Nghiên cứu tính toán và thiết kế mạch tích hợp quang băng rộng chuyển đổi và tách ghép mode (design and simulation of wideband photonic integrated circuits for multi mode (de)multiplexing and conversion)

High index is indicated by darker color...8 Fig 1.1.2 Schematic of SOI waveguide...10 Fig 1.1.3 Schematic of SOI Rib waveguide...10 Fig 1.2.1 Scheme of the effective index method for sol

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

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

Major: Telecommunications Engineering

Code: 9520208

DOCTORAL DISSERTATION

IN TELECOMMUNICATIONS ENGINEERING

SUPERVISORS:

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 ofwideband photonic integrated circuits for multi-mode (de)multiplexing andconversion", 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 onwork done by myself jointly with others, I have made exactly what was done by othersand what I have contributed myself

Hanoi, October, 2020Postgraduate Student

Tran Tuan Anh

SUPERVISORS

First and foremost, I would like to thank my supervisor Prof Dr Tran Duc Han forhis support and advice throughout my research time in Hanoi University of Scienceand Technology (HUST) His encouragement and full support led me to everysuccess of my study I have been able to learn a lot from him about being a goodteacher and researcher

I would like to express my gratitude to my supervisor, Dr Truong Cao Dung, forguiding and motivating me since I was an undergraduate student at HUST He hasgiven 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 studypostgraduate courses and sincere advices for my future career

I am also thankful to my research team, Ms Nguyen Thi Hang Duy, Mr Ta DuyHai, Ms Tran Thi Thanh Thuy and Mr Hoang Do Khoi Nguyen in Posts andTelecommunications Institute of Technology They gave me a lot of help during mylast two years

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

TRAN TUAN ANH

ii

Table of Contents

INTRODUCTION 1

CHAPTER 1 SOI WAVEGUIDE STRUCTURE, ANALYSIS AND FABRICATION

_8 1.2 Optical waveguide analysis and simulation methods 12

1.2.1 Wave equations _ 12

1.2.2 Effective index method _ 151.2.3 Finite difference method 17

1.2.4 Beam propagation method _ 18

1.2.5 Finite difference beam propagation method _ 19

1.3 Silicon-on-insulator waveguide fabrication 21

1.3.1 Separation by implanted oxygen (SIMOX) 21

1.3.2 Bond and Etch-back SOI (BESOI) 231.3.3 Wafer Splitting _ 24

1.3.4 Silicon Epitaxial Growth 25 1.3.5 Fabrication of surface etched features 25

1.4 Silicon-on-insulator waveguide structure used for MDM functionality _28

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

2.2 Conclusion _52 3.1 Cascaded N x N general interference MMI analysis _54

3.2 Three-mode division (De)multiplexer based on a trident coupler and two cascaded 3×3 MMI silicon waveguides _56

3.2.1 Design and structural optimization 563.2.2 Simulation and performance analysis 64

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 83

4.2.3 Proposal of experimental diagram _ 85

4.3 Conclusion _89

DISSERTATION CONCLUSION AND FUTURE WORKS _ 92 PUBLICATIONS DURING PHD COURSE 94

UNDER REVIEW PAPER 94 PUBLICATIONS BEFORE PHD COURSE 94

REFERENCE 95

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Chemical Mechanical PolishingChemical Vapor DepositionCoarse Wavelength Division MultiplexingDirectional Coupler

Dense Wavelength Division MultiplexingDevice Under Test

Deep Ultra VioletElectron Beam LithographyErbium Doped Fiber AmplifierEffective Index Method

Eigenmode ExpansionEigenvalue Mode SolverFinite Difference Beam Propagation MethodFinite Difference Method

Finite Difference Time DomainFast Fourier Transform Beam Propagation MethodFiber to the Home

General InterferenceInsertion Loss

v

On-off Keying SignalsPolarization Division MultiplexingPlasma-enhanced chemical vapor depositionPlanar Integrated Circuits

Polymethyl MethacrylatePlanar Lightwave CircuitsPassive Optical NetworkRestricted InterferenceSymmetric InterferenceSpatial Mode Division MultiplexingSeparation by Implanted OxygenSilicon on Insulator

Transparent Boundary ConditionTransverse Electric

Transverse ElectromagneticTransverse Magnetic

Wavelength Division MultiplexingCross Phase Modulation

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List of Tables

Table 1.4.1 Summary of different MMI types’ properties 41Table 2.2.1 Comparison of our proposed designs based on ADC with others designshaving similar structure 53

Table 3.3.1 Comparison of our proposed designs based on MMI with others designshaving similar structure 69

Table 4.3.1 Comparison of our proposed designs based on branch bus structure withothers designs having similar structure 90

List of Figures

Fig 1 Set up initial parameters of SOI waveguide and simulation method in RSoft 4

Fig 2 Pathway monitoring power at each output port of a design 5

Fig 1.1.1 Schematic of non-planar optical waveguides High index is indicated by darker color 8

Fig 1.1.2 Schematic of SOI waveguide 10

Fig 1.1.3 Schematic of SOI Rib waveguide 10

Fig 1.2.1 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 1.2.2 The cross-section of the waveguide is made discrete with a rectangular grid of points which have identical spacing 18

Fig 1.2.3 Comparison between FD-BPM (left) and FFT-BPM (right) simulation FD-BPM under TBC gives better simulation result as the simulated wave is smoother 20

Fig 1.2.4 Comparison between FD-BPM simulation time depending on computed step of grid size 0.05μm (a) verse grid size 0.01μm (b)m (a) verse grid size 0.01μm (a) verse grid size 0.01μm (b)m (b) 21

Fig 1.3.1 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 1300oC for several hours 22

Fig 1.3.2 The bond and etch-back process to form BESOI: (a) oxidation; (b) bonding; and (c) thinning 23

Fig 1.3.3 (a) Thermally oxidized wafer is implanted with a high dose (approximately 1017 cm−2) 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 1.3.4 (a) Schematic of a silicon rib waveguide (b) Electron micrograph of a silicon rib waveguide Reproduced by permission of Intel Corporation 26

Fig 1.3.5 Schematic of a confined AC-generated plasma suitable for silicon processing The processed wafer in placed on the lower, grounded electrode 27

Fig 1.4.1 Directional coupler consisting of slab optical waveguide 29

Fig 1.4.2 Periodic exchange of power between waveguide 1 and 2 30

Fig 1.4.3 Simulation of periodic exchange of power between waveguide 1 and 2 using BPM 30

Fig 1.4.4 Power transfer ratio verse phase mismatch parameter ∆ .31

Fig 1.4.5 The schematic configuration of MMI waveguide 33

Fig 1.4.6 Two-dimensional representation of a MMI waveguide 34

Fig 1.4.7 Power distribution of GI-MMI with = 3 (left), = 3 /2 (middle), = 3 /3 (right) using FD-BPM simulation 38

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Fig 1.4.8 Power distribution of 2x2 PI-MMI, input access waveguide is at ± /6

with = /2 (left), = (right) using FD-BPM simulation 40

Fig 1.4.9 Power distribution of SI-MMI showing to-3-way splitting (left) and 1-to-1 imaging (right) having same length and different width using FD-BPM simulation 41

Fig 1.4.10 Oscillating field pass through boundary between two isotropic media 41

Fig 1.4.11 Schematic structure of tilt branch bus waveguide 43

Fig 2.1.1 Schematic of the mode synthesizer based silicon waveguide 46

Fig 2.1.2 BPM simulation for the height of waveguides of the asymmetric directional 47

Fig 2.1.3 BPM simulation for power ratio as a function of the waveguide height 48

Fig 2.1.4 Transmission characteristic of on dependence of the coupling length of the asymmetric directional coupler by BPM simulation 48

Fig 2.1.5 Electric field patterns for the mode (de)MUXer 49

Fig 2.1.6 Wavelength response of the mode DMUXer in the C-band 49

Fig 2.1.7 1-nm-wavelength spectrum in the side of mode multiplexer 50

Fig 2.1.8 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 2.1.9 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 3.1.1 Schematic of cascade NxN GI MMI used for switching optical signal….52 Fig 3.2.1 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 3.2.2 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 3.2.3 BPM simulation for the phase angle Φ is a function of the central width of the phase shifter 64

Fig 3.2.4 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 3.2.5 Performances dependence on the wavelength of the proposed three mode-(de)MUXer: (a) insertion loss and (b) crosstalk 66

Fig 3.2.6 Influence of branching angles of the trident coupler on optical performances of the proposed (de)MUXer: a) insertion loss, and b) crosstalk 67

Fig 3.2.7 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 3.2.8 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 1 The proposed design of the three-mode channel separation device 71

Fig 4.1.2 Dependence of e ective index of the main bus waveguide on variation offfective index of the main bus waveguide on variation ofthe main waveguide width Wm at the height h of 220 nm 71Fig 4.1.3 The results of transmission characteristic of proposed device at the firsttilted waveguide as a function of the width Wa (nm), which passively affects themode selective coupling coefficients 73Fig 4.1.4 The results of transmission characteristic of proposed device at the secondtilted waveguide as a function of the width Wa (nm), which passively affects themode selective coupling coefficients 74Fig 4.1.5 Simulated electric field patterns for the proposed three mode

(de)multiplexer for: fundamental mode (a), first-order mode (b), second-order

mode (c) 74Fig 4.1.6 The characteristic optical performance of the device depends on the

wavelength, showing the I.L and Cr.T of each three mode outputs 75Fig 4.1.7 Variation of optical transmission performance of the proposed waveguidedepended on width tolerance ΔW (nm).W (nm) 76Fig 4.1.8 Variation of optical transmission performance of the proposed waveguidedepended on height tolerance ΔW (nm).h (nm) 76Fig 4.1.9 Transmissions at three output ports PO1, PO2 and PO3 as a function of twosimultaneous variables ΔW (nm).h (nm) and ΔW (nm).W (nm) of the bus waveguide when threemodes are excited: (a), (b), (c) for mode TE0, (d), (e), (f) for mode TE1 and (g), (h),(i) for mode TE2 77

Fig 4.2.1 The propose schematic of a four-mode (de)multiplexer device a) Topview b) Size view 78Fig 4.2.2 Dependence of effective indices by using numerical simulation for

different modes on variation of the waveguide width 79Fig 4.2.3 The results of transmission characteristic of proposed device for modeselective coupling coefficients a) at the A1 b) at the A2 and c) at the A3 82Fig 4.2.4 Simulated electric field patterns for the proposed four mode

(de)multiplexer for: a) fundamental mode, b) first-order mode, c) second-ordermode, d) third-order mode 83Fig 4.2.5 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 4.2.6 Power of the proposed device at four output ports O1, O2, O3 and O4 arefunctions of two simultaneous variables ΔW (nm).h (nm) and ΔW (nm).W (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 4.2.7 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 PatternGenerator, PC: Polarization Controller, EDFA: Erbium Doped Fiber Amplifier,DUT: Device under test, BPF: Band-pass filter, PD: Photodetector, BERT: bit errorrate tester, CLK: clock synthesizer, VOA: Variable Optical Attenuator, BERT: Biterror rate tester Gain1=10dB, Gain2=3dB 86Fig 4.2.8 Eye diagrams of the four-mode demultiplexer for four desired output portscorresponding to injected four modes, respectively 87

x

Fig 4.2.9 BER factor is a function of transmit power Tx of the tunable multimodelaser 87Fig 4.2.10 The BER was surveyed according to the bit rate of the communicationsystem when the transmit power Tx = -1dBm 88Fig 4.2.11 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 thecommunication infrastructure, especially optical communication, plays an importantrole in the success of the revolution After long distance fibers have been settled,research in the optical communication system field focused on functional photoniccomponents, which are used to connect the terminals Those components can be used

as optical splitters, (de)multiplexers, switches … The conventional way to constructthose components is to put each component into an individual temperaturecontrolled package and connect them to corresponding functional units However,this method is difficult to assemble and accounts for the major percentage of cost ofthe whole device After that, thanks to advanced technology and well developedsemiconductor fabrication technology, planar lightwave circuits (PLCs) had solvedsome major problems such as polarization dependence, temperature sensitivity andoptical loss, to become an essential part in the communication network PLCs havesome outstanding advantages as follows: enhanced functionality, compactness, highflexibility and reliability, low optical losses and feasibility of mass production due

to high integration density and low cost like its electronics integrated circuitscounterpart 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 accessnetworks Power splitters and (de)multiplexers are the basic block for passivefunction of FTTH networks Power splitters are used to divide the optical powerfrom input ports to different channels, while (de)multiplexers are for combining andseparating different wavelengths Different types of power splitters based on PLCtechnology had been proposed, such as Y-Branches [1], Mach-ZehnderInterferometer [2], Multimode Interference (MMI) [3] PLCs based devices aresuperior to conventional fused-fiber type splitters in terms of low cost and massproducing ability Regarding multiplexing function, one of the popular componentsused in FTTH networks is the optical network unit (ONU), which is located at eachusers’ places ONU contains a triple wavelength i.e 1310nm, 1490nm, 1550nm,(de)multiplexer, and opto-electronics devices such as laser diodes and photodetectors Most of current practical triplexer transceivers are bulky modules built ondiscrete optical components, which is difficult to integrate with other devices and topackage PLCs technology presents to be a solution for realizing triplexers withgood performance and lower layout complexity Recently, there are some works inthis field using MMI structure [4] [5] Hence, PLCs long term reliability for opticaltelecommunication has been already established

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

in optical communication systems, because this technology supports simultaneously alot of traffic wavelengths However, the available channel numbers in the C and Lbands for dense-WDM systems has been fully utilized In addition, there are still somelimitations that need to be solved in WDM regarding fiber nonlinearity, such as four-wave mixing (FWM), cross phase modulation (XPM) phenomena or stimulatedscattering effects On the other hand, mode division multiplexing (MDM) technologyhas been being paid attention as an emerging technology to enhance the capacity of theoptical communication system [9]–[13] besides mentioned above technology In thisMDM, each eigenmode carries a separated optical traffic Each of these eigenmodesdoes not couple with the others because of the orthogonality, hence enabling differentspatial modes, defined as different channels, to carry data separately Different fromapplications of WDM in long-distance transmission, MDM is more suitable fortransmission with short distance, ultra large capacity, like intra-chip communication[14] Therefore, a larger transmission capacity can be realized by combining MDMwith other multiplexing systems, for example, MDM with WDM

[15] Furthermore, combining MDM/WDM not only enhances capacity but alsodoes not affect the performance of photonic devices that were less withstand from theeffect of modal dispersion A new multiplexing method is introduced in a MDMsystem, enabling different spatial modes as different channels to carry data Morerecently, this technique not only has become popular for increasing the capacity of anoptical wavelength carrier by feeding multiple guided modes into a multimode opticalwaveguide but also is attractive in multiple-input, multiple-output (MIMO) signalsprocessing field [16], [17] Hence, MDM shows to be a promising technique, alongwith other (de)multiplexing schemes, that can be applied in on-chip opticalcommunication to increase capacity of the transmission systems

Objectives

By reviewing existing papers and research works, there are some spatial mode divisionmultiplexing (SDM) techniques that use few-modes [18]–[20] or multimode opticalfiber [21]–[23] to process the (de)multiplexing functions directly; however transmittingsignals is relatively complex as needing optoelectronic devices, processing the signal inoptical fiber links is not flexible, plus fabrication procedure is difficult to integrate inlarge scale photonics circuits In contrast to OEICs, PLCs

based on silicon material, as mentioned above, can be fabricated easily, plus have someadvantages, e.g low loss [24],[25], high confinement of light [26] due to significantrefractive index contrast between Si and SiO2 , thus guiding light with low bendingloss, high bandwidth [27], mass-producing ability [28] and compatible to CMOStechnology A compact and reconfigurable mode (de)multiplexer which can supportnumerous modes is essential for realizing MDM-WDM in integrated photonics [29].However, current works based on PLCs SOI waveguide applied in MDM still havesome weaknesses Some designs of on-chip (de)multiplexers have been proposed byconstructing on the platform of Multi-Mode Interference (MMI) couplers [30]–[33]typically had advantages: broadband, large tolerance fabrications but these structuresneed phase shifters also have a difference of propagation constants of spatial modesleading 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 tomanufacture in terms of making the mask in manufacturing process and have quite largeinsertion loss Recently, Dai et.al [40] proposed a four mode on-chip MDM structurewhich based on adiabatic asymmetric directional couplers However, these devices havesome drawbacks, e.g., high-order modal loss and modal dispersion while guiding into thewaveguides, so they have difficulty in coupling with the multimode fiber link or otherplanar lightwave circuits Moreover, many adiabatic couplers often required a relativelylarge footprint and were complicated to fabricate Similarly, several three mode(de)multiplexers based on adiabatic asymmetric resonators [41],[35] had been proposed torealize reconfigurable (de)multiplexing functions but those structures have a narrowresonant bandwidth Hence, the objective of this dissertation is to propose new mode(de)muxer designs based on different SOI structures that can overcome thosedisadvantages 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 SOIwaveguides Three most common SOI waveguide structures will be studied, namelyasymmetric directional coupler, multimode interference coupler and asymmetric Y-junction waveguide, due to their vast applications for different functionalities in PICfield, especially MDM and mode converter The scope of study is limited withinpassive devices made from silicone rib/ridge waveguide structure used for mode(de)multiplexing function only Rib/ridge waveguide height is designed based onCMOS fabrication standard, while width and length are determined according to thenumber of desired supporting modes and devices working principles respectively.Passive devices are concerned due to its simplicity and no need of routing orswitching optical signals for MDM function alone Silicon material is suitable for

3

passive devices at Band C due to its low-loss properties and especially compatibilitywith CMOS technology hence providing options for low-cost production.

Research methodology

All the designs’ structures are built based on theoretical foundation, includingcoupling theory, self-imaging reproduction theory of MMI and its transfer matrixfor calculating phase shifting and phase matching theory applied in branch buswaveguide structure Then, each device’s optical properties are investigated andoptimized numerically by simulation methods All the simulation processes areexecuted via RSoft software, which is developed by Synopsys Inc There are manytypes of simulation in RSoft such as FullWave using FDTD investigating fieldpropagation in time domain in complex structures such as array waveguide gratings

or BandSolve using FDTD investigating field propagation in time domain inphotonic crystal waveguide However, in the scope of this dissertation, in whichusing 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 SOIrib/ridge waveguide with 3D-BPM simulation in RSoft is shown in Fig 1 as below

Fig 1 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, capable to support a few modes, hence all devices performance will

be assessed according to those criteria They are defined as follow:

Fig 2 Pathway monitoring power at each output port of a design

I.L and Cr.T will be deployed to evaluate devices fabrication and bandwidthtolerance Although there is still no international unified criterion assessing whetherthe devices meet standard requirements or not because this research field is still indevelopment stage, we tried to structure our designs with 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 Thosefigures are common results and expectations from the PIC research community.Finally, our final results will be used to compare with other recent works in order todemonstrate pros and cons of the proposed designs as well as potential furtherimprovements or future research

Scientific contributions and practical applications

The dissertation has three main contributions as follows:

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1) We proposed a new design based on asymmetric directional coupler SOIwaveguide, which can (de)multiplex fundamental mode and 1st-order mode The resulthas been published in International Conference on Advanced Technologies forCommunications (ATC), 2016

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

3) We proposed a new mode sorting design based on branch tilt SOI waveguidesdiverted 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 formultimode (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 andcrosstalk; have small footprint, thus can be promising candidates for high bitrateMDM systems as well as on-chip photonic integrated circuits

Dissertation structure

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

- In chapter 1, SOI waveguides will be mentioned, regarding its common shapes,applications in PLCs components and their advantages compared to other materialsused in PLCs Then different numerical simulation methods are summarized Thefinite difference method is developed to solve the eigenmodes of the waveguidestructure The beam propagation method is used to investigate the light propagation indifferent waveguide structures Effective index method can be used in waveguide witharbitrary shape and refractive index distribution to simplify the calculation and savecomputing capacity After that, SOI waveguide fabrication process will be brieflyintroduced Finally, working principles of three types of SOI waveguide structuresused in this dissertation are introduced sequentially Firstly, the theory of couplingbetween two directional waveguides will be introduced, covering from the simplestcase, which is symmetric co-directional coupler, to general cases, which can beapplied to mode excitation coupling in asymmetric coupler Secondly, MMI couplerworking principles are introduced, especially its self-image properties will govern theapplications in MDM as well as other functionalities The last structure is Y-junctionwaveguide, in which MDM function can be achieved based on its phase matchingconditions

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- 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-Zehnderinterferometer (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 willsolve the major challenge in MDM systems, which is selectively injecting/ extractingindividual 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 inputport to fundamental modes at the output ports so as to be compatible with optical singlemode 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 effectiveoptical device namely broadband, low loss and large tolerance fabrications, hence beingrecently used for MDM [31], [33], [38]

- In chapter 4, a new MDM structure, which is designed based on multi-branch busSOI waveguide for selecting and converting guided modes, are introduced Thedesigns’ function of converting high order modes from the bus input port tofundamental mode at the output ports also prove the feasibility of the compatibilitybetween the proposed designs and single mode optical fiber and network on-chipsystems Those designs show some improvements compared to the designs using MMIcoupler [31], [43] which are still relatively complex as its structure requires lowfabricating tolerant passive phase shifters, and the designs based on asymmetricdirectional coupler [44], [45] which can only (de)multiplex 2 modes

CHAPTER 1 SOI WAVEGUIDE STRUCTURE, ANALYSIS AND FABRICATION

1.1 Shapes and functions of silicon-on-insulator waveguide

Optical waveguide is s basic unit of photonics components in PLCs Opticalwaveguide allows optical signal transferring along its propagation direction andconfines the light within the high refractive index region There are several non-planar schematics of waveguide shown in Fig 1.1.1

Fig 1.1.1 Schematic of non-planar optical waveguides High index is

indicated by darker color.

Buried channel waveguide: the guided mode channel is the core and surrounded bylower refractive index material

Strip-loaded waveguide: is formed by loading a planar waveguide, which alreadyprovides optical confinement in the x direction, with a dielectric strip of index n3 <

n1 or a metal strip to facilitate optical confinement in the y direction Strip-loadwaveguides do not require half-etching in waveguide fabrication

Ridge waveguide: consists of a silicon core on top of a silica cladding layer Ridgewaveguide can confine light well because it is surrounded by air, which can beconsidered as upper cladding with very low refractive index

Rib waveguide: consists of a slab waveguide and a strip waveguide, with the samerefractive 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

8

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

Diffused waveguide: high-index region is created inside the substrate throughdiffusion of LiNbO3 dopants with core formed by Titanium (Ti) The coreboundaries in the substrate are not defined clearly because of the diffusion process

A diffused waveguide thickness is determined by the diffusion depth of the dopantand 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 Thefeatures of each material are summed up in Table 1.1.1

LiNbO3 High Electro-Optic coefficient,

non-linear effect, excellent high High lossspeed modulation

device

Si High refractive index contrast, Indirect bandgap

high integration density andcompatible with Si electronicsPolymer Ease of fabrication, low cost, high Low life expectancy

Electro-Optic and Thermal-Opticperformance

speed modulation and light technology, large foot print

contrast between core andcladding layers

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

Apart from materials mentioned in the table, another material commonly used inoptical waveguide is chalcogenide (As2S3), which effective refractive index issignificantly high and sensitive to power intensity according to Kerr effect [54], thuscan be applied in nonlinear directional coupler However, in this dissertation, SOI isused for all of our design as it is the most favorable choice for passive devices withoutstanding features such as low cost, low loss, high density integration due to its highrefractive index contrast and good matching for single mode fiber Furthermore, opticalpower loss of C-band in silicon waveguide, which is used as input signal for all of ourdesigns and very popular in practical applications in analog CATV signal overlay, issignificantly low Schematic structure of SOI slab waveguide is shown in Fig 1.1.2, inwhich 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, which refractive indices are

3.45 and 1.46 respectively (Fig 1.1.3)

Surface silicon guiding layer Buried SiO 2 cladding

Silicon substrate

Fig 1.1.2 Schematic of SOI waveguide

H

Hd

SiO2, nc=1.46

Fig 1.1.3 Schematic of SOI Rib waveguide

There are several of 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

10

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 gratingperiod 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 adjacentwaveguides through the overlapping of the evanescent waves of the propagatingmodes This effect is described by the coupled mode formalism By setting designparameters, including waveguide spacing and coupler length, the ratio of powersbetween the two output ports may be set during the fabrication process between zeroand 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, in two separatewaveguide output ports An integrated optical element based on a lithium niobatesubstrate 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 asubstrate with a possibility of changing its refractive index by means of an externallyapplied field (thermal, acoustic, electric, etc.) The most common phase modulator isbased 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 propagationconstant of the propagating mode also changes; therefore, the light travelling throughthat 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 toperform this task is to build an integrated Mach-Zehnder interferometer (MZI) on anelectro-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 TMconversion 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 isbirefringence, and therefore the TE, TM modes have different effective refractiveindices (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 apiezoelectric transducer, creates a Bragg grating in the acousto-optic substrate thatinteracts with the propagating light in a specially designed region, giving rise todiffracted light that is frequency-shifted by the Doppler Effect This frequency shiftcorresponds 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, frequencyconverter, the arrayed waveguide grating (AWG), the integrated acousto-optictunable filters (AOTF), etc Examples of active devices are the integrated opticalamplifier, the integrated laser, etc

1.2 Optical waveguide analysis and simulation methods

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

It is well known that the light wave is an electromagnetic field and most of thephenomenon in photonic components can be described by Maxwell’s equationswhich are used to analyze the behavior of the electromagnetic fields However,solving Maxwell’s equations is only for simple structures, such as planar or channelwaveguides, 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 thedesign of PLCs devices Effective index method (EIM) is used to save computingcapacity by simplifying the three-dimension waveguide into two-dimensionwaveguide; Beam propagation method (BPM) and Finite Difference Method (FDM)are introduced to simulate the propagation of light in PLC devices FD-BPMsimulations are executed under Transparent Boundary Condition (TBC) in order toeliminate oscillating field reflection into the analysis window In the followingsections, 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:

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

1.2.2 Effective index method

Effective index method (EIM) is an appropriate analysis for calculating thepropagation modes of the channel waveguides It applies the tools developed forplanar waveguides to solve the problem of two-dimensional structure This method

is one of the simplest approximate methods for obtaining the spatial fielddistribution and the propagation constant in channel waveguides having arbitrarygeometry 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 ycoordinate) acts as a parameter In this way, we obtain a y-dependent effective indexprofile; this generated index profile is treated once again as a one-dimensionalproblem from which the effective index of the propagating mode is finally obtained

For propagating modes polarized mainly along the x direction ( ), the major components are , , The propagation of these polarized modes is similar to the TM mode in a one-dimension

has previously been calculated The modes for the second planar waveguide are TE polarized with , , as non-vanishing components because the light is mainly polarized along x direction.

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

u x, y , z , t u x exp j t j z 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 thespatial dependence of the fields along x and y axis in channel waveguide:

Add and subtract from Eq (1.2.16) the value of k 2

n2eff(x) and separate the equation into two independent equations:

( ) 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 1.2.1 will show how effective index mode works in practice The depth and width of

the core waveguide are a and b respectively.

Fig 1.2.1 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

16

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 to the p th

guided mode for this waveguide is denoted by

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 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 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:

Where x2 and y2 are spacing between two grids of points in x and y directions

respectively The smaller x2 and y2 are, the more accuracy the calculation will be but

also need more computing capacity

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

17

Condition (TBC) [56], [57] The first boundary conditions for the calculationwindow 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 theanalysis window It is a good approximation if there is a large index discontinuity atthe edge Nevertheless, it effectively reflects back the radiation to the analysisdomain To eliminate the back reflections or incoming fluxes into the analysiswindow, the TBC is applied It effectively allows radiation to pass through theboundary freely and leaves the analysis domain without appreciable reflection Inthis way, the unwanted interference in the core layer can be prevented [57].

X m+1

m-1

n-1 n n+1

Fig 1.2.2 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 propagationcharacteristics in integrated optics or fiber optics The Beam Propagation Method(BPM) is a widely used and indispensable numerical technique in today’s modelingand simulation of evolution of electromagnetic fields in an arbitrary inhomogeneousmedium BPM is eligible to apply in complex geometries and automaticallyconsider both guided and radiation modes [58] BPM is a particular approach forapproximating the exact wave equation for monochromatic waves and it can besolved numerically by FDM [59], [60] In this section, the main feature of BPM andits boundary condition will be solved with polarization negligibility and restriction

of propagation to a narrow range of angles A harmonic dependence of the electricand 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 Then theequation which describes such wave is the vectorial Helmholtz equation:

k 2 n 2 ( x , y , z ) E 0

dx 2 dy 2 dz2

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 u

( x, y, z) multiplied by a fast oscillating wave exp( jkn0 z) moving in z direction:

Equation (1.2.23) is a para-axial 3D BPM equation 3D BPM can be simplified into

2D by omitting one of x or y axis, but z axis, which is propagation direction, must

be kept The next section will introduce the calculation of 2D-BPM

1.2.5 Finite difference beam propagation method

To simplify the calculation, we analyze BPM based on FDM in 2D only, hence

y-direction dependency can be omitted Equation (1.2.23) can be rewritten as:

Approximation (n2 − n2) ≅ 2n 0 (n − n 0 ) is not applied in equation (1.2.24), hence this equation can be used in both strong and weak

guiding conditions In general, a differential equation is of the form:

u A( x , z )

19

Where x and z are the compute steps in the x axis and z axis, i and m are grid points

along the x axis and z axis, respectively Replacing parameters A and B from equation

With initial electric field u i m0 is at z = 0 and electric field u i m is at the next propagation

step z=zm can be obtained from equation (1.2.31) In order to fully investigate field u in

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

Fig 1.2.3 Comparison between BPM (left) and FFT-BPM (right) simulation BPM under TBC gives better simulation result as the simulated wave is smoother

FD-20

TBC is used in FD-BPM simulation to eliminate the back reflections or incomingfluxes into the analysis window, in which radiation disappears into the boundarywithout any reflection when reaching the edge of the simulation window AlthoughFFT-BPM is not analyzed in this dissertation, I would like to show Fig 1.2.3 as anexample of comparing between FFT-BPM and FD-BPM with TBC Simulation offield 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 reasonthat we use 3D FD-BPM to optimize and simulate all of our proposed designs inthis dissertation There is another factor that needs to be considered, which is thecomputed step The smaller computed step is, the more accurate the results will bebut the tradeoff is very long computing and simulating time, as can be seen in Fig1.2.4(b), that it might take 16.7 minutes to complete the simulation Normally, x, y

and z are set as 0.05μm (a) verse grid size 0.01μm (b)mas can be seen in Fig 1.2.4(a)

Fig 1.2.4 Comparison between FD-BPM simulation time depending on computed step

of grid size 0.05μm (a) verse grid size 0.01μm (b)m (a) verse grid size 0.01μm (a) verse grid size 0.01μm (b)m (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 ofSOI material The essential part in manufacturing SOI in the SIMOX method isimplanting a large amount of oxygen ions below the surface of a silicon wafer Themost common way to illustrate the total volume of any ion species embedded into awafer is by the implanted ion dose The dose is just the whole amount of ions passingthrough one square centimeter of the wafer surface and is measured in units ofions/cm2 The total implantation dose required in the SIMOX process is usually

>1018cm−2 Under normal room-temperature conditions upper layer of silicon crystalmight change to an unwanted amorphous stage during the implantation of the oxygen

21

ions To avoid this effect, the silicon substrate is retained at a temperature of

approximately 600oC 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 To

achieve the low electrical resistance requirement, boron (p-type dopant) and arsenic

(n-type dopant) would typically be implanted to a dose of less than 1016 cm−2, that

the maximum amount is less than ones in the SIMOX process

The energy used to implant oxygen ions into crystalline silicon is up to 200 keV The

depth of the SiO2 and consequently the thickness of the silicon upper layer depends on

that energy Figure 1.3.1 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 with all implanted species, at low doses (<1016 cm−2), the oxygen

concentration can be illustrated by a shape according, but not identical, to that of a

Gaussian function (Figure 1.3.1a) 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 1.3.1b) 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 of >1018cm−2, the silicon wafer is annealed at a

temperature of roughly 13000C 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 1.3.1c)

Fig 1.3.1 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 1300 o C for several hours

The implant energy determines the depth and thickness of the buried SiO2 layer.For instance, a 200keV energy would create the buried SiO2 thickness to a valuearound 0.5µm with a crystalline silicon over layer of 0.3µm To make the scopes ofthis structure more appropriate for the manufacture of wider cross-sectionwaveguides, epitaxial growth technique is used to increase the thickness of siliconlayer 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 intophysical contact and this phenomenon managed to form the BESOI process Theassembly of BESOI has three phases presented schematically in Figure 1.3.2: (a)oxidation of the two wafers to be bonded; (b) formation of the chemical bond; (c)thinning (etching) of one of the wafers

The details of the bonding chemistry will not be discussed in this dissertation Inbrief, the wafers are taken into physical contact at room temperature, at which thestarting bond is created The bond strength is enhanced to the level of bulk materialvia subsequent thermal influencing to temperatures as high as 1100oC

Wafer thinning can be achieved via a number of two common methods The mostpopular one is chemical mechanical polishing (CMP) technique, which is usedwidely in making wafer planar in microelectronics The wafer surface must beweakened and then detached during a single processing step in the CMP method Ingeneral, the silicon surface, which needs to be polished, is handled with a rotatingpad, and at the same time contacted with a chemically reactive slurry containing anabrasive component such as alumina and glycerin weaken The process eradicatesthe majority of one of the bonded wafers, hence a wafer silicon upper layer on aburied SiO2 layer left, sustained by a silicon substrate

Fig 1.3.2 The bond and etch-back process to form BESOI: (a)

oxidation; (b) bonding; and (c) thinning

An improvement in SOI thickness homogeneousness, which consequence is reducingsilicon upper layer thickness, can be achieved by the use of another technique in thethinning process reducing or even removing the need of CMP [62] Before bonding

23