Design and simulation of wideband photonic intergrated circuits for multi mode (de) multiplexing and conversion

10 Fig 1.4 Scheme of the effective index method for solving the propagation constant of a step-index channel waveguide.. 54 Fig 3.2 Proposed schematic of a three mode demultiplexer based

MINISTRY OF EDUCATION AND TRAINING

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY

-0 -

TRAN TUAN ANH

DESIGN AND SIMULATION OF WIDEBAND PHOTONIC INTEGRATED CIRCUITS FOR MULTI-MODE (DE)MULTIPLEXING

AND CONVERSION

DOCTORAL DISSERTATION

IN TELECOMMUNICATIONS ENGINEERING

HANOI – 2020

MINISTRY OF EDUCATION AND TRAINING

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY

-0 -

TRAN TUAN ANH

DESIGN AND SIMULATION OF WIDEBAND PHOTONIC INTEGRATED CIRCUITS FOR MULTI-MODE (DE)MULTIPLEXING

PROF DR TRAN DUC HAN

DR TRUONG CAO DUNG

HANOI – 2020

DECLARATION OF AUTHORSHIP

I, Tran Tuan Anh, declare that this dissertation entitled, "Design and simulation of wideband photonic integrated circuits for multi-mode (de)multiplexing and conversion", and the work presented in it is my own

- Where I have consulted the published work of others, this is always clearly attributed

-Where I have quoted from the work of others, the source is always given

- With the exception of such quotations, this dissertation is entirely my own work

- I have acknowledged all main sources of help Where the dissertation is based on work done by myself jointly with others, I have made exactly what was done by others and what I have contributed myself

First and foremost, I would like to thank my supervisor Prof Dr Tran Duc Han for his support and advice throughout my research time in Hanoi University of Science and Technology (HUST) His encouragement and full support led me to every success

of my study I have been able to learn a lot from him about being a good teacher and researcher

I would like to express my gratitude to my supervisor, Dr Truong Cao Dung, for guiding and motivating me since I was an undergraduate student at HUST He has given me the very first guidance until I finished my doctoral dissertation

I special thanks to Prof Dr Vu Van Yem for his constant help during my study postgraduate courses and sincere advices for my future career

I am also thankful to my research team, Ms Nguyen Thi Hang Duy, Mr Ta Duy Hai,

Ms Tran Thi Thanh Thuy and Mr Hoang Do Khoi Nguyen in Posts and Telecommunications Institute of Technology They gave me a lot of help during my last two years

Finally, I would like to express my grateful thanks to my parents, Mr Tran Quoc Hung and Mrs Tran Thi Huong, and my uncle, Mr Tran Quoc Dung, for their support and encouragement

TRAN TUAN ANH

Table of Contents

INTRODUCTION 1 CHAPTER 1 SOI WAVEGUIDE STRUCTURE, ANALYSIS AND FABRICATION 8

1.1 Shapes and functions of silicon-on-insulator waveguide _8 1.2 Optical waveguide analysis and simulation methods 12

1.2.1 Wave equations _ 121.2.2 Effective index method _ 151.2.3 Finite Difference Method _ 171.2.4 Beam Propagation Method 181.2.5 Finite Difference Beam Propagation Method 19

1.3 Silicon-on-insulator waveguide fabrication 21

1.3.1 Separation by implanted oxygen (SIMOX) 211.3.2 Bond and Etch-back SOI (BESOI) 231.3.3 Wafer Splitting _ 241.3.4 Silicon Epitaxial Growth 251.3.5 Fabrication of surface etched features 25

1.4 Silicon-on-insulator waveguide structure used for MDM functionality _27

1.4.1 Directional coupler 271.4.2 Multimode interference _ 321.4.3 Asymmetric Y-junction waveguide _ 41

1.5 Conclusion _43

CHAPTER 2 MODE DIVISION MULTIPLEXER BASED ON ASYMMETRIC

DIRECTIONAL COUPLER _ 45

2.1 Two mode division (De)multiplexer based on an MZI asymmetric silicon waveguide _45

2.1.1 Design and structural optimization 452.1.2 Simulation and performance analysis 49

3.2.1 Design and structural optimization 563.2.2 Simulation and performance analysis 64

4.1.2 Simulation and performance analysis 74

4.2 Four-mode multiplexed device based on tilt branched bus structure using silicon

waveguide 78

4.2.1 Design and structural optimization 784.2.2 Simulation and performance analysis 834.2.3 Proposal of experimental diagram _ 85

4.3 Conclusion _89

DISSERTATION CONCLUSION AND FUTURE WORKS _ 92 PUBLICATIONS 94 UNDER REVIEW PAPER 94 REFERENCE 95

Abbreviation

FD-BPM Finite Difference Beam Propagation Method

FFT-BPM Fast Fourier Transform Beam Propagation Method

LER Line Edge Roughness

OEICs Opto-electronic Integrated Circuits

PECVD Plasma-enhanced chemical vapor deposition

List of Mathematical Symbols

n c Refractive effective index of cladding layer

n s Refractive effective index of substrate layer

n r Refractive effective index of core layer

n eff Effective refractive effective index

F

x



 Differential equation of function F by variable x

mn

 Uncoupled coefficients of m-th order mode at n-th

order output port

mn

 Coupled coefficients of m-th order mode at n-th order

output port

List of Figures

Fig a Set up initial parameters of SOI waveguide and simulation method in RSoft 4

Fig b Pathway monitoring power at each output port of a design 5

Fig 1.1 Schematic of non-planar optical waveguides High index is indicated by darker color 8

Fig 1.2 Schematic of SOI waveguide 10

Fig 1.3 Schematic of SOI Rib waveguide 10

Fig 1.4 Scheme of the effective index method for solving the propagation constant of a step-index channel waveguide Starting from a 2D waveguide, the problem is split into two step-index planar waveguides 16

Fig 1.5 The cross-section of the waveguide is made discrete with a rectangular grid of points which have identical spacing 18

Fig 1.6 Comparison between BPM (left) and FFT-BPM (right) simulation FD-BPM under TBC gives better simulation result as the simulated wave is smoother 20 Fig 1.7 Comparison between FD-BPM simulation time depending on computed step of grid size 0.05μm (a) verse grid size 0.01μm (b) 21

Fig 1.8 Variation of the oxygen profile during the SIMOX process (a) Low-dose; (b) high-dose (peak is at the stoichiometric limit for SiO2); and (c) after implantation and annealing at high temperature for several hours 22

Fig 1.9 The bond and etch-back process to form BESOI: (a) oxidation; (b) bonding; and (c) thinning 23

Fig 1.10 (a) Thermally oxidized wafer is implanted with a high dose of hydrogen (b) A second wafer is bonded to the first as in the BESOI process (c) Thermal processing splits the implanted wafer at a point consistent with the range of the hydrogen ions 24

Fig 1.11 (a) Schematic of a silicon rib waveguide (b) Electron micrograph of a silicon rib waveguide Reproduced by permission of Intel Corporation 26

Fig 1.12 Schematic of a confined AC-generated plasma suitable for silicon processing The processed wafer in placed on the lower, grounded electrode 27

Fig 1.13 Directional coupler consisting of slab optical waveguide 29

Fig 1.14 Periodic exchange of power between waveguide 1 and 2 30

Fig 1.15 Simulation of periodic exchange of power between waveguide 1 and 2 using BPM 30

Fig 1.16 Power transfer ratio verse phase mismatch parameter ∆𝛽𝐿𝑜 31

Fig 1.17 The schematic configuration of MMI waveguide 33

Fig 1.18 Two-dimensional representation of a MMI waveguide 34

Fig 1.19 Power distribution of GI-MMI with 𝐿 = 3𝐿𝜋 (left), 𝐿 = 3𝐿𝜋/2 (middle), 𝐿 = 3𝐿𝜋/3 (right) using FD-BPM simulation 38

Fig 1.20 Power distribution of 2x2 PI-MMI, input access waveguide is at ±𝑊/6 with 𝐿 = 𝐿𝜋/2 (left), 𝐿 = 𝐿𝜋 (right) using FD-BPM simulation 40

Fig 1.21 Power distribution of SI-MMI showing 3-way splitting (left) and 1-to-1 imaging (right) having same length and different width using FD-BPM simulation 41

Fig 1.22 Oscillating field pass through boundary between two isotropic media 41

Fig 1.23 Schematic structure of tilt branch bus waveguide 43

Fig 2.1 Schematic of the mode synthesizer based silicon waveguide 46

Fig 2.2 BPM simulation for the height of waveguides of the asymmetric directional 47

Fig 2.3 BPM simulation for power ratio as a function of the waveguide height 48

Fig 2.4 Transmission characteristic of dependence of the coupling length of the asymmetric directional coupler by BPM simulation 48

Fig 2.5 Electric field patterns for the mode (de)MUXer 49

Fig 2.6 Wavelength response of the mode DMUXer in the C-band 49

Fig 2.7 1-nm-wavelength spectrum in the side of mode multiplexer 50

Fig 2.8 Crosstalk of the modes in the structure for MUXer and deMUXer devices as a function of the etched depth tolerance: H=h1=500 nm 50

Fig 2.9 Sidewall roughness loss calculation for two modes and two polarization states of the waveguide in two cases: a) σ = 2 nm, Lcor = 50 µm and b) σ = 0.4 nm, Lcor = 10 µm 52

Fig 3.1 Schematic of cascade NxN GI MMI used for switching optical signal 54

Fig 3.2 Proposed schematic of a three mode (de)multiplexer based on a trident coupler and two multimode interference couplers on the platform of silicon on insulator waveguides 56

Fig 3.3 Schematic diagram and transmittance properties of the trident coupler: a) schematic diagram and b) BPM simulation for transmittance properties of the trident coupler as a function of the length of the sinusoidal 59

Fig 3.4 BPM simulation for the phase angle Φ is a function of the central width of the phase shifter 64

Fig 3.5 Electric field patterns of the proposed three - mode (de)MUXer for: fundamental mode (a), first-order mode (b), second-order mode (c), and total of three modes (d) 65

Fig 3.6 Performances dependence on the wavelength of the proposed three modes-(de)MUXer: (a) insertion loss and (b) crosstalk 66

Fig 3.7 Influence of branching angles of the trident coupler on optical performances of the proposed (de)MUXer: a) insertion loss, and b) crosstalk 67

Fig 3.8 Fabrication tolerances of the proposed (de)MUXer: a) length tolerance of the second MMI coupler LMMI2, and b) width tolerance of the input width W0 67

Fig 3.9 Insertion loss and crosstalk in the proposed structure for three mode - (de)MUXer device as functions of the etched depth tolerance 68

Fig 4.1 The proposed design of the three-mode channel separation device 71

Fig 4.2 Dependence of effective index of the main bus waveguide on variation of the main waveguide width Wm at the height h of 220 nm 71

Fig 4.3 The results of transmission characteristic of proposed device at the first tilted waveguide as a function of the width Wa (nm), which passively affects the mode selective coupling coefficients 73

Fig 4.4 The results of transmission characteristic of proposed device at the second tilted waveguide as a function of the width Wa (nm), which passively affects the mode selective coupling coefficients 74Fig 4.5 Simulated electric field patterns for the proposed three mode (de)multiplexer for: fundamental mode (a), first-order mode (b), second-order mode (c) 74Fig 4.6 The characteristic optical performance of the device depends on the

wavelength, showing the I.L and Cr.T of each three mode outputs 75Fig 4.7 Variation of optical transmission performance of the proposed waveguide depended on width tolerance ΔW (nm) 76Fig 4.8 Variation of optical transmission performance of the proposed waveguide depended on height tolerance Δh (nm) 76Fig 4.9 Transmissions at three output ports PO1, PO2 and PO3 as a function of two simultaneous variables Δh (nm) and ΔW (nm) of the bus waveguide when three modes are excited: (a), (b), (c) for mode TE0, (d), (e), (f) for mode TE1 and (g), (h), (i) for mode TE2 77Fig 4.10 The proposed schematic of a four-mode (de)multiplexer device a) Top view b) Size view 78Fig 4.11 Dependence of effective indices by using numerical simulation for

different modes on variation of the waveguide width 79Fig 4.12 The results of transmission characteristic of proposed device for mode selective coupling coefficients a) at the A1 b) at the A2 and c) at the A3 82Fig 4.13 Simulated electric field patterns for the proposed four mode

(de)multiplexer for: a) fundamental mode, b) first-order mode, c) second-order mode, d) third-order mode 83Fig 4.14 The characteristic optical performance of the device depends on the

wavelength of the four-mode a) Insertion loss (I.L) b) crosstalk (Cr.T) 84Fig 4.15 Power of the proposed device at four output ports O1, O2, O3 and O4 are functions of two simultaneous variables Δh (nm) and ΔW (nm) of the bus

waveguide when four modes are excited (a), (b), (c), (d) for mode TE0; (e), (f), (g), (h) for mode TE1; (i), (j), (k), (l) for mode TE2 and (m),(n),(o),(p) for mode TE3 85Fig 4.16 System level simulated setup for the mode demultiplexer measurement The optical and the electrical connections are shown as gold and blue lines,

respectively PRBS: Pseudo Random Binary Sequence, PPG: Programmable Pattern Generator, PC: Polarization Controller, EDFA: Erbium Doped Fiber Amplifier, DUT: Device under test, BPF: Band-pass filter, PD: Photodetector, BERT: bit error rate tester, CLK: clock synthesizer, VOA: Variable Optical Attenuator, BERT: Bit error rate tester Gain1=10dB, Gain2=3dB 86Fig 4.17 Eye diagrams of the four-mode demultiplexer for four desired output ports corresponding to injected four modes, respectively 87Fig 4.18 BER factor is a function of transmit power Tx of the tunable multimode laser 87Fig 4.19 The BER was surveyed according to the bit rate of the communication system when the transmit power Tx = -1dBm 88Fig 4.20 The BER factors are functions of wavelength in 100nm of the wavelength band in the third telecom windows 89

Motivation

The world is now coming in the era of the industrial revolution 4.0, in which the communication infrastructure, especially optical communication, plays an important role in the success of the revolution After long distance fibers have been settled, research in the optical communication system field focused on functional photonic components, which are used to connect the terminals Those components can be used

as optical splitters, (de)multiplexers, switches … The conventional way to construct those components is to put each component into an individual temperature controlled package and connect them to corresponding functional units However, this method

is difficult to assemble and accounts for the major percentage of cost of the whole device After that, thanks to advanced technology and well developed semiconductor fabrication technology, planar lightwave circuits (PLCs) had solved some major problems such as polarization dependence, temperature sensitivity and optical loss,

to become an essential part in the communication network PLCs have some outstanding advantages as follows: enhanced functionality, compactness, high flexibility and reliability, low optical losses and feasibility of mass production due to high integration density and low cost like its electronics integrated circuits counterpart PLCs are becoming a chief technology for guiding, splitting, (de)multiplexing, amplifying, switching and detecting optical signals

One of the practical applications of PLCs is optical splitters used in FTTH systems FTTH networks had been considered as the ultimate solution for broadband access networks Power splitters and (de)multiplexers are the basic block of passive function

of FTTH networks Power splitters are used to divide the optical power from input ports to different channels, while (de)multiplexers are for combining and separating different wavelengths Different types of power splitters based on PLC technology had been proposed, such as Y-Branches [1], Mach-Zehnder Interferometer [2], Multimode Interference (MMI) [3] PLCs based devices are superior to conventional fused-fiber type splitters in terms of low cost and mass producing ability Regarding multiplexing function, one of the popular components used in FTTH networks is the optical network unit (ONU), which is located at each users’ places ONU contains a triple wavelength i.e 1310nm, 1490nm, 1550nm, (de)multiplexer, and opto-electronics devices such as laser diodes and photo detectors Most of current practical triplexer transceivers are bulky modules built on discrete optical components, which

is difficult to integrate with other devices and to package PLCs technology presents

to be a solution for realizing triplexers with good performance and lower layout complexity Recently, there are some studies in this field using MMI structure [4] [5] Hence, PLCs long term reliability for optical telecommunication has been already established

Another main stream in the optical communication research field is to improve bandwidth for wideband applications such as video on demand, mobile communications, big data or cloud computing Therefore, different strategies to upgrade the capacity of optical transmission systems, which are considered the back-born of information networks, have been proposed There are some available techniques, such as WDM [6], [7] multilevel modulation format [8], polarization division multiplexing (PDM) Until nowadays, WDM technology is still very popular

in optical communication systems, because this technology supports simultaneously

a lot of traffic wavelengths However, the available channel numbers in the C and L bands for dense-WDM systems has been fully utilized In addition, there are still some limitations that need to be solved in WDM regarding fiber nonlinearity, such as four-wave mixing (FWM), cross phase modulation (XPM) phenomena or stimulated scattering effects On the other hand, mode division multiplexing (MDM) technology has been being paid attention as an emerging technology to enhance the capacity of optical communication system [9]–[13]besides the mentioned above technologies In this MDM, each eigenmode carries a separated optical traffic Each of these eigenmodes does not couple with the others because of the orthogonality, hence enabling different spatial modes, defined as different channels, to carry data separately Different from applications of WDM in long-distance transmission, MDM

is more suitable for transmission with short distance, ultra large capacity, like chip communication [14].Therefore, a larger transmission capacity can be realized

intra-by combining MDM with other multiplexing systems, for example, MDM with WDM [15].Furthermore, combining MDM/WDM not only enhances capacity but also does not affect the performance of photonic devices that were less withstand from the effect of modal dispersion A new multiplexing method is introduced in a MDM system, enabling different spatial modes as different channels to carry data More recently, this technique not only has become popular for increasing the capacity of an optical wavelength carrier by feeding multiple guided modes into a multimode optical waveguide but also is attractive in multiple-input, multiple-output (MIMO) signals processing field [16], [17] Hence, MDM shows to be a promising technique, along with other (de)multiplexing schemes, that can be applied in on-chip optical communication to increase capacity of transmission systems

Objectives

By reviewing existing papers and research works, there are some spatial mode division multiplexing (SDM) techniques that use few-modes [18]–[20] or multimode optical fiber [21]–[23] to proceed the (de)multiplexing functions directly However, transmitting signals is relatively complex as needing optoelectronic devices, thus processing the signal in optical fiber links is not flexible Furthermore, fabrication procedure is difficult to integrate in large scale photonics circuits In contrast to

OEICs, PLCs based on silicon material, as mentioned above, can be fabricated easily and have some advantages, e.g low loss[24],[25], high confinement of light [26] due

to significant refractive index contrast between Si and SiO2 , thus guiding light with low bending loss, high bandwidth[27], mass-producing ability [28] and compatible

to CMOS technology A compact and reconfigurable mode (de)multiplexer which can support numerous modes is essential for realizing MDM-WDM in integrated photonics [29] However, current works based on PLCs SOI waveguide applied in MDM still have some weaknesses Some designs of on-chip (de)multiplexers have been proposed by constructing on the platform of Multi-Mode Interference (MMI) couplers [30]–[33] typically had advantages: broadband, large tolerance fabrications but these structures need phase shifters, in which a difference of propagation constants of spatial modes can lead to mismatch of the haft beat lengths, thus causing significant crosstalk and loss Others based on asymmetric directional couplers [34]–[37] and symmetric Y-junctions couplers [38] [39] are relatively complex to manufacture in terms of making the mask in manufacturing process and have quite large insertion loss Recently, Dai et.al [40] proposed a four mode on-chip MDM structure which based on adiabatic asymmetric directional couplers However, these devices have some drawbacks, e.g., high-order modal loss and modal dispersion while guiding into the waveguides, so they have difficulty in coupling with multimode fiber links or other planar lightwave circuits Moreover, many adiabatic couplers often required a relatively large footprint and were complicated to fabricate Similarly, several three mode (de)multiplexers based on adiabatic asymmetric resonators [41],[35] have been proposed to realize reconfigurable (de)multiplexing functions but those structures have a narrow resonant bandwidth Hence, the objective of this dissertation is to propose new mode (de)muxer designs based on different SOI structures that can overcome those disadvantages above or have better overall performances regarding number of (de)multiplexed modes, loss and footprints

Research objects and scope

This dissertation focuses on designing new MDM structures based on SOI waveguides Three most common SOI waveguide structures will be studied, namely asymmetric directional coupler, multimode interference coupler and asymmetric Y-junction waveguide, due to their vast applications for different functionalities in PIC field, especially MDM and mode converter The scope of this study is limited within passive devices made from silicone rib/ridge waveguide structure used for mode (de)multiplexing function only Rib/ridge waveguide height is designed based on CMOS fabrication standard, while width and length are determined according to the number of desired supporting modes and devices working principles respectively Passive devices are considered due to its simplicity and no need of routing or switching optical signals for MDM function alone Silicon material is suitable for

passive devices at Band C due to its low-loss properties and especially compatibility with CMOS technology thus providing possibilities for low-cost production

Research methodology

All the designs’ structures are built based on theoretical foundation, including coupling theory, self-imaging reproduction theory of MMI and its transfer matrix for calculating phase shifting and phase matching theory applied in branch bus waveguide structure Then, each device’s optical properties are investigated and optimized numerically by simulation methods All the simulation processes are executed via RSoft software, which is developed by Synopsys Inc There are many types of simulation in RSoft such as FullWave using FDTD investigating field propagation in time domain in complex structures such as array waveguide gratings

or BandSolve using FDTD investigating field propagation in time domain in photonic crystal waveguide However, in the scope of this dissertation, namely using SOI material and investigating field propagation in one direction, 3D FD-Beam propagation method (BPM) in conjunction with effective index method (EIM) are used to perform and achieve all simulation results Initial set up of SOI rib/ridge waveguide with 3D-BPM simulation in RSoft is shown in Fig a below

Fig a Set up initial parameters of SOI waveguide and simulation method in RSoft

In MDM, the most important features of the devices are low loss, low crosstalk, high bandwidth, capability to support a few modes, hence all devices performance will be assessed according to those criteria They are defined as follows:

I L 10log out

in

P

Fig b Pathway monitoring power at each output port of a design

I.L and Cr.T will be deployed to evaluate devices fabrication and bandwidth tolerance Although there is still no international unified criterion assessing whether the devices meet standard requirements or not because this research field is still in development stage, we tried to structure our designs with the following criteria Insertion loss is greater than -5dB, crosstalk is smaller than -15 dB, 3-dB bandwidth

is greater than 40 nm, 3-dB geometrical tolerance is greater than ±10 nm Those figures are common results and expectations from the PIC research community Finally, our final results will be used to compare with other recent studies in order to demonstrate pros and cons of the proposed designs as well as potential further improvements or future research

Scientific contributions and practical applications

The dissertation has three main contributions as follows:

1) We proposed a new design based on asymmetric directional coupler SOI waveguide, which can (de)multiplex fundamental mode and 1st-order mode The result has been published in International Conference on Advanced Technologies for Communications (ATC), 2016

2) We proposed a new design based on 3x3 MMI couplers and trident SOI waveguide, which can (de)multiplex fundamental mode, 1st-order mode and 2nd-order mode The result has been published in Optical and Quantum Electronic

3) We proposed a new mode sorting design based on branch tilt SOI waveguides diverted from bus SOI waveguide, which can (de)multiplex multi high-order modes Our designs can (de)multiplex up-to 4 modes so far, hence show a high potential for multimode (de)multiplexing development One of the results has been published in

Photonics and Nanostructures-Fundamentals and Applications

All of our designs can operate within band C range with low insertion loss and crosstalk; have small footprint, thus can be promising candidates for high bitrate MDM systems as well as on-chip photonic integrated circuits

Dissertation structure

The dissertation consists of 4 chapters and is organized as follows:

- In chapter 1, SOI waveguides will be mentioned, regarding its common shapes, applications in PLCs components and their advantages compared to other materials used in PLCs Then different numerical simulation methods are summarized The finite difference method is developed to solve the eigenmodes of the waveguide structure The beam propagation method is used to investigate the light propagation

in different waveguide structures Effective index method can be used in waveguide with arbitrary shape and refractive index distribution to simplify the calculation and save computing capacity After that, SOI waveguide fabrication process will be briefly introduced Finally, working principles of three types of SOI waveguide structures used in this dissertation are introduced sequentially Firstly, the theory of coupling between two directional waveguides will be introduced, covering from the simplest case, which is symmetric co-directional coupler, to general cases, which can

be applied to mode excitation coupling in asymmetric coupler Secondly, MMI coupler working principles are introduced, especially its self-image properties will govern the applications in MDM as well as other functionalities The last structure is Y-junction waveguide, in which MDM function can be achieved based on its phase matching conditions

- In chapter 2, a new structure of two-mode on chip (de)multiplexing devices (de)MUXer) is proposed, built in the form of a compact Mach-Zehnder interferometer (MZI) by using asymmetric directional coupler silicon waveguides

(TM In chapter 3, cascaded MMI working principle in optical switching is introduced Then, a new mode (de)muxer structure based on cascaded MMI is presented MMI will solve the major challenge in MDM systems, which is selectively injecting or extracting individual modes of a multimode link, using its self-imaging properties and phase shifters Furthermore, MMI devices have functions of converting high order modes from the input port to fundamental modes at the output ports so as to be compatible with optical single mode fiber as well other network-on chip systems, thus being able to reach high flexibility of light signals processing[42] MMI coupler also meets the requirements of an effective optical device namely broadband, low loss and large tolerance fabrications, hence being recently used for MDM [31], [33], [38]

- In chapter 4, a new MDM structure, which is designed based on multi-branch bus SOI waveguide for selecting and converting guided modes, are introduced The designs’ function of converting high order modes from the bus input port to fundamental mode at the output ports also prove the feasibility of the compatibility between the proposed designs and single mode optical fiber and network on-chip systems Those designs show some improvements compared to the designs using MMI coupler [31], [43] which are still relatively complex as its structure requires low fabricating tolerant passive phase shifters, and the designs based on asymmetric directional coupler [44], [45] which can only (de)multiplex 2 modes

CHAPTER 1 SOI WAVEGUIDE STRUCTURE, ANALYSIS

1.1 Shapes and functions of silicon-on-insulator waveguide

Optical waveguide is basic unit of photonics components in PLCs Optical waveguide allows optical signal transfer along its propagation direction and confines the light within the high refractive index region There are several non-planar schematics of waveguide as shown in Fig 1.1

Fig 1.1 Schematic of non-planar optical waveguides High index is indicated by darker

Rib waveguide: consists of a slab waveguide and a strip waveguide, with the same refractive index, superimposed on it Although a rib waveguide cannot be a single-mode waveguide technically, however well designed one can make power of high-order mode leak out after very short propagation distance and thus only fundamental

mode is guided through the whole device Rib waveguide has lower propagation loss but higher design footprint than one of ridge waveguide

Diffused waveguide: high-index region is created inside the substrate through diffusion of LiNbO3 dopants with core formed by Titanium (Ti) The core boundaries

in the substrate are not defined clearly because of the diffusion process A diffused waveguide thickness is determined by the diffusion depth of the dopant and its width

is defined by the distribution of the dopants

Optical waveguide can be made of different materials such as: LiNbO3 [46], SiO2[47], [48], Silicon on Insulator [49], [50], Polymer [51], InP [52], [53], etc The features of each material are summarized in Table 1.1.1

LiNbO3 High Electro-Optic coefficient,

non-linear effect, excellent high speed modulation

High loss

device

Si High refractive index contrast,

high integration density and compatible with Si electronics

Indirect bandgap

Polymer Ease of fabrication, low cost, high

Electro-Optic and Thermal-Optic performance

Low life expectancy

InP Direct bandgap, good for high

speed modulation and light emitters

High cost, complex technology, large foot print due to low refractive index contrast between core and cladding layers

Table 1.1 Pros and Cons of different materials used in fabricating PLCs devices

Apart from the materials mentioned in the table, another material commonly used in optical waveguide is chalcogenide (As2S3), of which effective refractive index is significantly high and sensitive to power intensity according to Kerr effect [54], thus can be applied in nonlinear directional coupler However, in this dissertation, SOI is used for all of our designs as it is the most favorable choice for passive devices with outstanding features such as low cost, low loss, high density integration due to its high refractive index contrast and good matching for single mode fiber Furthermore, optical power loss of C-band in silicon waveguide, which is used as the input signal for all of our designs and very popular in practical applications in analog CATV signal overlay, is significantly low Schematic structure of SOI slab waveguide is shown in Fig 1.2, in which a uniform layer of SiO2 is placed in the middle between thin silicon

core layer and thick silicon substrate layer, which is on top and at the bottom respectively

However, slab waveguide is rarely used in practical applications as fields can only be dispersed in one dimension while many applications need to consider field distribution in two dimensions Rib and ridge channel waveguides are widely used, where core and cladding are made from Si and SiO2, refractive indices of which are 3.45 and 1.46 respectively (Fig 1.3)

Silicon substrate

Surface silicon guiding layer

Buried SiO 2 cladding

Fig 1.2 Schematic of SOI waveguide

H

h0

Hd

Si, nr=3.45SiO2, nc=1.46

Fig 1.3 Schematic of SOI Rib waveguide

There are several basic blocks and optical elements that perform some basic common functions in many PLCs as below:

1 Interconnect This basic element serves to connect optically two points of a

photonic chip It can also act as a spatial filter, maintaining a Gaussian-like mode throughout the chip architecture In order to interconnect different elements which are not aligned with the optical axis of the chip, a bend WG is needed, and therefore

a bend WG is often called an offset WG These are also used to space channel WGs

at the chip end faces, so that multiple fibers may be attached to it

2 Power splitter 1x2 A power splitter 1x2 is usually a symmetric element which

equally divides power from a straight WG between two output waveguides The simplest version of a power splitter is a Y-branch A different version of a power splitter is the MMI element The advantage of this design is the short length of the MMI compared to that of the Y-branch For specific purposes, it is possible to fabricate splitters with N output WGs, then 1xN splitter is called

3 Waveguide reflector The waveguide reflector performs the task of reflecting back

the light in a straight WG There are some methods of performing this task: to put a metallic mirror at the end of the channel WG; A multi-stack dielectric mirror is used

if one needs the reflection to occur only for a particular wavelength or a grating period

WG under Bragg condition

4 Directional coupler This element has two input ports and two output ports and is

composed of two closely spaced WGs The working principle of the coupler is based

on the periodical optical power exchange that occurs between two adjacent waveguides through the overlapping of the evanescent waves of the propagating modes This effect is described by the coupled mode formalism By setting design parameters, including waveguide spacing and coupler length, the ratio of powers between the two output ports may be set during the fabrication process between zero and one

5 Polarizer A waveguide polarizer allows passing light having a well-defined

polarization character, either TE or TM light, by filtering one of them The fabrication

of a waveguide polarizer is simple as depositing a metallic film onto a waveguide

6 Polarization beam splitter In some integrated optical devices, it is necessary to

divide the input light into its two orthogonal polarizations TE and TM, into separate waveguide output ports An integrated optical element based on a lithium niobate substrate can perform this function

7 Phase modulator An integrated optical phase modulator performs a controlled

shift on the phase of a light beam and consists of a channel WG fabricated on a substrate with a possibility of changing its refractive index by means of an externally applied field (thermal, acoustic, electric, etc.) The most common phase modulator is based on the electro-optic effect: an electric field applied to an electro-optic material, such as LiNbO3, induces a change in its refractive index, then the propagation constant of the propagating mode also changes; therefore, the light travelling through that region undergoes a certain phase shift

8 Intensity modulator One of the most important functions of an optical chip is

intensity modulation of light at very high frequencies One of the simplest ways to perform this task is to build an integrated Mach-Zehnder interferometer (MZI) on an electro-optic substrate

9 TE/TM mode converter In a normal situation, TE and TM modes are orthogonal

and then the power transfer between them cannot occur Nevertheless, TE to TM conversion can be achieved by using electro-optic substrate, which must have non-zero off-diagonal elements in the electro-optic coefficient matrix If Lithium Niobate

is used as a substrate, a period electrode is required because this crystal is birefringence, and therefore the TE, TM modes have different effective refractive indices (propagation speeds) By combining phase modulators and a TE/TM converter, a fully integrated polarization controller can be built

10 Frequency shifter Frequency shifting in integrated optics can be performed by

means of the acousto-optic effect An acoustic surface wave generated by a piezoelectric transducer, creates a Bragg grating in the acousto-optic substrate that interacts with the propagating light in a specially designed region, giving rise to diffracted light that is frequency-shifted by the Doppler Effect This frequency shift corresponds to the frequency of the acoustic wave

The photonic elements can be found in an optical passive or active device Examples

of passive devices are the power splitter, directional couplers, frequency converter, the arrayed waveguide grating (AWG), the integrated acousto-optic tunable filters (AOTF), etc Examples of active devices are the integrated optical amplifier, the integrated laser, etc

1.2 Optical waveguide analysis and simulation methods

Analysis and simulation play a very important role in proposing efficient designs that provide good performance, namely low signal loss and crosstalk effect, compactness, and making the cost for product development reduce dramatically It also helps to evaluate tolerance of the design so that to determine whether it is feasible to manufacture the device according to current fabrication technology

It is well known that the light wave is an electromagnetic field and most of the phenomenon in photonic components can be described by Maxwell’s equations which are used to analyze the behavior of the electromagnetic fields However, solving Maxwell’s equations is only for simple structures, such as planar or channel waveguides, whereas most waveguides in PLC have complex structure and cannot be solved straightforwardly Analyzing the behavior of these designs should be done by numerical methods

In this dissertation, several different numerical methods have been developed for the design of PLCs devices Effective index method (EIM) is used to save computing capacity by simplifying the three-dimension waveguide into two-dimension waveguide; Beam propagation method (BPM) and Finite Difference Method (FDM) are introduced to simulate the propagation of light in PLC devices FD-BPM simulations are executed under Transparent Boundary Condition (TBC) in order to eliminate oscillating field reflection into the analysis window In the following sections, the basic principles of these methods are summarized

and H r t , is electrical field and magnetic field respectively Maxwell’s equation in

a medium is presented as follows:

,,

2 2

c t



 (1.2.7) This equation is called wave equation, where c0 = 1/√ε0μ0 is speed of light in free space and u represents any of the three components (𝐸𝑥, 𝐸𝑦, 𝐸𝑧) of E r t , and

(𝐻𝑥, 𝐻𝑦, 𝐻𝑧) of H r t , .

In the scope of this section, monochromatic electromagnetic waves are considered All the components of the electric and magnetic are harmonic functions of time of the same frequency These components are expressed in terms of their complex amplitudes as below:

where 𝐸(𝑟 ) and 𝐻(𝑟 ) are complex amplitudes of the electric and magnetic fields, ω

is angular frequency Substituting δ δt⁄ = jω in Maxwell’s equations, in the case of linear, homogenous, non-dispersive and isotropic medium, we obtain:

k is wavenumber and 𝜆 is the optical wavelength, n is the refractive index of the environment

1.2.2 Effective index method

Effective index method (EIM) is an appropriate analysis for calculating the propagation modes of the channel waveguides It applies the tools developed for planar waveguides to solve the problem of two-dimensional structure This method is one of the simplest approximate methods for obtaining the spatial field distribution and the propagation constant in channel waveguides having arbitrary geometry and index profiles It consists of solving the problem in one dimension; described by the

x coordinate in such a way that the other coordinates (the y coordinate) acts as a parameter In this way, we obtain a y-dependent effective index profile; this generated index profile is treated once again as a one-dimensional problem from which the effective index of the propagating mode is finally obtained

For propagating modes polarized mainly along the x direction (𝐸𝑞𝑝𝑥 ), the major components are 𝐸𝑥, 𝐻𝑦 , 𝐸𝑧 The propagation of these polarized modes is similar to the TM mode in a one-dimension planar waveguide, and their solutions will correspond to the effective indices NI The second planar waveguide is considered to

be built from a guiding film of refractive index NI, which has previously been calculated The modes for the second planar waveguide are TE polarized with 𝐸𝑦, 𝐻𝑥 , 𝐻𝑧 as non-vanishing components because the light is mainly polarized along x direction

Considering a channel waveguide where field propagates in z axis of Cartesian coordinate, electric and magnetic fields take the form as below:

u x y z t , , , u x expj t  j z  (1.2.12)

Given a refractive index distribution n(x,y) that defines the channel waveguide, the

equations for the electromagnetic fields are reduced and this enables exact solutions

to be found for the complex field amplitude u(x,y) as well as the propagation

constant β Substituting equation (1.2.12) into wave equation yields the equation describing the spatial dependence of the fields along x and y axis in channel waveguide:

With EIM, we assume that the field E(x,y) could be expressed as:

E x y , X x Y y    (1.2.15) Substitute Eq (1.2.15) into Eq (1.2.14) and divide it by (XY)

𝑛𝑒𝑓𝑓(𝑥) is called the effective index distribution corresponding to x direction and can

be solved with Eq (1.2.17a) by using the method in the slab dielectric waveguide The propagation constant then can be solved in equation (1.2.17b) and the final

solution is defined by two integer number q and p, reflecting the qth (in x direction) and pth (in y direction) order solution (modes) of equations (1.2.17a) and (1.2.17b)

Following example in Fig 1.4 will show how effective index mode works in practice

The depth and width of the core waveguide are a and b respectively

n r

a b

Channel Waveguide x

y z

n c

n s

p I

I

II N c

n

s n

s

f n

Fig 1.4 Scheme of the effective index method for solving the propagation constant of a step-index channel waveguide Starting from a 2D waveguide, the problem is split into two

step-index planar waveguides

The waveguide core with refractive index n r is embedded in a substrate of refractive

index of n s being upper part delimited by the cover with refractive index n c Starting from the channel waveguide, we first build an asymmetric step-index planar

waveguide, which consists of a film of width a and refractive index n r, surrounded by

cover and substrate having refractive indices n c and n s , respectively This is marked

as the planar waveguide I, and the effective index associated with the p th guided mode

for this waveguide is denoted by 𝑁𝐼𝑝

The second step is to consider a symmetric step-index planar waveguide, denoted as waveguide II, formed by a core film of thickness b, whose refractive index is the effective index 𝑁𝐼𝑝 calculated previously The film is surrounded on both sides by a medium with refractive index equal to the substrate refractive index ns The new waveguide can easily be solved by conventional methods applied to planar structures The effective index 𝑁𝐼𝐼𝑝𝑞 of the q th order guided mode calculated by this planar

waveguide corresponds to the modal effective index for the channel waveguide

1.2.3 Finite difference method

An arbitrary electromagnetic field propagating along a waveguide can be decomposed into many elementary discrete guided modes, which can be also called eigenmodes Besides Maxwell’s equation, numerical methods help to solve eigenmodes in complicated waveguide geometrics and Finite Difference Method (FDM) is one of the Eigenvalue Mode Solver (EMS) methods Numerical methods will simplify the calculation by maximizing the approximation of the exact solution and minimizing errors at the same time With FDM, the cross-section of the waveguide is made discrete with a rectangular grid of points which might be of identical or variable spacing as illustrated in Figure 1.2.2 In each of the subdivisions,

a two-dimensional wave equation is replaced with an appropriate Finite Difference relationship which is derived from a five-point Taylor series formula Each grid of points is assigned to an arbitrary electric field value Due to the subdivisions being rectangular, thus the FDM is appropriate for rectangular waveguide structure As

shown in Figure 1.2.2, by defining u to be electric field component to be calculated,

the relationships are shown in equations below:

There is a variety of boundary conditions that can be imposed at the edge of the analysis window such as Dirichlet, Neumann [55] and Transparent Boundary Condition (TBC) [56], [57] The first boundary conditions for the calculation window are categorized as fixed boundary condition This means that the field (electric or magnetic fields) is required to be set to zero at the boundary of the analysis window

It is a good approximation if there is a large index discontinuity at the edge Nevertheless, it effectively reflects back the radiation to the analysis domain To eliminate the back reflections or incoming fluxes into the analysis window, the TBC

is applied It effectively allows radiation to pass through the boundary freely and leaves the analysis domain without appreciable reflection In this way, the unwanted interference in the core layer can be prevented [57]

n-1 n n+1

m+1

m m-1

X

Y

Fig 1.5 The cross-section of the waveguide is made discrete with a rectangular grid of

points which have identical spacing

1.2.4 Beam propagation method

FDM can solve the waveguide eigenmode, but cannot be used to solve propagation characteristics in integrated optics or fiber optics The Beam Propagation Method (BPM) is a widely used and indispensable numerical technique in today’s modeling and simulation of evolution of electromagnetic fields in an arbitrary inhomogeneous medium BPM is eligible to apply in complex geometries and automatically consider both guided and radiation modes [58] BPM is a particular approach for approximating the exact wave equation for monochromatic waves and it can be solved numerically by FDM [59], [60] In this section, the main feature of BPM and its boundary condition will be solved with polarizationnegligibility and restriction of propagation to a narrow range of angles A harmonic dependence of the electric and magnetic fields, in the form of monochromatic waves with angular frequency w, is in such a way that the temporal dependence will be of the form 𝑒𝑖𝑤𝑡 Then the equation which describes such wave is the vectorial Helmholtz equation:

Propagation in z direction and refractive index changes along this direction, then electrical field can be presented as the complex field u of slow axial variation of ( , , z)

u x y multiplied by a fast oscillating wave exp(jkn z0 ) moving in z direction:

E x y z( , , )u x y( , , z) exp(jkn z0 ) (1.2.20) Where no is the refractive index of cladding Substituting equation (1.2.20) to (1.2.19), we have:

2

0 0

, equation (1.2.22) can be written as:

1.2.5 Finite difference beam propagation method

To simplify the calculation, we analyze BPM based on FDM in 2D only, hence direction dependency can be omitted Equation (1.2.23) can be rewritten as:

2

0 2

in z propagation, boundary condition also need to be imposed into analysis window

Fig 1.6 Comparison between FD-BPM (left) and FFT-BPM (right) simulation FD-BPM under TBC gives better simulation result as the simulated wave is smoother

TBC is used in FD-BPM simulation to eliminate the back reflections or incoming fluxes into the analysis window, in which radiation disappears into the boundary without any reflection when reaching the edge of the simulation window Although FFT-BPM is not analyzed in this dissertation, Fig 1.7 is shown as an example of comparing between FFT-BPM and FD-BPM with TBC Simulation of field propagation along Y-branch with equal shape arms is taken into consideration It is clear that FD-BPM with TBC gives better results, which explains the reason that we use 3D FD-BPM to optimize and simulate all of our proposed designs in this dissertation There is another factor that needs to be considered, which is the computed step The smaller computed step is, the more accurate the results will be but the tradeoff is very long computing and simulating time, as can be seen in Fig 1.7(b), that it might take 16.7 minutes to complete the simulation Normally, x,

y

 and  are set as 0.05μm as can be seen in Fig 1.7(a) z

Fig 1.7 Comparison between FD-BPM simulation time depending on computed step of

grid size 0.05μm (a) verse grid size 0.01μm (b)

1.3 Silicon-on-insulator waveguide fabrication

1.3.1 Separation by implanted oxygen (SIMOX)

The SIMOX process is the most common method to fabricate a massive quantity of SOI material The essential part in manufacturing SOI in the SIMOX method is implanting a large amount of oxygen ions below the surface of a silicon wafer The most common way to illustrate the total volume of any ion species embedded into a wafer is by the implanted ion dose The dose is just the whole amount of ions passing through one square centimeter of the wafer surface and is measured in units of ions/cm2 Under normal room-temperature conditions upper layer of silicon crystal might change to an unwanted amorphous stage during the implantation of the oxygen ions To avoid this effect, the silicon substrate is retained at a certain high temperature

during implantation To have the first glance of the relative amount of the dose required for SIMOX, it can be compared with the dose implanted in a typical doping process for the creation of source and drain contacts in manufacturing complementary metal-oxide semiconductor (CMOS) transistors

There is a need of high energy in order to implant oxygen ions into crystalline silicon The depth of the SiO2 and consequently the thickness of the silicon upper layer depends on that energy Figure 1.8 shows the schematic development of the oxygen concentration as a function of depth from the uppermost silicon wafer surface The graphs are simply meters of the growth of oxygen concentration versus depth at typical execution stages Similar to all implanted species, the oxygen concentration can be illustrated by a shape according, but not identical, to that of a Gaussian function (Figure 1.8a) As the implantation process continues and the dose rises, the ultimate concentration of oxygen ions (O+), saturates to a plague figure of that found

in stoichiometric SiO2 (Figure 1.8b) With further implantation the oxygen ions cannot be more condensed, forming a solid, continuous layer of SiO2 After being implanted with oxygen to a dose up to the concentration level, the silicon wafer is annealed at a constant high temperature for several hours This anneal process produces an unbroken, buried SiO2 layer with separate boundaries with the two adjacent silicon layers The annealing ensures the silicon over layer is prevented from primary lattice broken defects (Figure 1.8c)

Sub-SiO2 Stoichiometric

SiO2 formation concentration

SiO2 formation concentration

Depth from Si wafer surface (b)

Depth from Si wafer surface (c)

Fig 1.8 Variation of the oxygen profile during the SIMOX process (a) Low-dose; (b) high-dose (peak is at the stoichiometric limit for SiO2); and (c) after implantation and

annealing at high temperature for several hours

The implant energy determines the depth and thickness of the buried SiO2 layer To make the scopes of this structure more appropriate for the manufacture of wider cross-section waveguides, epitaxial growth technique is used to increase the thickness of silicon layer up to several microns[61]

1.3.2 Bond and Etch-back SOI (BESOI)

A very strong bond of two SiO2 wafers appears when their surfaces are brought into physical contact and this phenomenon managed to form the BESOI process The assembly of BESOI has three phases presented schematically in Figure 1.9: (a) oxidation of the two wafers to be bonded; (b) formation of the chemical bond; (c) thinning (etching) of one of the wafers

Wafer thinning can be achieved via a number of two common methods The most popular one is chemical mechanical polishing (CMP) technique, which is used widely

in making wafer planar in microelectronics The wafer surface must be weakened and then detached during a single processing step in the CMP method In general, the silicon surface, which needs to be polished, is handled with a rotating pad, and at the same time contacted with a chemically reactive slurry containing an abrasive component such as alumina and glycerin weaken The process eradicates the majority

of one of the bonded wafers, hence a wafer silicon upper layer on a buried SiO2 layer left, sustained by a silicon substrate

to the etchant, leaving a silicon upper layer whose depth and uniformity are defined

by the foundation of the doped layer

An upgraded version of this method has been used recently to produce wafers typically used to fabricate silicon waveguides [63] A further, undoped original layer

is epitaxially grown on the wafer surface subsequently after the formation of the high concentration p-type dope layer Moreover, a second nonselective etch process is used

to eradicate the exposure of the p-type layer resulting from the selective etch The final wafer structure is the one of an undoped silicon upper layer on the buried SiO2

1.3.3 Wafer Splitting

A thermally oxidized wafer is implanted with hydrogen to a certain concentration The implanted hydrogen ions concentration function has the form similar to Gaussian profile The distance from the wafer surface to the highest condense of the profile relies on the H+ ion energy, but is normally in the range of a few hundred nanometers

to a few microns The H+ ions are at their maximum concentration at this depth, in which the silicon lattice is tremendously weakened due to the damage from the stopping of the ions

After the implantation step, the wafer is brought into interaction with a second handling wafer, which surface may or may not be covered by thermal SiO2 From the contact, room-temperature bonding happens similar to that of the BESOI method Subsequent impacted thermal at the same degree in which of SIMOX process firstly separates the implanted wafer along the high concentration of the implanted H+ ions profile, then reinforces the bond between the former and latter wafer

A careful CMP process is deployed to decrease roughness of SOI surface After that, epitaxial silicon growth can build up the thickness of the silicon upper layer if needed The inhomogeneity thickness of the implanted hydrogen profile peak are only a few percent Importantly, although the upper layer is implanted with a high dose quantity, the small mass of the hydrogen ions guarantees the negligible remaining destruction

at the end of the thermal treatment The buried SiO2 thickness may be varied from nanometers to several microns due to the determination of the thermal oxidation process

The adaptability, high quality and efficient use of silicon presented from this method makes it a brilliant platform to fabricate silicon photonics with low cost

1.3.4 Silicon Epitaxial Growth

‘Epitaxial’ is from Greek word where “epi” means “above” and “taxy” means “in order manner”, hence the whole word depicts the process of growing a mono-crystal layer in an order, especially when fabricating micro- or opto-electrical devices The deployment of epitaxial silicon as the waveguide medium has the supplementary benefit of doping and defect levels below ones found in wafers cut

The most popular epitaxial silicon growth technique is chemical vapor deposition (CVD) CVD is a method which places a solid film on the surface of a silicon wafer

by the reaction of a gas mixture on that surface Regarding silicon deposition, the source gas is usually dichlorosilane (SiH2Cl2) It is an obligation that the wafer surface’s temperature is raised to a typical value to provide enough energy to elevate the chemical reaction Although either a vapor or a solid source can be used in molecular beam epitaxy (MBE), the criteria of thickness of the film in silicon waveguide fabrication determined that vapor phase epitaxy is more proper The uniformity and repeatability of the commercially accessible technologies and practices can restrict non-uniformities thickness being less than 1% A description of the gas conveyance and reaction kinetics of CVD is mentioned in [64], while [65] depicted some of the numerous available equipment in detail

1.3.5 Fabrication of surface etched features

1.3.5.1 Photolithography

Photolithography is the standard method of printed circuit board (PCB) and microprocessor fabrication The process uses optical radiation, which changes the photoresist layers, to make the conductive paths of a PCB layer and the paths and electronic components in the silicon wafer of microprocessors

The width of a rib waveguide shown in Figure 1.11 is mainly created by the photolithographic process, so the regulator of the photo process is one of the most vital tasks in silicon photonic manufacture Moreover, it is not enough to guarantee local governor, but to preserve both inter- and intra-wafer dimensions within a constricted tolerance over long duration of operation Although such manufacturing strict requirements are required for all fabrication processes, a large quantity of specific process parameters make photolithography one of the most crucial disciplines in silicon device fabrication

Thanks to many years of research, application, reproduction and improvement, the microelectronics industry has been conquered by deep-submicron technologies, in which minimum feature sizes are now well below 100 nm with critical dimension (CD) control at the 10 nm level This critical dimension control is way beyond the requirements to fabricate the most basic of silicon photonic waveguide such as the large-cross-section, single-mode silicon rib where minimum dimension is several

microns and, by cautious select of the objective dimensions, CD control can be widen

to several hundred nanometers [66] However, the silicon photonics manufacturer may insist on the very strict CD when fabricating more complicated shape submicron-dimension devices or waveguides

Photolithography technique uses deep ultraviolet light to transfer a mask pattern to the surface of a wafer The pattern is printed on the wafer using a photoresist Many formulas and procedure variants have been introduced to guarantee good, application-specific photolithography, but the primary structure of all photo-processes depends

on specific common steps, namely wafer preparation, photoresist application, soft bake, exposure to ultraviolet light, photoresist developing and hardbake

Fig 1.11 (a) Schematic of a silicon rib waveguide (b) Electron micrograph of a silicon

rib waveguide Reproduced by permission of Intel Corporation

1.3.5.2 Silicon etching

Etching process is executed to precisely remove redundant material from the silicon wafer surface by a chemically reactive or physical method There are two general approaches: wet and dry etching Each approach has benefits and drawbacks, however dry etching prevails in reproducing structures of submicron scales Low-loss silicon waveguides, having dimensions typically >1µm, have been shaped by both wet [67] and dry [68] etching, but with the requirement for flexible process capability, tight tolerances and reproducible production, dry etching is regarded as the most suitable

solution

Dry etching is done through the development of a low pressure plasma The physical processes, which consist of the formation and stabilization of a plasma, are out of the scope of this dissertation However, because of the prevalence of plasmas in silicon processing (e.g etching, deposition, photoresist removal, ion implantation) it is appropriate to point out some of the elementary principles

A plasma is an ionized gas, almost neutral in general, consisting of electrons, ions and mostly neutral particles The formation of a localized plasma, which is contained

in an isolated chamber, can be achieved by the application of either DC or AC power

to a process gas Although DC one is infrequently used in practical applications because it is unsuitable with insulating electrodes causing surface charging and an unbalanced plasma AC power avoids this issue by accumulating charges in one half-cycle, followed by neutralizing charges in the next half Therefore, AC plasma generation triumphs in the design of semiconductor etching equipment A representation of a typical plasma chamber setup is shown in Figure 1.12

PLASMA GLOW

Sheath Electrodes

Fig 1.12 Schematic of a confined AC-generated plasma suitable for silicon processing

The processed wafer in placed on the lower, grounded electrode

CF4 gas is normally used to derive plasma in the silicon etching process F atoms, which can be dissociated from CF4 at certain conditions, are used as active elements

to etch both Si and SiO2 However, using plain CF4 as a plasma environment will slow down the etching rate as CF3 and F can recombine to form the original stage

CF4 Hence, O2 is added into the gas mix to promote significantly the etching rate due

to the reaction of oxygen with CF3 inhibiting F recombination and hence increasing the free F concentration

1.4 Silicon-on-insulator waveguide structure used for MDM functionality

1.4.1 Directional coupler

Coupling theory has been applied extensively in guided-wave optics as a mathematical tool for the analysis of electromagnetic wave propagation and