 3C, 4H and 6H-SiC stacking structure viewed in the 1120 plane.
The gray frame shows the unit cell of each structure. . . . . . . . . . 6
1.4 Left: Local hexagonal (2H-SiC) or cubic (3C-SiC) environment
changes crystal field on atoms in bilayers of 4H-SiC. Right: 3D view
of 4H-SiC crystal structure with 4 possible divacancy configuration.
1.5 Impression of atoms interacting with light in a Fabry-Perot cavity. . . 8
2.1 4 types of divacancies that occupy different carbon/silicon lattice sites. 10
2.2 Photoluminescence of divacancies in a HPSI 4H-SiC sample excited
by 780nm laser at 8.4 K. . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3 c-axis and basal divacancy energy level structure in 4H-SiC for C3v
and C1h symmetry. Marks next to the red arrows specify the polarization of electric field with respect to c-axis for electric dipole allowed
transitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Photoluminescence of Cr ions and divacancies in a Cr implanted
4H-SiC sample excited by 780nm laser at 8.6 K. . . . . . . . . . . . 12
2.5 Photoluminescence of Cr ions in 4H-SiC and 6H-SiC samples in
better resolution at liquid nitrogen temperature ( 80 K) . . . . . . . . 13
2.6 Cr4+ energy level structure in 4H and 6H-SiC for Td and C3v symmetry. ZPL of Cr4+ is associated with the transition 1 E−→3 A2 . The
number at left on level bars denotes state degeneracy and Γ specifies the irreducible representation of corresponding symmetry group.
Marks next to the red arrows specify the polarization of electric field
with respect to c-axis for electric dipole allowed transitions. . . . . . 14

ix
2.7

2.8
2.9
2.10
2.11

2.12

2.13
2.14
3.1
3.2

3.3

3.4
3.5

3.6
3.7

Optical lifetime measurement of Cr4+ ions in doped 6H-SiC at liquid
helium temperature. The fitting function is Io exp(−t/τ) and reveals
optical lifetime of 144 µs. . . . . . . . . . . . . . . . . . . . . . . .
Optical lifetime measurement fitting residual shows the goodness of
fitting with single exponential Io exp(−t/τ). . . . . . . . . . . . . . .
Summary of optical lifetime measurements of Cr4+ ions in implanted
4H-SiC and doped 6H-SiC samples at different temperature. . . . . .
Photoluminescence of V ions in semi insulating 4H-SiC sample excited by 780 nm laser at liquid helium temperature. . . . . . . . . . .
V4+ energy level structure in 4H-SiC for Td and C3v symmetry. ZPL
of V4+ is associated with the transition 2T2 −→2 E. The number at
left on level bars denotes state degeneracy and Γ specifies irreducible
representation of corresponding symmetry group. Marks next to
red arrows specify polarization of electric field to c-axis for electric
dipole allowed transitions. . . . . . . . . . . . . . . . . . . . . . . .
Photoluminescence of Mo5+ ions in implanted sample (orange) in
comparison with PL4 divacancies in a HPSi sample (blue) excited by
780 nm laser at 8.6K . . . . . . . . . . . . . . . . . . . . . . . . . .
Photoluminescence of Cu ions in Cu implanted Si excited by 780 nm
laser at 8.2K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Photoluminescence of Cu ions in Cu implanted Si excited by 780 nm
laser at different temperatures . . . . . . . . . . . . . . . . . . . . .
Spin population and ODMR signal change when microwave is on/off
Schematic of the MW gold line deposited on a 4H-SiC sample. The
right figure shows the image taken from CCD camera with 780nm
excitation laser on. . . . . . . . . . . . . . . . . . . . . . . . . . . .
MW setup around samples. Initial setup with a single wire on samples
is replaced with more robust method with wire bonding and gold line
deposition directly on sample. . . . . . . . . . . . . . . . . . . . . .
ODMR signal collection method . . . . . . . . . . . . . . . . . . . .
Our ODMR signal collected on undoped HPSI 4H-SiC at liquid
helium temperature (∼20 K) at left side. Right side shows results
from Koehl et al. [32] . . . . . . . . . . . . . . . . . . . . . . . . .
ODMR signal collected on undoped HPSI 4H-SiC at liquid helium
temperature (∼20 K) with wider MW sweep range. . . . . . . . . . .
Power broadening of ODMR signal of ensemble divacancies PL2 . .

15
16
17
18

19
20
21
23

24
25

26
27
27

3.8
4.1

4.2
4.3
4.4

4.5
4.6

4.7

4.8
4.9
4.10
4.11
5.1
5.2

5.3

ODMR signal of PL1 and PL2 divacancies in Cr implanted 4H-SiC
under 0.15 T at liquid nitrogen temperature. . . . . . . . . . . . . . .
Left: c-Si ring resonator on 4H-SiC for spin-photon interfaces. c-Si
is drawn in red, while the transparent part underneath is 4H-SiC.
RIght: Cross section showing the ring resonator near color centers in
the 4H-SiC underneath it, that can couple to the evanescent field of
the cavity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Intrinsic quality factor of Si ring resonator surrounded by air at different temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . .
Electric and magnetic component positions in Yee algorithm. . . . .
2D cylindrical ring simulation (a) Refractive index setting (green:
SiC/n=2.64, yellow: Si/n=3.55 and blue: air/n=1.00)(b)ln|Ez | with
colormap(c) Plot of ln|Ez | at the ring width center cross section. . . .
2D cylindrical ring simulation quality factor vs. ring radius with
height 360 nm and width 300 nm. . . . . . . . . . . . . . . . . . . .
3D ring simulation with waveguides. (a)Refractive index setting
(color distribution same with figure 4.4) (b)ln|Ez | (c)Quality factor
vs. waveguide distance . . . . . . . . . . . . . . . . . . . . . . . . .
2D grating simulation normalization simulation on the left. Main
simulation is on the right. Top figures are refractive index configuration and bottom figures are plotting ln|E |. . . . . . . . . . . . . . .
2D grating flux depending on period and duty cycle. . . . . . . . . .
2D grating diffraction angle change depending on duty cycle (fixed
period) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2D grating diffraction angle change depending on period (fixed duty
cycle) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3D grating simulation configuration. Each figure is at the center
plane of the simulated space. . . . . . . . . . . . . . . . . . . . . . .
SEM image of 4H-SiC membrane surface transferred by smart cut
method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
SEM images of a-Si roughness. (a) a-Si deposited before any patterning procedure (b) A grating coupler after etching and cleaning.
process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
AFM images for comparison of roughness. (a) Deposited a-Si. (b)
Deposited 20nm alumina then a-Si. (c) Transferred c-Si all on top of
4H-SiC. (d) AFM on the 4H-SiC substrate. . . . . . . . . . . . . . .

30
31
34

35
36

39
39
40
40
41
44

xi
5.4
5.5
5.6
5.7
5.8

5.9
5.10
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8

A.1
A.2
A.3

(a)Design of the photomask (b)Etched SOI chip after photolithography (light gray: Si, dark gray:SiO2 ) . . . . . . . . . . . . . . . . . .
Cleaning by transferring a floating membrane to clean water . . . . .
Picking up the membrane, drying and attachment on the substrate. . .
Successful membrane transfer. Most membranes are single but some
of them are connected. . . . . . . . . . . . . . . . . . . . . . . . . .
Failed membrane transfer. Water scattered underneath the membrane.
Heating on a hot plate caused water to evaporate and made bulges on
membranes. Wrinkles in membranes allow water to enter and flush
of the entire membrane. . . . . . . . . . . . . . . . . . . . . . . . .
Residue of ZEP cleaned with O2 plasma . . . . . . . . . . . . . . . .
SEM image of a c-Si on 4H-SiC final ring resonator device . . . . . .
The optical confocal microscope setup diagram. . . . . . . . . . . .
The actual setup (left) viewed from top and (right) viewed from the
right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The actual Littman configuration in the setup. The red solid lines
show the main laser path and the dotted line shows the feedback path.
The internal cavity resonances change due to different diode current
(40-60 mA). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The actual Littman configuration in the setup. The red solid lines
show the main laser path and the dotted line shows the feedback path.
The ECDL power drift over 8 hours. . . . . . . . . . . . . . . . . . .
Main measurements were performed through the drop port. . . . . .
(a)Coarse measurement through the drop port with supercontinuum
laser. (b)Coarse measurement through the thoroughput port. Arrows
indicate the locations of resonances. (c) Fine measurement with
tunable laser scanning. The Lorentzian fit reveals Q∼23000. . . . . .
3D periodic photonic crystal bandgap simulation. . . . . . . . . . . .
3D photonic crystal simulation with defect at the center . . . . . . . .
Transferring a part of devices using a nanomanipulator (a) Cut through
between the 2 patterned lines before grating couplers because undercut wasn’t enough to detach grating couplers from the substrate (b)
The probe at the left side is welded to platinum, deposited around the
grating tapered part, and the device is lifted up. . . . . . . . . . . . .

49
49
51
52

52
54
55
57
57
58
59
60
61
61

62
73
73

xii

LIST OF TABLES
Number
Page
5.1 List of samples with different ion implantation and photoluminescense 43
5.2 a-Si recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.3 c-Si transfer procedure . . . . . . . . . . . . . . . . . . . . . . . . . 47
5.4 SOI chip square patterning procedure . . . . . . . . . . . . . . . . . 48
5.5 E bean writing resist related procedure . . . . . . . . . . . . . . . . 53
5.6 Si pseudo-bosch etching recipe . . . . . . . . . . . . . . . . . . . . 54
A.1 a-Si recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Chapter 1

INTRODUCTION
1.1

Optical defects and their applications in quantum information technologies

Quantum technologies have been extensively pursued for practical applications
which classical system cannot achieve. This includes quantum key distribution
(QKD) for unconditionally secure communication [1–3], quantum computers for efficiently simulating complex physical quantum systems [4–6] and quantum sensing
with higher sensitivity [7–9]. Quantum technologies take advantage of the quantum
mechanical aspects of systems such as the no cloning theorem [10], superposition
states and entanglement to surpass the classical limit. Analogous to the term "bit"
used for classical information, a unit of quantum information can be denoted as
quantum bit, or "qubit". A qubit can be |0i, |1i or any superposition state of the two
states [11]:
|ψi = α0 |0i + α1 |1i

(1.1)

|α0 | 2 + |α1 | 2 = 1

(1.2)

This is unlike classical bits, which can only be in the 0 or 1 state. Qubits are two-level
quantum systems in the Hilbert space spanned by |0i and |1i states. Quantum information networks will have an important role in scaling up to globally distributed
quantum technologies by interconnecting quantum computers or communication
sites[12–14]. Qubits with long coherence time are necessary for quantum information storage. Photons are ideal for transport of quantum information because they
can travel a long distance with minimum decoherence [15]. That is why qubitphoton interfacing via bright optical transitions is highly desired. There are three
essential requirements for qubits that can be practically used for optical quantum
communication [16]:
(1) There are two long-lived and coherent spin states that are nondegenerate, which
corresponds to pure |0i and |1i state. (Qubit state longevity)
(2) There exists optical pumping cycles that can polarize the spin to each pure qubit
state. (Optical qubit state initialization)

(3) Luminescense corresponding to each pure qubit state can be differentiated with
intensity, wavelength or in other ways. (Optical qubit state readout).
For an example the lowest two states of a spin-1 particle,|ms = −1i and |ms = 0i
can be used as |0i and |1i of a qubit [17, 18]. How well this system works compared
to an ideal two-level quantum system is characterized by the decoherence induced
by coupling to other existing states[19]. A good measure of decoherence for a
single qubit is the lifetime of an arbitrary superposition state such as (α0 |0i +
α1 |1i)/ |α0 | 2 + |α1 | 2 , denoted by T2 .
As shown in figure 1.1, a scalable optical quantum network should include the
following three components: quantum channels, quantum processors and quantum
repeaters [20]. Quantum channels are used to transmit qubits either via free space or
via optical fibers. Quantum processors at the end nodes can range from processing
simple measurements of qubits for communication to complex qubit manipulation
for computing. Because photon loss cannot be avoided, error correction of transmitted quantum information is necessary. Quantum repeaters are inserted at regular
intervals in the quantum channels to correct errors accumulated in transmission at
long distance.
An initial optical quantum network was demonstrated with trapped atoms in optical
resonators [21, 22]. Although the technology for controlling trapped atoms is mature
[23], trapping a single atom requires a relatively large and complicated setup and is
hard to scale it up due to its volume. On the other hand, solid state system can host
many qubits in the crystal within a small volume. Solid state qubits are practical
for scaling up due to the potential for compact chip size and easiness of on-chip
integration [24, 25]. Many different solid state qubits have been investigated, such
as semiconductor quantum dots, defects or impurities in diamond, silicon carbide
(SiC), silicon and rare earth ions.
The state of the art QKD demonstration was performed with nitrogen vacancy (NV)
centers in diamond. This experiment established entanglement between two NV
electron spins separated by 1.3 km confirmed by a loophole-free Bell inequality
test [18]. The capability of purifying entangled states was also demonstrated,
an important milestone in scaling up the quantum network [26]. However, NV
centers suffer from a low fraction of coherent photons emitted into the zero phonon
line (ZPL) and spectral diffusion, which hinders the entanglement rate. Also, the
nanofabrication procedure for diamond photonic devices is not easy. It is highly
possible to create surface charges on the host material during fabrication that increase

spectral diffusion of optical linewidth [27, 28]. The state of the art experimental
achievements in NV centers stimulated the search for other candidate qubits in other
materials that are closer to ideal qubits with long coherence time and with better
optical stability.
It is reasonable to search for color centers in wide bandgap materials similar to
diamond, which can have optically active deep level states. It would be beneficial if
these materials are common and affordable semiconductors, such as silicon, GaAs,
or SiC for future mass production. These materials are also more compatible
with existing photonic integrated circuits than diamond. With these ideas in mind,
different defects in SiC were recently investigated and found to be attractive as
qubits. Among these, divacancies in 4H-SiC have the longest coherence time so far.
In the following few sections, I will discuss different types and structure of the host
material silicon carbide and divacancies in 4H-SiC in more detail.

Figure 1.1: An optical quantum network consists of three components: Quantum
channels (black or green lines), quantum processors (laptop icons) and quantum
repeaters (star icons)

1.2

Silicon Carbide (SiC) material background

Silicon carbide (SiC) has been considered as a promising material for power electronics because of its excellent thermal conductivity, high maximum current density,
small coefficient of thermal expansion and high melting point. It also has good mechanical properties and is suitable for MEMS devices. These advantages led to the
development of wafer mass production and microfabrication in SiC. Although pure
SiC has excellent properties, its commercialization was delayed compared to silicon
due to poor electric performance caused by defects created during growth and fabrication process. The removal of the defects to unleash the electronic capability of
SiC is an ongoing challenge. Some defects and impurities in SiC have been found
to emit light at specific wavelength. Photoluminescence spectroscopy can be used
to identify different defects and impurities in SiC. The existence of a rich literature
about optical identification of these unwanted defects, accelerated the identification
of potential qubits.
1.3

Polytypes of SiC and 4H-SiC crystal structure

In this section, the crystal structure of SiC is discussed for explaining divacancy
photoluminescense in the later section. SiC is known to occur in different crystalline
forms. Within those polymorphs, there are more than 150 polytypes [29]. Polytypes
have the identical layer structure but differ in stacking sequence in the direction of
crystal axis. The smallest periodic component of the SiC crystal structure is shown
in figure 1.2. Ideally, 4 silicon atoms and one carbon atom (or vice versa) form a
tetrahedron in this structure. If you look at any plane that intersects two siliconcarbon bonds (the 1120 plane and others related by a 120◦ rotation around c-axis),
the structure looks like the right side of figure 1.2. If we set the crystal axis (c-axis)
parallel to one bond (c), another in-plane bond (a) forms a ∼109.5◦ angle with this
c-axis. In perfect tetrahedra, c=a. However, the different stacking sequence of SiC
layers change the equilibrium of electron structure which results in an elongated (c)
bond for hexagonal SiC polytypes [30].
The common commercially used SiC polytypes are 3C, 4H, and 6H-SiC. 3C-SiC has
cubic close-packed (fcc) crystal structure and 2H-SiC has hexagonal close-packed
(hcp) structure. The stacking of 3C, 2H, 4H and 6H-SiC is shown in figure 1.3.
Polytypes are often characterized by hexagonality, the fraction of local hexagonal
crystal environment in the entire crystal structure, which is an important parameter
influencing physical properties of SiC [31]. Carbon and silicon layers in 4H-SiC
stack in ABCB pattern. 4H-SiC has half layers of quasi-hexagonal environment

and 50% hexagonality. Quasi-hexagonal (h) sites and quasi-cubic (k) lattice sites
occur when silicon-carbon bilayers alternate between 2H-SiC and 3C-SiC as shown
in the left side of figure 1.4. A particular bilayer experiences a different crystal field
depending on whether it sees itself in hexagonal or cubic environment, considering
the nearest neighbors.
1.4

Divacancies (VC VSi ) in SiC as promising qubits

As its name suggests, a single divacancy defect consists of double vacancies at
neighbor carbon and silicon sites. Depending on the locations of each vacancy,
either h or k site, there are 4 combinations of a divacancy defect shown in the right
side of figure 1.4. They are labeled as c-axis divacancies hh (PL1) kk (PL2) and
basal (off-axis) divacancies hk (PL3) and kh (PL4). In this thesis, divacancies refer
neutrally charged divacancies ([VC VSi ]0 ).
The quantum potential of divacancy defects was discovered initially by Koehl et
al. [32]. This work demonstrated optically detected magnetic resonance (ODMR)
and coherent spin polarization of ensemble divacancies. The ground spin state of
divacancies can be initialized by a pulse of light and coherently manipulated by microwave pulses. The Ramsey (T2∗ ) and Hahn echo (T2 ) microwave pulse sequences
were applied to measure spin decoherence characteristics. T2∗ characterizes the decoherence due to all sources, inhomogeneity of magenetic field within proximity and
random spin-spin interactions. T2 measurements add another pi pulse in the middle
of the Ramsey sequence to cancel out the near DC magnetic field inhomogeneity,
so T2 is mainly related to decoherence due to random spin-spin interactions. The
ensemble inhomogeneous spin coherence time T2∗ is ∼ 1.5 µs for basal divacancies
at 20K and ∼ 200 ns for c-axis divacancies at 200K. The ensemble Hahn-echo
homogeneous spin coherence time T2 is ∼ 200 µs for basal divacancies at 20K and
∼250 µs for c-axis divacancies at 200K. Later Christle et al. [33] investigated more
on single divacancy properties. T2∗ of single divacancy is 1 - 5 µs at 20 K, similar to
ensemble divacancies. T2 of single PL2 divacancy is 1.2 ms at 20K, which is comparable to that of a NV center [33]. Considering that these results were measured on
naturally isotopic 4H-SiC sample (including paramagnetic nuclear spin species 13 C
1.1%, 29 Si 4.7%), it is one of the longest Hahn-echo coherence time of an electron
spin in solid state crystals [34]. The typical Rabi oscillation period is 0.3 µs [33],
which suggests there can be ∼4000 qubit polarization operations before the qubit
information is erased by decoherence. This satisfies the practical requirement of
fast single qubit operation with high fidelity.

Figure 1.2: Left: the smallest periodic component of the SiC unit cell. The center
black sphere shows a Si (C) atom and the white spheres show C (Si) atom. Right:
The SiC ideal tetrahedral component viewed in the plane that is parallel to connected
straight line connecting two nearest atoms of same kind (1120 plane).

Figure 1.3: 2H, 3C, 4H and 6H-SiC stacking structure viewed in the 1120 plane.
The gray frame shows the unit cell of each structure.
1.5

Coupling optical defects to cavities

Optical quantum networks using solid state qubits require quantum information
transmitted by photons to be stored for processing at the end nodes. In free space,

Figure 1.4: Left: Local hexagonal (2H-SiC) or cubic (3C-SiC) environment changes
crystal field on atoms in bilayers of 4H-SiC. Right: 3D view of 4H-SiC crystal
structure with 4 possible divacancy configuration.
the interaction or absorption cross section between atoms and photons is very small
and it is hard to deterministically transfer quantum information between them with
time much shorter than the time it can be preserved (atomic coherence time) [35].
Placing optically addressable solid state qubits in an optical cavity enhances the
interaction rate between the qubit and the photon because the cavity traps the photon
for a longer time and also confines it thus increasing the electric field corresponding
to a single photon. This significantly boosts the light-matter interaction and is
necessary for deterministic photon-qubit interaction. The cavity-qubit coupling is
characterized by the g parameter which scales as √1 , where V is mode volume of
the cavity.
d 3 r(r)|E(r)| 2
V=
(1.3)
(r max )|E(r max )| 2
The system composed of a qubit coupled to a cavity is characterized by the cooperativity parameter. A cooperativity greater than one means that the interaction occurs
mainly between the atom and the photon trapped in the cavity before other sources
of decoherence become dominant.
There are different types of optical cavities such as Fabry-Perot cavities, microspheres [36], whispering-gallery mode resonators [37], ring resonators [27], photonic crystals [38], etc. Ring resonators are easier to fabricate than photonic crystal

but have large mode volume. Photonic crystals can often achieve less than unit mode
volume.
Cavities have the important role to enhance emission of solid state qubits for entanglement generation in QKD application. The state of the art entanglement generation
rate using NV centers is 40 Hz [39]. The time to generate quantum entanglement
compared to the spin decoherence time indicates how many multiple quantum network links can be maintained. Currently it is on the order of 1 and it needs to be
much larger than 1 to reach practical level. Coupling coherent photoluminescence of
qubits to optical cavities can greatly reduce its spontaneous emission rate by Purcell
enhancement [40], can enhance the emission of a particular transition of interest,
and enables better coupling into optical channels like optical fibers, which leads to
a significant increase in the entanglement generation rate.

Figure 1.5: Impression of atoms interacting with light in a Fabry-Perot cavity.

22
Chapter 3

OPTICALLY DETECTED MAGNETIC RESONANCE OF
DEFECTS IN 4H-SIC
3.1

Principles of ODMR

Optically detected magnetic resonance (ODMR) refers to optical readout of qubit
spin states or optical polarization of spin states using microwave fields driving the
resonance between different spin states. This effect is very useful in developing
different optical quantum technologies. The signal of ODMR is the optical signal
emitted by the optically addressable qubits in the ZPL or the phonon sidebands.
Depending on the population ratio between different spin sublevels, the ZPL counts
either increase or decrease. This contrast of ZPL counts gives information about spin
polarization. For PL1 and 2 c-axis aligned divacancies in 4H-SiC, this is enabled
by the non radiative decay path, so called intersystem crossing between the excited
and ground triplet states [41, 44], with level structures similar to negatively charged
nitrogen vacancy centers in diamond[43, 47, 69]. Microwaves are used to resonantly
address different spin sublevels, which generates different optical emission intensity.
A simplified energy level structure and ODMR mechanism for c-axis divacancies is
shown in figure 3.1.
In the left side of the figure3.1, microwaves are off and divacancies are continuously
excited non resonantly. Excited divacancies emit photoluminescence through spin
conserving relaxation. The excited ms = ±1 sublevels in excited states are more
strongly coupled to singlet states that lie between the triplet states, which gives rise
to non radiative relaxation. These singlet states are believed to be preferentially
coupled to the ground ms = 0 sublevel. Therefore continuous optical cycling
between excited and ground triplet states will result in most divacancies populated
in ms = 0 sublevel. Because divacancies in excited ms = ±1 sublevels have higher
possibility to go through non radiative relaxation, there are less photon counts if
more divacancies are populated in ground ms = 0 sublevel. In the beginning of
optical excitation/initialization, ZPL is darker as there are almost equal population
in ms = 0 and ms = ±1 sublevel. However, continuous optical excitation will
eventually achieve non- Boltzmann steady state with most spins to ms = 0 and reach
brighter ZPL emission.

23
In the right side of the figure, a microwave field is used to drive the spin transition.
When the microwaves are on and the frequency is resonant with the energy gap
between ground ms = 0 and ms = ±1 sublevels, the microwaves pump some
of the population in the ms = ±1 state, which leads to a change in the emitted
photoluminescence. When the microwaves are not resonant with the spin transition
there is no significant effect on the luminescence.

Figure 3.1: Spin population and ODMR signal change when microwave is on/off
3.2

ODMR setup

Our final ODMR setup uses a microwave (MW) line deposited on the SiC samples
directly as shown in figure 3.2. The design was inspired from Koehl et al. [32]
supplementary material. We glued a round PCB board around the copper cold
finger and the gold MW lines (the design is shown in figure 3.2) were wire bonded
to conductive segments on the board. Those segments were connected to an external
SMA port with soldered wires (figure 3.3). The first version with a single wire put
across the samples didn’t provide good attachment to samples and the wire was prone
to separation from the sample surface. With higher power MW applied in cryostat,
the wire often moved away or across samples due to heat expansion resulting in
weak MW drive amplitude on sample surface.
The ODMR signal shown in our results was defined by the equation shown in figure

24
3.4. ZPL of each divacancies was spectrally filtered by adjustable long pass and
short pass filters. ODMR is the contrast of filtered ZPL with MW applied and
ZPL without MW applied. As you can see in the typical spectrum of Cr implanted
4H-SiC or undoped 4H-SiC, PL4 is bright and its phonon side band counts of PL4
is comparable to ZPL of PL3, also lying on PL1 and PL2. This creates overlap of
PL4 ODMR signal on PL1-3 ODMR signal that will be shown in the next section.

Figure 3.2: Schematic of the MW gold line deposited on a 4H-SiC sample. The
right figure shows the image taken from CCD camera with 780nm excitation laser
on.

Figure 3.3: MW setup around samples. Initial setup with a single wire on samples
is replaced with more robust method with wire bonding and gold line deposition
directly on sample.
3.3

ODMR results on ensemble divacancies and on Cr ions

We observed similar ODMR signal to that shown in literature of divacancy ODMR
[32]. The measurements were performed on highly purified semi insulating (HPSI)

Figure 3.4: ODMR signal collection method
4H-SiC sample from CREE Inc without any post processing. Divacancies observed
in this sample are incorporated intrinsically. Most of divacancies ODMR signal is in
the range of 1.28-1.38 GHz. The comparison of our results (left) and the results from
[32] (right) is shown in figure 3.5. Our ODMR signal peaks are generally broader
than theirs, which suggests a power broadening effect considering that they used the
same type of HPSI 4H-SiC samples. ODMR signal of PL3 at approximately 1.305
GHz is overlapped with background PSB ODMR signal of PL4. However PSB of
PL4 on PL1 and PL2 ZPL is much smaller than their ZPL and there’s no noticeable
PL4 influence. Figure 3.6 shows a wide range of ODMR signals. A signal at 1.45
GHz is an artifact due to heating of the sample and change of the focus. You can see
larger power broadening with larger MW power as shown in figure 3.7. The power
label at the left side is the MW source power and this is amplified by 20dB through
amplifier before MW is delivered to the sample gold lines.
ODMR measurements on Cr ions on Cr implanted 4H-SiC was attempted both with
and without magnetic field. As zero field splitting parameter D of Cr A and CrC was
known to be <1.2 GHz and ∼ 6.0 GHz by Son et al. [48], we applied magnetic field
to c-axis direction for 0.15 T, which gives expected ODMR signal around 1.7 GHz.
We observed PL1 and PL2 ODMR at corresponding magnetic field calculated with
2gµB B/h at around 2.75 and 2.78 GHz as shown in figure 3.8 but we didn’t observe
any ODMR signal from CrC with this continuous wave ODMR method.

Figure 3.5: Our ODMR signal collected on undoped HPSI 4H-SiC at liquid helium
temperature (∼20 K) at left side. Right side shows results from Koehl et al. [32]

Figure 3.6: ODMR signal collected on undoped HPSI 4H-SiC at liquid helium
temperature (∼20 K) with wider MW sweep range.

Figure 3.7: Power broadening of ODMR signal of ensemble divacancies PL2

Figure 3.8: ODMR signal of PL1 and PL2 divacancies in Cr implanted 4H-SiC
under 0.15 T at liquid nitrogen temperature.

Chapter 2

PHOTOLUMINESCENSE OF DEFECTS AND IMPURITIES IN
SIC
2.1

Divacancies in 4H-SiC

Divacancies have 4 different configurations in the crystal lattice as shown in figure
2.1. They are associated with 4 different zero-phonon line (ZPL) labeled as PL1-4
shown in 2.2. ZPL emissions correspond to pure electronic transitions and often
are observed with phonon-side-band (PSB) emission at higher wavelength that are
phonon mediated transitions. As described in section 1.3, 4H-SiC has an elongated
c-axis bonds. This makes a tetrahedron with one elongated bond parallel to c-axis
with three identical bonds. If two adjacent defects occupy lattice sites parallel to
c-axis, 120◦ rotations around c-axis still gives identical crystal configuration. caxis divacancies have C3v symmetry. If two adjacent defects occupy sites that are
not parallel to c-axis, out of 3 neighboring bonds of each defect, one neighboring
bond corresponds to an elongated bond and a rotational symmetry is removed. Only
reflection against the plane that is parallel to c-axis and to the two defect bond makes
the crystal unchanged. Basal divacancies have C1h (Cs ) symmetry.
A single neutrally charged divacancy has 6 active electrons, 3 from nearby carbons
and 3 from nearby silicons. From molecular orbital theory and ab initio density
functional calculations, electrons in C3v symmetry occupy orbital states a21 a21 e2 ,
which generates orbital singlet spin triplet 3 A2 , orbital doublet spin singlet 1 E, and
orbital/spin singlet 1 A1 in the order of the lowest energy level first [41–43]. The next
excited state is a21 a11 e3 , which generates 3 E and 1 E levels. ZPL of c-axis divacancies
(PL1,2) is associated with spin allowed transitions 3 E−→3 A2 [44]. In reduced C1h
symmetry, E level splits into A’ and A" levels. ZPL of basal divacancies (PL3,4)
is associated with 3 A0−→3 A” [45]. Due to the fully allowed transition, the optical
lifetime of the excited state of PL1-4 divacancies is relatively short, ∼15 ns[46]. The
energy diagram for c-axis and basal divacancies is shown in figure 2.3. Two spin
singlet states lying between spin triplet excited and ground state of ZPL transition
are coupled to spin triplet states with spin orbit coupling. Intersystem crossing
between excited spin triplet state to singlet and then to ground spin triplet state is
considered as main cause of spin dependent luminescence observed in magnetic

10
resonance (3.1)[47]. The Debye-Waller factor, the fraction of emission in ZPL out
of the total emission is only ∼5% [33].

Figure 2.1: 4 types of divacancies that occupy different carbon/silicon lattice sites.
2.2

Cr4+ ions in 4H, 6H-SiC

Cr4+ ions show different ZPL depending on the substitutional locations of Cr ions
in SiC. As mentioned in 1.3, 4H-SiC has 2 inequivalent lattice sites (h) and (k)
that experience different crystal field. 6H-SiC have 3 of those. For 4H-SiC, Cr A
corresponds to Cr ions occupying quasi-cubic (k) sites with Td symmetry that emit
ZPL observable at ∼1070 nm. CrC corresponds to those at hexagonal sites (h) with
ZPL observable at ∼1042 nm [48]. Symmetry of CrC is reduced to C3v due to

Figure 2.2: Photoluminescence of divacancies in a HPSI 4H-SiC sample excited by
780nm laser at 8.4 K.

Figure 2.3: c-axis and basal divacancy energy level structure in 4H-SiC for C3v and
C1h symmetry. Marks next to the red arrows specify the polarization of electric field
with respect to c-axis for electric dipole allowed transitions.

12
elongated bond in the direction of c-axis as mentioned in 1.3. ZPL of Cr ions with
intrinsic divacancies in Cr implanted HPSI 4H-SiC is shown in figure 2.4. Higher
resolution ZPL of Cr4+ in 4H and 6H-SiC is shown in figure 2.5. Cr4+ in 6H-SiC
were doped during the crystal growth process and ZPL peaks are much sharper than
those in 4H-SiC due to less sample damage.

Figure 2.4: Photoluminescence of Cr ions and divacancies in a Cr implanted 4H-SiC
sample excited by 780nm laser at 8.6 K.
The electron configuration for Cr4+ is 2 electrons in 3d shell (3d2 ). Using group
theory [49–51], we can determine the ground state and other existing states of free
ions. For free ions having 3d2 configuration, the ground state is 3 F, where left
upperscript denotes spin multiplicity 2S+1 (S: total spin angular momentum). The
next excited state depends on how much crystal field the ions feel in the crystal
and the energy of taking each state changes according to the field strength. Group
theory can determine how states of free spherical ions split when the symmetry is
lowered with crystal field. In tetrahedral Td symmetry, 3 F −→3 A2 +3 T1 +3 T2
as generating methods described in section 9.3 of Cotton [51]. A(B), E and T are
Mulliken symbol that means 1, 2 and 3-dimensional irreducible representations of
certain symmetry group, where the dimension corresponds to orbital degeneracy of
states. For example, 3T2 means orbital triplet and spin triplet, 9 states in total.
To know which of these is ground state and the next excited state, Racah parameters B,C and crystal field splitting parameter Dq needs to be measured based on

Figure 2.5: Photoluminescence of Cr ions in 4H-SiC and 6H-SiC samples in better
resolution at liquid nitrogen temperature ( 80 K)
spectroscopy experiments. Derived parameters combined with Tanabe-Sugano formalism are often used to show the summary of energy of states vs. crystal field
for complex metal ions [52]. From Tanabe-Sugano diagram for Cr4+ we can determine its ground state to be 3 A2 (F) and the next excited state to be either 3T2 (F)
or 1 E(D)[53, 54]. Zeeman splitting measurements were performed to conclude the
next excited state is actually 1 E because each ZPL of spin triplet component of
3 A only splits to doublet excluding the possibility of 3T with S=1 [48]. Cr4+ is
in relatively high field system for 4H and 6H-SiC. ZPL of Cr4+ is associated with
transition 1 E−→3 A2 .
The energy diagram of Cr4+ ions is shown in figure 2.6. Cr A with Td symmetry and
CrC with C3v symmetry theoretically has the same energy level degeneracy when
only the crystal field is considered. With spin orbit coupling in C3v symmetry,

14
ground state ms = ±1 states (Γ3 ) and ms = 0 become non degenerate. The electric
dipole selection rule is shown next to red arrows. ZPL comes from spin forbidden
but orbitally allowed transition.

Figure 2.6: Cr4+ energy level structure in 4H and 6H-SiC for Td and C3v symmetry.
ZPL of Cr4+ is associated with the transition 1 E−→3 A2 . The number at left on level
bars denotes state degeneracy and Γ specifies the irreducible representation of corresponding symmetry group. Marks next to the red arrows specify the polarization
of electric field with respect to c-axis for electric dipole allowed transitions.
The lifetime of Cr4+ ZPL is in the order of 10 - 100 µs depending on the doping condition. The relatively long optical lifetime is expected for spin forbidden transitions
that require spin flips. The photoluminescense decay profile from the excited state
to the ground state can be measured by accumulating the timing of each emitted
photon after excitation, expressed by I(t) = Io exp(−t/τ). τ is the optical lifetime
and Io is the photon counts right after the excitation in the first time bin. The PL
decay curve of the lifetime measurement is shown in figure 2.7. The goodness of
the fit was assessed by the zero offset and symmetry of the residual of the fit in
figure 2.8. The table 2.9 shows the measured lifetime on implanted 4H-SiC samples
(originally vanadium doped SI or highly purified SI wafer) and on doped 6H-SiC
samples. There is not much difference in lifetime between Cr ions at different sites.
At LHe temperature, Cr ions in 6H-SiC have lifetime 150µs that is close to the
values observed in doped 4H-SiC [55]. This 6H-SiC is expected to have the least
damage and longest lifetime in the crystal compared to other 4H-SiC samples.
The inhomogeneous spin coherence time T2∗ of Cr4+ in 4H-SiC was recently mea-

Figure 2.7: Optical lifetime measurement of Cr4+ ions in doped 6H-SiC at liquid
helium temperature. The fitting function is Io exp(−t/τ) and reveals optical lifetime
of 144 µs.
sured to be 37 ns. [55].This result was published at the same period when I was
looking into optical properties of Cr4+ ZPL. Due to this short coherence time, divacancies are more promising candidates as qubits so we will focus on them in later
chapters.
2.3

Other color centers

Besides the previous divacancies and Cr ions I discussed, I also measured optical
spectra and looked at some other color centers such as Vanadium, Molybdenum ions
in SiC and Cu in Si. In this section, they are briefly reviewed.
V4+ ions in 4H-SiC
Conventionally, vanadium is doped in SiC as minority carrier lifetime killer to
create semi insulating SiC wafer [56]. Depending on the position of the Fermi
level, vanadium ions exist in either V3+ , V4+ , V5+ form[57][58]. In our semi
insulating 4H-SiC samples, V4+ ions ZPL was observed as shown in figure 2.10.
ZPL associated with (h) sites is labeled as α lines and can be observed around

Figure 2.8: Optical lifetime measurement fitting residual shows the goodness of
fitting with single exponential Io exp(−t/τ).
wavelength 1280 nm. ZPL associated with (k) sites is labeled as β lines and can be
observed around wavelength 1335 nm [59].
The energy level of V4+ is shown in figure 2.11. V4+ has 3d1 electronic configuration and single electron doesn’t experience repulsion, which is the simplest case
considering energy levels. In Russel-Saunders coupling scheme, a free V4+ ion
takes only one energy level 2 D. Under tetrahedral field, it splits to the ground state
2 E and the excited state 2T . In trigonal field, 2T further splits to 2 E and 2 A states.
With spin-orbit coupling, all states split into Kramers doublets. In the spectroscopy
setup, we illuminated our sample with polarization perpendicular to c-axis and the
middle transitions in four α lines are expected to be stronger due to orbitally allowed
transitions.
The spin relaxation time T1 around 4 K is 1 µs or shorter depending on lattice
sites[60].

Figure 2.9: Summary of optical lifetime measurements of Cr4+ ions in implanted
4H-SiC and doped 6H-SiC samples at different temperature.
Mo5+ ions in 4H-SiC
Photoluminescense associated with Mo ions were observed in 4H-SiC around 1076
nm as shown in 2.12. The corresponding configuration of Mo ions in 4H-SiC
can be either substitutional or assymetric split vacancy [61] and different electric
charge state, which have not been determined in previous works [62–64] until recent
work using two laser spectroscopy under magnetic field [65]. The result indicates
substitutional Mo5+ at (h) site due to ground state Lande g-factor anisotropy. Mo5+
has 4d1 electronic configuration, which results in the same energy level structure
with V4+ ions. The measured optical lifetime of excited state is 56 ns. The
inhomogeneous spin coherence time T2∗ is 320 ns [65].

Figure 2.10: Photoluminescence of V ions in semi insulating 4H-SiC sample excited
by 780 nm laser at liquid helium temperature.
Cu in Si
Cu in Si and exhibit bright and sharp photoluminescense around 1228 nm with
optical lifetime 30 ns [66–68]. The PL spectra at different temperature are shown
in figure 2.13 and 2.14. The spin relaxation or coherence time of these centers have
not yet been investigated and the potential for qubits is still unknown.

Figure 2.11: V4+ energy level structure in 4H-SiC for Td and C3v symmetry. ZPL
of V4+ is associated with the transition 2T2 −→2 E. The number at left on level bars
denotes state degeneracy and Γ specifies irreducible representation of corresponding
symmetry group. Marks next to red arrows specify polarization of electric field to
c-axis for electric dipole allowed transitions.

Figure 2.12: Photoluminescence of Mo5+ ions in implanted sample (orange) in
comparison with PL4 divacancies in a HPSi sample (blue) excited by 780 nm laser
at 8.6K

Figure 2.13: Photoluminescence of Cu ions in Cu implanted Si excited by 780 nm
laser at 8.2K

Figure 2.14: Photoluminescence of Cu ions in Cu implanted Si excited by 780 nm
laser at different temperatures

29
Chapter 4

DESIGN AND SIMULATIONS OF PHOTONIC RESONATORS
This chapter explains why silicon is a good material for near IR wavelength photonic
devices at low temperature. The basic theory of finite difference time domain
(FDTD) simulations is explained. Then the entire FDTD simulation procedure is
described, which is used to determine the parameters for Si ring resonators on SiC.
4.1

Silicon photonic devices for near IR wavelength

The emission of qubits can be improved by using scalable on-chip cavity devices
that couple to the optical transition to generate lifetime limited emission and channel
it into optical waveguides. One strategy to develop on-chip photonic devices is to
fabricate them directly in the qubit host material. For this technique, it is required
to start with thin membranes on a low refractive index substrate, or on a substrate
that can be etched away or undercut. Even if some techniques exist to produce
membranes, it is not always the case that these membranes can host high quality
quantum emitters. Additionally, fabrication process often damages the material and
leaves unwanted charges that degrades qubits’ properties. For 4H-SiC, heteroepitaxial growth is not available and creating thin membranes is not straightforward.
An alternative is to make hybrid devices in a high refractive index layer located
on top of the substrate hosting the qubits, such that the emitters are coupled to the
evanescent field. In my research project, we used a crystalline silicon (c-Si) hybrid
platform of ring resonators and waveguides fabricated on top of SiC substrate shown
in figure 4.1.
We want to choose the right device layer material for the hybrid platform. We can
check if the material has large enough refractive index contrast to possibly confine
light well and if it has minimal absorption for the wavelength range of interest. The
intrinsic quality factor of the Si ring resonator surrounded by air is calculated for
different temperature as shown in figure 4.2. This is calculated based on absorption

30
coefficient of Si [70, 71] and resonator theory [72, 73]:
a2 = e−αL

(4.1)

∆θλres
(4.2)
πne f f L − λres ∆θ
1 + a2 |t1 | 2 |t2 | 2
∆θ = cos−1 2 −
(4.3)
2a|t1 ||t2 |
a is single round amplitude transmission and α is absorption coefficient. L is the
round trip length. t1 and t2 are self-coupling coefficient for two waveguides. λres
is the resonant wavelength. ne f f is the effective refractive index. These intrinsic
quality factor values correspond to silicon ring resonators with perfectly smooth
surfaces (no scattering loss) with material absorption loss, characterized by a single
round amplitude transmission a. Silicon has a bandgap at 1.11 eV ( 1120 nm
wavelength of light) at 300K [74]. At lower temperature the bandgap decreases and
silicon has less interband absorption. From the figure 4.2, at 1050 nm and 20K
the intrinsic quality factor exceeds 108 . At this low temperature Si shows sufficient
transparency to be used as a device layer coupling divacancy ZPLs ranging in the
interval 1080-1130 nm.

FW H M =

Figure 4.1: Left: c-Si ring resonator on 4H-SiC for spin-photon interfaces. c-Si is
drawn in red, while the transparent part underneath is 4H-SiC. RIght: Cross section
showing the ring resonator near color centers in the 4H-SiC underneath it, that can
couple to the evanescent field of the cavity.
4.2

Principles of finite-difference time-domain (FDTD) method

The finite-difference time-domain (FDTD) method is a systematic computational
method for electromagnetic fields using the central difference approximation of

Figure 4.2: Intrinsic quality factor of Si ring resonator surrounded by air at different
temperature.
coupled Maxwell’s curl equations (Faraday’s law and Ampere’s law) [75]. Space
and time is divided into grids, which is called Yee lattice to update the results
of both electric and magnetic field at certain location/time to those of neighbor
location/time. In an actual simulation, computation starts in a volume with finite
grids in space at time zero and, using initial condition of electric or magnetic field,
the field value at the neighbor grid in space at next time step will be calculated. This
continues until all field values at that time step of interest are computed. Then time
is incremented by one time step and the field calculation for the same region starts
again.
If we consider an electromagnetic (EM) wave in isotropic media, the electric displacement field D and auxiliary magnetic field H are parallel to electric field E and
magnetic field B accordingly.
D = εE

(4.4)

B = µH

(4.5)

where ε is electric permittivity and µ is magnetic permeability. The Maxwell’s curl

32
equations in isotropic media can be written as:
∂H
=0
∂t
∂E
∇×H −ε
=J
∂t
∇×E+µ

(4.6)
(4.7)

Each component of the electric field and auxiliary magnetic field is written,
∂E x 1 ∂Hz ∂Hy
= (
− Jx )
∂t
ε ∂y
∂z
∂E y 1 ∂Hx ∂Hz
= (
− Jy )
∂t
ε ∂z
∂x
∂Ez 1 ∂Hy ∂Hx
= (
− Jz )
∂t
ε ∂x
∂y
∂Hx
1 ∂Ez ∂E y
= (
∂t
µ ∂y
∂z
∂Hy
1 ∂E x ∂Ez
= (
∂t
µ ∂z
∂x
∂Hz
1 ∂E y ∂E x
= (
∂t
µ ∂x
∂y

(4.8)
(4.9)
(4.10)
(4.11)
(4.12)
(4.13)

where J is the electric current density. According to the Yee algorithm[75, 76],
if we denote any function evaluated at a grid point in space and time with lattice
increment (∆x,∆y,∆z,∆t) in x, y, z and t coordinates,
u|i,n j,k = u(i∆x, j∆y, k∆z, n∆t)

(4.14)

the partial differential equations of time are approximated using centered finite
difference expressions at a space point (i, j, k):
∂u|i,n j,k
∂t

n+ 1

n− 1

u|i, j,k2 − u|i, j,k2
∆t

+ O[(∆t)2 ]

(4.15)

Partial differential equations of space coordinates can be approximated in similar
manner. As an example, using this approximation on equation 4.10 , it can be
written as following:

∆t ©
n+ 1
Ez |i, j,k2 =

Hy | n 1

i+ 2 , j,k

− Hy | n 1

i− 2 , j,k

∆x

Hx | n

i, j+ 21 ,k

− Hx | n

i, j− 21 ,k

∆y

n− 1
− Jz |i,n j,k ® + Ez |i, j,k2
(4.16)

33
As we can see from this equation, Ez is approximated by a combination of Hx and
Hy at a half previous time step and Ez at the previous time step. Now we want to
know how to approximate Hx and Hy using equations 4.11, 4.12, and 4.15.

n− 1

n− 1

n−
n−
− E x | 12
E | 2
Ez |i+1,2j,k − Ez |i, j,k2 ª
i+ 2 , j,k− 12
∆t © x i+ 12 , j,k+ 21
® + Hy | n−11
Hy |i+ 1 , j,k =
i+ 2 , j,k
∆z
∆x
(4.18)

As a further example, we write down E x component used in Hx above:
∆t ©
=
Ex | 1
i+ 2 , j,k+ 12
n− 12

Hz | n−11

i+ 2 , j+ 12 ,k+ 12

i+ 2 , j− 12 ,k+ 12

∆y

n−1
− Jx |i+
+ Ex |
, j,k+ 1

Hy | n−11

− Hz | n−11

i+ 2 , j,k+1

− Hy | n−11

i+ 2 , j,k

∆z

n− 32

i+ 21 , j,k+ 12

(4.19)
You can see the half step coordinate offset between electric field and magnetic
field component in these equations. With centered difference approximation, each
electric field and magnetic field component lie at a different 3D spatial lattice point
offset by half of the increment, in order to update them in time sequence. Also, the
time step is half of the increment different for electric and magnetic field. This is
shown in figure 4.3.
4.3

Comparison with other EM simulation method

Finite element method (FEM)
FEM replaces the Maxwell equations in continuous space with simpler interpolation
functions in smaller subspaces (elements). By doing this, functions with infinite
degree of freedom can be approximated by solving finite coefficients of simpler
functions. The first step is discretization of the space that will be simulated. The
entire space is divided into small elements that can take shapes of triangles or
rectangles etc. in 2D, tetrahedra or rectangular blocks etc. in 3D. The size and distribution of the elements are carefully decided so that the numerical approximations

Figure 4.3: Electric and magnetic component positions in Yee algorithm.
are sufficiently accurate with appropriate computation time. The principle is that
electromagnetic waves behave in a way that they minimize their total energy. FEM
is used in COMSOL Multiphysics software offered by COMSOL, Inc.
4.4

MEEP simulation of c-Si on SiC ring resonator devices

We used the open-source software MEEP[77] to simulate our Si ring resonator
devices on SiC with FDTD method. This section explains details of the MEEP
simulation steps. These simulations were run in multi-core computers using the
parallel computing version of MEEP, meep-mpi. The most time consuming simulation described in the section is a 3D ring simulation with waveguide, typically
taking 2-3 hours with 20 processors.
2D cylindrical ring simulation
In this first simulation step, we want to simulate ring resonators by looking at the
modes confined in a 2D space assuming cylindrical symmetry. We’d like to choose
the ring’s radius, width and height at the end of the simulation step. We prefer

35
smaller ring radius (smaller mode volume), smaller ring height (More evanescent
field underneath the substrate) and high quality factor. We wanted to simulate single
TM mode ring resonator. The refractive index configuration is shown in figure 4.4
(a). TM mode was chosen because stronger field can exist beneath the Si and SiC
interface compared to the transverse electric mode due to the field discontinuity,
which is shown in figure 4.4 (b)(c). This simulates the ring structure without any
waveguide. Because it has continuous rotational symmetry, one dimension in φ is
reduced and we can only think about field change in r and z coordinates. In MEEP,
you can evaluate the quality factor by using special harmonic inversion function at a
given point inside the ring. The simulated quality factor vs. ring radius with a fixed
height 360 nm and width 300 nm is shown in figure 4.5. One can see more light
leaking out through the substrate to the external ring direction when the radius of the
ring is smaller. In this ring design, the radiation limit was reached with radius ∼3.25
µm with simulated Q<1000. The radius 3.75 µm with simulated Q was chosen to
minimize the ratio of the quality factor Q=7 × 105 to mode volume V considering
that the quality factor in the current fabricated devices is limited by scattering losses
to Q=23000. The simulation gives a calculated V of 19.5 (λ Z PL /nSi )3 . The 2D
cylindrical ring simulation code is attached in the appendix ??.

Figure 4.4: 2D cylindrical ring simulation (a) Refractive index setting (green:
SiC/n=2.64, yellow: Si/n=3.55 and blue: air/n=1.00)(b)ln|Ez | with colormap(c)
Plot of ln|Ez | at the ring width center cross section.
3D ring simulation
3D ring simulation is necessary if we introduce waveguides that guide light to grating
couplers. In contrast to 2D ring simulation with perfectly smooth sidewalls, roughness on rings is inevitable because of the computational grids (i.e. the resolution).
In typical resolution of 40 pixels per unit length, 1 um used in these simulation, the

Figure 4.5: 2D cylindrical ring simulation quality factor vs. ring radius with height
360 nm and width 300 nm.
refractive index assignment causes rough radial surfaces with roughness of order
∼10 nm. So we should consider the simulated quality factor in 3D a lower bound of
that of fabricated ring resonators only with scattering effect. To fabricate close to
critically coupled ring resonators, we simulated ring resonators with waveguides at
different distances from rings. The typical simulation setup and results are shown in
figure 4.6 (a)(b). The change in quality factor depending on waveguide-ring distance
is shown in figure 4.6 (c). The intrinsic quality factor in this 3D simulation was
2.1 × 105 . From this result, we choose to fabricate arrays of ring resonators with
different waveguide separation that gives 20-80% of intrinsic quality factor. The 3D
ring-waveguide simulation code is attached in the appendix ??.
2D and 3D grating coupler simulation
To efficiently collect and detect emission from the divacancies grating couplers were
added to the end of waveguides for diffracting light to a microscope objective. Basic

Figure 4.6: 3D ring simulation with waveguides. (a)Refractive index setting (color
distribution same with figure 4.4) (b)ln|Ez | (c)Quality factor vs. waveguide distance
grating coupler parameters such as grating period and duty cycle were simulated
for wavelength 1080 nm. To calculate the grating coupler efficiency we place a
flux region in the simulated space where the fields are scattered and evaluate the
electromagnetic flux or integral of Poynting vector going through that region. The
following figure 4.7 depicts the typical simulation setup in 2D. The two lines are
the flux regions in this simulation for evaluating diffracted light in almost vertical
or angled direction accordingly. Also, a waveguide transmission simulation is
performed to evaluate the flux going through the end of the waveguide, which is
set to the same length of grating coupler in the other simulation. The grating
coupler efficiency in these simulations is calculated by the normalization flux (F1)
divided by the sum of the flux going through vertical/angled direction (F2+F3) in
the grating coupler simulation, as shown in figure 4.7. In 2D simulations, gratings
were considered to be straight and infinitely long in z direction.
I started the flux simulations by sweeping the grating period and duty cycle to find
a parameter range that gives significant amount of F2 flux and a good wave profile.
Our objective lens can collect light from a light cone of angle less than ∼ 38◦ , so we
also wanted to pick parameters that ensure the grating doesn’t diffract significantly
beyond that angle. Then we simulated the flux in a finer sweep of parameters in
this range and also took electric field output snapshots at the end of the simulation.
The summary of the flux simulations with the finer sweep is shown in figure 4.8.
We needed to look at the electric field diffraction pattern by plotting the snapshot
to make sure the grating actually diffracts. Even if there seems to be a lot of flux
going through F2, light might be scattered with the first grating without propagating

38
much. We wanted to see plane wave like pattern similar to what is shown in the right
bottom figure 4.7. In this design of simple grating couplers, increasing the duty
cycle with fixed period increases diffraction angle (figure 4.9) and increasing period
with fixed duty cycle also increases diffraction angle (figure 4.10). This trend can
be seen in the right panel of figure 4.8 by F2/F3 flux. To ensure the diffraction angle
is not too steep I chose parameters with F2/F3 >10 and F2 is close to maximum in
the left panel of 4.8. From this simulation we picked grating parameters of grating
period 470 nm and duty cycle 82 % (Grating width 385 nm and gap 85 nm) for
fabrication.
3D simulations use concentric grating couplers, that are implemented in fabrication
to see changes in efficiency compared to straight gratings. The 3D simulation
configuration is shown in figure 4.11. The simulation revealed the concentric
design doesn’t change much the optimized parameters obtained in 2D simulation.
The best parameters obtained from 3D simulation is period 490 nm and duty cycle
80 %. The The 2D/3D simulation codes are included in appendix ??.

Figure 4.7: 2D grating simulation normalization simulation on the left. Main
simulation is on the right. Top figures are refractive index configuration and bottom
figures are plotting ln|E |.

Figure 4.8: 2D grating flux depending on period and duty cycle.

Figure 4.9: 2D grating diffraction angle change depending on duty cycle (fixed
period)

Figure 4.10: 2D grating diffraction angle change depending on period (fixed duty
cycle)

Figure 4.11: 3D grating simulation configuration. Each figure is at the center plane
of the simulated space.

56
Chapter 6

PHOTONIC DEVICE CHARACTERIZATION
Experimental setup
A home-built optical confocal microscope setup is used to characterize the fabricated
ring resonators. The diagram of the setup is shown in figure 6.1 and the pictures
of the actual setup are in figure 6.2. A 950 nm long-pass dichroic mirror was
used to filter 780 nm excitation laser for spectroscopy measurements. For ODMR
measurements, the nitrogen gas transfer port was replaced by SMA ports that can
be connected to MW sources. Each ZPL of divacancies (PL1-4) was filtered using
tunable longpass and shortpass filters. A superconducting nanowire single photon
detector (SNSPD) was used for lifetime measurements on divacancies and Cr ions.
An InGaAs detector after a beam splitter was used for the timing input to the time
correlated photon counting board. A supercontinuum laser with repetition rate of
20 MHz and 2 kHz was used for divacancies (lifetime ∼15 ns) and Cr ions (lifetime
∼130 µs) accordingly. The coarse resonance measurements of Si ring resonators
were performed using a near IR spectrometer with a supercontinuum source. The
gratings in the spectrometer are able to measure quality factors up to ∼30,000
reasonably. The nitrogen gas tuning can typically tune resonances of silicon ring
resonators for ∼1.5 nm at 1070 nm.
To further characterize the resonance in higher resolution, I built a tunable external
cavity diode laser with Littman-Metcalf configuration using Thorlabs kit (TLKL1050M) with AR coated diode (LD-1050-0050-AR-2) purchased from Toptica as
shown in figure 6.3. The coherent light was generated by stimulated emission with
the help of an external cavity between the end face of the diode and the mirror.
The feedback light that selects the wavelength of amplified light comes from the
1st order diffraction from the grating, and it was reflected back by a mirror in
Littman configuration. The direction of the output laser is fixed during tuning
because the output is the reflected light (0th order diffraction) from the grating,
which is a main advantage over Littrow configuration. The wavelength tuning can
be performed by moving the angle of the mirror and by sending back light with a
different wavelength. The mirror can be controlled either with a DC servo motor
(Z812) or with a piezoelectric actuator attached to the contact point of the motor

57
and the mirror arm. The maximum power is 50 mW around 1040 nm and > 10 mW
in the range 1020-1085 nm before fiber coupling.

Figure 6.1: The optical confocal microscope setup diagram.

Figure 6.2: The actual setup (left) viewed from top and (right) viewed from the
right.
Mode hop free tuning for a relatively large frequency range was required for scanning
a resonant peak of an optical resonator. The mode hops occur when the next mode

Figure 6.3: The actual Littman configuration in the setup. The red solid lines show
the main laser path and the dotted line shows the feedback path.
has more optical feedback than the current mode, which often happens when the
resonant peak of internal cavity formed by two end diode faces and of the external
cavity don’t match. We need to maintain both cavity gain peaks aligned during
wavelength tuning. The internal cavity resonance moves by changing the diode
current. The current and piezoelectric actuator voltage need to be changed at the
same time with an optimized ratio to prevent mode hops[91]. The wavelength change
of the internal cavity mode peak against diode current is expressed by β = ∆I∆λLD . To
measure β, the laser diode output without feedback was measured using an optical
spectrum analyzer for different diode current. Part of the measurements for low
current 40-60 mA are shown in figure 6.4. β=2.2 GHz/mA at low current and β=2.6
GHz/mA at high current around 150 mA.
After lasing was confirmed with alignment, laser modes are monitored using a
scanning fabry-perot interferometer. When the feedback is not optimal the laser
operates in multimode with next mode separated by 1.9 GHz corresponding to
∼8 cm external cavity length. After single mode operation is confirmed at fixed
wavelength, the output power is maximized by optimizing the alignment. Then

Figure 6.4: The internal cavity resonances change due to different diode current
(40-60 mA).
piezo tuning as a function of applied voltage ∆V∆λ
was measured with a fixed fabryPZT
perot resonance. With previously measured β, I built an inverting amplifier that
controls the laser diode current depending on the piezoelectric actuator voltage so
that internal and external cavity modes move at the same rate. I used a potentiometer
for one of the 2 resistors to adjust the change of β at higher diode current during
tuning. The external signal proportional to the piezo voltage is input to the inverting
amplifier and its output was fed to the laser current controller.
After single mode operation in a full piezo scan without mode hops was confirmed,
piezo calibration was performed. Piezo movements are not linear against applied
voltage and the wavelength change per unit voltage change at different piezo voltages
was measured as shown in figure 6.5. Piezo modulation of 1 Hz triangular wave
(0-150 V) is used for measurements. The InGaAs detector of the IR spectrometer
continuously takes frames during the scanning and the photon counts at every
wavelength pixel is integrated for each frame as output signal. Because the linewidth

60
of laser was not measured and it is less than the 67 MHz scanning fabry-perot
resonance FWHM, the scanning frequency is adjusted so that this scanning method
can give 95 MHz resolution. 1 GHz separated sidebands were added by electrooptic modulator as a standard and changed the resonance of a scanning fabry-perot
to measure peak to peak separation in the range of 0-150 V. The resulting curve was
fitted and used for correction of resonance scan data.

Figure 6.5: The actual Littman configuration in the setup. The red solid lines show
the main laser path and the dotted line shows the feedback path.
The laser power is modulated during scanning and the laser power versus diode
current was measured to provide correction to scan data as well. The laser power
is almost linear to the diode current as shown in the left panel of figure 6.6. The
stability of the laser power was measured over 8 hours to verify that the laser is stable
enough for scanning measurements as long as a couple seconds each, as shown in
the right panel of figure 6.6. The wavelength shift was < 1.0 pm/hr.
c-Si on SiC resonators measurement results
The measurements of the quality factor of ring resonators were mostly performed by
focusing the laser on the input port and collecting the output from the drop port as
shown in figure 6.7. One of the best ring resonators has a quality factor of 23000 at
1078 nm measured at 20 K. The measurement results are shown in figure 6.8. The
condition for critical coupling of ring resonators coupled with two waveguides is
α = tt12 , where α is ring round-trip loss coefficient, t1 is the self coupling coefficient

Figure 6.6: The ECDL power drift over 8 hours.
from input to throughput port and t2 is self coupling coefficient from add to drop
port. Because there is always loss (α , 1), the symmetrical waveguide design that
we used is never at critical coupling condition.

Figure 6.7: Main measurements were performed through the drop port.

Figure 6.8: (a)Coarse measurement through the drop port with supercontinuum
laser. (b)Coarse measurement through the thoroughput port. Arrows indicate the
locations of resonances. (c) Fine measurement with tunable laser scanning. The
Lorentzian fit reveals Q∼23000.
The Purcell factor for a qubit in hybrid cavities is[36]:
3
3 λ Z PL nc Q E(r qu bit )
FZ PL = 2
nc
nh V E(r max )
4π

(6.1)

Based on simulation and measurements, the mode volume of the ring resonator is
19.5 and the best measured quality factor is 23000 at a wavelength of 1078 nm.
This would result in a Purcell enhancement factor of 36 assuming perfect dipole
alignment for an emitter located at 10 nm below the surface. The estimated Purcell
enhancement factor for an emitter at a depth of 100 nm is 12 due to a 3 times smaller
field.
6.1

Conclusion

We were able to fabricate on-chip silicon ring resonator on 4H-SiC with quality
factor of 23000. The crystalline silicon membrane transfer method described
in 5.4 can be used to successfully place membranes as a photonic device layer
on silicon carbide and potentially other host materials. The smooth surface of
crystalline silicon has the potential to achieve better quality factor than amorphous
silicon devices. The change from a-Si to c-Si or using resist reflow technique only
improved the quality factor by order of 2. This suggests the limiting factor is surface
or material absorption of silicon used in this work.

63
Chapter 7

CONCLUDING REMARKS
In my Ph.D. projects, I fabricated Si on SiC hybrid ring resonators to couple ZPL
emissions of divacancies in 4H-SiC. Photonic devices such as ring resonators can be
used to enhance coherent emission for indistinguishable photons used in quantum
networks. Quantum entanglement generation rate is a key measure for the distance at
which quantum communication can be established. This rate scales linearly or with
higher order with indistinguishable photon generation rate, which makes enhancing
coherent emission of qubits an important engineering challenge.
Among different qubits, divacancy defects in 4H-SiC recently emerged as promising
candidates with long spin coherence time and good optical stability compared to
NV centers in diamond (See chapter 2). I alsoe studied a few other impurities like
Cr and Mo ions in 4H-SiC and they were found to possess relatively short T2 < 1 µs,
which does not satisfy the high fidelity qubit polarization condition. My research
is mainly focused on divacancies in 4H-SiC and fabrication of photonic devices on
4H-SiC. The ZPL emission of divacancies is useful as indistinguishable photons
for entanglement generation, which only consists of ∼5% of total emission. In
order to unleash the potential of divacancies it is important to enhance only the
usable coherent emission with narrow-linewidth photonic devices. In my research
I developed a fabrication method for silicon ring resonators on SiC (or on other
materials). Silicon is used for the photonic device layer. This hybrid approach
avoids charge build-up around the qubits, which is believed to degrade optical
properties of the emitters. It is transparent and suitable for coupling divacancy’s
near IR wavelength from 1050 nm as shown in chapter 4.
4H-SiC is widely used for power electronics devices and readily available in mass
production. Recently, a single divacancy residing in commercially available p-i-n
diodes showed T2 ∼1 ms at 5K [92]. Integrating qubit host materials with classical
semiconductor devices might be beneficial as a new type of quantum devices. The
Si photonic devices shown in this thesis are compatible with this platform as long as
divacancies are located in the proximity to the surface. Silicon integrated photonics
is currently accepted as a next generation power-efficient classical telecommunication platform [93]. The advantage is low-cost and high-volume silicon photonic

64
on-chip devices manufacturing that is compatible to the CMOS technology. The
Si hybrid devices can be readily integrated with a variety of Si components such
as filters, multiplexers, modulators and sensors. Additionally, integration between
silicon photonics and superconducting nanowire single photon detectors (SNSPDs)
[94] can enable on-chip spin-spin entanglement platform and a range of quantum
technologies.
For quantum emitters with lower than 1050 nm wavelength, different material is
required for the optical device layer. For example, silicon vacancies (VS i)in 4H-SiC
exhibits ZPL at 860 and at 920 nm [95]. Materials such as GaAs with bandgap
1.44 eV (300 K) is transparent enough for silicon vacancies at low temperature.
Currently, our group is developing GaAs hybrid photonic devices for Yb3 + ions in
YVO with optical transition at 984 nm [96]. GaP with bandgap 2.24 eV (300 K) can
be used for confining light with shorter wavelength > 600 nm including ZPL of NV
centers in diamond at 637 nm [97].
Direct device fabrication on SiC membranes can achieve largest light confinement
at the the spot of qubits in SiC, achieving strong enhancement of the emission.
Vuckovic group showed 4H-SiC photonic crystal on insulator with fusion bonding
technique [98]. If this can be expanded to wafer scale bonding, mass production of
on-chip quantum networks will be possible.

42
Chapter 5

FABRICATION OF ON-CHIP PHOTONIC DEVICES FOR
COUPLING TO DEFECTS IN SIC
In this chapter I describe the fabrication procedure for on-chip photonic devices for
coupling to luminescent defects in silicon carbide. The most successful effort was
hybrid devices based on crystalline silicon (c-Si) placed on top of 4H-SiC.
5.1

Qubits generation in 4H-SiC

Ion implantation and divacancies
The concept of the hybrid devices that we aim to fabricate is that the photonic
mode is confined in a silicon device and is evanescently coupled to luminescent
centers located close to the surface of the substrate. In this case we aim to couple
to divacancies. Divacancies are common and intrinsic in 4H-SiC and the ZPL of
ensemble divacancies can be readily measured in our high-purity semi-insulating
4H-SiC wafers purchased from CREE Inc[32, 34]. Divacancies can also be created
using Si or C implantation[38, 78] or electron irradiation[45]. Using implantation
is advantageous in our case because the divacancies are created close to the surface.
Since we also wanted to generate other color centers based on other elements, we
also created divacancies by implantation of ions from the elements Cr and Mo.
Before implantation, we estimated the depth distributions of the implanted ions
using computer simulations for Stopping and Range of Ions in Matter (SRIM)[79].
Having divacancies closer to the surface is beneficial because it leads to stronger
coupling to the resonator mode. However, generally the proximity to surfaces leads
to degradation in the optical and spin properties of the divacancies. Since we were
not sure about these tradeoffs, we had some of our samples implanted with 10 and
150 keV implantation energy. For example for Cr implantation the distribution of
implanted ions peaked between 9nm and 90nm. We assumed that divacancies will
be created similarly to this distribution. The Cr ion density at 10nm depth with dose
1013 is estimated to be 1019 /cm3 . The results of our implantation is shown in the
following table, which also indicates if divacancies were observed.

43
Implanted ion
Ni
Cr
Mo

Implantation
energy (keV)
150
150
10, 150
200

dose (cm2 )
109 ,1011 ,1013
109 ,1011 ,1013
109 ,1011 ,1013
5×109 , 5×1010

Photoluminescense detected?
(1000-1500nm)
Divacancies
Divacancies
Divacancies, Cr ions
Divacancies, Mo ions

Table 5.1: List of samples with different ion implantation and photoluminescense
Annealing
An annealing process is required such that the generated vacancies migrate and
form divacancies. We annealed implanted 4H-SiC in Argon at 900 ◦ C. We chose
this temperature because divacancy formation decreases and trivacancies formations
starts to dominate over 1400 ◦ C [80]. We tried different annealing time, 30, 120,
240 mins and observed how the ZPL of specific divacancies change. The annealing
process includes additional ramp up/down time of 30 mins each, which is kept the
same for different annealing time. We note that it might be better to decrease the
ramp time to increase PL of divacancies, as suggested by Gällström et al. [81]. The
following ?? shows the ZPL of divacancies under different annealing temperature
condition.
5.2

4H-SiC transfer

When starting this project, we first attempted to make photonic devices directly in
the host material, SiC. Heteroepitaxial growth is available for 3C-SiC but not for
4H, or 6H-SiC. The alternative method is transferring a thin membrane of 4H-SiC
onto a different material and fabricating the device directly into the SiC membrane.
We transferred a thin layer of ion-sliced 4H-SiC on silica following the procedure
similar to the one described in Lee et al. [82].
The transferred membranes were inspected under SEM. As it can be seen in figure
5.1, generally they have large roughness >10nm on the surface. We considered this
surface too rough to have good photonic devices fabricated on and changed to hybrid
approach that will be discussed in next 2 sections. Also, we did photoluminescence
measurements on this material and we discovered that it was full of defects, including
divacancies with very broad linewidth (∼1 nm for PL1), which would make it difficult
to develop devices that work at single photon level.

Figure 5.1: SEM image of 4H-SiC membrane surface transferred by smart cut
method.
5.3

a-Si:H Deposition

The next technique that we tried was by depositing amorphous silicon onto SiC, with
the goal of fabricating the devices directly into the silicon for evanescent coupling to
defects in SiC. We deposited hydrogenated amorphous Si (a-Si:H) on 4H-SiC with
plasma enhanced chemical vapor deposition (PECVD). We used parameters in table
5.2.The deposition rate is approximately 26 nm/min. The ring resonator devices
we fabricated using a-Si only gave best Q ∼ 5000. SEM inspection revealed there
is noticeable roughness on the surface of a-Si as shown in 5.2. The surface shows
grains of a-Si [83, 84]. We tried depositing alumina Al2 O3 for 20 nm to reduce
this effect as there might be substrate dependence on roughness [85, 86]. A 20nm
thin layer of alumina between SiC and a-Si doesn’t disturb the confined light profile
according to simulation. Measurements with higher resolution of roughness were
performed under atomic force microscope (AFM). The measured surface roughness
was slightly improved compared between a-Si deposition with and without alumina
as shown in figure 5.3 (a)(b). The roughness comparison AFM images of a-Si, c-Si
and the original substrate are shown in figure 5.3. However, this roughness was
still considered too high so we decided to fabricate devices in a crystalline silicon
membrane transferred on top of SiC.

45
Deposition parameters

Values

RF forward power

10 W

5% SiH4 in Ar flow rate

40.0 sccm

Chamber pressure

801 mTorr

Wafer temperature

200 ◦ C

Deposition rate

26 nm/min

Table 5.2: a-Si recipe

Figure 5.2: SEM images of a-Si roughness. (a) a-Si deposited before any patterning
procedure (b) A grating coupler after etching and cleaning. process
5.4

c-Si Membrane Transfer

The fabrication process of the hybrid devices starts with transferring c-Si membrane
from silicon on insulator (SOI) chips by Soitec. The SOI wafer has a Si device
layer thickness of 500nm, close enough to the desired 360 nm height for the ring
resonators. Si is B doped p-type and the buried oxide thickness is 3 um. The c-Si
transfer procedure is summarized in table 5.3. The details of each step is described
in following sections. This c-Si transfer procedure was inspired from work by Li
et al. [87].

Figure 5.3: AFM images for comparison of roughness. (a) Deposited a-Si. (b)
Deposited 20nm alumina then a-Si. (c) Transferred c-Si all on top of 4H-SiC. (d)
AFM on the 4H-SiC substrate.
Cleaning
Purchased SOI wafers were dipped in Nanostrip(H2 SO4 , H2 O2 ) for one hour. Then
they were cleaned in typical solvent rinsing (acetone, methanol, IPA).
Thinning c-Si to desired layer depth
Because it is hard to find SOI chips with the exact Si thickness of what we desire to
use for the devices, this step is required to adjust the thickness of the membranes.
The oxidization rate can be calculated and fitted based on the theory described by
McGuire [88]. The rate depends on different factors such as Si surface charges,
dopant concentration or oxygen distribution, pressure, etc. We took a few data
points of (oxidation time, oxide thickness) and generated a MATLAB code that
fits these to the theoretical curve to estimate the correct oxidation time, which is
included in ??. This calculates for both wet or dry oxidation.
Based on the calculated oxidation time, we performed wet oxidation of 32 mins at
1000 ◦ C. Before and after the oxidation process, there is 1.5 hrs of ramp up/down
time in nitrogen environment from/to 700◦ C. After the oxidation process, we

47
Step

Description

Cleaning

SOI chips are cleaned with Nanostrip.

Thinning the Si layer

Oxidation and HF wet etching are performed.

Dicing Si membranes

500 µm×500 µm squares are patterned.

Releasing membranes

HF wet etching of BOX layer are performed.

Cleaning 4H-SiC substrate

The surface is changed to hydrophilic state.

Picking up membranes

Quick pick-up with the substrate was performed.

Slow natural drying

Membranes are attached without air or water underneath.

Check membranes quality

Optical microscope and SEM examination are performed.

Table 5.3: c-Si transfer procedure
removed the generated oxide by wet etching with buffered HF. The final thickness
of the Si device layer is fitted and calculated in a spectral reflectance analyzer by
Filmetric with >95% goodness of fit and is <±10 nm from the desired thickness.
Dicing Si membranes
This step is required to make membranes in small size so that it takes a short time
to release the membranes and also increases the success rate of attachment of the
membrane to the SiC substrate. Initially we hand cleaved an oxidized SOI chip into
3 mm square small pieces and tried to release the membranes in 52% HF. After 24
hours some of them were still not released and the Si membranes show gradation of
color suggesting etching and damage by HF. Also, transferring released membranes
in large size easily induce bending and cracking of membranes, which prevents good
attachment to the substrate. When the attached membrane will be cleaned or spin
coated later, one small opening between the substrate can allow liquid to flow in
and the membrane can be flushed away. The same problem occurred when we tried
transferring a large membrane with holes spaced regularly. Due to these reasons,
we tried membranes with a smaller size of 500 µm × 500 µm and this worked well
with >50% yield.
We used a positive resist AZ 5214E for patterning squares on SOI chips. We exposed

48
spin coated chips with a photomask in a mask aligner photo-lithography system.
The mask design is shown in 5.4 (a). The details of the patterning procedure is
shown in 5.4. The etch will remove silicon from the exposed part of SOI chips and
create separated Si membranes. We used an etching recipe described in table . A
patterned SOI chip is shown in 5.4 (b) under optical microscope.
Step

Description

Step

Put SOI chips in the container for 3 mins.

Spin coating

1500 rpm/ 60 s (> 2 µm).

Soft baking

110 ◦ C/ 45 s.

Exposure

5 s (75 mJ in total with 15 mJ /s).

Development

70 s in MF-319 developer.

Cleaning

Solvent cleaning with sonication for 5 mins.

ICP/RIE etching

pseudo-bosch for 8 mins.

Resist removal

Dip in acetone for 3 mins.

Table 5.4: SOI chip square patterning procedure
Releasing the membranes
This step releases Si membranes by detaching the Si device layer from its handle
layer. We put small pieces of patterned SOI chips in 52 % HF filled in a small
polypropelene jar Si side facing up. Generally it takes 15-30 mins to release all
the membranes. We can identify this by the color change of the membranes due to
removal of the BOX layer. We prepared large containers filled with water for rinsing
membranes. Then we take the chip out slowly without tilting it to prevent membranes
from floating away. We put it in water angled to make water go underneath the
membrane and flush them away from the handle layer. The membranes are floating
on the surface of water. We scoop a single membrane using a plastic spoon and
transfer to different containers filled with water several times for cleaning the back
side that will be attached to the substrate as shown in figure 5.5. At the end, we
transferred the cleaned membrane to a large container filled with clean water where

Figure 5.4: (a)Design of the photomask (b)Etched SOI chip after photolithography
(light gray: Si, dark gray:SiO2 )
we will be picking it from. At this stage, any membrane that looks bent or folded
is discarded. Bending or folding of a membrane often allows water to exist at the
interface of the membrane/substrate, which is concluded with >30 trials.

Figure 5.5: Cleaning by transferring a floating membrane to clean water

50
Cleaning the 4H-SiC substrate
Right before the pick-up process, oxygen plasma cleaning was performed to the
4H-SiC substrate. This step is required to make the substrate hydrophilic such that
the bending angle of a picked-up membrane while drying won’t be too large. Also,
it makes the substrate clean such that water underneath the substrate is easier to
move away when the membrane is pushed and attached by Van der Waals force,
preventing for water left under the membrane. This step was essential for achieving
a high yield of usable membrane area.
Picking up membranes and drying
This step involves transferring floating membranes to the substrate and natural
attachment of membranes using Van der Waals force. We hold a cleaned substrate
underneath a cleaned floating membrane and quickly pull it upward and toward the
membrane out of water. This requires some speed to ensure the membranes stay on
the substrate before they flow away. After picking-up the membranes, the substrate
is placed in a place without disturbance and the membrane dries slowly. Rapid
drying using a hot plate didn’t gain good results with many bubbles underneath a
membrane. If the substrate is smooth and the membrane is flat, Van der Waals force
will push water away and shouldn’t leave any water underneath the membrane that
can be seen by eye (figure 5.6). After the substrate dried fully we put it on a hot plate
with temperature > 150 ◦ C and inspect if any water is left. The following figures 5.7,
5.8 show examples of successful and failed attempts of membrane transfer. After this
step, if the membrane has more than 50 % area left without any water or other defects,
we will use it in next electron beam writing step. This entire c-Si transfer procedure
overall gives ∼50 % yield of such usable membranes. Because this transferring
method requires physical dexterity and we don’t have control over where to put the
membrane on the substrate, we wanted to find more reliable methods of fabricating
hybrid devices. For this, we attempted to transfer GaAs photonic crystal devices
using a nanomanipulator implemented in FIB/SEM system, which is described in
A.3.
5.5

c-Si on SiC device patterning and fabrication

Electron beam lithography
All the device patterning was performed under Raith EBPG 5000+ or 5200 system operated at electron energy of 100 keV. ZEP520A positive tone resist is used.
Also, our SiC substrate is not conductive so we spin coated conductive polymers,

Figure 5.6: Picking up the membrane, drying and attachment on the substrate.
AQUASAVE to prevent electron beam trajectory distortion due to built up charges.
The spin coating and development parameters are shown in table 5.5. Ring resonators are patterned with 300 pA, approximately 2 nm beam spot size. The
electron scattering induces undesired exposure to nearby exposed locations. Such
proximity effect can be corrected by knowing how much electron energy is exposed
to neighbor resist by a single pixel exposure. The point spread function distortion
due to proximity effect is simulated by Monte Carlo simulation, PENELOPE [89].
We simulated the proximity effect with settings of 10M electrons for the sample
layers from the substrate up to ZEP resist.
ICP/RIE etching
A resist reflow technique is used to improve the sidewall roughness caused by
resist roughness in the process of development[90]. By heating the resist at right

Figure 5.7: Successful membrane transfer. Most membranes are single but some of
them are connected.

Figure 5.8: Failed membrane transfer. Water scattered underneath the membrane.
Heating on a hot plate caused water to evaporate and made bulges on membranes.
Wrinkles in membranes allow water to enter and flush of the entire membrane.

53
Steps

Parameters

Resist spin coating

5000 rpm / 60 s

Baking

180 ◦ C / 3 mins.

AquaSAVE spin coating

1500 rpm / 60 s

Baking

70 ◦ C / 5 mins.

Development

Dip in ZED (slowly stirred) / 3 mins
then rinse with MIBK / 30s and with water.

Resist reflow

145 ◦ C / 10 mins

Table 5.5: E bean writing resist related procedure
temperature it slowly melts and roughness in the resist is reduced. We put the sample
in an oven at 145 ◦ C for 10 mins, which is empirically determined by monitoring
the resulted sidewall angle under SEM. As described in a later section for our
devices that have quality factor ∼ 20000, the resist reflow did not result in a huge
improvement in the quality factor (< 10%).
After the reflow process, we etched the sample in SF6 /C4 F8 plasma for ∼ 6 mins
with 60 nm /min etching rate. Santovac oil is applied at the back of the sample for
fixing the sample and for thermal conduction, which can be easily removed with
IPA or acetone. The Si pseudo-bosch recipe we used for etching a-Si and c-Si ring
resonators is shown in following table. 5.6.
ZEP resist removal
After etching, we removed the ZEP by dipping the sample in N-Methyl-2-pyrrolidone
(NMP) based solvent Remover PG for >12 hrs at 80◦ C, then we did oxygen plasma
treatment for 10 mins and acetone/IPA flush at the end. Some byproducts of oxygen
plasma reacting with ZEP are not volatile and there will be residue left as shown in
figure 5.9 without solvent cleaning. Dipping in nanostrip after these steps should
clean the samples more thoroughly but in my work, all devices were cleaned only
with PG remover, oxygen plasma and solvent.

54
Etching parameters

Values

RF forward power

23 W

ICP forward power

1200 W

DC bias voltage

70 - 90 V

SF6 flow rate

15.0 sccm

C4 F8 flow rate

40.0 sccm

Chamber pressure

11.0 mTorr

Wafer temperature

15 ◦ C

Helium backing pressure

4.0 Torr

Etching rate

60 nm/min

Table 5.6: Si pseudo-bosch etching recipe

Figure 5.9: Residue of ZEP cleaned with O2 plasma
Final fabricated c-Si on SiC devices
Figure 5.10 shows a fabricated c-Si on 4H-SiC ring resonator device. Devices
written on clean membrane surface without visible bubbles or change in color rarely

55
had the problem of detaching from the substrate after all the fabrication and cleaning
process.

Figure 5.10: SEM image of a c-Si on 4H-SiC final ring resonator device

BIBLIOGRAPHY

[1] Stephen Wiesner. “Conjugate coding”. In: ACM Sigact News 15.1 (1983),
pp. 78–88.
[2] Hoi-Kwong Lo, Marcos Curty, and Kiyoshi Tamaki. “Secure quantum key
distribution”. In: Nature Photonics 8.8 (2014), p. 595.
[3] Umesh Vazirani and Thomas Vidick. “Fully device independent quantum key
distribution”. In: Communications of the ACM 62.4 (2019), pp. 133–133.
[4] Peter JJ O’Malley et al. “Scalable quantum simulation of molecular energies”.
In: Physical Review X 6.3 (2016), p. 031007.
[5] Benjamin P Lanyon et al. “Towards quantum chemistry on a quantum computer”. In: Nature chemistry 2.2 (2010), p. 106.
[6] John Preskill. “Quantum Computing in the NISQ era and beyond”. In: Quantum 2 (2018), p. 79.
[7] Hannah Clevenson et al. “Broadband magnetometry and temperature sensing
with a light-trapping diamond waveguide”. In: Nature Physics 11.5 (2015),
p. 393.
[8] Christian L Degen, F Reinhard, and P Cappellaro. “Quantum sensing”. In:
Reviews of modern physics 89.3 (2017), p. 035002.
[9] Quntao Zhuang, Zheshen Zhang, and Jeffrey H Shapiro. “Distributed quantum
sensing using continuous-variable multipartite entanglement”. In: Physical
Review A 97.3 (2018), p. 032329.
[10] William K Wootters and Wojciech H Zurek. “A single quantum cannot be
cloned”. In: Nature 299.5886 (1982), p. 802.
[11] Yazhen Wang et al. “Quantum computation and quantum information”. In:
Statistical Science 27.3 (2012), pp. 373–394.
[12] H Jeff Kimble. “The quantum internet”. In: Nature 453.7198 (2008), p. 1023.
[13] Jeremy L O’brien, Akira Furusawa, and Jelena Vučković. “Photonic quantum
technologies”. In: Nature Photonics 3.12 (2009), p. 687.
[14] Stefano Pirandola and Samuel L Braunstein. “Physics: Unite to build a quantum Internet”. In: Nature News 532.7598 (2016), p. 169.
[15] DL Moehring et al. “Quantum networking with photons and trapped atoms”.
In: JOSA B 24.2 (2007), pp. 300–315.
[16] JR Weber et al. “Quantum computing with defects”. In: Proceedings of the
National Academy of Sciences 107.19 (2010), pp. 8513–8518.

66
[17] Wolfgang Pfaff et al. “Unconditional quantum teleportation between distant
solid-state quantum bits”. In: Science 345.6196 (2014), pp. 532–535.
[18] Bas Hensen et al. “Loophole-free Bell inequality violation using electron
spins separated by 1.3 kilometres”. In: Nature 526.7575 (2015), p. 682.
[19] Michael A Nielsen and Isaac Chuang. Quantum computation and quantum
information. 2000.
[20] Stephanie Wehner, David Elkouss, and Ronald Hanson. “Quantum internet:
A vision for the road ahead”. In: Science 362.6412 (2018), eaam9288.
[21] Tatjana Wilk et al. “Single-atom single-photon quantum interface”. In: Science 317.5837 (2007), pp. 488–490.
[22] Stephan Ritter et al. “An elementary quantum network of single atoms in
optical cavities”. In: Nature 484.7393 (2012), p. 195.
[23] Dietrich Leibfried et al. “Quantum dynamics of single trapped ions”. In:
Reviews of Modern Physics 75.1 (2003), p. 281.
[24] Lilian Childress and Ronald Hanson. “Diamond NV centers for quantum
computing and quantum networks”. In: MRS bulletin 38.2 (2013), pp. 134–
138.
[25] David D Awschalom et al. “Quantum technologies with optically interfaced
solid-state spins”. In: Nature Photonics 12.9 (2018), pp. 516–527.
[26] Norbert Kalb et al. “Entanglement distillation between solid-state quantum
network nodes”. In: Science 356.6341 (2017), pp. 928–932.
[27] Andrei Faraon et al. “Coupling of nitrogen-vacancy centers to photonic crystal cavities in monocrystalline diamond”. In: Physical review letters 109.3
(2012), p. 033604.
[28] Sara L Mouradian and Dirk Englund. “A tunable waveguide-coupled cavity design for scalable interfaces to solid-state quantum emitters”. In: APL
Photonics 2.4 (2017), p. 046103.
[29] Ajit Ram Verma and Padmanabhan Krishna. “Polymorphism and polytypism
in crystals”. In: 1966, 341 P. JOHN WILEY AND SONS, INC., 605 THIRD
AVENUE, NEW YORK, N. Y. 10016 (1965).
[30] F Bechstedt et al. “Polytypism and properties of silicon carbide”. In: physica
status solidi (b) 202.1 (1997), pp. 35–62.
[31] Gary Lynn Harris. Properties of silicon carbide. 13. Iet, 1995.
[32] William F Koehl et al. “Room temperature coherent control of defect spin
qubits in silicon carbide”. In: Nature 479.7371 (2011), p. 84.
[33] David J Christle et al. “Isolated electron spins in silicon carbide with millisecond coherence times”. In: Nature materials 14.2 (2015), p. 160.

67
[34] Hosung Seo et al. “Quantum decoherence dynamics of divacancy spins in
silicon carbide”. In: Nature communications 7 (2016), p. 12935.
[35] Andreas Reiserer and Gerhard Rempe. “Cavity-based quantum networks with
single atoms and optical photons”. In: Reviews of Modern Physics 87.4 (2015),
p. 1379.
[36] C Santori et al. “Nanophotonics for quantum optics using nitrogen-vacancy
centers in diamond”. In: Nanotechnology 21.27 (2010), p. 274008.
[37] Michael Gould et al. “Large-scale GaP-on-diamond integrated photonics platform for NV center-based quantum information”. In: JOSA B 33.3 (2016),
B35–B42.
[38] Greg Calusine, Alberto Politi, and David D Awschalom. “Cavity-enhanced
measurements of defect spins in silicon carbide”. In: Physical Review Applied
6.1 (2016), p. 014019.
[39] Peter C Humphreys et al. “Deterministic delivery of remote entanglement on
a quantum network”. In: Nature 558.7709 (2018), p. 268.
[40] Edward M Purcell, H Co Torrey, and Robert V Pound. “Resonance absorption
by nuclear magnetic moments in a solid”. In: Physical review 69.1-2 (1946),
p. 37.
[41] Adam Gali et al. “Theory of neutral divacancy in SiC: a defect for spintronics”.
In: Materials Science Forum. Vol. 645. Trans Tech Publ. 2010, pp. 395–397.
[42] A Lenef and SC Rand. “Electronic structure of the N-V center in diamond:
Theory”. In: Physical Review B 53.20 (1996), p. 13441.
[43] MW Doherty et al. “Theory of the ground-state spin of the NV- center in
diamond”. In: Physical Review B 85.20 (2012), p. 205203.
[44] David J Christle et al. “Isolated spin qubits in SiC with a high-fidelity infrared
spin-to-photon interface”. In: Physical Review X 7.2 (2017), p. 021046.
[45] Kevin C Miao et al. “Electrically driven optical interferometry with spins in
silicon carbide”. In: arXiv preprint arXiv:1905.12780 (2019).
[46] Abram L Falk et al. “Electrically and mechanically tunable electron spins
in silicon carbide color centers”. In: Physical review letters 112.18 (2014),
p. 187601.
[47] Jeronimo R Maze et al. “Properties of nitrogen-vacancy centers in diamond:
the group theoretic approach”. In: New Journal of Physics 13.2 (2011),
p. 025025.
[48] NT Son et al. “Photoluminescence and Zeeman effect in chromium-doped
4H and 6H SiC”. In: Journal of applied physics 86.8 (1999), pp. 4348–4353.
[49] Daniel C Harris and Michael D Bertolucci. Symmetry and spectroscopy: an
introduction to vibrational and electronic spectroscopy. Courier Corporation,
1989.

68
[50] Bodie E Douglas and Charles A Hollingsworth. Symmetry in bonding and
spectra: An introduction. Academic Press, 2012.
[51] F Albert Cotton. Chemical applications of group theory. John Wiley & Sons,
2003.
[52] Yukito Tanabe and Satoru Sugano. “On the absorption spectra of complex
ions II”. In: Journal of the Physical Society of Japan 9.5 (1954), pp. 766–779.
[53] C Deka et al. “Optical spectroscopy of Cr 4+: Y 2 SiO 5”. In: JOSA B 10.9
(1993), pp. 1499–1507.
[54] Hergen Eilers et al. “Spectroscopy and dynamics of Cr 4+: Y 3 Al 5 O 12”.
In: Physical Review B 49.22 (1994), p. 15505.
[55] William F Koehl et al. “Resonant optical spectroscopy and coherent control
of C r 4+ spin ensembles in SiC and GaN”. In: Physical Review B 95.3 (2017),
p. 035207.
[56] Sergey A Reshanov. “Growth and high temperature performance of semiinsulating silicon carbide”. In: Diamond and Related Materials 9.3-6 (2000),
pp. 480–482.
[57] Karin Maier, Harald D Müller, and Jürgen Schneider. “Transition metals in
silicon carbide (SiC): vanadium and titanium”. In: Materials Science Forum.
Vol. 83. Trans Tech Publ. 1992, pp. 1183–1194.
[58] K Maier et al. “Electron spin resonance studies of transition metal deep level
impurities in SiC”. In: Materials Science and Engineering: B 11.1-4 (1992),
pp. 27–30.
[59] M Kunzer, HD Müller, and U Kaufmann. “Magnetic circular dichroism and
site-selective optically detected magnetic resonance of the deep amphoteric
vanadium impurity in 6H-SiC”. In: Physical Review B 48.15 (1993), p. 10846.
[60] Gary Wolfowicz et al. “Vanadium spin qubits as telecom quantum emitters
in silicon carbide”. In: arXiv preprint arXiv:1908.09817 (2019).
[61] Viktor Ivady et al. “Asymmetric split-vacancy defects in SiC polytypes: A
combined theoretical and electron spin resonance study”. In: Physical review
letters 107.19 (2011), p. 195501.
[62] Andreas Gällström, Björn Magnusson, and Erik Janzén. “Optical identification of Mo related deep level defect in 4H and 6H SiC”. In: Materials Science
Forum. Vol. 615. Trans Tech Publ. 2009, pp. 405–408.
[63] Andreas Gällström et al. “A defect center for quantum computing: Mo in
SiC”. In: (2015).
[64] J Baur, M Kunzer, and J Schneider. “Transition metals in SiC polytypes, as
studied by magnetic resonance techniques”. In: physica status solidi (a) 162.1
(1997), pp. 153–172.

69
[65] Tom Bosma et al. “Identification and tunable optical coherent control of
transition-metal spins in silicon carbide”. In: npj Quantum Information 4.1
(2018), p. 48.
[66] M Steger et al. “Reduction of the Linewidths of Deep Luminescence Centers
in Si 28 Reveals Fingerprints of the Isotope Constituents”. In: Physical review
letters 100.17 (2008), p. 177402.
[67] Hisashi Sumikura et al. “Ultrafast spontaneous emission of copper-doped
silicon enhanced by an optical nanocavity”. In: Scientific reports 4 (2014),
p. 5040.
[68] Feng Tian et al. “All-optical dynamic modulation of spontaneous emission
rate in hybrid optomechanical cavity quantum electrodynamics systems”. In:
arXiv preprint arXiv:1901.07691 (2019).
[69] Michael Lurie Goldman et al. “Phonon-induced population dynamics and
intersystem crossing in nitrogen-vacancy centers”. In: Physical review letters
114.14 (2015), p. 145502.
[70] Martin A Green. “Self-consistent optical parameters of intrinsic silicon at
300 K including temperature coefficients”. In: Solar Energy Materials and
Solar Cells 92.11 (2008), pp. 1305–1310.
[71] KG Svantesson and NG Nilsson. “Determination of the temperature dependence of the free carrier and interband absorption in silicon at 1.06 µm”. In:
Journal of Physics C: Solid State Physics 12.18 (1979), p. 3837.
[72] Dominik G Rabus. Integrated ring resonators. Springer, 2007.
[73] Wim Bogaerts et al. “Silicon microring resonators”. In: Laser & Photonics
Reviews 6.1 (2012), pp. 47–73.
[74] Charles Kittel, Paul McEuen, and Paul McEuen. Introduction to solid state
physics. Vol. 8. Wiley New York, 1996.
[75] Allen Taflove and Susan C Hagness. Computational electrodynamics: the
finite-difference time-domain method. Artech house, 2005.
[76] Kane Yee. “Numerical solution of initial boundary value problems involving
Maxwell’s equations in isotropic media”. In: IEEE Transactions on antennas
and propagation 14.3 (1966), pp. 302–307.
[77] Ardavan F Oskooi et al. “MEEP: A flexible free-software package for electromagnetic simulations by the FDTD method”. In: Computer Physics Communications 181.3 (2010), pp. 687–702.
[78] Gary Wolfowicz et al. “Optical charge state control of spin defects in 4H-SiC”.
In: Nature communications 8.1 (2017), p. 1876.

70
[79] James F Ziegler, Matthias D Ziegler, and Jochen P Biersack. “SRIM–The
stopping and range of ions in matter (2010)”. In: Nuclear Instruments and
Methods in Physics Research Section B: Beam Interactions with Materials
and Atoms 268.11-12 (2010), pp. 1818–1823.
[80] WE Carlos et al. “Annealing of multivacancy defects in 4 H- SiC”. In: Physical
Review B 74.23 (2006), p. 235201.
[81] Andreas Gällström et al. “Influence of Cooling Rate after High Temperature Annealing on Deep Levels in High-Purity Semi-Insulating 4H-SiC”. In:
Materials science forum. Vol. 556. Trans Tech Publ. 2007, pp. 371–374.
[82] Jae-Hyung Lee et al. “Smart-cut layer transfer of single-crystal SiC using spinon-glass”. In: Journal of Vacuum Science & Technology B, Nanotechnology
and Microelectronics: Materials, Processing, Measurement, and Phenomena
30.4 (2012), p. 042001.
[83] Joohyun Koh et al. “Correlation of real time spectroellipsometry and atomic
force microscopy measurements of surface roughness on amorphous semiconductor thin films”. In: Applied physics letters 69.9 (1996), pp. 1297–1299.
[84] YA Kryukov et al. “Experimental and theoretical study of the evolution
of surface roughness in amorphous silicon films grown by low-temperature
plasma-enhanced chemical vapor deposition”. In: Physical Review B 80.8
(2009), p. 085403.
[85] Michio Kondo et al. “Substrate dependence of initial growth of microcrystalline silicon in plasma-enhanced chemical vapor deposition”. In: Journal of
applied physics 80.10 (1996), pp. 6061–6063.
[86] H Fujiwara et al. “Assessment of effective-medium theories in the analysis of
nucleation and microscopic surface roughness evolution for semiconductor
thin films”. In: Physical Review B 61.16 (2000), p. 10832.
[87] Luozhou Li et al. “Nanofabrication on unconventional substrates using transferred hard masks”. In: Scientific reports 5 (2015), p. 7802.
[88] Gary E McGuire. “Semiconductor Materials and Process Technology Handbook for Very Large Scale Integration(VLSI) and Ultra Large Scale Integration(ULSI)”. In: Noyes Data Corporation, Noyes Publications, Mill Rd. at
Grand Ave, Park Ridge, New Jersey 07656, USA, 1988. 675 (1988), pp. 46–
72.
[89] J Baro et al. “PENELOPE: an algorithm for Monte Carlo simulation of the
penetration and energy loss of electrons and positrons in matter”. In: Nuclear
Instruments and Methods in Physics Research Section B: Beam Interactions
with Materials and Atoms 100.1 (1995), pp. 31–46.
[90] Matthew Borselli, Thomas J Johnson, and Oskar Painter. “Beyond the Rayleigh
scattering limit in high-Q silicon microdisks: theory and experiment”. In: Optics express 13.5 (2005), pp. 1515–1530.

71
[91] C Petridis et al. “Mode-hop-free tuning over 80 GHz of an extended cavity
diode laser without antireflection coating”. In: Review of Scientific Instruments 72.10 (2001), pp. 3811–3815.
[92] Christopher P Anderson et al. “Electrical and optical control of single spins
integrated in scalable semiconductor devices”. In: Science 366.6470 (2019),
pp. 1225–1230.
[93] David Thomson et al. “Roadmap on silicon photonics”. In: Journal of Optics
18.7 (2016), p. 073003.
[94] Simone Ferrari, Carsten Schuck, and Wolfram Pernice. “Waveguide-integrated
superconducting nanowire single-photon detectors”. In: Nanophotonics 7.11
(2018), pp. 1725–1758.
[95] David O Bracher, Xingyu Zhang, and Evelyn L Hu. “Selective Purcell enhancement of two closely linked zero-phonon transitions of a silicon carbide
color center”. In: Proceedings of the National Academy of Sciences 114.16
(2017), pp. 4060–4065.
[96] Jonathan M Kindem et al. “Characterization of Yb 3+ 171: YVO 4 for photonic quantum technologies”. In: Physical Review B 98.2 (2018), p. 024404.
[97] Emma R Schmidgall et al. “Frequency control of single quantum emitters in
integrated photonic circuits”. In: Nano letters 18.2 (2018), pp. 1175–1179.
[98] Daniil M Lukin et al. “4H-silicon-carbide-on-insulator for integrated quantum
and nonlinear photonics”. In: Nature Photonics (2019), pp. 1–5.
[99] Qimin Quan and Marko Loncar. “Deterministic design of wavelength scale,
ultra-high Q photonic crystal nanobeam cavities”. In: Optics express 19.19
(2011), pp. 18529–18542.

72
Appendix A

GAAS PHOTONIC CRYSTALS
This chapter describes initial attemps of fabricating GaAs photonic crystal devices
for coupling Yb3 + ions in YVO4 with optical transition at 984 nm [96]. This only
shows the starting point of the fabrication optimization and parameters or procedures
described here will be greatly improved in the future. The plan of fabrication of GaAs
devices is as following. They are first fabricated on GaAs-AlGaAs-GaAs substrate
then undercut to be released from the substrate. We use a nanomanipulator to pick
up a device and transfer it deterministically on YVO4 substrate.
GaAs periodic photonic crystal band diagram
In this simulation, we simulate only a unit lattice of a periodic PhC and see if there
are forbidden modes (bandgap) exist so the PhC will reflect those mode propagating
inside acting like a mirror. We sweep parameters (width, height, hole period and
hole radius) with initial guess chosen based on the strategy descriped in Quan and
Loncar [99]. The goal is to find a parameter set that gives a wide bandgap around
wavelength 980 nm with GaAs layer height around 240nm which corresponds to
the top layer height of GaAs/AlGaAs/GaAs samples we had for tests. The PhC
refractive index is set to GaAs and the surrounding medium including holes in PhC
are air. The optimized parameters are (width, height, hole period and hole radius) =
(1, 0.7, 1, 0.25) that corresponds to (343 nm, 240 nm, 343 nm, 86 nm) if set height
to 240 nm. The band diagram with these parameters is shown in figure A.1. The
second 3D simulation is to check that the partial periodic PhC acts as a mirror. In
this configuration ,shown in figure A.2, PhC with 3 holes is sandwiching a defect at
the center. A light source at the center generates field around the wavelength of the
bandgap center. A harmonic inversion function recognizes the resonance created
with the structure,thus supporting the result of the previous bandgap simulation.
A.1

GaAs photonic crystal fabrication

The first attempt of GaAs photonic crystal was based on the parameters described in
the previous section mainly to optimize dry etching recipe and device transfer. The
initial dry etching recipe of ICP-RIE etcher is based on Ar:SiCl4 =3:10 flow rate.
With varying RF/ICP power, the etched sidewall remained rough.

Figure A.1: 3D periodic photonic crystal bandgap simulation.

Figure A.2: 3D photonic crystal simulation with defect at the center
AlGaAs undercut
The undercut procedure for 100 nm thickness AlGaAs is shown in the following
table ??.
Photonic crystal transfer by nanomanipulator
Transferring smaller structures or single photonic devices to desired location can be
performed using a nanomanipulator. In the FIB/SEM system, this methods allows
for device examination in microscopic level and transfer at the same time. In this
method, platinum is deposited where we want to hold and is welded to the probe.
In order to avoid deposition on the device itself, We patterned two lines along with
the PhC and cut and transfer a larger area including the device with FIB as shown
in A.3.

Procedure

time (s)

Dip in citric acid

Dip in 3.5% HF

Dip in water

Repeat dipping in HF then water twice

9 total HF dip time

Dip in citric acid

Put still wet sample to IPA, gently take out (never blow dry)
Table A.1: a-Si recipe

Figure A.3: Transferring a part of devices using a nanomanipulator (a) Cut through
between the 2 patterned lines before grating couplers because undercut wasn’t
enough to detach grating couplers from the substrate (b) The probe at the left
side is welded to platinum, deposited around the grating tapered part, and the device
is lifted up.

75
Appendix B

RELATED CODES

76
Si oxidation time estimation based on desired thickness

1 % Calculates oxidation rate from Equations taken from a chapter written by
2 % B. E. Deal in Semiconductor materials and process technology handbook
3 %: for very large scale integration (VLSI) and ultra large scale integration (ULSI)
4 %/ edited by Gary E. McGuire. (pp. 48-57)
6 %Input%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
7 mode=1;%Oxidation condition 1:wet,2:dry
8 siori=1;%Si orientation 1:(100),2:(111)
9 T=1000;%Temperature in Celcius
10 xi=2.5;%Initial oxide thickness (nm)
11 xsi=250;%Final thickness of Si consumed (nm), e.g. if you have 500nm Si and
12
%want to make it 360nm, xsi=140nm
13
14 fit=1; %Fit the actual data below to scale the theoretial curve. 1:yes,2:no
15 %Acutual data of time(hr) and xsi(um)
16
17 % %Newer wet oxidation data (after 3/24 when furnace 1 is replaced with new tube)
18 p1=[4/3,0.24176];%(hr,(oxidized si thickness)um)
19 p2=[32/60,0.13901];
20 p3=[1.5,0.26377];
21
22 %Newer dry oxidation data
23 % p1=[0.3,0.01146];
24 % p2=[0.1667,0.00676];
25
26 data=cat(1,p1,p2,p3);
27
28
29 %Basic calculation%%%%%%%%%%%%%%%%%%%%%%%%
30 oxd=2.20*10^22;%molecular density of SiO2 (/cm^3)
31 sid=4.99*10^22; %Atomic density of Si(/cm^3)
32 %Oxide thickness:consumed Si thickness=
33
34 xo=xsi*sid/oxd;%Final oxide thickness (nm)
35 fprintf('Final oxide thickness %f\n\n',xo)
36
37 xi=xi/1000;%change units to um
38 xo=xo/1000;
39 %%%%%%%%%%%%%%%%%%%%%%%%%
40
41 %Parameters for oxidation thickness equation%%%%%%%%%%
42 C1d=7.72*10^2;%(um^2/hr)
43 C2d=6.23*10^6;%(um/hr)
44 E1d=1.23; %(eV)
45 E2d=2.0;
46
47 C1w=3.86*10^2;
48 C2w=1.63*10^8;
49 E1w=0.78; %(eV)
50 E2w=2.05;
51 k=8.617*10^(-5);%eV/K
52 %%%%%%%%%%%%%%%%%%%%%%%%%%%
53
54 if siori==1
55
C2d=C2d/1.7;
56
C2w=C2w/1.7;

77
Si oxidation time estimation based on desired thickness

57 end
58
59 switch mode
60
case 1
61 B=C1w*exp(-E1w/k/(T+273));
62 B_A=C2w*exp(-E2w/k/(T+273));
63
64
case 2
65 B=C1d*exp(-E1d/k/(T+273));
66 B_A=C2d*exp(-E2d/k/(T+273));
67 end
68 A=B/B_A;
69
70 %Oxidation thickness
71 tau=xi^2/B+xi/B_A;
72 t=xo/B_A+xo^2/B-tau;% calculate the time needed to have final ox thickness
73 t_list=linspace(0,2*t,300);
74 xo_list=1/2*(-A+sqrt(A^2+4*B*t_list+4*B*tau));
75 hr=floor(t);
76 min=floor((t-hr)*60);
77 sec=floor(((t-hr)*60-min)*60);
78 fprintf('Theory oxidation time %d:%d:%d\n\n',hr,min,sec)
79
80 %Fitting actual data%%%%%%%%%%%%%%
81 if fit==1
82 xop=data(:,2)*sid/oxd;%oxide thickness for data
83 func=@(a,t_data)(1/2*(-a(1)+sqrt(a(1)^2+4*a(2)*t_data+4*a(2)*tau)));
84 iguess=[A,B];
85 [beta,R]=nlinfit(data(:,1),xop,func,iguess,statset('MaxIter', 1e6));
86 xo_scaled=1/2*(-beta(1)+sqrt(beta(1)^2+4*beta(2)*t_list+4*beta(2)*tau));
87 t_scaled=xo*beta(1)/beta(2)+xo^2/beta(2)-tau;
88
89 shr=floor(t_scaled);
90 smin=floor((t_scaled-shr)*60);
91 ssec=floor(((t_scaled-shr)*60-smin)*60);
92 fprintf('Scaled theory oxidation time %d:%d:%d\n\n',shr,smin,ssec)
93 %%%%%%%%%%%
94
95 plot(t_list,xo_list,t_list,xo_scaled,'r',data(:,1),xop,'ro')
96 legend('Theory','Scaled theory','data')
97 title('Oxidation calculation')
98 ylabel('Oxide thickness (um)')
99 xlabel('time (hr)')
100 else
101 plot(t_list,xo_list)
102 ylabel('Oxide thickness (um)')
103 xlabel('time (hr)')
104 end
105
106
107

78
B.1

MEEP codes

79
2D cylindrical ring resonator simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20180927_c-Si_ring_on_SiC_Q_vs_gap\2D\Ring_Si_on_SiC_TM_2D.ctl

Wednesday, September 11, 2019 3:40 PM

(define-param xo 0)
(define-param yo 0)
(define-param h 0.36) ;height of the ring
(define-param radi 3.75) ;external radius of the ring
(define-param w 0.30) ;width of the ring
(define-param res 40) ;resolution
(define-param fcen 0.9341)
; pulse center frequency 1070nm
(define-param df 0.005)
; pulse width (in frequency)
(define-param tim 1000) ;running time
(define-param dpml 0.5) ; thickness of PML (one side)
(define-param pad 0.5) ; thickness of pad b/w PML and edge of the ring (one side)
(define n_Si 3.550) ; refractive index of c-Si at 1070nm
(define n_SiC 2.637) ; refractive index of SiC
(define-param sx (+(* radi 2) (* dpml 2) (* pad 2)))
(define-param sy (+(* radi 2) (* dpml 2) (* pad 2)))
(set! geometry-lattice (make lattice (size sx sy no-size)))
(set! default-material (make medium (index 1))) ; air
(set! geometry (list
(make cylinder (center xo yo) (radius radi) (height infinity)
(material (make dielectric (index n_Si)))) ; Si ring
(make cylinder (center xo yo (/ h 2)) (radius (- radi w)) (height infinity)
(material (make dielectric (index 1)))) ; center hole

))
(set! pml-layers (list (make pml (thickness dpml))))
(set! sources (list
(make source
(src (make gaussian-src (frequency fcen) (fwidth df)))
(component Ez)
(center (+ xo (- radi (/ w 2))) yo) (size h h))
))
(set-param! resolution res) ;Resolution
(run-sources+ tim
(at-beginning output-epsilon)
(after-sources (harminv Ex (vector3 (+ xo (- radi (/ w 2))) yo ) fcen df))
(after-sources (harminv Ez (vector3 (+ xo (- radi (/ w 2))) yo ) fcen df))
(run-until (/ 1 fcen) (at-every (/ 1 fcen 8) output-efield))

-1-

80
3D ring resonator with waveguides simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20180927_c-Si_ring_on_SiC_Q_vs_gap\3D\Ring_Si_on_SiC_wg_TM.ctl

Wednesday, September 11, 2019 3:43 PM

(define-param xo 0)
(define-param yo 0)
(define-param h 0.36) ;height of the ring
(define-param radi 3.75) ;external radius of the disk
(define-param w 0.3) ;width of the ring
(define-param sp 0.3) ;ring waveguide spacing
(define-param wgw 0.3) ;width of the waveguide
(define-param res 40) ;resolution
(define-param fcen 0.9285)
; pulse center frequency 1070nm
(define-param df 0.01)
; pulse width (in frequency)
(define-param tim 1000) ;running time
(define-param dpml 0.5) ; thickness of PML
(define-param pad 0.5) ; thickness of pad b/w PML and edge of the ring (one side)
(define n_Si 3.550) ; refractive index of Si at 1070nm
(define n_SiC 2.637) ; refractive index of SiC

(define-param sx (+(* radi 2) (* dpml 2) (* pad 2)))
(define-param sy (+(* radi 2) (* dpml 2) (* pad 2) (* sp 2) (* wgw 2)))
(define-param sz (+ h (* dpml 2) (* pad 2)))
(set! geometry-lattice (make lattice (size sx sy sz)))
(set! default-material (make medium (index 1))) ; air
;(define-param guide? true);
(set! geometry (list
(make block (center xo yo (/ sz -4)) (size sx sy (/ sz 2))
(material (make dielectric (index n_SiC)))) ; SiC substrate
(make cylinder (center xo yo (/ h 2)) (radius radi) (height h) (axis 0 0 1)
(material (make dielectric (index n_Si)))) ; Si ring
(make cylinder (center xo yo (/ h 2)) (radius (- radi w)) (height h) (axis 0 0 1)
(material (make dielectric (index 1)))) ; center hole
(make block (center xo (+ yo (* radi -1) (* sp -1) (* wgw -0.5)) (/ h 2)) (size sx
wgw h)
(material (make dielectric (index n_Si)))) ; waveguide
(make block (center xo (+ yo radi sp (* wgw 0.5)) (/ h 2)) (size sx wgw h)
(material (make dielectric (index n_Si))))
))
(set! pml-layers (list (make pml (thickness dpml))))
(set! sources (list
(make source
(src (make gaussian-src (frequency fcen) (fwidth df)))
(component Ez)
(center (+ xo radi (/ w -2)) yo (/ h 4)) (size h h h))
))
(set-param! resolution res)
(run-sources+ tim
(at-beginning output-epsilon)
(after-sources (harminv Ez (vector3 (+ xo radi (/ w -2)) yo (/ h 4)) fcen df))
-1-

81
3D ring resonator with waveguides simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20180927_c-Si_ring_on_SiC_Q_vs_gap\3D\Ring_Si_on_SiC_wg_TM.ctl

(run-until (/ 1 fcen) (at-every (/ 1 fcen 4) output-efield))

-2-

Wednesday, September 11, 2019 3:43 PM

82
2D grating coupler flux simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\2D grating for TM\2D_Si_grating_flux_TM.ctl

Wednesday, September 11, 2019 3:35 PM

; 2D waveguide with gratings on the right, source in the waveguide polarized in the TM
direction (Ey)
(define-param per 1.00)
(define-param duty 0.2)
(define-param h 0.54)
(define-param dpml 0.5)
(define sx 15)
(define sy 10)
(define-param ref false); if true, it's just a waveguide
(define n_Si 3.550) ; refractive index of Si at 1070nm
(define n_SiC 2.637) ; refractive index of SiC
(define-param fcen 0.9341)
(define-param df 0.01)

; pulse center frequency 1070nm
; pulse width (in frequency)

(define-param nfreq 10) ; number of frequencies at which to compute flux
(set-param! resolution 40) ; simulation resolution
(set! geometry-lattice (make lattice (size sx sy no-size)))
(set! geometry
(append
(list
(make block (center 0 (+ (/ sy -4) (/ h 2))) (size sx h) ;Grating
(material (make dielectric (index n_Si))))
(make block (center 0 (* sy (/ -3 8))) (size sx (/ sy 4)) ;Substrate
(material (make dielectric (index n_SiC)))))
(geometric-object-duplicates (vector3 per 0 0) 0 36 ;Grating trenches
(make block
(center (/ sx -4) (+ (/ sy -4) (/ h 2)))
(size (* (- 1 duty) per) h)
(material (make dielectric (index 1)))))))

(set! pml-layers (list (make pml (thickness dpml))))

(set! sources (list (make source
(src (make gaussian-src (frequency fcen) (fwidth
df)))
(component Ey) (center (+ (/ sx -2) dpml 0.1) (+ (/ sy -4) (/ h 2))) (size 0 h))))
(define trans ; transmitted flux to y direction
(add-flux fcen df nfreq
(make flux-region
(center (- (/ sx 8) (/ dpml 2)) (- (/ sy 2) dpml 0.5)) (size (- (* sx
0.75) dpml) 0))))
(define trans2 ;transmitted flux to x
direction
(add-flux fcen df nfreq
(make flux-region
(center (- (/ sx 2) dpml 0.5) (/ sy 8)) (size 0 (- (* sy 0.75) 2)))))

(run-sources+
(stop-when-fields-decayed 50 Ey
(vector3 (+ (/ sx -2) dpml 0.1) (+ (/ sy -4) (/ h 2)))
1e-3)
-1-

83
2D grating coupler flux simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\2D grating for TM\2D_Si_grating_flux_TM.ctl

;(run-until 50 (at-beginning output-epsilon) (at-every 10 output-efield) )
(display-fluxes trans trans2)

-2-

Wednesday, September 11, 2019 3:35 PM

84
2D grating coupler flux normalization (simple waveguide)

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\2D grating for TM\2D_Si_wg_on_SiC_TM.ctl

Wednesday, September 11, 2019 3:36 PM

; 2D waveguide with gratings on the right, source in the waveguide polarized in the TM direction
(define-param h 0.54)
(define-param dpml 0.5)
(define sx 15)
(define sy 10)
(define n_Si 3.550) ; refractive index of Si at 1070nm
(define n_SiC 2.637) ; refractive index of SiC
(define-param fcen 0.9341)
(define-param df 0.01)

; pulse center frequency 1070nm
; pulse width (in frequency)

(define-param nfreq 10) ; number of frequencies at which to compute flux
(set-param! resolution 40) ; simulation resolution
(set! geometry-lattice (make lattice (size sx sy no-size)))
(set! default-material (make medium (index 1))) ; air
(set! geometry
(list
(make block (center 0 (+ (/ sy -4) (/ h 2))) (size sx h)
(material (make dielectric (index n_Si))))
(make block (center 0 (* sy (/ -3 8))) (size sx (/ sy 4))
(material (make dielectric (index n_SiC))))))

(set! pml-layers (list (make pml (thickness dpml))))

(set! sources (list (make source
(src (make gaussian-src (frequency fcen) (fwidth
df)))
(component Ey) (center (+ (/ sx -2) dpml 0.1) (+ (/ sy -4) (/ h 2))) (size 0 h))))
(define fluxi ;initial flux (corresponding right at the starting point of grating in other
programs)
(add-flux fcen df nfreq
(make flux-region
(center (/ sx -4) (+ (/ sy -4) (/ h 2))) (size 0 (* h 2)))))
(define fluxf ;flux go through the end
(add-flux fcen df nfreq
(make flux-region
(center (- (/ sx 2) dpml 0.1) (+ (/ sy -4) (/ h 2))) (size 0 (* h 2)))))
(run-until 150
(at-beginning output-epsilon)
(at-end output-efield))
(run-sources+
(stop-when-fields-decayed 50 Ey
(vector3 (- (/ sx 2) dpml 0.1) (+ (/ sy -4) (/ h 2))) 1e-4))
;(run-until (/ 1 fcen) (at-every (/ 1 fcen 8) output-efield))
(display-fluxes fluxi fluxf)

-1-

85
3D grating coupler flux simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\3D grating for TM\Si_curved_grating_on_SiC_flux_TM.ctl

Wednesday, September 11, 2019 3:31 PM

; TM mode (Ez)
(define-param wgh 0.24) ;height of the waveguide + grating
(define-param wgl 0.50) ;length of the waveguide (doesn't include pad or dpml)
(define-param wgw 0.40) ;width of the waveguide
(define-param gangle (* (/ 105 180) pi)) ;Full angle of the grating (deg)
(define ga (* (/ gangle 180) pi));Full angle of the grating (rad)
(define-param gper 0.470) ;grating period
(define-param gduty 0.82) ;duty cycle of the grating
(define ggap (* gper (- 1 gduty))) ;width of the grating gap
(define-param gn 6) ;Grating number
(define-param i 0)
(define-param res 40) ;resolution
(define-param fcen 0.9341)
; pulse center frequency 1070nm
(define-param df 0.01)
; pulse width (in frequency)
(define-param tim 100) ;running time
(define-param dpml 0.5) ; thickness of PML (one side)
(define-param pad 0.5) ; thickness of pad b/w PML and edge of the ring (one side)
(define-param n_Si 3.550) ; refractive index of c-Si at 1070nm
(define-param n_SiC 2.637) ; refractive index of SiC
(define-param nfreq 10) ; number of frequencies at which to compute flux
(define sx (- (+ wgl (* gper 6) (* pad 2) (* dpml 2)) ggap))
(define sy (+ (* pad 2) (* dpml 2) (* (sin (/ ga 2)) gper 12)))
(define sz 7.5)
(set! geometry-lattice (make lattice (size sx sy sz)))
(set! default-material (make medium (index 1))) ; air

(set! geometry (list

(make cylinder (center (- (+ (/ sx -2) dpml pad wgl) ggap) 0 (+ (/ sz -4) (/ wgh
2))) (radius (* gper 6)) (height wgh) (axis 0 0 1)
(material (make dielectric (index n_Si)))) ; c-Si cylinder (most outer grating
one)
(make cylinder (center (- (+ (/ sx -2) dpml pad wgl) ggap) 0 (+ (/ sz -4) (/ wgh
2))) (radius (- (* gper 6) (- gper ggap))) (height wgh) (axis 0 0 1)
(material (make dielectric (index 1)))) ; air cylinder (make a grating
shape)
(make cylinder (center (- (+ (/ sx -2) dpml pad wgl) ggap) 0 (+ (/ sz -4) (/ wgh
2))) (radius (* gper 5)) (height wgh) (axis 0 0 1)
(material (make dielectric (index n_Si)))) ; c-Si cylinder (most outer grating
one)
(make cylinder (center (- (+ (/ sx -2) dpml pad wgl) ggap) 0 (+ (/ sz -4) (/ wgh
2))) (radius (- (* gper 5) (- gper ggap))) (height wgh) (axis 0 0 1)
(material (make dielectric (index 1)))) ; air cylinder (make a grating shape)
(make cylinder (center (- (+ (/ sx -2) dpml pad wgl) ggap) 0 (+ (/ sz -4) (/ wgh
2))) (radius (* gper 4)) (height wgh) (axis 0 0 1)
(material (make dielectric (index n_Si)))) ; c-Si cylinder (most outer grating
one)
(make cylinder (center (- (+ (/ sx -2) dpml pad wgl) ggap) 0 (+ (/ sz -4) (/ wgh
2))) (radius (- (* gper 4) (- gper ggap))) (height wgh) (axis 0 0 1)
(material (make dielectric (index 1)))) ; air cylinder (make a grating shape)
(make cylinder (center (- (+ (/ sx -2) dpml pad wgl) ggap) 0 (+ (/ sz -4) (/ wgh
2))) (radius (* gper 3)) (height wgh) (axis 0 0 1)
-1-

86
3D grating coupler flux simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\3D grating for TM\Si_curved_grating_on_SiC_flux_TM.ctl

Wednesday, September 11, 2019 3:31 PM

(material (make dielectric (index n_Si)))) ; c-Si cylinder (most outer grating
one)
(make cylinder (center (- (+ (/ sx -2) dpml pad wgl) ggap) 0 (+ (/ sz -4) (/ wgh
2))) (radius (- (* gper 3) (- gper ggap))) (height wgh) (axis 0 0 1)
(material (make dielectric (index 1)))) ; air cylinder (make a grating shape)
(make cylinder (center (- (+ (/ sx -2) dpml pad wgl) ggap) 0 (+ (/ sz -4) (/ wgh
2))) (radius (* gper 2)) (height wgh) (axis 0 0 1)
(material (make dielectric (index n_Si)))) ; c-Si cylinder (most outer grating
one)
(make cylinder (center (- (+ (/ sx -2) dpml pad wgl) ggap) 0 (+ (/ sz -4) (/ wgh
2))) (radius (- (* gper 2) (- gper ggap))) (height wgh) (axis 0 0 1)
(material (make dielectric (index 1)))) ; air cylinder (make a grating shape)
(make cylinder (center (- (+ (/ sx -2) dpml pad wgl) ggap) 0 (+ (/ sz -4) (/ wgh
2))) (radius (* gper 1)) (height wgh) (axis 0 0 1)
(material (make dielectric (index n_Si)))) ; c-Si cylinder (most outer grating
one)
(make cylinder (center (- (+ (/ sx -2) dpml pad wgl) ggap) 0 (+ (/ sz -4) (/ wgh
2))) (radius (- (* gper 1) (- gper ggap))) (height wgh) (axis 0 0 1)
(material (make dielectric (index 1)))) ; air cylinder (make a grating
shape)

(make block (center (- (+ (/ sx -2) dpml pad wgl) ggap (* 3 gper (sin (/ ga 2))))
(* gper 3 (cos (/ ga 2))) (+ (/ sz -4) (/ wgh 2)))
(size (* 12 gper) (* 6 gper) wgh) (e1 (cos (/ ga 2)) (sin (/ ga 2)) 0) (e2 (sin
(/ ga 2)) (- 0 (cos (/ ga 2))) 0) (e3 0 0 1)
(material (make dielectric (index 1)))) ; Air block at +y direction (to make the
grating angle)
(make block (center (- (+ (/ sx -2) dpml pad wgl) ggap (* 3 gper (sin (/ ga 2))))
(* gper -3 (cos (/ ga 2))) (+ (/ sz -4) (/ wgh 2)))
(size (* 12 gper) (* 6 gper) wgh) (e1 (cos (/ ga 2)) (- 0 (sin (/ ga 2))) 0) (e2
(sin (/ ga 2)) (cos (/ ga 2)) 0) (e3 0 0 1)
(material (make dielectric (index 1)))) ; Air block at -y direction (to make the
grating angle)

(make block (center (/ (- (+ dpml pad wgl) sx) 2) 0 (+ (/ sz -4) (/ wgh 2))) (size
(+ dpml pad wgl 0.2) wgw wgh)
(material (make dielectric (index n_Si)))) ; c-Si waveguide
; (make block (center (- (/ (+ pad dpml) 2) 0.2) 0 (- (/ sz 2) dpml 0.5)) (size (sx (* dpml 2) pad wgl) (- sy (* dpml 2)) 0.2)
; (material (make dielectric (index n_Si)))) ; test flux block
; (make block (center (- (/ sx 2) dpml 0.2) 0 (- (+ (/ sy 8) (* wgh 1.5) (* dpml
-0.5)) 0.2)) (size 0.2 (- sy (* dpml 2)) (- (* sz 0.75) dpml (* wgh 3)) )
; (material (make dielectric (index n_Si)))) ; test flux block
(make block (center 0 0 (* sz (/ -3 8))) (size sx sy (/ sz 4))
(material (make dielectric (index n_SiC)))) ; SiC substrate
))
(set! symmetries (list
(make mirror-sym (direction Y) (phase -1))

;Use odd mirror symmetry for xz plane at y=0

))
(set! pml-layers (list (make pml (thickness dpml))))
-2-

87
3D grating coupler flux simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\3D grating for TM\Si_curved_grating_on_SiC_flux_TM.ctl

Wednesday, September 11, 2019 3:31 PM

(set! sources (list
(make source
(src (make gaussian-src (frequency fcen) (fwidth df)))
(component Ez)
(center (+ (/ sx -2) dpml 0.1) 0 (+ (/ sz -4) (/ wgh 2))) (size 0 wgw wgh))
))
(set-param! resolution res)
;Setting flux region to compute flux through specified area
(define trans ; transmitted flux to y direction
(add-flux fcen df nfreq
(make flux-region
(center (- (/ (+ pad dpml) 2) 0.2) 0 (- (/ sz 2) dpml 0.5)) (size (- sx (*
dpml 2) pad wgl) (- sy (* dpml 2)) 0))))
(define trans2 ;transmitted flux to x
direction
(add-flux fcen df nfreq
(make flux-region
(center (- (/ sx 2) dpml 0.2) 0 (- (+ (/ sy 8) (* wgh 1.5) (* dpml -0.5))
0.2)) (size 0 (- sy (* dpml 2)) (- (* sz 0.75) dpml (* wgh 3)) ))))

(run-until 300 (at-beginning output-epsilon) (at-every 30 output-efield) )
(display-fluxes trans trans2)

-3-

88
3D grating coupler flux normalization (simple waveguide)

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\3D grating for TM\Si_wg_on_SiC_TM.ctl

Wednesday, September 11, 2019 3:33 PM

; TM mode (Ez)
(define-param wgh 0.24) ;height of the waveguide + grating
(define-param wgl 0.50) ;length of the waveguide (doesn't include pad or dpml)
(define-param wgw 0.40) ;width of the waveguide
(define-param gangle 0) ;Full angle of the grating (deg)
(define ga (* (/ gangle 180) pi));Full angle of the grating (rad)
(define-param gper 0.470) ;grating period
(define-param gduty 0.82) ;duty cycle of the grating
(define ggap (* gper (- 1 gduty))) ;width of the grating gap
(define-param gn 6) ;Grating number
(define-param i 0)
(define-param res 40) ;resolution
(define-param fcen 0.9341)
; pulse center frequency 1070nm
(define-param df 0.01)
; pulse width (in frequency)
(define-param tim 100) ;running time
(define-param dpml 0.5) ; thickness of PML (one side)
(define-param pad 0.5) ; thickness of pad b/w PML and edge of the ring (one side)
(define-param n_Si 3.550) ; refractive index of c-Si at 1070nm
(define-param n_SiC 2.637) ; refractive index of SiC
(define-param nfreq 10) ; number of frequencies at which to compute flux
(define sx (- (+ wgl (* gper 6) (* pad 2) (* dpml 2)) ggap))
(define sy (+ (* pad 2) (* dpml 2) (* (sin (/ ga 2)) gper 12)))
(define sz 7.5)
(set! geometry-lattice (make lattice (size sx sy sz)))
(set! default-material (make medium (index 1))) ; air

(set! geometry (list

(make block (center (/ (- (+ dpml pad wgl) sx) 2) 0 (+ (/ sz -4) (/ wgh 2))) (size
(* sz 3) wgw wgh)
(material (make dielectric (index n_Si)))) ; c-Si waveguide

(make block (center 0 0 (* sz (/ -3 8))) (size sx sy (/ sz 4))
(material (make dielectric (index n_SiC)))) ; SiC substrate
))
(set! symmetries (list
(make mirror-sym (direction Y) (phase -1))

;Use odd mirror symmetry for xz plane at y=0

))
(set! pml-layers (list (make pml (thickness dpml))))
(set! sources (list
(make source
(src (make gaussian-src (frequency fcen) (fwidth df)))
(component Ez)
(center (+ (/ sx -2) dpml 0.1) 0 (+ (/ sz -4) (/ wgh 2))) (size 0 wgw wgh))
))
(set-param! resolution res)
-1-

89
3D grating coupler flux normalization (simple waveguide)

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\3D grating for TM\Si_wg_on_SiC_TM.ctl

Wednesday, September 11, 2019 3:33 PM

;Setting flux region to compute flux through specified area
(define trans ; transmitted flux right before going into grating
part
(add-flux fcen df nfreq
(make flux-region
(center (+ (/ sx -2) dpml pad wgl) 0 (+ (/ sz -4) (/ wgh 2))) (size 0 (*
wgw 1.5 ) (* wgh 1.5 )) )))

(define trans2 ;transmitted flux to x
direction
(add-flux fcen df nfreq
(make flux-region
(center (- (/ sx 2) dpml 0.1) 0 (+ (/ sz -4) (/ wgh 2))) (size 0 (* wgw
1.5 ) (* wgh 1.5 )) )))

(run-until 300 (at-beginning output-epsilon) (at-every 30 output-efield) )
(display-fluxes trans trans2)

-2-

On-chip Photonic Devices for Coupling to Color Centers
in Silicon Carbide

Thesis by

Chuting Wang

In Partial Fulfillment of the Requirements for the
Degree of
Doctor of Philosophy

CALIFORNIA INSTITUTE OF TECHNOLOGY
Pasadena, California

2020
Defended December 16, 2019

Chuting Wang
ORCID: 0000-0002-3711-682X

iii

PUBLISHED CONTENT AND CONTRIBUTIONS

TABLE OF CONTENTS

vii
Appendix B: Related codes . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
B.1 MEEP codes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

viii

LIST OF ILLUSTRATIONS

ix
2.7

2.8
2.9
2.10
2.11

2.12

2.13
2.14
3.1
3.2

3.3

3.4
3.5

3.6
3.7

15
16
17
18

19
20
21
23

24
25

26
27
27

3.8
4.1

4.2
4.3
4.4

4.5
4.6

4.7

4.8
4.9
4.10
4.11
5.1
5.2

5.3

30
31
34

35
36

39
39
40
40
41
44

xi
5.4
5.5
5.6
5.7
5.8

5.9
5.10
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8

A.1
A.2
A.3

49
49
51
52

52
54
55
57
57
58
59
60
61
61

62
73
73

xii

Chapter 1

INTRODUCTION
1.1

Optical defects and their applications in quantum information technologies

(1.1)

|α0 | 2 + |α1 | 2 = 1

(1.2)

Figure 1.1: An optical quantum network consists of three components: Quantum
channels (black or green lines), quantum processors (laptop icons) and quantum
repeaters (star icons)

1.2

Silicon Carbide (SiC) material background

Polytypes of SiC and 4H-SiC crystal structure

Divacancies (VC VSi ) in SiC as promising qubits

Figure 1.3: 2H, 3C, 4H and 6H-SiC stacking structure viewed in the 1120 plane.
The gray frame shows the unit cell of each structure.
1.5

Coupling optical defects to cavities

Optical quantum networks using solid state qubits require quantum information
transmitted by photons to be stored for processing at the end nodes. In free space,

Figure 1.5: Impression of atoms interacting with light in a Fabry-Perot cavity.

Chapter 2

PHOTOLUMINESCENSE OF DEFECTS AND IMPURITIES IN
SIC
2.1

Divacancies in 4H-SiC

10
resonance (3.1)[47]. The Debye-Waller factor, the fraction of emission in ZPL out
of the total emission is only ∼5% [33].

Figure 2.1: 4 types of divacancies that occupy different carbon/silicon lattice sites.
2.2

Cr4+ ions in 4H, 6H-SiC

Figure 2.2: Photoluminescence of divacancies in a HPSI 4H-SiC sample excited by
780nm laser at 8.4 K.

Other color centers

Figure 2.12: Photoluminescence of Mo5+ ions in implanted sample (orange) in
comparison with PL4 divacancies in a HPSi sample (blue) excited by 780 nm laser
at 8.6K

Figure 2.13: Photoluminescence of Cu ions in Cu implanted Si excited by 780 nm
laser at 8.2K

Figure 2.14: Photoluminescence of Cu ions in Cu implanted Si excited by 780 nm
laser at different temperatures

22
Chapter 3

OPTICALLY DETECTED MAGNETIC RESONANCE OF
DEFECTS IN 4H-SIC
3.1

Principles of ODMR

Figure 3.1: Spin population and ODMR signal change when microwave is on/off
3.2

ODMR setup

Figure 3.2: Schematic of the MW gold line deposited on a 4H-SiC sample. The
right figure shows the image taken from CCD camera with 780nm excitation laser
on.

Figure 3.3: MW setup around samples. Initial setup with a single wire on samples
is replaced with more robust method with wire bonding and gold line deposition
directly on sample.
3.3

ODMR results on ensemble divacancies and on Cr ions

We observed similar ODMR signal to that shown in literature of divacancy ODMR
[32]. The measurements were performed on highly purified semi insulating (HPSI)

Figure 3.5: Our ODMR signal collected on undoped HPSI 4H-SiC at liquid helium
temperature (∼20 K) at left side. Right side shows results from Koehl et al. [32]

Figure 3.6: ODMR signal collected on undoped HPSI 4H-SiC at liquid helium
temperature (∼20 K) with wider MW sweep range.

Figure 3.7: Power broadening of ODMR signal of ensemble divacancies PL2

Figure 3.8: ODMR signal of PL1 and PL2 divacancies in Cr implanted 4H-SiC
under 0.15 T at liquid nitrogen temperature.

29
Chapter 4

Silicon photonic devices for near IR wavelength

30
coefficient of Si [70, 71] and resonator theory [72, 73]:
a2 = e−αL

(4.1)

FW H M =

Principles of finite-difference time-domain (FDTD) method

The finite-difference time-domain (FDTD) method is a systematic computational
method for electromagnetic fields using the central difference approximation of

(4.4)

B = µH

(4.5)

where ε is electric permittivity and µ is magnetic permeability. The Maxwell’s curl

32
equations in isotropic media can be written as:
∂H
=0
∂t
∂E
∇×H −ε
=J
∂t
∇×E+µ

(4.6)
(4.7)

(4.8)
(4.9)
(4.10)
(4.11)
(4.12)
(4.13)

(4.14)

the partial differential equations of time are approximated using centered finite
difference expressions at a space point (i, j, k):
∂u|i,n j,k
∂t

n+ 1

n− 1

u|i, j,k2 − u|i, j,k2
∆t

+ O[(∆t)2 ]

(4.15)

Partial differential equations of space coordinates can be approximated in similar
manner. As an example, using this approximation on equation 4.10 , it can be
written as following:

Hy | n 1

i+ 2 , j,k

− Hy | n 1

i− 2 , j,k

∆x

Hx | n

i, j+ 21 ,k

− Hx | n

i, j− 21 ,k

∆y

n− 1
− Jz |i,n j,k ® + Ez |i, j,k2
(4.16)

n− 1

n− 1

n−
n−
− E x | 12
E | 2
Ez |i+1,2j,k − Ez |i, j,k2 ª
i+ 2 , j,k− 12
∆t © x i+ 12 , j,k+ 21
® + Hy | n−11
Hy |i+ 1 , j,k =
i+ 2 , j,k
∆z
∆x
(4.18)

Hz | n−11

i+ 2 , j+ 12 ,k+ 12

i+ 2 , j− 12 ,k+ 12

∆y

n−1
− Jx |i+
+ Ex |
, j,k+ 1

Hy | n−11

− Hz | n−11

i+ 2 , j,k+1

− Hy | n−11

i+ 2 , j,k

∆z

n− 32

i+ 21 , j,k+ 12

Comparison with other EM simulation method

MEEP simulation of c-Si on SiC ring resonator devices

Figure 4.7: 2D grating simulation normalization simulation on the left. Main
simulation is on the right. Top figures are refractive index configuration and bottom
figures are plotting ln|E |.

Figure 4.8: 2D grating flux depending on period and duty cycle.

Figure 4.9: 2D grating diffraction angle change depending on duty cycle (fixed
period)

Figure 4.10: 2D grating diffraction angle change depending on period (fixed duty
cycle)

Figure 4.11: 3D grating simulation configuration. Each figure is at the center plane
of the simulated space.

42
Chapter 5

Qubits generation in 4H-SiC

43
Implanted ion
Ni
Cr
Mo

Implantation
energy (keV)
150
150
10, 150
200

dose (cm2 )
109 ,1011 ,1013
109 ,1011 ,1013
109 ,1011 ,1013
5×109 , 5×1010

Photoluminescense detected?
(1000-1500nm)
Divacancies
Divacancies
Divacancies, Cr ions
Divacancies, Mo ions

4H-SiC transfer

Figure 5.1: SEM image of 4H-SiC membrane surface transferred by smart cut
method.
5.3

a-Si:H Deposition

45
Deposition parameters

Values

RF forward power

10 W

5% SiH4 in Ar flow rate

40.0 sccm

Chamber pressure

801 mTorr

Wafer temperature

200 ◦ C

Deposition rate

26 nm/min

Table 5.2: a-Si recipe

Figure 5.2: SEM images of a-Si roughness. (a) a-Si deposited before any patterning
procedure (b) A grating coupler after etching and cleaning. process
5.4

c-Si Membrane Transfer

47
Step

Description

Cleaning

SOI chips are cleaned with Nanostrip.

Thinning the Si layer

Oxidation and HF wet etching are performed.

Dicing Si membranes

500 µm×500 µm squares are patterned.

Releasing membranes

HF wet etching of BOX layer are performed.

Cleaning 4H-SiC substrate

The surface is changed to hydrophilic state.

Picking up membranes

Quick pick-up with the substrate was performed.

Slow natural drying

Membranes are attached without air or water underneath.

Check membranes quality

Optical microscope and SEM examination are performed.

Description

Step

Put SOI chips in the container for 3 mins.

Spin coating

1500 rpm/ 60 s (> 2 µm).

Soft baking

110 ◦ C/ 45 s.

Exposure

5 s (75 mJ in total with 15 mJ /s).

Development

70 s in MF-319 developer.

Cleaning

Solvent cleaning with sonication for 5 mins.

ICP/RIE etching

pseudo-bosch for 8 mins.

Resist removal

Dip in acetone for 3 mins.

Figure 5.5: Cleaning by transferring a floating membrane to clean water

c-Si on SiC device patterning and fabrication

Figure 5.7: Successful membrane transfer. Most membranes are single but some of
them are connected.

53
Steps

Parameters

Resist spin coating

5000 rpm / 60 s

Baking

180 ◦ C / 3 mins.

AquaSAVE spin coating

1500 rpm / 60 s

Baking

70 ◦ C / 5 mins.

Development

Dip in ZED (slowly stirred) / 3 mins
then rinse with MIBK / 30s and with water.

Resist reflow

145 ◦ C / 10 mins

54
Etching parameters

Values

RF forward power

23 W

ICP forward power

1200 W

DC bias voltage

70 - 90 V

SF6 flow rate

15.0 sccm

C4 F8 flow rate

40.0 sccm

Chamber pressure

11.0 mTorr

Wafer temperature

15 ◦ C

Helium backing pressure

4.0 Torr

Etching rate

60 nm/min

Table 5.6: Si pseudo-bosch etching recipe

55
had the problem of detaching from the substrate after all the fabrication and cleaning
process.

Figure 5.10: SEM image of a c-Si on 4H-SiC final ring resonator device

56
Chapter 6

57
and the mirror arm. The maximum power is 50 mW around 1040 nm and > 10 mW
in the range 1020-1085 nm before fiber coupling.

Figure 6.1: The optical confocal microscope setup diagram.

Figure 6.7: Main measurements were performed through the drop port.

(6.1)

Conclusion

63
Chapter 7

BIBLIOGRAPHY

72
Appendix A

GaAs photonic crystal fabrication

Figure A.1: 3D periodic photonic crystal bandgap simulation.

Procedure

time (s)

Dip in citric acid

Dip in 3.5% HF

Dip in water

Repeat dipping in HF then water twice

9 total HF dip time

Dip in citric acid

Put still wet sample to IPA, gently take out (never blow dry)
Table A.1: a-Si recipe

75
Appendix B

RELATED CODES

76
Si oxidation time estimation based on desired thickness

77
Si oxidation time estimation based on desired thickness

78
B.1

MEEP codes

79
2D cylindrical ring resonator simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20180927_c-Si_ring_on_SiC_Q_vs_gap\2D\Ring_Si_on_SiC_TM_2D.ctl

Wednesday, September 11, 2019 3:40 PM

-1-

80
3D ring resonator with waveguides simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20180927_c-Si_ring_on_SiC_Q_vs_gap\3D\Ring_Si_on_SiC_wg_TM.ctl

Wednesday, September 11, 2019 3:43 PM

81
3D ring resonator with waveguides simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20180927_c-Si_ring_on_SiC_Q_vs_gap\3D\Ring_Si_on_SiC_wg_TM.ctl

(run-until (/ 1 fcen) (at-every (/ 1 fcen 4) output-efield))

-2-

Wednesday, September 11, 2019 3:43 PM

82
2D grating coupler flux simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\2D grating for TM\2D_Si_grating_flux_TM.ctl

Wednesday, September 11, 2019 3:35 PM

; pulse center frequency 1070nm
; pulse width (in frequency)

(set! pml-layers (list (make pml (thickness dpml))))

(run-sources+
(stop-when-fields-decayed 50 Ey
(vector3 (+ (/ sx -2) dpml 0.1) (+ (/ sy -4) (/ h 2)))
1e-3)
-1-

83
2D grating coupler flux simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\2D grating for TM\2D_Si_grating_flux_TM.ctl

;(run-until 50 (at-beginning output-epsilon) (at-every 10 output-efield) )
(display-fluxes trans trans2)

-2-

Wednesday, September 11, 2019 3:35 PM

84
2D grating coupler flux normalization (simple waveguide)

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\2D grating for TM\2D_Si_wg_on_SiC_TM.ctl

Wednesday, September 11, 2019 3:36 PM

; pulse center frequency 1070nm
; pulse width (in frequency)

(define-param nfreq 10) ; number of frequencies at which to compute flux
(set-param! resolution 40) ; simulation resolution
(set! geometry-lattice (make lattice (size sx sy no-size)))
(set! default-material (make medium (index 1))) ; air
(set! geometry
(list
(make block (center 0 (+ (/ sy -4) (/ h 2))) (size sx h)
(material (make dielectric (index n_Si))))
(make block (center 0 (* sy (/ -3 8))) (size sx (/ sy 4))
(material (make dielectric (index n_SiC))))))

(set! pml-layers (list (make pml (thickness dpml))))

-1-

85
3D grating coupler flux simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\3D grating for TM\Si_curved_grating_on_SiC_flux_TM.ctl

Wednesday, September 11, 2019 3:31 PM

(set! geometry (list

86
3D grating coupler flux simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\3D grating for TM\Si_curved_grating_on_SiC_flux_TM.ctl

Wednesday, September 11, 2019 3:31 PM

;Use odd mirror symmetry for xz plane at y=0

))
(set! pml-layers (list (make pml (thickness dpml))))
-2-

87
3D grating coupler flux simulation

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\3D grating for TM\Si_curved_grating_on_SiC_flux_TM.ctl

Wednesday, September 11, 2019 3:31 PM

(run-until 300 (at-beginning output-epsilon) (at-every 30 output-efield) )
(display-fluxes trans trans2)

-3-

88
3D grating coupler flux normalization (simple waveguide)

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\3D grating for TM\Si_wg_on_SiC_TM.ctl

Wednesday, September 11, 2019 3:33 PM

; TM mode (Ez)
(define-param wgh 0.24) ;height of the waveguide + grating
(define-param wgl 0.50) ;length of the waveguide (doesn't include pad or dpml)
(define-param wgw 0.40) ;width of the waveguide
(define-param gangle 0) ;Full angle of the grating (deg)
(define ga (* (/ gangle 180) pi));Full angle of the grating (rad)
(define-param gper 0.470) ;grating period
(define-param gduty 0.82) ;duty cycle of the grating
(define ggap (* gper (- 1 gduty))) ;width of the grating gap
(define-param gn 6) ;Grating number
(define-param i 0)
(define-param res 40) ;resolution
(define-param fcen 0.9341)
; pulse center frequency 1070nm
(define-param df 0.01)
; pulse width (in frequency)
(define-param tim 100) ;running time
(define-param dpml 0.5) ; thickness of PML (one side)
(define-param pad 0.5) ; thickness of pad b/w PML and edge of the ring (one side)
(define-param n_Si 3.550) ; refractive index of c-Si at 1070nm
(define-param n_SiC 2.637) ; refractive index of SiC
(define-param nfreq 10) ; number of frequencies at which to compute flux
(define sx (- (+ wgl (* gper 6) (* pad 2) (* dpml 2)) ggap))
(define sy (+ (* pad 2) (* dpml 2) (* (sin (/ ga 2)) gper 12)))
(define sz 7.5)
(set! geometry-lattice (make lattice (size sx sy sz)))
(set! default-material (make medium (index 1))) ; air

(set! geometry (list

(make block (center (/ (- (+ dpml pad wgl) sx) 2) 0 (+ (/ sz -4) (/ wgh 2))) (size
(* sz 3) wgw wgh)
(material (make dielectric (index n_Si)))) ; c-Si waveguide

(make block (center 0 0 (* sz (/ -3 8))) (size sx sy (/ sz 4))
(material (make dielectric (index n_SiC)))) ; SiC substrate
))
(set! symmetries (list
(make mirror-sym (direction Y) (phase -1))

;Use odd mirror symmetry for xz plane at y=0

89
3D grating coupler flux normalization (simple waveguide)

C:\Users\Faraon Lab\Documents\Andrei_lab\MEEP\20170418_c-Si_ring_on_SiC\3D grating for TM\Si_wg_on_SiC_TM.ctl

Wednesday, September 11, 2019 3:33 PM

(define trans2 ;transmitted flux to x
direction
(add-flux fcen df nfreq
(make flux-region
(center (- (/ sx 2) dpml 0.1) 0 (+ (/ sz -4) (/ wgh 2))) (size 0 (* wgw
1.5 ) (* wgh 1.5 )) )))

(run-until 300 (at-beginning output-epsilon) (at-every 30 output-efield) )
(display-fluxes trans trans2)

-2-