Integrated Silicon Electro- Optical Modulators for Data ......Integrated Silicon Electro-Optical...

Integrated Silicon Electro-

Optical Modulators for

Data/Telecom Applications

Von der Fakultät für Elektrotechnik und Informationstechnik der Rheinisch-Westfälischen Technischen Hochschule

Aachen zur Erlangung des akademischen Grades eines Doktors

der Ingenieurwissenschaften genehmigte Dissertation

vorgelegt von

Saeed Sharif Azadeh

aus Tehran, Iran

Berichter: Prof. Dr. Jeremy Witzens

Dr. Laurent Vivien

Tag der mündlichen Prüfung: 04.09.2019

Diese Dissertation ist auf den Internetseiten der Universitätsbibliothek online verfügbar

I

Summary

Ongoing growth of cloud computing and streaming is creating significant challenges

for interconnect systems in data centers and high performance computing systems

mainly in terms of data-rate, power consumption, size and cost. Maturing silicon pho-

tonics (SiP) technology allowing mass production of integrated photonic devices at a

competitive cost due to the utilization of existing CMOS infrastructure, and enabling

high integration of optical devices such as modulators at the wafer scale is expected

to be particularly competitive to service an emerging need for extended reach high-

speed data center interconnects. Tremendous efforts have been made in the past dec-

ade to maximize the speed and reduce the power consumption of SiP modulators. In

this thesis, we are going to address some of the challenges of SiP modulators: Full

suppression of crosstalk and bandwidth improvement in travelling wave modulators,

as well as reduction of fabrication sensitivity of silicon ring resonator modulators. We

also introduce lumped element meandered modulators with improved power consump-

tion while maintaining high optical bandwidth. Furthermore, a novel vertical phase

shifter structure based on epitaxially grown silicon layer stack is introduced, designed,

fabricated and characterized. The proposed vertical phase shifter exhibits one of the

highest reported modulation efficiencies among silicon depletion based modulators.

Finally, we explore alternative modulation mechanisms which can be realized in SOI

platform by integration of novel material. In particular, we investigate the electro-optic

(Pockels) effect in nitride cladded strained silicon Mach-Zehnder interferometers,

Franz-Keldysh effect in germanium tin grown on germanium virtual substrate for mid-

infrared applications, as well as Moss-Burstein effect in graphene-silicon slot wave-

guide absorption modulators.

II

Zusammenfassung

Die zunehmende Nutzung von Cloud Computing und Streaming stellt

Verbindungssysteme in Rechenzentren und Hochleistungsrechnersystemen vor

erhebliche Herausforderungen, vor allem in Bezug auf Datenraten, Stromverbrauch,

Größe und Preis. Die Silizium-Photonik (SiP) -Technologie, die durch die Nutzung der

vorhandenen CMOS-Infrastruktur, die Massenproduktion integrierter photonischer

Bauelemente zu wettbewerbsfähigen Kosten ermöglicht, und hohe Integration

optischer Bauelemente wie Modulatoren im Wafer-Maßstab ermöglicht, dürfte

besonders wettbewerbsfähig darin sein den wachsenden Bedarf an

Hochgeschwindigkeitsverbindungen mit erweiterter Reichweite für Rechenzentren zu

decken. In den letzten zehn Jahren wurden enorme Anstrengungen unternommen, die

Geschwindigkeit zu maximieren und den Stromverbrauch von SiP-Modulatoren zu

senken. In dieser Arbeit werden die folgenden der Herausforderungen von SiP-

Modulatoren behandelt: Die vollständige Unterdrückung des Übersprechens und die

Bandbreitenverbesserung in Wanderwellenmodulatoren, sowie die Verringerung der

Fertigungsempfindlichkeit von Siliziumringresonatormodulatoren. Mäanderförmige

Modulatoren mit konzentrierten Elementen und verbessertem Stromverbrauch bei

gleichzeitig hoher optischer Bandbreite werden vorgestellt und eine neuartige vertikale

Phasenschieberstruktur basierend auf einem epitaktisch gewachsenen

Siliziumschichtstapel eingeführt, entworfen, hergestellt und charakterisiert. Der

vorgeschlagene vertikale Phasenschieber weist einen der höchsten berichteten

Modulationswirkungsgrade unter den Modulatoren auf der Basis von

Siliziumverarmung auf. Schließlich untersuchen wir alternative

Modulationsmechanismen, die in der SOI-Plattform durch Integration von neuartigen

Materialien realisiert werden können. Insbesondere untersuchen wir den

elektrooptischen (Pockels) Effekt in Nitrid-beschichteten, gestreckten Silizium-Mach-

Zehnder-Interferometern, den Franz-Keldysh-Effekt in Germanium-Zinn, das auf

einem virtuellen Germaniumsubstrat für Anwendungen im mittleren Infrarotbereich

gewachsen wurde, sowie den Moss-Burstein-Effekt in Graphen-Silizium-

Schlitzwellenleiter-Absorptionsmodulatoren.

III

Acknowledgment

First and foremost, I would like to express my sincere gratitude for my Doktorvater Prof.

Dr. Jeremy Witzens, who believed and invested in me from the start, for directing the

thesis with his immense help and his continuous support, encouragement and guid-

ance. He did not only help me become a better researcher, but taught me how to be a

better person. He will always be my role model. With a deep sense of gratefulness, I

wish to thank Dr. Florian Merget who helped me in every step of the way, from design,

to fabrication and characterization. I could never figure out how he always had a well-

thought answer to all my questions throughout these years.

I would like to express my deepest appreciation to all the members of IPH, present and

past, who are and will always be my second family. Working alongside these lovely

friends was truly an amazing experience, and made my PhD years the most joyful

period of my life. Special thanks goes to Doro Pawelzick and Anne Schröder, who are

the backbone of our institute, for their continuous support during these years. I would

like to deeply thank Haijo Ehlen for his influential technical support. Although only my

name is written on this thesis, each IPH member had a direct or indirect contribution in

this work. In particular, I am thankful to Manuel Ackerman, Juliana Müller, and Jovana

Nojic also for proofreading the manuscript of the thesis. I am grateful to Dr. Alvaro

Moscoso especially for his immense help in the RF design. I would like to extend my

gratitude to Dr. Jens Richter, Prateek Pahalwan, and Ines Kluge with whom I shared

the joy and pain of fabrication. It is important to mention that part of the present work

is done by brilliant former Master students at IPH: Juliana, Jovana, and Roger Ponce

whom I am honored to have been given the chance to work with. I am immeasurably

happy that they are now my best friends, even though I overloaded them with tasks

and encouraged them to work harder than PhD students! I wish them the best in the

rest of their academic and personal life.

Many of the measurements performed in this work are made possible by the setup

developed at IPH by Bin Shen whom I sincerely appreciate. Throughout the PhD years,

I was also fortunate to have shared the same office with two of my best friends Alireza

Mashayekh and Andrea Zazzi, which made working at IPH even more pleasant.

The fabrication process was made possible by kind support of the members of IHT

group. In particular, I would like to thank Prof. Dr. Joachim Knoch, Noel Wilk, Dr. Stefan

SchoIz and Ms. Birgit Hadam. I am also grateful to Dr. Dan Buca and Dr. Nils von der

Driesch from PGI 9 at Jülich Research Center. I really enjoyed their collaboration.

IV

This thesis is dedicated to my lovely family, Dr. Noushin Tarkian, Dr. Mohammad Reza

Sharif Azadeh, Dr. Shadi Sharif Azadeh and Dr. Yousef Maknoon, to whom belongs

all the time I spent writing it. Their unconditional love and support made this journey

possible, and they continue to inspire me every day. No matter how far we are, you

are and will always be close to me in my heart.

Saeed Sharif Azadeh,

Aachen, 15.06.2019

V

Contents

1 Introduction ................................................................................................. 1

2 Segmented Electrode Travelling Wave Mach-Zehnder Modulators ....... 5

2.1 Introduction ................................................................................................... 6

2.2 Design of Travelling Wave Mach-Zehnder Modulators ................................. 8

2.2.1 Phase shifter design ......................................................................... 8

2.2.2 Device performance simulation ...................................................... 12

2.2.3 Signal driving scheme .................................................................... 16

2.2.4 Transmission Line design .............................................................. 18

2.2.5 Segmented electrode transmission line ......................................... 21

2.3 Experimental Results .................................................................................. 22

2.3.1 Low junction capacitance MZI modulators ..................................... 22

2.3.2 High junction capacitance MZI modulators .................................... 27

2.4 Conclusion .................................................................................................. 28

3 Rectilinear and Resonance based Lumped Element Modulators......... 30

3.1 Introduction ................................................................................................. 31

3.2 Performance Metrics of Lumped Element Modulators ................................ 32

3.2.1 Bandwidth limitations in LE Modulators .......................................... 32

3.2.2 Power consumption in LE modulators ............................................ 34

3.3 Lumped Element Meandered Modulators ................................................... 36

3.3.1 Concept and Design ....................................................................... 36

3.3.2 Experimental results and discussion .............................................. 39

3.4 Ring Resonator Modulators ......................................................................... 42

3.4.1 RRM Design: Static and dynamic models ...................................... 44

3.4.2 Sensitivity reduction to fabrication inaccuracies ............................. 50

3.4.3 Design of Optical Add-Drop Multiplexer (OADM) ........................... 52

3.4.4 Experimental results ....................................................................... 54

3.5 Conclusion .................................................................................................. 57

4 High Efficiency SiP Modulators with Vertical Phase-Shifters ............... 59

4.1 Introduction ................................................................................................. 60

4.2 Phase Shifter Concept ................................................................................ 61

4.3 Phase Shifter Design and Proposed Fabrication Process ........................... 64

4.3.1 Ion implanted epitaxially overgrown phase shifter .......................... 64

4.3.2 In-situ doped phase shifter ............................................................. 70

4.4 Modulators based on Vertical Phase Shifter ............................................... 71

4.4.1 Ion implanted epitaxially grown phase shifter ................................. 71

4.4.2 In-situ doped phase shifter ............................................................. 73

4.5 Fabrication .................................................................................................. 75

4.6 Experimental Results .................................................................................. 84

4.7 Conclusion .................................................................................................. 86

VI

5 Hybrid Silicon Modulators ....................................................................... 87

5.1 Introduction ................................................................................................. 88

5.2 Measuring Pockels Effect in Strained Silicon MZIs ..................................... 89

5.3 Germanium Tin Absorption/Phase Modulator ............................................. 94

5.3.1 Introduction .................................................................................... 94

5.3.2 Modeling FKE and PDE and parameter space............................... 95

5.3.3 Phase shifter design and proposed fabrication process ................. 98

5.3.4 Expected performance of GeSn absorption/phase modulators .... 100

5.4 Graphene Silicon Slot-Waveguide Absorption Modulator.......................... 102

5.4.1 Introduction and state-of-the-art ................................................... 102

5.4.2 Device configuration and modeling of MBE ................................. 103

5.4.3 Expected performance of absorption modulator........................... 104

6 Conclusions and Prospects .................................................................. 107

References .................................................................................................... 111

Appendix: List of Publications .................................................................... 123

VII

Formula Symbols and Abbreviations

𝐶𝑙 F/m Linear capacitance

ℎ𝑠 m Slab height

𝐸𝐹 e.V Fermi level

𝑅𝑙 Ω.m Linear resistance

𝑛𝑒𝑓𝑓 Effective refractive index

𝑛𝑔 Group index

𝛼𝑅𝐹 1/m Attenuation constant of RF mode

CMOS Complementary metal oxide semiconductor

DE Deep etched

DOE Design of experiment

E/O Electro-optical

ECV Electrochemical capacitance voltage

EDFA erbium doped fiber amplifier

ER dB Extinction Ratio

F Finesse

FDTD Finite difference time domain

FE Full etched

FEM Finite element model

FKE Franz-Keldysh effect

FOM Figure of merit

FSR m Free spectral range

GC Grating coupler

HFCV high frequency capacitance voltage

HJC High junction capacitance

LE Lumped element

LJC Low junction capacitance

MBE Moss-Burstein effect

MMI Multi-mode interferometer

MPW Multi-project wafer

MZM Mach-Zehnder modulators

VIII

OADM Optical add-drop multiplexer

OMA dB Optical modulation efficiency

PDE Plasma dispersion effect

PDK Process design kit

PIC Photonics integrated circuit

PRBS Pseudo-random bit sequence

RBS Rutherford backscattering spectrometry

RF Radio frequency

RRM Ring resonator modulators

RTA Rapid thermal annealing

SC Standard cleaning

SE Shallow etched

SiP Silicon photonics

SOI Silicon on insulator

TDR Time domain reflectometry

TW Travelling wave

VNA Vector network analyzer

VS Virtual substrate

WDM Wavelength division multiplexing

𝑡 Transmission (in a directional coupler)

𝛼 1/m Attenuation constant of optical mode

𝛽 1/m Wavenumber

휀 F/m Absolute permittivity

𝜅 Coupling coefficient

𝜇 H/m Permeability

1

1 Introduction

2 1. Introduction

It is projected [1] that until the year 2022, the global internet traffic will triple, reaching

350 Exabytes per month, with online video streaming, cloud computing/sharing, and

smart vehicles playing a significant role. In order to address this ever increasing de-

mand, faster and cheaper data transmission systems are required, and the standards

should be constantly upgraded; as in 2019, the standard transceivers in data centers

are moving from the state-of-the-art 100G towards 400G systems. Since the electrical

signal attenuation over distance grows with the speed, in such high data rates, con-

verting the data from electrical to optical domain becomes a necessity even for mid-

range/short distances. It has been shown [2] that in practice, for data rate distance

products above 1000 Gbps∙m, e.g. transmission of 100 Gbps over 10 meter distance,

utilizing optical links has become the method of choice. One key component of the

optical links is the electro-optical modulator, i.e. devices which convert the electrical

signal into optical, and as such, faster, cheaper and less power consumption modula-

tors are constantly required.

In principle, the integration of electro-optic devices with small footprint on a chip, e.g.

photonic integrated circuits (PICs), can allow for more scalable and low power con-

suming devices. Traditionally, unlike in electrical ICs where silicon has been the

dominant material, the most commonly utilized material platforms for PICs have been

direct bandgap semiconductors such as indium phosphide (InP) as well as gallium ar-

senide (GaAs), which allow for realization of efficient on-chip light sources. In the past

decade however, silicon photonics (SiP) has emerged as a promising platform to real-

ize both passive [3, 4] and active [5, 6] optical devices on Silicon on Insulator (SOI)

wafers.

What gives SiP an upper hand –despite the known limitations of silicon as a photonic

material– is its compatibility with complementary metal oxide semiconductor (CMOS)

technology which provides a low cost platform, especially when it comes to mass pro-

duction [7]. This also allows for co-integration of passive and active photonic devices,

as well as co-integration of photonics with electronics in a single chip. Several key

building blocks of the optical link such as photodetectors are already mature in SiP

technology. Although silicon is transparent over the entire telecommunication wave-

length range and thus can offer relatively low loss on-chip interconnect, efficient high-

speed photodetectors are realized in combination with germanium [8, 9]. Moreover, in

comparison with the aforementioned photonic technologies, the high refractive index

contrast between silicon (as waveguide core) and silicon dioxide (as cladding) results

in a high confinement of the light inside a small (~400 nm wide) waveguide. This high

confinement allows very small bending radii (several micrometer) and hence extremely

dense integration of the optical devices. In particular, for electro-optic modulators high

confinement is beneficial due to higher overlap between the guided mode and the al-

terated refractive index region. Since the implementation of the first gigahertz

bandwidth [10] silicon modulator in 2005, enormous effort has been made in order to

improve the power consumption, reduce the optical losses and increase modulation

speed of the devices [11, 12]. In fact, the main motivation behind commercial utilization

1. Introduction 3

of SiP has been to address the demand of interconnects for data centers. For this

purpose, fast, low loss and low power modulation is a necessity.

One of the main challenges to realize an efficient and low loss modulation in silicon is

the lack of electro-optic effect due to its centrosymmetricity. To date, the majority of

successful SiP modulators harness plasma dispersion effect as their modulation mech-

anism [11]: The alteration of the refractive index of the material, by injection/depletion

of the carriers. Carrier injection via an external current source results in a high modu-

lation depth, due to the large amount of carriers being displaced with respect to the

applied signal. This can be simply realized in silicon platform by forming a pn-junction

in forward bias. However, the speed of injection based modulators is limited to around

1 GHz due to the slow recombination time of the carriers. Thus, depletion based mod-

ulators are favorable in terms of modulation speed as well as power consumption per

bit. The latter is due to the fact that forward bias modulators are usually used together

with power hungry pre-emphasis/equalizer systems to achieve high data-rates [13, 14].

In contrast, depletion based modulators are normally a reversely biased pn-junction,

with very small current. The power consumption (in its simplest form, for a short linear

modulator) boils down to charge and discharge of the depletion junction capacitance.

As a drawback, since the amount of displaced carriers is limited, the efficiency (phase

shift for a given voltage) of depletion based modulators is limited. In this thesis, we are

going to address some of the important challenges facing different types of silicon

modulators. First, in order to reduce the required drive voltage of SiP modulators, trav-

elling wave (TW) Mach-Zehnder modulators (MZM) with long linear phase shifters are

utilized. The modulation mechanism of these devices is based on the plasma disper-

sion effect (PDE). We address the main challenges of improving the modulation speed

of TW modulators, that is, to reduce radio frequency (RF) losses along the transmis-

sion line, and also the RF crosstalk between the MZM arms, while keeping phase

matching and impedance matching conditions. We introduce novel methods to fully

suppress RF crosstalk without increase the device footprint, and also to reduce the RF

losses and thus increasing the modulation bandwidth without perturbing the device

characteristic impedance. We then experimentally demonstrate the performance im-

provements of SiP TW modulators using the proposed structural modifications.

Subsequently, in order to reduce the power consumption of the modulators, we use

compact devices in lumped element (LE) configuration. We first quantitatively show

how LE configuration can improve the power consumption and the device bandwidth.

Then we demonstrate two types of devices in lumped element configuration: 1) Mean-

dered modulators which allow for long phase shifters inside a LE device and are

optically wideband, and 2) Ring resonator modulators (RRMs) which are widely used

in wavelength division multiplexed (WDM) systems. For the latter, we introduce meth-

ods to reduce their sensitivity to fabrication inaccuracies, and finally experimentally

validate the designs. In the second half of this thesis, we introduce a new type of phase

shifters which is based on epitaxially grown vertical junctions, with the benefit of in-

creasing the modulation efficiency, allowing for realization of short devices with low

4 1. Introduction

drive voltage. These devices are a deviation from standard SiP processes, and are

thus fabricated at IPH. We explain the design steps, fabrication process, measurement

results, and the prospect of using this phase shifter in different modulation schemes.

All the aforementioned demonstrated devices harness PDE as the modulation mech-

anism. In the final chapter we explore other candidate modulation mechanisms in

modulators realized in hybrid SiP platforms: We investigated exploitation of the

Pockels effect in strained silicon modulators, and experimentally address its chal-

lenges. Then we utilize the Franz-Keldysh effect to design relatively compact

absorption and phase modulators based on germanium tin (GeSn), a material which

has emerged as a group IV compound with a direct and tunable bandgap and has

shown a high potential to implement IRB lasers [15] as well as photodetectors [16], for

mid-infrared applications. Finally, we propose compact slot-waveguide graphene-sili-

con modulators which utilize Moss-Burstein effect as the modulation mechanism.

5

2 Segmented Electrode Travelling Wave Mach-

Zehnder Modulators

6 2. Segmented Electrode Travelling Wave Mach-Zehnder Modulators

In the absence of Pockels effect in center-symmetric crystalline silicon, the majority of

the modulators realized in the silicon platform rely on the plasma dispersion effect

(PDE), that is, the alteration of the complex refractive index of material, by modification

of the carrier density. The low efficiency of PDE in depletion based silicon modulators

can be compensated by increasing the modulator length, which in turn necessitates

the deployment of travelling wave (TW) transmission lines along the device. The high-

speed performance of such modulators can be penalized by both crosstalk between

the signals propagating along different arms of the device, and also the radio frequency

(RF) loss along the transmission line. In this chapter we introduce two main methods

to mitigate crosstalk and RF loss of silicon TW modulators by modifying the driving

scheme, and introducing segmented transmission line, respectively. We present the

design and experimental demonstration of segmented TW modulators based on PDE,

fabricated on silicon on insulator (SOI) wafers using the standard CMOS-compatible

process provided by multi-project wafer (MPW) runs.

2.1 Introduction

Following the first demonstration of electro-optical modulation with near 1 GHz band-

width in silicon [10], tremendous efforts have been made by several groups around the

world to provide high speed and low drive voltage silicon photonics (SiP) modulators

on SOI platform. In the following years, variety of mechanisms in SiP modulators, in-

cluding PDE modulation in both injection [17, 18] and depletion mode [19, 20, 21],

silicon organic hybrid polymer modulation [22, 23] and strained silicon modulators

based on the Pockels effect [24, 25], have been explored. We discuss the challenges

of the strained silicon modulators in chapter 5 of this thesis. For PDE modulation, as

mentioned earlier in chapter 1, driving the modulators in forward bias results in exces-

sive bandwidth limitations bellow 1 GHz due to the slow recombination lifetime of the

carriers. Therefore, all the PDE modulators presented in this thesis are depletion based

modulators, which are widely used both for commercial and research goals [11, 12],

and have so far proven to be the most reliable and manufacturable approach for high-

speed operation.

Among depletion based SiP modulators, the lumped element modulators (as will be

discussed in the chapter 3) including resonance based devices [26] and Mach-Zehnder

Modulators (MZMs) with distributed drivers [27] each allow for reduction of the RF

power consumption. However, they also impose their own set of constrains: Reso-

nance-based devices, especially in silicon with a high thermo-optical coefficient, are

temperature sensitive and require power hungry active control systems; MZMs with

distributed drivers require a dense interconnection network between the electronics

and the electro-optical modulator. Thus, travelling wave electro-optical modulators -

while not offering the lowest power consumption or drive voltage - remain the easiest

to deploy [28]: They are much less temperature sensitive than ring resonator modula-

tors and require only a single RF port. The fabrication of travelling wave MZMs is also

relatively straightforward since they can be implemented using a single metal intercon-

nect, as we will show later in this chapter.

2. Segmented Electrode Travelling Wave Mach-Zehnder Modulators 7

The focus of this chapter is on TW carrier depletion MZI modulators. Due to the short

carrier transit time in the reverse biased pin junctions that constitute this type of mod-

ulators high data rates are attainable [29]. However, difficulties in achieving high

bandwidth operation arise from RF losses of the loaded transmission line [29, 30], and

phase mismatch between the light and the travelling RF wave [28]. Moreover, the im-

pedance mismatch between the 50 Ω driver and the modulator should be minimized in

order to avoid RF power back reflections and the resulting reduction of modulation

efficiency [31].

In this chapter, we are going to present the implementation process – from design and

layout to characterization – of two different travelling wave Mach-Zehnder modulators,

developed at IPH:

1. Low junction capacitance (LJC) MZM [28]: This device is fabricated via the shut-

tle service OpSIS at Singapore’s Institute of Microelectronics (IME). Low doping

levels (~3e17 cm-3) resulting in low capacitance in the pn-junction, are suited for

lengthy (>3 mm) travelling wave modulators. We have opted the length of 4 mm

for this device. This modulator is designed in a way to be fully compatible with

the standard fabrication process made available by MPW runs at IME. Through-

out this chapter, we will refer to this device as “Low junction capacitance MZM”,

or LJC.

2. High junction capacitance (HJC) MZMs [31]: These devices are fabricated in

the IMEC process line, with higher doping levels (~1e18 cm-3) which allow for

realization of shorter MZM devices. The “high junction capacitance modulators”

are fabricated in two versions, with 2.5 mm long and 1.2 mm long phase shifters.

Throughout this chapter, we will refer to these devices as “high junction capac-

itance” modulators, or HJC.

For both types of devices, two approaches are used in order to improve the high-speed

performance: 1) introducing metal extensions in each segment of the transmission line,

which (as we will show) results in a reduction in RF loss along the transmission line,

and thus increases the E/O bandwidth; 2) modification of the driving scheme to fully

suppress the crosstalk between the arms, which allows for more compact integration

of travelling wave MZIs with less interconnect metal layers. First, the design steps of

such devices are explained, which include the design of the phase shifter for the de-

sired specifications, and the design of the transmission line. Then, the approaches we

employed to improve the high-speed performance are presented. Next, the experi-

mental results and their analysis are presented, as well as a discussion about the

possible applications of the proposed modulator structure.

Device MZM

length

Doping levels (cm-3) St. Fabrication

process n p

LJC 4.0 mm 4e17 1.5e17 IME

Short HJC 2.5 mm 1e18 1e18 IMEC

Long HJC 1.2 mm 1e18 1e18 IMEC

Table 2.1 The three devices presented in this chapter


2.2 Design of Travelling Wave Mach-Zehnder Modulators

In this section we describe the design rationales and characteristics of two travelling

wave MZMs respectively optimized for two different technology platforms. The process

begins with cross section design of a pn-junction based on the calculated doping pro-

file. Then we proceed with the calculation of the DC characteristics of the device and

the optimization of the device length, based on the transmission line design. Lastly, the

implementation of a segmented transmission line and significance of crosstalk sup-

pression are discussed.

2.2.1 Phase shifter design

We begin the device design with the calculation of the doping profile inside the wave-

guide. For this purpose, we use Sentaurus process in Synopsys TCAD software. Given

that the energy and the dosage in the ion implantation process both for p-doping (bo-

ron) and n-doping (phosphorus) is set by the fabrication process, we can calculate the

doping distribution inside the waveguide. In the fabrication process prior to the ion im-

plantation, a 10 nm thick silicon dioxide is deposited on top of silicon acting as a

protective layer to minimize the damage to the crystalline structures of silicon, and also

to prevent tunneling of the ions. A rapid thermal annealing (RTA) step (at 1030 degrees

for 5 s) is performed both to activate the ions as well as anneal the crystalline structure

of silicon. Figure 2.1 shows the doping distribution inside silicon for LJC modulator

calculated by Sentaurus process TCAD in a 400 nm wide waveguide with 90 nm thick

slabs. It should be mentioned that the average doping levels for p-doping and n-doping

are around 4e17 cm-3 and 1.5e17 cm-3 respectively. If the energy and dosage of the ion

implantation process is not known, as is the case for HJC, for the next simulation steps,

we use the nominal doping (e.g. 1e18 cm-3 for HJC) as sharp rectangles.

Figure 2.1 (a) Calculated doping profile inside a 400 nm wide waveguide for LJC waveguide with etch

depth of detch=130 nm. (b) Red curve: n-doping (phosphorous) concentration on the left cutline, blue

curve: p-doping (boron) concentration on the right cutline.

The calculated doping profile in TCAD is then exported to COMSOL Multiphysics soft-

ware which allows for solving coupled systems of partial differential equations (PDEs)

based on finite element analysis. In COMSOL, we calculate the voltage across the


junction as well as the carrier distributions inside the waveguide under different volt-

ages applied at the contacts by iteratively solving drift-diffusion equations and Poisson

equation. Figure 2.2 (a) shows the illustration of the carriers inside the pn-junction in a

2D cross section of the waveguide under different applied voltages in reverse bias. As

shown in Figure 2.2 (b) which represents the carrier concentration on a horizontal cut-

line inside the waveguide, the depletion width of the junction is modified in response

to the applied voltage.

Figure 2.2 Calculated carrier distributions (p-doping: left, n-doping: right) overlaid with the TE0 mode

profile for different applied bias voltages, in (a) 2D cross section of the waveguide (b) a horizontal cutline

inside the waveguide. The color coding in (a) shows the log10 of the carrier concentration in 1/cm-3.

It should be mentioned that the finite element model (FEM) is not the most efficient

numerical method to iteratively solve Poisson/drift-diffusion equations in pn-junctions.

It is excessively sensitive to the initial values, meaning that in case the final solution is

far from the initial conditions (initial voltage across the junction, and also the initial car-

rier distribution) the iterative solution might not converge, or its convergence could be

very time consuming. To mitigate this problem, we apply small perturbations (e.g. small

voltage changes in each simulation step) to the previous solution (which is used as the

initial condition of the next step) and use extremely fine meshing (<2 nm). Regardless,

we opted for COMSOL due to its capability of coupling different physics (in form of

PDEs) into the same solver, which allows for calculation of the important device char-

acteristics such as junction capacitance and series resistance, as well as the guided

TE0 mode profile and in turn calculation of optical loss and refractive index change

based on the carrier distribution.

Optical loss and refractive index change

The electric field of the guided mode propagating in z-direction inside the waveguide

can be expressed as

z

zi eeyxEzyxE 2),(),,(

(2.1)

where 𝛼 is the attenuation constant, 𝐸(𝑥, 𝑦) corresponds to the mode field profile at the

cross section of the waveguide, and 𝛽 is the wavenumber. The first exponential term

refers to the periodic phase variation of the mode along the waveguide, while the sec-

ond term accounts for the exponential decay of the field in a lossy waveguide. The

accumulated phase of the E-field can be expressed as


LnLnL effeff

22. (2.2)

where 𝜆 is the light wavelength (1550 nm in our case), and 𝑛𝑒𝑓𝑓 refers to the effective

index of the mode. Based on equation (2.2), modifying the refractive index of the wave-

guide results in a change in the complex effective index of the mode (Δ𝑛𝑒𝑓𝑓) which is

translated into phase shift. In the depletion based modulators, the refractive index of

the waveguide is perturbed by modifying the depletion width. For calculation of the

carrier induced change in refractive index of silicon at 1550 nm, we use the empirical

study by Soref and Benett [32]:

))(108.8108.8( 8.01822

he NNn (2.3)

he NN 1818 106105.8 (2.4)

Here, 𝛥𝑛 and 𝛥𝛼 are changes in silicon refractive index and absorption, with 𝛥𝑁𝑒 and

𝛥𝑁ℎ as free-electron and free-hole carrier concentrations respectively, in 1/cm.

The amount of variation in the effective refractive index of the optical mode with respect

to the applied voltage is dependent on its overlap with those regions that are depleted

from carriers and experience the modification in the material refractive index. It can be

expressed in terms of the overlap integral as

*

2

0

0

Re HE

Ennneff

(2.5)

which is an indicative of how much the optical mode will “see” the material refractive

index change, given that 𝐸 and 𝐻 are the mode electrical and magnetic fields, and 휀0

and 𝜇0 are the vacuum permittivity and permeability. The integral in the numerator is

calculated on the perturbed surface, and the denominator is a normalization factor,

representing the total power of the mode. We will discuss the overlap integral maximi-

zation with the goal of increasing the modulation efficiency in chapter 5. Here, we

calculate the new 𝑛𝑒𝑓𝑓 (after perturbation) based on ab initio solution of the wave equa-

tion inside the perturbed waveguide, which is a more exact approach than calculating

the overlap integral, provided that the error margin is low. Figure 2.3 (a) shows the

calculated effective index change for both HJC and LJC phase shifter.

Figure 2.3 (a) Effective refractive index change, and (b) carrier-induced optical loss of the phase shifter

for different applied voltages in reverse bias.


Based on Kramers-Kronig relations, a change in the real part of the complex refractive

index induces a change in the imaginary part of the refractive index, which determines

the optical loss. In particular, additional carriers inside the waveguide which are re-

sponsible for modification of the refractive index can also absorb the light and hence

induce losses, which is numerically determined using equation (2.4). Figure 2.4 (b)

shows the carrier induced loss of the optical mode inside the phase shifter.

It is noteworthy that based on the calculated 𝛥𝑛𝑒𝑓𝑓 and the optical loss, one might

assume that higher doping levels are inferior, while the HJC phase shifter (red curve)

offers only twice the modulation efficiency (𝛥𝑛𝑒𝑓𝑓) ) of the LJC (blue curve), but induces

around 4 times more optical loss. The reason is that the carriers are present in the

whole waveguide and will fully interact with the mode, and thus almost linearly (equa-

tion (2.4)) increase the absorption, while 𝛥𝑛𝑒𝑓𝑓 results only from the variation of the

depletion width which has square root dependency on the doping level. However, this

interpretation is incomplete, since higher doping levels allow for achieving the required

phase shift in shorter devices and thus (as we will see in the next section) a higher

electro-optical bandwidth can be achieved.

Series resistance and voltage dependent capacitance

To calculate the device performance characteristics, e.g. the electro-optical bandwidth,

it is necessary to calculate the junction capacitance and its series resistance accu-

rately. Once the voltage and the electric field inside and outside (in the vicinity of the

waveguide) are calculated, we can determine the junction capacitance using the

Gauss’s flux theorem, expressed by the following integral:

app

linesolid

xOxapp

linedashed

xSiJ VdlEVdlEC 00

(2.6)

on a line crossing the depleted zone of the junction (both solid line and dashed line in

Figure 2.4 (a)), where 𝑉app is the applied voltage in reverse bias, 𝐸𝑥 is the x-component

of the E-field and 휀0, 휀Si, and 휀Ox are respectively the values of the permittivity of air,

silicon and oxide. The second term takes the fringing capacitance into account, which

is of importance in further calculation of the electro optical bandwidth [33].

Figure 2.4 (a) The calculated electric field in the pn-junction with fringing E-field out of waveguide (on

solid line), corresponding with eq. 2.6, (b) calculated voltage dependent junction capacitance of LJC and

HJC phase shifters.


As shown in Figure 2.4 (b), just like the 𝛥𝑛eff, the capacitance per unit length (further

on referred to as linear capacitance 𝐶𝑙) of the HJC is around a factor 2 higher than of

the LJC (at 2 V bias) phase shifter. The calculated series resistance (𝑅𝑙) for the HJC

and LJC, assuming the highly doped region to be 800 nm far from the waveguide edge,

and the metal to be 10 µm away from the waveguide, are 17 mΩ.m and 8 mΩ.m,

respectively.

2.2.2 Device performance simulation

In the previous section we calculated the optical loss (dB/cm), the effective index

change Δneff of the mode, the junction capacitance (F/m), and series resistance (Ω.m)

for the 2D cross section of the HJC and LJC phase shifters. Here, based on these

values, we can simulate the static performance of the modulator, and find the suitable

device length to reach the desired device metrics. To convert the change in refractive

index into intensity modulation, we use a Mach-Zehnder Interferometer (MZI) in push-

pull configuration. As schematically shown in Figure 2.5 (a) the MZI consists of two

arms each comprising a phase shifter. The input light splits equally via a Y-junction (or

similarly a one by two multi-mode interferometer as used for HJC MZMs) into the arms

and accumulates a certain phase shift (see equation (2.2)) based on the applied volt-

age (Vapp) along the phase shifter. We use the MZI in push-pull configuration, meaning

that the electrical signal applied to two phase shifters have opposite sign, resulting in

the opposite sign of the accumulated phase shifts, and thus doubling the modulation

efficiency compared to the single ended configuration. This configuration has also the

benefit of avoiding additional chirp (changing frequency throughout pulse), since the

output of an MZI (with lossless phase shifters) can be written as [11]

,2cos1 21 inOut PP (2.7)

2

21212cos

i

inOut eEE (2.8)

where 𝜑1 and 𝜑2 refer to the applied phase shifts in each arm. In the case when they

have opposite signs and equal amplitude, the exponential term, and thereby the chirp,

is suppressed. We will discuss the chirp arising from voltage dependent loss in chap-

ter 4. The output power of an MZI vs. applied voltage is shown in Figure 2.5 (b).

Figure 2.5 (a) schematic of an MZM in push-pull configuration (b) output optical power of the MZM vs.

the applied voltage. The black circle indicates the bias point and the performance metrics, i.e. extinction

ratio (ER), modulation penalty (MP) and insertion loss are indicated. P1, P0 and Pin are the power levels

of output optical “1”, output optical “0”, and the input optical signal, respectively.


The biasing point of the MZMs (the black circle in Figure 2.5 (b)) is set to be at the -

3dB point in order to maximize the phase shift with respect to 𝑉app, and also linearizing

the voltage dependence of the phase shift for small signals. The voltage swing around

the bias point results in a change in the output power of the MZM. Extinction ratio (ER)

in dB can be defined as:

0

110log10

P

PER (2.9)

Even at full extinction (applying 𝑉π/2 to each arm), 𝑃1 would be smaller than 𝑃in due to

the optical loss of the phase shifters. This ratio is defined as insertion loss (IL) and is

expressed in dB in Figure 2.6. The blue curves in this figure show the IL for both HJC

and LJC MZMs which linearly increase with the device length. It should be mentioned

that in addition to carrier induced loss (shown in Figure 2.3 (b)), the intrinsic loss of a

the silicon waveguide (4 dB/cm for 400 nm waveguide) due to scattering and sidewall

roughness, as well as the absorption of the highly doped regions (700 nm and 800 nm

distance from the waveguide edge for HJC and LJC, respectively) are taken into ac-

count.

Figure 2.6 Insertion Loss (IL) and Vπ for both LJC (solid lines) and HJC (dashed line) phase shifters

versus the modulator length. The values for IL are shown at bias voltage of 1V.

The voltage required to be applied to a single arm of the modulator in order to achieve

a full extinction (𝑉𝜋) based on equation (2.2) is shown in Figure 2.6 (red curves) for

HJC and LJC phase shifters. For a 5mm long LJC phase shifter, 8 V are required to

be applied to one arm, in order to achieve full extinction, which yields a 𝑉𝜋 ∙ 𝐿 product

of 4 V∙cm for this type of phase shifter, while the same length of a HJC phase shifter

has 𝑉𝜋 of 3.6 V, leading to a 𝑉𝜋 ∙ 𝐿 of HJC phase shifter of 1.8 V∙cm.

Figure 2.6 shows the obvious tradeoff between the efficiency or ER, and the modulator

IL in this type of modulators, regarding the optimum choice for the device length. A

useful modulator metric, the optical modulation efficiency (OMA) is thus defined to take

both metrics into account and can be expressed as

)(log10 0110

inP

PPOMA

(2.10)

For MZMs in push-pull configuration, the OMA can be written [11] in form of


LOMA dB sinlog10 10 (2.11)

where ∆𝜑 is the phase shift swing reached in each arm, and 𝛼𝑑𝐵 is the attenuation

constant expressed in dB/m and 𝐿 is the device length. Figure 2.7 (a) shows the OMA

versus the length of the LJC and HJC modulators when 2 Vpp is applied to each arm

of the MZM. In order to keep the diode of the phase shifter in reverse bias, a DC voltage

of -1 V is added to the 2 Vpp. Unlike the ER or IL which monotonously increase or

decrease with respect to the device length, the OMA of HJC modulator reaches its

peak at around 2 mm length and gets smaller for longer devices. The reason is that

according to equation 2.11, too short modulators suffer from insufficient phase shift

(and thus small OMA), but also excessively long modulators are penalized by high

absorption loss. The same process happens also for LJC MZMs. However, the OMA

reaches its peak at longer than 5 mm long device, and is not shown in the plot. The

green dots mark the points that are picked for the final devices, that is, 4 mm long MZM

with LJC phase shifter and 2 versions of 2.5 and 1.2 mm long MZMs for HJC structure.

The green points are chosen close to the peak of HJC (yellow curve), while for LJC the

optimal point was chosen based on the bandwidth requirements, not on the maximum

value of the OMA.

Figure 2.7 (a) The optical modulation amplitude (OMA) of LJC and HJC vs the MZI length, when a drive

voltage of 2 Vpp is applied to the arms, at 1 V reverse bias (b) analytically calculated electro-optical

bandwidth of MZI modulators (eq. 2.15), when the phase shifters are biased at 1 V. (c) OMA vs the

bandwidth of MZI modulator at Vpp = 2 V and Vbias = 1 V. The green dots indicate the final devices

The bandwidth of the TW modulators is mainly limited by the RF loss along the trans-

mission line. At low modulation frequencies, the RF loss is negligible, and thus the

whole length of the MZM effectively takes part in the modulation. At high-speeds, due

to the RF loss the effective length (𝐿𝑒𝑓𝑓) of the modulator reduces depending on the

frequency. This reduction of the effective length of the modulator causes the roll off in

the electro-optical response of the MZMs. Here, we use a simplified analytical model

to estimate the bandwidth of TW MZMs, solely based on RF loss in TL, in order to

choose the desired device length; a thorough analysis of the transmission using nu-

merical simulations is presented in the next section. The excess frequency dependent

RF losses below the intrinsic cutoff frequency of the diode can be written as

2

10 fff (2.12)

where 𝛼0 is the scaling factor for the baseline losses of the transmission line and 𝛼1 is

the scaling factor for the Ohmic losses inside silicon. At high frequencies, the second

term becomes dominant, and the RF losses can be written as


22

1 )2( lTLl CfZRff (2.13)

with 𝑍𝑇𝐿 being the characteristic impedance of the loaded transmission line, and 𝑅𝑙

and 𝐶𝑙 being the linear resistance and capacitance of the waveguide, respectively.

Though 𝐶𝑙 varies in response to the actual modulation peak to peak voltage, we can

assume it to be constant in small signal regime. The effective modulation length can

be defined as

L

x

eff dxeL RF

0

2/ (2.14)

where 𝐿 is the actual device length, and 𝛼𝑅𝐹 is the RF power attenuation constant.

Assuming a linear phase shift versus the applied voltage (again valid for small signal

regime), this corresponds to an ideal modulator with frequency dependent length. Pro-

vided that the RF loss is the main source of electro-optical bandwidth limitation, in order

to calculate the device E/O bandwidth 𝑓−3𝑑𝐵,𝑜𝑝𝑡 (the frequency at which E/O S21

reaches the -3dB point), we can set 𝐿𝑒𝑓𝑓 = 0.707𝐿 in the equation (2.14). In this way

the RF constant is calculated to be 𝛼𝑅𝐹 = 1.48/𝐿. It corresponds to the point where the

electrical S21 reaches -6.4dB attenuation, since 20𝑙𝑜𝑔10(exp (𝐿 ∗ 0.74/𝐿)) = 6.4 𝑑𝐵.

Therefore, the electro-optical bandwidth of the modulator can be calculated as [11]

))2/((174.0 22

,3 DevlTLloptdB LRZCf (2.15)

Based on this equation, the electro-optical bandwidths of the devices are calculated

and plotted in Figure 2.7 (b), assuming the characteristic impedance of the transmis-

sion line 𝑍𝑇𝐿 to be 50 Ω. In the next section we explain how we implement the 50 Ω

matching condition. Apart from the impedance matching, to calculate these bandwidth

values, the phase mismatch between the RF signal and the optical mode is neglected,

which results in an overestimation of the bandwidth. On the other hand, we have also

ignored the screening of the capacitance, and the implementation of the segmented

structures (discussed in section 2.2.5) which leads to an underestimation of the band-

width. Nevertheless, equation 2.15 yields a useful analytical tool to compare different

possible devices and to choose the one with the best relative performance.

Provided that the RF loss is the main source of electro-optical bandwidth limitation, the

point where the electrical S21 reaches -6.4dB point, the E/O S21 reaches -3dB

(at 𝑓−3𝑑𝐵,𝑜𝑝𝑡).

It is noticeable that the calculated bandwidths of HJC and LJC MZMs (shown in Fig-

ure 2.7 (b)) are not significantly different for a distinct device length. The reason is, that

by increasing the doping level, the linear resistance 𝑅𝑙 decreases almost linearly. At

the same time, the linear capacitance 𝐶𝑙 has a square root dependency on the doping

level. However, based on equation 2.15, the E/O bandwidth has square root depend-

ency on 𝑅𝑙 and linear dependency on 𝐶𝑙. In fact, the minor difference between the two

curves, arises merely from a constant series resistance of the highly doped regions.

Overall, however, the phase shifters with higher doping levels are more suitable for


high speed performance, since they provide a higher phase shift per length, thus al-

lowing for realization of shorter devices and with higher E/O bandwidths.

Figure 2.7 (c) encapsulates the analysis required for opting for the right device length

depending on the required bandwidth, where the OMA, at 2 Vpp is plotted versus the

E/O bandwidth at 1 V reverse bias voltage. For each given bandwidth, an HJC and an

LJC MZM with different OMAs are available. Given 2 Vpp signal at 1 V reverse bias

voltage, for devices with E/O bandwidth above 18 GHz the HJC MZMs are superior,

since they offer a higher OMA. If a higher efficiency for a smaller data-rate is required,

then MZMs based on LJC phase shifters are preferable. The green circles mark the

final designs of the MZMs. This might raise the question about the advantage of the

2.5 mm HJC device to the LJC MZM. What is hidden in the Figure 2.7 (c), is the layout

size of the MZMs. Indeed, the selected LJC modulator is longer than both HJC MZMs

combined. Small footprint is advantageous especially in SiP since it allows for compact

integration of the devices on the same chip. Another advantage of the 2.5 mm HJC

device over the LJC device is that its short length eases the realization of a sufficient

phase matching. As mentioned, in the calculation of these bandwidth values, we have

assumed a perfect phase matching between the optical mode and the RF signal. As

will be discussed in section 2.2.4, providing the phase matching condition becomes

more challenging for longer devices.

2.2.3 Signal driving scheme

Before engaging into the details of the transmission line design, we need to briefly

explain the rationale behind our chosen driving scheme and the phase shifter connec-

tivity. Any signal driving scheme, in order to drive a depletion based MZMs in push-pull

configuration, should fulfill two conditions:

1) The pn-junctions in each arm of the MZM require a DC bias voltage in order to

be kept in reverse working region. (As in the previous section, throughout this

chapter we always assume 𝑉𝑏 = −𝑉𝑝𝑝/2 to maximize the modulation efficiency)

2) The RF signal should be applied to each arm of the MZM in a way to provide an

opposite phase shift in each arm of the MZM, i.e. 𝜑1 = −𝜑2 as discussed fol-

lowing the equation 2.8.

A simple solution that satisfies both conditions is shown in Figure 2.8 (a). In this con-

figuration, both arms are biased with a positive DC voltage to maintain reverse bias

operation. In order to implement the push-pull condition 𝜑1 = −𝜑2, one of the arms is

connected to the Ground (G) and Signal (S) line, while the other arm is connected to

the inverted RF signal (S) line. The applied voltage 𝑉𝑏 + 𝑉𝑅𝐹 is shown in Figure 2.8 (b).


Figure 2.8 (a) Schematic illustration of GSSG driving scheme and diode connectivity. Green arrows

indicate the electrical field. (b) Signals for a GSSG driving scheme for each signal line.

The drawback of implementing the GSSG configuration is that since S and S are dif-

ferent RF signals and indeed exactly the opposite of each other, the crosstalk between

the signal lines can become an issue. Since crosstalk is frequency dependent (sub-

stantially increases at higher frequencies) it can directly affect the E/O bandwidth of

the modulator. This impact, which is more significant for long MZMs, can be modeled

as the two arms of the MZM behave as an RF directional coupler, with 𝐿𝜋 of

fnncL asymRFsymRF )(2 ,,0 (2.16)

with 𝑛𝑅𝐹,𝑠𝑦𝑚 and 𝑛𝑅𝐹,𝑎𝑠𝑦𝑚 being symmetric and asymmetric mode indices, respectively,

and 𝐿𝜋 the required length for an RF signal on one arm to be fully coupled to the other

arm. The details of the calculation of RF indices are explained in the next section.

Figure 2.9 (a) shows the calculated crosstalk between the two signal lines for a 4mm

long MZM with LJC phase shifters, in an ideal case of a lossless transmission line.

Similar to any directional coupler, the value of crosstalk depends on both the device

length, as well as the distance between the two arms.

Figure 2.9 (a) Crosstalk between the MZM arms for different signal to signal line gaps (SSgap). (b) The

crosstalk-induced RF penalty for an ideal transmission line. Both (a) and (b) are calculated for a 4mm

long LJC MZM.

One method to mitigate the crosstalk between the signal lines is to increase the dis-

tance between the MZM arms. It can be directly observed from Figure 2.9 (b), that

given a 150 µm clearance between signal lines, the crosstalk penalty falls below 1dB

over a wide frequency range up to 36GHz. In this way, the beating between the two

super-modes is suppressed. This solution comes with the obvious drawback of a big-

ger layout size. Another method for crosstalk suppression would be to isolate the MZM

arms using an additional ground metal layer fully surrounding each of the arms. How-

ever, this method requires additional metal layers.


Our chosen method to fully suppress the crosstalk talk between the arms is to use the

GSSG driving scheme as is schematically shown in Figure 2.10 (a). In this configura-

tion, from the RF point of view, the exact same signal is applied to each arm of the MZI

and therefore the crosstalk penalty is suppressed. In this case, in order to keep each

pn-junction in reverse bias, a different DC voltage needs to be applied to each arm, as

shown in Figure 2.10 (b).

Figure 2.10 (a) Schematic illustration of GSSG driving scheme and diode connectivity. (b) Signals for a

GSSG driving scheme for each signal line.

2.2.4 Transmission Line design

In order to design and simulate the performance of complex travelling wave structures,

we perform full electromagnetic simulations. In the first step, we make the geometry

including the metal, oxide and silicon layers, according to the Process Design Kit (PDK)

provided by the fabrication facility, which is shown in Figure 2.11 (a). The waveguide

capacitance (plotted in Figure 2.4 (b)) at the bias voltage, is incorporated into the model

in the middle of signal and ground lines (the inset of Figure 2.11 (b)) using the calcu-

lated linear capacitance of the junction, and the series resistance of the diode is taken

into account by the doped silicon region connecting the metal lines to the waveguide.

Figure 2.11 (a) Out of plane component of the current density 𝑱𝒁 in GSSG configuration for HJC MZM

at 16 GHz. (b) Calculated x component of RF electric field (𝑬𝒙) in the same transmission line. Inset


shows 𝑬𝒙 inside the reverse biased pn-junction. Line Graphs: Calculated frequency dependent (c) char-

acteristic impedances, (d) effective indices, and (e) RF Losses per unit length, in the loaded transmission

lines of the symmetric super-modes for HJC (red) and LJC (blue) MZMs.

Using the FEM in COMSOL Multiphysics software, we then solve the Maxwell’s equa-

tions for the frequency range of interest (from 1 GHz to 36 GHz) in order to find the

electromagnetic modes. As discussed in the previous section, the symmetric super-

mode is of interest. The calculated z-component (propagation direction) of the current

density (𝐽𝑍) in the GSSG configuration for driving HJC phase shifters at 16 GHz is

shown in Figure 2.11 (a). In these simulations, for HJC transmission line we have opted

for the signal to signal line gap (SSGap) to be 5 µm, and the signal to ground distance

SGGap to be 30 µm, while the widths of the signal line (wS) and ground line (wG) are 10

and 50 µm, respectively. For MZMs with LJC phase shifter, we opted for SSGap of 20

µm, SGGap of 50 µm, wS and wG of 30 and 100 µm, respectively.

The rationale behind choosing these parameters for the transmission line, is to provide

50 Ω impedance matching between the driver and the device, thus avoiding the RF

back reflection which lowers the OMA; and also to avoid back reflections at the end of

the MZM, since the RF signal is terminated using a standard 50 Ω load at the end of

the transmission line. Thus, we try to provide 50 Ω condition by adjusting the distance

between the signal and ground lines. We will discuss the limitations of the method,

using a simplified analytical model in Section 2.2.5. The calculated characteristic im-

pedance of the transmission lines is plotted in Figure 2.11 (c). It should be noted that

the characteristic impedance is slightly frequency dependent, and thus the perfect im-

pedance matching condition can only be satisfied for a specific frequency, meaning

that the 𝑍𝑇𝐿 of the device will be slightly higher, or lower than the targeted 50 Ω for the

rest of frequency range.

In addition to the impedance matching, in the design of a transmission line suitable for

travelling wave modulators, phase matching condition should also be taken into ac-

count to ensure that group velocity (𝑉g) of the optical mode matches the phase velocity

of the RF signal. The group index (𝑛g) of the optical mode is defined as

0

0

d

dnnn

eff

effg (2.17)

where 𝜆0 is the wavelength in vacuum (1.55 µm). We calculate the optical group indices

using Photon Design FIMMWAVE software, for 400 nm wide waveguide, to be 𝑛g =3.82

and 𝑛g=4.3 for partially etched (120 nm etch depth), and fully etch waveguides, respec-

tively. Compared with RF indices plotted in Figure 2.11 (d), it can be seen that the RF

signal is slower than the optical mode since 𝑛RF>𝑛g. In order to compensate for this

velocity mismatch, we increase the waveguide length by implementing regularly placed

optical delay lines [27, 28] in discrete sections of the phase shifter, as is schematically

shown in Figure 2.12 (a). In SOI waveguides, due to the high index contrast between

the core and the cladding, small bends with low bending losses can be implemented

and thus the design of phase recovery loops is straightforward. We included such re-

covery loops, increasing the optical path and equalizing the group delay of the optical

path to the phase delay of the transmission line. In order to determine the required


length of the recovery loops (𝐿𝑟𝑒𝑐), we should first calculate the additional penalty aris-

ing from the phase mismatch. For a straight MZM with length L, the ratio of the phase

shift at DC ∆𝜑(0), and the phase shift at RF ∆𝜑(𝜔𝑅𝐹) is given by [11]

L

zznnc

iRF dzee

L

RFRFg

RF

0

2)(

01

)0(

)(

(2.18)

if z is the coordinate along the length of the waveguide. Thus the bandwidth of a phase

mismatch limited modulator (the effect of 𝛼𝑅𝐹 is already taken into account) is given by

gRFf 44.0 (2.19)

where 𝜏𝑔 and 𝜏𝑅𝐹 are respectively the transit time of the photons and the transit time of

the RF signal, and can be simply calculated as

,0cLn optgg 0cLnRFRF (2.20)

In this case the length of the optical path is 𝐿𝑜𝑝𝑡 = 𝐿 + 𝐿𝑟𝑒𝑐. This ratio is shown in Fig-

ure 2.12 (b) in dB scale for LJC modulators and in Fig 2.12 (c) for HJC, for three

different lengths of the recovery loops. Due to fabrication tolerances, 𝑛𝑔 and 𝑛𝑅𝐹 can

in practice be different from the simulated values. Hence, we decided to implement

three different variations of MZMs for LJC modulators with different recovery loop

length, i.e. 𝐿𝑟𝑒𝑐 = 0, 0.3𝐿, and 0.6𝐿 per loop, with 1 mm spacing (total of three). For HJC

modulators, the 𝑛𝑅𝐹/𝑛𝑔 ratio at 16 GHz is around 1.75, and thus we opted to

choose 𝐿𝑟𝑒𝑐 = 0.75𝐿. We implemented four 300 µm long recovery loops in each section

of the MZM (400 µm) as shown in Figure 2.12 (a).

Figure 2.12 (a) layout of the recovery loop for HJC with Lrec=0.75L (b) OMA reduction for 4mm long LJC

modulator at 16GHz, depending on the nRF (c) OMA reduction of a 2.5 mm HJC modulator at 16GHz for

Lrec=0.75L.

By comparing Figure 2.12 (b) and (c), it is evident that the device length is the dominant

parameter to determine the effect of phase mismatch, meaning that the bandwidth of

the shorter devices is less penalized by a wrong choice of the recovery length. As

shown by the results reported in section 2.3, the LJC modulator (though 3 different

recovery loops were implemented) still suffers bandwidth limitation due to the phase

mismatch, but the bandwidth of short HJC modulators is not limited by phase mis-

match.


2.2.5 Segmented electrode transmission line

In the previous section we designed the transmission line using advanced simulation

tools in a way to satisfy the 50 Ω impedance matching condition. Providing 50 Ω con-

dition can only be achieved when the linear junction capacitance (𝐶𝑙) does not exceed

a certain level. We could also provide quasi-phase matching by implementing the re-

covery loops, owning to the fact that the RF signal was slower than the optical mode.

Here, we look at the phase matching and impedance matching in a more general case,

using a simplified analytical model, and we can show how metal extensions can be

helpful to achieve these requirements. Generally, since the waveguide adds a capaci-

tive load to the transmission line, the characteristic impedance of the device can be

described as

UlUTL CCLZ (2.21)

where 𝐿𝑈 and 𝐶𝑈 are given by the metal electrode layout and correspond to the linear

inductance and capacitance of the unloaded transmission line, respectively. For higher

doping levels where linear capacitance is higher, the signal-ground gap should be in-

creased in order to maintain impedance matching condition. Increasing the gap

between the signal and ground lines, reduces the capacitance and increases the in-

ductance and thus makes the 50 Ω matching achievable. As a drawback the high-

speed performance of the device is compromised, since the additional gap causes an

increase in the series resistance of the junction, and according to equation 2.15 re-

duces the device bandwidth. Our method to mitigate this problem is to introduce metal

extensions in the transmission line as is schematically shown in Figure 2.13 (a). These

finger structures reduce the series resistance of the waveguide, without increasing the

capacitance of the transmission line. The distance between each two finger structures

on the same line is 10 µm, which according to the 3D RF simulations does not signifi-

cantly increase the capacitance of the line. As shown in Figure 2.13 (b), to avoid

additional capacitance, and also reduce the longitudinal current, the finger structures

are 5 µm offset on the other signal line.

The RF index (𝑛𝑈) of the unloaded transmission line (in the absence of the junction

capacitance) can be written as

UUU CLcn 0 (2.22)

Changing the spacing between the ground and signal lines does not significantly affect

the overall phase velocity of the RF signal (when 𝐶𝑈 is increased, 𝐿𝑈 is decreased and

vice-versa). In the loaded transmission line, the RF index is increased due to additional

capacitive load. As mentioned, for a slow RF signal, introducing the recovery loops can

provide the phase matching condition. However, in the case of 𝑛𝑅𝐹<𝑛𝑔, in order to

maintain the phase matching, the capacitive load of the transmission line needs to be

increased to reduce the phase velocity of RF signal.

The T-shaped structures shown in Figure 2.13 (c) further slow down the RF wave by

adding extra capacitive loading to the transmission line. This technique has been ex-

tensively applied to GaAs modulators [34, 35] and more recently to SiP modulators


[36, 37]. Typically, segmented TL electrodes as shown in Figure 2.13 (b) are useful for

highly doped, high-capacitance phase shifters for which the phase velocity of the trans-

mission line is low and impedance matching to high impedances is difficult, while slow

wave transmission line as shown in Figure 2.13 (c) are useful for lower doping levels,

for which impedance matching to 50 Ω is not problematic, but achieving phase match-

ing might require slowing down the RF mode.

Figure 2.13 The 3D view (a) and top view (b) of the interdigitated transmission line, (c) top view of the

slow transmission line.

We have used the segmented electrode transmission line for both LJC and HJC mod-

ulators. As is confirmed by the experimental results presented in the next section, for

LJC phase shifters the measured RF index at 1 V bias is smaller than the group index

of the optical mode. Thus, the use of the T-shaped extensions to slow down the RF

wave would have been the right choice. For HJC however, the measurements show a

very good agreement with the simulated group and RF indices, and thus using the

segmented transmission line for HJC was the right choice. To summarize, introducing

the extensions to the segments of transmission line provides an additional degree of

freedom to either reduce the phase velocity of the RF wave, or to increase the device

bandwidth without perturbing the characteristic impedance or introducing additive ca-

pacitance.

2.3 Experimental Results

In this section we report on the measurement results of the LJC (4 mm long) and HJC

(1.25 mm, and 2.5 mm) segmented electrode electro-optical modulators, and compare

the outcome with the results predicted by the simulations.

2.3.1 Low junction capacitance MZI modulators

A microscope image of the device is shown in Figure 2.14 (a) which consists of four

phase shifter sections each 1 mm long. In between the sections, recovery loops are

placed as explained in section 2.2.4, which introduce a gap of 90 µm between each

two phase shifter sections. On each arm, a low speed phase tuner based on forward

bias pin-junction is implemented, in order to enable tuning of the MZI to the quadrature

point. However, the low speed tuners are not used in the following measurements;

instead we used a tunable laser for this purpose. In total, 5 MZI modulators were taped

out on the same chip with the same length. The redundancy is mainly due to variation


of the recovery loop lengths; additionally, one MZM was designed without the metal

extensions for benchmarking, and is referred to as the baseline modulator.

Figure 2.14 (a) Microscope image of the LJC MZI modulator (b),(c) Wavelength shift of the normalized

optical transmission for different DC voltages applied to one arm of the MZI. The two vertical dashed

lines in (c) correspond to π and π/2 phase shift.

The arms of the MZI are deliberately imbalanced by about 100 µm, which results in a

free spectral range (FSR) of around 5.6 nm in the output of the MZM. Generally, bal-

anced MZI modulators are optically wideband. Here, the imbalance is just introduced

in order to ease the measurement process, since in an imbalanced MZI, the phase

shift in each arm can be easily observed in terms of a wavelength shift, as can be seen

in Figure 2.14 (b) where the output power spectrum of the MZM is plotted for different

voltages. The black curve shows the output in the absence of an applied voltage. It

can be seen that by applying 10 V to one of the arms (green curve) full extinction is

achieved (at a wavelength which initially features the maximum transmission). The

phase shift for any given voltage is then calculated as

FSR

2 (2.23)

and is plotted in Figure 2.14 (c), where the vertical dashed lines mark the 𝜋 and 𝜋/2

phase shift of each arm. The results show the efficiency of the modulator expressed in

terms of 𝑉𝜋 ∙ 𝐿 is 4 V∙cm. It should be noted that in many papers, the 𝑉𝜋 ∙ 𝐿 is not re-

ported at 𝑉𝜋 (which is at 10 V in our case), but instead is calculated based on a linear

extrapolation of the phase shift at lower voltages, which always results in a lower value

for 𝑉𝜋 ∙ 𝐿 and overstates the phase shifter efficiency. For instance, in our case 𝑉𝜋 ∙ 𝐿 is

3.2 and 2.4 V∙cm and at 4 V and 1 V, respectively. The discrepancy comes from the

fact that the voltage dependence of the phase shift (Figure 2.14 (c)) is not linear, but

can be fitted well with square root fit approximation, as is expected from the depletion

width voltage dependency.

Based on the equation (2.2), the measured phase shift corresponds to ∆𝑛𝑒𝑓𝑓 of 9e-5

at 4 V, which is in close agreement with the simulated results, as shown in Figure 2.3

(a). Indeed, the measured value of ∆𝑛𝑒𝑓𝑓 was slightly higher, and the difference could

arise from slightly higher doping level than anticipated. This was also confirmed by


measuring the capacitance of the waveguide. In fact, using small signal (0.1 V) high

frequency capacitance voltage (HFCV) measurements at frequency of 1 MHz, we ex-

tracted the junction capacitance 𝐶𝑙 of the waveguide to be 360 pF/m and 250 pF/m at

0 and 2 V respectively; while simulated capacitance predicted 310 pF/m and 230 pF/m

at 0 and 2 V (shown in Figure 2.4 (b)). From RF measurements we derive an 𝑅𝑙 of 13.9

mΩ•m, as opposed to 17 mΩ•m simulated value, further confirming slightly higher dop-

ing levels. After de-embedding the optical loss of the grating couplers, we measured

the insertion loss of MZIs to be 8.8 dB, by far exceeding the simulated loss. This can

partially be attributed to a higher doping level. However, the excess loss is mainly due

to the on-chip interconnects: In the input of the MZIs, we have used two back to back

Y-junctions, which results in an additional 3 dB optical loss. This design allowed as to

apply the laser power, both from a grating coupler, and an edge coupler. In fact, it is

fairer to de-embed this additional loss since only 5.8 dB of the light is lost on the phase

shifter itself. This additional loss could have been avoided if we had used a directional

coupler, instead of back-to-back connected Y-junctions.

In the next step, we characterize the high-speed performance of the device. The meas-

urement setup used for S21 measurement of the devices is shown if Figure 2.15 (a).

The output of the tunable laser is amplified to 10 dBm to compensate for the grating

coupler and interconnect losses, using an erbium doped fiber amplifier (EDFA) and is

then connected to a fiber array and coupled into the chip using grating couplers. The

RF signal is generated by a 50G vector network analyzer (VNA) which sweeps the

output frequency between 100MHz and 30GHz to measure the S21 and enables direct

bandwidth measurement. In order to keep the diodes in reverse bias, a 1 V bias voltage

is added to the RF signal using a bias-T. At the end of the transmission line, the RF

signal is terminated using a standard 50 Ω resistor to avoid back reflections. To sup-

press DC power consumption, the 50 Ω termination is isolated from the device using a

DC block. The output of the MZM is connected to a commercial 40G photo receiver

and is converted back to an electrical signal.

Figure 2.15 (a) Measurement setup of the bandwidth measurement of the MZI modulators. (b) Normal-

ized electro-optical S21 of the baseline and segmented electrode modulators measured at 1 V bias.


The normalized electro-optical S21 measurements of the devices with medium long

recovery loop at DC voltage bias of 1V for baseline modulator (blue curve) and seg-

mented modulator (green curve) are shown in Figure 2.15 (b). The losses arising from

the electrical cables and DC probes are de-embedded using a standard calibration

process. It shows a -3dB bandwidth of 16.2 GHz and 14.5 GHz for the segmented

electrode modulators and the baseline modulator, respectively. It should be mentioned

that the device without a recovery loop had a slightly higher bandwidth, but in order to

be able to benchmark against the baseline modulator, which is only taped out with

medium size recovery loops, we just report the bandwidth of this device. Another con-

vention to express the modulator bandwidth is where the S21 reaches -6dB point, since

the photo receiver converts the input optical power into current, and then the VNA

calculates the output power of the photo receiver. Therefore, at a point where the OMA

of the MZM halves, the S21 becomes 4 times smaller. However, since the conventional

(electrical) definition of the bandwidth refers to the -3dB point of the measured S21,

we stick to the electrical definition and only report the conventional electrical band-

width. The high-speed performance of the device is still suffering from the phase

mismatch. In fact, by fitting the RF loss and removing the effect of phase mismatch,

we can see that the bandwidth of the devices could increase to 18 GHz and 23 GHz

for baseline and segmented modulators respectively. This effect is also seen in S21

plots, as at very high frequencies (𝑓>𝑓-3dB) the green and blue curve merge. This is

simply due to the fact that when the effect of phase mismatch becomes increasingly

substantial at high frequencies, the modulator with lower RF losses suffers more, since

it has a longer effective length (as discussed in chapter 2.2.2).

As explained in chapter 2.2.5, in the segmented electrode modulators, ideally the im-

plementation of the metal extensions does not increase the capacitance of the line,

and solely reduces the series resistance. In this case, the characteristic impedance of

the segmented electrode modulator and baseline modulators should be identical.

Thus, in order to experimentally confirm that introducing the metal extensions does not

(or minimally does) perturb the characteristic impedance and/or RF phase velocity, we

performed time domain reflectometry (TDR) as shown in Figure 2.16.

Figure 2.16 TDR measurement of S11 for baseline (blue curve) and segmented electrode (green curve)

MZI modulators


To perform a TDR measurement, we measure the RF back reflection (S11) in the time

domain, as a response of an impulse signal emulated by the VNA. In fact the VNA

emulates the time domain S11 using the reverse Fourier transformation.

Discontinuities in the impedance of a transmission line cause a measurable increase

in the reflection coefficient. The magnitude of the reflection coefficient is thus a meas-

ure of the impedance mismatch that causes the reflection. The temporal distance

between two reflections can be translated into a signal velocity or an effective dielectric

constant when correlated with a spatial distance. To identify the beginning of the trans-

mission line, we measured the reflection coefficient with the probe tips lifted up from

the chip to get a strong reflection from the open end of the probe tip. Next, we landed

the probe tip on the input pads of the modulator transmission line leaving the output

pads unterminated. This reduces the reflection from the input of the transmission line

due to the better impedance match while at the same time also gives a second strong

reflection from the unterminated output pads. Thus, the phase velocity of the RF signal

can be directly measured according to the time delay between the two peaks. By this

method we have measured an RF index of 4.125 for both devices with and without

electrode extensions. This indicates that the introduction of the electrode extensions

does not add an additional phase mismatch between the RF-driving signal and the

optical wave. In addition, the reflections from the input of the transmission lines have

the same magnitude in both cases. This shows that both transmission lines have al-

most identical impedances. Therefore, we can conclude that the introduction of the

segmented electrode extensions did not have a substantial impact on the impedance

matching and phase matching of the modulator.

In order to further experimentally validate the high frequency performance of the de-

vice, we used the measurement setup shown in Figure 2.17 (a) to measure the eye

diagram. Here, we used a 32Gbps bit error rate tester (BERT) in order to generate

pseudo-random bit sequence (PRBS) at high speed, and the output is connected to a

20GHz real time oscilloscope. The drive voltage applied to the modulator was 2Vpp,

with an added offset of 1V to keep pn-junctions in reverse bias.

Figure 2.17 (a) Measurement setup used to measure the eye diagram of the MZI modulators. (b) 32

Gbit/s eye diagram of the modulator (2 Vpp dual drive) measured with a 40 GHz receiver from U2T

visualized with a 20 GHz real time oscilloscope.

The recorded eye diagram at 32 Gb/s is shown in Figure 2.17 (b) which was the max-

imum achievable speed of our measurement setup. As in the previous measurements,


the optical power in the input of the MZM was set to 10 dBm to compensate for the

coupling and interconnect losses.

2.3.2 High junction capacitance MZI modulators

The HJC modulators which were fabricated in two versions, with a 2.5 mm long and a

1.25 mm long phase shifter, are shown in Figure 2.18 (a). Since we have extensively

explained the effect of segmentation of the transmission line of the MZMs in the previ-

ous chapter, here we only report the performance of the segmented modulators.

Figure 2.18 (a) Microscope image of the long (2.5mm) and short (1.25mm) HJC MZI modulators (b) and

(c) wavelength shift versus applied voltage to one of the arms. The dashed vertical lines correspond to

π and π/2 phase shift.

Figure 2.18 (b) shows the wavelength shift for different applied voltages for a 2.5 mm

long modulator. In this graph, the optical loss of the grating couplers (9 dB per pair) is

de-embedded, which shows a 6.5 dB insertion loss of the device. As the results of an

imbalance in the length of the MZI arms, an FSR of 6 nm is visible at the output of the

MZM.

A 𝜋 phase shift is achieved in single arm configuration when 8 volts (0V to -8V) are

applied to a single arm, which corresponds to a 𝑉𝜋 ∙ 𝐿 of 2 V∙cm, twice the 𝑉𝜋 ∙ 𝐿 of the

LJC phase shifters due to the higher doping levels. The insertion loss of the short de-

vice is measured to be 4.5 dB. The phase shift versus the applied voltage for this

modulator is shown in Figure 2.18 (c), where green and red dashed lines show π and

π/2 phase shifts. Since in a push-pull configuration each arm is required be driven with

𝑉𝜋/2, required dual-drive drive voltages for full extinction are respectively 3.2V and 7V.

The measured values are in very good agreement with simulated results explained in

chapter 2.2.2, e.g. the efficiency was simulated to be 1.8 V∙cm and optical loss to be

around 6 dB for the 2.5mm long device (see Figure 2.6).


Figure 2.19 Calibrated electro-optical S21 of the (a) 2.5mm long and (b) 1.25mm long HJC MZI

modulators. (c) Recorded eye diagrams at 10, 20 and 32 Gb/s for the 2.5mm modulator measured at

1V DC bias visualized by a 20GHz real time oscilloscope.

The electro-optical S21 measurement results for long and short devices are shown in

Figure 2.19 (a) and (b), respectively. The setup used for these measurements is similar

to the one shown in Figure 2.15 (a). The -3 dB electro-optical cut-off frequency of the

modulator (f-3dB) at 1 V bias is 17 GHz for the long modulator and 23 GHz for the shorter

modulator (3 dB cut-off in the electrical convention). The high-speed measurement

results are in close agreement with the simulated electro-optical S21 of the devices,

which is a clear indication that phase matching was not a limiting factor in the HJC

modulator (since in the simulations, we had assumed a perfect phase matching). Also,

the measured electrical S21 shows that the electro-optical cutoff frequency is very

close to the same frequency where the RF signal reaches 6.4 dB attenuation, which is

a further confirmation that the E/O bandwidth was only limited by the RF loss. Fig-

ure 2.19 (c) shows the measured eye diagrams for the 2.5 mm long MZI modulator

with a drive voltage of 2 Vpp, a bias voltage of 1 V and a laser output power of 10 mW

at 1541 nm at speeds up to 32 Gbps, limited by the measurement setup.

2.4 Conclusion

Simultaneously increasing the bandwidth and the modulation efficiency of Silicon Pho-

tonics electro-optical modulators is a challenge that also constitutes the focus of the

work presented in this chapter. The travelling wave Mach-Zehnder modulators, as one

of the most commonly used types of silicon modulators require impedance and phase

matching, and a low RF loss for high speed applications. First, we explained the design

steps of the phase shifters, as well as the transmission line in this type of modulators.

We then introduced segmented electrodes which allow for circumventing some of the

limitations of coplanar transmission line designs for linear travelling wave Silicon Pho-

tonic modulators in simple single layer or double layer interconnect back-end

processes. In particular, they facilitate impedance matching in modulators with highly

doped phase tuners as well as phase matching in modulators with lower doped phase


tuners. Subsequently, we demonstrated a low junction capacitance travelling wave

modulator, and showed how by modifying the driving scheme we could fully suppress

the cross talk between the MZI arms. We also demonstrated that introducing the metal

extensions could increase the device electro-optical bandwidth by 17% without affect-

ing the impedance or phase matching. Then the high junction capacitance travelling

wave modulators with a dual drive 50 Ω matched input were demonstrated with full

extinction at 3.2 V signal level, 6.5 dB on-chip insertion losses and a 17 GHz electro-

optic bandwidth for 2.5 mm long device, and 4.5 dB insertion loss and a 23 GHz band-

width for the shorter device. Open 32 Gb/s eye diagrams were demonstrated with 2 V

signal levels and 10 dBm laser power. All the presented devices in this chapter are

implemented in a standard fabrication process.

31

3 Rectilinear and Resonance based Lumped

Element Modulators

3. Rectilinear & Resonance based Lumped Element Modulator 31

Driving electro-optical modulators in lumped element (LE) configuration is attractive

since it allows for small footprint, low power consumption, and potentially improved

high speed performance. In this chapter, we first try to quantify the general power con-

sumption improvements as well as the bandwidth enhancement in LE modulators

compared to the travelling wave modulators. Then we explain the design, implemen-

tation and experimental results of two different types of LE modulators we developed

at IPH: 1) Meandered Mach-Zehnder modulators, which jointly provide low drive volt-

age by means of a long phase shifter, and smaller power consumption due to compact

RF length and thus satisfying LE condition, and 2) highly doped ring resonator modu-

lators (RRM) which enhance the modulation efficiency for a limited optical wavelength

range.

3.1 Introduction

As opposed to travelling wave devices, lumped element configuration refers to a device

which is sufficiently smaller than the RF wavelength in the device (𝜆𝑅𝐹 = 𝜆0/𝑛𝑅𝐹), so

that it can be considered a point load from an RF point of view. As a rule of thumb, it

is often asserted that when a device is shorter than a tenth of the RF wavelength, it

can be regarded as a lumped element. However, the transition from this LE condition

is not abrupt, and surpassing this length gradually penalizes the bandwidth.

Although the travelling wave modulators (as explained in chapter 2) provide a low drive

voltage due to their long phase shifters, and are generally optically wideband, they

suffer from high power consumptions, as the RF signal is terminated at the end of the

transmission line. Moreover, the main limiting factor of the bandwidth in the travelling

wave modulators is the RF loss along the transmission line. In a lumped element mod-

ulator, both (the termination of the RF signal, and the RF attenuation along the device)

are absent, and thus the LE modulators potentially allow for power efficient fast mod-

ulation. However, the naturally short phase shifter length of LE modulators (a tenth

of 𝜆𝑅𝐹) penalizes the phase shift (see equation (2.2)) and necessitates high drive volt-

ages. This can counteractively suppress the power consumption improvement, since

the required energy per bit in a LE modulator, which can be expressed as [38]

2

4

1Dbit CVE (3.1)

quadratically increases with the drive voltage 𝑉𝐷. Note that in this equation, C refers to

the total capacitance (𝐶𝑙 ∙ 𝑙) of the device. Thus, one might suggest that by increasing

the device length, power consumption can be reduced, since, e.g. doubling the length

(𝑙), results in two times higher C, but also reduces the required voltage VD to half, and

thus the Ebit is reduced by a factor 2. This idea is sound but not applicable, since the

LE condition severely limits the device length to a tenth of 𝜆𝑅𝐹.

The first solution to address this problem is to decouple the optical length and the RF

length of the device, using a meandered MZM as presented in chapter 3.3. The device

is designed in a way to be short from RF point of view (remains a point load up to tens

of gigahertz) but has a long phase shifter (above 1mm) same as of the travelling wave

32 3. Rectilinear & Resonance based Lumped Element Modulators

modulators. The second solution, is to use resonance based devices, in particular a

ring resonator modulator, which is widely used in SiP and is presented in chapter 3.4.

3.2 Performance Metrics of Lumped Element Modulators

Before we move on to explain the design and experimental results of our meandered

and resonance based modulators, it is necessary to see how a transition to LE config-

uration will affect the power consumption, and also discuss the bandwidth limitations

of LE modulators compared to travelling wave devices.

3.2.1 Bandwidth limitations in LE Modulators

Generally, there are two factors limiting the bandwidth of a LE modulator: 1) The RF

power transferred to the device at high speeds, i.e. the speed at which the phase shifter

can be actuated according to its circuitry (see Figure 3.1), and 2) the transit time of

light along the device. We address the two limiting factors independently.

Electrical cutoff frequency

The actuation speed is typically limited primarily by the capacitance and series imped-

ance. Here, it is useful to define the intrinsic cutoff frequency of the phase shifter (𝑓𝑅𝐶),

that is, the maximum cutoff frequency of the modulator. In the absence of driver limita-

tions or pre-emphasis of the signal, it can be expressed as

llll

RCCRlClRRC

f 2

1

))(/(2

1

2

1

(3.2)

Hence, the intrinsic bandwidth is independent of the device length, since C and R scale

with 𝑙 and 1/𝑙, respectively. In practice however, as shown in Figure 3.1 (a), the output

impedance of the driver (or a 50 Ω cable connecting the device to the RF source)

reduce the cutoff frequency, as the time constant increases to (𝑅𝑙/𝑙 + 𝑅𝑑𝑟)𝐶𝑙, and the

aggregate bandwidth can be written as

)(2

1

))(/(2

13,

lCRCRlCRlRf

ldrllldrl

dBelec

(3.3)

This clearly shows that the measurable bandwidth of the modulator depends both on

the device length, and the output impedance of the driver and thus it is beneficial to

use a low output impedance driver for the LE modulators, to get closer to the intrinsic

bandwidth. This is quantitatively shown in Figure 3.1 (b), assuming the device length

to be 500 µm and the phase shifter to be the same as the HJC structure explained in

chapter 2 (𝐶𝑙=380 nF/m and 𝑅𝑙=8 mΩ∙m). It can be seen that replacing the 50 Ω con-

nection by a low impedance (10 Ω) driver increases the bandwidth from 11 GHz (blue

curve) to above 30 GHz (green curve). Note that in this figure, the delivered electrical

power to the device is plotted, however, it can be interpreted as the electro-optical S21

of the modulator, provided that actuation speed is the only limiting parameter of the

device bandwidth.

Apart from the output impedance of the driver, the series inductance induced by wire

bonds also plays a role in the frequency response of the device. In fact the inductance


together with the phase shifter capacitance forms an LC resonator which results in a

peak in the S21 of the modulator. It can potentially increase the device bandwidth pro-

vided that the resonance frequency is close to or above the cutoff frequency of the

device. However, it can distort the signal if the inductance is too big and thus the res-

onance frequency is too far below the cutoff. To quantify this effect, we can estimate

the inductance of a wire bond with 25 µm of diameter using the rule of thumb of 1

nH/mm [39]. In Figure 3.1 (c), the blue curve does not take the inductive effect of wire

bond for a 50 Ω driver and is kept as a reference. The other curves correspond to

0.5mm, 1mm and 1.5mm long wire bonds. It shows that a small additional inductance

can increase the cutoff frequency to 16 GHz (yellow curve). However, further increase

of the series inductance reduces the bandwidth, and distorts the signal, and even more

disruptively, increase the back RF reflection which can damage the driver or cause

horizontal eye closure at frequencies far below the -3dB cutoff frequency.

Figure 3.1 a) Equivalent circuit of LE configuration. (b) Power delivered to the LE modulator using a

50Ω (blue) and 10Ω (green) driver (c) The effect of inductance of wire bonds on cutoff frequency of a

LE modulator. Blue curve is the reference S21, same as blue curve in (b).

It is important to notice that the mentioned limitations of bandwidth apply to both types

of modulators presented in this chapter. However, this effect is more dominant in lim-

iting the bandwidth of rectilinear LE modulators, since they have a longer phase shifter

size and thus a smaller series resistance and a higher capacitance. In comparison, in

the presented ring modulators, with a circumference of around 60µm, the output im-

pedance of the driver does not significantly limit the device bandwidth. Instead, in ring

modulators, the main limiting factor is the transit time of the light.

Transit time of the light

In a LE device it can be assumed that the same voltage is applied along the entire

device length, which can be simply written as 𝑉 = 𝑉0𝑐𝑜𝑠(𝜔𝑅𝐹𝑡) where 𝑉0 is the ampli-

tude of the RF signal and 𝜔𝑅𝐹 is its angular frequency. Let 𝜏𝑔 be the time taken by

photons to pass through the device, which can be simply calculated as 𝜏𝑔 = 𝑙/(𝑐0/𝑛𝑔)


with 𝑛𝑔 being the group index. At low frequencies (𝜔𝑅𝐹𝑡𝑔 ≪ 1) the maximum modula-

tion output 𝑃1 corresponds to the maximum applied voltage 𝑉0. At high frequencies

(where 𝜏𝑔 is comparable with the RF period), the maximum modulation output corre-

sponds to the photons entering the device at the time 𝜏𝑔/2 before the RF signal

reached its peak ( 𝑉0) and exit it 𝜏𝑔/2 after the peak of the RF signal, since in this case

they have accumulated the maximum phase shift. Thus, the frequency dependent

phase shift can be written as:

2

2

)cos(1

)0(

)(g

g

dttRF

g

RF

(3.4)

The integral corresponds to the maximum voltage that is effectively applied to the op-

tical mode at 𝜔𝑅𝐹 compared to DC. The -3dB cutoff is reached where this ratio

equals 1 √2⁄ . Hence,

2

12sin2

)0(

)(

RF

gRF

g

RF

(3.5)

yields 𝜔𝑅𝐹 = 2.79/𝜏𝑔 and thus the device E/O bandwidth can be written as 𝑓𝑜𝑝𝑡,−3𝑑𝐵 ≈

0.44/𝜏𝑔. It should be noted that generally it does not add a new bandwidth limitation to

the LE modulators beyond the LE condition, at least for simple straight phase shifters.

However, for both types of devices presented in this chapter, equation (3.5) should be

considered as a bandwidth limiting factor, since (as explained in chapter 3.3) the wave-

guide length of our proposed devices can by far exceed the limited length imposed by

LE condition.

3.2.2 Power consumption in LE modulators

In this section, our focus is on the RF power consumption of the device, that is, the

power consumption associated with delivery of the RF signal to the device. However,

it is important to mention that especially for devices with small optical bandwidth, e.g.

the resonance based modulators discussed in chapter 3.4, an active control system is

required for stabilizing the bias point [11]. This is the main motivation to introduce

lumped element devices which also feature a relatively wide optical bandwidth, such

as meandered modulators presented in chapter 3.3, as well as wideband ring assisted

MZI modulators [40, 41], and slow light photonic crystal modulators [42, 43]. Apart from

the power consumed by control circuitry, the internal power consumption of the driver

also depends on the modulator characteristics, as a high capacitive load necessitates

a higher current sourcing by the driver [11].

As we mentioned in the introduction, and is commonly argued, generally LE modula-

tors are more power efficient than travelling wave devices, since they do not have a 50

Ω termination to constantly dissipate power. In fact in a LE, the modulation process

boils down to charging and discharging of a capacitor, and thus the average power

consumption per bit is the same as explained by equation (3.1), since a LE device

needs power only for switching a bit. On the other hand the total power consumption

in a travelling wave modulator can be calculated as [44]


TL

DDTW

Z

VP

2

2

1 (3.6)

with 𝑍𝑇𝐿 as the characteristic impedance of the a single arm of the MZM, and 𝑉𝐷𝐷 the

drive voltage. The factor ½ is based on the assumption that the MZI is driven in push-

pull configuration, and hence during the modulation one of the arms stays at zero

phase shift condition, and thus has no power consumption. This is valid, only in the

case when the modulator is biased at half of the drive voltage. This was the case for

all travelling wave modulators presented in the previous chapter, but in many cases,

in order to achieve a higher bandwidth, the modulators are biased at a higher reverse

voltage (for example in [45] and [46]) resulting in a higher power consumption than is

estimated here. Thus, it can be said that this equation yields a lower boundary of the

travelling wave modulator power consumption.

In order to be able to compare 𝑃𝑇𝑊 (given by equation (3.6)) with 𝐸𝑏𝑖𝑡,𝐿𝐸 (given by

equation (3.1)) we should make an estimation of the maximum achievable data rate of

the given travelling wave modulator. Indeed, we would like to calculate the power con-

sumption of the same travelling wave device, when driven as LE (in practice can be

realized using a distributed driver [27]). Adding the screening effect of the capacitive

load at high frequencies, to the equation (2.13), we can calculate the RF power loss

along the waveguide to be

VCR

CZR

dx

dV

RFll

lRFTLl

)(1

)(

2

12

(3.7)

with 𝑉 the voltage along the phase shifter, and 𝑥 the propagation direction. At the in-

trinsic cutoff frequency (𝜔𝑅𝐹 = 𝜔𝑐) based on equation (3.2), the equation (3.7) equals

to −1/4(𝑅𝑙𝑍𝑇𝐿𝜔𝑐2𝐶𝑙

2), As mentioned in chapter 2.2.2, if the bandwidth of the travelling

wave modulator is only limited by RF loss along the waveguide, we can assume the

device length to be 74% of the 1/e decay length of the modulator, where the RF loss

falls -6.4 dB below the DC level. In practice, the actual bandwidth of travelling modu-

lator is slightly smaller and can be estimated to be 𝜔𝑇𝑊,−3𝑑𝐵 = 0.6/𝑅𝑙𝐶𝑙 [44]. Since the

data rate 𝐷 can be typically 1.4 times larger than the bandwidth, it can be assumed to

be 𝐷 = 0.86/2𝜋𝑅𝑙𝐶𝑙 ≈ 0.14𝜔𝑐. To calculate the total capacitance, the device length 𝑙

needs to be estimated. As explained, it can be calculated based on the 1/e decay

length

lcTLlcTLl CZCZR

l

96.2

)(

474.0

2

(3.8)

Thus, the total power consumption of the modulator, when is driven in LE configuration,

is given by

TW

TL

DD

lcTL

lcbitLE PZ

VV

CZCEDP 2.01.0

96.2

4

114.0

22

(3.9)

It means by changing the driving scheme from traveling wave to lumped element for

the same phase shifter, which has the same length and insertion loss, power consump-

tion is reduced by around a factor 5. It should be mentioned that in this derivation we

assumed that 1) the travelling wave modulator is modulating at its maximum possible


bandwidth. However, if the data rate is slower, e.g. the modulator length is limited by

its insertion loss, and not the RF loss, the power consumption improvement would be

higher. In this case, most of the RF power reaches the end of the transmission line

(even at the highest modulation frequency) and is dissipated in the termination resistor.

2) We also assumed that the bandwidth of the LE modulator is equal to the intrinsic

bandwidth 𝜔𝑐, which is only the case if it is not limited by light transit time, and also the

driver has extremely small output impedance. If these assumptions are violated, the

energy per bit enhancement drops.

It is also interesting to investigate the improvement of the device bandwidth per energy

per bit ratio for LE devices compared to travelling wave modulators. If we again assume

that the bandwidth of the LE modulator is close to the intrinsic bandwidth (small driver

output impedance and short photon transit time) the bandwidth improvement is 0.6 as

discussed before, and thus this enhancement is around a factor 8. This is only valid

when the bandwidth of the travelling wave modulator is around 𝜔𝑇𝑊,−3𝑑𝐵 = 0.6/𝑅𝑙𝐶𝑙. If

the modulator is longer 𝜔𝑇𝑊,−3𝑑𝐵 ≪ 0.6𝜔𝑐, less power is dissipated in the resistive ter-

mination, and thus this enhancement factor drops. In a more general case, in [44] we

have shown that this enhancement remains above 6 regardless of the length of the

travelling wave modulator.

3.3 Lumped Element Meandered Modulators

In the quest to shrink the size of the modulator below lumped element condition, and

simultaneously keep the phase shifter length suitable for a low drive voltage, we pro-

pose meandered modulators in lumped element configuration. First, we explain the

design of such devices, simulated performance as well as the device layout. Next, we

explain the measurement results of the fabricated devices, and discuss the potential

improvements.

3.3.1 Concept and Design

A short modulator with a length of 250 µm can be regarded as a lumped element device

(based on rule of thumb of 𝑙𝑅𝐹 < 𝜆𝑅𝐹/10) up to 30 GHz assuming the 𝑛𝑅𝐹 is ~4. In this

case, in the conventional LE modulators as schematically shown in Figure 3.2 (a), the

length of the phase shifter 𝑙𝑃𝑆 also needs to be 250 µm. Assuming the modulation

efficiency to be 2 V∙cm (as is the case for typical PDE modulators and is also the effi-

ciency of the HJC phase shifter presented in chapter 2) the drive voltage for each arm

of the MZI in order to achieve a full extinction 𝑉𝜋/2 is as high as 40 V. In a simple

CMOS NOT gate (inverter) where only 2 Vpp is available at high speed, this high 𝑉𝜋/2

severely penalizes the OMA and results in eye closure. To mitigate this problem, we

propose the meandered modulator. The layout of one arm of the MZI is shown in Fig-

ure 3.2 (b). In this device, RF length of the modulator, i.e. the length of the electrodes,

is still kept around 250 µm, but the phase shifter length of the device is 1.4 mm, which

results in a dual drive voltage 𝑉𝜋/2 of 7 V∙cm for the same phase shifter. The improve-

ments discussed in chapter 3.2 are still applicable to this structure, provided that the

device is unterminated.


The microscope image of the fabricated device is shown in Figure 3.2 (c). We used

one by two multi-mode interferometers (MMIs) both in the input and output of the de-

vice, and the MZI is slightly imbalanced to ease the phase shift measurement. The vias

are placed in the vicinity of the waveguides so that the RF signal is transferred through

the metal lines, and not along the waveguides. In principle, geometrically there is al-

most no limit to the length of the phase shifter that can be squeezed inside the device,

thanks to the high index contrast between silicon and oxide which allows for small

bending radii. However for an increased phase shifter length, the photon transit time

(as explained in chapter 3.2.1) emerges as a limiting factor for the device bandwidth.

Based on equation (3.5), the 𝑓−3𝑑𝐵,𝑜𝑝𝑡 is about 25 GHz for our 1.4 mm long phase

shifter, given that the group index of the 400 nm wide 120 nm etched waveguide is

calculated to be 3.8, using CAD FIMMWAVE software. The second limiting factor of

the device length is of course the insertion loss. The meandered modulators were fab-

ricated on three different wafers. The three devices are identical in terms of the layout

and fabrication process, apart from the phase shifter doping. The first wafer (W1) has

the same doping profile as the LJC phase shifters and thus has an identical optical

loss. Therefore for the meandered modulator on W1, the optical loss is expected to be

2.4 dB. The doping levels for W2 and W3 are higher, and is shown in Table 2.1 (see

chapter 2). The expected insertion losses for W2 and W3 modulators are 4.8 dB and

8.3 dB, respectively.

Figure 3.2 (a) Schematic of a conventional lumped element device. (b) Actual layout of one arm of the

meandered modulator. The yellow strips show the vias, connecting top metal layer to the device. (c)

Microscope image of the fabricated meandered MZI modulator. (d) 3D HFSS simulation of the device,

at 4 different frequencies, at maximum applied field. The red arrows show the field strength.

The results of the simulations (same method as explained in chapter 2.2.1) show that

based on the effective index change for 2 V applied voltage, for W1, W2, and W3 the

dual drive voltage required for full extinction in the 1.4 mm long modulator is 8.6 V, 4.7

V, and 3.7 V, respectively.

According to the length of the device from RF viewpoint, the device will behave as a

lumped element (same voltage along the device) at least up to 25 GHz, taking the

maximum metal distance as the device RF length. Nevertheless, in order to accurately

calculate the voltage received by each point along the modulator, a 3D simulation is

required1. In principle, by calculating the voltage at each point of the waveguide, given

that 𝑛𝑔 of the optical mode is known, one can calculate the exact frequency dependent

OMA penalty for high frequencies beyond the LE condition, using the equation [11]

1The 3D simulation in HFSS was performed by my colleague Dr. A. Moscoso Martir at IPH.


L

zizn

ci

RF dzeezVLV

RFg

RF

00

0)(1

)0(

)(

(3.10)

which is the more general form of equation 2.18. Similarly, here z is the curvilinear

coordinate along the phase shifter, and |𝑉(𝑧)| and 𝜑𝑅𝐹 are respectively the magnitude

and phase of the RF field along the phase shifter. For this purpose, the layout of the

device is exported to the HFSS software, and the field along the waveguide is calcu-

lated, as is shown in Figure 3.2 (d). The simulations confirm that at least for below 25

GHz, the field across the device has no phase delay and thus the device could be

regarded as a lumped element. Since we are not interested in the transition frequen-

cies (high enough frequencies for the device to begin to deviate from LE assumption)

due to the fact that the bandwidth is limited to 25 GHz due to photon transit time, the

electro-optical bandwidth of the device can be calculated with the assumption of LE

behavior, using the equivalent circuit that is shown in Figure 3.1 (a).

Figure 3.3 Simulated electro optical bandwidth of the low doped (blue), medium doped (red) and highly

doped (yellow) LE meandered modulators, Solid lines: 50Ω output impedance of the driver, and device

not terminated; dashed lines: 50Ω output impedance of the driver, and device is 50Ω terminated; dotted

lines: 7Ω output impedance of the driver without termination

The RC limited bandwidth 𝑓−3𝑑𝐵,𝑅𝐶 depends on the driver impedance. In Figure 3.3 the

solid lines show the electro-optical S21 of the device, provided that it is only limited by

the voltage delivered to the device, when the device is driven using 50 Ω probes and

is not terminated. It predicts the electrical cutoff frequency of the devices to be 6.3

GHz, 4.8 GHz, and 3.9 GHz for W1, W2 and W3 modulators respectively. The dotted

lines show the device bandwidth, when driven by a 7 Ω driver, and is left unterminated.

In this case the cutoff frequency of W1, W2 and W3 modulators are calculated to be

23.7 GHz, 22.7 GHz, and 20.1 GHz, respectively. In our case, in the absence of low

impedance driver, we terminated the LE modulators using a targeted 50 Ω on-chip

resistor. This goes against the purpose of the LE modulators, but allows for high speed

measurement and validation of the model. The predicted electro-optical bandwidth of

the device in this case is plotted in Figure 3.3 with dashed lines. It predicts the cutoff

frequencies for W1, W2, and W3 to be 11 GHz, 8.9 GHz, 7.3 GHz, respectively. This


can be achieved, at the expense of 6 dB reduction in OMA at low frequencies. In fact,

at low frequencies the termination resistor and the 50 Ω of the driver act as a voltage

divider, hence, only half of the RF power would be transferred to the device. Moreover,

unlike the usual case in LE modulators, the power is also dissipated even in the ab-

sence of voltage switching. The additional power consumption heats up the device and

makes the modulator thermally unstable.

In practice, the photon transit time also reduces the bandwidth. The overall bandwidth

of the device can be estimated as

2/1

2

,3

2

,3

3

11

optdBRCdB

dBff

f (3.11)

The overall bandwidth of the devices for three different configurations, and three dif-

ferent doping levels, are shown in Table 3.1. With the 50 Ω on-chip termination driven

by 50 Ω cables (as is the case for our measurement environment) the bandwidth of

W1, W2 and W3 meandered modulators are limited to 10.1 GHz, 8.3 GHz, and 7 GHz.

Doping level Ph.Shift.

length

∆𝑛𝑒𝑓𝑓 at

-2V

E/O 𝑓−3𝑑𝐵 at 2V

No termination 50Ω ter.

P doping N doping Rdr=50Ω Rdr=7Ω Rdr=50Ω

W1 1.3e17 cm-3 4e17 cm-3 1.4 mm 6e-5 6.1 GHz 17.1 GHz 10.1 GHz

W2 9e17 cm-3 1.1e18 cm-3 1.4 mm 11e-5 4.7 GHz 16.8 GHz 8.3 GHz

W3 2.1e17 cm-3 2.6e18 cm-3 1.4 mm 14e-5 3.9 GHz 15.6 GHz 7.0 GHz

Table 3.1 Simulated performance of the meandered modulators

3.3.2 Experimental results and discussion

An image of the electro-optical meandered modulator device, fabricated at institute of

microelectronics (IME) at Singapore, is shown in Figure 3.2(c). As mentioned, the de-

vices are fabricated on three different wafers, W1, W2, and W3, with different doping

levels. Using a tunable (1.49 µm to 1.61 µm) laser, we measure1 [42] the optical trans-

mission of the devices. After de-embedding the optical loss of the grating couplers (~9

dB for a grating couplers pair) the insertion loss of the three devices are measured to

be 5 dB, 6.3 dB, and 9.1 dB for W1, W2 and W3 devices, respectively. Compared to

the simulated values of the insertion loss, in each case the loss is higher by an average

of 1.5 dB. It should be mentioned that in simulation of the optical loss of the meandered

modulators, the bending loss was assumed to be negligible, which could partially ex-

plain the discrepancy. Moreover, we notice that Metal1 layer, which is only 600 nm

above the silicon layer, has some crossings with the waveguide inside the device. It is

unlikely to be caused by excessive high doping levels, since the offset between the

simulated and measured values is almost constant on different wafers. Moreover, the

phase shift observed in all three modulators does not show a deviation from the ex-

pected values.

The effective index change measured for applied voltages is shown in Figure 3.4 (a).

It is necessary to mention that since the meandered modulators are in parallel with a

1 These devices were characterized by Jovana Nojic, as a part of her M.Sc. project at IPH [42]


50 Ω termination resistor, these measurements are performed on linear 1 mm and 2

mm long phase shifters, which have the exact same layout for the phase shifter, but

are unterminated. The measurement results are in a good agreement with simulations,

as an effective index change of 6e-5, 10e-6, and 15e-6 are measured at 2V applied

voltage. The extracted modulation efficiency is plotted in Figure 3.4 (b). It shows that

for the given length of the phase shifter, the required dual drive voltage to achieve full

extinction for W1 meandered modulator is around 9.3 V (extrapolated with 2.6Vcm

measured at 2 V). For W2 and W3 meandered modulators, this value is reduced to 5.3

V and 3.8 V, respectively, which correspond to the measured 1.5 V∙cm and 1.1 V∙cm

measured efficiencies at 2 V. To have a fair comparison between the performances of

the three phase shifters, it is useful to calculate the figure of merits of 𝑉𝜋𝑙 ∙ 𝛼𝑑𝐵 with unit

of V∙dB and also 𝐶𝑙(𝑉𝜋𝑙)2/8 with cm∙pJ/b unit. The former is an already mentioned

tradeoff between the loss and efficiency, and corresponds to the required drive voltage

for a phase shifter short enough to exhibit 1 dB loss. This value is measured to be 93,

67, and 73 V∙dB respectively for W1, W2, and W3 phase shifters, which are by far

higher than is expected from the phase shifter, due to the additional losses. The latter,

corresponds to the power consumption of a device sized to have a unit length, and is

2.45, 1.2, and 0.82 cm∙pJ/b for W1, W2, and W3 phase shifters, respectively. In these

calculations the linear capacitances of the phase shifters are simulated values of 2.9,

4.1, and 5.4pF/cm which are in a good agreement with measurements.

Figure 3.4 Measured results of (a) effective index change and (b) efficiency (V∙cm) of the meandered

modulators versus the applied voltage in reverse bias for three doping levels.

The measured normalized electro-optical S21 of the three meandered modulators at

different bias voltages are plotted in Figure 3.5. Since all the modulators have an on-

chip 50 Ω termination resistor, and the RF signal is transmitted to the devices using 50

Ω cables, these curves should be compared with the dashed lines in Figure 3.3, alt-

hough in that graph, only the RC limitation was taken into account. Considering the

photon transit time, the S21 curves are pushed closer together, and the expected val-

ues for bandwidth are written in Table 3.1 (first column from right). The measurement

setup is similar as what was shown in Figure 2.15 (a). The measured S21 curves at -

2 V bias cross the -3dB point at 8.7 GHz, 8.1 GHz, and 7 GHz respectively for W1,

W2, and W3 modulators, which is in a good agreement with the simulated electro-

optical bandwidth of the devices.


Figure 3.5 Measured small signal electro optical S21 for (a) W1 (b) W2 and (c) W3 meandered

moudlators, using a 50Ω driver and with an on chip termination with 50Ω resistor.

In order to verify the measured bandwidths of the meandered modulators, we also

performed data transmission tests, using a setup similar to Figure 2.17 (a), with the

difference that here, in order to be able to measure the extinction ratio ER and modu-

lation penalty MP, we added an in-line power meter between device and the photo-

detector. The measured eye diagrams for the 3 wafers at different speeds are shown

in Figure 3.6. For all measurements, the laser power was set to 20 mW, mainly in order

to compensate for the 9 dBm loss arising from the grating coupler pair, and 2Vpp was

applied to the modulators at 2V bias. These measurements further confirm that the W3

modulator has a smaller bandwidth, due to the eye closure at 25 Gbps. However, the

open eyes at 25 Gbps for W1 and W2 suggest that the measured electro-optical S21

for W1 and W2 modulators could have slightly under estimated the device bandwidth,

since they cross the -6dB line below 12.5 GHz.

Figure 3.6 Measured PRBS15 eye diagrams for W1 (first row), W2 (second row), and W3 (third row) at

different speeds recorded by a 20GHz real time oscilloscope. The values for extinction ratio (ER) and

modulation penalty (MP) are written in each diagram.

In summary, we introduced meandered modulators as a method allowing to drive a

modulator in LE configuration while keeping the length of the phase shifter long enough

to feature an acceptable extinction ratio at 2Vpp drive voltage. We implemented three

devices with different doping levels to test the performance of such devices. The W2

meandered modulator with a moderate doping level of ~1e18 cm-3 features a low 𝑉𝜋/2

of 5.4 V and an insertion loss of 6.3 dB and open eye diagrams at 25 Gbps, for the


terminated device, using a 50 Ω probe. The -3dB bandwidth of an unterminated device

would exceed 20 GHz, in case it is wire bonded to a 4 Ω output driver. In order to

increase the speed of such devices, it is necessary to use a low output impedance

driver in the vicinity of the device, wire bonded to the chip. High speed modulator driv-

ers with an output impedance of 4 Ω are commercially available. Provided that they

can support the output current required for the capacitance of the device, these devices

can offer an optically wideband, low power consumption and low drive voltage modu-

lation.

3.4 Ring Resonator Modulators

Resonance based modulators and in particular ring resonator modulators (RRMs) im-

plemented in silicon technology [10] have been extensively explored in the past decade

to realize efficient modulation in the SOI platform [47, 48], and have the potential of

becoming a major building block in future short reach interconnect systems [49, 50].

Silicon RRMs exhibit a combination of advantages such as extremely small footprint

(~tens of micrometers), low power consumption (in the range of tens of fJ/bit) [51], and

high modulation speeds (above 25 Gb/s) [52, 53]. Moreover, their natural frequency

selective behavior allows for implementation of an array of RRMs in order to realize

wavelength division multiplexed (WDM) transmitters on a single bus waveguide [54,

55]. Nevertheless, such systems are extremely temperature sensitive and thus require

an active control system to fine tune the working frequency of the RRMs to the desired

points.

An RRM in its simplest form consists of a shallow-etched ring, coupled (with coupling

coefficient of 𝜅1) to a bus waveguide as shown Figure 3.7 (a). A portion of the input

light in the bus waveguide (entering from port A) is coupled into the ring. Assuming a

lossless coupling, light is either coupled into the ring (with 𝜅2 power ratio) or is trans-

mitted (with 𝑡2 power ratio). Thus, one can write

122 t (3.12)

At a certain wavelength 𝜆𝑟, where the circumference of the ring is a multiple of the

wavelength inside the waveguide, the coupled light builds up inside the ring, forming a

resonance. This resonance condition can thus be expressed as

effr nmR /2 (3.13)

where 𝑅 is the radius of the ring, 𝑛𝑒𝑓𝑓 is the effective index of the mode inside the ring,

and 𝑚 is an integer, the mode number of the resonator. At the resonance wave-

length 𝜆𝑟, light coupling back to the bus waveguide from the ring has a π–phase

difference with the input light, and thus destructively interferes with it. The π–phase

difference is due to the fact that light experiences a π/2 phase shift at each coupling

transition. This destructive interference can be seen in the transmission spectrum of

the ring (at port B) as shown in Figure 3.7 (b). It is notable that the transmitted power

𝑃𝐵 reaches exactly to zero only if the coupling loss is exactly equal to the round trip

loss of the mode. This case is called critical coupling, and its condition can thus be

expressed as


212

2exp

tR (3.14)

with 𝛼 the linear power losses (−𝜕𝑃/𝜕𝑧) for normalized power. It means that regarding

the optical loss, the coupling coefficient can be set to the value 𝜅𝑐𝑐 to achieve the

critically coupling (cc) condition. If 𝜅 is set to a smaller value (𝜅 < 𝜅𝑐𝑐), or a higher value

(𝜅 > 𝜅𝑐𝑐), the conditions are called under coupling, and over coupling, respectively.

At this point, the modulation mechanism in RRMs can be directly seen from equation

(3.13), where any modification of the mode effective index 𝑛𝑒𝑓𝑓 results in variation of

the resonance wavelength, and thus changes the transmitted power. This is schemat-

ically shown in Figure 3.7 (b), where the blue curve and green curve correspond to the

ring power transmission at two different applied voltages. In our implemented RRMs,

we exploit PDE in reverse bias to alter the effective index of the guided mode, using a

similar phase shifter structure, as explained in chapter 2. Qualitatively, the high effi-

ciency of the RRMs in comparison with rectilinear modulators stems from the multiple

cycles light makes inside the resonator, and hence will “see” the RF signal for a longer

time. In fact the resonator provides virtually a longer phase shifter, which can be ex-

pressed as an enhancement factor, depending on the Finesse (𝐹) of the ring resonator.

It will be quantitatively revealed in chapter 3.4.1 where the RRM design is explained.

It should be mentioned that the monitor tap with output at port D is not a necessary

part in RRMs. However, we implemented this waveguide as well, with a small coupling

coefficient of 𝜅2 ≪ 𝜅1 in order to use 𝑃𝐷 as a feedback signal, for the control of the

RRMs.

Figure 3.7 (a) Schematic illustration of an RRM device. Orange and purple colors represent different

doping types in the phase shifter. (b) Transmission power measurable at port B.

On the negative side, the RRMs are very sensitive to fabrication inaccuracies, such as

small variations in the gap between the ring and the bus waveguide, the etch depth of

the waveguide, and the waveguide width. In chapter 3.4.2 we try to address these

issues by implementing modifications to the RRM waveguide in order to minimize their

effects. Subsequently, we explain the design of an optical add-drop multiplexer re-

quired for the receiver side, and finally we report the experimental results of the

fabricated devices. Before we dive into the details, it is important to mention that the

design process of the ring modulators is more complicated than the explained rectilin-

ear devices, since, as will be shown, bandwidth and OMA are highly wavelength

dependent, and also the coupling coefficient adds a new degree of freedom to the


design space. In the following, a design method which was first introduced by Müller

et al [56], is used in order to find the optimal design parameters.

3.4.1 RRM Design: Static and dynamic models

Similar to travelling wave MZMs and also meandered modulators, we begin the design

process with the calculation of key metrics of the modulator including linear capaci-

tance 𝐶𝑙 (F/m) and resistance 𝑅𝑙 (Ω.m), as well as effective refractive index change

(∆𝑛𝑒𝑓𝑓) and absorption 𝛼 (dB/m), in the cross section of the phase shifter. We per-

formed all these calculations for different doping levels ranging from 2e17 cm-3 to

4e18cm-3 in small steps, and under different applied voltages. The method is similar to

what was explained in detail in chapter 2.2.1, as the doping profile is calculated using

Synopsys TCAD, and the modulator metrics are calculated using FEM in COMSOL

Multi-Physics.

Once the performance of the cross section of the phase shifter is known, we can cal-

culate the RRM behavior. Our goal is to implement an RRM which features an electro-

optical 3dB bandwidth of above 20GHz, a minimum extinction ratio (ER) of at least 5

dB, and an optical modulation amplitude (OMA) better than -7 dB. All should be

achieved with an applied voltage of 2Vpp. The initial step in order to design the RRM,

is to calculate the static behavior of the device namely ER and OMA. This is not as

trivial as in rectilinear modulators, since it is highly wavelength dependent. It also

strongly depends on the chosen coupling coefficient 𝜅1. Thus, we calculate ER and

OMA for a wide range of possible detuning (the wavelength difference between the

resonance wavelength 𝜆𝑟 and the carrier wavelength 𝜆𝑐) and also a wide range of 𝜅1

(from highly under coupled to highly over coupled). For these calculations we need the

static model of the ring resonator. First, based on equation (2.2) we can calculate the

phase 𝜑 of the field inside the ring (for either 0V or 2V applied) as

Rn VVeffVV

2

22/0,2/0 (3.15)

where 𝑅 is the ring radius. It indicates that right from the beginning of the design, we

need to fix the ring radius in order to calculate the rest of the performance metrics.

Generally in RRM design, the upper limit of the radius is dictated by the Free Spectral

Range (FSR) required for the multi-channel WDM system, since

gnR

FSR

)2(

2

(3.16)

with 𝑛𝑔 the group index of the mode. In our case, the minimum required 𝐹𝑆𝑅 yields

R<11µm. The lower constrain of R is dictated by the bending loss, which strongly de-

pends on the waveguide geometry, and together with the other aspects of geometrical

design, it will be covered in chapter 3.4.2. Based on these two constrains we picked

the radius of R=10 µm for our design. Since we have calculated 𝛼0𝑉 and 𝛼2𝑉 in dB/m,

the linear optical loss indicator 𝑎 can be then calculated with

R

VV

VV

a

2

20

2/0

2/0

10 (3.17)


Based on these equation, the coupled light field 𝐸𝐶 inside the ring can be written as

212/02/0

12/0,

exp1 ttia

iE

VVVV

VVC

(3.18)

where 𝑡1 and 𝑡2 are the directional coupler transmissions at the bus waveguide and

monitor port, respectively. Therefore, the transmitted power 𝑃𝐵 (power at port B in Fig-

ure 3.7) can be simply written as

212/02/0

2/02/0212/0,

exp1

exp

ttia

iattE

VVVV

VVVVVVB

(3.19)

The field in the monitor port 𝐸𝐷 can then be calculated as

212/02/0

2/02/021

2/0,exp1

)2

exp(

ttia

iai

EVVVV

VVVV

VVD

(3.20)

In our design, based on the power budget calculations and also the minimum required

power for the on-chip germanium photo-detectors, we fixed the output power of the

monitor port 𝑃𝐷 to be 3% of the input power 𝑃𝐴 at resonance, by adjusting the correct

𝜅2 using equation (3.20).

In order to calculate the OMA and ER of the RRMs at each detuning point, we use

equation (3.19) to calculate the transmitted power 𝑃𝐶 under 0V and 2V applied volt-

ages, for each doping level and each coupling point, and then use the equations (2.9)

and (2.10). In the simulations, the coupling coefficient is swept in a wide range

(𝜅 = 0.5𝜅𝑐𝑐 to 𝜅 = 2𝜅𝑐𝑐). The optical transmissions of two different RRMs is plotted in

Figure 3.8 (a). To simplify the figure, the calculated performance metrics are shown

only for one specific doping (1.2e18 cm-3) and two specific coupling points, one of

which is over coupled (𝜅 = 1.2𝜅𝑐𝑐), and the other one is under coupled (𝜅 = 0.8𝜅𝑐𝑐). It

can be seen that both ER and OMA are highly wavelength dependent, as they are

smaller close to the resonance frequency and reach their maximum value slightly fur-

ther from resonance. Note that the maximum ER and OMA are not necessarily

achieved at the same wavelength, and their difference depends on the drive voltage.

Figure 3.8 (d) shows the calculated electro-optical bandwidth of the RRM, when it is

only limited by the photon lifetime inside the ring. It can be seen that this bandwidth

also depends on the detuning and is thus wavelength dependent. In order to calculate

this optical response of the RRM, we needed to use the dynamic model of the ring

behavior. We start with the time-dependent equation [57]

ACrC EiEit

E

1 (3.21)

where 𝐸𝐶 and 𝐸𝐴 are respectively the amplitude of the field inside the RRM, and in the

bus waveguide, 𝜔𝑟 is the angular resonance frequency, and 𝜏 is the 1/e decay time of

the field amplitude, and 𝜇 is the coupling strength factor between the resonator and the

bus waveguide, coupling in and out of the RRM. This time-domain coupling parameter

can be written as


Ln

c

g

0 (3.22)

with 𝐿 being the circumference of the RRM.

Figure 3.8 (a) Optical transmission of the RRM near resonance under 0V (solid lines) and 2V (dashed

line) applied voltage. Calculated wavelength dependent (c) extinction ratio, and (d) optical modulation

amplitude for 2Vpp. (d) Delay time limited electro-optical bandwidth of the RRMs.

In order to calculate 𝜏 in equation (3.21), we first need to calculate the loaded quality

factor 𝑄𝑙𝑜𝑎𝑑 of the RRM at bias voltage, as

21

,

2

biasr

g

biasload

nQ (3.23)

where 𝜆𝑟 is the resonance wavelength, 𝛼𝑏𝑖𝑎𝑠 is the loss caused by the carriers at bias

voltage (𝛼𝑏𝑖𝑎𝑠 = 2 log(𝑎) /𝐿) and 𝛼1 and 𝛼2 are the coupling losses to the bus wave-

guide and monitor waveguide, respectively. Then the field lifetime 𝜏 inside the RRM

can be directly calculated using the definition of the quality factor, with

0

,

2

2

c

Q rbiasloaded

(3.24)

By applying a sinusoidal modulation voltage with angular frequency of 𝜔𝑚 and small

amplitude of 𝛿𝑉, the resonance frequency will be shifted to 𝜔𝑟 + 𝛿𝜔𝑟sin (𝜔𝑚𝑡) assum-

ing a linear phase shifter. Though in practice the phase shifters are not linear, this

assumption is still valid we assume small signal modulation here. With this assumption,

in [49] we can derive the small signal electro-optical response of the RRM using per-

turbation theory to be

rm

CACrr

rm

CACrEO

ii

EiEE

ii

EiEES

0

***

0

*

,2111

(3.25)


where 𝜔𝑟 is the frequency of the optical carrier, 𝐸𝐴 is the amplitude of the input light,

and 𝐸𝐶 exp(−𝑖𝜔0𝑡) is the value of 𝐸𝐶 in the absence of modulation voltage. It should be

noted that the loss modulation results in an asymmetry in the RRM small signal re-

sponse with respect to the sign of the detuning wavelength (𝜆𝑑 = 𝜆𝑚 − 𝜆0). Based on

this equation, the electro-optical bandwidth of the RRMs at different detunings are plot-

ted in Figure 3.8 (d), and the bandwidth is clearly different on the two sides of the

resonance. Hence, to improve the high speed performance it is beneficial to tune the

RRM far from the resonance. However, the improvement comes at the cost of smaller

ER and OMA as is shown in Figure 3.8 (b) and (c).

It is notable that based on equation (3.25), at the point where the modulation frequency

is equal to the detuning, one of the sidebands falls into the resonance, and thus expe-

riences an enhancement, which appears as a peak in the RRM electro optical S21.

This peaking effect yields a post-fabrication degree of freedom to trade-off the band-

width and the OMA, which is significantly important especially since a small change in

fabrication-sensitive coupling coefficient can change OMA and bandwidth in different

directions. Another significance of the peaking effect is that it allows modulation be-

yond the linewidth limitation of the RRM [58, 59], since for high values of detuning, the

peaking will appear at higher frequencies and thus extends the modulation bandwidth

of the RRM.

The simulation results are summarized in Figure 3.9 where each point indicates the

corresponding bandwidth (x-axis) and the OMA (y-axis) of one individual doping level

and coupling coefficient. Each individual curve in this graph corresponds to one spe-

cific doping level, which is varied between 1.25e18 to 5e18 cm-3. On each curve, the

coupling coefficient is swept from 0.6𝜅𝑐𝑐 (under-coupled, left) to 1.4𝜅𝑐𝑐 (over-coupled,

right), with 𝜅𝑐𝑐 the coupling factor in case of critical coupling in accordance with the

optical loss. For each point of each curve, the detuning is swept around the resonance

frequency (in the range of the full width half max, FWHM), and the results at each

detuning are compared against each other, and only the best point is shown in this

figure. The best point indicates the detuning, at which the OMA reaches its maximum

value for that special doping and coupling. These points are shown together in Fig-

ure 3.9 as solid curves.

Since the device is aimed to deliver an extinction ratio greater than 6 dB, the devices

with extinction ratios less than 6 dB are excluded from the plot in the dashed curves.

As can be seen, for low doping levels (e.g. on the blue curve), the chosen points with

the maximum OMA (solid lines) also satisfy the ER>6dB condition. However, this is not

the case for higher doping levels (e.g. red curve) and the best detuning point is pushed

closer to the resonance (see Figure 3.8) and thus burdens both the OMA and the

bandwidth.


Figure 3.9 The best achievable optical modulation amplitude (at 2Vpp drive voltage) vs. corresponding

bandwidth for various doping levels and coupling coefficients. Each color corresponds to a specific

doping level. On each curve, 𝜿 is increased from left to right. The dashed lines are taking the ER>6dB

condition into account. The black square indicates the selected point.

Thus, provided that the doping levels and the coupling coefficients can be freely cho-

sen by the designer, the best achievable devices should be traced on the envelope of

the dashed curve, since they offer the maximum achievable OMA for a given band-

width. In this regard, the best point is found to be at a doping of Nd=2.5e18 cm-3

(dashed green curve) with κ1=0.304 and κ2=0.061. At this point, we expect to achieve

an OMA of 6.1 dB, a bandwidth of 28 GHz, optical loss of 61 dB/cm in the absence of

bias voltage, a capacitance of 530 pF/m, and resistivity of 3 mΩ∙m. The chosen point

is indicated by a black square in Figure 3.9.

Figure 3.10 Envelope of the constrained curves, for the case ER greater than 6dB for 1V (red) and 2V

(green) applied voltages.

The aforementioned envelopes are shown in Figure 3.10. The green curve represents

the envelope of the constrained curves shown in Figure 3.9. It is also interesting to

investigate the best achievable design point, given a 1Vpp drive voltage represented

by the red curve in Figure 3.10, and in this case, clearly, either the OMA or modulation


speed should be compromised. For instance, to achieve an OMA of -6 dB, the band-

width is reduced to 12GHz (6 dB crossing on red curve) instead of 27GHz (6 dB

crossing on green curve). Nevertheless, even with 1Vpp applied voltage, it is possible

to achieve a 20GHz bandwidth device with an ER of 6 dB and an OMA of -9 dB. The

3 dB additional modulation penalty comes from the fact that the RRM should be biased

closer to the resonance. The doping level, and also the coupling coefficient of the 1Vpp

driven RRM, are required to be smaller. This is almost a general trend: low doping

levels in RRMs generally offer a higher OMA, at a lower bandwidth. Both stem from

the fact that for small doping the optical loss is smaller, and thus the quality factor and

equivalently the Finesse of the RRM is increased. However, the additional photon de-

cay time results in a lower electro-optical cutoff frequency, as explained in

chapter 3.2.1. In fact, to achieve a high ER, the designer is forced to also reduce the

coupling coefficient (in order to get close to critical coupling condition) which further

penalizes the bandwidth. In our project, since we had 2Vpp available, we opted to

implement the highly doped device, illustrated by the green curve.

Low junction capacitance RRM

In an ideal case, the doping level of the RRM phase shifter can be freely set by the

designer. The RRM design process that is so far explained relies on this freely control-

lable doping level. However, it is interesting to investigate how any required bandwidth

and ER in RRMs can be achieved by a fixed doping level, which is dictated by a stand-

ardized fabrication process, e.g. optimized for other devices present on the same

wafer. In this regard, we designed and implemented a second RRM type, with a low

doped (exactly identical to LJC introduced in chapter 2.1) phase shifter. This doping

level is almost one order of magnitude smaller than the optimized doping already

shown in this chapter. The smaller phase shifter doping, as explained, drastically pe-

nalizes the bandwidth by increasing the photon decay time (𝜏𝑔) inside the RRM. To

address this problem one might suggest to increase the coupling between the bus

waveguide and the ring, to reduce 𝜏𝑔 and thus to increase the bandwidth. Though this

method can mitigate the bandwidth problem, it significantly burdens the ER, since ex-

tremely high coupling, together with a small round trip loss (resulting from low doping)

results in a highly over coupled RRM, and thus even the maximum achievable ER

would be very small.

A possible solution to mitigate this problem is to bring the highly doped regions closer

to the waveguide, as is demonstrated in [60]. In this approach the bandwidth is in-

creased not only by reduction of 𝜏𝑔 due to high absorption of contact doping, but also

by reducing the series resistance of the waveguide. Hence, this method does not re-

quire a very low coupling coefficient to maintain critically coupling, and thus can provide

an acceptable ER. However, the actual additional optical loss induced in this method

is not simply controllable since the optical loss increases exponentially with regards to

the highly doped region distance from the waveguide. Moreover, the additional loss

varies independently of the coupling coefficient in the fabrication process, which ne-

cessitates a 2D space design of experiment (DOE) variation on the layout, to ensure

achieving the required performance.


Our approach to simultaneously increase bandwidth in LJC RRMs while maintaining a

high ER is to increase the coupling to the tap waveguide 𝜅2. As mentioned, the tap

waveguide (port D in Figure 3.7) in the previous design was only weakly coupled to the

ring in order to provide a feedback for the control system. However, a higher 𝜅2 in-

creases the extinction ratio (since it is regarded as the round trip loss) as well, with the

benefit that it would be scaled with the same ratio as the bus coupling 𝜅1, since the

waveguides are fabricated during the same process step.

Figure 3.11 Maximum achievable optical modulation amplitude vs. modulation bandwidth for various

coupling coefficients to the bus (𝜿𝟏) and to the tap (𝜿𝟐) waveguides, for 2Vpp drive voltage, and extinc-

tion ratio above 5dB. The black square represents the selected design point.

The design steps are similar to the ones explained for highly doped RRMs and there-

fore will not be repeated here. The final results are summarized in Figure 3.11, which

shows achievable design points which all provide ER>5dB given a 2Vpp drive voltage.

All points on the same curve have the same value for tap coupling 𝜅2, and on each

curve the bus coupling increases from left to right. This is in essence equivalent to the

dashed curves in Figure 3.9, with the difference that 𝜅2 is varied instead of the doping

level. The drawback is clear: for any given bandwidth, the OMA is more penalized than

for the high-doping case, since the additive penalty due to the smaller quality factor is

not partially compensated by an increase in refractive index change. The black square

marks the selected design point which offers a bandwidth of 12.5 GHz with an ER of 5

dB and an OMA above 7 dB.

3.4.2 Sensitivity reduction to fabrication inaccuracies

After calculation of the required coupling coefficients, in the next step, we need to prac-

tically design the RRM layout and the bus/tap waveguides in order to realize the

targeted coupling factors. For this purpose, we used the RSoft software for 3D-time

domain simulations of the coupling section. As shown in Figure 3.12 (a), we opted to

bend the bus waveguide in the coupling section. This slight modification comes with

two advantages: 1) it reduces the optical loss in the directional coupler (since the var-

iation of the gap becomes more adiabatic) and 2) as it will be shown, it reduces the

uncertainty of the coupling factor resulting from fabrication tolerances (Δ𝜅). We vary

the gap between the bus waveguide and the RRM in order to tune the coupling. As


shown in Figure 3.12 (b), the required gap (defined as the minimum spacing between

the bus/tap and the ring waveguide edge) is found to be 302 nm in order to achieve the

targeted 𝜅1=0.304, and for the tap port should be 540 nm to achieve 𝜅2=0.06. Note

that the radius of the RRMs is set to 10.1 µm to achieve a free spectral range of of

FSR=9.7 based on group index of ng=3.87 which is calculated by FimmWave CAD

Software.

Figure 3.12 (a) Top view of the structure used in FDTD 3D-simulations of the coupling section of the

RRM. The inset with cross section shows ridge Si waveguides (red) with oxide cladding (blue) at the

coupling point (b) Calculated coupling coefficient vs. gap size. The inset shows a simulated propagating

TE0 mode.

In practice, a common source of fabrication variation is that due to over-exposure of

the photo-resist, the width of the waveguide can be slightly smaller and thus the gap

size becomes larger than anticipated. Similarly, under-exposure will yield wider wave-

guides and smaller gaps. We simulated this undesired effect by accordingly changing

the width and the gap of the coupled waveguides. For instance in Figure 2.13 (a) each

point on the red curve corresponds to a different lithography bias, where the target

point is indicated by a black circle. The difference between the coupling factor of the

maximum over-exposure (smallest width, most right point) and maximum under-expo-

sure (largest width, most left point) is 0.34-0.3 = 0.04. These coupling factors were

calculated for a conventional coupling structure shown in the inset of Figure 3.13 (a).

It should be noted that a wider waveguide possesses a smaller coupling factor since

the modes are more confined inside each waveguide, and this effect is larger than the

effect of the gap size.

Figure 3.13 Coupling coefficient versus correlated variation of gap and width (as a result of under/over-

exposure) for (a) conventional and (b) optimized design, for three different heights of the slabs. The

insets show the top view of the coupling structures for which 𝜿 is calculated.


Another major source of coupling coefficient uncertainty (Δ𝜅) resulting from fabrication,

is the etch-depth tolerance. Nominally the etch depth should be 130 nm resulting in a

90 nm slab height (corresponding to the red curve in Figure 3.13). However, it is pos-

sible for the etch depth to vary by about 10%, which is undesirable. Thus, we assume

80 nm and 100 nm for the minimum and maximum possible slab heights (ℎ𝑠), respec-

tively, with coupling coefficients shown in blue and yellow curves in Figure 3.13.

As shown in Figure 3.13 (b) our new design drastically reduced the dependency of ĸ

factor on ℎ𝑠 since by bending the waveguide, variations in ℎ𝑠 will push both modes to

the same direction (inwards in case of a deeper etch and outwards in case of shallower

etch). Hence, it does not significantly affect their mode overlap, while in the conven-

tional design (Figure 3.13 (a)) it only displaces the mode inside the ring and modifies

the overlap substantially. By applying fine tuning corrections, the uncertainty arising

from “etch depth” and “exposure” is reduced from Δ𝜅 = 0.11 to only Δ𝜅 = 0.03. The

same concept is also applied for the design of LJC RRM, and the values of the gaps

are calculated to be 440 nm and 470 nm to achieve coupling coefficients of 𝜅1=0.12

and 𝜅2=0.1, respectively.

3.4.3 Design of Optical Add-Drop Multiplexer (OADM)

Ring resonators are suitable for WDM systems due to their wavelength selective per-

formance. On the receiver side, there needs to be an optical filter, e.g. an optical add-

drop multiplexer (OADM) before sending the signal to a wideband photodetector, in

order to demultiplex the channel. The OADMs should ideally be wideband enough not

to add additional penalty to the signal. However, excessively high bandwidth results in

crosstalk between neighboring channels and can result in eye closure. In our case, we

aimed for 20GHz bandwidth for the OADMs.

Apart from bandwidth, optical loss in the OADMs should be limited: ideally all the re-

ceived optical power for a given channel should be transmitted to the drop port. This

requires the device to function at the critical coupling condition. The critical coupling

condition is achievable by respecting the condition 𝜅1 = 𝜅2, provided that the intrinsic

waveguide loss is negligible, since it implies that the round trip loss would be equal to

the coupling loss.

The top-view and the cross section of the coupling region of the designed OADM are

shown in Figure 3.14. Generally, the design of the OADMs is more straightforward than

that of the RRMs since they do not need to be doped or electrically connected. It mainly

consists in 3D FDTD optical simulations performed in RSoft. First, as mentioned, the

critical coupling condition requires equal coupling coefficients on both sides 𝜅1 = 𝜅2

since the other sources of loss are negligible mainly due to the absence of doping.

Moreover, in the OADM the waveguide does not have to be a ridge waveguide and

can be fully etched. Hence, the etch depth is removed as a source of fabrication-in-

duced uncertainty of the coupling coefficient.


Figure 3.14 (a) Top view of the designed OADM with Wwg=430nm and LRT=5.5µm. The inset shows

fully etched waveguides in the cut-line of the coupling section. (b) The dependency of coupling coeffi-

cient on wgap in the depicted OADM, (c) the variation of quality factor (red curve, right) and the device

bandwidth (blue curve, left) with respect to coupling factor.

Based on our simulation results, it is preferable to increase the width of the waveguide

and then to increase the length of the straight coupling section (called racetrack) to

achieve a targeted coupling coefficient. This approach reduces the sensitivity of the

device to fabrication tolerances, since the length has less uncertainty than the width,

according to their one order of magnitude difference in sizes. Also the coupling coeffi-

cient depends linearly on the racetrack length and exponentially on the waveguide

width and gap. Figure 3.14 (b) shows the calculated coupling factor for a waveguide

width of Wwg = 430 nm and a racetrack length of LRT = 5.5 µm.

In order to set a suitable coupling coefficient, according to the dynamic model of the

ring resonator, we calculated the optical transfer function of the OADM for various cou-

pling values. It should be noted that unlike the RRMs, here 𝜆𝐵𝑖𝑎𝑠 is forced to be set

exactly at the resonance wavelength in order to transmit maximum power to the output.

Similar to what was explained for the peaking effect in RMMs, in the case that the

OADM is not exactly tuned to the laser wavelength, the detuning causes an increase

in the bandwidth, which comes at the cost of higher optical loss. We picked 𝜅 = 0.36

as the optimum point which yields a bandwidth of 23 GHz and still avoids intersymbol

interference. We fixed the radius of the ring to R=7.8 µm, which leads to an FSR of

9.1nm. The bending loss at this radius is still negligible for our fully etched waveguide

according to finite element model simulations. We calculated the FSR based on the

group index calculated by FimmWave CAD Software with the value of 𝑛𝑔=4.38 for our

waveguide structure at 𝜆=1.55 µm. The optical loss of the OADM is calculated to be

0.6 dB.


3.4.4 Experimental results

Characterization of resonance based devices is slightly more complicated than of the

rectilinear devices since due to the wavelength dependency of the performance, ER,

OMA and bandwidth should be measured simultaneously, or should be measured in a

wide wavelength range and then expressed as a function of detuning1. A block diagram

of the high speed measurement setup is shown in Figure 3.15 (a). The output of a

tunable laser (1510 nm to 1640 nm) is coupled into the RRMs, to which a small signal

voltage provided by a 50 GHz VNA is applied. The signal is then transmitted through

a fiber to a commercial 30 GHz photo-receiver, and the output is sent back to the VNA

to measure the electro-optical S21. For low speed measurements, at each detuning

close to the resonance the wavelength sweep is recorded for both 0 V and 2 V, and

the values for OMA and ER are calculated. It should be noted that since the RRMs are

naturally sensitive to fabrication, for the sake of comparison, here we present the

measurement results of two RRMs with a similar layout, which we simply call RRM1

and RRM2.

Figure 3.15 (a) Measurement setup used for electro-optical S21 measurements. (b,c) Optical

modulation amplitude (blue curves, left) and Extiction Ratios (red curve, right) of two RRMs versus

detuning assuming 2Vpp drive voltage. (d,e) Electro-optical cutoff frequency of the two RRMs versus

wavelength.

The measured OMA (blue curve, left) and ER (red curve, right) of the RRM1 and RRM2

devices are respectively shown in parts (b) and (c) of Figure 3.15. They are measured

in the vicinity of the resonance frequency, within a FWHM detuning range. Although

the exact values vary upon different devices, they all deliver an OMA better than -7 dB

at the detuning where 5 dB ER is achieved by applying 2Vpp. The reason for the asym-

metric response of the RRMs in regards to detuning is explained already in

chapter 3.4.1. The electro-optical cutoff frequencies of the RRM1 and RRM2 devices

are shown in parts (d) and (e) of Figure 3.15. It can be seen that at these points the

RRM1 and RRM2 devices feature 28.5 and 31 GHz bandwidths, which is in a very

good agreement with the 29 GHz bandwidth that was targeted. The distinguishing fea-

tures of the wavelength dependent bandwidth, i.e. the asymmetricity on the sides of

1 The devices were characterized by Jovana Nojic at IPH.


the resonance frequency, as well as a sharp dip close to the resonance, are exactly

matching with predictions of our dynamic model of the rings (see Figure 3.8 (d)). This

sudden jump gets more significant for over-coupled RRMs, as is the case in our imple-

mented RRM device.

On the variation of different RRM device performances along the same wafer, it should

be mentioned that usually devices with a higher OMA have a smaller bandwidth, and

vice-versa, as is also clear in comparison of RRM1 and RRM2 performances. As a

matter of fact, most fabrication inaccuracies which result in a higher OMA (e.g. a

smaller coupling factor) result in a lower bandwidth (e.g. by increasing the photon de-

cay time). However, if these deviations from the targeted values are small, the OMA

and bandwidth can be traded-off by changing the detuning of the ring. For instance,

for higher detunings, the bandwidth is increased while the OMA is reduced. Thus, small

variations of coupling factor or doping level can be compensated by exploiting the

wavelength dependency of the RRMs. To verify this, and also to exhibit the high fre-

quency performance of the RRMs, the eye diagrams of several RRMs (with almost

identical layouts) at 28 Gb/s data rate are recorded and illustrated in Figure 3.16. The

eye diagrams are measured by applying 2Vpp to the RRMs, added with 1V DC, where

the laser power was set to 13 mW, and no optical or electrical amplification is used. It

can be seen that by correctly adjusting the laser wavelength (or similarly by tuning the

RRM with the thermal phase shifter) all the fabricated RRM devices can offer an ER of

at least 5 dB with an OMA better than -7 dB. According to the S21 measurements, the

RRMs should be capable of transmitting 50 Gb/s data rate. The speed of the meas-

urements shown in Figure 3.16 are only limited by the measurement setup. An in-line

power meter is used between the RRM and the photo-receiver in order to calculate the

values of OMA, the ER is calculated based on responsivity of the photo-receiver (150

V/W).

Figure 3.16 Eye-diagram measurements for similar RRMs at 28 Gb/s under 2 Vpp applied voltage, and

laser output power of 13 mW.

High speed performance of OADMs

To measure the high speed performance of the OADM devices, we used a measure-

ment setup schematically shown in Figure 3.17 (a). The modulator signal is produced

using a commercial 30GHz electro-optical modulator and is then transmitted to the on-

chip OADMs. The output is then sent to a high speed photo-receiver and is sent back

to the VNA for S21 measurement. In order to extract the S21 of the OADM, the other

sources of bandwidth limitation should be subtracted. Thus the same measurement is

performed in the absence of the OADM and is subtracted from the measured S21.


Figure 3.17 (a) Measurement setup used for S21 optical measurement. (b) S21 measurements of three

similar OADMs. (c) Eye diagram measurements at 14, 20 and 25 Gb/s.

The results of the S21 measurements after this calibration are shown in Figure 3.17

(b) for three different OADM devices with the same layout. Though there are slight

performance variations between the three, all the measured devices feature the tar-

geted bandwidth of 20 GHz. The insertion losses of the OADMs are measured to be

around 1.5 dB, that is 1 dB higher than expected from the simulations, which can be

attributed to excessive intrinsic waveguide loss (due to scattering defects or higher

sidewall roughness) as well as directional coupler loss which is neglected in our static

model as mentioned under equation (3.12).

In order to confirm the high speed performance of OADMs, a modulated signal (using

a commercial 30G modulator) was fed to the OADMs, detected by the aforementioned

photo-receiver and is then visualized by a 20 GHz real time oscilloscope. The open

eyes up to 25 Gbps are shown in Figure 3.18 (c). It should be noted that though the

bandwidth of the OADMs is about 21 GHz, the 20 Gbps eye diagrams measured with

and without (not shown here) OADMs are indistinguishable, meaning that using the

OADM does not much penalize the eye opening up to 10 GHz. The reason can be

seen in the electro-optical S21 diagrams of the OADMs, where the additional penalty

of OADM below 10 GHz is negligible. This is important for the system design since

calculating the aggregate bandwidth of a system is not straight-forward, and a com-

monly used equation like 1/𝑓𝑠𝑦𝑠𝑡𝑒𝑚2 = ∑ 1/𝑓𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡

2 could be an over-simplification,

especially for systems including RRMs and OADMs since due to the peaking effect,

their transfer functions could be highly non-linear. In our case, using the simplified

equation results in an under-estimation of the overall bandwidth. Indeed to our

knowledge the only accurate way of designing/characterizing the full system is to ana-

lyze the pseudo-random bit sequence along the system.


Performance metrics of LJC RRMs

Low doped RRMs are generally suitable for applications which require a high OMA and

ER, at a low modulation speed. Both high efficiency and low bandwidth stem from a

long photon lifetime inside the ring. Since we were interested in measuring open eyes

at least up to 25 Gb/s, in the design of LJC modulators we intentionally reduced photon

decay time by increasing the light coupling to the tap port, which also drives the mod-

ulator back to critically coupling regime and thus offers a high ER. The measured

wavelength-dependent OMA (blue curve) and the ER (red curve) under 2Vpp drive

voltage are shown in 3.18 (a). For a 4 GHz detuning (marked with dashed lines) -4 dB

of OMA and 6 dB extinction ratio is achieved. At the very same detuning, the 3 dB

electro-optical cutoff frequency of the RRM is measured to be 9 GHz. It is noteworthy

that the device bandwidth is increased to around 20 GHz, when the detuning is set to

8 GHz. However, at this point the values of OMA and ER are reduced to -7 dB and 2

dB, respectively. For a data transmission system, this penalty requires applying a

higher optical power, or similarly using an optical amplifier after the RRM to avoid non-

linear effects. Both approaches will drastically increase the power consumption. How-

ever, it should be noted that LJC RRMs have a 3 fold smaller capacitance than the

highly doped RRMs, which results in a reduction in RF power consumption.

Figure 3.18 (a) Measured wavelength-dependent OMA (blue, left) and ER (red, right) values under

2Vpp drive voltage (b) Small signal bandwidth of the RRMs at 1V bias voltage. (c) Eye diagrams of the

LJC RRMs under 2Vpp and 20mW laser power.

To verify the high speed performance of the LJC RRMs, eye diagrams are measured

under the same conditioned as explained before in the current chapter for high doping

RRMs. To avoid eye closure the RRM is detuned further from the resonance which

results in a lower OMA, and thus the laser power is increased to 20mW. The overshoot

visible in the eye diagrams are caused by the peaking effect of the LJC RRMs.

3.5 Conclusion

Compact lumped element modulators allow for dense integration of the electro-optical

devices on chip. In this chapter, we first investigated the performance improvements


of the lumped element modulators and compared their performance with widely used

travelling wave devices both in terms of bandwidth and power consumption. Since

such compact devices do not suffer from RF losses inside the device, and do not re-

quire an external RF termination resistor, they feature at least a 5 fold improved power

consumption compared to a well-designed travelling wave modulator. The bandwidth

of lumped element devices is highly dependent on the output impedance of the driver,

which makes the co-integration of an electronic driver and the optical chip advanta-

geous. We then introduced meandered MZMs as lumped element devices which are

compact from an RF point of view while they possess a long phase shifter as in the

travelling wave devices. The latter allows for reduction of 𝑉𝜋 and the drive voltage com-

pared to the traditional lumped element modulators. The implemented devices showed

open eyes at 32 Gb/s using a 50 Ω driver, while being terminated. Reaching high

speeds up to 50 Gb/s for a non-terminated device requires low output impedance driv-

ers to be wire bonded to the chip.

We then investigated the resonance based modulators, and using static and dynamic

models of the rings, we designed and implemented high speed RRMs. We demon-

strated RRMs with ER above 5 dB, OMA better that -7 dB and an electro-optical cutoff

frequency of 29 GHz.

In comparison with other optical wide band modulators, the meandered modulators

potentially have the lowest possible power consumption amongst them. Compared to

short lumped element modulators, the power consumption is reduced since by increas-

ing the phase shifter length, the capacitance increases and drive voltage decreases

with the same scaling factor, but the power consumption is reduced due to its quadratic

dependence on the drive voltage. However, the bandwidth limitation arising from the

output impedance of the driver is the main drawback of this structure. The driver should

also be capable of driving a high capacitance with a high current which is challenging

at high speeds. One solution to reduce the capacitance of meandered modulators is

to use them in a Michelson interferometer structure. The recent developments in the

on-chip isolators/circulators makes it possible to use Michelson interferometers without

inducing back-reflection to the laser. In contrast, the bandwidth of the RRM devices is

less sensitive to the type of drivers. Moreover, their selective wavelength performance

enables realization of WDM systems on a single bus waveguide.

59

4 High Efficiency SiP Modulators with Vertical

Phase-Shifters

61 4. High Efficiency SiP Modulators with Vertical Phase Shifters

The focus of the last two chapters was to optimize the device “architecture” in SiP

electro-optical modulators. All the devices that are so far proposed and demonstrated

in this thesis rely on the same phase shifter with a cross section shown in Figure 2.1

(a), only with a modified doping level. Utilizing the same type of phase shifter allows

for implementing the modulators based on the process design kits that are provided by

multi-project wafer runs. In this chapter, we turn our attention on optimizing the modu-

lator phase shifter, i.e. the cross section of the device. In particular, we aim to enhance

the modulation efficiency (∆𝑛𝑒𝑓𝑓 for a given voltage) by increasing the overlap between

the optical mode and the altered depletion region. Realization of such proposed mod-

ulators requires in-house fabrication, which will be explained in this chapter. The

proposed phase shifter can be used in any of the aforementioned structures, i.e. trav-

elling wave, meandered, compact lumped element and ring resonator modulators.

4.1 Introduction

Depletion type phase shifters based on the alteration of the free carrier density in a

reverse biased diode have been established as one of the most promising approaches

in silicon electro-optical modulators. They are capable of extremely high-speed modu-

lation fundamentally limited only by their RC time constant (since carrier transit time is

typically not the limiting factor). The efficiency of depletion based phase shifters is a

function of the amount of displaced carriers with respect to the applied reverse voltage,

and thus equivalently of the linear capacitance (with higher capacitances resulting in

higher efficiencies in terms of phase shift per volt). Therefore, increasing the modula-

tion efficiency requires a higher linear capacitance. As mentioned in the previous

chapter, increased capacitance penalizes the modulation bandwidth (𝑓𝑖𝑛𝑡 = 1/2𝜋𝑅𝑙𝐶𝑙),

and even more so for travelling wave modulators where the RF loss has quadratic

dependency on 𝐶𝑙. In order to keep the time constant at a low level, the series re-

sistance should be decreased, which in turn requires a higher doping level, and thus

increases the optical loss. Moreover, the capacitance of the phase shifters depends

on the depletion width of pin junctions and thus on the applied voltage. Consequently,

both bandwidth and the DC modulation efficiency depend on the applied voltage levels,

which leads to nonlinearities in device performance and limits their suitability to com-

plex modulation formats. As we described in detail in [44], when a phase shifter is

extremely highly doped, it can be helpful to achieve both goals. In this case, the device

behaves more linearly, since depletion width and thus capacitance are almost constant

with respect to the applied voltage. Moreover, the capacitance, and thus also the mod-

ulation efficiency, are increased by the high doping levels and become independently

adjustable by the width of the intrinsic region interposed between the p and n doped

layers [44]. The high doping comes with a major drawback which is clearly the higher

optical loss due to absorption by carriers. Our method to address this problem is to

define a structure which is highly doped only in the vicinity of the depletion width, and

consists in defining lightly doped (or ideally not doped) in regions where carriers cause

excess waveguide losses without contributing to index modulation. The hard part is to

define a fabrication process for practical realization of such a structure. In this chapter

4. High Efficiency SiP Modulators with Vertical Phase Shifters 61

we propose the fabrication of two different depletion based phase shifters with 1) com-

bination of selective ion implantation and epitaxial overgrowth, and 2) in-situ doped

epitaxial growth phase shifters. Both allow unprecedented control over the definition of

the doping profiles and thus allows breaking previously limiting design tradeoffs. Spe-

cial emphasis is placed on achieving high modulation efficiency and low power

consumption, while maintaining acceptable insertion losses and high bandwidth.

In chapter 4.2, we first introduce the basic geometry of the proposed phase shifters

and compare their performance metrics with the state of the art. In chapter 4.3, the

fabrication of the device is described and modeled, and the expected performance of

the phase shifter is simulated for both types of phase shifters. Design examples of

lumped element (LE) and travelling wave (TW) modulators relying on the proposed

phase shifters are given in chapter 4.4 to validate their applicability. The fabrication

process which is followed to realize the devices is explained in chapter 4.5. Finally, the

experimental results of fabricated devices are reported, and then we explain the pos-

sible improvements.

4.2 Phase Shifter Concept

The modulation efficiency of depletion type silicon photonic phase shifters is funda-

mentally determined by the two factors: 1. the linear junction capacitance 𝐶𝑙, which

determines the number of free carriers being displaced inside the waveguide vs. the

applied voltage as 𝐶 = 𝑞/𝑉 and 2. the overlap between the capacitance and the optical

mode. Higher doping levels lead to a higher capacitance and thus a higher efficiency.

However, they also result in a higher free carrier absorption and thus in increased in-

sertion losses. For example, increasing the n and p doping levels by a factor 5 in the

phase shifter shown in Figure 4.1 (a), from n = p = 5e17 cm−3 to n = p = 2.5e18 cm−3,

results in an effective index change Δ𝑛𝑒𝑓𝑓 increase from 8e-5 to 16e-5 for a 2Vpp ap-

plied voltage (with 1 Vbias) and optical losses increasing from 1.2 dB/mm to 7.1 dB/mm

(calculated for a waveguide with 400 nm width, 220 nm height, a 100 nm slab height

and a 20 nm intrinsic region width) [44]. The loss increases by a factor 6 while Δ𝑛𝑒𝑓𝑓

is only doubled. The two quantities scale differently, mainly because the variation of

the depletion region width (Δ𝑊𝑑𝑒𝑝) is proportional to the square root of the junction

doping. Also the overlap between the mode and the capacitance is reduced for high

drive voltages. On the other hand the waveguide losses scale directly with the dopant

concentrations (even slightly supra-linear [32]) for a fully doped waveguide.

In such configuration, assuming a fixed applied peak to peak voltage, trading off inser-

tion losses against OMA results in an upper limit to the practical carrier density in such

a configuration, beyond which the total optical loss becomes unacceptable. On the

other hand, the intrinsic bandwidth of depletion based phase shifters scales favorably

with increasing doping levels. For instance, the low doped and high doped versions of

Figure 4.1 (a) (n=p= 5e17 cm−3 and n=p = 2.5e18 cm−3) have intrinsic bandwidths of

35 and 61 GHz, respectively. This improvement stems from linear dependency of the

conductivity on doping level, and square root dependency of 𝐶𝑙 on doping concentra-

tion.


Figure 4.1 Schematic cross-section of different phase shifter configurations. (a) Conventional and (b,c)

modified lateral junctions with (b) narrow highly doped regions in the vicinity of the junction and (c)

doping compensation at the corners of the ridge waveguide. (d,e) Vertical junctions with narrow highly

doped regions in the vicinity of the junction with (d) top contacting with polycrystalline or amorphous

Silicon or (e) contacting by means of the highly doped n+ and p+ layers (the proposed phase shifter).

(f) Silicon-insulator-Silicon capacitive phase shifter (SISCAP). (g) In-situ doped epitaxially grown phase

shifter [44].

Based on these arguments, one may conclude that the highly doped regions should

be restricted to the immediate proximity of the depletion region rather than to the whole

phase shifter waveguide cross section. In the ideal case, where the highly doped re-

gions only exist in the immediate vicinity of the depletion region, waveguide losses and

phase shift efficiency will follow similar scaling with doping concentrations, making it

possible to freely trade them off against each other [44]. The structure shown in Fig-

ure 4.1 (b) represents a hypothetical (in a sense that it is close to impossible to be

fabricated) illustration of this concept. Following our already explained example, if in

this structure the doping concentrations are set to a high value of n+=p+ = 2.5e18 cm−3

within 15 nm of the 20 nm wide intrinsic region (we picked 15 nm width for p+ and n+

regions so that the depletion region remains confined in the highly doped regions under

of 2 V drive voltage) and the rest of the waveguide is lightly doped with n-, p- = 5e17

cm−3, an optical loss of 1.7 dB/mm almost equal to the low doped version of Fig-

ure 4.1(a)) and a Δ𝑛𝑒𝑓𝑓 of 16e-5 (identical to the index change of the highly doped

version of Figure 4.1(a)) can be simultaneously achieved. Thus, this idea (if it could be

practically implemented) yields a substantial improvement. In this case, since the linear

resistance 𝑅𝑙 remains the same, and linear capacitance 𝑅𝑙 is increased, the intrinsic

bandwidth of the phase shifter is reduced to 23 GHz, which is still reasonably high. In

fact, the unnecessarily high intrinsic bandwidth of the phase shifter has been reduced

to a practical level (23 GHz is compatible with 28 Gb/s) to increase the modulation

efficiency without sacrificing the insertion loss of the phase shifter. It should be noted

that the actual insertion loss can be even reduced, and the reduction in device band-

width can be partially compensated, since higher efficiency allows for shorter devices,

since the total insertion loss is 𝛼𝐿𝑑𝑒𝑣, and as we have seen in chapters 2 and 3 the

device length for both travelling wave and lumped element modulators increases when

the device length is shortened.

In practice however, since this structure is impractical to fabricate due to the lack of

control over horizontal dopant distribution (requires almost nm accuracy), alternative

solutions need to be explored. In this regard, in [61], a doping compensation method


is used to reduce the carrier density in the regions that are far from the junction, i.e.

waveguide corners, by locally reverse doping of the ridge waveguide, which yields a

device schematically shown in Figure 4.1 (c). The optical losses is improved to around

1 dB/mm and the modulation efficiency of 2.67 V∙cm is measured, which corresponds

to a Δ𝑛𝑒𝑓𝑓 of 5.8e-5 for 2Vpp, and 25.6 GHz bandwidth. Nevertheless, in this approach

the control over doping profiles is far from optimum.

Figure 4.1 (d) shows a cross-section of a modulator relying on the same concept as

(b), but with a vertical junction. This structure can be fabricated, e.g. by means of epi-

taxial growth of an in situ doped Silicon layer stack [62]. In this way, the thickness of

each layer can then be controlled in the range of a few nanometers, since it is not

formed with a mask, but with epitaxial growth of silicon which is a relatively slow pro-

cess and the layer thicknesses can be controlled by growth time. Nevertheless, the

structure shown in Figure 4.1 (d) is a big deviation from standard process, since it

requires planarization of the oxide cladding e.g. by chemical mechanical polishing

(CMP), followed by the deposition of poly- or amorphous silicon to define the top con-

tact. Amorphous and poly silicon are inherently lossy materials in contrast to single

crystalline silicon, due to defects and dangling bonds, and require treatments, e.g. by

hydrogen atoms to reduce absorption to a practical level [63]. Moreover, doping pro-

cesses to establish n-contact would be challenging, since they are not optimal in terms

of optical losses per material conductivity [64]. Though in principle a local recrystalli-

zation of such materials is possible since the amorphous or poly-silicon is partially

grown directly on single crystalline silicon [65], it is a complex process. The silicon-

insulator-silicon capacitive phase shifter (SISCAP) shown in Figure 4.1 (f) [66], while

offering a very high modulation efficiency for the aforementioned reasons, suffers from

similar constraints due to growth of non-crystalline silicon in terms of optical loss versus

electrical connectivity.

It should also be mentioned that interdigitated doping patterns [67, 68] have also been

used as another means to increase the phase shifter efficiency of depletion based

modulators. This doping method can very effectively increase the capacitance and thus

the modulation efficiency and significantly reduce 𝑉𝜋𝐿 [69] to around 1 V∙cm. As a ben-

efit, interdigitated modulators can be fabricated by dopant compensation which is a

relatively straight-forward fabrication process. However, in their moderately or low

doped form, they do have a much reduced linearity compared to the device proposed

here. Furthermore, the performance of such devices are highly dependent on the

overly accuracy of the p and n doping layers, which is a challenge at the wafer scale.

The structures shown in Figure 4.1 (e) and (g) on the other hand do not require an

additional poly- or amorphous silicon layer for contacting the device, since the thin p+

and n+ layers defining the pin diode can also be used for electrical connectivity [44]. In

these structure, most of the volume of the phase shifter is left undoped, which results

in a lower optical loss, and thus the doping level can be pushed higher which is bene-

ficial both in terms of increasing efficiency and decreasing the series resistance. Here,

we introduce two main methods to realize such a device:

1) Sequential selective implantation and epitaxial overgrowth [44],


2) In-situ doped epitaxial growth of silicon [62].

The latter (phase shifter cross section shown in Figure 4.1 (g)) is simpler to fabricate,

with the obvious drawback of high optical losses in the interconnect waveguides. The

former (phase shifter cross section shown in Figure 4.1 (e)) has the additional benefit

that the capacitor defined by the overlay of the n+ and p+ regions can be restricted to

the waveguide core and further freely sized to trade off modulation efficiency against

bandwidth.

A side benefit of both proposed configurations is enhancement of the phase shifter

linearity. As mentioned, since a high volume of the phase shifter is not doped, it is

possible to increase the doping levels to very high concentrations, up to 1e19 cm-3.

Applying very high doping levels, the linear capacitance is primarily determined by the

intrinsic region and remains almost constant for various applied voltages. Thus, both

the modulation efficiency and the bandwidth of the phase shifter remain more stable

under different applied voltages.

4.3 Phase Shifter Design and Proposed Fabrication Process

In order to realize the proposed structures shown in Figure 4.1 (e) and (g), the ap-

proach for device fabrication is to alternate local masked ion-implantation with epitaxial

overgrowth, and thus fabrication process is required to provides a sufficient vertical

control over the doping profile. Here, we introduce two different methods to realize the

vertical phase shifters. We optimize the doping levels to achieve an acceptable overall

performance. It is important to note that unlike a specific device design, here we are

optimizing the cross section of a phase shifter, which can be used in any modulator

structure, i.e. travelling wave MZMs, meandered or short LE MZI modulators, and res-

onance based modulators. Thus, we define a general figure of merit and sweep

different parameters including high doping in the junction (p+, n+) in the quest to max-

imize the FOM. We address the two introduced methods separately.

4.3.1 Ion implanted epitaxially overgrown phase shifter

Before modeling the device with the actual dopant distribution resulting from the mod-

eling of a realistic fabrication flow, we performed a preliminary design study based on

idealized dopant distributions with sharp interfaces (as represented in Figure 4.1 (e)).

This design optimization served to target the process flow of the fully modeled device.

As explained in chapter 2, the doping levels in the p- and n-doped regions inside the

waveguide are the result of a tradeoff between optical loss, modulation efficiency and

electro-optical bandwidth. In addition, the height of the intrinsic region ℎ𝑖𝑛𝑡 will also

affect the linear capacitance and consequently the bandwidth. It also affects the line-

arity of the device, as ℎ𝑖𝑛𝑡 ≫ Δ𝑊𝐷𝑒𝑝 is required for a high linearity.

We define the figure of merit (FOM) as Δ𝑛𝑒𝑓𝑓2 . 𝑓𝑐/(𝛼𝐶𝐿) and we choose the parameters

in order to maximize it. This FOM is especially useful for the design of a lumped ele-

ment modulator for a fixed dual drive voltage (push-pull). The effective index change

is calculated between 0 V and 2 V. The insertion losses resulting from free carrier


absorption 𝛼𝐿𝜋/2 (with 𝐿𝜋/2 the phase shifter length required to achieve 𝜋/2 phase

shift) are proportional to 𝛼/Δ𝑛𝑒𝑓𝑓, and the energy per bit proportional to 𝐶𝑙𝐿𝜋/2 and thus

also 𝐶𝑙/Δ𝑛𝑒𝑓𝑓. Thus, maximizing this FOM strikes a good balance between insertion

losses, intrinsic phase shifter bandwidth and power consumption.

Figure 4.2 (a) Effective index change for 2Vpp drive voltage. (b) Required phase shifter length for MZM

in push-pull configuration. (c) Phase shifter loss per cm (d) Total loss (calculated based on (b) and (c)).

(e) Intrinsic bandwidth of phase shifter 𝒇𝒄 = 𝟏/𝟐𝝅𝑹𝑪 at 1V bias. (f) Figure of merit. The crosses indicate

doping level maximizing the figure of merit which is chosen for the final phase shifter [44].

We evaluated the FOM for intrinsic layer heights ℎ𝑖𝑛𝑡 ranging from 30 to 90 nm, opti-

mizing for each ℎ𝑖𝑛𝑡 the doping levels n+ and p+, as well as the overlay of the highly

doped layers. The thicknesses of the highly doped layers were fixed to ℎ𝑛+= 20 nm

and ℎ𝑝+ = 35 nm as we did not intend to attempt the fabrication of thinner layers. The

cumulative thickness of the bottommost intrinsic region (between the underlying oxide

and the p+ layer) and of the p+ layer was set to 70 nm, the waveguide height and width

were respectively set to 290 nm and 470 nm since these numbers resulted in good

modal confinement and optical overlap. The etch defining the slab regions on the sides

of the waveguide was assumed to reach the top of the n+ layer. Moreover, the distance

between the edge of the waveguide and the onset of the highly doped contact wells

was assumed to be 800 nm, chosen as a tradeoff between waveguide losses and

phase shifter series resistance. Trading off phase shift efficiency for device linearity,

we found ℎ𝑖𝑛𝑡= 40 nm and a p+/n+ layer overlay of 250 nm to yield good results, in

which case n+ = 6e18 cm−3 and p+ = 5e18 cm−3 maximizes the FOM (resulting in ΔW𝑑𝑒𝑝

= 17 nm at 2 V reverse bias). This results in an intrinsic cutoff frequency ℎ𝑖𝑛𝑡 = 49.2

GHz, waveguide losses 𝛼 = 3.0 dB/mm, and a capacitance per unit length 𝐶𝑙= 1.14

pF/mm (all at 1 V reverse bias), as well as an effective index change Δ𝑛𝑒𝑓𝑓 of 22e-5

for a 2 Vpp drive voltage, resulting in 𝑉𝜋𝐿 of 0.70 V∙cm.

Figure 4.2 shows Δ𝑛𝑒𝑓𝑓 for 2Vpp versus doping concentrations assuming ℎ𝑖𝑛𝑡= 20nm,

as well as 𝛼, 𝑓𝑐, 𝑉𝜋/2 the total loss of a phase shifter sized to achieve π/2 phase shift

with a 2Vpp drive (𝛼𝐿𝜋/2) and the maximized metric Δ𝑛𝑒𝑓𝑓2 . 𝑓𝑐/(𝛼𝐶𝐿), all at 1 V reverse


bias. The calculated intrinsic bandwidth of the phase shifter improves at higher doping

levels, since the capacitance asymptotically converges to that of a parallel plate ca-

pacitor with electrodes spaced by a separation ℎ𝑖𝑛𝑡, while the series resistance

continues to drop at high doping concentrations. Also Δ𝑛𝑒𝑓𝑓 improves at higher con-

centrations, while the total loss improves at lower doping levels. As explained above,

the FOM strikes a balance between these quantities.

It should be noted that unlike our design space in chapters 2 and 3, where we assumed

p and n doping levels to be equal, here we sweep them independently. The main rea-

son is that since the thickness of the two layers are picked to be slightly different (due

to limitations arising from the fabrication process) we believed it might be beneficial to

opt for different doping levels for p+ and n+. It is also noteworthy that it would be ideal

to reduce the p+ and n+ layer thicknesses, and increase the doping with the same scale.

For instance, dividing the thickness by a factor 2 and at the same time doubling the

doping concentration, does not considerably change the 𝛼 (doping dependency of ab-

sorption is only slightly supra-linear), and almost does not change conductivity (slightly

reduces due to deteriorating carrier mobility), nor changes the capacitance significantly

(since it is mainly determined by ℎ𝑖𝑛𝑡) but can increase the Δ𝑛𝑒𝑓𝑓 due to higher doping

level of the junction. However, in practice it was challenging to fabricate layers shal-

lower than 20 nanometer.

The so far mentioned simulations for the idealized case (with abrupt change in doping

layers) are useful to determine the required doping level. Nevertheless, in order to

investigate the performance of a device obtained from a realistic fabrication flow we

need to model the fabrication process. Our proposed process [44] is shown in Fig-

ure 4.3. The modelled process which is fully implemented in TCAD starts with SOI

wafers with a 2 μm buried oxide layer with a 220 nm thick silicon layer on the top. First

a thinning process (for 70 nm) of the silicon layer is performed by thermal oxidation

followed by wet etching in a buffered HF solution. The local boron implantation is ap-

plied through a 10 nm protective oxide layer following a corresponding lithography step

with a dose of 4.5e13 cm−2, an implantation energy of 10 keV and a 0° tilt angle. Due

to the high diffusivity of boron atoms, and due to the difficulty of forming shallow, highly

implanted wells, it is crucial to start with the p-doping at the bottom of the stack. After

removal of the lithography mask and of the scattering oxide, a high temperature dopant

activation step is applied for 5 s at 1030°C. Next, a moderate temperature pre-cleaning

step (4 min at 700°C) is applied followed by an 80 nm epitaxial silicon overgrowth

performed by low pressure chemical vapor deposition (CVD) for 16 minutes at 800°C.

Disilane (Si2H6) is used as a precursor and deposition occurs at a rate of 5 nm/min.

The temperature of the process is kept at the lower end to ensure minimal boron diffu-

sion. The n-doped layer is defined by local phosphorus implantation through a 10 nm

sputtered scattering oxide layer with a cumulative dose of 8e12 cm−2 applied in two

steps, respectively with 15 and 30 keV and a 0° tilt angle. Since phosphorus is a heav-

ier atomic species, the implantation depth of the n-doped layer can be better controlled.

After removal of the lithography mask and scattering oxide and following dopant acti-

vation and surface pre-cleaning, the silicon stack is completed by a second 140 nm


silicon epitaxial overgrowth step. This layer is required to ensure light confinement in-

side the waveguide. The total thickness of the layer stack was targeted to be 290 nm

and was jointly optimized with the partial silicon etch depth of 140 nm stopping at the

interface to the n+ layer defining the 470 nm wide ridge waveguides in order to maxim-

ize mode overlap. All feature sizes, including waveguide definition, are compatible with

deep UV 193 nm optical lithography. In order to provide contacts to the back-end Al

interconnects, highly doped regions with a targeted doping levels of 1e20 cm−3 are

defined on either side of the waveguides by ion implantation, here too spaced 0.8 µm

from the waveguide edge. For ion activation and crystal annealing a rapid thermal an-

nealing step is applied at 1030°C for 5 seconds. The diffusion of the dopants are also

taken into account in our TCAD mode and finally, a metal layer is deposited using lift-

off of sputtered Al to form the electrical contacts.

Figure 4.3 Fabrication flow of the proposed phase shifter relying on sequential ion-implantation and

epitaxial silicon growth [44].

The explained fabrication process is modeled in TCAD and the resulted structure is

shown in Figure 4.3 (a). It can be seen that a mean doping level of 6e18 cm−3 and

7e18 cm−3 are respectively obtained for p and n doped regions over thicknesses ℎ𝑝+=

40 nm and ℎ𝑛+= 15 nm which can be seen in Figure 4.3 (b), with an intrinsic layer

thickness ℎ𝑖𝑛𝑡= 40 nm, which we define as the region with dopant concentrations below

1e16 cm−3, which is close to what was initially targeted. Nevertheless, the thickness of

the p-doped layer is higher than initially targeted due to the difficulty of obtaining shal-

low boron implants due to the high diffusivity of boron atoms. The increased p-doped

region width and peak dopant concentrations result in increased waveguide losses (4.2


dB/mm at 1 V reverse bias) in comparison with the idealized device already described.

Moreover, the p and n dopant concentrations respectively drop from 6e18 cm−3 and

7e18 cm−3 to 1e16 cm−3 over 10 nm and 6 nm wide intermediate regions, the effect of

both of which is to reduce the junction capacitance and increase 𝑉𝜋𝐿 by a small amount.

In fact the capacitance is 1e-9 F/m at a 1 V DC bias and the efficiency is increased to

0.74 V⋅cm between 0V to 2V applied voltage).

Figure 4.4 (a) Realistic dopant distributions inside the phase shifter as simulated by TCAD, with positive

concentrarion representing n-doping and negative, p-doping. (b) Carrier distribution along the dashed

line in (a). (c) Optical field profile of the guided mode [44].

Next, we need to calculate the voltage dependent performance metrics of the device.

We used the same simulation pipeline as explained in detail in chapter 2.2.1. Figure 4.5

shows the calculated characteristics of the modeled phase shifter versus voltage. It

should be mentioned that the linear capacitance of the phase shifter is only varied by

around 17% from 0V (1.16 nF/m) to 2V (0.97 nF/m) applied voltage, which results in

small nonlinearities. Reversely, the linear resistance of the phase shifter is increased

by a low amount from 3 mΩ∙m to 3.3 mΩ∙m as can be seen in Figure 4.5 (a) (green

curve), which partially compensates the capacitance reduction in terms of a stable in-

trinsic bandwidth, which is shown in Figure 4.5 (b).

It is noteworthy that chirping due to variation of the loss inside the phase shifters is an

issue for depletion based silicon modulators. The higher doping levels cause ℎ𝑖𝑛𝑡 to be

considerably bigger than Δ𝑊𝑑𝑒𝑝, and thus the loss-induced modulation to be small. As

can be seen in Figure 4.5 (c) the phase shifter loss is varied from 4.4 dB/mm to 3.9

dB/mm under a 2V applied voltage.


Figure 4.5 DC characteristics and bandwidth of the ion-implanted phase shifters vs. applied voltage: (a)

Series resistance (green curve, right) and capacitance (blue curve, left). (b) Intrinsic cutoff frequency,

(c) optical insertion loss, and (d) effective index change versus applied reverse bias [44].

A crucially important aspect of device manufacturability is its performance dependency

on misalignment and fabrication tolerance. In particular, misalignment of doping layers

can affect the performance of the conventional phase shifters quite dramatically. As

shown in [70] a misalignment of 150 nm can decrease the modulation efficiency (in-

crease 𝑉𝜋𝐿) by a factor 3. In a horizontal phase shifter a misalignment in doping layers

changes the gap (shown in Figure 4.6(a)) while in a vertical structure it varies the junc-

tion capacitance size or the overlay. As shown in Figure 4.6 (b) and (c), for the vertical

phase shifter (solid lines) 50 nm misalignment results in a modification of the modula-

tion efficiency by less than 20%, while it results in a reduction of the modulation

efficiency by 40% for the lateral phase shifter. It is important to mention that an increase

of the effective index change, as seen for the vertical phase shifter for negative misa-

lignment can have the same negative impact on the device performance, since it

increases the junction capacitance and thus reduces the intrinsic phase shifter band-

width.

Figure 4.6 (a) Schematic of a conventional (up) and vertical (down) junction phase shifters. Zero misa-

lignment is defined as zero gap and 250 nm overlay, respectively for lateral and vertical junction phase

shifters. (b) Effective index change versus misalignment for a 2 Vpp drive signal and (c) percent change

of the effective index change relative to the nominal value versus misalignment. In all curves, equal p-

and n-doping concentrations are assumed, as labeled in the legend (in units of cm−3) [44].


4.3.2 In-situ doped phase shifter

We use the aforementioned method in order to optimize the doping levels, i.e. n+ and

p+, for the in-situ doped epitaxially grown silicon phase shifter with the cross section

shown in Figure 4.1 (g). As explained, the doping levels are result of a tradeoff between

the bandwidth and modulation efficiency. The effective index change (under 2Vpp ap-

plied voltage) and the optical loss per unit length (at 1V DC bias) are shown in

Figure 4.7 (a) and (c) respectively, as a function of doping concentrations. The height

of the intrinsic region in the pin junction is fixed to ℎ𝑖𝑛𝑡=50 nm, while the height of the

doped layers are ℎ𝑝+ =30 nm and ℎ𝑛+ =20 nm, respectively. The phase shifter length

required to achieve a full extinction in the MZM in push-pull configuration is calculated

based on Δ𝑛𝑒𝑓𝑓, and is shown in Figure 4.7 (b) as 𝐿𝜋/2 = 𝜆/(4 Δ𝑛𝑒𝑓𝑓). The resulting

insertion losses (𝛼𝐿𝜋/2) is plotted in Figure 4.7 (d). The calculated intrinsic bandwidth

of the phase shifter (shown in Figure 4.7 (e)) improves at higher doping concentrations

due to proportional reduction of linear resistance and sub-linear increase of the linear

capacitance (𝐶𝑙) which is mainly determined by the intrinsic region between the two

doped layers. Similar to the previous process, we used the FOM Δ𝑛𝑒𝑓𝑓2 . 𝑓𝑐/(𝛼𝐶𝐿) to

choose the optimal doping levels for the phase shifters, as can be seen in Figure 4.7

(f) doping concentrations of n+=4e18 cm-3 and p+=8e18 cm-3 maximize the FOM.

Figure 4.7 Performance metrics of in-situ doped modulators vs. n, p doping levels: (a) Effective index

change between 0 V and 2 V reverse bias. (b) 𝑳𝝅/𝟐 derived from (a). (c) Optical loss per cm. (d) Total

loss for a phase shifter reaching 𝝅/𝟐 phase shift (e) intrinsic bandwidth (f) the figure of merit. The

crosses mark doping level maximizing the figure of merit and is chosen for the final phase shifter doping

[44].

In contrast to ion-implanted phase shifter, the simulations based on ideal layers with

abrupt transition, should be close to the fabricated device. The fabrication process will

be explained in more details in chapter 4.5. The high doping concentrations yield a

phase shifter with linear capacitance of 1.62 nF/m and a low linear resistance of 2.3

mΩ∙m both at 0 V bias, and thus a moderate intrinsic cutoff frequency of 42 GHz. An


effect index change of Δ𝑛𝑒𝑓𝑓=2.4e-7 by 2Vpp is achieve, while the average carrier in-

duced losses is 4.5 dB/mm.

4.4 Modulators based on Vertical Phase Shifter

After performance modeling and designing the cross section of the phase shifter, in

order to illustrate the device performance utilizing the proposed phase shifters, we

evaluate complete device designs for both ion-implanted and in-situ doped silicon wa-

fers. For each phase shifter type, we explain the design of both travelling wave (TW)

and lumped element (LE) modulators, with emphasis obtaining relatively low drive volt-

age. The main benefit of the proposed phase shifters is their relatively high efficiency

(small 𝑉𝜋𝐿) which stems from a high junction capacitance.

In terms of intrinsic bandwidth, the negative effect of the additive capacitance can be

partially compensated by a low linear resistance. This is especially the case for LE

modulators since the bandwidth is limited only to the RC time constant of the circuit

(𝑓𝐿𝐸 = 1/2𝜋(𝑅 + 𝑅𝑑𝑟)𝐶), provided that the output impedance of the driver is relatively

small (𝑅𝑑𝑟<50Ω). In contrast, for TW MZM, the RF losses as the main source of the

bandwidth limitation (as explained in chapter 2), quadratically increase with 𝐶𝑙, while

linearly decrease with reduction of 𝑅𝑙. Moreover, the relatively high optical losses of

phase shifters (4.2 dB/mm for ion-implanted and 4.5 dB/mm for in-situ doped) further

limits the OMA of the TW MZMs. Nonetheless, the long phase shifters of the TW MZMs

allow for realization of low drive voltage modulators.

4.4.1 Ion implanted epitaxially grown phase shifter

In the fabrication process of the proposed phase shifter (see Figure 4.3) the local ion-

implantation should be performed at the wafer scale. Hence, fabrication of the pro-

posed devices requires wafer size masks. In fact, design and layout of the structures

should be prepared prior to the wafer preparation and silicon deposition. Selective ion

implantation, forming the junction capacitance, allows for accurate implementation of

the vertical junction by delicately setting the overlay (see Figure 4.6), in order to max-

imize the overlap and avoid fringing capacitances. In the following, two different

devices are going to be presented which utilize the ion implanted layer stack.

Travelling wave modulator

The layout of the 1.6 mm long TW MZM is shown in Figure 4.8 (a). Due to the relatively

high capacitance of the phase shifter (𝐶𝑙=1 pF/mm), the RF mode is slowed down. This

increases the phase mismatch between the optical mode and the RF signal along the

transmission line. Thus, in order to establish a quasi-phase matching, the optical path

is made longer by introducing recovery loops (see chapter 2.2.4) as is shown in (b) at

three sections along the MZM with 400 µm spacing. The length of the recovery loop is

opted to be 280 µm, to increase the optical path length by 70%. The reason for this

choice can be seen in Figure 4.8 (c) where the RF index of the travelling signal is

shown at the frequency of interest (17 GHz), the RF refractive index is 6.9, while the

group index of the optical mode is 3.89 and 4.38, respectively for the shallow etched

and fully etched waveguides. The spacing between each two sections is relatively short


in order to avoid RF back reflections. The recovery loops are opted to be fully etched,

to allow low bending radii (10 µm) and thus keeping the interconnect waveguides short.

As can be seen in Figure 4.8 (b), the metal extensions with 15 µm spacing are imple-

mented along the transmission line in order to reduce the linear resistance and

consequently increase the electro-optical bandwidth [28].

In general, it is preferable for MZMs to target 50 Ω impedance matching to be compat-

ible with the commonly used RF cables, and to avoid RF back reflections. Here, due

to the extremely high junction capacitance of the phase shifters, achieving 50 Ω by

replacing the signal and ground lines is out of reach. Moreover, a lower characteristic

impedance reduces RF loss along the transmission line (see equation (2.13)) and thus

increases the device bandwidth. Therefore, we opted for 25 Ω impedance target. The

calculated characteristic impedance of the device is shown Figure 4.9 (a).

Figure 4.8 (a) Layout of the travelling wave device. (b) Detailed view of the recovery loops used to

obtain phase matching. (c) RF effective index of the transmission line as a function of frequency [44].

Based on the 25 Ω characteristic impedance, the RF loss along the transmission line

is calculated and shown in Figure 4.9 (b). Based on that, we can calculate the electro

optical bandwidth of the 1.6mm long modulator to be 17 GHz at 1V DC bias. The low

bandwidth is mainly due to the high junction capacitance, which reduces the required

drive voltage for full extinction to only 2.3 V. With this length, the insertion loss of the

device is 6.7 dB at 1V DV bias.


Figure 4.9 (a) Characteristic impedance of the loaded transmission line (b) RF loss per transmission

line unit length as a function of RF modulation frequency.

Straight lumped element modulator

The low 𝑉𝜋𝐿 of the vertical junction allows for realization of very compact, high band-

width modulators based on a compact LE phase shifter. Here we consider a 250 µm

long MZM, with a slightly modified overly between n+ and p+ layers (see Figure 4.6

(a)). We increased the overlay from 250 nm to 310 nm and also decreased the distance

between the waveguide edge and the highly doped regions from 800 nm to 550 nm.

The former modification yields a higher 𝐶𝑙 of 1.25 pF/mm, and the latter reduces 𝑅𝑙 to

2.66 mΩ⋅m and consequently keeps the intrinsic bandwidth at 48 GHz, all specified at

1 V DC bias as for the previous configuration of the phase shifter. The phase shifter

efficiency is thus increased to 0.6 V⋅cm enhanced by the increased overlay in order to

accommodate such a small device, at the cost of increased waveguide losses (6

dB/mm). The proposed device has an aggregate bandwidth of 34 GHz when a 4 Ω

driver is used. Due to the short modulator length the device is a lumped element up to

35 GHz. The total optical insertion loss of the device is 1.5 dB.

4.4.2 In-situ doped phase shifter

In this type of phase shifters, since all the wafer is doped, interconnects are extremely

lossy. The in-situ doped phase shifter is therefore only suitable for stand-alone devices,

unless by implementation of low loss interconnects, e.g. by deposition of silicon nitride

on top of the oxide cladding, and use it for on-chip waveguides. Nevertheless, the

junction capacitance is higher than of the ion-implanted phase shifters, which results

in a lower 𝑉𝜋𝐿, but also penalizes the bandwidth. Therefore, the devices which are ob-

tained by the in-situ doped phase shifter are more compact compared with ion-

implanted phase shifter devices. In order to reduce the fringe field, the waveguide in

all the devices which rely on in-situ doped phase shifters are asymmetrically etched:

p- and n- sides are etched 200 nm and 150 nm respectively. Since high capacitive

phase shifters are more suited for short modulators, we first illustrate a LE element

modulator based on in-situ doped phase shifter.

Straight lumped element modulator

The layout of the 250 µm long LE modulator is shown in Figure 4.10 (a). As mentioned,

in an LE modulator the electro-optical bandwidth of the device is only limited by the RC


time constant and thus, assuming an ideal driver, similar scaling of the linear capaci-

tance 𝐶𝑙 and the inverse linear diode series resistance 1/𝑅𝑙 does not affect the intrinsic

bandwidth. On the other hand, a higher capacitance enhances modulation efficiency.

Moreover, the short device length makes it less sensitive to waveguide losses. Thus,

LE modulator designs naturally gravitate towards high doping levels, a high capaci-

tance and a low resistance. In that design space, the output impedance of the driver

𝑅𝑑𝑟 plays an important role since the series resistance of the modulator is small. The

calculated electro-optical bandwidth is shown in Figure 4.10 (b). For our device, the

total series resistance of the modulator is 9.2 Ω. A driver output impedance of 𝑅𝑑𝑟=10

Ω (Figure 4.10 (b), blue curve), halves the cutoff frequency. Reducing the driver im-

pedance to a low but still realistic value 𝑅𝑑𝑟=4 Ω leads in a cutoff frequency of 35 GHz.

For this device, the total insertion loss is calculated to be 1.3 dB. However, the device

requires 11Vpp drive voltage for full extinction.

Figure 4.10 (a) Layout of the 250 µm lumped element MZM. The red and blue layers respectively rep-

resent p- and n-doped wells, the green layer represents metal electrodes. (b) Electro-optic S21 of the

lumped element MZM for two driver output impedances [62].

Travelling wave modulator

In order to further reduce the required drive voltage, longer phase shifters are required

and using TW devices becomes a necessity. One main difference between the TW

modulators based on in-situ doped and the ion-implanted phase shifters is that, for the

former, discrete recovery loops are no longer an option. This is mainly due to the fact

that the whole wafer is doped, and thus the recovery loops are as lossy as the phase

shifters. Hence, a 70% recovery loop, will results in 70% additional insertion losses

which is unacceptable. On the other hand, due to extremely high linear capacitance of

the in-situ doped phase shifter (1.62 pF/mm at 0V) the RF signal is drastically slowed

down, so that use of recovery loops remains necessary to provide phase matching.

We tackle this problem by introducing continuous phase mismatch compensation by

meandering the waveguide. The layout of the proposed device is shown in Figure 4.12

(a). Since the bent waveguides are not fully etched, the minimum allowed bending

radius in order to avoid high bending losses is calculated to be above 30 µm. Hence,

the increased distance between the metal lines and the waveguide emerges as a prob-

lem, which we address by implementing finger structures as shown in Figure 4.12 (a),

which reduce the linear resistance of the loaded transmission line (see chapter 2.2.5).


For our proposed TW modulator, the 2D simulations based on FEM (which we used in

chapter 2.2.4 to design standard TW modulators) does not suffice and cannot predict

the crucial transmission line parameters, i.e. the RF index and the RF loss along the

device. Hence, a full 3D simulation was performed1 using HFSS software to evaluate

the device performance. In these simulations, the RF mode (with RF frequencies rang-

ing from 1 GHz to 36GH) is launched at one end of the transmission line, and the E-

field is calculated along the waveguide. The complex electrical S21 yields the attenu-

ation of the RF signal along the device, and the differential phase allows for calculation

of the RF mode. The results are used to modify the bending radius (equivalent to re-

covery loop length), and also to calculate the electro-optical bandwidth of the TW

modulator. The calculated E-field along the waveguide at 21 GHz is shown in Fig-

ure 4.11 (b).

With a total phase shifter length of 1.4 mm, the TW modulator based on in-situ doped

phase shifter requires only 2 Vpp drive voltage in push-pull configuration in order to

achieve full extinction, as 𝑉𝜋𝐿 at 2 V is 0.5 V∙cm for this type of phase shifter. The

insertion loss resulting from carrier absorption is 6.3 dB. Added with other loss sources

i.e. the sidewall roughness and scattering loss (as will be explained in the next chapter)

the total insertion loss is 8 dB. The electro-optical cutoff frequency calculated by HFSS,

is predicted to be 21GHz. This bandwidth is mainly limited by RF loss along the trans-

mission line mainly due to the high junction capacitance. It is important to mention that

the TW modulator has a targeted characteristic impedance of 25 Ω, while achieving 50

Ω is very challenging due to high junction capacitance. Nevertheless, the TW modula-

tor will have around -9.5 dB back reflection, even if measured in a 50 Ω system.

Figure 4.11 (a) Layout of the travelling wave modulator with continuous phase mismatch compensation

(b) Intensity of E-field along the waveguide calculated by 3D HFFS simulations at 21GHz. The device

layout is fully exported to commercial HFFS software. In this figure, the other layers (metal lines, etched

silicon etc.) are not shown, in order to reveal the E-field.

4.5 Fabrication

The first step to realize the proposed modulators is to prepare the wafers including the

silicon doped layer stack either by ion-implantation and silicon overgrowth or by epi-

taxial growth of in-situ doped silicon layers. Since we did not have a chemical vapor

deposition (CVD) tool available, the wafer preparation was done in collaboration with

Peter Grünberg Institute (PGI 9) at Jülich Research Center through Jülich Aachen Re-

search Alliance (JARA). They used low pressure chemical vapor deposition (LPCVD)

1The 3D simulation in HFSS was performed by my colleague Dr. A. Moscoso Martir at IPH.


for silicon growth. For ion implanted wafers (Figure 4.3), which required silicon over-

growth on highly doped (~5e18 cm-3) regions, although 8 inch size masks were

designed and taped out and were ready to be used in ion-implantation process of the

wafer, an undesirable outcome stopped the wafer preparation process. It turned out

that the silicon growth rate on top of highly doped regions was slower than the growth

rate on top of intrinsic (undoped) silicon regions. Nonetheless, they achieved a high

crystalline quality of overgrown silicon on top of doped areas, but the different growth

rate necessitated at least a CMP process to level out the surface on wafer with high

accuracy, and could further complicate the fabrication process. Hence, we focused our

effort to fabricate the vertical phase shifter modulators based on achievable in-situ

doped phase shifters.

Figure 4.12 Illustration of the fabrication flow of in-situ doped phase shifter [62]

Compared to the ion-implanted phase shifter, the in-situ doped one comes with its own

benefits and drawbacks: Its most obvious advantage is the relative ease of the wafer

deposition process, since the entire wafer can be grown in one CVD step. It also does

not induce additional ion-implantation caused damages to the crystalline silicon struc-

ture. Moreover, in contrast to ion-implantation, in-situ doping gives higher control over

the doped layer thicknesses, especially for boron for which the formation of highly

doped shallow layers is very challenging for ion-implantation. Furthermore, in-situ

doped silicon does not require dopant activation and thus the thermal exposure after

deposition of in-situ doped layers is limited to the subsequent silicon deposition, i.e.

800°C. On the negative side, since the entire wafer is doped, high fringe capacitance

penalizes the bandwidth. Moreover, interconnects will have a high optical loss. We try

to address the former by asymmetrically etching the waveguide, as can be seen in

Figure 4.12.

The required process flow of the device is shown in Figure 4.12. It starts from a com-

mercially available silicon on insulator (SOI) wafer with 220 nm thick silicon on top of

2 µm buried oxide. After thinning down the device layer to 50 nm by thermal oxidation


followed by wet etching in a buffered HF solution, the crystalline silicon is homoge-

nously deposited by CVD using Disilane as a precursor at a temperature of 800°C with

a deposition rate of about 5 nm/min [62]. Subsequently, dopants are intruded by dibo-

rane (B2H6) and phosphine (PH3) gases to the chamber, respectively for p- and n-

doping. The total thickness of the deposited silicon stack is chosen to be 290 nm. This

part is successfully done at PGI 9. The waveguides need to be defined by etching the

top silicon layer, asymmetrically by 200 nm and 150 nm on the p and n sides, respec-

tively. As mentioned, we try to restrict the capacitor to the waveguide region, which

can be partially achieved by the deeper etch on the p-contact side. Unfortunately, in

this process flow the capacitor is extended up to the n++ well on the n-contact side,

resulting in a suboptimum capacitance. Although in principle it can be compensated by

a reverse doping, we were reluctant to add more complexity to the process flow.

Once the waveguides are formed, the highly doped regions are realized on both sides

of the waveguide by ion implantation targeting a doping level of ~1e20 cm-3 which is

enough to overcompensate the p+ doping (in-situ doped) in the highly n-doped side.

The high doping level is required in order to establish an ohmic contact between the

silicon and the metal and thus reduce the contact resistance. In order to minimize the

contact well mediated excess optical losses while maintaining an adequate RC band-

width, the highly doped regions are defined 500 nm and 800 nm (target values) far

from the waveguide edge, respectively. Subsequently, gold contacts are deposited by

means of thermal evaporation with a thickness of 0.2 m and patterned with a lift-off

process. We explain each process in more detail in the following.

Figure 4.13 First row shows LC phase shifter, and second row shows HC phase shifter. (a),(d) The

targetted cross section of the phase shifters. (b),(e) Rutherford backscattering spectrometry (RBS)

measurements performed on the grown epitaxial layer stack. (c),(f) Doping concentration along the

vertical axis inside the silicon layer stack (with origin on top) from Electrochemical Capacitance Voltage

(ECV) measurement.


We opted to develop two slightly different layer stacks, one with the exact same cross

section and performance metrics explained on chapter 4.3, and also a second one with

a higher linear capacitance which allows for lower 𝑉𝜋𝐿, in the cost of a lower electro-

optical bandwidth and higher optical loss. The former layer stack which has a lower

capacitance (LC) is more suitable for TW modulator whose bandwidth scales with the

square of 𝐶𝑙. On the other hand, the high capacitance (HC) phase shifter is more suited

for very short LE modulators, since the additional capacitance can be partially com-

pensated with a reduced linear resistance, and also their length is not limited to

insertion losses. The cross section of the LC and HC phase shifters are shown in Fig-

ure 4.13 (a) and (d), respectively. The doping level of the n-doped layer is slightly

higher in HC wafer, and also both layers are slightly thicker (to reduce 𝑅𝑙 to compen-

sate the higher 𝐶𝑙). But the main difference is the shorter intrinsic region between the

n- and p-doped layers (30 nm) which results in a higher capacitance.

Figure 4.14 Simplified flowchart of the fabrication process flow for symmetrically etched modulator after

wafer preparation. The numbers on top right of boxes show the order.

As shown in Figure 4.13 (b) and (d) respectively for LC and HC silicon layer stacks, a

Rutherford backscattering spectrometry (RBS) measurement is performed by PGI 9,

which confirms the relatively high crystalline quality of the wafers. The real doping pro-

files inside the wafers are also measured by Electrochemical Capacitance Voltage

(ECV) measurement which confirms that the achieved doping concentration inside the

wafer does not deviate much from the targeted doping profile.

Figure 4.14 shows the process flow after the wafer preparation. First, a standard clean-

ing (SC) process is required to fully remove the protective resist from the samples,

which we coated prior to dicing the 8 inch wafer into 2 by 2 cm pieces. Note that two

steps of SC are particularly effective for removing polymer contamination, e.g. photo

resist: Piranha, which is a mixture of 50 ml sulfuric acid (H2SO4) and 150 ml hydrogen

peroxide (H2O2), and also RCA1 which contains 3 parts of deionized water, 1 part hy-

drogen peroxide and 1 part ammonia (NH3). After the SC process, we define the

regions which require a shallow etch process using electron beam lithography (EBL),

which was done for us in service mode at the Institute Semiconductor Electronics (IHT).

Since we required adiabatic tapers between shallow etched (SE) waveguide to deep

etched (DE) or fully etched (FE) waveguide, to minimize the exposure time of EBL, we

used the positive photoresist of Poly-methyl methacrylate (PMMA). Thus, the wave-

guides are defined by etching 3 µm on both sides of the waveguide. These trenches

allows for reduction of EBL writing time, since it covers a smaller area. It would have

been also possible to define the tapers as well as asymmetric waveguides by a nega-

tive resist, but it required defining a hard mask (e.g. SiN) on top of the waveguide,

which could further complicate the fabrication process. Note that SiO2 cannot be used


as a hard mask since any process removing the hard mask could damage the buried

oxide layer.

Once the SE patterns are defined by EBL, we use the reactive ion etching (RIE) tool

equipped with interactively coupled plasma (ICP) to etch the top silicon layer. We opted

to use a cryogenic process in order to avoid additional surface and sidewall roughness

in the waveguide and thus to reduce the excessive optical losses. In the cryo etching

process we use SF6 and O2 gases simultaneously in order to etch the cooled silicon

wafers. The advantage of cryo-RIE is that, in this process the passivation mechanism

happens only on the cooled silicon surfaces, and sidewall passivation and etching of

the silicon surfaces occurs simultaneously [71]. When the sample warms up from cry-

ogenic condition to room temperature, the passivation layers desorb and thus the

passivation mechanism in this process avoids the scalloping effect in the sidewall pro-

file and leaves behind clean wafer surfaces and reactor walls [72]. Moreover, the cryo-

etching process allows for very shallow etching due to the low thickness (<5 nm) of the

passivation layer. It also yields a very high etch selectivity to photoresist masks (>15:1),

which is a necessity, especially since a high EBL precision, requires thin photoresist.

In addition to reduction of the sidewall/surface roughness, we also prefer to reduce the

etch rate. The performance of our final device is highly sensitive to the etch depth, as

over-etching increases the series resistance and thus reduces the modulation band-

width, and under-etching causes high optical losses arising from increased mode

overlap with highly doped regions. Therefore, it is crucial to slow down the etch rate

and to have a decent control over the etch depth. The ICP-IRE tool was optimized for

the Bosch process, as well as deep trench etching, and was very suitable for our FE

process. However, we needed to develop a process in order to achieve a slow etch

rate for SE, while maintaining the surface/sidewall roughness at a minimum.

Generally, in a cryo ICP-IRE process, there are four ways to reduce the etch rate: 1)

to decrease the ICP power, 2) to reduce RF power, 3) to reduce the temperature (has

a small effect), 4) to reduce SF6:O2 flow ratio. The latter is due to reduction of Fluorine

radical density compared to Oxygen radical density, which results in more passivation

than actual silicon etching. Reducing the pressure can also decrease the etch rate.

However, both approaches (reduction of SF6:O2 and pressure reduction) drastically

impact the etching profile as a side effect. We decided to reduce the etch rate by re-

duction of ICP power, which has the side effect of decreasing the aspect ratio. We tried

to compensate these negative effects by fine tuning temperature and gas flow. After

tuning the parameters, we opted for an ICP power of 450 watt. This drastic reduction

of ICP power (from 700 watt), made an undesirable problem, that is, since the auto-

matic impedance matching system of the tool was designed for higher power levels,

the plasma could not ignite in some cases. The problem was solved by slightly increas-

ing the RF power to 15 watt at -125°C, with SF6 and O2 gas flow of 37.5 sccm and 14

sccm, respectively at a pressure of 5 mTorr with 10 sccm Helium background flow.

This process could yield a relatively slow etching process of 1.5 nm/s. However, it

undesirably pushed the sidewall profile to positive angles.


Figure 4.15 SEM picture of the test samples for shallow etching process, after (a) 60 seconds and (b)

100 seconds. (Note: sidewall roughness is caused by opt. lith. resist). Etch rate (c) and etch depth (d)

of shallow etching process vs. time. SEM picture of sample after (e) 20 sec, and (d) 30 sec etching time.

Figure 4.15 (a) and (b) show the SEM picture of a cryo etched silicon using the SE

process for 60 seconds. Note that the structure is defined by optical lithography with

the sole purpose of evaluating the etch depth, and the extreme sidewall roughness is

mainly due to the shape of the resist, while our actual waveguides are defined by EBL

which uses a fairly thin PMMA layer (180 nm). The averaged extracted etch depth and

etch rate vs. time are plotted respectively in Figure 4.15 (c) and (d). It shows that using

the SE process results in 140 nm etch to require 80 seconds. However, the measure-

ments (Figure 4.15 (c)) suggest that the etch rate decreases with time. It could be

attributed to ignition stage, where as in the first 5 seconds of the etching process the

ICP power should be set at a high level (>1500 W) to ensure formation of plasma. This

step was mandatory since without formation of plasma, the high back reflection could

damage the ICP-RIE tool, and the ignite time could not be reduced to less than 4 sec-

onds, since otherwise plasma could not be formed.

Another important issue in our etching process is the etching selectivity between silicon

and the oxide. We prefer to maximize the Si/SiO2 selectivity since some regions on the

chip (including the tapers) are exposed in 2 different etch steps (for instance both SE

and FE). As mentioned, we used a rapid process for fully etched waveguides, with an

etch rate of 16 nm/s. In a case where Si/SiO2 selectivity is not high enough, the buried

oxide layer can be partially etched away, which undermines the mechanical stability of

the silicon waveguides. Moreover, we prefer to over etch in case of FE process, to

ensure the full removal of the silicon layer. Figure 4.15 (e) shows a fully etched silicon

structure using the FE process for 20 seconds. It can be clearly seen that the sidewall

angle is close to 90°, as is the case for higher RF and ICP power levels. We tested the

effect of over-etching on silicon dioxide by over-etching other samples by performing

the FE process for 30 seconds. The additional 10 seconds correspond to 160 nm extra

etching of silicon. However, as shown in Figure 4.15 (f) the oxide layer is not affected

by over-etching (at least not visible in SEM), which confirms the high selectivity of our

process (at least better than 20:1 for Si:SiO2).


We used grating couplers (GCs) in order to couple the light into\out of the silicon chip.

We first designed the GCs based on a simplified 1D model explained in [73]. Then an

FDTD simulation was performed with RSoft. We used focusing grating couplers in or-

der to minimize the required length, and also the GCs are apodized to maximize the

overlap with output Gaussian mode of our standard single mode fiber. There are two

main challenges to fabricate GCs: 1) the proximity effect especially for gaps below 200

nm results in a slower etch rate 2) for very small feature sizes, the resist is not exposed

to the beam in the ideal form, and thus the line width would be different from the mask,

as can be seen in Figure 4.16 (a). We addressed the latter by defining a different EBL

layer for the gratings which used a higher exposure dosage, and resolution. We then

performed a design of experiment (DOE) by fabricating a 13 by 13 matrix (Figure 4.16

(b)) of GC pairs on different samples and measured their optical transmission. We

varied the gap on each row, and varied the grating width on each column. The GC pair

in the center (in the 7th row and column) corresponds to the nominal design. The optical

transmission spectrum of the GCs close to center are shown in Figure 4.16 (c), and

we picked the GC on 6th row and 8th column (green curve) for the fabrication.

Figure 4.16 (a) SEM picture of a fabricated grating coupler (the grating couplers are fabricated on in-

situ doped samples). Left: zoomed in picture of the gaps and grades. (b) Microscope image of the DOE


test sample. (c) Experimental result of the optical transmission of 9 of the grating coupler pairs with

0dBm input laser power. The yellow curve is the optical transmission of the targeted grating coupler,

while the green curve shows the maximum optical transmission. The nominal design in the 7th row and

7th column (R07C07).

Using cut-back structures, we measured the optical losses of the waveguides to be 15

dB/cm for fully-etched and 14 dB/cm for shallow etched waveguides, with 470 nm

width, while the optical losses of the multi-mode waveguides (with 2 µm width) is

around 2 dB/cm. These values are high compared to the state-of-the-art which is below

5 dB/cm for single mode waveguides. However in our case, since the length of the

MZMs are relatively short (<1 mm), the high scattering loss is bearable. Another source

of optical losses inside the MZM and also in interconnect waveguides is the bending

loss of the mode in the shallow etched waveguides. To evaluate this we fabricated

cutback structures (Figure 4.17 (a)) with various number of bends and three different

radii, i.e. 5, 10 and 15 µm. The measurement results are plotted in Figure 4.17 (b) vs

the bending length. Subtracting these measured values from the intrinsic waveguide

loss results in 25 dB/cm for 15 µm bends. We set the bending radius to be 30 µm for

the fabrication.

Figure 4.17 (a) Microscope image (polarized for edge enhancement) of the test sample used to measure

the bending loss for 140 nm etched waveguides. (b) Measured optical transmission of the cut-back

structures with respect to the bending length for 5, 10 and 15 µm bending radii.

After the etching process, the photoresist hardens due to bombardment by high speed

ions. Hence, in order to fully remove the resist from the chip surface since standard

cleaning (even with longer piranha step) was not sufficient, we perform O2 plasma

ashing with an oxygen flow of 40 sccm and 250 watt RF power for 2 hours, followed

by standard cleaning. The perfect removal of photoresist is important to avoid contam-

ination for the next etching steps. As shown in the process flow (Figure 4.12) after each

etching step, we measure the on-chip cutback structures to verify the quality of etching,

as a quality control step. In the illustrated process flow shown in Figure 4.12 it is as-

sumed that only two etch steps are formed on the chip, that is the case for a symmetric

waveguide, while realization of an asymmetric waveguide requires three etch steps

including a full etch, a deep etch and a shallow etch step. The shallow etch forms also

the grating coupler, but with a different exposure dosage in EBL.


Once the waveguides are formed and the photoresist is striped, we need to define

highly doped wells close to the waveguides in order to establish an ohmic contact be-

tween metal and silicon. Generally, a low doping level under metal contacts results in

a low quality electrical contact and can penalize the bandwidth by creating a Schottky

contact. Moreover, the highly doped regions are tailored close (<1 µm) to the wave-

guide edge to reduce the linear resistance of the device and thus increase the

bandwidth. In our case, reaching a very high doping level in contact wells is even more

crucial since they need to overcompensate the p+ and n+ doping regions of the junction,

in order to reduce the capacitance. Based on our process simulations in TCAD, we

decided each well doping to be done in two steps. For p++ doping, boron is implanted

with the dosage of 5e15 cm-2 with energy levels of 10 and 45 keV respectively. For n++

doping, phosphorus atoms are doped with dosage of 5e16 cm-2 and energy levels of

10 keV and 100 keV respectively. The second energy level is chosen in a way that the

phosphorous atoms can overcompensate the p+ doping at a 250 nm depth into the

silicon. Both implantations are done without an oxide scattering layer and with 7° tilt.

These high energy levels necessitate the use of a very thick photoresist in order to

avoid penetration of the ions into the silicon layer at resist-covered surfaces. Since our

EBL tool was not optimized for the exposure of thick (1.5 µm) PMMA we had to use

optical lithography to define the highly doped wells. As a drawback, the optical lithog-

raphy has a high inaccuracy (around 1 µm) for overlying the layers. Thus, we utilized

a large optical contact lithography mask with a DOE containing various distances of

highly doped regions (dp++ and dn++), each having a 500 µm offset against each other.

This was for short devices, as we could fit 25 LE MZMs practicable to have five different

values to for each dp++ and dn++.

Figure 4.18 (a) ideal cross section of the device, (b) fabricated device cross section. (c) Microscope

image of the MZMs after metallization, left: Y-junction, right: zoomed in picture of the phase shifter.


After both ion implantation steps (for p++ and n++), and removal of the photoresist via

plasma asher and the standard cleaning process, we perform an annealing step using

Rapid Thermal Annealing (RTA), at 1030°C for 6 seconds. Apart from annealing the

crystalline structure of silicon, this step is necessary to activate the implanted ions.

After defining the contacts using optical lithography step, we deposit a 200 nm thick

layer of gold on top of 10 nm thick titanium to enable the electrical contacts. The thin

titanium layer is necessary for mechanical stability and adhesion of the metal layer. In

the optical lithography step, we use a relatively thick (2 µm) photoresist (AZ 5114) in

image reversal. This process yields a negative sidewall profile for the photoresist, and

makes the lift-off process easier. We then lift-off the photoresist using a warm acetone

bath for an extended time.

The cross section of the targeted final device is shown in Figure 4.18 (a). As explained,

it is beneficial to asymmetrically etch the sides of the waveguide in order to reduce the

capacitance. However, for an easier fabrication process, we implemented the cross

section shown in Figure 4.18 (b), which is symmetrically matched. In fact, the fabrica-

tion process flow of the device whose characteristics are being reported, is exactly as

shown in Figure 4.12. The microscope image of the fabricated device is shown in Fig-

ure 4.18 (c).

4.6 Experimental Results

Here, we report the measurement results of a 100 µm long LE MZM with the illustrated

cross section and top view shown in Figure 4.18 (b) and (c). First, in order to measure

the optical losses, we used different types of cutback structures. These structures are

also doped with the same doping level of the device junction (in-situ doped wafer). In

order to decouple the optical losses arising from the carrier absorption, and intrinsic

(scattering) losses, on the same chip we implemented single mode (470 nm wide) and

multimode (2 µm) cutback structures. For the latter, we expect negligible scattering

losses (as confirmed by the test samples) due to a high confinement of the field inside

the silicon and low overlap with the sidewalls. Hence, the optical losses measured from

the multi-mode structures can be fully attributed to the junction doping (n+ and p+),

and was 41 dB/cm for LC and 62 dB/cm for HC phase shifters. Using the single mode

cutback structures, we extracted to intrinsic loss to be ~15 dB/cm for 470 nm wide

waveguide, as was expected according to the previously fabricated test samples.

Therefore, the total insertion losses of LE MZMs are 0.56 dB and 0.77 dB respectively

for LC and HC modulators. It should be noted that one of the major issues regarding

the device, is its unclear dp++ and dn++ due to low overlay accuracy of optical lithogra-

phy. Based on simulations for dp++=0.5 µm and dn++ =0.8 µm the additional optical loss

resulting from highly doped regions is 7 dB/cm. Therefore, the total insertion losses of

LE MZMs are extracted to be 0.63 dB and 0.84 dB for LC and HC modulators, respec-

tively.

In order to measure the modulation efficiency of the MZMs, we applied DC voltages to

one arm of MZM, and measured the optical transmission spectrum. Figure 4.19 (a) and

(b) show the measured optical power respectively for LC and HC MZM, when voltage


is applied to one MZM arm, from which we could calculate the modulation efficiency of

the MZMs. As shown in Figure 4.19 (c), the 𝑉𝜋𝐿 measured at 2 V for the LC and HC

devices are 0.37 V∙cm and 0.28 V∙cm. For the latter, it suggests that a TW MZM with

device length of 0.7 mm, can provide a full extinction with a drive voltage of 2V. This

value is one of the best reported efficiencies for depletion based modulators. Never-

theless, it should be noted that for an asymmetrically etched waveguide (targeted

device), which can offer an acceptable bandwidth, the efficiency drops (gets closer to

the simulated 𝑉𝜋𝐿 reported in chapter 4.3) due to reduction of capacitance. This reduc-

tion might not be significant, since the overlap between the fringing capacitance and

the guided mode is small.

Figure 4.19 (a) The modulation efficiency of high capacitance (blue) and low capacitance (red) modu-

lators measured at different bias voltages. (b) Normalized electro-optical S21 of the HC MZM.

Figure 4.19 (d) shows the measured electro-optical bandwidth for an LC MZM, the

cross section of which is shown in Figure 4.18 (b), with the waveguide width of 450

nm, and total length of 100 µm. The measurement setup is similar to what was shown

in Figure 3.15 (a), as we used a 50 GHz VNA with 1 Vpp output voltage added with a

DC bias voltage, and the output of the modulators was connected to a commercial

wideband photo-receiver. The electro-optical bandwidth of the device is measured to

be 6.1 GHz, 6.7 GHz and 8.5 GHz respectively at 1 V to 3 V bias voltages. Note that

as discussed in detail in chapter 3.2, the bandwidth of the LE modulators drastically

depend on the output impedance of the driver. While all the measurements are per-

formed in a 50 Ω environment, using a low impedance driver could increase the

bandwidth above 20 GHz. Moreover, by asymmetrical etching of the sides of the wave-

guide, the capacitance could decrease by more than 30%, which could further increase

the modulation bandwidth.


4.7 Conclusion

In this chapter, we presented two new concepts for the phase shifter geometry based

on highly doped vertical junctions. The ion-implanted epitaxially grown phase shifter

allows for realization of systems with small optical losses in interconnect waveguides,

while the in-situ doped phase shifter requires to use low loss intermediate materials

such as nitride if it is used in a system.

The high doping of the phase shifter has a side benefit: the linear capacitance of the

modulator is mainly dependent on the intrinsic region between p+ and n+ layers, and

varies insignificantly with respect to the applied voltage. The invariance of the device

bandwidth can be helpful for more complex modulation schemes [44]. We explained

the fabrication process of the devices based on the in-situ doped wafer, for which we

developed two different types of wafers: one with higher doping and a smaller intrinsic

region between the doped layers, which is more suitable for LE devices, and the other

with slightly smaller doping and a larger intrinsic region, which can be used to realize

longer TW modulators. The LE devices on the HC wafer featured a modulation effi-

ciency of 0.28 V∙cm (calculated based on phase shift at 2 V) and a high carrier

absorption loss of 6.2 dB/mm at 1 V bias. The LC devices have a lower efficiency of

0.37 V∙cm with a more acceptable loss of 4.1 dB/mm (at the same conditions). Inter-

estingly, despite the high optical loss, the device length would not be limited by optical

losses, as for HC phase shifter, an MZI modulator with a length of 700 µm can yield a

full extinction under 2 Vpp in push-pull configuration. As a proof of concept, we meas-

ured the fabricated devices using a 50 Ω driver, which drastically penalizes the

bandwidth. We measured the electro-optical bandwidth of 100 µm long device to be

6.7 GHz at 2 V bias. It should be noted that the presented device was symmetrically

etched, and thus part of the bandwidth reduction (>30%) is resulting from the fringe

capacitance on the p side of the modulator. Moreover, in order to improve the high

speed performance of the device, it would be beneficial (if a high speed low output

impedance is unavailable) to drive the device in travelling wave configuration with a

termination at the end of the line. It also seems necessary to use EBL (or an optical

lithography with a higher overlay accuracy) for defining the highly doped regions, since

in addition to reduction of the linear resistance, the highly doped wells in our device

also reduce the fringe capacitance and as such, higher accuracy is required in the

lithography process.

87

5 Hybrid Silicon Modulators

88 5. Hybrid Silicon Modulators

5.1 Introduction

All the devices that have so far been demonstrated in this thesis exploited the plasma

dispersion effect (PDE) as their modulation mechanism. PDE is widely used in silicon

modulators, and in particular depletion based modulators are the mainstream in mon-

olithic silicon modulators. As we showed in detail in the previous chapters, the main

problem of using PDE as the modulation mechanism is the relatively high optical losses

resulting from free carrier absorption. Moreover, the loss modulation arising from dis-

placement of the carriers inside the waveguide results in a relatively high signal

chirping which is undesirable especially for long haul communications.

It is therefore compelling to explore other possible modulation mechanisms in hybrid

silicon platforms, which are still compatible with CMOS technology. The high potential

of novel hybrid material integration for the realization of high performance electro-op-

tical/absorption modulators has already attracted a great deal of attention in the past

few years. Integration of other materials into silicon platforms can induce alternative

modulation mechanisms which can be advantageous in terms of optical loss or modu-

lation efficiency compared to PDE silicon modulators. For instance, on-chip integration

of lithium niobate (LiNbO3) on silicon, makes it possible to use the strong electro-optic

(Pockels) effect of this material and has recently been shown to yield a promising per-

formance in electro-optical modulators [74] in a CMOS compatible environment [75].

Nevertheless, integration of LiNbO3 requires wafer boding and a complex fabrication

process. Another approach implemented to exploit the Pockels effect in the SOI plat-

form is to deposit an amorphous silicon nitride (SiN) layer on top of the silicon

waveguide, which breaks the centrosymmetricity of the silicon lattice by compressively

straining it and thus unlocks the Pockels effect in silicon. Nonetheless, the PDE is also

present and takes part in the modulation, and especially since the observed electro-

optic effect is quite small, it might play a big role in the measured transmission spec-

trum. We will address this issue in chapter 5.2.

Since PDE is a wideband mechanism, its application can be extended to mid- and even

far-infrared (IR) wavelengths [76]. Alternatively for mid-IR applications, it is possible to

harness the Franz Keldysh Effect (FKE) to realize a high efficiency and low chirp mod-

ulation, provided that hybrid materials are integrated in SOI platform. Such materials

must have a direct bandgap to exhibit FKE and its bandgap should ideally be adjusta-

ble. Besides, for this purpose, it is desirable to use group four materials, which can be

monolithically grown on silicon without excessive contamination. Germanium tin

(GeSn) has emerged as a group four compound with a direct and tunable (correspond-

ing to tin content) band gap and has shown a high potential to implement IRB lasers

[15] as well as photodetectors [16]. In chapter 5.3, we present a practical design for a

GeSn electro-optical modulator based on FKE for mid-IR applications.

Optical properties of 2D materials and compounds including hexagonal boron nitride

(h-BN) [77, 78] as a dielectric, tungsten diselenide (WSe2) [79] as a semiconductor,

and graphene [80] as a semi-metallic material have attracted a lot of attention in the

past few years. In particular, graphene is well suited for integration into silicon platform

[81, 82] due to its promising potentials including efficient optical modulation, extremely

5. Hybrid Silicon Modulators 89

wideband performance in modulation and photo-detection [83] and compatibility with

CMOS technology. However, to date, most of the modulators based graphene-silicon

waveguides suffer from a low optical bandwidth, or require complicated fabrication pro-

cesses. In chapter 5.4 we present the design of a practical slot waveguide graphene-

silicon absorption modulator based on Pauli-block Burstein Moss effect.

5.2 Measuring Pockels Effect in Strained Silicon MZIs

As mentioned in the introduction, one of the most popular methods to break the cen-

trosymmetricity of crystalline structure and thus unlocking the Pockels effect in silicon

is to deposit a SiN layer on top of the silicon waveguide. It was initially shown by Ja-

cobsen et al. [24] that the amorphous Si3N4 layer acts as a straining layer, which tries

to expand the structure underneath in both horizontal directions. It is important to men-

tion that in this paper, a great effort was made in order to ensure that the measured

phase shift is solely caused by Pockels effect. For instance, a spacing SiO2 layer with

a thickness of 1 µm was deposited in between the nitride and silicon layers, in order to

minimize the overlap of the guided mode with the nitride layer. Moreover, optical trans-

mission measurements have been performed before and after deposition of the nitride

layer to ensure that the measured phase shift is resulting from nitride deposition. Nev-

ertheless, they used a photonic crystal waveguide to measure the 𝜒(2) effect.

Accurately measuring the group index inside the photonic crystal waveguide is not

straightforward due to its high wavelength dependency near the optical bandgap, and

thus adds to the uncertainty of the measured Pockels effect (𝜒𝑒𝑛ℎ(2)

= 𝑛𝑔𝜒(2)/𝑛). Finally,

a nonlinear coefficient of 𝜒(2) ≈15 pmV-1 was reported [24]. Strikingly, there appeared

to be a considerable gap between the experimentally [24, 84] and theoretically [85]

reported values of the nonlinear coefficient of strained silicon, with the experimental

results measuring a much larger coefficient. Some [86] suggested that the discrepancy

could be due to important missing physics in the existing theoretical calculations, e.g.

taking only the nearest neighbor interaction into account.

Regardless, in the following years many efforts were made to further improve the per-

formance of the modulators based on electro-optic effect in strained silicon, especially

by enhancing the strain induced Pockels effect [87, 25], and nonlinear coefficients as

large as 𝜒(2) ≈40 pmV-1 [88] and 190 pmV-1 [89] were reported. The increase in strain

induced Pockels effect was attributed to removal of the oxide layer which results in a

higher strain in silicon waveguides. Nevertheless, the measurement results were devi-

ating more from the predicted theoretical values. Motivated by these outcomes, we

developed [90] the structure shown in Figure 5.1 to investigate the electro-optic effect

in the strained silicon. The device shown in this figure consists of a 1 mm long MZI with

fully etched silicon waveguides. As can be seen in Figure 5.1 (b), a 350 nm thick silicon

nitride layer is deposited directly on top of the wafer. A spacing layer of oxide with

thickness of 850 nm is deposited below the aluminum metal contact to apply the E-

field along the MZI. The spacing between the waveguides of the MZI arms is 45 µm.

1 The devices were fabricated by our former colleague Dr. Maziar Nezhad [90]


Figure 5.1 (a) Micrograph of the Mach–Zehnder interferometer used for the experiments, (b) schematic

of the device cross section, and (c) close-up view of the waveguide junction [90].

We measured the optical transmission of the MZI by applying voltage 1) only to one of

the arms (single ended driving scheme), 2) to the two arms of the MZI with opposite

polarity (differential push-pull configuration), and 3) equally to the two MZI arms. When

we applied a voltage to either of the MZI arms, we observed [90] a phase shift of 0.025

rad/V. In push-pull configuration, the phase shift increased to 0.05 rad/V. In both cases,

the sign of the phase shift was flipped as we inverted the voltage. Note that in all the

measurements we set the substrate to common ground.

The measured phase shift (see Figure 5.2 (a), black curve) exhibiting an inverted sign

with respect to the applied voltage, had been commonly regarded as the smoking gun

for the presence of Pockels effect in the strained silicon MZIs. However, upon a closer

look at the device characteristics, we could also observe some peculiar characteristics

in the performance of the device.

Figure 5.2 (a) Normalized MZI optical transmission vs. applied differential voltage. The x-axis indicates

the voltage V1 applied to arm 1 of the MZI. (b) The differential phase shift induced in the waveguides,

extracted from (a). The black curve in (a) was measured by starting the voltage sweeps from 0 V, after

letting the device rest for a day at 0 V. The red and blue curves were measured by starting the voltage

sweep respectively from V1= −100 V and 100 V after letting the device rest for 10 min in that state. In all

cases, the opposite voltage was applied to arm 2 of the MZI. Note that though we used a symmetric

MZI, the differential phase applied to the waveguides is not zero at 0 V in the black curve due to a static

phase arising from fabrication variability-induced waveguide mismatch [90].


First, we observed a hysteresis behavior in the measured phase shift of the MZI output,

as it can be seen in Figure 5.2 (a), where the black curve shows the MZI output when

both arms were resting at 0 V for several minutes, while blue and red curves show the

MZI optical output in case the arms are soaked at ±100 V. The hysteresis character-

istics can be seen more evidently in Figure 5.2 (b) which shows the phase shifts

extracted from the MZI transmission as function of the applied voltage in the push-pull

configuration. After letting the MZI stay at a certain voltage for 10 min in either high-

voltage configurations (100 V applied to one MZI arm and -100 V applied to the other

arm), the phase response of the MZI was shifted in one or the other direction, resulting

in the hysteresis featured in Figure 5.2 (b). The same characteristics are observed in

the case that a single ended voltage is applied only to one arm of the MZI [90]. The

measurement results which correspond to the single-ended driving of one arm of the

MZI can be seen in Figure 5.3. Again the hysteresis feature of the device is evident as

the device transfer function heavily depends on the initial voltage of arm 2.

Figure 5.3 (a) Transmission through the MZI as a function of the single-ended voltage applied to arm2

of the MZI. (b) Phase shift induced in the waveguide, extracted from (a). The red (blue) curve was

measured by starting the voltage sweep from -200 V (+200 V), after letting waveguide 2 soak at -200 V

(+200 V) for 10 min. The dashed and dotted curves in (b) show modeling results based on the free-

carrier plasma effect [90].

The second anomaly observed in the device characteristics was the fact that the ac-

cumulated phase shift was accompanied by an excess optical loss. In order to

investigate the voltage dependent loss, we applied a common voltage to both arms of

the MZI in order to alter the attenuation without changing the differential phase shift.

The results are shown in Figure 5.4 (a).

Interestingly, also a charging effect was observed in the case that the time step in the

voltage sweep was increased. Figure 5.4 (b) is equivalent of Figure 5.3 (a), with the

difference that here, instead of smooth alteration of voltage with small voltage steps,

we performed the voltages sweep with 10 V steps. Between each two voltages, we

gave the device a relaxation time of 20 seconds. We started the voltage sweep from -

200 V after 10 minutes of soaking at -200V. It can be seen that for the first 150 V

change (from -200 V to 50 V) the output phase responds quickly to the applied voltage.

For applied voltages above -50 V, we observed a combination of a fast response fol-

lowed by a slow response in the opposite direction, which partially levels out the fast

response. This cannot be caused by the fast electro-optic effect. Instead, we attribute


the slow change in the output phase of the MZI to the charge accumulated in the SiN

layer, and the fast response to charge accumulated in the silicon waveguides. Similar

behavior was observed for sweeps starting from 0 V and +200 V. In fact in any case

when the voltage drifts by more than 100 V from the initial state (provided that the

device was initially relaxed at that voltage), the slow response in the MZI output begins

to appear. Interestingly, the voltage regions where the modulator response drifts in

Figure 5.4 (b) coincide with the regions where the modulator response flattens out in

Figure 5.3 (b) and 5.4 (a), suggesting that the drift can have caused the flattening.

Furthermore, the coincidence between the voltage dependent optical losses shown in

Figure 5.4 and the phase shift as depicted in Figure 5.3 (b) strongly supports the inter-

pretation that the latter is due to the plasma dispersion effect. In fact, when sweeping

from -200 V to +200 V, we a 4 dB extinction is measured as well as a phase shift of

2.4 rad, which results in 0.6 rad/dB. Assuming both to be caused by free carriers, the

expected ratio between excess optical loss and induced phase shift can be calculated

(based on equations (2.3) and (2.4) taken from [32]). Using these equations, we expect

0.65 rad/dB calculated assuming a 4 dB extinction for varying electron density and 1.3

rad/dB calculated assuming a 4 dB extinction for varying hole density. In fact the volt-

age dependent optical losses and induced phase shift are not only qualitatively

correlated, but also quantitatively scaled as expected under the hypothesis of free-

carrier effects [90]. It should be also noted that the measurements were performed on

a temperature controlled stage, and also the measured leakage currents at the highest

applied voltages of +200 V were below 70 pA which indicate that the thermal effects

were negligible.

Figure 5.4 (a) Normalized transmission of MZI as a function of the common voltage applied to wave-

guides 1 and 2. The maximum transmission was normalized to 1. The red (blue) curve was measured

by starting the voltage sweep from −200 V (+200 V), after letting both waveguides soak at −200 V (+200

V) for 10 min. The dashed and dotted curves show modeling results based on the PDE. (b) Voltage

sweep ranging from −200 V to +200 V applied to waveguide 2. Individual voltage increments are inter-

spaced by 20-second soaking times. The x-axis shows the time starting from the beginning of the sweep.

The observed hysteresis, and the drifts observed during relaxation time in Figure 5.4

(b) further suggest that a charging effect plays a role in the measured data. It could be

expected, since the amorphous SiN layer is known to accumulate a surface charge via

charged defects, with typical surface charge densities on the order of a few 1e12 cm−2,


an effect that is used for example in the passivation of solar cells [91, 92]. This surface

charge is attributed to the charging of K-centers [93]. Both the positively and negatively

charged states are thermodynamically more stable than the neutral state [90]. Moreo-

ver, the K+ state is thermodynamically favored over the K− state and thus SiN films are

usually positively charged. However, in the case of a direct contact between SiN and

a semiconductor (silicon), or even with a spacing layer of oxide in between, thin enough

for tunneling, it is possible to invert the polarity of that charge by applying a high voltage

[93]. We attribute the hysteresis seen in our measurements to a mirror charge in the

silicon waveguide building up as a response to the surface charge in the SiN film.

Moreover, the drifts seen during soaking in Figure 5.4 (b) are also attributed to the

progressive buildup of charge inside the SiN layer once the polarity of the applied volt-

age has been inverted.

It is important to mention that the absence of hysteresis during relaxation does not

necessarily indicate the absence of PDE. The reason of hysteresis observation is the

SiN film being deposited directly on top the silicon waveguide. Electrical isolation be-

tween the waveguide and the SiN film via an intermediate SiO2 layer can effectively

suppress the dynamic charge inversion, in which case the SiN film can be assumed to

be in its native positively charged state regardless of the applied voltage. Apart from

the hysteresis behavior of the device, the electric charge of the SiN film is important in

explaining the linearity of the observed voltage-dependent phase shifts around the re-

laxation voltage, i.e. 0 V in the absence of applied voltage. In the absence of such

surface charges, it could be expected that the modulator should yield a phase shift with

an equal polarity for positive and negative applied voltages (respectively corresponding

to the accumulation of electrons and holes, both reducing the refractive index of the

silicon), resulting in a very low phase shift in push-pull configuration. By applying a

positive voltage, electrons would be accumulated on the top surface of the waveguide,

and holes will accumulate at the bottom, assuming the applied voltage to be high

enough to reach the charge accumulation regime

The simulated waveguide losses and effective index change ∆𝑛𝑒𝑓𝑓 as a function of the

applied voltage to the MZI arms are shown in Figure 5.5. Each curve is based on a

different assumption of SiN surface charge concentrations. The simulations were per-

formed with TCAD from Synopsys with grid refinements close to the surface of the Si

waveguide in order to accurately model charge accumulation, after which the overlap

integral with the waveguide mode was computed [90].

In the absence of surface charge the ∆𝑛𝑒𝑓𝑓 and optical loss have the same polarity for

both positive and negative voltages, and the small offset between the point of the zero

loss and minimum ∆𝑛𝑒𝑓𝑓 for V=0 is due to the assumed low doping level of the wave-

guide. In presence of surface charge in the nitride the curves are shifted to lower or

higher voltages depending on the charge polarity, and exhibit a non-zero derivative at

0 V which results in an invertible ∆𝑛𝑒𝑓𝑓. The dashed and dotted curves in Figure 5.3

(b) and Figure 5.4 (a) show simulation results assuming nitride surface charge of

1 The simulations were performed by Dr. Florian Merget at IPH [90]


7.5e12 cm−2 and -4e12 cm−2 after soaking at respectively -200 V and +200 V. The

dashed portion of the curves is in a good agreement with the measured results. The

dotted portion deviates from the measurement results due to the fact that drifting of the

nitride surface charge at high voltages was not taken into account. It should be men-

tioned a common corrective factor of 4 had to be applied to both waveguide losses and

effective index change to fit the modeling with the measurements. While the corrective

factor was the same for both metrics, it does not invalidate the conclusion that the

proportionality between phase shift and waveguide losses reflects the coefficients from

equations (2.3) and (2.4).

Figure 5.5 Simulated waveguide losses (a) and effective index change (b) as a function of voltage

applied to the electrode for a single waveguide. The curves show simulation results for several assumed

surface charge concentrations in the SiN film, ranging from +8e12 cm−2 (leftmost curve) to -10e12 cm−2

(rightmost curve) in increments of -2e12 cm−2. The red curve corresponds to zero surface charge [90].

At the end, it should be noted that this study, along with other reports [94, 95] coming

after, could help the community to try to distinguish the two effects with more accuracy.

In fact inducing Pockels effect in silicon is still an active field of study with ground

breaking outcomes [96, 97]. Nevertheless, the confirmed values of the electro-optic

coefficient achieved by nitride deposition on silicon are reported to be smaller than 10

pmV-1 [96].

5.3 Germanium Tin Absorption/Phase Modulator

5.3.1 Introduction

There have been great efforts for expanding the application of SiP to longer wave-

lengths including mid-IR [98]. Germanium tin (GeSn) has emerged as a promising

material for future laser integration. It is a group IV compound which can be monolith-

ically integrated on SOI wafers with standard CMOS processing, and is a direct

bandgap material provided that the tin content is above a minimum level (>8%). Re-

cently, direct bandgap GeSn IRB lasers have been demonstrated [15, 99] which offers

the possibility for establishing a complete group four mid-IR platform, if reliable electri-

cally pumped room temperature lasers can be realized [100]. Although important


progress has already been accomplished on extended wavelength GeSn photodetec-

tors [101, 102], few studies have been made on the realization of GeSn modulators.

Theoretical studies have been mostly focusing on the physical modelling of absorption

modulation using the quantum confined Stark effect (QCSE) [103, 104], or the Franz-

Keldysh Effect (FKE) [105], and not a comprehensive device design which relies on a

proven fabrication flow.

Here, we present high-speed and low power consumption FKE GeSn modulator design

for both phase and absorption modulation, which relies on a strain relaxed GeSn layer

grown on germanium virtual substrate as is already experimentally realized in [15]. We

first briefly explain the model we use in order to calculate the optical response of bulk

GeSn to the applied voltage, based on FKE, as well as the empirical data used to

estimate the sub-band absorption and also PDE in GeSn. We then explain the device

design and propose the fabrication process. Finally, the predicted device performance

for both electro-absorption and electro-refraction modulators well be presented.

5.3.2 Modeling FKE and PDE and parameter space

Based on FKE in the presence of an external electric field, the optical absorption edge

of the material shifts towards lower energy. The redshift stems from the wavefunctions

of electron/holes leaking into the band gap. In fact, under an applied field, the elec-

tron/hole wavefunctions become Airy functions (instead of plane waves) which include

a tail extending to the bandgap. This red shift of the absorption edge, can significantly

change the optical absorption of the photons with energies slightly below 𝐸𝑔. Thus FKE

can be used as a modulation mechanism for light with energies slightly below the gap.

Beside alteration of absorption spectrum (as one can expect form Kramers-Kronig re-

lations) the applied filed also varies the real part of refractive index of the material. The

latter can be used in order to realize a phase modulation at wavelengths close to the

gap. In order to quantitatively model the alteration of the absorption ∆𝑘 and refractive

index ∆𝑛 under an external field 𝐹, we model (presented in detail in [106]) the FKE

based on Aspnes [107] relations, within Bennet-Soref approximation [108] as

Δ𝜅(𝜔, 𝐹) =𝐵

2𝑛𝜔2[𝜇𝑒ℎℎ

∗ 3/2(1 +

𝑚0

𝑚ℎℎ∗ ) √Θℎℎ𝐻(𝑥ℎℎ) + 𝜇𝑒𝑙ℎ

∗ 3/2(1 +

𝑚0

𝑚𝑙ℎ∗ ) √Θ𝑙ℎ𝐻(𝑥𝑙ℎ)] (5.1)

Δ𝑛(𝜔, 𝐹) =𝐵

2𝑛𝜔2[𝜇𝑒ℎℎ

∗ 3/2(1 +

𝑚0

𝑚ℎℎ∗ ) √Θℎℎ𝐺(𝑥ℎℎ) + 𝜇𝑒𝑙ℎ

∗ 3/2(1 +

𝑚0

𝑚𝑙ℎ∗ ) √Θ𝑙ℎ𝐺(𝑥𝑙ℎ)] (5.2)

where 𝜔 is the angular frequency of the wave, 𝑚∗ is the effective mass, 𝜇∗ is the re-

duced effective mass, 𝑚0 is the electron mass, and the indices 𝑙ℎ and ℎℎ refer to light

holes and heavy holes. The functions 𝐺(𝑥) and 𝐻(𝑥) are the so-called electro-optic

functions of the first and second kind, given by as

𝐺(𝑥) = 𝜋[𝐴𝑖′(𝑥)𝐵𝑖′(𝑥) − 𝑥𝐴𝑖(𝑥)𝐵𝑖(𝑥)] + √𝑥𝜃(𝑥) (5.3)

𝐻(𝑥) = 𝜋[ |𝐴𝑖′(𝑥)|2 − 𝑥𝐴𝑖2(𝑥)] − √−𝑥𝜃(−𝑥) (5.4)

where 𝐴𝑖(𝑥) and 𝐵𝑖(𝑥) are two linearly independent Airy functions [109], 𝜃(𝑥) is heavy-

side step function with argument 𝑥𝑙ℎ/ℎℎ = (𝜔𝑔 − 𝜔)/Θ𝑙ℎ/ℎℎ (with 𝜔𝑔 the angular


frequency of the energy gap). The parameters Θ𝑙ℎ and Θℎℎ refer to the two valence

bands available for the transition

Θ𝑙ℎ/ℎℎ = (𝑒2𝐹2

2𝜇𝑒𝑙ℎ/𝑒ℎℎ∗ ℏ

)

1/3

(5.5)

where 𝑒 is the electron charge, and ℏ is the reduced Planck constant. Note that in this

model, the two valence bands are equally considered with respect to their energy, and

only their specific effective masses are taken into account. This assumption is true for

unstrained GeSn where the two bands are degenerate at Γ valley [106]. However, in

our case due to the residual compressive strain, the bands of light holes and heavy

holes are split, and as such, only the heavy hole band, preferentially interacting with

TE polarized light, is taken into account [100].

The constant 𝐵 in equations (5.1) and (5.2) is the perturbation parameter, and can be

calculated by

𝐵 = 𝐶𝑛𝑐

𝜇𝑒ℎℎ∗ 3/2 (1 +

𝑚0

𝑚ℎℎ∗ ) + 𝜇𝑒𝑙ℎ

∗ 3/2 (1 +𝑚0

𝑚𝑙ℎ∗ )

(5.6)

with 𝑐 the speed of light. Note that the effective masses were calculated using the 8

band k∙p method, resulting in 0.22𝑚0 for the heavy holes and 0.03𝑚0 for the -valley

electron mass, both taken in the growth direction along which the electric field is ap-

plied [100]. The parameter 𝐶 is empirically obtained from fitting experimental direct

bandgap absorption to the well-known square root dependency 𝛼 = 𝐶(𝜔 − 𝜔𝑔)1/2/𝜔,

with 𝛼 being the absorption coefficient and 𝜔𝑔 the bandgap frequency. We have used

the empirical measurement data reported in [110] for the absorption of GeSn near

the 𝐸𝑔. This data is plotted and shown in Figure 5.6 (a) for three different tin contents.

Ideally, in the absence of an external E-field, the optical absorption of materials should

be zero for photon energies smaller than the bandgap. However, disorder leads to finite

absorption below the bandgap of the ideal material. The absorption coefficient 𝛼(𝐸)

exponentially tails off (Urbach tail) at energies below the energy gap. Undesirably in

GeSn, random incorporation and defects lead to a high disorder and thus significant

sub-band absorption is experimentally measured [110] which drastically penalizes the

performance of the modulator. The exponential decay is clearly visible for energies

smaller than energy gap in Figure 5.6 (a). It should be noted that the properties of the

utilized material (Ge0.875Sn0.125 with residual strain of 0.4%) are extrapolated by shifting

the absorption curves to the proper bandgap, which is measured as 440 meV at room

temperature. This is not a far estimation since as can be seen in Figure 5.6 (a), the

absorption spectrum mainly shifts with respect to the tin content (bandgap size) and

topologically does not significantly change. We used the data for 11% tin content and

shifted it by the change in bandgap.


Figure 5.6 (a) The experimental data [110] of the optical absorption of GeSn alloy taken for different tin

content. The wavelength dependent (b) absorption of doped (1e18 cm-3) silicon (c) refraction of doped

(1e18 cm-3) silicon (d) absorption of doped (1e18 cm-3) germanium, and (e) refraction of doped (1e18

cm-3) germanium. The experimental values (dotted curves) for GeSn are extracted from [111] and [112].

Since in the proposed device (as will be shown), the materials are doped, it is also

necessary to calculate the PDE not only in GeSn but also in Ge and SiGeSn which are

used as bottom and top cladding, respectively. An analytical approach to calculate the

effect of the doping at a desired wavelengths on absorption and refraction of the ma-

terial is to use the Drude model [32] as

𝛥𝑛 = −𝑒2𝜆2

8𝜋2𝑐2휀0𝑛(𝛾1

𝛥𝑁𝑒

𝑚𝑒∗ + 𝛾2

𝛥𝑁ℎ

𝑚ℎ∗ ) (5.7)

𝛥𝜅 =𝑒3𝜆3

16𝜋3𝑐3휀0𝑛(𝛾3

𝛥𝑁𝑒

𝑚𝑒∗ 2𝜇𝑒

+ 𝛾4

𝛥𝑁ℎ

𝑚ℎ∗ 2𝜇ℎ

) (5.8)

where 𝜆 is the light wavelength, 휀0 is the free space permittivity, 𝛥𝑁𝑒 and 𝛥𝑁ℎ are the

change of carriers inside the material, and 𝑛 is the refractive index of the unperturbed

materials. However, it has been observed that the experimental results normally devi-

ate from the values predicted by Drude model [32], which is mainly attributed to the

intraband transitions. This equations are in fact a more general version of equations

(2.3) and (2.4). The coefficients 𝛾1−4 are corrective factors introduced to take these

deviations into account. Fortunately, the experimental data for 𝛥𝑛 and 𝛥𝜅 at mid-IR is

available in the literature, for both silicon [111] and germanium [112], which we used


in order to estimate the deviations from the model for GeSn. We studied the main

deviations of silicon and germanium from the model, and separately modelled the large

deviations from Drude model, the large inter-valence-band absorption of germanium,

assumed to apply for p- doped GeSn. Moreover, the large excess electron absorption

of silicon assumed to apply for n-doped SiGeSn. These deviations can be seen in Fig-

ure 5.6 (b) to (d). Based on this study, we extracted the gamma values for silicon to be

𝛾1 =0.7, 𝛾2 =2.4, 𝛾3 =1, and 𝛾4 =2. We also added 90 dB/cm at 1e18 cm-3 n-doping to

electron-induced losses (see Figure 5.6 (b), blue curves). For germanium, we ex-

tracted the corrective factors to be 𝛾1 =0.6, 𝛾2 =1, and 𝛾3 =2. For 𝛾4, i.e. the effect of

p-doping in the absorption of germanium, we assumed a constant value of 500 dB/cm,

since the deviation of the experimental and theoretical values is very high, due to intra-

band absorption (compare solid and dotted red curves in Figure 5.6 (d)). Same values

as germanium are used for GeSn for the estimation of the carrier dependent refrac-

tion/absorption based on the modified Drude model due to high level of germanium in

the alloy. Similarly, the coefficients used for modified Drude model of SiGeSn are as-

sumed to be worst case (minimum values for 𝛾1,2 and maximum for 𝛾3,4) of germanium

and silicon, as 𝛾1 =0.6, 𝛾2 =1, and 𝛾3 =2 (+90 dB/cm), and 𝛾4 =2 (+500 dB/cm). Based

on these corrective factors, we calculated the carrier dependent loss and Δ𝑛𝑒𝑓𝑓 in re-

sponse to an applied voltage, using the same method explained in chapter 2.2.1.

5.3.3 Phase shifter design and proposed fabrication process

The modulator is based on a vertical stack of 1 µm Ge-virtual substrate (VS), 400 nm

thick GeSn, and 300 nm SiGeSn layers which are grown on silicon. The upper layer

(SiGeSn) is moderately doped to 1e18 cm-3, while the top 30 nm has a high 2e19 cm-

3 n-doping to provide a better top contacting. On the bottom side, the lower germanium

layer is left intrinsically p-doped with a concentration of 3e16 cm-3 (note that doping

this germanium VS layer to higher levels, slightly increases the device bandwidth due

to a smaller linear resistance, but dramatically increases the optical loss of interconnect

waveguides). These p- and n- dopings are required in order to form the pin junction.

Ideally, we would like the GeSn layer to be vacant of the carriers, so that in a reversely

bias pin junction, the field can fully drop inside the GeSn layer. However, the GeSn

layer is intrinsically p-type (~1e17cm-3) due to native point defects. Figure 5.7 shows

the proposed fabrication process required to realize the device. It begins with deposi-

tion of germanium VS (1 µm, intrinsically p-doped) as a buffer layer on top of silicon

wafer, followed by deposition of GeSn (400 nm, intrinsic), a SiGeSn layer (300 nm,

1e18 cm-3 in-situ n-doped) with a thin highly doped (30 nm thick) region on top. The

GeSn and SiGeSn layers are etched away everywhere on the chip except in the active

region of the device to enable reduced optical losses in the interconnect waveguide,

which is based on 2 µm wide partially etched Ge waveguides. Thus, a second etch

step is required to etch the Ge layer for 600 nm on the sides and form the waveguide.

The residual p-doping of Ge still results in ~0.15 dB/mm loss in interconnect. The final

cross section of the proposed device is shown in Figure 5.7. Note that both electro-

absorption and electro-refraction modulators presented here use the same layer stack

to ease the fabrication, and just the active region width is larger (for 0.3 µm) in the


electro-absorption modulator. It is also noteworthy that the thickness of the GeSn layer

should have been ideally thinner (~300 nm), since the non-depleted region of the GeSn

layer does not play a role in the modulation (due to absence of E-field) but only adds

to the insertion loss (due to sub-band absorption). However, this design was based on

the available wafers developed at PGI 9 in Jülich Research Center [100].

Figure 5.7 Left: Fabrication flow of the GeSn modulator. Right: The cross section of the final device.

Coupling the guided mode from 1 µm thick Ge interconnect waveguide to 1.7 µm thick

active region of the device occurs using a linear taper, with a starting width of 0.2µm,

and a final width of 1.4 µm and 1.1 µm for electro-absorption and electro-refraction

modulators, respectively, as illustrated in Figure 5.8 (a). The transition between the Ge

waveguide and GeSn waveguide must be adiabatic to avoid optical loss, back-reflec-

tion and to transfer the light to the GeSn. Based on BeamPROP simulations in RSoft,

(Figure 5.8 (b)) a taper length of 50 µm and 30 µm is respectively required for absorp-

tion and refraction modulators [106]. In these simulations, refractive indices of Ge,

GeSn and SiGeSn are set to 4.03, 4.20, and 4.03, respectively. The calculated values

for the required taper length are very high, and cause substantial insertion loss. Thus,

it is necessary to use the tapers for modulation. Therefore, for high speed performance,

good contact is required. As can be seen in Figure 5.8 (a), the metal should also extend

close to starting point of the taper. The 2D cross sections show the structures (white

lines) which are used in order to simulate the device performance, by interpolating the

result in between the simulated sections.

Different methods can be used in order to implement the contacting scheme. First, to

deposit metal directly on top of the waveguide (considered here in the presented de-

vices). This is the simplest way in terms of fabrication since it does not require any

additional process. However, it results in a considerable loss due to proximity of a wide

metal to the optical mode. The additional losses are simulated to be 39 dB/cm for the

center of the device (1.4 µm wide GeSn), while top SiGeSn cladding makes a buffer

between optical mode and highly absorptive metal. Nevertheless, in practice, this value

can be higher due to diffusion of the metal inside the waveguide.


The second contacting method is to cover the device with an insulator layer, and define

vias under the metal layer, as is shown in Figure 5.8 (c). The separation between the

waveguide core and wide metal layers could reduce the optical losses. Nevertheless,

this method requires additional fabrication process. Also it should be noted that silicon

dioxide cannot be used, since, at frequencies above 2.5µm, its absorption substantially

increases. The third method is to rely on segmented contacting of the waveguide, as

is schematically shown in Figure 5.8 (d). It allows for contacting without any metal in-

duced excess losses and only requires one additional fabrication process step (etching

of the top layers for p-side contacts).

Figure 5.8 (a) 3D representation of the taper in the transmission from Ge interconnect waveguides to

the device. (b) Longitudinal cross section of the device, the mode is calculated using BeamPROP in

RSoft. (c) Contacting scheme provided the definition of the vias. (d) Proposed contacting scheme using

segmented electrical connections.

5.3.4 Expected performance of GeSn absorption/phase modulators

Applying a reverse voltage (positive to top contact and ground to the bottom germa-

nium layer) across the stack partially depletes the GeSn layer, and results in the

application of an electric field inside the space charge region, so that both the FKE and

free carrier absorption contribute to the variable absorption or refraction. By applying

2 V to the device, the absorption of GeSn changes as shown in Figure 5.9 (a) (depletion

region width≈250 nm). For wavelengths closer to the gap, both the baseline loss, and

variation of absorption due to FKE (Δ𝜅𝐹𝐾𝐸) increase. In absorption modulators, it is

normal to set the parameters (including working wavelength) at the point where the

perturbation to loss ratio (Δ𝜅𝐹𝐾𝐸/𝜅) finds its maximum. As can be seen in Figure 5.9

(c), this ratio reaches its maximum value just below the gap. However, we have opted

to use a slightly longer wavelength (2.89 µm) due to the side benefit of small chirping,

while as plotted in Figure 5.9 (b), at 𝜆 =2.89 µm, the chirp is close to zero. It should be

mentioned that the loss perturbation resulting from carrier depletion (Δ𝜅𝑃𝐷𝐸) has the

opposite sign of Δ𝜅𝐹𝐾𝐸, however, it plays a small role in the ER since Δ𝜅𝑃𝐷𝐸 is around

three orders of magnitude smaller. The imaginary part of the GeSn refractive index is

shown in Figure 5.9 (d). The insertion loss of the device (loss at 0V) is 3.3 dB, 2.3 dB


of which results from the GeSn baseline loss. As a LE, the electro-optical bandwidth is

calculated based on equation (3.3) and is calculated to 35 GHz with a 50 Ω driver.

Figure 5.9 Calculated perturbation of absorption (a) and refraction (b) by FKE in Ge0.875Sn0.125 under

8V/µm versus wavelength. The violet (green) dashed line marks the wavelength of electro-absorption

(electro-refraction) modulation. (c) Absorption change over absorption ratio near the absorption edge.

(d) Calculated imaginary part of refractive index vs. voltage at 2.88µm (d) Δ𝑛𝑒𝑓𝑓 vs. voltage at 2.82µm.

For phase modulator, we set the wavelength very closer to the gap energy (𝜆 =2.89

µm). At this wavelength, the refractive index change arising from the FKE Δ𝑛𝐹𝐾𝐸 is

around two orders of magnitude larger than PDE and thus the effect of Δ𝑛𝑃𝐷𝐸 is negli-

gible. The simulated effective index change of the mode with respect to the applied

voltage is plotted at Figure 5.9 (e). We opted to apply 1Vpp as drive voltage, in order

to reduce the optical losses. The device consists of two linear tapers (30 µm long) and

22 µm straight waveguide in the center. The choice of 1.1 µm GeSn waveguide width

allows for shortening the taper to 30 µm. The calculated insertion losses of the refrac-

tion modulation is 4.3 dB. The bandwidth is slightly increased due to shortening of the

device to 36 GHz. Table 5.1 summarizes the performance metrics of the two proposed

modulators.

𝜆 Device

length

Vpp

@Vbias 𝐸𝑅

Insertion

Loss

Power

consump. 𝑂𝑀𝐴 𝑓−3𝑑𝐵

2.89 µm 102 µm 2Vpp

@-1V 6.0 dB 3.3 dB 70 fJ/bit -4.6 dB 35 GHz

2.82 µm 82 µm 1Vpp @

-0.5V 5.2 dB 4.3 dB 31 fJ/bit -5.8 dB 36 GHz

Table 5.1 Summary of the characteristics and performance metrics of the proposed absroption

modulator (2nd row) and phase modulator (3rd row).


5.4 Graphene Silicon Slot-Waveguide Absorption Modulator

5.4.1 Introduction and state-of-the-art

Graphene, a single sheet of carbon atoms forming a honeycomb lattice, has attracted

significant attention in the recent years due to its exceptional optical [113, 114] and

electrical [115, 116] properties. In particular, some of its unique electrical and optical

characteristics make it a promising option to be used in electro-optical modulation.

From an electrical stand point, graphene has an extremely high carrier mobility which

is theoretically unlimited based on its band structure. The high mobility stems from

electrons propagating without scattering over long distances (several micrometers)

due to the reduced phonon scattering. In practice, carrier mobility as high as 1e6 cm2

V-1 s-1 is reported in graphene [117], only limited to the fabrication induced defects and

surface interactions. As will be shown, this extremely high carrier mobility allows for

reduction of series resistance in the modulator.

From optical view point, although graphene consists of a single atomic layer, it couples

so strongly to light, that it can be seen under an optical microscope. Moreover, the

wideband optical absorption spectrum of graphene can be controlled by shifting the

Fermi level 𝐸𝐹, e.g. by applying an external voltage: In the absence of an external field,

the 𝐸𝐹 of (undoped) graphene stays at the crossing point of conduction and valance

bands, and thus the electrons of the valance band can absorb the incident photons

and excite to the (mainly) free states of the conduction band. Applying an external

positive voltage results in a blue shift of 𝐸𝐹 and hence reduction of the photon absorp-

tion due to the occupied states of the conduction band which blocks excitation of

electrons due to the Pauli Exclusion Principle. Similarly, a negative voltage results in

reduction of the absorption, due to the unoccupied states in the conduction band. This

effect, also known as Moss-Burstein effect (MBE) can be used as a strong modulation

mechanism to realize graphene based electro-optical modulators.

Since the first demonstration of graphene-silicon absorption modulator [82], where

MBE was realized by covering an asymmetrically etched p-doped silicon waveguide

with a single graphene layer on the top, and featured ~1 GHz bandwidth with ER of

2.4 dB by 3 V drive voltage, a great deal of effort has been made in order to jointly

improve the bandwidth and modulation depth of the modulators. Most recently, by in-

creasing the doping level of the silicon waveguide, a 5 GHz bandwidth phase

modulator was demonstrated [81] with a high efficiency of 0.28 V∙cm and 9 dB insertion

losses. However, to date, most of the phase shifters in this platform suffer from low

bandwidth or low efficiency. One of the main challenges is the relatively small overlap

of the graphene layer with the optical mode, especially with TE modes in silicon single

mode waveguides. The small overlap pushes the design to increase the overlay be-

tween the graphene layer and the silicon waveguide, and thus penalizes the bandwidth

by increasing the linear capacitance. To address this problem, many efforts have

aimed at implementing plasmonic/graphene hybrid modulators [118, 119], with the

drawback of high insertion losses. Just in the past months, many novel approaches

have been proposed aiming to increase the overlap, such as silicon wafer thinning


[120], or using 50 nm gap silicon slot waveguide [121] as well as oxide deposition on

top of suspended graphene layers [122], all of which increase the overlap. However,

the challenge is that such devices necessitate complex and hard to control fabrication

processes including CMP and regrowth. Here, we propose an absorption graphene-

silicon modulator as well as phase modulator based on MBE with enhanced overlap

which does not require any complex fabrication processes.

5.4.2 Device configuration and modeling of MBE

Fabrication of the proposed structure relies only on one RIE etch (full etch), which is

modified in order to reduce the side wall steepness. In our design, the sidewalls should

have a profile angle of 30°. Before we move on, it is necessary to explain how this

profile angle can be achieved: In a cryo RIE ICP process (see chapter 4.5) there are 4

ways to make the profile angle more positive: 1) reducing ICP power, 2) reducing tem-

perature 3) reducing the pressure, and 4) reducing the SF6:O2 ratio. Note that reducing

the RF power results in a less vertical profile angle. Among these available solutions,

increasing the oxygen flow has been seen to be the most effective method. Note that

as a side effect, it also results in a smaller etch rate, which can be compensated by

increasing the etching time. The angled sidewalls are in practice easy to realize. In

fact, the reason we chose 30° sidewall angle in this structure was that we had fabri-

cated it in our test samples.

Contrary to generally accepted paradigms, the optimum here does not consist in 90°

sidewall angles. Instead, slanted side walls are targeted: First, this facilitates deposi-

tion of the graphene film on top of the structure, since it can now follow the smoothed

shape. Moreover, one can start with larger feature sizes while still reaching a narrow

feature size at the bottom of the slot. Finally, as the graphene film is expected to reach

the bottom of the slot in this smoothed out structure, it will be located at the narrowest

slot region were the enhancement remains.

The cross section of the device is shown in Figure 5.10 (a). The device can be imple-

mented using a standard 220 nm SOI wafer. First, a modified full etch process defines

the waveguides and couplers. The graphene layer can be transformed on top of the

silicon layer. After defining the device using a lithography step, graphene should be

etched e.g. using O2 plasma ashing. Then a layer of Al2O3 layer with the thickness of

𝑡𝐴𝑙2𝑂3=10 nm is deposited on top of the graphene layer in order to form the capacitance.

After transformation of the second graphene layer and O2 plasma, a metal depositing

step (followed by lift off) will define the contacts, as is shown in Figure 5.10 (a). In our

design, the width of each slot is set to 100 nm, and the gap between the two slots

(bottom) is set to 80 nm.

In Figure 5.10 (a), the overlay of two graphene layers are shown with a dotted red lines,

while the rest of graphene layer is shown as solid red. In our design, the overlay of the

two graphene layers is set to 200 nm. In order to model MBE in the proposed structure,

we need to separately calculate the optical conductivity of two graphene regions (dot-

ted and solid lines). For the non-overlaid part (solid line), the optical conductivity of

graphene is simply 𝜎0 [123], which is the universal conductivity defined as 𝑒2/4ℏ with


𝑒 as the electron charge and ℏ as reduced Planck constant, and can be calculated to

be around 60 µS. We then calculate the optical conductivity of overlapped graphene

layers as a function of 𝐸𝐹. The optical conductivity of this region, is the result of both

interband and intraband transition, and can be calculated by non-interacting linear re-

sponse theory [124]:

𝜎(𝜔) =𝜎0

2[tanh (

ℏ𝜔 + 2𝐸𝐹

4𝑘𝐵𝑇) + tanh (

ℏ𝜔 − 2𝐸𝐹

4𝑘𝐵𝑇)]

− 𝑖𝜎0

2𝜋log [

(ℏ𝜔 + 2𝐸𝐹)2

(ℏ𝜔 − 2𝐸𝐹)2 + 4(𝑘𝐵𝑇)2] + 𝑖

4𝜎0

𝜋

𝐸𝐹

ℏ𝜔 + 𝑖ℏ𝛾

(5.9)

While the first two terms correspond to the interband electron-photon scattering pro-

cess, the third term is the contribution of intraband transitions. In this equation, 𝛾 is the

intraband scattering rate (taken from [124]), 𝑇 is the temperature (300 K), 𝑘𝐵 is the

Boltzmann constant, and 𝜔 is the angular frequency of the light (𝜆 =1.55 µm). The

Fermi level of graphene is dependent on the applied voltage, and can be calculated as

[121]

𝐸𝐹 = 𝑠𝑔𝑛(𝑉) ℏ𝑢𝐹√𝜋휀0휀𝐴𝑙2𝑂3|𝑉|/𝑡𝐴𝑙2𝑂3

𝑒 (5.10)

with 𝑢𝐹 being the Fermi velocity and is 1e6 m/s in our simulation, and 휀0 and 휀𝐴𝑙2𝑂3re-

spectively the permittivity of vacuum and aluminum. Thus, at each point the optical

conductivity of the graphene layers is calculated. Then, in order to calculate the per-

turbation of optical losses (for absorption modulator) and also effective index change

(for phase modulation) we performed FEM simulations using COMSOL Multiphysics

software and calculated the complex effective index of the guided TE mode (shown in

Figure 5.10 (b)) under different external voltages applied to the two graphene layers.

Figure 5.10 (a) Schematic cross-section of the proposed device. (b) Calculated E-field inside the slot

waveguide.

5.4.3 Expected performance of absorption modulator

Based on the model explained in chapter 5.4.2, voltage dependent effective index as

well as optical loss is calculated and plotted in Figure 5.11.


Figure 5.11 Calculated absorption (red) and refraction (blue) change with respect to the applied voltage

For small bias voltages (close to 0 V), every section of the graphene layers have con-

ductivity of 𝜎0 and thus the mode has its maximum loss, which is calculated to be 0.33

dB/µm. By applying an external voltage, the occupation of conduction band (on the

dotted red line in Figure 5.10 (a)) reduces the absorption of those regions, while the

absorption of the unperturbed graphene layers (solid lines) remains at its maximum

value (corresponding to conductivity of 𝜎0). However, since the overlap of the mode is

maximized with the dotted lines, the absorption reduces to less than a third compared

to 0 V absorption. Thus, a clear tradeoff between bandwidth on one side, and jointly

ER and insertion loss on the other side is clear: by increasing the overlap between the

two layers, the loss at high voltages is reduced (which results in a higher ER and a

lower insertion loss) while the bandwidth drops (due to a larger capacitance). Another

clear trade off comes directly from equation (5.10): by increasing the thickness of the

oxide, the bandwidth is improved (due a reduction in linear capacitance), while the

Fermi level shift for a given applied voltage drop. The demonstration of this change is

widening both curves plotted in Figure 5.11 in x axis. Thus, for a certain drive voltage,

ER and insertion loss are both penalized.

For the absorption modulation, in order to reduce the drive voltage, the device should

be biased at 2.5 V DC, since the absorption curve has the maximum derivative. At this

point by applying 1Vpp drive voltage, the absorption swings between 0.25 dB/µm and

0.11 dB/µm. By applying 2Vpp, and 2V DC bias, absorption changes from 0.33 dB/µm

to 0.1 dB/µm. Hence, an absorption modulator with 10 µm length, features 2.2 dB ex-

tinction ratio and 1 dB insertion loss.

In order to calculate the device bandwidth based on equation (3.3), we first need to

calculate the linear resistance of the device. The device series resistance results from

a summation of 1) sheet resistance of graphene and 2) contact resistance. The latter

is the result of resistance between the metal contacts and graphene layer. The use the

experimentally reported value of 1 Ω∙mm [125] which is a conservative assumption

[121]. For sheet resistance of graphene, we took experimental data from [126] which

is 550 Ohm/sq. Thus, since in our simulations the distance between the metal contact

and the overlaid graphene layers were set to 0.8 µm, the total linear resistance 𝑅𝑙 of


the device is calculated to be 2.44 Ω∙mm. On the other hand, the total linear capaci-

tance (estimated based on parallel plate capacitor) is 1.71 nF/m. This yields an intrinsic

bandwidth of 39 GHz. However, when the absorption modulator is in combination with

a 50 Ω driver, the bandwidth drops to 32 GHz, which should still be sufficient for 50

Gbps performance.

117

6 Conclusions and Prospects

118 6. Conclusions and Prospects

In this work, we addressed some of the important challenges facing the integrated

electro-optical modulators in silicon photonics. The first half of the thesis (chapters 2

and 3) was dedicated to improving the performance of such devices by applying struc-

tural modifications in device architecture. First, we addressed the main issues limiting

the performance of TW modulators. Our proposed modifications did not require addi-

tional fabrication process steps or metal layers. We showed the effectiveness of our

modifications in crosstalk suppression as well as bandwidth improvement, and then

systematically compared different designs, i.e. high capacitance and low capacitance

phase shifters for addressing distinct applications.

We then turned our attention to compact modulators, which, in addition to low power

consumption, allow for dense integration of PICs. First, we systematically studied the

improvements resulting from the lumped element configuration and compared it with

state-of-the-art travelling wave modulators, both in terms of electro-optical bandwidth

and power consumption. Then we presented design and experimental results of high

speed ring resonator modulators suitable for WDM systems, for which we also imple-

mented optical add-drop multiplexers required in the receiver side.

One main challenge regarding the RRMs is their high sensitivity to the inaccuracies in

fabrication process. The effects of common sources of performance-deviation of the

RRMs arising from fabrication inaccuracies were studied, based on which we applied

modifications in the geometry of the coupling section in order to decrease the device

sensitivity to the fabrication inaccuracies. The performance of the fabricated devices,

are in full agreement with the design targets, demonstrated the effectiveness of the

applied improvements. The main drawback of the lumped element modulators is their

relatively small modulation depth, due to the small phase shifter length. To mitigate

this problem, resonance based devices, e.g. RRMs, are widely utilized in SOI plat-

forms. Nevertheless, the high sensitivity of such devices to the operation wavelength

(since they are optically narrowband) necessitates utilization of an active control sys-

tem which works against the initial goal of lowering power consumption. In order to

address this problem, we introduced meandered modulators, as an intermediate de-

vice possessing both optically wideband performance, and relatively low power

consumption. We explained the design challenges of such devices, and also demon-

strated the performance of the implemented devices. We studied the impact of the

modulator drivers as well as wire bonding on the performance of such devices. In the

future, such devices can be ideally co-integrated with high speed CMOS drivers to

improve their high speed performance. In order to improve the performance of mean-

dered modulators and reduce the constraints on the driver, it is also beneficial to

implement meandered modulators in Michelson interferometer (MI) configuration ra-

ther than MZI. Especially with the recent progress in low loss on-chip circulators, it

could be advantageous for all LE devices (including RRMs) to be implemented in MI

configuration. It is also important to mention that the meandered modulators are espe-

cially suitable for PAM4 modulation scheme, with two cascaded modulators of different

length, since (unlike TW devices) their intrinsic RC time-constant limited bandwidth is

independent of their phase shifter length, and (unlike RRMs) they do not require a

separate thermal phase tuner, as their performance is fully wavelength independent.

6. Conclusions and Prospects 119

In the second half of the thesis (chapters 4 and 5) we focused on improvement of the

performance of the SiP modulators by applying modifications to the phase shifter itself.

In chapter 4 we presented a novel phase shifter, which takes advantage of high overlap

with the optical mode using a vertical pin junction. In our proposed phase shifter, the

majority of the waveguide is left undoped, which allows for implementing extremely

high doping levels (~7e18cm-3, around one order of magnitude higher than in the state-

of-the-art modulators) without excessively increasing the insertion losses. To design

this general-purpose phase shifter (which can be utilized both in TW and resonance

based modulators) we introduced a figure of merit, which allowed us to systematically

compare the performance of various phase shifters realized to date. Two different

methods were introduced in order to realize such phase shifters, i.e. ion implantation

of epitaxially overgrown phase shifters, and in-situ doped silicon deposition. We then

explained our approach to fabricate electro-optical modulators based on these phase

shifters, and reported the experimental results for the fabricated modulator.

In terms of modulation efficiency, our proposed modulator features one of the smallest

𝑉𝜋𝐿 ever reported for depletion based modulators, (0.37 V∙cm for LC and 0.28 V∙cm for

HC phase shifter). However, in order to improve the modulation bandwidth more effort

on the fabrication process is still required: An asymmetric etching of the waveguide

(while not penalizing the modulation efficiency) can increase the bandwidth by remov-

ing the fringing capacitance. Moreover, definition of highly doped region requires a

better overlay accuracy than was available (1 µm) which can increase the bandwidth

by further reducing the series resistance.

It should be mentioned that in the proposed vertical phase shifter (as is necessary to

achieve high efficiency) we increased the junction capacitance, and in order to keep a

high bandwidth, decreased the series resistance of the junction. Such phase shifters

are more suitable for resonance-based devices rather than travelling wave devices

(whose bandwidth is reduced quadratically with increasing capacitance). According to

the high intrinsic bandwidth of our proposed phase shifter (>40 GHz) very high data

rates can be achieved by implementing RRMs. As a follow up, one may realize low

loss interconnect waveguides by silicon nitride deposition on top of the oxide top clad-

ding in order to use these devices in a system.

The vertical highly doped phase shifter pushes the design of the depletion based SiP

modulators to an edge; it is extremely difficult to come up with a better efficiency, using

plasma dispersion effect (PDE) in depletion mode, due to the limited carrier mobility in

silicon. In fact, increasing the doping to above 1e19 cm-3 in the junction is not realistic,

both due to fabrication limitations, and also excessive losses induced by carriers. An-

other limitation of this modulation mechanism is that it introduces high optical losses

due to free carrier absorption. Thus, it is compelling to explore alternative modulation

mechanisms besides PDE. Other modulation mechanisms require incorporation of

other materials, which are compatible with CMOS technology. In the final chapter, we

first investigated the Pockels effect in silicon nitride cladded strained silicon MZIs. The

unavoidable presence of PDE in such structures adds more complexity to the accurate

device characterization and verification of the strain-induced electro-optic coefficient.

111 6. Conclusions and Prospects

Then we investigated the utilization of Franz-Keldysh effect (FKE) in germanium tin

layers grown on silicon substrate, mediated by a germanium virtual substrate. The de-

sign of both electro-absorption and electro-refraction modulators were presented.

The drawback of using FKE as a modulation mechanism is its optically limited perfor-

mance wavelength (a few tens of nanometer below the energy gap) which necessitates

utilization of thermal control systems and also limits the wavelength range at which the

device can perform, which is mid-IR range in case of GeSn modulators. As a solution,

optically wideband Burstein-Moss effect can be exploited by transferring graphene lay-

ers on top of a fully etched silicon waveguide. In principle, the operation wavelength of

such modulators can be tuned by applying a different bias voltage and thus modifying

the graphene Fermi level in off-state. In the last chapter, we explained the challenges

facing the state-of-the-art graphene silicon modulators, and presented our design

which is based on silicon slot waveguide to address these issues. The main advantage

of the presented device was the relative ease of its fabrication, which only relies on

one etch step, and does not require an additional ion implantation step. Nevertheless,

the proposed modulator due to its compact size and high bandwidth can be used in

complex modulation schemes.

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Appendix: List of Publications 123

Appendix: List of Publications

1. F. Merget, S. Sharif Azadeh, J. Mueller, B. Shen, MP. Nezhad, J. Hauck, and J.

Witzens “Silicon photonics plasma-modulators with advanced transmission line

design,” Opt. Express, 21 (17), 19593–19607, 2013.

2. F. Merget, S. Sharif Azadeh, B. Shen, MP. Nezhad, J. Hauck, and J. Witzens,

“Novel transmission lines for Si MZI modulators,” Group IV Photonics (GFP),

IEEE 10th International Conference on, 61-62, 2013.

3. J. Müller, F. Merget, S. Sharif Azadeh, J. Hauck, SR. García, B. Shen, and J.

Witzens, “Optical peaking enhancement in high-speed ring modulators,” Sci.

Rep., 4(1), 6310, 2014.

4. S. Sharif Azadeh, J. Müller, F. Merget, S. Romero-García, B. Shen, and J.

Witzens, “Advances in silicon photonics segmented electrode Mach-Zehnder

modulators and peaking enhanced resonant devices,” Photonics North,

928817-928817-15, 2014.

5. S. R. García, B. Marzban, S. Sharif Azadeh, F. Merget, B. Shen, and J. Witzens,

“Misalignment tolerant couplers for hybrid integration of semiconductor lasers

with silicon photonics parallel transmitters,” SPIE Photonics Europe, 91331A-

91331A-12, 2014.

6. J. Müller, F. Merget, S. Sharif Azadeh, J. Hauck, SR. García, and J. Witzens,

“Peaking in ring modulators and application to ISI reduction,” Group IV Photon-

ics (GFP), 2014 IEEE 11th International Conference on, 9-10, 2014.

7. S. Sharif Azadeh, F. Merget, MP. Nezhad, and J. Witzens, “On the measure-

ment of the Pockels effect in strained silicon,” Opt. Letters 40 (8), 1877–1880,

2015.

8. S. Sharif Azadeh, F. Merget, SR. García, AM. Mártir, N. Driesch, J. Müller, S.

Mantl, D. Buca, and J. Witzens, “Low Vπ Silicon photonics modulators with

highly linear epitaxially grown phase shifters,” Opt. Express, 23 (18), 23526–

23550, 2015.

9. J. Müller, J. Hauck, B. Shen, S. Romero-García, E. Islamova, S. Sharif Azadeh,

S. Joshi, N. Chimot, A. Moscoso-Mártir, F. Merget, F. Lelarge and J. Witzens

124 Appendix: List of Publication

“Silicon photonics WDM transmitter with single section semiconductor mode-

locked laser,” Adv. Opt. Technol., 4 (2), 119–145, 2015.

10. J. Müller, J. Hauck, B. Shen, S. Romero-García, E. Islamova, S. Sharif Azadeh;

S. Joshi, N. Chimot, A. Moscoso-Mártir, F. Merget; F. Lelarge, J. Witzens, “Sili-

con photonics WDM interconnects based on resonant ring modulators and

semiconductor mode locked laser,” Proc. of SPIE Vol 9368, Optical Intercon-

nects XV, 93680M, 2015.

11. S. Sharif Azadeh, S. Romero-García, F. Merget, A. Moscoso-Mártir, N. Driesch,

D. Buca, and J. Witzens, “Epitaxially grown vertical junction phase shifters for

improved modulation efficiency in silicon depletion-type modulators,” SPIE Op-

tics+ Optoelectronics, 95160T-95160T-7, 2015.

12. J. Müller et al, “WDM transceiver with semiconductor mode locked laser,” Group

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Appendix: List of Publications 125

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