i ELECTROABSORPTION MODULATORS FOR CMOS …Optoelectronic modulators using this technology can be fabricated with conventional CMOS foundry processes, possibly on the same chips as

i

ELECTROABSORPTION MODULATORS FOR CMOS COMPATIBLE OPTICAL INTERCONNECTS IN III-V AND GROUP IV MATERIALS

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF ELECTRICAL ENGINEERING

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Jonathan Edgar Roth

August 2007

ii

© Copyright by Jonathan Edgar Roth 2007

All Rights Reserved

iii

I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy.

________________________________ David A. B. Miller, Principal Adviser


________________________________ James S. Harris


________________________________ Olav Solgaard

Approved for the University Committee on Graduate Studies.

iv

v

Abstract While electrical systems excel at information processing, photonics is useful in

systems for high-bandwidth, low-loss signal transmission. As photonics technology

has become increasingly widespread and has been deployed at shorter distance scales

than traditional long-haul networks, it has become important to efficiently integrate

photonics components with electrical integrated circuits. Optoelectronic modulators

used as transmitters are an important class of device for use in optical interconnects.

Many optoelectronic modulator designs use waveguides. Coupling light into

waveguides requires a difficult alignment step. This dissertation will describe a

number of optoelectronic modulators that do not have the tight alignment constraints

associated with waveguide-based modulators. The eased alignment constraints may

be important for the practical manufacturing and packaging of systems using optical

interconnects.

Most currently deployed photonics technologies also use substrates other than silicon

and materials incompatible with CMOS manufacturing. Recently we discovered a

strong quantum-confined Stark effect in Ge/SiGe quantum well structures that can be

used to create efficient optoelectronic modulators on silicon substrates.

Optoelectronic modulators using this technology can be fabricated with conventional

CMOS foundry processes, possibly on the same chips as CMOS circuits.

In this dissertation, an optical interconnect operating in the C-band will be presented.

We believe this is the first such device employing an optical transmitter flip-chip

bonded to silicon CMOS. A number of novel modulators will be presented, which are

fabricated on silicon substrates, and employ Ge/SiGe quantum well structures. These

modulators include a novel architecture known as the side-entry modulator, which is

designed for monolithic integration with electronics. One side-entry modulator

achieved over 3 dB of contrast in the telecommunications C-band for a voltage swing

of 1V. Such a device is compatible with both the voltage swing of modern CMOS

vi

circuits, and long-distance telecommunications technologies including low-loss optical

fiber and erbium-doped fiber amplifiers.

vii

Acknowledgments I’ve been fortunate to be part of a great academic culture at Stanford. This is a place

where expert knowledge, dedication, and enthusiasm are easy to come by. Also,

material concerns have been largely taken care of so that it has been possible to focus

on research. For these things I have to thank Stanford University, Ginzton Laboratory,

the Electrical Engineering Department, and all the people who support these

organizations’ work. Most importantly, I’d like to thank the Miller Lab. David Miller

has been an excellent role model of personal integrity, clear thinking, and clear

communication. All the group members I have interacted with, past and present, have

been great to work with, learn from, and discuss ideas with. I’d especially like to

thank Noah Helman for being an able and patient teacher, Onur Fidaner, my teammate

in material growth efforts, who has impressive great endurance for long nights in the

cleanroom, and the rest of the students working on silicon germanium, Stephanie, Liz,

Shen, Rebecca, and Emel, for working well together in the last year, and enabling us

to get a lot done in a short time.

I’d like to thank Olav Solgaard and James Harris for serving on my reading

committee. Olav was also my academic advisor when I arrived at Stanford, and

without Coach, the work making up the bulk of this dissertation covering modulators

made in silicon germanium epitaxy would not have happened.

I’d like to thank Dave Bour for generously growing all the indium phosphide epitaxy

we needed, Yu-Hsuan Kuo for developing the growth recipe for Ge/SiGe quantum

well structures and allowing us to join in on this work, Lawrence Semiconductor for

carefully growing a large run of wafers for us, and Sam Palermo for working together

with me on our optical transceiver project. I’d like to thank Tom Carver, Tim Brand,

Ryan Macdonald, and the staff of SNF for technical assistance, and Ingrid Tarien for

taking care of administrative concerns.

viii

This work would not have been possible without family, who told me that this would

be possible in the first place, and who have always been there for me. I also want to

thank everyone who has been a friend for their support and for helping make my time

here a lot of fun.

ix

Table of Contents Abstract................................................................................................................................v

Acknowledgments .............................................................................................................vii

Table of Contents ...............................................................................................................ix

List of tables .....................................................................................................................xiv

List of figures ....................................................................................................................xv

Chapter 1: Integration of photonics and electronics............................................................1

1.1 Why integrate photonics and electronics? ...............................................................1

1.1.1 Photonics applied to interfacing outside the electrical circuit........................2

1.1.2 Photonics to improve electronic systems .......................................................3

1.1.3 Advantages of close physical integration of photonics and electronics .........4

1.2 Motivations for signaling with optics......................................................................5

1.2.1 Long-haul communications ............................................................................5

1.2.2 Medium-distance interconnects......................................................................7

1.2.3 Short distance interconnects ...........................................................................7

1.2.4 Photonics components for integration with electronics................................11

1.3 Optical signal transmitter devices .........................................................................11

1.3.1 Lasers............................................................................................................11

1.3.2 Modulators....................................................................................................12

1.3.3 Comparing optical interconnects using modulators and lasers ....................20

1.4 Methods of integrating photonics and electronics.................................................20

1.4.1 Hybrid Integration ........................................................................................21

1.4.2 Monolithic integration ..................................................................................21

1.5 Silicon-based photonics.........................................................................................22

1.5.1 Some advantages of silicon-based photonics ...............................................22

1.5.2 Drawbacks of silicon as an optoelectronic material .....................................22

1.5.3 Attempts at silicon-based emitters and transmitters .....................................23

1.6 Commercial optical interconnects efforts..............................................................24

1.7 Summary................................................................................................................25

x

1.8 Organization of Thesis ..........................................................................................25

1.9 References .............................................................................................................26

Chapter 2: A 1550 nm optical interconnect transceiver using an optoelectronic

modulator flip-chip bonded to CMOS.........................................................................32

2.1 The QWAFEM, a novel modulator architecture ...................................................33

2.1.1 QWAFEM geometry ....................................................................................33

2.1.2 QWAFEM advantages..................................................................................35

2.1.3 Method of simulations..................................................................................36

2.1.4 Fabrication....................................................................................................37

2.2 CMOS Transceiver................................................................................................38

2.2.1 Transceiver Architecture ..............................................................................39

2.2.2 Modulator Driver..........................................................................................39

2.2.3 Integrating and Double-Sampling Receiver .................................................43

2.3 Experiment ............................................................................................................44

2.4 Conclusions ...........................................................................................................50

2.5 References .............................................................................................................51

Chapter 3: Ge/SiGe Quantum Wells Grown on Si for Electroabsorption.........................53

3.1 Materials for the quantum confined Stark effect in quantum wells ......................53

3.1.1 Typical Materials for quantum wells............................................................53

3.1.2 Direct versus Indirect Absorption ................................................................54

3.1.3 Attempts at Electroabsorption in Quantum Wells Using Group IV

Materials ..........................................................................................................55

3.1.4 Germanium/silicon germanium quantum wells............................................55

3.2 Epitaxially grown Ge/SiGe wafers for optoelectronic modulators .......................58

3.2.1 Description of wafers contracted from Lawrence Semiconductor

Research Laboratory........................................................................................58

3.2.2 Wafer Characterization.................................................................................59

Secondary Ion Mass Spectrometry..................................................................61

3.2.3 Surface Roughness .......................................................................................64

3.2.4 Optical Spectroscopy....................................................................................67

xi

3.2.5 Band Structure Calculations .........................................................................73

3.2.6 Future Work..................................................................................................75

3.3 Conclusions ...........................................................................................................75

3.4 References .............................................................................................................76

Chapter 4: Analysis of Asymmetric Fabry-Perot Modulators, and Demonstration

of a Surface-Normal Device........................................................................................80

4.1 Cavity Resonators in Optics ..................................................................................80

4.2 Description and Analysis of Asymmetric Fabry-Perot Modulators ......................82

4.2.1 Fabry Perot resonators..................................................................................82

4.2.2 Modulators using asymmetric Fabry-Perot cavities .....................................92

4.2.3 Conclusion/Summary for the Design of AFPMs........................................100

4.3 Demonstrations of Surface-Normal Asymmetric Fabry-Perot Modulators ........101

4.3.1 Thinned wafer AFPM.................................................................................101

4.3.2 Substrate-removed AFPM ..........................................................................102

4.4 Conclusions .........................................................................................................108

4.5 References ...........................................................................................................109

Chapter 5: Side-entry modulator .....................................................................................111

5.1 Motivation for Side-Entry Modulators ................................................................111

5.1.1 Simple processing.......................................................................................111

5.1.2 Integration with CMOS ..............................................................................112

5.2 Device Concept ...................................................................................................112

5.2.1 Side Entry Architecture ..............................................................................112

5.2.2 Advantages of oblique incidence in side-entry modulators .......................113

5.2.3 Effect of graded index ................................................................................114

5.3 Devices ................................................................................................................115

5.3.1 Fabrication..................................................................................................115

5.3.2 Test Geometry ............................................................................................116

5.3.3 Spot Size.....................................................................................................117

5.4 Spectral Measurements........................................................................................118

5.5 Results and Discussion ........................................................................................118

xii

5.5.1 Maximum Contrast Ratio ...........................................................................118

5.5.2 Misalignment Tolerance.............................................................................120

5.5.3 Modeling Transmission through the Devices.............................................123

5.5.4 Critical Coupling ........................................................................................125

5.6 Conclusions .........................................................................................................131

5.7 References ...........................................................................................................132

Chapter 6: Low Voltage Side-Entry Modulator Operating in the C-Band Using a

Silicon-On-Insulator Wafer .......................................................................................134

6.1 Device Concept ...................................................................................................134

6.1.1 The Difficulty of Creating High-Reflectivity Interfaces in Si/SiGe

Epitaxy...........................................................................................................134

6.1.2 Silicon-On-Insulator Wafers as Substrates.................................................135

6.1.3 Frustrated Total Internal Reflection applied to Side Entry Modulators .....137

6.2 Analysis of FTIR Mirrors....................................................................................142

6.3 Device Design and Fabrication ...........................................................................145

6.4 Experiment ..........................................................................................................146

6.4.1 Experimental Setup ....................................................................................146

6.4.2 Absorption Coefficient ...............................................................................147

6.4.3 Transmission Spectra..................................................................................147

6.4.4 Contrast Ratio.............................................................................................149

6.4.5 Misalignment Tolerance.............................................................................149

6.5 Modeling..............................................................................................................150

6.6 Discussion............................................................................................................152

6.7 Other possible uses of SOI wafers for optical resonators....................................153

6.8 Conclusions .........................................................................................................153

6.9 References ...........................................................................................................154

Chapter 7: Conclusions....................................................................................................156

Appendix A: Transfer Matrix Technique to Calculate Reflection and Transmission

from a Dielectric Stack..............................................................................................159

Appendix B: Gaussian Beam Plane Wave Decomposition.............................................169

xiii

Appendix C: Matlab Software for Matching Transmission Experiments with

Transfer Matrix Simulations......................................................................................172

Appendix D: Wafers Grown by Lawrence Semiconductor Research Laboratory ..........176

Appendix E: Fabrication Recipes, Side Entry Modulator and Photocurrent Test

Sample .......................................................................................................................178

Appendix F: Matlab Software for Calculating Exciton Energy and Overlap

Integrals .....................................................................................................................182

Appendix G: Further information on MATLAB Codes..................................................185

xiv

List of tables Number Page

Table 2.1 Transmission Characteristics of Optical Link. . ..............................................49

Table 3.1. Designed total epitaxy thickness versus thickness measured by surface

profilometry. ....................................................................................................60

Table 3.2. Designed layer thicknesses for Wafer 1 versus thickness measured by

scanning electron microscopy .........................................................................61

Table 3.3. Comparison of SIMS measurements by Evans Analytical Group and by

Lawrence Semiconductor Research Laboratory..............................................63

Table 3.4. Comparison of wafer surface roughness measured using different

techniques. .......................................................................................................66

Table 3.5. Material properties of bulk materials and strained QWs at 300K...................74

Table 4.1. Material properties for the AFPM simulation ................................................105

Table 5.1. Dielectric layers used in electromagnetic simulation of 60QW side-

entry modulator. ............................................................................................124

Table 6.1. Layer thicknesses of frustrated TIR side-entry modulator, after tuning

etch. . ............................................................................................................146

xv

List of figures Number Page

Figure 1.1. Distance scales in which optical interconnects can be utilized, as well

as number of channels for wavelength division multiplexing (WDM)

and (SDM). .......................................................................................................5

Figure 1.2. Attenuation of silica, the material from which optical fiber is made.

Common windows of operation for optical communications are around

1.3 μm and 1.55 μm...........................................................................................6

Figure 1.3. Type I alignment of a semiconductor quantum well and barriers..................14

Figure 1.4. Illustration of how the wavefunction overlap and the absorption energy

change as a result of applied electric field in a quantum well.........................15

Figure 1.5. Absorption coefficient of strained InGaAsP quantum wells, showing

the quantum-confined Stark effect.. ................................................................16

Figure 1.6. Surface normal and waveguide modulator architecturest. ..............................18

Figure 1.7. Illustration of hybrid integration using flip-chip bonding.. ............................21

Figure 2.1. The QWAFEM architecture...........................................................................34

Figure 2.2. Triple-bounce geometry which is used in the QWAFEM .............................34

Figure 2.3. Diagram of how a partial reflector creates a resonance .................................35

Figure 2.4. SEM image of QWAFEMr .............................................................................38

Figure 2.5. Optical Transceiver Architecture ....................................................................40

Figure 2.6. Pulsed-cascode output stage............................................................................40

Figure 2.7. Transient simulation of pulsed-cascode output stage .....................................41

Figure 2.8. Integrating and double-sampling receiver front-end.......................................43

Figure 2.9. Pulsed- Transceiver link schematic.................................................................45

Figure 2.10. (a) Die micrograph of CMOS transceiver. (b) 1550nm photodiodes

wirebonded to receivers...................................................................................46

Figure 3.1. Illustration of the process for absorption of a photon at the band edge

energy in direct and indirect materials ............................................................54

Figure 3.2. Illustrations of the band structures of materials in our epitaxial growth.

.........................................................................................................................56

xvi

Figure 3.3. Band lineup for quantum wells and barriers and SiGe relaxed buffer. ........57

Figure 3.4. Diagram of fabricated PIN photodiode in SiGe epitaxy.. ...............................59

Figure 3.5. Scanning electron micrograph of Wafer 1. s...................................................61

Figure 3.6. SIMS of Wafer 1 .............................................................................................62

Figure 3.7. SIMS of Wafer 7 .............................................................................................64

Figure 3.8. White light interferometry measurement of surface roughness. .....................65

Figure 3.9. Atomic force microscopy measurement of surface roughness. ......................65

Figure 3.10. Atomic force microscopy of Wafer 5 showing submicron scale

defects..............................................................................................................66

Figure 3.11. Absorption in QW superlattice of Wafer 5 ...................................................67

Figure 3.12. Single pass transmission through Wafer 5\..................................................68

Figure 3.13. Absorption of Wafer 1 (10QW) ....................................................................69

Figure 3.14. Absorption of Wafer 5 (60QW) ....................................................................70

Figure 3.15. Comparison of exciton width for small applied field in Wafer 1

(10QW) and Wafer 5 (60QW).........................................................................71

Figure 3.16. Absorption coefficient of Wafer 5 (60QW) for 1V reverse bias for

different temperatures......................................................................................72

Figure 3.17. Overlayed absorption coefficient of quantum well superlattice versus

energy plus displacement in eV.......................................................................73

Figure 3.18. Fit of quantum well transition energies for Wafer 7. ...................................74

Figure 4.1. Four types of optical resonators. .....................................................................81

Figure 4.2. Transmittance of a 1 mm thick glass slab ......................................................83

Figure 4.3. Schematic of a Fabry-Perot resonator. ...........................................................83

Figure 4.4. Solution for fields of forward and backward propagating wave

components at material boundaries for a Fabry-Perot resonator.....................85

Figure 4.5. Transmittance and reflectivity of dielectric slabs at normal incidence...........87

Figure 4.6. Transmittance and reflectivity of a dielectric slab ..........................................89

Figure 4.7. Reflectivity of a 3-period Silicon /Silicon Dioxide distributed Bragg

reflector deposited on silicon...........................................................................90

xvii

Figure 4.8. Asymmetric Fabry-Perot modulator containing quantum wells, with

DBR mirrors on either side of the active region..............................................92

Figure 4.9. Modulator reflectivity R for Rf=37%, varying Rb from 0% to 100%. ...........94

Figure 4.10. Modulator reflectivity R for Rf=85%, varying Rb from 0% to 100%. ..........95

Figure 4.11. The absorption coefficient contrast of Ge QWs is at most ~4 times ...........97

Figure 4.12. This figure shows the modulator reflectivity, and how the use of a

back reflector of less than 100% limits the maximum modulator

reflectivity of the device in the low-cavity-absorption range..........................98

Figure 4.13. Schematic of wafer-bonded asymmetric Fabry-Perot modulator. ..............103

Figure 4.14. Reflectivity from 60 QW asymmetric Fabry-Perot modulator

operated at 70°C. ...........................................................................................104

Figure 4.15. Contrast ratio of 60 QW asymmetric Fabry-Perot modulator operated

at 70°C. The plot shows the maximum contrast ratio achievable for

voltage swings of 2.5V, 5V, and 10V, though the bias voltage was not

set to a constant value in the creation of the plot. .........................................104

Figure 4.16. Comparison of experimental reflectivity spectrum of (a) 60QW

AFPM (with uncalibrated units) and (b) simulation using Kramers-

Kronig relations. ............................................................................................105

Figure 4.17. Reflectivity vs. angle for air - Si.1Ge.9 (n=4.15) interface. ........................108

Figure 5.1. Side-entry optoelectronic modulator schematic...........................................113

Figure 5.2. Percentage reflectivity of Si-SiGe interfac. ..................................................115

Figure 5.3. Diagram of the PIN diode mesa fabricated in a sample with 60

quantum wells for side-entry modulation......................................................116

Figure 5.4. Diagram of side-entry modulator in experimental setup. .............................116

Figure 5.5. Percentage transmission through 60 QW side-entry modulator at room

temperature. ...................................................................................................118

Figure 5.6. Left: Contrast ratio (dB) of 60 QW side-entry modulator at room

temperature. Right: Insertion loss..................................................................120

Figure 5.7. Maximum contrast ratio (dB) of 60 QW side-entry modulator 1473 nm,

for beam misalignments in the ‘wide' direction ............................................121

xviii

Figure 5.8. Maximum contrast ratio (dB) of 60 QW side-entry modulator 1473 nm,

for beam misalignments in the ‘deep’ direction ............................................121

Figure 5.9. Actual and simulated percentage transmission through the 60QW side-

entry modulator .............................................................................................123

Figure 5.10. Percentage transmission through 60 QW side-entry modulator at

60°C...............................................................................................................126

Figure 5.11. Zoom-in of transmission from Fig. 11 showing probable critical

coupling .........................................................................................................126

Figure 5.12. Absorption coefficient of a 60 quantum well diode mesa measured by

surface-normal transmission..........................................................................127

Figure 6.1. Schematic illustrating frustrated total internal reflection..............................139

Figure 6.2. The above graph shows the dependence of transmission through an

SiO2 layer in Si upon the SiO2 layer thickness..............................................140

Figure 6.3. Reflectivity of SiO2 layer with Si on either side for 1550 nm light .............143

Figure 6.4. Reflectivity of a 50 nm SiO2 layer with Si on either side, varying the

layer thickness along the horizontal axis.......................................................143

Figure 6.5. Reflectivity of an interface from Si to Si.1Ge.9 for 1550 nm

wavelength.....................................................................................................144

Figure 6.6. Reflectivity of a 50 nm SiO2 layer with Si on either side, varying the

wavelength along the horizontal axis. ...........................................................145

Figure 6.7. Absorption coefficient of the 10 QW sample on SOI at 100ºC,

calculated from photocurrent spectra ............................................................148

Figure 6.8. Transmission through frustrated TIR side-entry modulator at 100°C .........148

Figure 6.9. Left: Peak contrast ratio (dB) of the frustrated TIR side-entry

modulator. Right: Insertion loss. ...................................................................150

Figure 6.10. Transmission through frustrated TIR side-entry modulator .......................151

1

Chapter 1: Integration of photonics and

electronics

In this chapter the integration of photonics and electronics is discussed. First,

applications where it is useful to integrate optics and photonics are described.

Reasons are given for why it is advantageous to integrate the two domains closely in

systems. As signal communication is a very important application of photonics in

electrical systems, the reasons why photonics conveys advantages for communications

are described, with a special emphasis on short-distance optical interconnects, since

they are a subject of current research. Optical transmitter devices are described,

especially optoelectronic modulators using the quantum-confined Stark effect, which

are the main topic of this thesis. Important strategies for the close physical integration

of photonics and electronics are described. A brief introduction to the field of silicon

optics is given, with an explanation of how this field aims to integrate photonics and

electronics components. Finally the chapter is summarized, and the contents of the

rest of the thesis are described.

1.1 Why integrate photonics and electronics?

Integrated circuits based on silicon electronics are everywhere and inside all kinds of

machines. The archetypal example of their application is the personal computer, but

they are also found in wristwatches, airplanes, toasters, and everything in between.

Photonics is defined as the “The branch of technology that deals with the applications

of the particle properties of light, esp. (in later use) applications to the transmission of

information” [1]. Optics, in contrast, is a word which was first used scientifically

when only the wave properties of light were known. The term photonics is used in the

current discussion partially to make an analogy to electronics, and also because the

2

applications to be discussed are heavily weighted towards communications, and make

use of coherent sources and photodetectors, both of which rely on the particle

properties of light.

Photonics can be integrated with silicon electronics in a vast range of applications. To

broadly illustrate the usefulness of integrating photonics and electronics, a number of

applications where the two are used in conjunction are described. For this discussion,

the applications will be divided into two categories: 1) Applications where photonics

is used to interface with the world outside the electrical circuit, and 2) Applications

where photonics is used to enhance the performance of electrical systems, including

signaling within or between electrical systems.

In both of these categories, a common theme is the use of photonics for transmitting,

receiving, or sensing information. Though more detail will be given later on the

reasons for using photonics in signaling, especially at high bandwidths, some of the

more important reasons are immunity to electromagnetic interference on optical

channels, and the low loss and dispersion possible in optical materials compared to

wires.

1.1.1 Photonics applied to interfacing outside the electrical circuit

For most electronics applications, the circuit must interface with the world outside of

itself, if only to receive instructions of what to do, or to output the results of a

calculation. For a subset of electronics applications, the ideal method of interfacing to

the outside may involve photonics. A common one of these applications is data

storage to optical media. In CD and DVD writers and players, a laser and detector are

required to write data to and read data from the optical medium. During these

operations, feedback from detectors is used to keep the optical components aligned

with the data track on the disc. Due in part to the possibility to make measurements

without physical contact and without modifying the subject of measurement, photonics

has found many sensing applications, including those in the fields of biology, surface

and materials characterization, chemical analysis, and environmental monitoring.

3

Sensing applications may make use of spectrometers to separate light at different

frequencies. Light sensors frequently use parallel arrays of detectors for applications

including spectroscopy and imaging. Imaging devices, including CMOS-based CCD

arrays, can be used for computer vision, security systems, high-speed imaging, and

medical imaging. Arrays of emitters or modulators can be used as the basis for

projection systems. Photonics can also be used in processes to create physical changes

in materials, such as in laser printing, maskless lithography, and manufacturing using

laser ablation and welding.

1.1.2 Photonics to improve electronic systems

Photonics can also be of use within or between electrical systems. A good example is

fiber-optics for long-haul telecommunications, where higher-bandwidth signals can be

sent with reduced requirements for signal amplification and regeneration compared

with signals on electrical wires. In addition, fiber-based communications are used in

local-area networks, and short distance optical interconnects have been demonstrated

for high-speed data transmission, even between points on the same chip. Mode-locked

lasers can provide very short-duration pulses with a stable timing frequency. They

have been explored to enhance applications in electronics which require timing

accuracy, such as clock distribution on a chip [2], and the conversion of analog

electrical signals to digital signals [3].

Other examples of uses of photonics in electronics systems are free-space data links,

such as infrared ports between computers that do not require cables, and television

remote controls. Also, optical signaling between circuits can provide voltage

isolation, which may be useful in noise-sensitive applications or medical devices

where connections to high-voltage sources could be a safety concern.

4

1.1.3 Advantages of close physical integration of photonics and

electronics

Systems combining photonics and electronics components may see improved

performance through close physical integration of components between the two

domains.

Frequently, electrical connections can only be made to the edges of a chip, but

integrating optics on a chip may allow for two dimensional arrays of inputs and

outputs. Also, placing optical transmitters and receivers close to the electrical chip

reduces the parasitics which occur when long bond wires are needed. This is

especially important for high bandwidth signaling, including applications where

signals are multiplexed or demultiplexed in the electrical domain, such that the optical

bandwidth may be several times the clock frequency on the chip.

Close integration may aid the performance of arrayed sensors or image pixels with a

high aggregate data bandwidth. In one such application, CMOS imaging cameras can

take advantage of dense integration by having extremely high frame rates, and

integrating signal processing at the pixel level of the camera sensor. It is even

possible to have rapid feedback between the electronics and detectors by resetting a

pixel once it has accumulated a certain amount of charge, leading to an improved

dynamic range [4].

Close integration of electronics and photonics can also result in cost savings.

Decreases in cost may come about by a reduction in the number of steps in

manufacturing, reduction of the number of components, improved reliability, or

simplified packaging. The field of silicon photonics aims to fabricate optics onto

silicon chips, including monolithic integration of optics and electronics, and could end

up simplifying systems significantly and removing the cost barriers to integration.

The degree to which integration of photonics and electronics will reduce system costs

remains to be seen, and the ideas explored in this work and others may help reach this

goal.

5

1.2 Motivations for signaling with optics

As described in the previous sections on applications of photonics integrated with

electronics, signaling applications are of great importance. In this section the reasons

and challenges of using optics at different length scales will be explained in more

detail. Especially in the domain of short interconnects, where the integration of optics

is more a topic of research than practical application at present, enumeration of the

reasons for optical interconnects as well as the challenges to introduction is in order.

The different length scales of optical interconnects are shown in Fig. 1.

Figure 1.1. Distance scales in which optical interconnects can be utilized, as well as number of channels for wavelength division multiplexing (WDM) and (SDM). The figure is from [5].

1.2.1 Long-haul communications

The motivations for using optics for long-haul communications have been known for

some time. Signals traveling over optical fibers are immune to electromagnetic

interference, and compared to copper cable, the rates of attenuation and dispersion per

6

unit distance are far lower. Long-haul optical communications relies on single-mode

optical fiber made from silica. The attenuation of silica is shown in Fig. 2.

Figure 1.2. Loss in pure-silica-core fiber (PSCF) per unit distance in the infrared. The conventional fiber performance has a loss peak due to water absorption between the useful windows around 1.3 μm and 1.55 μm, while in newer fibers, the water peak can be reduced or removed. Adapted from [6].

There are low-attenuation windows in the spectrum near 1.3 μm and 1.55 μm. Both of

these wavelength ranges can be used for communications. Despite the fact that there

is less dispersion in fiber at 1.3 μm, 1.55 μm is the preferred wavelength because of

the existence of an inexpensive all-optical amplifier technology known as the erbium-

doped fiber amplifier (EDFA), which allows the amplification of wavelength division

multiplexed signals without the need for demodulation or conversion to the electrical

domain. Optical fiber also happens to have very low loss around 1550 nm. Use of

EDFAs allows for transmission of signals across transcontinental fibers without ever

being converted back to the electrical domain for regeneration. While single optical

channels can already carry a huge bandwidth, it is possible to fill the optical

7

bandwidth of the low-loss windows of fiber by using dense wavelength-division

multiplexing (WDM), sending a number of channels of data at different optical carrier

frequencies.

1.2.2 Medium-distance interconnects

Medium-distance interconnect applications include campus networks, metropolitan

area networks (MAN), and fiber-to-the-home (FTTH). On this scale, fiber remains

useful for its high bandwidth. To accommodate traffic in networks with many users,

high-capacity channels are needed. The demands for bandwidth typically come in

bursts. When browsing the web, a user will typically spend time reading a page,

demanding no bandwidth, then load another page, and expect a fast load time. As a

result of the burstlike nature of traffic on these networks, the system must be able to

handle packets of data being routed between different points on the network. A high-

capacity optical backbone makes this possible. In medium-distance applications,

coarse WDM may be used, as well as less expensive lower-performance optical

components, such as multimode fiber.

Deployment of fiber to homes will enable higher bandwidth applications for individual

users. Some applications are high definition television and real-time

videoconferencing. As home internet connections are slow compared with the

capabilities of personal computers, it is likely that programmers will find ways to

utilize the new bandwidth, and the deployment of fiber to the home will be

accompanied by the development of new applications [7].

1.2.3 Short distance interconnects

Looking to the shorter distance scales of backplanes, computer buses, and even on-

chip connections, optical signaling can be used to provide performance improvements,

though the source of performance improvements over electrical connections and the

challenges in creating a viable technology are different from medium-distance and

long-haul interconnects.

8

Currently personal computers have processor clock frequencies of nearly 4 GHz,

though the data rates across buses are closer to 1 GHz, limiting the rate of

communication between elements of a computer system. The communications link

between the processor and the memory is especially important for high-performance

computing, though currently the speed of this link is just as much limited by the speed

of the memory itself as by the bus. Manufacturers are also moving towards creating

multiple processor cores on a single chip. Some of the reasons for are the difficulty in

increasing chip clock speeds given the dispersion and loss when signaling over longer

wires on a chip die, and the difficulty in keeping synchronous operation across a large

die. As a result, the multi-core solution uses multiple processors that execute different

sets of instructions in parallel, and require another level of hierarchy to manage multi-

threaded applications. In addition, computer software must be redesigned to take

advantage of multiple cores. The multi-core paradigm is one strategy to deal with the

physical limitations to improving computer performance, and short-distance optical

interconnections may at some point allow improved performance on ICs by enabling

larger synchronous areas on and between chips, and higher clock frequencies.

Reasons why this may be possible are explained in the following section.

Other reasons for optics short-distance optical interconnects As has been mentioned, optical links can communicate at higher bandwidths than

electrical links, with no crosstalk between lines. On the short distance scale, several

new arguments for optics in signal communications emerge, which will be explained

here [8].

Difficulty of ‘high aspect ratio’ wires The number of bits per second that can be sent down an electrical interconnect is set

by the ratio of the wire length to the square root of the cross sectional area. The

problem for further performance enhancements for integrated circuits is that the

current trend involves using increasingly larger dies while shrinking feature

dimensions. As a result, the wires are being squeezed to increasingly high aspect

ratios, and there is no chip area left to allow the wires to be widened [8].

9

Clock signals and chip synchronization Precision timing of electrical circuits is difficult due to loss-dependent distortion in

wires and due to fluctuations in phase of signals which occur in part due to

temperature dependence in conductive materials used for wiring. Optical fibers are far

less susceptible to synchronization problems, in part because the change in refractive

index with temperature is not large.

Short optical pulses In addition, optical clocking using stable mode-locked sources with narrow pulse

widths makes possible a large reduction in jitter and skew of clocking signals, and

may reduce the power and chip area required for electrical clock distribution [2].

Mode-locked pulses may also be used to simultaneously send signals and allow for

time synchronization [9]. This method of time synchronization could allow for very

large (meters in size) systems to operate synchronously.

Impedance Matching Impedance matching can be difficult in electrical systems with broadband modulation.

For optical signals, the modulation bandwidth of the signal is small compared to the

carrier frequency, and impedance matching can be performed simply with an

antireflection coating.

Wavelength division multiplexing WDM may be used for short interconnects as well. Doing so would require the

splitting of a mode-locked pulse into multiple channels which could be modulated

separately. The result would be increased capacity per optical channel.

2D interconnects Optical transmitters or receivers can be arrayed in two dimensions across a chip

surface, thus allowing for dense interconnections to a chip.

10

New interconnect geometries Compared with electrical interconnects which typically use wires running across

boards or chips, or cables containing wires in parallel, optical signaling provides more

possibilities. While on-chip waveguides and fiber cables are analogous to the

possibilities available in electronics, optical beams can overlap one another, and

multiple beams can be focused with a lens. Using a lens or diffractive optical

elements it is possible to focus a 2D array of optical outputs from one chip surface

onto another vertically stacked chip, or to distribute the output of a laser to many

modulators [10].

Some practical challenges

Power dissipation One difference between long-haul and short distance interconnects is that power

dissipation becomes more critical at short distances. At shorter length scales a high

density of optical interconnects may be desirable, and it may prove difficult to remove

the heat generated. This is especially an issue at the chip scale, where power

dissipation per area is large and already challenges chip designers. As a result, optical

interconnects would likely not be favored if the power consumption were greater than

that of electrical interconnections. A reduction in power consumption for optical

interconnects could be achieved, at least at the backplane distance scale, provided the

system is well optimized [11]. To maximize and extend the benefits of optical

interconnects, optical transmitters with low capacitance, drive voltage, and high

contrast ratio must be developed. However, if low power components are developed,

industry will likely become very interested in optical interconnects.

Established infrastructure One practical consideration for the adoption of short-distance optical interconnects is

that the semiconductor industry has a large investment in infrastructure for chip

fabrication. The introduction of optics into computing systems will likely occur if the

optical interconnect solutions can save power, but the savings will have to be

11

sufficient to justify the expense of modifying the manufacturing process and any

additional per-unit expense.

1.2.4 Photonics components for integration with electronics

Integration of photonics with electronics requires optical transmitters and receivers,

and circuitry designed for signal transduction between the optical and electrical

domains. In addition, many of the applications overviewed here require additional

components or impose certain constraints. For example, for communications

applications, sources and detectors operating at 1.3 μm or 1.55 μm are desired, and

sensing applications may require sources, detectors, or filters for other wavelengths.

For spectroscopy and WDM, components will be required to separate and combine

different wavelengths. Waveguides, lenses, and diffractive optical elements may be

required to control the flow of light and couple energy between different modes.

Some active components which may be required are variable attenuators and switches.

The strategy for integration of photonics and electronics will depend upon the

requirements of the application, and different applications will require the

incorporation of different materials for active and passive components.

1.3 Optical signal transmitter devices

For optical interconnects applications, electrical to optical conversion requires an

electrical driver circuit and an optical transmitter. The optical transmitter may either

emit light or modulate light from an optical source.

1.3.1 Lasers

The preferred light emitters for optical communications are lasers. Lasers emit

coherent light, and can be designed to have a well-defined optical frequency and a

single mode of emission. Incoherent light sources such as light-emitting diodes

12

(LEDs) are too slow and have too broad emission spectra to be useful as transmitters.

For interconnect applications, vertical-cavity surface-emitting lasers (VCSELs)

integrated to silicon chips are suitable devices [12]. They emit light vertically from a

chip surface or through a transparent substrate, they can be arrayed in two dimensions,

and they can be designed to have single-mode output.

1.3.2 Modulators

Optoelectronic modulators can be used in conjunction with continuous-wave or

modelocked lasers to convert signals from the electrical to optical domain.

Optoelectronic modulators can be made using a number of different physical effects.

For the sake of this discussion, effects will be considered which use changes in electric

field to change the optical properties of a medium, in order to control the flow of light.

Methods of modulation

Electroabsorption Modulation Electroabsorption modulators act by using a change in electric field across a material

to change the optical absorption in the material. The optoelectronic modulators

described in this thesis all utilize the quantum-confined Stark effect (QCSE), a

mechanism of electroabsorption modulation, which will be described in a later section.

Electrorefractive Modulation In electrorefractive modulation, an electric field across a material changes the

refractive index of the material. Many such modulators are called electro-optic

modulators because they utilize the linear electrooptic effect, also known as the

Pockels effect, which is a refractive index change proportional to the applied field. A

commonly used material for electro-optic modulators is lithium niobate. While

electrorefractive effects tend to be weak, they have an advantage over

electroabsorption in that a beam can be steered or switched between different paths.

In general, to switch a beam between two possible paths, it is necessary to change the

refractive index such that over the beam path, the effective path length is shifted by

13

one half wavelength. Resonances can be used to enhance the interaction of the beam

with the electrorefractive material, but the loss to absorption must be low, or there will

be a large insertion loss. With electroabsorption, a comparable beam switching effect

would difficult or impossible to obtain without large insertion loss or small optical

bandwidth. As predicted by the Kramers-Kronig relations [13,14], changes in

absorption coefficient and refractive index are related, so some materials which are

suitable for electroabsorption modulation could also be used for electrorefractive

modulation.

All-Optical Modulation It is also interesting to note that electroabsorption and electrorefraction can occur

when the electric fields from intense light change the optical properties of materials.

This ‘self-modulation’ is responsible for mode-locking in lasers with saturable

absorbers, and for the self-focusing of beams. Also, devices have been engineered

which use carriers generated from the absorption of one optical beam to control the

electrical field in an electroabsorbing material to affect another beam. Such a device

can be used as an optically-controlled optical gate for wavelength conversion [15].

QCSE The quantum-confined Stark effect (QCSE) [16], used in the modulators described in

this thesis, causes an electric-field dependent shift in the absorption spectrum of

semiconductor quantum wells. This effect enables energy-efficient modulation, and

can lead to fast devices since the change in absorption depends only upon the change

in electric field and not the motion of carriers. It is analogous to a weaker effect

which occurs in bulk semiconductors known as the Franz-Keldysh effect.

In the Franz-Keldysh effect, an electric field is applied to the semiconductor, and the

band edge absorption spectrum becomes broadened and shifted to a longer wavelength

[17,18].

14

WELLBARRIER BARRIER

CONDUCTION BAND

VALENCE BAND

Figure 1.3. Type I alignment between a semiconductor quantum well and the surrounding barriers. The barriers have a greater conduction band energy than the well, and a lesser valence band energy, leading to the possibility of discrete electron and hole states in the well.

In the QCSE, a semiconductor quantum well bounded by barriers with type-I

alignment, as shown in Fig. 3, will have discrete bound electron and hole energy states

in the well. Absorption of a photon can result in a creation of an electron-hole pair in

the bound states. The photon energy must be at least large enough to excite a carrier

from the valence band to the conduction band. When an electric field is applied

perpendicular to the plane of the quantum well, the wave functions of the electron and

hole will shift within the quantum well, and the overlap of the wave functions will

change. The change in energy difference between the electron and hole states

involved in absorption changes the wavelength of the onset of absorption, and the

change in the overlap changes the strength of absorption. A schematic diagram

illustrating the change in electron and hole wavefunctions with applied field in the

QCSE is shown in Fig. 4, and a sample absorption spectrum is shown in Fig. 5.

15

Ene

rgy

eV

Ene

rgy

eV

distance distance(a) No applied field (b) With field

Quantum-Confined Stark Effect, Band energy and wavefunctions

Figure 1.4. Illustration of how the wavefunction overlap and the absorption energy change as a result of applied electric field in a quantum well. Green = Conduction Band, Blue = Heavy Hole, Red = Light Hole, Dotted lines = electron and hole state energy, Black curves = wavefunctions. The calculations and the resulting plots were made with our QWELF software described in Appendix F.

InP based modulators

The QCSE has typically been used in III-V semiconductors, mostly on InP and GaAs

substrates. In these materials, it is possible to integrate lasers and modulators on the

same chip. InP based devices can be designed to operate in the telecommunications

C-band. In Chapter 2 of this thesis, a transceiver using an InP-based modulator flip-

chip bonded to a silicon-based integrated circuit is described.

16

Figure 1.5. Absorption coefficient of strained InGaAsP quantum wells, showing the quantum-confined Stark effect. The plot is derived from photocurrent spectroscopy. The applied reverse bias voltage ranges from -0.25V (slightly forward biased) to 3.5V. Increasing the applied reverse bias voltage causes the absorption peak amplitude to decrease and shift to longer wavelengths.

Novel SiGe modulators

Recently, a method of growing Ge quantum wells with SiGe barriers on Si substrates

was developed [19], and we have demonstrated the QCSE in these indirect bandgap

quantum wells, as described in several references [20,21] and in Chapter 3. These

devices are compatible with operation in the telecommunications C-band (centered at

1.55 μm) when heated, as demonstrated in Chapter 6. The band structure of Ge has a

local minimum in the conduction band at the gamma point, and the QCSE modulation

changes the absorption coefficient around the energy of this direct bandgap. While

indirect absorption is also present, it is a weaker effect than the direct absorption. As

absorption modulation due to the QCSE is accompanied by a refractive index change

beyond the band edge, it may be possible to optimize the SiGe epitaxial growth to

create efficient electrorefractive devices in the C-band, and perhaps also to create

electroabsorption modulators at 1.3 μm. The development of a growth technique for

17

these quantum well materials on silicon substrates improves the prospects for silicon-

based optics.

Modulator designs and figures of merit Design of optoelectronic modulators involves trade-offs between different parameters.

Some of the metrics of the performance and design are described here. This list was

made with electroabsorption modulators based on the QCSE in mind:

Contrast Ratio (CR): The intensity of light in the 1 state (high output power) of the

modulator divided by the intensity in the 0 state (low output power).

Change in transmission/reflectivity (ΔR): The difference in the fraction of light

passed in the 1 state and the 0 state.

Insertion Loss: The loss (typically in decibels) in the 1 state. This is related to CR

and ΔR.

Voltage swing: The difference in applied voltage in the 1 and 0 state

Bias voltage: The voltage swing is not always between 0 V and a different applied

voltage. A bias voltage may be applied.

Leakage current: A reverse-biased PIN diode may have a leakage current which

consumes power.

Capacitance and contact resistance: These affect the power required to drive the

device and the maximum signal bandwidth attainable.

Maximum digital bandwidth: This may be influenced by a number of other

modulator properties, including the RC time constant, and by the electrical driver

circuit.

18

Power dissipation: This can be calculated for a PIN diode modulator as ½CV2f,

where C is capacitance, V is voltage swing, and f is the operation frequency. This

calculation assumes there is no dark current.

Optical bandwidth: This is dependent upon material properties and the design of any

resonant cavity that may be used.

Temperature sensitivity: As materials for QCSE have an intrinsic temperature

variation, the temperature sensitivity may be related to the optical bandwidth, and it

could possibly also vary based on the quantum well design.

Size and geometry: These determine how much wafer space must be allocated to the

modulator, the alignment tolerance of the modulator to optical beams, and the

geometry and density of interconnections which can be made to the modulator.

Number of quantum wells: A greater number of wells requires a larger voltage

change to give the same electric field change than a smaller number of wells.

Well/Barrier width and material composition: These factors determine the

absorption spectra of quantum wells.

(a) surface normal (b) waveguide

Common modulator architectures

Figure 1.6. Surface normal and waveguide modulator architectures, in which the light is incident (a) normal to the active region, or (b) parallel to it.

19

Desirable modulator characteristics for optical interconnects Short distance optical interconnects have been mentioned as an important application

for optoelectronic modulators. Such modulators do not require as high contrast ratio

as is required for long distance fiber optic communications. This is because their

signal does not need to be amplified many times between the transmitter and receiver,

so degradation of the signal is less of an issue. For the receiver, the total change in

signal intensity is important, which is most closely associated with ΔR. A contrast

ratio of at least 3 dB coupled with low insertion loss, perhaps less than 5 dB, will

permit ΔR of at least 15%. If ΔR is reduced, the laser source amplitude must be

increased to get the same change in signal at the receiver. An operating voltage under

1V is desired so that modulators can be driven by CMOS signals. Bandwidth of at

least 10 GHz is desired, and the power dissipation of modulators should be several

times smaller than electrical interconnects, such that an entire optical interconnect will

not dissipate more power than an electrical interconnect at a comparable distance.

Modulator architectures, and importance for packaging Typically, modulators utilize either a surface-normal architecture or waveguide

architecture, both of which are shown in Fig. 6. Waveguides typically confine light in

a material with high refractive index. It may be difficult to align beams to couple into

waveguide modes, and waveguides are better candidates for 1-dimensional arrays than

2-dimensional arrays. However, waveguides tend to have low capacitance, and they

can be used to get an arbitrarily long interaction length between the light and the

optical material used for modulation. Also, new methods of coupling beams between

fibers and waveguides ease the difficulties of mode alignment [22,23].

In surface-normal modulator architectures, the light is normally incident upon the

optical material. Such devices may operate in a transmission or in a reflection mode.

As the strength of the modulation is dependent upon the interaction length with the

optical material, it may be difficult to get adequate modulation on a single pass. Also,

since modulation is dependent upon changing the electric field, a thicker material

growth for stronger modulation will result in a device requiring a large voltage swing.

20

The interaction length of the light with the optical material can be enhanced through

the use of resonant structures, such as distributed Bragg reflector (DBR) mirrors above

and below the active region of the device. Strongly resonant devices are of limited

usefulness since they have a limited bandwidth of operation, and will also have tight

tolerances on fabrication parameters and operating temperature. Surface normal

devices can be easily arrayed in two dimensions, and easily be coupled with fibers or

free-space beams. As their area tends to be larger than waveguide devices, they have

larger capacitance and power dissipation.

1.3.3 Comparing optical interconnects using modulators and lasers

Some differences between modulators and lasers for optical interconnects were

described by Helman [24]. Cho compared the power dissipation in links using

quantum-well modulators and vertical-cavity surface-emitting lasers (VCSELS), and

concluded that modulators consumed less power at frequencies less than 15 Gb/s and

shorter interconnect distances [25]. The recent research focus on silicon-based optics

changes some of the arguments between using modulators and lasers, since arguably

no practical lasers on silicon substrates exist. Though every transmitter using a

modulator will require a laser source to send the signal, perhaps located off-chip, it

should be possible to use one laser to feed a large number of modulators. Components

such as waveguide splitters may be used to split light to multiple waveguide

modulators, or diffractive optical elements may be used to send light to multiple free-

space-coupled modulators.

1.4 Methods of integrating photonics and electronics

Two important methods of integrating photonics and electronics are using hybrid

integration and monolithic integration of devices on the same wafer. Each will be

discussed.

21

1.4.1 Hybrid Integration

For reasons which will be explained in the section below on silicon-based optics,

silicon itself is not an ideal material for the emission, or modulation of light. Many

materials used for optics cannot be epitaxially grown on silicon wafers, or are

incompatible with silicon electronics fabrication. III-V compound semiconductors are

frequently used for optics applications, and these materials tend to suffer from both of

these problems. A solution to the problem is to fabricate separate chips for optics and

electronics, and integrate the two together at the end of the processing. This is known

as hybrid integration, and it can result in very short interconnections between the

optical devices and electronic circuits. A common method of hybrid integration is

flip-chip bonding, which occurs when solder bumps are deposited on one of the two

chips, and they are aligned and heated, so that the solder bridges between the chips

[26]. A schematic of flip-chip bonded chips is shown in Fig. 7.

III-V Substrate with lasers (or modulators, detectors, etc)

Si substrate with electronics

Solder bumps

III-V Substrate with lasers (or modulators, detectors, etc)

Si substrate with electronics

Solder bumps

Figure 1.7. Illustration of hybrid integration using flip-chip bonding. Solder bumps join the faces of two substrates and electrically connect electronics and optical devices. The red arrows represent the output from vertically-emitting lasers, at a wavelength where the substrate is transparent.

1.4.2 Monolithic integration

Another option is to fabricate optics and electronics on the same chip. Since silicon

electronics has reached such a high level of development, and since silicon is an

22

inexpensive and plentiful material, current research efforts towards monolithic

integration are primarily focused on silicon-based optical devices.

1.5 Silicon-based photonics

Following is a brief discussion of efforts to create optical devices on silicon substrates

and from silicon.

1.5.1 Some advantages of silicon-based photonics

Silicon can be an effective material for creating waveguide structures and resonators

due to the fact that silicon and silicon dioxide have very different refractive indices

(3.53 and 1.53 at 1550 nm wavelength). Materials with high index surrounded by low

index materials can confine light using total internal reflection. Silicon-on-Insulator

(SOI) wafers have frequently been used for silicon photonics applications in which the

light is confined in structures fabricated in the top silicon layer [27]. Silicon can be

used as a detector in the ultraviolet and blue, and work has been performed towards

using silicon detectors for optical clock injection [28] .

1.5.2 Drawbacks of silicon as an optoelectronic material

Despite these advantages, designing all the elements of transceivers and other devices

in silicon is problematic since silicon does not have efficient processes for emitting

light, modulating absorption, or modulating refractive index [29,30]. One reason is

that silicon is an indirect-bandgap material. In an indirect-bandgap material, carrier

transitions between the conduction and valence band typically involve a change in

momentum, and require the presence of a phonon. As a result, the preferred method

of carrier recombination in silicon is not by optical transitions, but instead typically

involves the creation of phonons, and not the emission of photons. Also there is not

an efficient QCSE with indirect absorption.

23

1.5.3 Attempts at silicon-based emitters and transmitters

Silicon-based lasers and LEDs Attempts at silicon-based lasers have not yet led to devices with desirable properties.

Two silicon-based lasers have been demonstrated which required external optical

sources for pumping [31,32], and an AlInGaAs-based laser was hybrid-integrated to

silicon, such that light from the laser was coupled into a waveguide mode on an SOI

wafer [33]. A good Si-compatible laser technology would use a simple fabrication

process with materials that are compatible with silicon electronics. It would use

electrical pumping instead of optical pumping, and result in power-efficient light

emission at room temperature and above, in a wavelength range where suitable

waveguides, modulators, and detectors were available.

The development of efficient LEDs has been a prerequisite for developing lasers in

novel semiconductor materials. Efforts towards creating LEDs in silicon have largely

been aimed at changing the band structure such that when carrier recombination

occurs, the material looks more like a direct-gap material. This can be done by

introducing dislocations into the silicon [34], using quantum confinement [35,36], and

including materials better suited to emission than silicon, such as rare-earth ions [37].

It is possible that at some point in the future these efforts will lead to efficient Si-based

lasers.

Silicon-based modulators Recently silicon-based modulators have gained much attention, with several devices

reported using the free carrier plasma dispersion effect [38,39], including examples

employing ring resonators [40] and photonic crystals [41] to increase the interaction of

light with the active material. As the underlying physical effect is not strong, these

efforts have led to large structures with high capacitance, or devices employing strong

resonances which consequently have a small bandwidth of operation. As is the case

with light emitters on silicon, the inclusion of other materials which may be

compatible with silicon electronics manufacture may enable more efficient modulation

24

mechanisms. Germanium in particular is an interesting material since it has already

been used in silicon electronics due to its high mobility. It has a direct bandgap at

1.55 μm at room temperature, though compressive strain shifts the bandgap to shorter

wavelengths. Strained SiGe composites and strained silicon display a linear electro-

optic refractive index modulation which has been exploited in several devices [42,43],

and an electroabsorption modulator was demonstrated based on the Franz-Keldysh

effect in strained SiGe [44]. Recently, Yu-Hsuan Kuo in James Harris’s research

group led the discovery of a strong QCSE in compressively strained Ge quantum wells

(QWs) with tensile strained SiGe barriers. This effect provides an efficient

mechanism for modulation which should enable low-voltage, low-capacitance

modulators which are compatible with silicon electronics. The exciton energy was

found to shift by about 0.79 nm/ºC, making it possible to modulate light in the C-band.

The performance of the Ge QCSE appears to be comparable to or better than the

QCSE in III-V devices at similar wavelengths, and SiGe based quantum wells could

potentially displace III-V modulators for such wavelengths.

1.6 Commercial optical interconnects efforts

Two companies working in the area of relatively dense integration of optoelectronics

and electronics are Infinera and Luxtera. Infinera makes optical networking

components, and has designed a solution for wavelength division multiplexing on a

single InP chip, greatly reducing the number of fiber couplings and components

necessary for high bandwidth telecommunications [45]. The technology enables

inexpensive optical-electrical-optical conversion, removing a barrier to building active

optical networks, and adding flexibility to the way that signals are switched and

routed. Luxtera has developed a fabrication process for CMOS electronics on SOI

which incorporates photonics components. Two of their accomplishments are the

development of an efficient component to couple light between optical fibers and

waveguides on a chip, and the first demonstration of Ge photodetectors fabricated as

25

part of a CMOS manufacturing process. Their efficient method of fiber-coupling also

enables wafer-scale testing of optical components [46].

1.7 Summary

The integration of photonics and electronics has been an enabling technology for

telecommunications, and may provide benefits for shorter-distance communications

down to the chip scale. The ability to inexpensively and simply integrate photonics

into electrical systems and the development of efficient transmitter devices will lead to

increased penetration of photonics into electrical systems for communications and

other applications. Modulators based on the quantum-confined Stark effect are one

class of transmitter device which have been widely used, and will continue to find new

applications, especially with the recent discovery of the effect in germanium quantum

wells grown on silicon substrates. This thesis will focus on the development of

efficient optoelectronic modulators and their use in systems.

1.8 Organization of Thesis

I began my PhD work improving the performance of optoelectronic modulators grown

on InP substrates using a novel architecture called the quasi-waveguide angled-facet

electroabsorption modulator (QWAFEM) in which the light impinges upon the active

region of the device at oblique incidence [47]. This device was used in a transceiver

link utilizing a novel modulator driver and receiver circuit. This work is described in

Chapter 2. During my time working at Stanford we discovered the strong QCSE in Ge

quantum wells. The physical effect and some measurements from Ge quantum wells

are described in Chapter 3. Chapter 4 gives a mathematical description of asymmetric

Fabry-Perot modulators (AFPM), which are interesting because they can in theory

have a contrast ratio which approaches infinity. Results from experiments with a

SiGe-based surface normal AFPM are shown as well. Chapter 5 describes another

SiGe modulator using an oblique-incidence architecture similar to the QWAFEM,

26

known as a side-entry modulator. In Chapter 6, an improved side-entry modulator is

described which leverages the established technology of silicon-on-insulator wafers to

create a better optical resonator by frustrated total internal reflection. Finally,

conclusions from the thesis are given.

1.9 References

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27

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[10] McCormick, FB, Cloonan, TJ, Tooley, FAP, Lentine, AL, Novotny, RA,

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[11] Cho, H, Kapur, P, and Saraswat, KC, Power comparison between high-speed

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32

Chapter 2: A 1550 nm optical interconnect transceiver using an optoelectronic modulator flip-chip bonded to CMOS

As described in Chapter 1, optoelectronic modulators using the quantum confined

Stark effect (QCSE) [1] are effective optical interconnect transmitter devices due to

their potential for high frequency operation and low power dissipation. Typically,

they use either surface normal or waveguide architectures. Surface normal devices

typically require a thick multiple quantum well (MQW) region to get adequate

contrast, and thus require a large operating voltage to achieve the necessary electric

field for switching. The thickness and voltage swing may be reduced by use of a

Fabry-Perot resonator, but the resulting design is constrained by a narrow wavelength

band of operation and strong temperature dependence. Waveguide devices avoid

these problems, though they require specialized structures to couple from free-space or

fiber modes to waveguide modes, and waveguides are typically only arrayed in one

dimension of a wafer surface.

This chapter describes the demonstration of an optical interconnect transceiver [2] at

1550 nm using a modulator architecture that combines benefits of both surface normal

and waveguide modulators, the quasi-waveguide angled-facet electroabsorption

modulator (QWAFEM). These devices have previously been demonstrated to operate

over a wavelength range of 16 nm [3]. They allow for surface-normal access to

spatially separated input and output ports, and simple beam alignment. They have a

low drive voltage of 2 V, and can be directly flip-chip bonded to CMOS without high-

speed electrical packaging.

In order to explore the use of these modulators in high-density chip-to-chip optical

interconnect applications, two dimensional modulator arrays are flip-chip bonded

directly to a CMOS transceiver chip, thus eliminating the need for high-speed

33

electrical packaging. The transceiver is fabricated in a 90 nm CMOS process and

employs a novel pulsed-cascode modulator driver [4] that is capable of supplying an

output voltage swing of 2 V (twice the nominal 1 V supply) without overstressing

thin-oxide core CMOS devices. Completing the optical link is a low voltage

integrating and double-sampling receiver front-end [5] that eliminates the requirement

of a high bandwidth transimpedance amplifier (TIA).

This work is believed to be the first demonstration of an optical interconnect

transceiver operating at 1550 nm with a III-V output device directly integrated onto

CMOS. First, the novel QWAFEM architecture is described, including the fabrication

procedure for devices on InP substrates. A description is then given of the electrical

circuits used in the transceiver. The experimental setup and procedure are described,

and results reported. Last, conclusions are drawn from this work.

2.1 The QWAFEM, a novel modulator architecture

2.1.1 QWAFEM geometry

The QWAFEM, shown in Fig. 1, is a modulator with surface-normal access which

uses angled mirrors to direct the beam along an obliquely incident pathway through

the p-i-n diode active region of the device. The mirrors are etched using a selective

etch which stops at a {111} plane of the substrate. Because the etch angle is greater

than 45° to the wafer surface, the beam undergoes three bounces, and because they are

each beyond the critical angle in the substrate material, the beam undergoes total

internal reflections. As shown in Fig. 2, this geometry ensures that for a surface

normal input beam, the output beam will exit normal to the surface as well. Also, the

displacement between the input and output beams is constant, such that this modulator

is tolerant to beam misalignments.

34

Input Output

Substrate

PIN diode

P and N contacts

Antireflection coating

Input Output

Substrate

PIN diode

P and N contacts


Input Output

Substrate

PIN diode

P and N contacts


Figure 2.1. The QWAFEM architecture. The diagram shows that the input beam enters through the substrate normal to the surface, impinges upon the p-i-n diode active region at oblique incidence after reflection from a flat mirror, and after a second reflection, exits the substrate normal to the surface and displaced from the input beam.

Figure 2.2. The triple-bounce geometry which is used in the QWAFEM is such that a lateral displacement of the input beam results in an equal lateral displacement of the output beam. The beams' separation is fixed by the spacing and angle of the mirrors. Adapted from [3]

35

Figure 2.3. Diagram (a) shows a single reflection at a semiconductor-air interface beyond the critical angle, where the beam is totally internally reflected. Diagram (b) shows the situation where there is a partial reflector, forming an asymmetric Fabry-Perot cavity on resonance. In the actual operation, successive passes of the beam may overlap one another due to the finite spot size, and a fraction of the beam leaks out on successive passes of the resonator. Figure is from [3].

2.1.2 QWAFEM advantages

The architecture has a number of advantages. Since the input and output ports are

surface-normal, devices can be arrayed in two dimensions. Also, since the input and

output are through the modulator substrate, the architecture is well suited to hybrid

integration of a chip containing modulators with a chip with electrical circuits, such

that the surfaces of the two wafers containing devices can be in physical contact, while

the beams do not need to pass through the electronics chip. Separation of the input

and output beams avoids the need for an optical components to separate the beams,

such as beamplitters, which in many implementations will entail a fourfold insertion

loss. In addition, the constant separation distance means that once a test setup is

aligned to measure the response of one device, by realigning the optical chip, it is easy

to test multiple modulators on a chip without making any adjustments in the rest of the

optical apparatus. For future parallel link implementations, it should be possible to

perform a one-step alignment of an array of lensed fibers for input and output coupling

36

to the modulator chip, provided the pitches of the fibers and the modulators are

matched.

The oblique incidence of the beam upon the active region leads to several advantages,

the first of which is a longer interaction distance of the light with the active region by

a factor of about 1/cos(θ), where θ is the angle from normal within the quantum well

superlattice. Also, a large angle of incidence increases the Fresnel reflection

coefficients between materials with modest refractive index differences. TE incidence

is used in this device since it gives a higher reflectivity due to Fresnel reflections than

TM oblique incidence. As a result of increased reflectivity at dielectric interfaces

compared with normal incidence, an epitaxially grown distributed Bragg reflector

(DBR) of only three layer pairs is sufficient to create an asymmetric Fabry-Perot

resonator with substantial reflectivity. A schematic showing how a DBR mirror

enhances interaction of light with the active region is shown in Fig. 3. Oblique

incidence results in a large optical bandwidth both because the wave accumulates

phase more slowly in the surface-normal direction with respect to a surface-normal

beam, and because the enhanced-reflectivity DBR mirrors have a shorter effective

optical penetration distance, measured in number of layers, than in a surface-normal

architecture using layers with the same index contrast.

2.1.3 Method of simulations

The optical design of QWAFEM wafers was performed using simulations from a

transfer matrix method described in Appendix A. In order to model absorption in the

quantum well superlattice, a wafer with a p-i-n structure containing quantum wells

was grown, and photodiodes with antireflection coatings on both sides were

fabricated. Photocurrent spectra were measured while sweeping the wavelength of

excitation light from a tunable laser and sweeping the applied reverse bias voltage.

From these photocurrent spectra, the absorption coefficient was calculated, and a

complex index of refraction was calculated using the Kramers-Kronig relations. The

refractive indices of the substrate and the InGaAsP DBR mirror layers were modeled

37

using data from ellipsometry measurements. Transfer matrix simulations of devices

were used in conjunction with a multivariate optimization code to optimize

parameters. The optimization code worked by choosing a fitness parameter from the

simulation to be maximized (such as the contrast ratio, or absolute change in fraction

of emitted light ‘ΔR’), and iteratively finding the change of the fitness parameter per

unit change in each layer thickness, and updating the structure in each iteration. A

notable trade-off in the device design involves the reflectivity of the DBR mirror and

the focused spot size. As the reflectivity of DBR is raised, the optical bandwidth of

the device will decrease, and the minimum focused spot size usable in the resonator

and the maximum contrast ratio may increase. But, a tightly focused spot is desirable

to allow the use of a reduced-size device mesa. A smaller mesa will reduce the

capacitance, though it will decrease the tolerance of the design to misalignments of the

optical beam As a result, choosing the focal spot size and resonator reflectivity

involves a trade-off affecting the contrast ratio, capacitance, optical bandwidth, and

beam misalignment tolerance.

2.1.4 Fabrication

The modulators are fabricated on a double-side polished (100) InP wafer, upon which

InGaAs/InP epitaxial layers have been grown via metal-organic chemical vapor

deposition. The growth consists of a PIN diode, containing a MQW structure in the

intrinsic region and a 3-period InGaAsP/InP distributed Bragg reflector (DBR) in the

N-doped region. Mesas are etched for the diodes, and metal P and N contacts are

deposited in an evaporator. On two opposite sides of each mesa, mirrors are

selectively etched in the substrate to reveal the {111} planes, using a two-step wet

etch [6], using the bottom-most InGaAsP layer as a hard etch mask. The back surface

of the InP substrate is antireflection coated with Si3N4 to minimize insertion loss.

Building upon previous work [3], in this implementation of the QWAFEM, the

spacing of modulators was changed to match the pitch of the CMOS transceiver chip,

and the diode mesas were resized to reduce capacitance. The devices fabricated range

38

from 20x60 μm to 40x90 μm in diode area, corresponding to designed capacitances

ranging from 700 fF-2.5 pF. To avoid stringent growth thickness calibration, three

epitaxial wafers were grown with different resonator lengths. Each resonator had two

sacrificial layers, of which none, one, or both could be selectively etched to optimize

the resonator length. The optimal combination of wafer and number of sacrificial

layers etched was chosen after experimental comparison of nine fabricated device

arrays. A SEM image of the modulators used in this study is shown in Fig. 4.

AB

C D

E

AB

C D

E

AB

C D

E

Figure 2.4. SEM image of QWAFEM. A: Diode mesa, B: P contact, C: N contact, D: Electrically isolated N-doped region, E: Selectively etched mirror

2.2 CMOS Transceiver

An optical interconnect transceiver was designed by my colleague Sam Palermo. The

transceiver was designed with the goal of minimizing power consumption through the

39

use of an innovative architecture, while driving efficient optical devices with a small

voltage swing. This section summarizes his design for completeness in this discussion.

2.2.1 Transceiver Architecture

The optical interconnect transceiver architecture is shown in Fig. 5. In order to enable

short bit periods without consuming excessive area and power in clock generation and

distribution, a multiple-clock-phase multiplexing architecture is used at both the

transmitter and receiver. In the transmitter frequency synthesis phase-locked loop

(PLL), a five-stage ring oscillator provides five sets of complementary clock phases

spaced a bit period apart. These phases are used to switch a level-shifting multiplexer

to produce a serial data stream with a data rate of five times the clock frequency. The

multiplexer serial output is then buffered by the modulator driver output stage [4]. At

the receiver side, the input photocurrent is integrated onto the input node capacitance

and a double-sampling technique is used to resolve the data bits [5,7]. A

demultiplexing factor of five is achieved directly at the input node using five uniform

clock phases from the clock recovery system.

2.2.2 Modulator Driver

For modern CMOS technologies, an output swing greater than the nominal power

supply is required in order to provide an appropriate contrast ratio with integrated

surface normal electroabsorption modulators. This conflicts with CMOS reliability

considerations [8,9] which constrain the maximum static voltages across a core

transistor’s gate, source, and drain terminals to be no more than the nominal power

supply, while transient voltage spikes must not exceed more than 20-30% above this

limit. Thick oxide I/O devices that are rated for higher voltage operation could

potentially be used to supply the necessary modulator drive voltages, but these thick

oxide devices cannot match the core CMOS devices’ speed. Thus, the challenge is to

provide at high data rates an acceptable output swing without overstressing the core

devices. To address this, a pulsed-cascode output stage is used that reliably supplies a

40

voltage swing of twice the nominal supply and consists of only core devices for

maximum switching speed.

[4:0]

D[4:0]

DataGeneration

QWAFEM

RefClk

Pout

TXRX

Pin

Iavg

Cin

DataRX

DataRX

DataRX

DataRX

DataRX

DataRX

DataRX

DataRX

DataRX

PhaseRX

CDR

[4:0]

DRX[4:0]

Ph[4:0]

Vin

LowPassFilter

Tb

5-to-1Mux

Bias

PDBias

Photodiode

DataVerifier

PinDhigh

QWAFEMDriver

Dlow

Multi-PhasePLL

Figure 2.5. Optical Transceiver Architecture

Figure 2.6. Pulsed-cascode output stage

41

Fig. 6 shows the pulsed-cascode output stage which accepts both a “low” input, INlow,

that swings between Gnd and the nominal chip Vdd and a “high” input, INhigh, with

the same data value that has been level-shifted to swing between Vdd and Vdd2,

where Vdd2 is nominally twice the voltage of Vdd. The level-shifting multiplexer

circuitry is detailed in [4]. Static voltage overstress is eliminated in the output stage

cascode structure by splitting the output voltage equally across the series transistors.

Pulsing the gates of the cascode transistors (MN2 and MP2) during transitions with

NAND-pulse and NOR-pulse gates respectively, allows this driver to eliminate

transient drain-source voltage (Vds) overstress present in static-biased cascode drivers

[10] and prevents transistor degradation from hot-carrier injection [11].

(a)

(c)

(a) (b)

Figure 2.7. Transient simulation of pulsed-cascode output stage: falling transition (a) nMOS gate voltages (b) nMOS drain voltages (c) nMOS Vgs and Vds

42

Fig. 7 shows simulation waveforms of the pulsed-cascode modulator driver with a

nominal CMOS supply of 1 V providing a 2 V output transition from high to low. A

falling transition from the “low” input switches the bottom nMOS (MN1) to drive

node midn to Gnd and a simultaneous falling transition on the “high” input triggers a

positive pulse from the NOR-pulse gate that drives the gate of MN2 from Vdd to near

Vdd2 to allow the output to begin discharging at roughly the same time that the MN2

source is being discharged (Fig. 4(a), (b)). Thus, the cascode nMOS drain-source

voltage does not overly exceed the nominal supply voltage (Fig. 4(c)). The NOR-

pulse gate is sized such that the gate of MN2 does not swing all the way to Vdd2 and

the edge-rate of the pulse signal also matches the falling rate of midn. Therefore,

during the transition, a gate-source voltage that does not overly exceed the nominal

supply is developed across MN2. The “high” input also activates a pull-down nMOS

(MN3) to drive node midp from Vdd2 to Vdd to prevent excessive Vds stress on MP2.

Similarly, during an output transition from low to high, the “high” input switches the

top pMOS (MP1) to drive node midp to Vdd2 and the “low” input triggers a negative

pulse from the NAND-pulse gate that drives the gate of MP2 transistor from Vdd to

near Gnd. For ratios of Cout/Cmidn from 1.3 (unloaded) to 15.5, no voltage spikes

between the gate, source, and drain terminals of any output devices exceeds more than

20% above the supply voltage.

It is important that the cascode transistors have similar drive strength as the top or

bottom transistors to reduce Vds stress during transients. Thus, in order to minimize

the body voltage effect on the cascode transistors, they are placed in separate wells

that are dynamically biased with replica circuitry to track their source voltages. This

reduces the cascode transistors’ threshold voltages, resulting in a similar voltage drop

across the two series driving transistors. The increased drive strength of the cascode

transistor also serves to reduce the modulator driver’s output transition time. Little

power and area overhead is necessary for the replica bias circuitry, as the replica

transistors are sized to be less than 10% of the main driver transistors.

43

2.2.3 Integrating and Double-Sampling Receiver

While receiver circuitry power and area may not be a primary issue for traditional

telecom applications which demand high sensitivity, in high density optical

interconnect applications performance parameters such as sensitivity must be balanced

with power and area constraints. A receiver front-end architecture that reduces the

number of linear gain elements, and thus is less sensitive to the reduced gain in

modern CMOS processes, is the integrating and double-sampling front-end [7]. An

absence of high gain amplifiers allows for savings in both power and area and makes

the integrating and double-sampling architecture more suitable for chip-to-chip optical

interconnect applications.

Figure 2.8. Integrating and double-sampling receiver front-end.

44

The integrating and double-sampling receiver front-end [5], shown in Fig. 8,

demultiplexes the incoming data stream with five parallel segments that include a pair

of input samplers, a buffer, and a sense-amplifier. Two current sources at the receiver

input node, the photodiode current and a current source that is feedback biased to the

average photodiode current, supply and deplete charge from the receiver input

capacitance respectively. For data encoded to ensure DC balance, the input voltage

will integrate up or down due to the mismatch in these currents. A differential

voltage, Δvb, is developed in each receiver segment by sampling at the beginning and

end of a bit period defined by the rising edge of the recovered clocks Φ[n] and Φ[n+1]

respectively. While in a previous implementation [9] Δvb was applied directly to an

offset-corrected StrongArm latch [12] used as a sense-amplifier for data regeneration,

the reduced supply voltage that comes with scaling technologies causes the integrating

input to exceed the sense-amp input range. In order to fix the sense-amp common-

mode input level and buffer the sensitive sample nodes from kickback charge, a

differential buffer is inserted between the samplers and the sense-amp. The power

penalty of the additional buffer is quite small (250 μW per segment), as buffer gain is

low to avoid sense-amp offset saturation and bandwidth requirements are relaxed due

to input demultiplexing. The use of pMOS samplers provides a receiver input range

from 0.6-1.1 V. Demultiplexing directly at the input allows the sense amp sufficient

time (five times the bit period) for data regeneration and precharging, thus eliminating

the requirement for a TIA operating at the bit rate.

2.3 Experiment

Three experimental configurations were used, shown in Fig. 9. In the first, laser light

was free-space coupled onto the modulators, and the output was collimated and

coupled onto a large area photodetector for DC contrast ratio measurements. In the

second configuration, light exiting the modulators was coupled into a fiber for

transition speed measurements with a high-speed oscilloscope. In the final

45

COPOM

HWP

O2

O1QM

HSD

BS

BS

A.

B.

C.

LAD

M

COPOM

HWP

O2

O1QM

HSD

BS

BS

A.

B.

C.

LAD

M

Figure 2.9. Pulsed- Transceiver link schematic, showing three configurations A-C for different measurements. Linear-polarized light enters through the fiber and free-space collimator (CO), and rotatable half-wave plate (HWP). Focusing onto the QWAFEM modulator (QM) is accomplished by a microscope objective (O1), and the spatially displaced output beam of the modulator is reflected by the pick-off mirror (POM). In (A) for DC contrast ratio measurements, collimated light is absorbed by a large-area photodetector (LAD). In B for high speed rise and fall time measurements, the light is reflected off a second mirror and focused into a single-mode fiber. In the full transceiver link, C, the light is focused by a second microscope objective (O2) onto a high speed detector (HSD). Alignment of the beam on the modulator and detector is accomplished with an IR camera (not shown), an LED for illumination, and two removable pellicle beamsplitters (BS).

configuration light was coupled into high-speed detectors to complete the transceiver

link.Common to all of the configurations, an array of InP QWAFEMs was flip chip

bonded to the CMOS transceiver chip with eight transmit channels sized for varying

drive strength and two receive channels, shown in Fig. 10(a). The transceiver was

fabricated in a 1V 90nm CMOS process.

46

(a)(a) (b)

Figure 2.10. (a) Die micrograph of CMOS transceiver. (b) 1550nm photodiodes wirebonded to receivers. The chip was placed in an open-cavity surface-mount package on a test board mounted on a 3-axis translation stage. An HP8133A pulse generator supplied the reference clock to the transmitter PLLs, and the transmit data sequence was controlled with an on-chip 20-bit register that can be programmed with a computer via a serial testing interface.

Light from an Agilent 81680A tunable laser with a range of 1457-1584 nm was

coupled via polarization-maintaining fiber into a free space collimator. The collimator

was followed by a half-wave plate, facilitating alignment such that the linear polarized

light in the QWAFEM’s resonator would be TE polarized (i.e., in the plane of the

quantum wells) for optimal performance. The collimated beam was focused onto the

modulator array with a Mitutoyo infinity-corrected 10x NIR objective with a free

space focal spot diameter of about 12 µm. Between the collimator and objective, a

removable pellicle beamsplitter was used for alignment of the beam with the

modulator array. The light entry and exit points on the array’s substrate were

separated by 200 μm. After collimation by the microscope objective, the beam exiting

the modulator was separated for detection by a pick-off mirror. A photodetector was

placed in the beam path for DC contrast ratio measurements. The default high-speed

47

modulation of the devices was bypassed by setting each bit in the 20-bit sequence the

same, and the modulators were switched by changing the bias voltage applied to the P-

contacts of all driven modulators. For each working device, the optimal combination

of bias voltage and wavelength were chosen to maximize the contrast ratio.

The maximum contrast ratio measured on a device was 2.43, measured at 1528 nm for

a 2 V swing. Upon coupling the beam into a single mode fiber, the same device

yielded a peak contrast ratio of 3.57 for the same conditions. Modulation of the beam

in this device could also result in change of shape of the beam, because different

angular components in the beam would interact differently with the resonator. Any

such change of shape corresponds effectively to coupling light into higher order

modes. Such higher-order modes would not propagate in the fiber, so any such power

in those modes would be lost, hence actually possibly increasing the contrast of the

modulator in the system and explaining the larger contrast ratio observed after

coupling into the single mode fiber. It was found that the contrast ratio decreased as

the optical power in the system was increased, which may be due to photogenerated

carriers screening the field applied across the MQW region. A test of contact

resistance on the modulator chip indicated that the metal contacts to the devices were

non-ohmic, which may be responsible for an inefficient sweep-out of the carriers, and

such imperfect contacts may also limit the response time of the modulator.

Rise and fall times of the QWAFEM modulators were measured using an Agilent

86109A 30 GHz oscilloscope. After the pick-off mirror, the setup was modified such

that the beam was reflected off a second mirror and into a single-mode fiber. The

fiber-coupled light passed through an erbium-doped fiber amplifier and a variable

attenuator, and into the oscilloscope. The devices were set to send a pattern of 10

sequential bits on, then 10 sequential bits off, to measure rise and fall time. The

fastest transmitter had a rise time of 1.2 ns and a fall time of 900 ps, measured 10% to

90%. That device’s estimated capacitance was 1.5 pF. The device with the highest

contrast ratio, which was used in the transceiver link, had a rise time of 3.8 ns and a

fall time of 3.9 ns, and its estimated capacitance was 1.8 pF.

48

For the high-speed transceiver link, the test setup was modified such that output light

from the pick-off mirror was coupled via a Mitutoyo infinity-corrected 20x NIR

objective into a 20 µm diameter high-speed InGaAs/InP photodetector (PDCS20T,

Albis Optoelectronics, Switzerland). The photodetectors are attached to the receivers

on a second identical CMOS transceiver chip via short wire-bonds (Fig. 10(b)). This

chip is also packaged and attached to a test board mounted to a 3-axis translation

stage. To enable measurements over a wider range of optical power, the output of the

Agilent 81680A tunable laser was coupled via non-polarization-maintaining fiber

through an erbium-doped fiber amplifier, a variable fiber attenuator, a polarization

controller, and into the free-space collimator. In this configuration it was possible to

optimize the phase and bias of the detectors. The received data is verified with an on-

chip 20-bit register whose output can either be scanned-out to a computer or also be

observed on an oscilloscope. The bit error rate of individual worst-case bit sequences

was measured as the input optical power and detection phase were adjusted.

While the CMOS transceiver was designed to operate nominally at 5-16 Gb/s, the rise

time of QWAFEMs did not permit operation at that speed. When the chip was

triggered too slowly its performance degraded due to limited voltage-controlled

oscillator (VCO) range. Thus, in order to get meaningful results from the transceiver

link, we synthesized a repeating 10-bit pattern by specifying the 20-bit sequence in

pairs of bits to allow the VCO to operate at a higher frequency. Since the receiver

chooses the decision threshold based on the average current at the photodetector, it

was necessary to send signals with an equal number of ones and zeros. We tested

several bit patterns, attempting to generate the worst-case detection scenario available

with 10 bits. By taking a histogram of each of the worst-case bits in the pattern we

were able to estimate the error rate. Transmission of 10-bit sequences was tested over

a range of 1 Gb/s to 1.8 Gb/s. At 1.8 Gb/s with an average detected power of -15.2

dBm, the BER estimated from the histogram was 10-10. The bit timing margin was

such that the BER was estimated at less than 10-9 over a total range of phase shift of

the receiver clock of 47% of the period of one bit. Table 1 shows the collected results

of our BER test. The lower data rates required uncharacteristically more power

49

because the link’s performance was degraded as the speed was decreased far below the

chip’s designed clock rate.

Table 2.1 Transmission Characteristics of Optical Link. Sensitivity is the minimum difference between on and off power at the receiver to attain an estimated BER=10-10. The bit timing margin represents the fraction of a bit period by which the sampler phase may be changed and still achieve an estimated BER=10-9.

Data Rate (Gbps) Sensitivity (dBm) Bit timing margin

1 -17.6 0.31 1.1 -17.1 0.35 1.2 -19.4 0.63 1.5 -17.7 0.63 1.6 -16.5 0.66 1.7 -15.6 0.68 1.8 -15.2 0.47

The measured 10%-90% rise and fall times correspond to a ~ 1.7 ns time constant

(assuming a simple one-pole system), which in turn corresponds in our simulations to

~ 1.3 Gb/s maximum data rate. Our measured rates of up to 1.8 Gb/s are somewhat

higher than this. It is possible that changing the bias voltage on the device during

optimization of the signal in the link may have also changed the rise and fall times

from the values measured, hence giving a different data rate limit..

Loss was measured for the optical path. From the laser source to the free space

collimated beam, loss was 0.7 dB. Between there and focusing through the

microscope, off of V-grooves, and separation by the pick-off mirror, loss was an

additional 7.8 dB. Focusing on the device mesa (in the ‘pass’ state of the device)

incurred loss of 2.3 dB. Focusing the beam on the detector the loss calculated from a

photocurrent measurement was 2.6 dB.

The total transceiver power dissipation is 23.6 mW at 1.8 Gb/s. The transmitter power

makes up 15.2 mW, with 3.8 mW to drive the QWAFEM, 8.8 mW for the multiplexer

and buffers, and 2.6 mW for the TX PLL. The receiver consumes 8.4 mW, with 4.5

50

mW from the integrating/double-sampling front-end, and 3.9 mW from the clock

recovery circuitry. Total transceiver area is 0.092 mm2, with 0.017 mm2 for the

transmitter and 0.075 mm2 for the receiver.

2.4 Conclusions

A novel optoelectronic modulator architecture known as the QWAFEM is described,

which combines positive characteristics of surface-normal and waveguide modulator

architectures. Namely, QWAFEM architecture is a good candidate for optical

interconnect systems due to its surface normal input and output ports, its ability to be

arrayed in two-dimensions, its beam misalignment tolerance, and its broad bandwidth

of operation. QWAFEMs were fabricated on InP substrates for operation in the

telecommunications C-band, which were suitable for integration to CMOS due to

simplicity of packaging via flip-chip bonding, and the low voltage drive compatible

with CMOS drivers.

The demonstration of an optoelectronic interconnect transceiver in this study is

believed to be the first such demonstration at 1550 nm using an output device directly

bonded to CMOS. The modulators are driven with a novel pulsed-cascode driver

capable of supplying an output voltage swing of 2 V (twice the nominal 1 V CMOS

supply) without overstressing thin-oxide core CMOS devices. At the receive side, a

sensitivity of -15.2 dBm is obtained with an integrating/double-sampling front-end.

The transceiver achieves 1.8 Gb/s operation with a power consumption of 23.6 mW.

51

2.5 References

[1] Miller, DAB, Chemla, DS, Damen, TC, Gossard, AC, Wiegmann, W, Wood, TH,

and Burrus, CA, Electric Field Dependence of Optical Absorption near the Bandgap of

Quantum Well Structures, Phys. Rev. B 32, 1043-1060, (1985).

[2] Roth, JE Palermo, S, Helman, NC, Bour, DP, Miller, DAB, Horowitz, M, An

optical interconnect transceiver at 1550nm using low voltage electroabsorption

modulators directly integrated to CMOS, accepted to IEEE Journal of Lightwave

Technology, (2007).

[3] Helman, NC, Roth, JE, Bour, DP, Altug, H, and Miller, DAB, Misalignment-

Tolerant Surface-Normal Low-Voltage Modulator for Optical Interconnects, IEEE J.

Sel. Topics. Quantum Electron., 11, No. 2, 338 – 342, (2005).

[4] Palermo, S, and Horowitz, M, High-speed transmitters in 90nm CMOS for high-

density optical interconnects, Proc. Eur. Solid-State Circuits Conf., pp. 508-511,

(2006).

[5] Palermo, S, Emami-Neyestanak, A, and Horowitz, M, A 90nm CMOS 16Gb/s

transceiver for optical interconnects, to be published in ISSCC Dig. Tech. Papers,

(2007).

[6] Bonsch, P, Wullner, D, Schrimpf, T, Schlachetzki, A, and Lacmann, R,

Ultrasmooth V-grooves in InP by two-step wet chemical etching, J. Electrochem. Soc.,

vol. 145, no. 4, pp. 1273–1276, (1998).

[7] Emami-Neyestanak, A, et al., A 1.6Gb/s, 3mW CMOS receiver for optical

communication, Symp. VLSI Circuits, pp. 84-87, (2002).

[8] Moazzami, R, and Hu, C, Projecting gate oxide reliability and optimizing

reliability screens, IEEE Trans. Electron Devices, vol. 37, no. 7, pp. 1643-1650

(1990).

52

[9] Emami-Neyestanak, A, et al., CMOS transceiver with baud rate clock recovery for

optical interconnects, Symp. VLSI Circuits, pp. 410-413 (2004).

[10] Woodward, T, et al, Modulator-driver circuits for optoelectronic VLSI, IEEE

Photon. Tecl. Lett., Vol. 9, No. 6, pp. 839-841 (1997).

[11] Leblebici, Y, and Kang, S, Modeling and simulation of hot-carrier-induced device

degradation in MOS circuits, IEEE J. Solid-State Circuits, vol. 28, no. 5, pp. 585-595

(1993).

[12]Montanaro, J, et al, A 160MHz, 32b, 0.5W CMOS RISC microprocessor, IEEE J.

Solid-State Circuits, vol. 31, no. 11, pp. 1703-1714, (1996).

53

Chapter 3: Ge/SiGe Quantum Wells Grown on Si for Electroabsorption

This chapter motivates and describes the quantum confined Stark effect in germanium

quantum wells with silicon germanium barriers, grown on silicon substrates. First, a

description of the use of the quantum confined Stark effect in III-V materials is given,

then the effect in Ge/SiGe quantum wells is introduced. The majority of the chapter

consists of a description of measurements from the epitaxial wafers grown for our

device fabrication efforts and physics experiments. Finally a description is given for

possible future work to further develop these materials for optoelectronic modulators.

3.1 Materials for the quantum confined Stark effect in quantum wells

3.1.1 Typical Materials for quantum wells

Electroabsorption modulators using the quantum confined Stark effect (QCSE) have

typically been made using quantum wells in III-V semiconductors, epitaxially grown

on GaAs or InP substrates. The QCSE was first demonstrated in GaAs/AlGaAs

quantum wells operating around 850 nm [1]. Many devices using InP substrates have

operated around 1500-1700 nm [2]. Some other examples of materials include

GaInNAs quantum wells grown on GaAs showing modulation around 1200-1300 nm

[3,4], and InGaN/GaN wells on sapphire substrates with modulation at 420 nm [5].

Since these modulators are typically used for communications links between

electronic systems, it is desirable to integrate them densely with silicon chips. Since

elements in groups III and V act as dopants for silicon, III-V semiconductors cannot

be easily integrated with CMOS electronics fabrication processes. Photonic-electronic

chip integration can be accomplished using flip-chip bonding [6].

54

phonon

E

k

e+

h-

photon

Direct Absorption Indirect AbsorptionE

e+

h-

photon

phonon

E

k

e+

h-

photon

Direct Absorption Indirect AbsorptionE

e+

h-

photon

Figure 3.1. Illustration of the process for absorption of a photon at the band edge energy in direct and indirect materials, using a representation of the band energy in energy – momentum space. Absorption of a photon creates an electron-hole pair. In indirect material, the absorption of a photon at the band edge energy requires creation or annihilation of a phonon to conserve momentum.

3.1.2 Direct versus Indirect Absorption

The previously mentioned III-V quantum well materials all have in common direct

bandgaps, meaning that the maximum energy in the valence band occurs at the same

momentum as the minimum energy of the conduction band. When a photon is

absorbed in a direct semiconductor with energy around the bandgap energy, it has a

finite probability of being absorbed and creating an electron near the conduction band

minimum and a hole near the valence band maximum. In an indirect semiconductor, a

photon with energy near the bandgap energy may also be absorbed, but when this

occurs a phonon must be either created or annihilated to account for the momentum

difference between the electron and hole created. Since the requirement of

simultaneous interaction with a phonon makes the event less probable, indirect

absorption is far weaker an effect than direct absorption. The processes are illustrated

in Fig. 1. As the QCSE is used to strongly modulate the absorption coefficient in

devices, it is almost always used in direct bandgap material, and only a few examples

of modulators exist using the QCSE in indirect bandgap material [7,8].

55

3.1.3 Attempts at Electroabsorption in Quantum Wells Using

Group IV Materials

In previous efforts to create a technology for modulators compatible with silicon

substrates, electroabsorption modulation was shown using quantum wells made from

SiGe compounds [9-11], though these demonstrations did not show a strong

modulation effect. There has also been work towards creating direct-gap group IV

materials using a ternary system of Si, Ge, and Sn [12,13], which could be grown on

silicon, though the goal of creating a direct-gap material has yet to be achieved.

3.1.4 Germanium/silicon germanium quantum wells

Description and Motivation Recently we demonstrated a strong quantum-confined Stark effect in strained Ge

quantum wells with SiGe barriers, grown on silicon substrates [14,15]. The work was

performed with a reduced-pressure chemical vapor deposition reactor, which is a

commercial technology commonly found in integrated circuit foundries. Germanium

is a group IV material compatible with silicon electronics, and SiGe composites are

already exploited in electronics by making channels of strained SiGe and exploiting

the high mobility of germanium [16]. CVD grown pure Ge has been integrated into a

CMOS process for monolithically integrated photodetectors. This leads us to believe

that our material will be compatible with silicon electronics.

Band Structure Ge is an indirect bandgap semiconductor, but has a local minimum in the conduction

band at the gamma point, where the global maximum of the valence band is located.

The indirect bandgap is 0.62 eV, while the direct gap is at 0.8 eV, corresponding to

1550 nm, the center of the C-band for telecommunications. Since the direct

absorption is stronger, the absorption spectrum near the band edge is dominated by the

direct bandgap absorption. The bandgap of silicon at the gamma point is >3 eV, and

there is type I alignment between strained Ge quantum wells and SiGe barriers at the

56

gamma point. In our initial demonstration, a relaxed buffer of Si.1Ge.9 was grown on

silicon, and lattice-matched strained Ge/Si.15Ge.85 quantum wells and barriers were

grown. Strain is inherent in these materials since the lattice constant of Ge is 4%

greater than that of Si. It was not known whether these materials would display the

QCSE at all, and whether the effect would be strong. Only a few demonstrations of

the QCSE in indirect gap material have been made [7,8], One concern was that the

electron lifetime would be so short that the exciton would be too broad to be useful for

modulating light, though this did not prove to be the case.

The bandgaps of the materials used are illustrated in Fig. 2.

Figure 3.2. Illustrations of the band structures of materials in our epitaxial growth. Figure is from Kuo et al [15].

We used linear interpolation from published values to calculate the band offsets

between wells and barriers at zone center for our materials, and found that the offsets

for the electron, heavy hole, and light hole were be 400meV, 101meV, and 47meV,

respectively. The band structure is illustrated in Fig. 3. This band structure illustrates

another interesting feature of this material, which is that in the conduction band, there

is large band offset at the direct gap, but a small band offset for the global minimum

indirect gap. The implication is that it may be possible to confine light in several

different electron states, while the carriers which are absorbed will scatter to the local

minimum, and be easily swept out of the intrinsic region.

57

The effect of strain on the bandgap of Ge has not been well quantified, but unstrained

Ge would have a bandgap of about 0.8eV at the Γ point, corresponding to 1550 nm.

The bilateral compressive strain will increase the bandgap, and in addition the

quantum confinement of the electron and hole states also gives the first exciton state a

larger energy than the bandgap. The exciton peak in our first study was

experimentally found to be at 0.88 eV or 1410 nm. Our work is distinct from previous

efforts using SiGe quantum wells, which used more Si-rich materials. It is necessary

to use pure Ge or high-Ge fraction SiGe such that there will be a local minimum in the

conduction band at the Γ point.

Figure 3.3. Band lineup for quantum wells and barriers and SiGe relaxed buffer. Figure is from Kuo et al [15]. In that work, Si0.1Ge0.9 buffers were used, and the band discontinuities of the heavy hole, light hole, and electron at the Γ point between wells (Ge) and barriers (Si0.15Ge0.85) were calculated to be 101 meV, 47 meV, and 400 meV, respectively.

58

3.2 Epitaxially grown Ge/SiGe wafers for optoelectronic modulators

3.2.1 Description of wafers contracted from Lawrence

Semiconductor Research Laboratory

For our group’s subsequent research on modulators and quantum well physics, we

contracted growth of twelve wafers from Lawrence Semiconductor Research

Laboratory (LSRL) in Tempe, AZ. It was possible to transfer the chemical vapor

deposition growth recipe developed at Stanford by Yu-Hsuan Kuo [7] to LSRL with

only minor adjustments for calibration in a different reactor. The robustness of the

original recipe gives further evidence that this material can be manufactured.

Epitaxial growths by LSRL, described in Appendix D, were done on 8” Si wafers,

which were subsequently sent to Ultrasil in Hayward, CA to be laser-cored to make

two 4” wafers per 8” wafer, plus excess material. 4” wafers are required for use in

some machines used for processing in Stanford Nanofabrication Facility.

The growth on each sample was a PIN diode, with quantum wells in the intrinsic

region. The wafers used were lightly p-doped, and initially a p-doped Si.1Ge.9 buffer

layer was grown in two steps, each followed by a high-temperature anneal [17]. The

anneals were used to reduce defects in the crystal and reduce surface roughness, in

order to obtain material of sufficient quality to grow a diode with low leakage current.

This was followed by a thin region of undoped buffer, then the strained Ge/Si.163Ge.837

superlattice. A top region of undoped Si.1Ge.9 buffer was deposited, followed by an n-

doped top contact region. The samples fabricated had 10, 20, 40, or 60 quantum wells

(QW). The target quantum well thickness and barrier thickness were 10 nm and 16

nm for the majority of samples, while samples with target quantum well thicknesses of

12.5 nm and 15 nm were also grown for experiments on quantum well physics.

59

For optical spectroscopy measurements, arrays of antireflection-coated PIN diode

mesas were fabricated from each wafer. This and other fabrication recipes are in

Appendix E, and a diagram of the diode mesa is in Fig. 4.

Figure 3.4. Diagram of fabricated PIN photodiode in SiGe epitaxy. Figure is from Kuo et al [12].

3.2.2 Wafer Characterization

Upon receipt by Stanford, the wafers were characterized using several methods to

discern how well they matched our specifications.

Total Epitaxial Growth Thickness

Profilometry First, wafers were patterned, and the entire epitaxy was removed with a selective etch

that removed SiGe composites but not Si [18]. The step heights were measured with a

profilometer, and it was found that the total epitaxial growths were 1.75 to 2.1 times

thicker than specified.

AR Coat

60

Table 3.1. Designed total epitaxy thickness versus thickness measured by surface profilometry.

Wafer # Designed thickness nm Measured Ratio 1 1176 2300 1.9558 2 921 1820 1.9761 3 1426 2690 1.8864 4 1970 3980 2.0203 5 2515 5300 2.1074 6 1245 2590 2.0803 7 1314 2430 1.8493

12 (SOI) 1050 1840 1.7524

Scanning Electron Microscopy Also, a Scanning Electron Micrograph of Wafer 1 was taken (Fig. 5), and thicknesses

were measured. These measurements roughly agreed with the step height

measurements.

Explanation of Thickness Discrepancy It was determined that the reason for the discrepancy between the designed and

measured thicknesses is that LSRL had calibrated the growth thicknesses using

incorrectly calibrated secondary ion mass spectrometry (SIMS) measurements. In

SIMS, a crater is sputtered in the material to be measured, and products removed from

the crater are analyzed with a mass spectrometer, giving a depth resolved

measurement of atomic species concentrations. The SIMS depth was calibrated to a

Si-rich SiGe calibration sample. It turned out that the sputter rate was about twice as

fast in our Ge-rich material compared to their Si-rich standard. Despite the error, the

epitaxial growths were useful for physics experiments and device demonstrations.

61

Figure 3.5. Scanning electron micrograph of Wafer 1. The quantum well region can just be discerned through the slight contrast in darkness of the quantum well and barrier layers.

Table 3.2. Designed layer thicknesses for Wafer 1 versus thickness measured by scanning electron microscopy

Designed thickness nm Measured nm Ratio Total thickness 1176 2120 1.8

Buffer + lower spacer 600 1150 1.92 QW region 276 530 1.92

Upper spacer + N-doped region 300 400 1.33

Secondary Ion Mass Spectrometry We contracted measurements via Secondary Ion Mass Spectrometry (SIMS) from

Evans Analytical Group (EAG) on Wafers 1 and 7. The SIMS of Wafer 1 is shown in

Fig. 6.

62

SiGe sample

1E+14

1E+15

1E+16

1E+17

1E+18

1E+19

1E+20

1E+21

0 0.5 1 1.5 2 2.5 3

DEPTH (µm)

CO

NC

ENTR

ATI

ON

(ato

ms/

cc)

1E+00

1E+01

1E+02

1E+03

1E+04

1E+05

1E+06

1E+07

1E+08

1E+09

Cou

nts

Per S

econ

dP(repeat)

P

Si(raw ion counts)->

As

B

C

O

Figure 3.6. SIMS of Wafer 1, showing dopants P, As, and B, as well as C and O.

This measurement was useful for measuring the thickness of individual layers, though

it was not possible to resolve the individual quantum wells to a sufficient degree to

determine their concentration. Of great interest here were the concentrations of carbon

and oxygen, as the presence of either could contribute to poor crystal quality. The

oxygen content was lower than a wafer grown at Stanford (4x1017/cm3 vs.

2x1018/cm3). and the carbon content was also lower (detection threshold of 2x1015/cm3

vs. 3x1016/cm3). Measurement of the doping with SIMS is also important. Doping

should be very high in the regions that are intentionally doped, and should be as low as

possible in the intrinsic region. High doping enables low-resistance contacts for high-

speed devices, while any stray doping in the intrinsic region leads to a non-constant

electric field through the device, and smears out the exciton absorption peaks,

reducing the ability to strongly modulate the absorption. In this SIMS measurement,

the intrinsic doping is at the detection threshold for all dopants. In the p- region, the

63

boron doping level was lower than specified. In the n-region, there was curiously a

spike in phosphorus doping, while no phosphorus was intentionally present in the

sample. This is curious since phosphorus was also unintentionally present in a wafer

grown at Stanford with a similar reactor from the same manufacturer, an ASM Epsilon

II reduced-pressure chemical vapor deposition system. The doping offsets are

important to determine the conversion between applied voltage and electric field,

which is used in the physics calculations for quantum wells. Measurements from this

SIMS scan are given in Table 3.

Table 3.3. Measurements from EAG SIMS (Achieved) compared with targeted values and LSRL’s SIMS results (plot not shown)

CRITERION TARGETED ACHIEVED LSRL SIMS said Ratio Ach/TargTotal Thickness nm 1176 nm 1940 nm 1.649659864Buffer Region nm 600 nm 930 nm 1.55QW Region nm 276 nm 555 nm 2.010869565Cap Region nm 300 nm 455 nm 1.516666667Doping Level B 5.00E+18 2.30E+17Doping Level As 1.00E+19 >1E18 (can't tell)Doping Level P 0 1.00E+18Doping Offset N nm 100 nm 110 nm 1.1Doping offset P nm 100 nm 0 nm 0Oxygen spike height 3.00E+18 1.50E+20Oxygen content in QW 4.00E+17 4.00E+19

The SIMS of Wafer 7 in Fig. 7 (quantum wells designed as 15 nm) was performed

largely to ascertain the doping offsets in the intrinsic region. Also, the Si and Ge

fractions were measured, and the buffer was found to agree well with the designed

concentration of Si.1Ge.9. Again, individual quantum wells and barriers could not be

resolved.

64

Sample 7

1E+14

1E+15

1E+16

1E+17

1E+18

1E+19

1E+20

1E+21

0 0.5 1 1.5 2 2.5 3

DEPTH (µm)

CO

NC

ENTR

ATI

ON

(ato

ms/

cc)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Com

posi

tion

Ge->

Si->

11B

P(repeat)

P

As

Figure 3.7. SIMS of Wafer 7, showing dopants P, As, and B, and concentrations of Si and Ge.

3.2.3 Surface Roughness

Ideally, wafer surfaces would be perfectly smooth. In reality, this is not the case.

Surface roughness may be an indicator of crystalline quality, but in addition, it may be

important for the performance of optical devices in which the surface is part of a

resonant optical cavity. We measured the RMS roughness of Wafers 1 and 5 (10 and

60 quantum wells) using two methods, white light interferometry and atomic force

microscopy (AFM). White light interferometry is fundamentally limited in lateral

resolution by the diffraction limit, and it does not work well on transparent or

translucent materials. Also, it will not accurately detect depths in surfaces which

reflect light at large angles, such that reflected light is not collected by the objective.

However, in contrast to atomic force microscopy, it is a simple noncontact evaluation

65

technique. If it were reliable enough to detect mirror surface quality, it would be

desirable to be able to use white light interferometry instead of AFM. The size of the

region evaluated is different between the two methods in the measurements shown

(180x130 μm for interferometry and 80x80 μm for AFM) but the regions in both sets

of measurements are large enough to capture roughness on the scale of a focused

optical beam (~70 μm diameter). The measurements between the two methods agree

within 25%.

Figure 3.8. White light interferometry measurement of surface roughness. Left: Wafer 1, 10QW, Right: Wafer 5, 60QW.

Figure 3.9. Atomic force microscopy measurement of surface roughness. Left: Wafer 1, 10QW, Right: Wafer 5, 60QW.

66

Table 3.4. Comparison of wafer surface roughness measured using different techniques.

Sample 1, 10QW Sample 5, 60QW White light interferometry 5.5 nm RMS 7.9 nm Atomic force microscopy 6.9 nm 9.2 nm

Atomic force microscopy was also used to look at the smaller scale features on Wafer

5. It reveals pits in the surface when viewed on a smaller scale, shown in Fig. 10.

Figure 3.10. Atomic force microscopy of Wafer 5 showing submicron scale defects

67

3.2.4 Optical Spectroscopy

The PIN photodiodes were used in experiments with a tunable laser, and absorption

coefficients of QW superlatices were calculated using either the measured

transmission through the device or the current through the diode due to optical

absorption. In Fig. 11, the absorption coefficient of Wafer 5 (60 QW) calculated from

photocurrent is shown, assuming a 3000nm absorbing region, for applied reverse bias

0V-35V. Fig. 12 shows the single-pass optical transmission of an antireflection-

coated diode in Wafer 5 over a smaller wavelength range. The transmission

measurement was only performed with Wafer 5, as the use of a large number of

quantum wells for the transmission experiment were necessary to show the large

percentage changes visible in Fig. 12.

1400 1420 1440 1460 1480 1500 1520 1540 1560 15800

200

400

600

800

1000

1200

1400

1600

1800Absorption in cm-1, (G)0V,2.5V,...35V(R)

Figure 3.11. Absorption in QW superlattice of Wafer 5, 60 QW, calculated from photocurrent, assuming a 3000 nm thick absorbing region. The measurement is for applied reverse bias ranging from 0V to 35V.

68

Depending on the sample and the measurement, for our samples with designed

quantum well thickness of 10 nm, the peak absorption was about 1500cm-1-2000cm-1,

and the maximum contrast of the absorption coefficient was about 4.5.

1430 1440 1450 1460 1470 148050

55

60

65

70

75

80

85

90

95

wavelength, nm

perc

enta

ge tr

ansm

issi

on

18.5V

0.5V

1430 1440 1450 1460 1470 148050

55

60

65

70

75

80

85

90

95

wavelength, nm

perc

enta

ge tr

ansm

issi

on

18.5V

0.5V

Figure 3.12. Single pass transmission through Wafer 5, 60 QW, for 0.5V-18.5V reverse bias.

Exciton Width We were interested in learning which of several factors is the main contributor to the

width of the excitons as measured. Assuming the coupling between quantum wells is

negligible, contributions to the exciton width can be grouped in two categories:

Exciton lifetime, and material variations. The lifetime of the exciton can be used to

calculate a Gaussian broadening of the exciton in the frequency domain [19]. As the

direct gap in Ge does not correspond to the global minimum in the conduction band,

the intervalley scattering between the Γ valley and the L valley may limit the lifetime.

This scattering time has been measured to be ~570 fs at low temperature [20].

69

Increasing the temperature may also increase the exciton width if phonon scattering

significantly shortens the exciton lifetime.

Structural variations include differences in quantum well width and applied electric

field over the region of quantum wells being probed. Quantum well widths may vary

in uniformity over the surface of the wafer, or the quantum wells grown in a

superlattice may not all be the same width. Differences in electric field across the

wells may be caused by unintentional doping in the intrinsic region of a sample. We

compared the spectra of the 10QW and 60QW samples (Wafers 1 and 5) to look for

structural variations. The hypothesis is that any structural variations would likely be

more pronounced in the 60QW sample’s absorption spectrum, evidenced by

broadening of the exciton. If unintentional doping were present in the wafers, it would

lead to a greater variation in the electric field across the intrinsic region of the 60QW

sample than the 10QW sample. The spectra shown in Figs. 13 and 14 were taken from

photocurrent measurements made in direct succession at a controlled temperature of

30°C.

1430 1440 1450 14601470 1480 14901500 1510 15200

500

1000

1500 X: 1453Y: 1549

Absorption in 1/cm -, (G)0V,0.25V,..6V(R)

Figure 3.13. Absorption of Wafer 1 (10QW), with peak absorption of 1549 cm-1 at 1453 nm. One tunable laser was used as a source for wavelengths up to 1460 nm, and another laser was used for longer wavelengths. A discontinuity is visible at the junction.

70

1430 1440 14501460 1470 1480 14901500 1510 15200

500

1000

1500

2000X: 1460Y: 2190

Absorption in 1/cm, (G)1V,2V,..35V(R)

Figure 3.14. Absorption of Wafer 5 (60QW), with peak absorption of 2190 cm-1 at 1460 nm.

The 60QW sample was measured for biases from 1V-35V. 0V was not used because

it does not yield a photocurrent proportional to other biases, likely because the carriers

are not swept out efficiently with a large intrinsic region and a small electric field.

The 10QW sample was scanned from 0V-6V. At 6V, its photocurrent curve appears

to correspond to a smaller electric field than the 35V scan on the 60QW sample. This

is likely because there is a finite doping offset around the quantum wells on both

samples, and if it is significant with respect to the total quantum well thickness, the

electric field per applied voltage will not scale linearly with the number of quantum

wells in the sample. It is surprising that the absorption coefficient is greater for the

60QW sample, and that the exciton in the 10QW sample peaks at a wavelength 10 nm

shorter than the 60QW sample. It is difficult to say why this is the case. It could be a

combination of structural variations between the wafers and imperfections in the

71

antireflection coating causing different optical power to enter each sample. The width

of the excitons at the smallest applied bias is compared between the samples in Fig.

15. The electric field across the intrinsic region in each case is not known, and the

exciton peak wavelength varies, so it is difficult to draw firm conclusions from this

plot, but the exciton is in fact narrower in the 60 QW sample, which is opposite of

what would be predicted if unintentional doping or variations in well width were

present there.

-30 -20 -10 0 10 20 30 40 50 60 700

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1Normalized absorption coefficient, Red: 10QW Exciton, 0V, Blue: 60QW Exciton, 1V

Δ wavelength nm

a.u.

Figure 3.15. Comparison of exciton width for small applied field in Wafer 1 (10QW) and Wafer 5 (60QW). Vertical axis is normalized photocurrent. Horizontal axis is displacement from absorption peak in nm.

72

Temperature Dependence The transition energy in the quantum well varies with wavelength. The shift was

measured using structures from the 60QW sample, using photocurrent spectroscopy

with a constant applied bias of 1V. Data are shown in Fig. 16.

0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.870

500

1000

1500(left to right) Absorption Coeff, 100'C 90'C 70'C 50'C 30'C

Energy eV

cm-1

Figure 3.16. Absorption coefficient of Wafer 5 (60QW) for 1V reverse bias for different temperatures.

The shift of the first exciton was found to be .438µeV/C or .788nm/C. It was also

shown that there is a slight broadening of the exciton with temperature. The plots are

overlaid in Fig. 17.

73

0.83 0.835 0.84 0.845 0.85 0.855 0.86 0.865 0.87 0.875 0.880

500

1000

1500

Energy eV

cm-1

100'C (RED) -- 90'C -- 70'C (BLUE) -- 50'C -- 30'C (GREEN)

Figure 3.17. Overlayed absorption coefficient of quantum well superlattice versus energy plus displacement in eV.

The fact that the exciton width is only weakly temperature dependent near room

temperature suggests that the exciton width is not dominated by interaction of the

exciton with thermal phonons. This marks a difference between Ge/SiGe quantum

well structures and GaAs/AlGaAs quantum well structures [21].

3.2.5 Band Structure Calculations

A tunneling resonance simulation was set up to simulate the transition energy in

quantum wells with different material properties at varying electric fields. The

software is described in Appendix F. These data were compared with experimental

data derived from the photocurrent measurements. The quantum well width and the

effective mass, bandgap energy, and band offset energy of strained wells and barriers

were fit to the experimental data. Fitting these parameters is important, since the

parameters are not all well described in the literature. Furthermore, using the fitted

74

parameters, better future quantum well designs will be possible. Using data derived

from tests of Wafer 7, the transition energies versus applied voltage and results of a

simulation fit to these data are shown in Fig. 18. The fit parameters are shown in

Table 5. All of the transitions shown here involve heavy holes. It should be noted that

these transitions will only be excited by light with an electric field polarized in the

plane of the quantum wells. For this reason, for oblique incidence modulators using

SiGe quantum wells, light incident upon the epitaxy will have TE linear polarization.

0.7

0.75

0.8

0.85

0.9

0 2 4 6 8 10

Electric Field (10^4 V/cm)

Tran

sitio

n En

ergy

(eV)

Figure 3.18. Fit of quantum well transition energies for Wafer 7, assuming quantum wells were 22.5nm wide. Photocurrent data (dots) and simulations (lines). The green lines represent, from bottom to top, Electron (E) 1 – Heavy Hole (HH) 1, E1-HH2, and E1-HH31, blue lines represent, from bottom to top, E2-HH1, E2-HH2, and E2-HH3, and the black line represents E3-HH1. Reproduced from [22].

Table 3.5. Material properties of bulk materials and strained QWs at 300K (*the electron mass of the relevant Si direct gap has not been experimentally verified. k•p and tight-binding give different results of 0.156 [23], and 0.528 [24], respectively, †Landolt-Börnstein [25]). Reproduced from [22]

Strained Material Properties Bulk Material Properties me mhh Eg(Γ) ΔEC ΔEHH me mhh Eg(Γ)

Si0.16Ge0.84 Barrier 0.0647 0.3556 1.283eV 0.061-

0.121* 0.325† 1.32(1)eV†

Ge Well 0.0483 0.242 0.827eV 0.38eV 0.114eV

0.042(5)[6] 0.284† 0.797eV†

75

3.2.6 Future Work

The primary goal of improving Ge/SiGe quantum wells in the future will be to

increase the maximum absorption contrast, to allow for high-performance modulators

with thin intrinsic regions and small applied voltages. One way this can be achieved is

by thinning the barriers between wells. To do this while maintaining strain balance,

the silicon fraction must be increased. It is likely that when the wells are pushed close

enough together, the wavefunctions between wells will become coupled, broadening

the excitons. Between the width where the wavefunctions couple and the current

separation of wells is likely an optimal separation to maximize absorption strength and

shift. Also, the well widths may be varied to change the absorption per well and the

wavelength where absorption occurs.

Other possible work includes thinning the strain-relaxed SiGe buffer, intentional

growth of pairs of coupled quantum wells, and growth of wells including a small

fraction of silicon. The latter would increase the exciton energy, and might be used to

create devices operating at 1.3 µm, or photorefractive devices operating around 1.55

µm.

3.3 Conclusions

This chapter described the observation of the quantum-confined Stark effect (QCSE)

in Ge quantum wells with SiGe barriers, grown on Si substrates. This observation is

significant in that it is the first observation of a strong QCSE in Group IV materials.

This achievement was possible since in our work, the strained Ge quantum well had a

local minimum energy at the gamma point for both the electron and hole

wavefunction, despite that the strained Ge had a global minimum indirect bandgap.

Devices created using the effect are expected to be compatible with silicon electronics

fabrication. Wafers fabricated for physics measurements and modulator fabrication

are described, as well as tests done on these wafers. It was possible to determine that

the main contribution to the exciton width is not the interaction of the excitons with

76

thermal phonons. It was also possible to fit material parameters to the experimental

measurement of exciton transition energies. These data can aid quantum well design

in the future.

3.4 References

[1] Miller, DAB, Chemla, DS, Damen, TC, Gossard, AC, Wiegmann, W, Wood TH,

and Burrus, CA, Electric Field Dependence of Optical Absorption near the Bandgap of

Quantum Well Structures, Phys. Rev. B32, 1043-1060 (1985).

[2] Barjoseph, I, Klingshirn, C, Miller, DAB, Chemla, DS, Koren, U, Miller, BI,

Quantum-confined Stark effect in InGaAs/InP quantum wells grown by

organometallic vapor phase epitaxy, Applied Physics Letters; vol.50, no.15, p.1010-12

(1987).

[3] Lordi, V, Yuen, HB, Bank, SR, and Harris, JS, Quantum-confined Stark effect of

GaInNAs(Sb) quantum wells at 1300-1600 nm, Applied Physics Letters; vol.85, no.6,

p.902-4 (2004).

[4] Jalili, YS, Stavrinou, PN, Roberts, JS, and Parry, G, Electro-absorption and

electro-refraction in InGaAsN quantum well structures, Electronics Letters; v.38, no.7,

p.343-344 (2002).

[5] Sari, E, Nizamoglu, S, Ozel, T, and Demir, HV, Blue quantum electroabsorption

modulators based on reversed quantum confined Stark effect with blueshift, Applied

Physics Letters; vol.90, no.1, p.11101-1-3 (2007).

[6] Goossen, KW, Walker, JA, Dasaro, LA Hui, SP, Tseng, B, Leibenguth, R,

Kossives, D, Bacon, DD, Dahringer, D, Chirovsky, LMF, e. al., GaAs MQW

modulators integrated with silicon CMOS, IEEE Photonics Technology Letters; vol.7,

no.4, p.360-2 (1995).

77

[7] Pezeshki, B, Lord, SM, Boykin, TB, Harris, JS, GaAs/AlAs quantum wells for

electroabsorption modulators, Applied Physics Letters, vol. 60, no. 22, pp. 2779-81

(1992).

[8] Goossen, KW, Yan, RH, Cunningham, JE, Jan, WY, AlxGa1-xAs-AlAs quantum

well surface-normal electroabsorption modulators operating at visible wavelengths,

Applied Physics Letters, vol. 59, no. 15, pp. 1829-31 (1991).

[9] Kuo, Y-H, Germanium-silicon electroabsorption modulators, Electrical


[10] Qasaimeh, O, and Bhattacharya, P, SiGe-Si quantum-well electroabsorption

modulators, Photonics Technology Letters, IEEE, Vol. 10, Issue 6, pp. 807 – 809

(1998).

[11] Miyake, Y, Kim, JY, Shiraki, Y, and Fukatsu, S, Absence of Stark shift in

strained Si{sub 1-x}Ge{sub x}/Si type-I quantum wells, Applied Physics Letters;

vol.68, no.15, p.2097-9 (1996).

[12] Soref, R, The past, present, and future of silicon photonics, IEEE Journal of

Selected Topics in Quantum Electronics; vol.12, no.6, pt.2, p.1678-87 (2006).

[13] Fang, YY, Tolle, J, Roucka, R, Chizmeshya, AVG, Kouvetakis, J, D'Costa, VR,

and Menendez, J, Perfectly tetragonal, tensile-strained Ge on Ge1-ySny buffered

Si(100), Applied Physics Letters; v.90, no.6, p.061915 (2007).

[14] Kuo, Y-H, Lee, Y-K, Ge, Y, Ren, S, Roth, JE, Kamins, TI, Miller, DAB, and

Harris, JS, Strong quantum-confined Stark effect in germanium quantum-well

structures on silicon, Nature 437, 1334-1336 (2005).

[15] Kuo, Y-H, Lee, YK, Ge, Y, Ren, S, Roth, JE, Kamins, TI, Miller, DAB, and

Harris, JS Jr., Quantum-Confined Stark Effect in Ge/SiGe Quantum Wells on Si for

Optical Modulators, IEEE J. Sel. Top. Quantum Electron. 12, 1503-1513 (2006).

78

[16] Jiang, H, and Elliman, RG, Electrical properties of GeSi surface- and buried-

channel p-MOSFET's fabricated by Ge implantation, IEEE Transactions on Electron

Devices; v.43, no.1, p.97-103 (1996).

[17] Nayfeh, A, Chui, CO, Saraswat, KC, and Yonehara, T, “Effects of hydrogen

annealing on heteroepitaxial-Ge layers on Si: Surface roughness and electrical

quality,” Appl. Phys. Lett. 85, 2815-2817(2004).

[18] Godbey, DJ, Krist, AH, Hobart, KD, and Twigg, ME, “Selective removal of Si1-

xGex from (100) Si using HNO3 and HF,” J. Electrochem. Soc. 139, 2943-2947

(1992).

[19] Sugawara, M, Fujii, T, Yamazaki, S, and Nakajima, K, “Theoretical and

experimental study of the optical-absorption spectrum of exciton resonance in

In0.53Ga0.47As/InP quantum wells,” Phys. Rev. B, Vol. 42., No. 15, 9587-9597

(1990).

[20] Mak, G, and Ruhle, WW, Femtosecond carrier dynamics in Ge measured by a

luminescence up-conversion technique and near-band-edge infrared excitation,

Physical Review B (Condensed Matter); vol.52, no.16, p.R11584-7 (1995).

[21] Chemla, DS, Miller, DAB, Smith, PW, Gossard, AC and Wiegmann, W, "Room

Temperature Excitonic Nonlinear Absorption and Refraction in GaAs/AlGaAs

Multiple Quantum Well Structures,” IEEE J. Quantum Electron. QE 20, 265 275

(1984)

[22] Schaevitz, RK, Roth, JE, Fidaner, O, and Miller, DAB, Material Properties in

SiGe/Ge Quantum Wells, Presentation FMC3, Frontiers in Optics, San Jose, CA, Sept.

2007.

[23] Cardona, M, and Pollak, FH, “Energy-band structure of Germanium and Silicon:

The k•p method,”Phys. Rev. B 72, 245316 (2005).

79

[24] Tserbak, C. et al. “Unified approach to the electronic structure of strained Si/Ge

superlattices,” Phys. Rev. B 27, 12, pp. 7466-7472 (1993).

[25] Semiconductors: Intrinsic Properties of Group IV Elements and III-V, II-VI and

I-VII Compounds, Landolt- Börnstein New Series Group III, edited by O. Madelung

(Springer, Berlin, 1987), Vol. 22, Part A.

80

Chapter 4: Analysis of Asymmetric Fabry-Perot Modulators, and Demonstration of a Surface-Normal Device

The goal of this chapter is to provide a description and tutorial of how asymmetric

Fabry-Perot modulators (AFPMs) can be designed. Methods for calculating several

figures of merit are provided. Examples of AFPM modulators fabricated in SiGe are

described, along with analysis of the modulators’ performance.

4.1 Cavity Resonators in Optics

In Chapter 2, a modulator was described which employed a resonator to enhance its

performance. In this section, a closer look will be taken at the role of a resonator, and

how properties of the resonator affect the device performance. A cavity resonator can

be roughly defined as a space which is bounded in such a way that energy can oscillate

inside it. Resonators have different patterns of oscillation, called modes, which can be

excited. It is possible that a resonator mode can have external coupling. When

coupling is present, energy stored in that mode will decay out of the resonator over

time. Also, energy from outside the resonator can couple in.

Some resonator cavities which are encountered in optics are shown in Fig. 1. When

excited at a resonant frequency, a resonator cavity can build up a high intensity of

energy. Looking at an optical resonator from a particle perspective, individual

photons can pass through the resonator several times in a cycle before being absorbed

or coupled out of the cavity. Optical resonators are used in lasers, which rely on the

resonant oscillations so that photons can excite the in-phase emission of other photons,

making a coherent wave. Resonators are also used in modulators, since the resonance

allows the photon to pass through the optical material multiple times, increasing the

81

100% reflector

partial reflector

Laser emission

Laser cavity mode

(a) (b)

(c) (d)

Figure 4.1. Four types of optical resonators. Red represents energy stored in electric fields (a) Laser resonator cavity between two concave mirrors (b) Fabry-Perot etalon formed in a slab of high-index material (c) Ring resonator coupled to a dielectric waveguide (d) 2-D photonic crystal slab with line-defect waveguides on either side of a central region with a point-defect resonator.

phase delay imposed in the case of electrorefraction, or increasing the chance of

absorption in lossy material.

82

4.2 Description and Analysis of Asymmetric Fabry-Perot Modulators

4.2.1 Fabry Perot resonators

What is a Fabry-Perot resonator? An example of a cavity resonator which is relatively simple to analyze is a Fabry-

Perot resonator [1]. In the current section, equations describing these resonators are

shown, and they are applied to the analysis of modulators using asymmetric Fabry-

Perot cavities. A Fabry-Perot etalon, as shown in Fig. 1b, can simply be a slab of

high-refractive index material. Upon excitation with a plane wave (the direction of

propagation of which is shown by the arrows), each internal or external reflection at

the air-slab interface results in a partial reflection and partial transmission. Successive

internal reflections within the slab add up in phase or out of phase, as do the

successive transmissions through the faces of the slab, resulting in overall

transmission and reflection from the resonator. The transmission and reflection

coefficients of the slab vary depending on whether the successive reflections line up in

phase. This means that the properties of the slab will be dependent upon the optical

wavelength. Fabry-Perot cavities have been used as wavelength filters, which have

applications in sensing, optical sources, and optical signal processing. To illustrate an

example of the filtering properties of these structures, Fig. 2 shows the optical

transmittance through a slab of glass 1 mm thick. Though the reflectivity is not

shown, since the material and the interfaces are lossless, the sum of the reflected and

transmitted power is equal to the incident power for all wavelengths. An interesting

property is that when operating at a resonant wavelength of the structure, all the light

incident upon the structure is transmitted, and none is reflected.

83

500 500.5 501

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1Transmittance of 1 mm thick glass slab

wavelength nm

Figure 4.2. Transmittance of a 1 mm thick glass slab to normally incident visible light showing regularly spaced interference fringes. Transmittance ranges from 83% to 100%.

Definition of the variables For constructing a mathematical analysis of the Fabry-Perot resonator, the variables

shown in the schematic in Fig. 3 will be used.

n1 n2 n3

θ1

θ2 θ3t12

t21

t23

t32

r12 r21r23 r32

Ei

Er

Et reference line

xy L

n1 n2 n3

θ1

θ2 θ3t12

t21

t23

t32

r12 r21r23 r32

Ei

Er

Et reference line

xy L

Figure 4.3. Schematic of a Fabry-Perot resonator, showing variables used in analysis.

84

In the figure, a plane wave is incident from the half-space of refractive index n1 upon

the n1-n2 interface at an incident angle of θ1, and the electric field complex amplitude

is equal to Ei at the intersection point of the reference line and the n1-n2 interface. The

wave reflected from the resonator has a complex amplitude of Er at the same point.

The transmitted light, in the half-space on the right side with refractive index n3, has a

complex amplitude of Et measured at the intersection of the reference line and the n2-

n3 boundary. The reflection and transmission coefficients may be due to Fresnel

reflections at the boundaries between regions of refractive index. Alternately the

boundary may be a finite-thickness region containing, for example, dielectric coatings

or metals. In this case, the coefficients for reflection and transmission can be

determined using the transfer matrix approach described in Appendix B. The

resonator region is of width L, and light propagates at an incident angle θ2 from the

reference line within the resonator.

If the reflection and transmission coefficients are only due to the refractive index

differences between the resonator and the materials on either side, reflection and

transmission coefficients are determined by the Fresnel equations, given here for TE

polarization, in which the electric field is pointing normal to the page in Fig. 3, and

TM polarization, in which the electric field points parallel to the page [2].

BBAA

BBAATEAB nn

nnr

θθθθ

coscoscoscos

, +−

= (1)

BBAA

AATEAB nn

ntθθ

θcoscos

cos2, +

= (2)

ABBA

ABBATMAB nn

nnrθθθθ

coscoscoscos

, +−

= (3)

ABBA

AATMAB nn

ntθθ

θcoscos

cos2, +

= (4)

For the Fresnel equations, the following equalities hold true for propagating waves at a

particular interface between two materials, though they are not true for reflection and

transmission coefficients in general from layers of finite thickness.

85

BAAB rr −= (5) TEABTEAB tr ,,1 =+ (6)

A

BTMABTMAB tr

θθ

coscos1 ,, =+ (7)

Reflection and Transmission Fields will be derived along the reference line in Fig. 3 to enable calculation of

wavelength-dependent reflection and transmission coefficients for the Fabry-Perot

cavity. Fields inside the cavity will be defined in terms of a complex amplitude Ec,

where the subscript stands for the circulating field. Fig. 4 shows the forward and

backward propagating field amplitudes along the reference line, defined at the material

boundaries.

3213

23

232

23

⎯⎯⎯⎯ →⎯⎯⎯⎯⎯⎯⎯ ⎯←⎯⎯⎯⎯⎯⎯ →⎯

⎯⎯←⎯→⎯ −

−−

−=

Lnikct

Lnikc

Lnkic

Lnikcc

r

i eEtE

eEreEr

eEE

E

E

Figure 4.4. Solution for fields of forward and backward propagating wave

components at material boundaries for a Fabry-Perot resonator.

In region 2, the forward propagating wave is of complex amplitude Ec at the boundary

with region 1. The projection of the wave vector in region 2 along the reference line

will be:

20

2 cos2 θλπnkn = (8)

In the equation, λ0 is the wavelength in a vacuum. Since the region is of length L, the

phase accumulated on a single pass of the resonator will be equal to knL. The modes

of the cavity occur at frequencies where the circulating fields’ phases differ by

86

multiples of 2π. If the sum of the phase of the two reflection coefficients is φ, then the

condition for a resonant mode of the system will be:

πφ 22 mLkn =+ (9) In this equation, m is any integer.

Continuing to define the field components in Fig. 4, at the right edge of region 2, the

forward-propagating field is of complex amplitude:

Lnik

c eE−

(10) Upon reflection at that boundary, the backward propagating component is multiplied

by r23, and after propagating back to the leftmost boundary, it accumulates phase equal

to an additional knL. Upon reflection to go forward again, the amplitude becomes:

Lnki

c errE2

2321

− (11)

Now it is possible to write an equality for the field at the region 1 – region 2 interface

and solve for Ec:

Lkii

iLki

cc n

n

errEt

EteErrE 22321

1212

22321 1 −

−

−=+= (12)

Given this solution, the values of r and t for the Fabry-Perot resonator follow:

Lki

Lik

i

tn

n

errett

EE

t 22321

2312

1 −

−

−== (13)

1222321

2232112

1r

errertt

EEr Lki

Lki

i

rn

n

+−

== −

−

(14)

These solutions are generally true for normal and oblique incidence, regardless of

whether the boundaries represent simple interfaces or more complex layers, and

regardless of whether the cavity contains lossy material.

87

0 50 100 150 200 250 3000

0.2

0.4

0.6

0.8

1

frequency GHz

R (Blue) and T (Red) through a dielectric slab, n=3, t=0.5mm

0 50 100 150 200 250 3000

0.2

0.4

0.6

0.8

1

frequency GHz

R (Blue) and T (Red) through a dielectric slab, n=3, t=2mm

(a) (b)

Figure 4.5. Transmittance and reflectivity of dielectric slabs at normal incidence. Slab thicknesses are (a) 0.5 mm, and (b) 2 mm. Frequencies are shown in the MHz range, as these thick slabs have very closely spaced resonances at optical frequencies.

Free spectral range and resonance width Building upon the understanding in the previous sections, now it is possible to show

some other relationships for Fabry-Perot cavities. First, a longer cavity will have more

densely spaced optical resonances than a shorter cavity, as illustrated in Fig 5, which

shows the transmittance and reflectivity of slabs of refractive index 3, of thicknesses

0.5 mm and 2 mm. The transmission and reflection are plotted against frequency, the

peaks are evenly spaced. In wavelength, the peaks are not evenly spaced, as

wavelength is inversely proportional to frequency†. The number of periods of the

wave that fit inside the cavity on a round trip is referred to as the cavity order and is

calculated as:

π2

2 Lkm n= (15)

† Though in Fig. 1 the peaks appeared to be evenly spaced, the fractional change in

wavelength was very small. A wider wavelength range was not used in that plot since the peaks were only separated by about 100 pm. If it were plotted over a wider range, the peaks would be more closely spaced at shorter wavelengths.]

88

In frequency units, the separation of successive resonances, known as the free spectral

range, can be calculated in terms of an approximate wavelength of operation λ1 and

the cavity order as:

mfsr

1λλ =Δ (16)

In optoelectronic modulators, the bandwidth of the resonances is important. The

bandwidth is defined as the range in optical wavelength for which useful modulation

can be obtained. Obviously, the bandwidth associated with a single resonance cannot

exceed the separation of resonances, so it is desirable to design cavities operating at a

low cavity order and therefore large free spectral range.

Effect of increasing mirror reflectivity, and oblique incidence Another factor affecting the width of the resonance is the reflectivity of the mirrors.

As the reflectivity at the interfaces is increased, the energy spends a longer time inside

the cavity before decaying out. For energy which is at a resonance wavelength, as the

energy takes multiple trips around the cavity, it stays in phase with energy which is

being coupled into the cavity. For energy which is slightly off the resonance, as it

goes through more and more trips around the cavity, its phase becomes further and

further mismatched from the energy which is being coupled into the cavity. If there is

enough change in phase, there will be destructive interference. The more trips around

the cavity the off-resonance energy takes, the more pronounced this will be. As a

result, as the reflectivity of the mirrors is increased and energy spends a longer time

inside, the optical resonances, reflected in the reflection and transmission spectra,

become narrower. Fig. 6 shows, side by side, the transmittance and reflectivity of the

0.5 mm cavity from Fig. 5 for normal incidence (a), and oblique incidence at 70° from

the normal (TE).

Several differences between the plots can be noted. At oblique incidence, both

reflectivity and transmittance span a larger range of the possible values from 0 to 1.

The width of the peak in transmission at the resonant frequencies is narrower for the

oblique incidence case. These differences are due to the change in reflectivity at the

89

interfaces. For normal incidence, the reflectivity at a single interface is 25%, and at

the incident angle of 70° used here, the reflectivity for internal and external reflections

is 62%. For design of modulators, increasing the reflectivity can lead to a design

trade-off. On one hand, the light interacts with the cavity more strongly, resulting in

more electrorefraction or electroabsorption. On the other hand, the resonances

become narrower, and the useful bandwidth range decreases.

0 50 100 150 200 250 3000

0.2

0.4

0.6

0.8

1

frequency GHz

R (Blue) and T (Red) through a dielectric slab, n=3, t=0.5mm

0 50 100 150 200 250 3000

0.2

0.4

0.6

0.8

1

frequency GHz

R and T, 70° from normal, n=3, t=0.5mm

(a) (b)

Figure 4.6. Transmittance and reflectivity of a dielectric slab, refractive index 3, width 0.5 mm. (a) Normal incidence, (b) Oblique incidence 70° from normal (TE). As in Fig. 5, frequencies are shown in the MHz range, as these thick slabs have very closely spaced resonances at optical frequencies.

Another difference between normal and oblique incidence is that the resonances are

spaced slightly further apart in the oblique incidence case. The angle of incidence

from air is 70°, but the angle within the cavity is only about 18° from normal.

Applying Equation 8, kn is changed by only about 5%. Though in this example the

change in kn is very small, in a device such as the QWAFEM modulator from Chapter

2 in which light is obliquely incident from within a high-index material, the change in

kn can be much greater than in the present example. For the QWAFEM, the use of

oblique incidence results in much larger optical bandwidth. In addition, oblique

incidence is desirable for optoelectronic modulators since the light travels at an angle

in the active material of the device, so that there is more absorption per pass through

the cavity.

90

Distributed Bragg reflectors In addition, it is possible to make high-reflectivity, lossless mirrors using a distributed

Bragg reflector (DBR), which is a series of alternating high- and low-index layers,

each one quarter optical wavelength thick. The reflectivity of a silicon/silicon dioxide

DBR designed for 1550 nm at normal incidence is shown in Fig. 7. This structure

consists of a semi-infinite silicon substrate (n=3.53) with three pairs of deposited

layers of silicon dioxide (n=1.53, width=253 nm) and silicon (width=110 nm). The

peak reflectivity of this structure from air is 99%.

1000 1500 2000 2500 3000 35000

0.2

0.4

0.6

0.8

1

optical wavelength nm

Reflectivity of a 3-period Si/SiO2 DBR designed for 1550 nm

Figure 4.7. Reflectivity of a 3-period Silicon /Silicon Dioxide distributed Bragg reflector deposited on silicon. Design wavelength was 1550 nm. (nSi=3.53, nSiO2=1.53)

The DBR works because reflections from each interface interfere constructively, such

that as the number of layers increases, the reflectivity approaches unity. However, the

designer must be aware that the use of a DBR will increase the order of the cavity.

This is because a finite amount of energy is stored inside the mirror. The effect can be

modeled by imagining the light reflects off a virtual reflection plane located

somewhere below the top surface of the DBR. The extra length added to the cavity

91

increases the phase accumulated per round trip of the cavity, and therefore increases

the cavity order and decreases the bandwidth.

In modeling the penetration distance in the DBR, the situation is compared to the

reflection from a real mirror at a distance from the point of observation. If it were not

possible to directly measure the distance to the mirror (which will be called x), its

distance could be inferred by measuring the phase change upon reflection at different

wavelengths. From reflection from the point of observation, the change in phase from

the incident to the reflected light due to traveling the distance x twice is:

xkn2=φ (17) There may also be a phase shift upon reflection from the mirror surface, but it can be

neglected, as the distance will be inferred from the change in phase as the incident

wavelength is changed. This phase change can be calculated as follows:

xλπφ 2*2= (18)

λλ

πφ xdd 24−

= (19)

Now the distance can be inferred from the phase change:

λφ

πλ

ddx

4

2−= (20)

So, Equation 20 can be used in conjunction with transfer matrix calculations to find

the effective penetration depth of DBR mirrors. It can be shown that DBR mirrors

made from materials with larger index contrast will have shorter effective penetration

depth. Also, oblique incidence, which increases the reflectivity at each interface, is

useful for decreasing the effective penetration depth.

92

4.2.2 Modulators using asymmetric Fabry-Perot cavities

How to obtain extremely high contrast ratio Now that a description has been given for Fabry Perot cavities, the analysis can be

extended to asymmetric Fabry-Perot cavities used in optoelectronic modulators.

Readers interested in further analysis on this topic are referred to previous

works [3-5]. Typically, an AFPM modulates reflected light, and has light normally

incident from one side of the cavity which has moderate reflectivity. The cavity

contains quantum wells for electroabsorption modulation, and the opposite side has a

high reflectivity. An illustration of what a DBR-based AFPM might look like is

shown in Fig. 8. DBR mirrors are useful because they can have a very high

reflectivity and potentially can be lossless. Also, they can be designed to have a

certain finite reflectivity by changing the number of layers or the layer thicknesses.

Another option for creating high-reflectivity mirrors is using total internal reflection

(TIR), as in the QWAFEM. Metals can also be used as reflectors, but unlike TIR or

DBR mirrors, they have a finite loss upon reflection.

Quantum Wells

Light

Top: thin DBR

Bottom: thick DBR

Substrate.

.

.

Quantum Wells

Light

Top: thin DBR

Bottom: thick DBR

Substrate.

.

.

Figure 4.8. Asymmetric Fabry-Perot modulator containing quantum wells, with DBR mirrors on either side of the active region. The thick bottom DBR (with many high/low index periods) had close to 100% reflectivity, while the top DBR (with fewer high/low index periods) has lower reflectivity. In addition to the layers shown in this schematic, a practical modulator would also require electrical contacts to either side of the quantum well region.

93

When calculating reflection from the AFPM using equation 14, loss can be added to

the cavity in one of two ways: Either the refractive index n2 can be made a complex

number, or, the back mirror reflection coefficient can be modified to take into account

loss in the round trip of the cavity. In the calculation of the reflection coefficient, the

loss is ‘lumped’ into the back-surface reflectivity using the following equation, in

which kni is the imaginary component of the wave vector found by using a complex

refractive index. From now on, the reflection of the interface r23 will be represented as

r23, and the ‘lumped’ absorption/reflection will be called rback or rb:

Lk

bnierr 2

23−= (21)

Assuming the cavity is operating on resonance ( πφ 22 mLkn =+ ), and the front

interface is lossless, the equation for cavity reflectivity reduces to:

( ) ( )b

bb

rrrrrrrr

12

12122

12

111

+++−

= (22)

As was noted before regarding Fig. 1, and as is also true in Figs. 5 and 6, at a

resonance frequency, all the light is transmitted and none is reflected. This conclusion

is counterintuitive since the front face of the resonator has finite reflectivity, but in

practice a large field builds up inside the cavity, and the phase and amplitude of the

backward-reflected light from the cavity are such that this cavity back-reflection

cancels out the reflection from the front surface. In general, a Fabry-Perot cavity will

not reflect any light when it is operated on resonance and when the front and back

internal reflectivity are equal. This can be shown in the above equation by replacing rb

with –r12, and solving to find that r=0. The reason for the difference in sign is that the

internal reflectivity of the cavity at the 1-2 boundary is r21, and for a simple Fresnel

reflection at the 1-2 boundary, rb=r21 is the same as rb=-r12. The operating condition

described, known as cricital coupling, can be exploited so that in the 0 state of an

AFPM, no light is reflected, and the contrast ratio can in theory approach infinity.

Typically a back reflector is used which transmits no light. For critical coupling, all

the light which enters the cavity is absorbed. The reader is referred to the discussion

of coupled mode theory and critical coupling in Haus’s book for more information [6].

94

Maximizing change in reflectivity To explore the design space for AFPMs, a modulator will be simulated for which

R23=100%, and the transmission on a double pass through the cavity can be made any

value in the range from 0% to 100%. The variables in the simulation will be Rf for

front (incident) surface reflectivity, and Rb for lumped back reflectivity (including

cavity loss). Figs. 9 and 10 show the overall modulator reflectivity R for two different

values of Rf.

0 20 40 60 80 1000

20

40

60

80

100Modulator %R vs. Rb%, for Rf= 37%

Rb %

Mod. %R

Figure 4.9. Modulator reflectivity R for Rf=37%, varying Rb from 0% to 100%. Rb represents the combination of back reflectivity and absorption. For back reflectivity=100%, absorbing region with absorption coefficient α and length L, Rb=100%*e-2αL

95

0 20 40 60 80 1000

20

40

60

80

100 Modulator %R vs. Rb%, for Rf= 85%

Rb %

Mod. %R

Figure 4.10. Modulator reflectivity R for Rf=85%, varying Rb from 0% to 100%.

Several important points can be seen on both plots:

• When Rb=Rf, R=0%

• When Rb=100%, R=100%

• When Rb=0%, R=Rf

An optimal modulator would change the cavity reflectivity between 0% and 100%.

To achieve this, it would be necessary to have the back surface reflectivity be 100%,

and modulate the cavity absorption between no absorption and the point where Rb=Rf

(meaning that the back reflectivity times the transmission of a single pass of the

96

cavity, squared, equals the front reflectivity). Using germanium quantum wells, it is

not possible to change the cavity absorption from being completely turned off to

having a finite value. The intensity of the transmission of light through absorbing

material is exponentially dependent upon the absorption coefficient and the thickness

of the material. Transmission is proportional to e-αL. In germanium quantum wells, so

far it has only been possible to change the absorption coefficient by about a factor of

4. This is thought to be primarily due to the presence of indirect-gap absorption at the

same wavelengths where the direct-gap absorption is being modulated. However,

work has been done in other material systems to optimize the absorption contrast [7],

and it is likely that some improvement could be made in the current system as well.

Using the present limitation of a maximum absorption contrast of 4, there are two

ways to attempt to maximize the change in reflectivity of the modulator: In either

case, in the 0 state, RB,0=RF0. In the 1 state, the design can be such that either

RB,1=RF04

or RB,1=RF00.25. In Fig. 11, the cavity modulator reflectivity is calculated for

both of these cases, graphing results for a range of RF from 0% to 100%. For a

maximum absorption coefficient contrast of 4, it is found that the overall reflectivity

approaches 36% as RF approaches 100%, whether the design was such that the 0 state

corresponded to the lowest absorption coefficient, or to the highest absorption

coefficient.

From the plot it can be seen that the maximum modulator R is higher when the low

absorption state is the on state, and that as Rf approaches 100%, the values approach

one another. Since the maximum R will be obtained for the low-cavity-absorption

case (where the maximum absorption attainable in the cavity is such that Rb=Rf), and

also since this case requires fewer quantum wells and therefore a smaller voltage

swing, a low-absorption design is desirable.

The maximum reflection coefficient can be calculated using Equation 22. Making the

substitution rB=-r12A, where A is the absorption coefficient contrast, and taking the

limit of r12->1, corresponding to the Rf=100% point on Fig. 11, the result, expressed as

the reflectivity, is:

97

2

11

⎟⎠⎞

⎜⎝⎛

+−

=AAR (23)

In the example of Ge quantum wells for which A=4 or A=0.25, r=.6 and the maximum

reflectivity from an AFPM capable of hitting the critical coupling condition is 36%.

0 20 40 60 80 1000

5

10

15

20

25

30

35

40AFPM Max %R for Ge QWs, Red:LoAbs=1state Blue:HiAbs=1state

Rf %

Mod

ulat

or R

max

%

X: 98Y: 36

Figure 4.11. The absorption coefficient contrast of Ge QWs is at most ~4 times. For critical coupling in the 0 state, the red curve shows the max. modulator R for a low absorption 1 state, and the blue curve shows the max R for a high abs. 1 state.

Design limitation from low back mirror reflectivity Another concern in real modulators is that the actual back reflectivity R23 will not be

unity. As shown in Fig. 12, if the back reflector is significantly lower than 100%, it

can severely limit R in the 1 state when that state corresponds to low absorption in the

cavity.

Low Rb is an issue with metal mirrors. Al and Au are good reflectors in the near IR,

both having about 98% reflectivity at an air-metal interface. Their reflectivity is

reduced at internal reflection from a Si.1Ge.9-metal interface, where Si.1Ge.9 has a

98

refractive index of 4.15. In this case the reflection coefficient of Al is 92%, and Au is

95%.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100Modulator %R vs. Back mirror %R, for Front mirror 85%

Mod

ulat

or R

Rb

Rb=0

Rmod=Rf

Rmod=0

Rb=Rf

Rb=100%

Rmod=100%

Actual R23 interface = 95%

Max Rmod for min. cavity absorption

Modulator Reflectivity for fixed front reflectivity Rf=85%, varying lumped back reflectivity Rb from 0% to 100%

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100Modulator %R vs. Back mirror %R, for Front mirror 85%

Mod

ulat

or R

Rb

Rb=0

Rmod=Rf

Rmod=0

Rb=Rf

Rb=100%

Rmod=100%

Actual R23 interface = 95%

Max Rmod for min. cavity absorption

Modulator Reflectivity for fixed front reflectivity Rf=85%, varying lumped back reflectivity Rb from 0% to 100%

Figure 4.12. This figure shows the modulator reflectivity, and how the use of a back reflector of less than 100% limits the maximum modulator reflectivity of the device in the low-cavity-absorption range.

Other issues Several of the other issues in design of AFPMs will be noted here.

One issue is the change in refractive index with change in absorption coefficient. This

effect can result in a larger maximum change in modulator reflectivity. If the 0 state

corresponds to critical coupling, then in the 1 state, the cavity resonance will shift in

wavelength, causing more light to be reflected than would be if the absorption

coefficient had been changed without shifting away from the optical resonance. The

change in refractive index can be described using the Kramers-Kronig relations in an

integral form [8]:

99

( ) ( )∫

∞

⎟⎠⎞

⎜⎝⎛−

Δ=Δ

0 22 ''1

,'2

1, λ

λλ

λαπ

λ dVVn (24)

In this expression, Δn represents the change in refractive index as a function of

wavelength and bias voltage, and Δα represents the change in absorption coefficient as

a function of wavelength and bias voltage from an absorption profile for which the

refractive index profile is presumably known. The change in refractive index is

affected by the change in absorption coefficient at all wavelengths. Our transfer

matrix simulation software, described in Appendix C, is designed such that the

Kramers-Kronig relations can optionally be employed to specify the deviation of the

real part of the refractive index from a constant value based on the change of the

absorption coefficient with wavelength and voltage. In the current implementation,

the effect of changing the absorption is only considered for the range of wavelengths

for a single set of quantum well absorption coefficient measurements. It might be

possible to obtain an even better match between simulation and experiment by

extrapolating the change in absorption at wavelengths beyond the range of the lasers

used for the quantum well absorption coefficient measurements.

Another issue is that it may be difficult to calibrate the growth rate or refractive index

of the material being grown by epitaxy. Designs for DBR mirrors have reasonably

good tolerance to growth thickness errors. However, use of high-reflectivity DBR

mirrors in a design leads to a narrow bandwidth of operation. Such designs will be

very sensitive to the cavity thickness and the operating temperature. In addition to the

narrow bandwidth, this high sensitivity is another reason high-reflectivity designs are

not desirable. Even when using designs that do not use high reflectivity mirrors, it is

still desirable to perform the best possible growth calibration so that the resonance

peak of the device will be lined up to the desired center operating wavelength.

Several factors may make the behavior of a device less than ideal when attempting to

hit the critical coupling condition. Important factors are diffraction, finite beam size,

surface roughness or non parallelism, and finite bandwidth of the laser. This is

because any of these factors can make it impossible to couple all the light into one

100

mode of the cavity, and achieve total absorption. Of these effects, finite beam size can

be accounted for by using Equation 14 for modulator reflection, while decomposing

the beam into a weighted sum of plane waves at different incident angles, following

the math in Appendix D.

4.2.3 Conclusion/Summary for the Design of AFPMs

In summary, AFPMs can be designed using the mathematics describing Fabry-Perot

resonators, and adding in loss to the cavity. Low order cavities are desirable for

maximizing the useful modulation bandwidth around a resonance. In the critical

coupling condition, there is no transmission through the back mirror, the lumped back

mirror reflectivity is equal to the front mirror reflectivity, and no light gets reflected.

In theory this makes it possible to get an infinite contrast ratio, though in practice the

characteristics of the optical beam or the cavity surfaces will make the performance

somewhat less than ideal. The most effective way to get a maximum change in

reflectivity between the critically coupled 0 state and the 1 state is to use a smaller

absorption coefficient in the 1 state than the 0 state. The maximum change in

reflectivity achievable in electroabsorbing materials can be found from Equation 23,

neglecting the resonant wavelength shift which can be calculated with the Kramers-

Kronig relations. Maximizing the change in reflectivity requires high reflectivity

mirrors. Metals tend to have too much loss for the best possible performance. High

reflectivity mirrors can be achieved using DBRs, though these have a finite

penetration depth, which increases the cavity order. Using oblique incidence, it is

possible to use TIR for a high-reflectivity mirror, and at the same time increase the

interaction length of the light per pass, and decrease the cavity order.

101

4.3 Demonstrations of Surface-Normal Asymmetric Fabry-Perot Modulators

Numerous examples of surface-normal modulators employing asymmetric Fabry-Perot

cavities exist in the literature [7,9,10]. In this section, two examples of AFPMs will be

described which use germanium quantum wells grown on silicon substrates.

4.3.1 Thinned wafer AFPM

The first asymmetric Fabry Perot modulator which was made used the 60QW epitaxial

sample, thinned and polished from the substrate side to a thickness of 100μm. Diode

mesas were fabricated before the wafer thinning, using the procedure described in

Chapter 2, but without depositing antireflection coatings. After thinning, aluminum

was deposited on the backside (i.e., on the bottom of the silicon substrate). The front

reflectivity of the air-SiGe interface is about 37%, and the back reflectivity is about

92%. Though gold has a higher reflectivity than aluminum, aluminum is preferred

since gold does not stick well to other materials. For this sample, the peak contrast

ratio was 5.4dB at 1467 nm using a 12V swing, though the usable bandwidth was only

0.4 nm. The maximum absorption per pass achievable (~45%) is more than enough to

achieve critical coupling. The biggest problem with this design is that the cavity is too

thick, leading to the small useful bandwidth. At 1467 nm, using the refractive index

of Si of 3.53, the cavity is operating at about 480th order. Using Equation 15, the

separation between adjacent resonances is 1467 nm / 450 ~3 nm. The solution to this

problem of very narrow bandwidth is to find a way to make an even thinner resonator.

A free standing membrane thinner than 100μm is very fragile, so any solution in

which the wafer is thinned will require the use of a mechanical support for added

stability.

102

P-SiGe

200 nm aluminumSodium silicate wafer bonding layer

Nitride-coated silicon wafer

SiGe 60 QWs

N-SiGe

P-SiGe

200 nm aluminumSodium silicate wafer bonding layer

Nitride-coated silicon wafer

SiGe 60 QWs

N-SiGe

Figure 4.13. Schematic of wafer-bonded asymmetric Fabry-Perot modulator.

4.3.2 Substrate-removed AFPM

Description The second demonstration of a surface-normal AFPM used substrate removal by wet

etching such that the resonator cavity only consisted of the epitaxial growth, while

another silicon wafer was used for mechanical support. The device used an aluminum

layer to get a relatively high r23, and r12 was due entirely to the air-SiGe interface. The

schematic of the fabricated device is shown in Fig. 13. To fabricate this device, first

200 nm of aluminum was evaporated on the surface of a wafer with SiGe epitaxy

containing 60 quantum wells. A double-side polished silicon wafer was prepared to

be the supporting substrate by depositing 200 nm of silicon nitride and 10 nm of

silicon dioxide on either side. Next, the aluminum and silicon nitride surfaces were

cleaned, and bonded using a sodium silicate solution. After the bond dried, the

substrate upon which the epitaxy had been grown was ground to a thickness of 40 μm.

The remaining silicon from that substrate was removed by etching in 30% potassium

103

hydroxide solution (KOH) heated to 85°C. Heated KOH etches silicon without

significantly attacking SiGe or the nitride coating on the carrier wafer [11,12].

At this point, the structure consisted of the epitaxy flipped upside down on another

substrate with aluminum between the epitaxy and the substrate. The processing was

completed by defining and etching mesas, and depositing Ti/Al contacts to the p- and

n-doped regions.

Figure 4.14. Reflectivity from 60 QW asymmetric Fabry-Perot modulator operated at

70°C.

Experimental results Light was focused on the top of a modulator on the chip through a pellicle

beamsplitter. Light which was reflected back from the sample and reflected by the

beamsplitter was collected at a photodetector, and the photocurrent was measured as

the bias voltage on the modulator was scanned. While the fraction of incident power

reflected by the beamsplitter was not calibrated, by comparing the current at the

photodetector at different bias voltages the contrast ratio was calibrated. Voltage

scans were taken over a range of wavelengths, and the procedure of scanning voltage

104

and wavelength was repeated at different modulator operating temperatures. The

temperature was tuned to 70°C, where the contrast ratio was found to be maximized,

and where peak in absorption at 0V bias lined up with the peak in the optical

resonance. The reflectivity spectrum of the modulator is shown in Fig. 14, and the

contrast ratio is shown in Fig. 15. Only a subset of the data taken (at a few of the

applied voltages) are shown for clarity.

1470 1475 1480 1485 1490 1495 1500 1505 1510

1

2

3

4

5

6

7

8

60QW Surface Normal Modulator @ 70C, Contrast(dB) (G)2.5V,5V,10V(R)

wavelength nm

Con

trast

dB

Figure 4.15. Contrast ratio of 60 QW asymmetric Fabry-Perot modulator operated at 70°C. The plot shows the maximum contrast ratio achievable for voltage swings of 2.5V, 5V, and 10V, though the bias voltage was not set to a constant value in the creation of the plot.

The peak contrast ratio reached 3dB at 1495 nm for 2.5V swing. For 5V swing, the

peak contrast ratio was 5.9dB, and the operating range (over which contrast exceeded

3 dB) was 1492-1498 nm. For 10V swing, the peak contrast ratio was 8.8 dB, and the

operating range was 1491-1499 nm. The bias voltage at each wavelength was chosen

to maximize the contrast ratio.

105

Analysis The estimated bottom reflectivity is 92%, and top reflectivity is 37%. To reach the

critical coupling condition, it would be necessary for the fraction of light not absorbed

per pass of the cavity to be 63%. Measuring from the single-pass transmission

spectrum of the 60 QW sample in Chapter 3, Fig 12, it should be possible to have

single-pass transmission as low as 55% and as high as 76% at the peak of absorption,

assuming the magnitude of absorption does not change much as the temperature is

increased. As a result, critical coupling should be easily attainable.

1470 1480 1490 1500 15100

5

10

15

20

25

30Relative Reflectivity EXPERIMENT, (G)19V,16V,..1V(R)

wavelength nm

a.u.

1470 1480 1490 1500 15100

5

10

15

20

25

30Relative Reflectivity EXPERIMENT, (G)19V,16V,..1V(R)

wavelength nm

a.u.

1470 1480 1490 1500 15100

20

40

60

80

% Light Reflected SIMULATION, (G)19V,16V,..1V(R)

wavelength nm

%

(a) (b)

Figure 4.16. Comparison of experimental reflectivity spectrum of (a) 60QW AFPM (with uncalibrated units) and (b) simulation using Kramers-Kronig relations.

The reflection spectra show a finite minimum reflectivity, and the wavelength of the

minimum shifts with applied bias voltage. The shift of the resonance enhances the

maximum contrast ratio, and is responsible for the double-peaking of the contrast ratio

spectrum in Fig. 15. The parameters for the simulation, which was carried out with

the software described in Appendix C, are shown in Table 1. A comparison of the

experiment and simulation is shown in Fig. 16.

106

Table 4.1. Material properties for the AFPM simulation

Material Refractive Index Thickness (nm)

Air 1 -

Si.1Ge.9 4.15 1000

Quantum Well Superlattice

4.15 plus variable real Kramers-Kronig component and variable absorption

60 QWs: 3000

Si.1Ge.9 4.15 935

Aluminum 1.44+16i -

The operating temperature was chosen both because it maximized the absorption at the

resonance peak, but also because trial and error tests showed that higher contrast ratios

were attainable at 70°C than at either higher or lower temperatures. It was actually

expected that a higher contrast ratio might be achieved when the absorption peak was

tuned away from the resonance, since the peak value of absorption was predicted to be

more than was necessary for critical coupling.. It is possible that the reason that the

temperature operating point used works as well as it does is because it maximizes the

index of refraction shift near the optical resonance. For an unknown reason the shift

in the resonant wavelength due to the Kramers-Kronig relations is larger in the

experiment than in the simulation. It is certainly possible that this occurs since the

Kramers-Kronig integral was only taken over a limited range in wavelength, from

1460-1550 nm. The maximum change in refractive index with applied bias at the

exciton peak was about 0.003. It is likely that a better model would include

extrapolation of the absorption coefficient over a wider wavelength range Though the

reflectivity scale from the experimental data is not calibrated, it appears that if the

scale on Fig. 16b can be mapped directly to Fig. 16a, at the peak contrast wavelength

of 1495 nm, there would be about 13% light reflected. The absorption coefficient

contrast attainable at the peak of absorption was 2:1 at room temperature. Using

Equation 23, from change in absorption coefficient alone, the maximum reflectivity

107

expected in the 1 state if the 0 state corresponded to critical coupling for a 2:1

absorption contrast would be 11%. As is mentioned in Chapter 1, an insertion loss

this large is undesirable, and the laser source may need to operate at a higher intensity

than if the insertion loss were lower.. To even obtain this number using only the

change in absorption coefficient would require that the back mirror reflectivity be

close to unity. As stated, the performance of this device is improved by the presence

of a shift in resonant wavelength with applied voltage.

0 20 40 60 8040

50

60

70

80

90

100% Reflectivity of Air-SiGe vs. incident angle, degrees

Incident angle ° from air

% R

efle

ctiv

ity

0 20 40 60 8040

50

60

70

80

90

100% Reflectivity of Air-SiGe vs. incident angle, degrees

Incident angle ° from air

% R

efle

ctiv

ity

Figure 4.17. Reflectivity vs. angle for air - Si.1Ge.9 (n=4.15) interface (TE incidence).

The finite reflection when critical coupling is expected is likely due to the roughness

in the bottom mirror surface, which corresponds to the top of the epitaxy as it was

grown. In Chapter 3 the RMS surface roughness of the 60 QW epitaxy sample was

measured to be 9.2 nm. Roughness leads to the cavity length being poorly defined,

and also leads to incoherent scattering of a fraction of the incident light upon

reflection. As the experimental data here are not calibrated to the absolute reflectivity,

a quantitative analysis will not be carried out, though an example of a quantitative

analysis of the deviation from perfect critical coupling will be shown in Chapter 5.

108

A possible way to improve the current device is to use oblique incidence. The primary

effect that changing the incident angle from normal incidence would have is raising

the reflectivity at the top surface. The reflectivity versus angle from air to SiGe

(n=4.15) is shown in Fig. 17. The critical angle in SiGe for this reflection is only 14°.

As a result, the path length inside the cavity and the reflectivity at the SiGe-Al

interface are hardly changed. Using oblique incidence could allow the same device to

operate at longer wavelengths where the reflectivity is lower, or allow the design of

AFPMs using fewer quantum wells.

In summary, an asymmetric Fabry-Perot modulator was demonstrated using a

substrate-removed SiGe epitaxy containing 60 Ge quantum wells. The peak contrast

ratio obtained was 8.8dB for 10V swing, and the maximum operating range with at

least 3dB of contrast was 1491 – 1499 nm. A device simulation deviates from the

measurement primarily in two ways: The shift in resonant wavelength with applied

voltage is greater than expected from applying the Kramers-Kronig relations to the

measured value for absorption. Also, the reflectivity in the critical coupling does not

decrease all the way to zero, and it is hypothesized that the primary reason is that there

are imperfections in the Fabry-Perot cavity due to surface roughness. The maximum

reflectivity at the wavelength where maximum contrast was achieved was estimated to

be 13%.

4.4 Conclusions

A description was given of Fabry-Perot resonators and of asymmetric Fabry-Perot

modulators. Equations were shown to describe maximum reflectivity, critical

coupling, and free spectral range. Two demonstrations of surface-normal asymmetric

Fabry-Perot modulators were described. The demonstrations showed that high

contrast ratios are obtainable near the critical coupling condition, and showed that

having a short cavity is important to designing a device with a useful optical

bandwidth.

109

4.5 References

[1] Fabry, C, and Pérot, A, ‘‘Sur les franges des lames minces argentées et leur

application à la mesure de petites épaisseurs d’air,’’ Ann. Chim. Phys. 12, 459–501

(1897).

[2] Inan, US, and Inan, AS. Electromagnetic Waves. Upper Saddle River, NJ:

Prentice-Hall, Inc., (1999).

[3] Pezeshki, B, Thomas, D, Harris, JS, Optimization of modulation ratio and insertion

loss in reflective electroabsorption modulators, Applied Physics Letters, vol. 57, no.

15, pp. 1491-2 (1990).

[4] Trezza, JA, Optimization of quantum well optoelectronic modulators, Electrical


[5] Garmire, E, Analytic performance analysis based on material properties for

electroabsorptive asymmetric Fabry-Perot reflection modulators, Applied Optics,

vol.41, no.8, p.1574-83 (2002).

[6] Haus, HA. Waves and Fields in Optoelectronics. Englewood Cliffs, NJ: Prentice-

Hall, Inc., (1984).

[7] Pezeshki, B, Thomas, D, and Harris, JS, Optimization of modulation ratio and

insertion loss in reflective electroabsorption modulators, Applied Physics Letters,

vol.57, no.15, p.1491-2 (1990).

[8] Whitehead, M, Parry, G, and Wheatley, P, “Investigation of etalon effects in

GaAs-AlGaAs multiple quantum well modulators”, IEE Proceedings J

(Optoelectronics), vol.136, no.1, p.52-8 (1989).

[9] Zouganeli, P, Stevens, PJ, Atkinson, D, and Parry, G, Design trade-offs and

evaluation of the performance attainable by GaAs-Al{sub 0.3}Ga{sub 0.7}As

110

asymmetric fabry-perot modulators, IEEE Journal of Quantum Electronics, v.31, no.5,

p.927-943 (1995).

[10] Law, KK, Merz, JL, and Coldren, LA, Effect of layer thickness variations on the

performance of asymmetric Fabry-Perot reflection modulators, Journal of Applied

Physics, vol.72, no.3, p.855-60 (1992).

[11] Williams, KR; Gupta, K, and Wasilik, M, Etch rates for micromachining

processing - Part II, Journal of Microelectromechanical Systems; vol.12, no.6, p.761-

78 (2003).

[12] Taraschi, G, Langdo, TA, Currie, MT, Fitzgerald, EA., and Antoniadis, DA.,

Relaxed SiGe-on-insulator fabricated via wafer bonding and etch back, Journal of

Vacuum Science & Technology B (Microelectronics and Nanometer Structures);

vol.20, no.2, p.725-7 (2002).

111

Chapter 5: Side-entry modulator

In this chapter an oblique incidence asymmetric Fabry-Perot modulator using SiGe

quantum wells is demonstrated in a device we have named a side-entry modulator [1].

In this architecture, the light enters and exits through the polished edges of the silicon

substrate. Unlike flip-chip bonded modulators and many silicon optics platforms,

getting light in and out of this side-entry modulator does not require optical ports on

the top or bottom faces of the chip. This could provide an advantage if the modulator

were integrated on a substrate with silicon electronics: Using current technology,

silicon integrated circuits frequently use the top chip surface for electrical contacts and

the bottom surface for heat removal. The design also is tolerant to misalignments

since it does not have a mode matching constraint, such as in a waveguide modulator.

In a side-entry modulator with 60 quantum wells, the contrast ratio peaked at 10 dB at

1472 nm for 11V swing, and exceeded 3 dB from 1465 nm to 1482 nm. 3 dB of

contrast was demonstrated for 2V swing. When tuned to achieve maximum contrast,

the beam was misaligned over a range of 200 μm and 280 μm in orthogonal directions

while maintaining contrast ratio greater than 3 dB. In addition, the device was heated,

shifting the exciton peak closer to the optical resonance, such that there was enough

absorption to demonstrate critical coupling in the resonator.

5.1 Motivation for Side-Entry Modulators

5.1.1 Simple processing

The previously described thin surface-normal asymmetric Fabry-Perot modulator in

SiGe required complex processing in order to create a high reflectivity mirror

underneath the epitaxial growth. The process of bonding wafers and removing the

substrate is complex and is not standard in the semiconductor industry. Similar to the

QWAFEM, the side-entry architecture uses oblique incidence to raise the reflectivity

112

of dielectric interfaces, so that complicated tricks, such as the insertion of a metal

layer in the stack as in the surface normal modulator, are not needed. The side-entry

modulator fabrication process is nearly as simple as the fabrication of photodiode

mesas as described in Chapter 3, with the only additional steps being the polishing of

the edge facets, and a cavity tuning etch.

5.1.2 Integration with CMOS

The side-entry modulator has great potential for integration with silicon electronics

since the devices are fabricated on silicon substrates. Integration with silicon

electronics is desirable for creation of a platform using optical interconnects for signal

transmission within the digital system. While optoelectronic integration would require

the incorporation of SiGe epitaxial growth in the CMOS fabrication process,

integration of germanium photodetectors with silicon electronics has already been

demonstrated by Masini et al. [2]. Though in that work it was stated that the total

epitaxial thickness for detectors should be sub-micron, it is likely that epitaxial

growths for the side-entry architecture could eventually hit this target. A functional

SiGe photodiode epitaxial growth grown at Stanford by Y.-H. Kuo was measured by

SIMS and found to have an annealed SiGe buffer only 240 nm thick.

5.2 Device Concept

5.2.1 Side Entry Architecture

A diagram of the side-entry modulator is shown in Fig. 1. A converging beam enters

the polished edge of the substrate at an angle, focusing on a photodiode mesa on the

top surface of the chip. For side entry modulators using Ge/SiGe quantum wells, the

beam is polarized with TE incidence as it reaches the mesa surface, since TE polarized

light can be absorbed by the lowest energy exciton transition of the Ge/SiGe quantum

wells, while for TM polarized light, the component of the light with an electric field

transverse to the plane of the quantum wells will not be absorbed. The top and bottom

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surfaces of the mesa are reflective, creating an asymmetric Fabry-Perot resonator,

enhancing the interaction of light with the optically active material contained in the

intrinsic region of the photodiode. The light reflected from the resonator exits through

the polished edge facet on the opposite edge from the entry facet.

Substrate

ReflectorsOptically active materialResonant cavity

Input port

Output port

Substrate

ReflectorsOptically active materialResonant cavity

Input port

Output port

Figure 5.1. Side-entry optoelectronic modulator schematic. The thickness of the optically active material is exaggerated. In the actual devices, beams undergo multiple reflections in the resonant cavity which overlap with one another.

The reflection at the bottom of the cavity can be achieved with an interface between

two materials of different index (as in our present device) or by a distributed Bragg

reflector, or by other methods. In the current device, reflectivity at the top face is

achieved by total internal reflection.

5.2.2 Advantages of oblique incidence in side-entry modulators

Oblique incidence confers upon the current design the same advantages as in the

QWAFEM modulator with respect to surface normal designs: Increased absorption

per pass of the modulator, higher reflectivity at dielectric interfaces, and broader

bandwidth lower-order resonances. Also, increased reflectivity from oblique

incidence is particularly useful for SiGe epitaxy as compared with other materials: As

explained in Chapter 3, it would be difficult to epitaxially grow distributed Bragg

reflectors in SiGe due to the lattice constant mismatch between Si and Ge. For an

114

abrupt interface between Si (n=3.53) and Si.1Ge.9 (n=4.15), at incidence normal to the

interface, the reflectivity would be 1%, while at the incident angle in the current

design (78.45° to normal in Si), for TE incidence, the reflectivity would be 28%, a

large improvement. In addition to a greater ability to modulate the energy in the

beam, another reason for using TE incidence is that the reflectivity of the interface will

be greater than for TM incidence. For all oblique angles not resulting in total internal

reflection, the Fresnel reflection coefficient at an interface between two dielectric

materials is of lower magnitude for TM polarized light than for TE polarized light, and

for TM incidence at Brewster’s angle, the reflectivity will equal zero.

5.2.3 Effect of graded index

It is expected that diffusion will occur at the Si/SiGe interface with annealing. It may

be possible to measure the profile accurately with SIMS, though such profiling has not

been attempted here. The SIMS profile in Chapter 3, Fig. 7 suggests that the

concentration gradient may be 100-200 nm deep, though the resolution of the SIMS at

the depth of the Si/SiGe interface is not known. Reflectivity of a graded Si/Si.1Ge.9

interface was modeled for a linear concentration and refractive index gradient at

78.45° from normal incidence from the Si substrate, as shown in Fig. 2. This data

shows that interdiffusion between Si and SiGe could decrease the interface reflectivity

by 50% for a 250 nm linear gradient with TE incidence. The uncertainty of the actual

reflectivity of the interface in the epitaxy makes modeling the device performance

more difficult.

115

0 50 100 150 200 250 300

12

14

16

18

20

22

24

26

Percentage reflectivity of Si-SiGe interface, oblique incidence

Width of linear gradient between Si and Si.1Ge.9 in nm

Figure 5.2. Percentage reflectivity of Si-SiGe interface, for TE incidence at 78.45º to

normal. The horizontal axis shows the width of a linear gradient between the index of

refraction of Si and SiGe to simulate interdiffusion.

5.3 Devices

5.3.1 Fabrication

Devices were fabricated on Wafers 1 – 5, containing 10, 20, 40, and 60 QWs.

Photodiode mesas were lithographically defined on the wafer surface, and etched. For

the experiment, the mesa aspect ratio was made closer to the size of the beam

projection on the surface for oblique incidence than in our previous published

experiment, for which the mesas were square [1]. Mesas on the mask measured 450

μm x 900 μm, 337 μm x 1012 μm, 225 μm x 675 μm, 150 μm x 450 μm, 100μm x

300 μm, and 67 μm x 200 μm. Ti/Au ring contacts were deposited. Au was used as a

116

contact metal instead of Al because it is resistant to wet etchants which are used for

cavity tuning. A mesa fabricated on the 60 QW sample (Wafer 5) is schematically

illustrated in Fig. 3.

Boron-SiGe (doping 3x1017/cm3) 1000 nm

Low boron doped Si substrate

Arsenic-SiGe (doping 1018/cm3) 920 nm

Ti/Au Contacts

MQW region: 60 QWs 3000 nm

Boron-SiGe (doping 3x1017/cm3) 1000 nm

Low boron doped Si substrate

Arsenic-SiGe (doping 1018/cm3) 920 nm

Ti/Au Contacts

MQW region: 60 QWs 3000 nm

Figure 5.3. Diagram of the PIN diode mesa fabricated in a sample with 60 quantum wells for side-entry modulation, not to scale.

The modulator chips were cleaved into one-dimensional arrays, and two parallel edges

of the chip were polished to form the entry and exit facets. The thicknesses of the top

Si0.1Ge0.9 layers of the mesas were individually adjusted with wet etching using a

selective etch [3]. Use of a selective etch was important so that the polished edge

facets would not be roughened.

5.3.2 Test Geometry

Modulator chips were placed on a gold mirror for testing. The configuration of the

device transmission tests is shown in Fig. 4. Light from a tunable laser is coupled out

of a polarization maintaining (PM) fiber through a focusing lens. The converging

beam impinges upon the gold mirror at 45° from normal, with TE polarization with

respect to the surface. The reflected beam is coupled through the edge facet into the

modulator wafer with a 78.4° angle to the wafer surface, and impinges upon the diode

mesa. Within the diode mesa, the angle to normal will be 54°, assuming a refractive

index of 4.15, increasing the optical path through the cavity by a factor of 1.7 times

117

per pass with respect to normal incidence, increasing the absorption per pass. The

light not absorbed in the photodiode is reflected and passes through the exit facet. It is

reflected from the gold mirror again, and measured by an InGaAs photodetector.

Gold Mirror

Si

11.6°78.4°

45°

1012

3500

5

350

350

Focal spot projection

Focused PM-fiber output

Photodetectordiode mesa60 QW 70µm x 484µm

Gold Mirror

Si

11.6°78.4°

45°

1012

3500

5

350

350

Focal spot projection

Focused PM-fiber output

Photodetectordiode mesa60 QW 70µm x 484µm

Figure 5.4. Diagram of side-entry modulator in experimental setup, not to scale. All unlabelled units are microns.

5.3.3 Spot Size

To best interpret the misalignment tolerance data, the beam spot size must also be

known in addition to the mesa size. The beam’s focused spot from the objective used

was measured by the knife-edge technique to have a Gaussian beam waist of 70 μm

diameter in air. To model the change in size in the device, one can model the beam

incident on the device from air as a cylinder of 70 μm diameter, neither converging or

diverging. The effects of refraction upon the cylinder shape can be calculated in order

to understand how the focal spot size of the real beam will be affected. At the

interface between air and Si at the edge facet, the angle of inclination is 45° from

normal to the edge facet on the air side, and 11.6° from normal to the edge facet on the

Si side. At this interface the cylinder dimension changes from 70 μm diameter in air

to an ellipse in silicon with dimensions 70 μm x 97 μm. At the interfacial surface

between Si and the SiGe epitaxy , the projection of the elliptic cylinder is an ellipse

with minor and major axes of diameter 70 μm by 484 μm. The implication from the

model for the actual focused beam is that the projection of the focused beam intensity

118

on the SiGe mesa in the actual device will be an elliptical Gaussian function with

minor and major diameters of 70 μm and 484 μm.

5.4 Spectral Measurements

The fraction of light transmitted through the samples was measured while scanning the

reverse bias applied voltage and the wavelength. The gold mirror on which samples

were measured was attached to a feedback-controlled resistive heater, and the devices

were tested at several operating temperatures, with the aim that the peak absorption

shift could be tuned to the wavelength of the cavity resonance. As mentioned in

Chapter 3, the band edge shifts by 0.788 nm/°C. All transmission data were

normalized to the detected signal when no sample was present, and when the light

underwent a single reflection from the gold mirror. This method of normalization

should be fairly accurate as the reflectivity from the gold mirror is around 99%.

5.5 Results and Discussion

5.5.1 Maximum Contrast Ratio

The best modulator performance was obtained with a 60 QW sample which had

undergone a 35 second tuning etch, removing about 150 nm from the top of the

epitaxial surface. The mesa measured 337x1012 μm. All transmission data included

in this chapter are from that device. The percentage transmission through the device at

room temperature is shown in Fig. 5 (for a subset of a data collected). Fig. 6 shows

the contrast ratio versus wavelength for different voltage swings, and the insertion loss

for 0V applied.

119

Figure 5.5. Percentage transmission through 60 QW side-entry modulator at room

temperature. Green = 0V, Red = 12V reverse bias.

For a voltage swing of 2V, the contrast ratio is greater than 3 dB over the range 1471

to 1477 nm, and for 11V, the peak contrast is 10 dB at 1472 nm, and exceeds 3 dB

from 1465 to 1482 nm. The insertion loss at the point of maximum contrast ratio is

9.5 dB. Capacitance of this device is estimated to be ε*Area/Thickness =

16*8.854x10-12F/m*337x10-6m*1012x10-6m/3.1x10-6m = 15.5 pF.

1460 1465 1470 1475 1480 1485 1490 1495 15000

5

10

15

20

25

30

35 % Reflectivity

Green=0V,2V..12V=Red

wavelength nm

% Refl.

120

5.5.2 Misalignment Tolerance

Contrast Ratio with Misalignment The misalignment tolerance of the device was measured. To do this, the beam

alignment and laser wavelength were adjusted such that the maximum contrast ratio

was achieved. Then the voltage was scanned while stepwise misaligning the device

first in the wide direction (the direction parallel to the wafer edge through which the

beam enters), and then in the deep direction (the direction perpendicular to the wafer

edge, such that the lens is moving closer and further from the sample). The contrast

ratio during misalignment of the device is shown in Figs. 7 and 8.

1460 1470 1480 1490

2

4

6

8

10CR (G)2V,4V,11V(R)

wavelength nm

Con

trast

ratio

dB

1460 1470 1480 14905

6

7

8

9

10

Insertion Loss (dB), 0V

wavelength nm

Inse

rtion

loss

dB

Figure 5.6. Left: Contrast ratio (dB) of 60 QW side-entry modulator at room temperature, for voltage swing of 2V (green dot), 4V (blue X), and 11V (red +). Right: Insertion loss of the modulator at 0V bias. The component of insertion loss which is due to reflections at entry and exit facets is about 4.9 dB.

121

0 100 200 300 400 500 6000

2

4

6

8

10

12

Misalignment μm

Con

trast

dB

Maximum Contrast Ratio vs. 'Wide' Misalignment, 1473 nm

Figure 5.7. Maximum contrast ratio (dB) of 60 QW side-entry modulator 1473 nm, at room temperature, for beam misalignments in the ‘wide’ direction, parallel to the entry facet.

0 100 200 300 400 500 6000

2

4

6

8

10

12

Misalignment μm

Con

trast

dB

Maximum Contrast Ratio vs. 'Deep' Misalignment, 1473 nm

Figure 5.8. Maximum contrast ratio (dB) of 60 QW side-entry modulator 1473 nm, at room temperature, for beam misalignments in the ‘deep’ direction, perpendicular to the entry facet.

122

From the spot size calculation, the beam is expected to have a projection on the device

mesa measuring 70 μm in the dimension referred to as the wide dimension, and 484

μm in the deep dimension. Given these values, the mesa size exceeds the beam size

by 267 μm (wide) and 528 μm (deep), and the mesa is proportionally larger than the

beam diameter by 4.8 times (wide) and 2.0 times (deep).

Explanation of Misalignment Tolerance

The contrast ratio exceeds 3 dB for misalignment by 280 μm in the wide direction and

200 μm in the deep direction. Given that the mesa was expected to exceed the beam

size by a greater absolute distance in the deep direction, this was not the expected

finding. In addition, the contrast ratio is ‘flat topped’ for translation in the wide

direction, while it is not in the deep direction, suggesting that the mesa is probably

larger than the beam in the wide direction, but perhaps not in the deep direction. A

likely explanation is that the beam focus was not perfectly aligned to the mesa. If the

focus occurred at a point along the beam path on either side of the mesa instead of at

the mesa, the beam size would be increased relative to the expected theory by a

proportionally equivalent amount in the wide and deep dimensions. If this occurred, it

would be possible for the beam to be larger than the mesa in the deep dimension but

smaller than the mesa in the wide dimension. To get an idea of the scale of error in

the alignment of the beam focus which would cause performance degradation, the

Rayleigh distance for the Gaussian beam focus is calculated by πw02/λ, or about 9mm

in silicon. This is longer than the width of the chip, so for the focus to be misaligned

by one Rayleigh distance, the focus would be in the air on either the entry or exit side

of the modulator. Another possible reason for the smaller-than-expected misalignment

range in the deep direction is that the beam projection may be slightly longer than

expected in the deep direction due to multiple reflections at oblique incidence.

However, this is probably a minor effect, since the absorption per pass is large, and the

beam size would only be extended by 21 μm in the deep direction per double pass. In

any case, the amount of misalignment tolerance suggests that the mesas’ sizes can be

reduced while still allowing adequate contrast for optical interconnects applications.

123

Such a reduction in mesa size would reduce capacitance, perhaps to values acceptable

for high speed data transmission.

5.5.3 Modeling Transmission through the Devices

Transfer matrix simulations The transfer matrix method was used for electromagnetic simulations of transmission

through this device, in order to match the experimental results in Figs. 5 and 6 to

theory. The beam was modeled in the simulation as having a Gaussian spot diameter

of 97 μm, expressed as a weighted sum of plane waves inclined at different angles

from the normal, centered at 78.4° from normal in the silicon substrate. The real part

of the quantum well superlattice index was set to 4.15, as using the Kramers-Kronig

integral did not improve the fit. The match between the simulation and data is shown

in Fig. 9, and the layer structure simulated is shown in Table 1. The screenshot in

Appendix C shows the settings used to obtain the simulation plot in Fig. 9.

1460 1470 1480 1490 15000

5

10

15

20

25

30

% Light transmitted, (G)0V,2V,..12V(R)

Figure 5.9. Actual and simulated percentage transmission through the 60QW side-entry modulator, points and dotted lines = actual performance, solid lines = simulation. Green = 0V, Red = 12V reverse bias.

124

Table 5.1. Dielectric layers used in electromagnetic simulation of 60QW side-entry modulator.

Material Refractive Index Thickness nm Silicon 3.53 - SiGe interdiffusion layer 3.83 0 Si.1Ge.9 4.15 1000 SiGe Quantum Well Superlattice

4.15 plus variable absorption

60 QWs: 3000

Si.1Ge.9 4.15 920 Air 1 -

Modeling the Maximum Achieved Transmission As shown in the data from Fig. 9, the maximum transmission is 33%. This figure is a

result of the maximum transmission through the entrance and exit facets of the device.

Reflection from the gold mirrors at 45° incidence was measured to be about 99%, a

small contribution to insertion loss. The theoretical fraction of power transmitted at

each air/Si boundary at the substrate edges is 56%, yielding an expected maximum

transmission through the device of 32%. This corresponds to 4.9 dB of insertion loss,

such that the insertion loss at the point of maximum contrast shown in Fig. 6 which is

due to absorption in the epitaxy is about 4.6 dB. It is expected that the 4.9 dB of

insertion loss associated with the edge facets could be reduced close to zero if the edge

facets were antireflection-coated.

Interdiffusion Layer As mentioned before, interdiffusion is expected at the Si/SiGe interface. Though in

the above simulation, it was not necessary to account for interdiffusion to achieve a

reasonable fit, in other simulations, a single layer was used to model interdiffusion to

achieve the best match with experimental data.

Absorption Coefficient The absorption coefficient used to simulate the quantum well superlattice was

calculated from photocurrent measurements (and in a later simulation, transmission

measurements) from photodiodes in the surface-normal configuration. The modeling

125

software described in Appendix C had the option of shifting the absorption data with

respect to wavelength to compensate for any temperature change, and for adjusting the

total power incident on the active region of the device to account for imperfections in

the antireflection coatings on diode used for the photocurrent measurement.

5.5.4 Critical Coupling

Transmission Data showing Critical Coupling Critical coupling, as described in Chapter 4, is demonstrated on the same 60 QW side-

entry modulator heated to 60°C. As a reminder, critical coupling occurs in a Fabry-

Perot cavity where the back mirror is not transmitting, and the absorption in the cavity

makes the net back reflectivity (actual interface reflectivity plus round-trip absorption)

equal to the front reflectivity. In the case of critical coupling, the reflection from the

cavity can theoretically be zero. In practice, to reach near-zero reflection would

require that the mirror surfaces be flat, the incident beam be a plane wave with no

diffraction, and the optical linewidth be very narrow.

In the transmission plots in Figs. 10 and 11 for the modulator heated to 60°C, at the

resonant frequency, the transmission increases for increasing absorption. To show that

this is the case, the absorption coefficient is shown in Fig. 12, where it can be seen that

for the lowest applied voltages, the absorption coefficient reaches a local maximum

around 1483 nm. The absorption decreases when shifting to higher or lower

wavelength or increasing the applied voltage. In Fig. 11, there is a clear increase in

transmission at the resonance peak around 1483 nm when the applied voltage is

decreased. The ‘green bump’ in this plot probably represents overcoupling, where the

effective bottom mirror reflectivity becomes lower than the front reflectivity, and the

overall cavity reflectivity increases. At the peak of the green bump, increasing or

decreasing the wavelength or increasing the voltage all result in increased absorption.

Increasing the absorption results in less transmission through the device, the opposite

of what is normally expected when the back reflectivity is greater than the front

reflectivity.

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1460 1470 1480 1490 1500 1510 1520 1530 0

5

10

15

20

25

30

35 % Ref. 4H35 Long60C14562153003-May-2007.mat Green=0V,2v..12V=Red

wavelength nm

Figure 5.10. Percentage transmission through 60 QW side-entry modulator at 60°C. Green = 0V, Red = 12V reverse bias

1474 1476 1478 1480 1482 1484 1486 1488 1490 1492 1494 0

0.5

1

1.5

2

2.5

3

3.5

4

% Ref. 4H35 Long60C14562153003-May-2007.mat Green=0V,2V..12V=Red

wavelength nm

Figure 5.11. Zoom-in of transmission from Fig. 11 showing probable critical coupling. The ‘green bump’ for which transmission increases with increasing absorption coefficient probably represents overcoupling at the intersection of the resonance peak and exciton peak.

127

1470 1475 1480 1485 1490 1495 15000

500

1000

1500

Absorption in cm-1, (G)0V,1V,..20V(R)

wavelength nm

abso

rptio

n co

effic

ient

cm

-1

Figure 5.12. Absorption coefficient of a 60 quantum well diode mesa measured by surface-normal transmission, showing maximum absorption around 1484 nm for 0V applied reverse bias voltage.

Simulation of Critical Coupling Experiment

Simulation with Flat Mirrors These data were also matched with simulations. The dielectric stack simulated is

shown in Table 2, and the comparison between the simulation and experimental data is

shown in Fig. 13. In the simulation, the transmission goes nearly to zero (despite the

finite focal spot size), while in the actual transmission data, the minimum transmission

is 0.8%.

128

Table 5.2. Dielectric layers used in electromagnetic simulation of 60QW side-entry

modulator.

Material Refractive Index Thickness nm Silicon 3.53 - SiGe interdiffusion layer 3.83 40 Si.1Ge.9 4.15 980 SiGe Quantum Well Superlattice

4.15 plus variable absorption

60 QWs: 3000

Si.1Ge.9 4.15 949 Air 1 -

Adding Mirror Roughness to the Simulation A likely explanation for the deviation between the measurement and simulation in Fig.

13 is that roughness in the mirror surface at the top of the epitaxy introduced

imperfections into the resonator. Roughness of the mirror can be added to the

simulation, following an approach outlined by Xu et al. [4] The RMS roughness of the

top of the epitaxy of the unprocessed 60 QW sample was measured by atomic force

microscopy to be 9 nm in Chapter 3. To simulate the variation in cavity length, an

integral is taken over the several transmission results while varying the top layer

thickness to simulate the roughness. 20 transmission simulation results are used, with

top layer thicknesses and weighting chosen so that the distribution of the top layer

thickness in the integral is normal with an RMS deviation of 9 nm. The results of the

simulations including the integration step, otherwise using the same parameters as

Table 2/ Fig. 13, are shown in Fig. 14. In this simulation the minimum transmission is

equal to 0.4%, closer to the minimum measured value of 0.8%.

129

1478 1480 1482 1484 1486 1488 0

0.5

1

1.5

2

2.5

3

3.5

4

wavelength nm

Figure 13. Top: Simulated percentage transmission through 60 QW side-entry modulator at 60°C. Bottom: Actual percentage transmission. In the simulation at left, transmission goes completely to zero, while in the actual experiment it does not.

1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488

0.5

1

1.5

2

2.5

3

3.5

4

4.5

wavelength nm

130

Figure 14. Simulated percentage transmission through 60 QW side-entry modulator at 60°C, with simulated roughness of 9 nm RMS on the top epitaxial surface, using a Gaussian weighted summation of simulations stepping the top layer thickness, as described in the text.

As was explained in Xu et al., there is also a component of the wave lost to diffraction

upon reflection from a rough mirror. Diffraction loss upon reflection from a rough

surface can be calculated using results of a statistical model derived by Davies [5]

meant to handle the reflection of radio waves from disturbed water surfaces, which

was later applied and experimentally verified for normal incidence upon rough optical

surfaces by Bennett and Porteus [6]. According to this model, the incoherently

scattered fraction of the intensity of a plane wave upon reflection from a rough surface

is equal to (16π2σ2/λ2)cos2ψ, where σ is RMS roughness, λ is wavelength, and ψ is

incident angle. For RMS roughness of 9 nm, incident angle of 54º, and a wavelength

in vacuum of 1484 nm, the fraction of light incoherently scattered upon total internal

reflection from Si.1Ge.9 (n=4.15) to air is 3.5%.

The effect of this incoherent scattering upon transmission from the resonator can be

described with another calculation. Using the dielectric materials and thicknesses

1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 0

0.5

1

1.5

2

2.5

3

3.5

4

wavelength nm

131

specified in the simulation of the critically coupled modulator, the front mirror (Si-

SiGe) is 27% reflective. For critical coupling, the net reflectivity of the back mirror

(including absorption in a double-pass of the quantum well superlattice) is also equal

to 27%. According to the model of Davies, the light reflected from the back mirror

would be accompanied by incoherently scattered light of intensity equal to 3.5% *

27% of the incident beam, or 0.95% of the incident beam. Assuming most of this light

from the first pass of the cavity traveled along the optical axis towards the detector, it

would result in an increase in the total detected transmission of 0.95% times the

maximum transmission with insertion loss of 32%, or 0.3% of the incident beam.

Added to the minimum 0.4% transmission obtained for transmission while integrating

over the top epitaxial layer thickness, the minimum transmission is now 0.7%, close to

the experimentally measured 0.8% minimum transmission.

Prospects for Improvement Upon the Current Critical

Coupling If the above analysis is correct, then the maximum contrast ratio of the device is

significantly degraded by the 9 nm RMS roughness of the epitaxial surface. It may be

possible to increase the contrast ratio to far greater than 10 dB by polishing the top

surface to be atomically smooth, provided that the polishing does not remove the top

N-contact layer, and results in a thickness where the exciton peak and the resonance

are well enough aligned as to be able to reach critical coupling. However, for short

distance optical interconnects with no analog signal amplification, the total change in

intensity between the pass and block states of the modulator may be more important

than the contrast ratio, depending on the receiver circuitry, rendering such

improvements unnecessary.

5.6 Conclusions

In this chapter, a novel side-entry modulator architecture was demonstrated using

SiGe epitaxy on a Si substrate. This architecture uses oblique incidence on a PIN

132

photodiode from within the Si substrate, where the modulator epitaxy acts as an

asymmetric Fabry-Perot modulator. Entry and exit ports for the light are on the

polished edges of the silicon substrate. This provides an advantage over other

modulator architectures for monolithic integration with silicon electronics: Since the

top and bottom of the chip are not needed for optical ports, they are freed to be used as

they currently are in silicon electronics, which is to use the top surface for electrical

interconnections and the bottom surface for heat removal. A modulator using 60

quantum wells is demonstrated with a peak contrast of 10 dB at 1472 nm, a maximum

operating range of 17 nm, and a minimum operating voltage of 2V. The beam

misalignment tolerance is measured to be 200 μm and 280 μm in orthogonal

directions. Deviations of the misalignment tolerance numbers from the expected

model are explained with the assumption that the beam is not at its focused minimum

spot size where it impinges upon the PIN diode mesa. When the 60 quantum well

modulator is heated from room temperature to 60°C, a shift in the band edge increases

the absorption on resonance and provides evidence of overcoupling, a condition where

increasing the absorption within a Fabry-Perot resonator increases the reflection from

the cavity. As overcoupling is occurring, it is inferred that for lesser absorption,

critical coupling is occurring, for which the theoretical resonator reflection (and hence

overall device transmission) is equal to zero. The minimum transmission through the

device of 0.8% is explained with a model of an asymmetric Fabry Perot cavity with a

rough back surface, using the wafer surface’s RMS roughness value of 9 nm which

was measured in Chapter 3.

133

5.7 References

[1] Roth, JE, Fidaner, O, Schaevitz, RK, Kuo, Y-H, Kamins, TI, Harris, JS, and

Miller, DAB, Optical modulator on silicon employing germanium quantum wells, Opt.

Express 15, 5851-5859 (2007).

[2] Masini, G, Capellini, G, Witzens, J, and Gunn, C, “A Four-Channel, 10Gbps

Monolithic Optical Receiver In 130nm CMOS with Integrated Ge Waveguide

Photodetectors”, OFC/NFOEC, March, 2007, Anaheim, CA

[3] Godbey, DJ, Krist, AH, Hobart, KD, and Twigg, ME, “Selective removal of Si1-

xGex from (100)Si using HNO3 and HF,” J. Electrochem. Soc. 139, 2943-2947

(1992).

[4] Xu, MG, Nener, BD, and Dell, JM, “Design of externally tuned asymmetric fibre

Fabry-Perot electroabsorption optical modulators”, IEE Proc.-Optoelectron., Vol. 145,

No. 6, 344-352 (1998).

[5] Davies, H, “The Reflection of Electromagnetic Waves from a Rough Surface”,

Proceedings of the Institution of Electrical Engineers, Vol. 101, No. 7, 209-214

(1954).

[6] Bennett, HE, and Porteus, JO, “Relation Between Surface Roughness and Specular

Reflectance at Normal Incidence”, J. Opt. Soc. Am. Vol. 51, No. 2, 123-9 (1961).

134

Chapter 6: Low Voltage Side-Entry Modulator Operating in the C-Band Using a Silicon-On-Insulator Wafer

In this chapter a side-entry modulator is described which uses Ge/SiGe quantum wells

grown on a silicon-on-insulator (SOI) substrate. The insulator layer of the SOI wafer,

made of SiO2, provides a high-reflectivity interface due to an effect known as

frustrated total internal reflection (frustrated TIR, from now on). The inclusion of a

high reflectivity layer on the substrate side of the asymmetric Fabry-Perot cavity

reduces the number of quantum wells required to achieve adequate contrast from a

minimum of 40 QWs [1] to 10 QWs. By heating the device to shift the absorption

edge, absorption contrast of 6.1 dB is possible in the telecommunications C-band. The

use of a 50 nm thick oxide layer is typical of applications of SOI wafers for high-

performance electronics, while integrated optics applications of SOI wafers typically

uses 1 μm insulator layers. The compatibility of the current design with high-

performance electronics makes it suitable as a component of an integrated platform for

optical communications and digital processing.

6.1 Device Concept

6.1.1 The Difficulty of Creating High-Reflectivity Interfaces in

Si/SiGe Epitaxy

As mentioned in Chapter 4, an issue with the use of optical resonators in

optoelectronic modulators utilizing the quantum-confined Stark effect in Ge/SiGe

quantum wells is the lack of lattice-matched materials with differing refractive indices

in SiGe epitaxial growth. This is due to the fact that the lattice constant of Ge is 4%

larger than Si. If a third element could be used to compensate for the difference in

135

lattice constant, it might be possible to grow lattice-matched stacks of materials with

differing refractive index. In well-developed III-V materials, ternary and quaternary

compounds are frequently used in this way. Some examples are structures made from

GaAs and AlGaAs [2], as well as InP and InGaAsP [3]. We have used oblique

incidence in asymmetric Fabry-Perot modulators (AFPMs) to enhance the reflectivity

of interfaces between materials of differing refractive index. We used this approach,

as described in the previous chapter, to create resonance-enhanced AFPMs with SiGe

epitaxy, where the reflectivity of the interface between the silicon substrate and the

annealed Si.1Ge.9 buffer layer was increased from 1% to an estimated 28% as a result

of the use of oblique incidence. Growth of the Si.1Ge.9 buffer on Si introduces defects

into the crystal lattice, and currently requires two high-temperature anneal steps which

add an estimated 45 minutes to the epitaxial growth time per wafer. Side-entry

modulators designed using the annealed buffer for a bottom layer required at least 40

QWs for adequate performance due to the limited reflectivity of the Si-SiGe interface.

It is not known whether the approach of growing differing SiGe composites and

annealing could be extended to make multilayer distributed Bragg reflector (DBR)

stacks, since it may be difficult to maintain a low defect density and surface roughness

after growing multiple strain-relaxed annealed layers on the Si substrate. These

difficulties led to the investigation of SOI wafers as substrates for epitaxial growth.

SOI wafers are a commercially available technology, in which a low-refractive index

layer (silicon dioxide) separates a thin top silicon layer from the bulk of the silicon

substrate.

6.1.2 Silicon-On-Insulator Wafers as Substrates

Description SOI wafers have been highly developed commercially due to their potential to extend

the performance of silicon electronics. A SOI wafer consists of a stack of three

materials. A bulk silicon substrate, known as the handle wafer, is covered by a buried

amorphous silicon dioxide layer, known as the buried oxide, or BOX. The BOX is

sandwiched between the bulk silicon and a thin crystalline silicon layer on the top.

136

Devices, whether they are integrated circuits, MEMS, or optical components, are

typically fabricated in the top silicon layer.

Fabrication Commercial SOI wafers are the result of highly developed wafer bonding processes.

Two processes are used most commercially [4]. The first is known as separation by

implanted oxygen (SIMOX), in which oxygen ions are implanted from above the

surface of a bulk Si wafer. The implantation is combined with carefully controlled

annealing which results in a crystalline top silicon layer and high-quality BOX with a

well-defined thickness. The second process, which was used for the SOI wafers in

this study, is known as the Smart Cut™ process. In this process, a wafer known as the

“seed” wafer is oxidized to the desired thickness for the BOX. Hydrogen ions are

implanted from the oxide side, leading to a segregation of hydrogen in a layer beneath

the BOX and within the seed wafer. The segregated hydrogen creates voids in a plane

of the wafer, weakening it. The surfaces of the BOX and a handle wafer are cleaned,

contacted, and bonded, and the pair of wafers are heated to 400°C- 600°C, causing the

wafers to split along the plane where hydrogen was implanted. Finally, the wafer is

polished.

Application of SOI in Electronics SOI wafers are useful for improving the performance of silicon electronics, and have

found widespread use, such as in portable computing applications and in the most

recent generation of video game consoles. SOI electronics can have lower operating

voltages, lower passive power dissipation, faster clock speeds, as well as other

advantages compared to electronics on standard silicon wafers. Two important classes

of advantages of SOI are (1) the lack of parasitic effects related to the presence of the

silicon substrate, as the devices are vertically isolated, and (2) a superior capability of

scaling devices on SOI, as the silicon film thickness can be scaled [4]. The latter

makes it possible to reduce drain-induced barrier lowering and short channel effects.

137

Typical wafers used for electronics have a top silicon layer tens of nanometers, and a

BOX around 100 nm thick.

Application of SOI in Optics SOI wafers have been a popular platform for photonic integrated circuits due to the

attractiveness of silicon substrates for photonics for future integration with CMOS

electronics, and due to the presence of a high index silicon layer on a low index oxide

[5]. There is a large index contrast between Si and SiO2 (n=3.53 / 1.53 at 1550 nm).

This index contrast makes possible confinement of light in modes in structures

fabricated in the top Si layer. To obtain adequate confinement, BOX thicknesses of 1

μm are typical [4]. SOI photonics platforms typically guide light using silicon

waveguides on oxide, or in lines of defects in photonic crystal structures fabricated in

the top silicon layer.

6.1.3 Frustrated Total Internal Reflection applied to Side Entry

Modulators

Description of Total Internal Reflection Before explaining frustrated total internal reflection, total internal reflection will be

briefly described. Total internal reflection is a phenomenon which occurs when light

is incident from a high index material on an interface with a low index material at

oblique angle larger than an angle from normal incidence known as the critical angle.

The critical angle is defined as θcrit=sin-1(nLOW/nHIGH). The wave will be totally

reflected from the interface. In the low index material, the wave amplitude decays

exponentially with increasing distance from the interface. No energy propagates in the

direction normal to the interface in the low-index material.

Description of Frustrated Total Internal Reflection Frustrated TIR, like TIR, occurs when light is incident from a high-index medium

upon a low-index medium at oblique incidence beyond the critical angle. However, in

138

frustrated TIR, the low-index medium is of finite thickness, and bounded by another

high index medium on its other side, which will be referred to as the ‘transmission

side’. On the transmission side, there will be a propagating wave. The situation has

been considered mathematically analogous to quantum mechanical tunneling through

a barrier [6]. Frustrated TIR was experimentally demonstrated by Hall using coupled

prisms [7], and has been exploited for a number of applications including

mechanically actuated optical switches [8], acoustic wave sensors [9], and

beamsplitters [10]. As in TIR, the wave in the low index material will be evanescent,

and the amplitude will be an exponential function of distance from the interface, as is

illustrated in Fig. 1a. If the wave is incident from only one side, and the transmitted

wave is not reflected back, the wave amplitude will decrease with increasing distance

from the incident side of the boundary. However, if the light is reflected back, the

wave amplitude may increase with distance from the incident boundary. This can

occur in the case where the frustrated TIR low-index layer defines the port of an

asymmetric Fabry-Perot resonator operating at or near the resonance. This case is

illustrated in Fig. 1b.

In Fig. 2, the transmission of a SiO2 layer with Si on either side is plotted versus SiO2

thickness for TE and TM incidence, calculated using the transfer matrix method. The

dependence of transmission upon the low-index region thickness is exponential for

thicker boundaries, as can be seen from the derivation in a paper by Gale [11].

139

nHIGH nLOW nHIGH

Incident plane wave directional ray

Incident region: Propagating wave

Transmission region: Propagating wave

FTIR region:

(a) Transmission region is unbounded on the right side

nHIGH nLOW nHIGH


Propagating wave

FTIR region: Exponentiallydecaying wave

Time snapshot of E2

(a) Transmission region is unbounded on the right side

TIR region: Exponentially decaying wave

nHIGH nLOW nHIGH



Resonator region: Propagating wave (on resonance)

FTIR region: Exponentially growing wave

Time snapshot of E2

intensity

(b) Transmission region is bounded by a TIR low index region

n LOWnHIGH nLOW nHIGH



Resonator region: Propagating wave (on resonance)

FTIR region: Exponentially growing wave

(b) Transmission region is bounded by a TIR low index region

n LOW

TIR region: Exponentially decaying wave

Figure 6.1. Schematic illustrating frustrated total internal reflection, (a) showing exponential decay of the field intensity if the transmission region is unbounded, and (b) showing an exponential growth of the field intensity if the frustrated TIR region couples light in and out of a resonator operating on resonance.

140

0 50 100 150 200

0

20

40

60

80

100Transmission of Si-SiO2-Si interface at 78.4° in Si and 1550nm vs oxide thickness

SiO2 layer thickness nm

Per

cent

age

trans

mis

sion

TETM

Figure 6.2. The above graph shows the dependence of transmission through an SiO2 layer in Si upon the SiO2 layer thickness. For thicker SiO2 layers the transmission approaches a decaying exponential function.

Application of Frustrated Total Internal Reflection to a Side-

Entry Modulator

The BOX as a High-Reflectivity Layer Under the SiGe

Epitaxy In contrast to most photonics applications using SOI wafers, the modulator described

here does not use the oxide layer to confine light in the top Si layer while it is

conducted between components in a waveguide mode. The 50 nm oxide layer has a

reflectivity of about 72% for TE incidence at an incident angle of 78.4° due to

frustrated TIR. For TM incidence at the same angle, the reflectivity would be 99%.

This reflectivity would result in too narrow a bandwidth of operation, and, as noted in

prior chapters, the lowest energy exciton of the Ge/SiGe quantum wells will not

absorb the portion of the light with an electric field component normal to the plane of

the quantum wells. For the design of resonant modulators, the 72% reflectivity is a

significant improvement over the maximum reflectivity of about 28% that is expected

141

at the Si/Si.1Ge.9 boundary. The reflection coefficient from frustrated TIR is a

function of the BOX layer thickness, and can be arbitrarily close to zero or unity,

circumventing the problem of creating high reflectivity interfaces underneath SiGe

epitaxial growths. The proper thickness can be chosen for a modulator design, such

that the designer has good control of the design trade-offs, including the modulator’s

contrast ratio, bandwidth, and voltage swing.

Original Concept The idea of creating an oblique-incidence AFPM in which one reflector in the

resonator was a TIR interface and the other was a low-index layer with frustrated TIR

was first proposed by my colleague Noah Helman [12]. The idea was proposed before

the development of Ge/SiGe QWs grown on Si. It was expected that devices using

this concept fabricated on InP substrates would require either wafer bonding to allow

inclusion of an SiO2 layer underneath the InP/InGaAsP epitaxy, or etching of a

sacrificial layer within the epitaxy to create an air gap. The development of Ge/SiGe

QWs grown on Si allows for implementation of the frustrated TIR modulator idea as a

simple extension of our side-entry modulator work by leveraging SOI wafers, a

commercially mature technology.

Convergence of SOI Wafer Parameters for Optics and

Electronics In the present application, the use of a thin BOX and top silicon region compared with

photonics applications is beneficial, since the thinner layers here are comparable with

the thicknesses preferred for high-performance electronics. The convergence of the

requirements on the SOI thicknesses for the present device with requirements for high-

performance electronics makes this device attractive for photonic and electronic

integration.

142

6.2 Analysis of Frustrated TIR Mirrors

The BOX layer in an SOI wafer is used in this side-entry modulator to solve the

problem of low interface reflectivity at the SiGe epitaxy/substrate interface. In this

section the results of calculations of BOX reflectivity will be shown, showing

dependence of the BOX reflectivity on different factors. It is desirable that the

reflectivity not be overly sensitive to parameters which may vary in fabrication or use,

or it would be difficult to simulate and then subsequently fabricate a side-entry

modulator structure using the BOX layer as a frustrated TIR reflector.

In Fig. 3, the reflectivity of the BOX is shown for 1550 nm light at the incident angle

used in the side-entry modulator. In the plot, the BOX thickness is varied along the

horizontal axis, and for a 50 nm thick BOX, the reflectivity is 72%. The BOX

thickness tolerance of the wafer used here is quoted as +-10%, though tolerances of at

least +-5% can be achieved in a manufacturing process [13]. For a +-10% variation in

a 50 nm BOX, the reflectivity can range from 67%-76%, so a well-controlled BOX

thickness be important for future devices. As the transmission through the low-index

layer in a frustrated TIR reflector is roughly an exponential function of the layer

thickness, it is desirable to have good control over the low-index layer thickness. The

existence of an established technology saves the researcher the trouble of developing a

process incorporating wafer bonding or another technique for integrating a low-index

layer of a well-controlled thickness in a wafer structure.

In comparison with the 50 nm SiO2 layer reflectivity of 72%, the reflectivity of an

abrupt Si/Si.1Ge.9 interface at the same incident angle is only 28%. In Figs. 4 and 5,

the reflectivity of a Si/Si.1Ge.9 interface and a 50 nm thick SiO2 layer are shown while

varying the incident angle. It can be seen in Fig. 5 that the reflection coefficients for

frustrated TIR differ from Fresnel reflections in that at large angles, the reflectivity of

TM polarized light exceeds that of TE polarized light.

143

0 50 100 150

0

20

40

60

80

100

Reflectivity of SiO2 layer at 78.4° from normal in Si and 1550nm

Oxide thickness nm

Per

cent

age

refle

ctiv

ityX: 50Y: 71.54

TETM

Figure 6.3. Reflectivity of SiO2 layer with Si on either side for 1550 nm light and incidence at 78.4° from normal in Si, varying the SiO2 layer thickness along the horizontal axis.

0 20 40 60 80

0

20

40

60

80

100

X: 78.4Y: 71.54

Reflectivity of 50nm SiO2 layer in Si vs. Incident angle

Incident angle °

Per

cent

age

refle

ctiv

ity

TETM

Figure 6.4. Reflectivity of a 50 nm SiO2 layer with Si on either side, for 1550 nm wavelength, varying the incident angle on the horizontal axis.

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0 20 40 60 80

0

20

40

60

80

100

X: 78.4Y: 27.83

Reflectivity of Si-to-Si.1Ge.9 interface vs. Incident angle

Incident angle °

Per

cent

age

refle

ctiv

ity

TETM

Figure 6.5. Reflectivity of an interface from Si to Si.1Ge.9 for 1550 nm wavelength, varying the incident angle on the horizontal axis.

At an incident angle of 78.4°, the change in reflectivity per unit change in angle is

slightly greater for the SOI interface than for the Si/SiGe interface; however, to obtain

a 72% reflectivity from the Si/SiGe interface, an incident angle of 87° would be

necessary. This would result in a very large focal spot on the device, and a very large

change in reflectivity per change in incident angle. As a result, it would not be

practical to attempt to get a reflectivity this high using a single Si/Si.1Ge.9 interface.

A disadvantage of distributed Bragg reflector (DBR) stacks is that they only have a

high reflectivity for a limited bandwidth around the design wavelength. This is not at

all the case with frustrated TIR reflectors. In Fig. 6, the reflectivity of the 50 nm BOX

as a function of wavelength is shown. The reflectivity only varies by several percent

over a large 200 nm bandwidth.

145

1400 1450 1500 1550 1600

70

75

80

85

90

95

100Reflectivity of 50nm SiO2 vs. wavelength, at 78.4° in Si

wavelength nm

Per

cent

age

refle

ctiv

ity

TETM

Figure 6.6. Reflectivity of a 50 nm SiO2 layer with Si on either side for light and incidence at 78.4° from normal in Si, varying the wavelength along the horizontal axis.

In conclusion, frustrated TIR reflectors such as used in this study have relatively weak

dependence of reflectivity upon wavelength, moderate sensitivity of reflectivity to

incident angle, and the reflectivity can be made arbitrarily high by varying the low

index layer thickness. The mature technology of SOI has adequate fabrication

tolerances for devices such as the one described here. SOI frustrated TIR mirrors

compare well to the reflectivity of oblique incidence at a Si/Si.1Ge.9 interface since the

reflectivity is much higher. SOI frustrated TIR mirrors compare well to DBR mirrors

because they are less sensitive to wavelength, and because DBR mirrors may be

difficult or impossible to fabricate in SiGe epitaxy.

6.3 Device Design and Fabrication

An SOI wafer was used as the substrate for epitaxial growth of Ge/SiGe quantum

wells. The layer thicknesses of the substrate and epitaxial layers are described in

Table 1. The same fabrication recipe was used as in the side-entry modulator

described in Chapter 5.

146

Table 6.1. Layer thicknesses of frustrated TIR side-entry modulator, after tuning etch. These thicknesses were used in the simulation of the device, and are a good match to the expected actual thicknesses.

Material Refractive Index Thickness

As Doped Si.1Ge.9 4.15 248 nm Undoped Si.1Ge.9 4.15 100 nm Quantum Well Superlattice 4.15 plus variable

absorption 496 nm

Undoped Si.1Ge.9 4.15 96 nm B doped Si.1Ge.9 4.15 900 nm Silicon-on-Insulator 3.53 100 nm Buried Oxide 1.53 50 nm Si substrate 3.53 730 μm

Rectangular mesas were defined with dimensions 225 μm x 625 μm, and the regions

around the mesas were etched to make contact to the boron doped layer. Ti/Au ring

contacts to the As- and B- doped regions were deposited, and two parallel edges of the

wafer were polished flat, with a chip width of 3.5 mm. Following processing and

initial device testing, about 40 nm material was etched from the top of the mesas to

shift the resonance to about 1540 nm.

6.4 Experiment

6.4.1 Experimental Setup

The experimental setup was the same as described in Chapter 5, in which a focused

beam from the tunable laser was incident on a gold mirror at 45º, light passed through

the device, and the light was collected on the other side by a photodetector. Unlike the

previously described side-entry modulator, this device operated in the C-band when

heated to 100°C, a temperature comparable to the operating temperatures of silicon

processor chips. Transmission spectra were collected as the bias voltage was varied

and the wavelength swept, and normalized to the reflectivity from a single reflection

from the gold mirror.

147

6.4.2 Absorption Coefficient

Another chip from the same epitaxial wafer was fabricated with diode mesas which

were antireflection coated on both sides, for measurement of the absorption

coefficient. Photocurrent spectra were collected at 30ºC and 100ºC while sweeping

the bias voltage in 0.25 V increments, and sweeping the wavelength in 1 nm

increments. From these data the absorption coefficient spectra were calculated. A

subset of the data collected at 100ºC is shown in Fig. 7. From the measurements at

two temperatures, the absorption spectra were found to shift by 0.76 nm/ºC. Since the

surface normal reflectivity from the 50 nm SiO2 layer is estimated to be 8%, to

roughly compensate in the calculation, the absorption coefficient is calculated as if the

quantum well superlattice were 8% longer than its actual length, or 540 nm long, and

light only made a single pass of the absorbing region. It is found that at 1540 nm,

where the device is operated, the maximum absorption change is between 660 cm-1

and 190 cm-1, a ratio of about 3.5.

6.4.3 Transmission Spectra

Transmission spectra from light passed through side entry modulators at 100ºC

showed a resonance peak at 1540 nm, and maximum transmission at the peak of 11%.

Based on calculated surface reflection losses from the entry and exit faces on the sides

of the device, in the absence of any absorption loss in the material, the maximum

transmission would be ~ 32%. Hence from this measured 11% peak transmission, we

can conclude that the insertion loss at the transmission peak due to optical absorption

loss in the device structure is then 4.6 dB. The transmission through the device is

shown in Fig. 8.

148

1460 1480 1500 1520 1540 1560 15800

200

400

600

800

1000

1200

1400

1600

1800

2000

wavelength nm

abso

rptio

n co

effic

ient

cm

-1

Absorption Coefficient of SOI 10 QW sample at 100°C, Green: 0V, 1V steps, Red: 5V

Figure 6.7. Absorption coefficient of the 10 QW sample on SOI at 100ºC, calculated from photocurrent spectra. The total thickness was assumed to be 540 nm instead of ~500 nm in the calculation to compensate for the backward reflection from the SiO2 interface. Data were collected in 0.25 V increments for reverse bias voltages 0V to 10V. Only a subset of that data (0V, 1V, …5V reverse bias) is shown here for clarity.

1530 1535 1540 1545 1550 15550

5

10

15

20

25

Transmission through SOI Modulator, Green: 1V,2V,...Red: 5V

wavelength nm

Per

cent

age

trans

mis

sion

Figure 6.8. Transmission through frustrated TIR side-entry modulator at 100°C. Data shown are from 1V to 5V in 1V increments, though the full data set was from 0V to 6V in 0.125V increments.

149

6.4.4 Contrast Ratio

The transmission data, taken in increments of 0.5 nm and 0.125 V, were used to find

the maximum contrast ratio at each wavelength for voltage swings of 1V , 2V, and 4V,

as shown in Fig. 9. For these curves, the bias voltages to obtain the maximum contrast

ratio shown are not always the same at each wavelength. For 1V swing, the device

has a contrast ratio above 3 dB from 1539 nm to 1542.5 nm, and the voltage swing at

the contrast ratio peak was from 3.625V to 4.625V. For 4V swing, the contrast ratio

exceeded 3 dB from 1536 nm to 1545 nm, and the peak contrast ratio is 6 dB for a

swing from 0.875V to 4.875V at 1541 nm. Unlike the modulators described in

previous chapters, this one requires several volts bias, though it requires only one volt

swing to obtain 3 dB contrast. The bias is needed because this modulator operates at a

wavelength longer than the exciton peak wavelength with no bias, so it is necessary to

apply several volts to shift the exciton to the operating wavelength. Fig. 9 also

contains insertion loss data. Given that the insertion loss due to the entry and exit

facets is about 4.9 dB, the maximum insertion loss of an antireflection-coated device

should be 4.4 dB.

6.4.5 Misalignment Tolerance

The tolerance of the device to misalignments was measured. The dimensions of the

elliptical projection of the beam on the device mesa are calculated to be 70 μm in the

wide direction and 484 μm in the deep direction (using definitions of wide and deep

given in Chapter 5). The mesa measures 225 μm (wide) x 625 μm (deep). At 1541

nm, the contrast ratio stays over 3dB over total translation in the wide direction of 51

μm for 1V drive and 102 μm for 4V drive. In the deep direction, the contrast ratio

stays over 3dB for a total translation distance of 32 μm for 1V drive and 90 μm for 4V

drive.

150

1530 1535 1540 1545 1550 1555

1

2

3

4

5

6Peak Contrast (dB), For swing of 1V (Green .), 2V (Blue X), and 4V (Red +)

wavelength nm

cont

rast

dB

1530 1535 1540 1545 1550 15555.5

6

6.5

7

7.5

8

8.5

9

Insertion Loss (dB), 0V

wavelength nm

Inse

rtion

loss

dB

Figure 6.9. Left: Peak contrast ratio (dB) of the frustrated TIR side-entry modulator for 1V, 2V, and 4V swing, with the bias voltage chosen at each wavelength and swing to maximize contrast ratio. Right: Insertion loss of the modulator at 0V applied bias. About 4.9 dB of loss is due to reflections at the entry and exit facets.

6.5 Modeling

The experimental results were modeled using the absorption data set of which a subset

was shown in Fig. 7, using the layer thicknesses in Table 1. The insertion loss due to

the surface reflections on the sides of the wafers was set in the simulation to

correspond to a total transmission in the absence of device absorption of 28% to best

match the experimental data. The measured transmission for 1V to 5V reverse bias in

1V increments and the corresponding simulation are shown in Fig. 10. While the

curves do not show a perfect match, the simulation shows a match to the resonance

peak center and to the width of the resonance. Obtaining a perfect match is difficult,

since a structure with many layers and uncertain refractive indices must be simulated,

using experimentally obtained absorption data. Using the Kramers-Kronig relations to

calculate the refractive index in the quantum well superlattice did not improve the fit,

so that region’s refractive index was set to have a real component equal to 4.15.

151

1530 1535 1540 1545 1550 15550

5

10

15

20

25

Transmission through SOI Modulator, Green: 1V,2V,...Red: 5V

wavelength nm

Per

cent

age

trans

mis

sion

Figure 6.10. Transmission through frustrated TIR side-entry modulator, for applied reverse bias from 1V to 5V, in 1V increments. Dots represent measured data, and solid lines represent simulation. Light green curves are for 1V bias, and red curves are for 5V bias.

The fact that the transmission does not dip as low in the real data as it did in the

simulation may be partially due to the surface roughness, as explained in the analysis

of the device in Chapter 5. Also, the frustrated TIR side-entry modulator mesa

measured here measured 225 μm x 625 μm instead of 337 μm x 1012 μm as in the last

study, so there is a greater chance that a portion of the energy in the beam reflected off

the top surface of the resonator outside the edges of the mesa than in the last study.

152

6.6 Discussion

Compared to the previous study with a 60 QW sample, the usable bandwidth (with

contrast ratio > 3 dB) in this study is only 9 nm instead of 17 nm. This is the case

because the cavity resonance is far stronger in the current device since the bottom

mirror reflectivity is over 70% compared with less than 30% in the 60 QW sample,

and also because there is less absorption per pass. The decrease in bandwidth is a

result in the increase in passes per cavity. As the higher bottom layer reflection

coefficient results in more passes through the cavity, less absorption is required per

pass to get adequate contrast, and only 10 QWs are needed. The thinner intrinsic

region in this device requires less swing in the applied voltage to obtain the same

change in electric field across the quantum wells, so this device operates at smaller

voltage swings. The capacitance of the device is increased by using a thinner intrinsic

region, and is estimated via calculation to be 33 pF. Since the power dissipation of a

modulator sending a bit stream at a frequency f with capacitance C and a voltage

swing of V is equal to ½CV2, it is generally desirable to decrease the intrinsic region

width. This is because C is inversely proportional to the intrinsic region width, and V

will be roughly proportional to the intrinsic region width, depending somewhat on the

device design. As a result power dissipation will roughly scale with the intrinsic

region width. Unlike the 60 QW modulator, the current device operates at longer

wavelengths than the 0V exciton peak where the absorption coefficient is smaller, yet

the fractional change in absorption coefficient is greater. As explained in Chapter 4,

for an asymmetric Fabry-Perot modulator, a larger fractional absorption contrast

enables devices with more a more optimal combination of low insertion loss and high

contrast ratio.

153

6.7 Other possible uses of SOI wafers for optical resonators

In the device described here, the oxide layer in an SOI wafer was used with oblique

incidence to provide a reflector using frustrated TIR, which could be designed to have

a reflectivity anywhere between zero and unity. Other possible uses of SOI wafers to

create optical resonators can also be imagined. The oxide layer could be made one

quarter wavelength thick, which would result in a reflectivity of 47% for normal

incidence, and higher for oblique incidence. In addition, it may be possible to iterate a

fabrication process for SOI wafers along the lines of the Smart Cut™ process to add

multiple layers of oxide and silicon to a substrate to create SOIOSOI wafers, or

(SOIO)nSOI wafers. Such a process could be used to created distributed Bragg

reflectors, upon which epitaxial SiGe could be grown, where the reflectivity of the

Bragg reflector beneath the epitaxy could approach unity. Another possibility would

be to fabricate photonic crystal mirrors in the stack to achieve a high reflectivity layer

during the substrate fabrication process. The stack could potentially consist of a

substrate, followed by an oxide layer, followed by a silicon layer with periodic holes,

followed by oxide, followed by the top silicon layer.

6.8 Conclusions

An electroabsorption modulator was demonstrated in C-band, operating with as little

as 1V swing. The modulator was fabricated on a silicon-on-insulator wafer with

epitaxially grown Ge/SiGe quantum wells providing electroabsorption via the

quantum-confined Stark effect. The modulator uses the previously demonstrated side-

entry architecture, though in the present case the asymmetric Fabry-Perot resonator

structure is enhanced by using a high-reflectivity frustrated total internal reflection

from the buried oxide layer of the silicon-on-insulator wafer. The modulator has 3.5

nm of bandwidth for 1V swing for a contrast ratio over 3 dB, and 9 nm of bandwidth

for 4V swing, with a peak contrast ratio of 6.1 dB at 1541 nm. At 4V, the contrast

154

ratio exceeded 3 dB over translation of the beam by 102 μm and 90 μm, parallel and

perpendicular to the substrate edge through which the beam entered. The operating

temperature is 100ºC, which is compatible with CMOS electronics, and the 50 nm

buried oxide layer is characteristic of SOI wafers used for high-performance electronic

circuits.

6.9 References

[1] Roth, JE, Fidaner, O, Schaevitz, RK, Kuo, Y-H, Kamins, TI, Harris, JS, and

Miller, DAB, Optical modulator on silicon employing germanium quantum wells, Opt.

Express15, 5851-5859 (2007).

[2] Thornton, RL, Burnham, RD, and Streifer, W, High reflectivity GaAs-AlGaAs

mirrors fabricated by metalorganic chemical vapor, Applied Physics Letters, v.45,

n.10, 1028-30 (1984).

[3] Yoo, SJB, Koza, MA, Bhat, R, and Caneau, C, 1.5 μm asymmetric Fabry-Perot

modulators with two distinct modulation and chirp characteristics, Applied Physics

Letters, v. 72, n. 25, 3246-8 (1988).

[4] Celler, GK, and Cristoloveanu, S, Frontiers of silicon-on-insulator, Journal of

Applied Physics, v. 93, n. 9, 4955-78 (2003).

[5] Jalali, B, Yegnanarayanan, S, Yoon, T, Yoshimoto, T, Rendina, I, and Coppinger,

F, “Advances in Silicon-on-Insulator Optoelectronics,” IEEE J. Quantum Electron.,

Vol 4, No. 6, pp. 938-946 (1998).

[6] Zhu, S, Yu, AW, Hawley, D, and Roy, R, Frustrated total internal reflection: a

demonstration and review, American Journal of Physics; vol.54, no.7, p.601-6 (1986).

[7] Hall, EE, Penetration of totally reflected light into the rarer medium, Physical

Review; v.15, p.73-106 (1902).

155

[8] Zhu, Y, Yao, C, Chen, J, and Zhu, R, Frustrated total internal reflection

evanescent switching, Optics and Laser Technology; vol.31, no.8, p.539-42 (1999).

[9] Spillman, WB Jr., and McMahon, DH, Frustrated-Total-Internal-Reflection

Multimode Fiber-Optic Hydrophone, Applied Optics; vol.19, no.1, p.113-16 (1980).

[10] Daehler, M, and Ade, PAR, "Michelson interferometer with frustrated-total-

internal-reflection beam splitter," J. Opt. Soc. Am. 65, 124- (1975).

http://www.opticsinfobase.org/abstract.cfm?URI=josa-65-2-124

[11] Gale, DS, Frustrated total internal reflection, American Journal of Physics;

vol.40, no.7, p.1038-9 (1972)

[12] Helman, NC, Optoelectronic Modulators for Optical Interconnects, Applied

Physics Ph.D. Dissertation, Stanford University, May 2005.

[13] Celler, George. Personal conversation. 20 July 2007.

156

Chapter 7: Conclusions

This dissertation describes electroabsorption modulators designed primarily for optical

interconnections to CMOS electronics. The main design goals were ease of

integrating modulators with electronics, a voltage swing compatible with CMOS, low

power dissipation, ease of optical alignment, and broad bandwidth operation in the

telecommunications C-band.

Chapter 2 describes a chip-to-chip optical interconnect using a quasi-waveguide

angled-facet electroabsorption modulator fabricated on an indium phosphide wafer.

An array of modulators was flip-chip bonded to a silicon CMOS transceiver circuit.

The link used light at a wavelength of 1550 nm and had a total electrical power

dissipation of 23.6 mW at 1.8 Gb/s. The low link power dissipation combined with the

simple packaging and alignment of the system makes this demonstration a step

towards practical systems for short-distance optical interconnects. Operation at 1550

nm suggests that optical interconnect systems bridging short and long distance scales

can be made.

The discovery of a strong quantum-confined Stark effect (QCSE) was reported in

Ge/SiGe quantum well structures grown on silicon substrates. Germanium is

compatible with silicon CMOS processing, so it should be possible to integrate

optoelectronic devices using germanium quantum wells with CMOS electronics.

Unlike most modulators on silicon substrates, modulators using the QCSE in

germanium quantum wells can achieve over three decibels of contrast without

requiring waveguides to achieve a long interaction length of light with the quantum

well structures. The best-performing device, a side-entry modulator grown on a

silicon-on-insulator wafer described in Chapter 6, operates with a voltage swing of 1

volt, and modulates light in C-band.

157

The modulators demonstrated using Ge quantum wells may be improved in several

ways. Epitaxy may be grown using thinner annealed buffers and thinner quantum

wells separated by proportionally thinner strain-balanced barriers of higher silicon

concentration. These changes will result in thinner devices with equal or better peak

contrast ratio and smaller voltage swings. The thinner devices will operate over wider

bandwidths because thinner asymmetric Fabry-Perot resonators will be more tolerant

to deviations from their resonant wavelengths.

All the modulators described in this thesis may be improved through optimization of

the focused beam spot size and the mesa size. This optimization results in a trade-off

between the device capacitance and the misalignment tolerance. The misalignment

tolerance of an optimized device will probably still greatly exceed that of waveguide

modulators, which frequently require alignments on the order of 0.1 µm. Smaller

mesas may be used if the spot size is reduced, but smaller focused spots converge over

a wider angular range. Components of the beam at extreme angles do not couple as

strongly to the Fabry-Perot resonator and decrease the overall contrast ratio.

Improved resonator designs may be used in future devices. A future wafer-bonded

device may incorporate a multilayer Bragg reflector instead of a metal mirror to

increase the reflectivity of one of the cavity mirrors. Photonic crystal slabs may also

be used in surface-normal devices, as they can create high reflectivity interfaces and

resonators with compact mode volumes.

Integration of germanium quantum well modulators with silicon CMOS is of primary

importance for systems employing interconnects. Once devices are integrated, it will

be possible to make optical interconnect transceivers like the one in Chapter 2 using

monolithically integrated devices with the simple optical alignment possible with

surface-normal and side-entry modulators.

I hope that the demonstration of modulators using the quantum-confined Stark effect

in germanium quantum wells as well as the exploration of novel modulator

158

architectures will help bring about the widespread adoption of CMOS compatible

optical interconnect technologies.

159

Appendix A: Transfer Matrix Technique to Calculate Reflection and Transmission from a Dielectric Stack

Introduction:

The technique describes the transmission and reflection coefficients of a stack of

dielectric (and/or magnetic) materials, as well as specifies the fields at all places inside

the stack. In order to do so, matrices are used to propagate the forward and backward

waves over distances of uniform material, and matrices are also used to convert

forward and backward waves to total E&H fields, to match their transverse

components at material boundaries. The calculation is made ‘back to front’: The

point where light exits the structure is used as a starting point for the calculation, since

initially this is the only place where the relation between the forward and backward

waves is known: The forward wave exists (transmitted component), and there is no

backward component. When the fields in the entire structure are calculated, this

transmitted component, and all other components, can be normalized to the input

forward wave.

1. Variables to describe plane waves

A1

B1

B2

A2

d

<Towardsincidentside ofstructure

Towards>transmittedside

160

Consider a dielectric layer with parallel planar boundaries for which the reflection and

transmission coefficients are to be described. The field amplitude entering the

material from the left side is A1, and the amplitude leaving the material on the right is

A2. Reflected amplitude is B1, and B2=0. The phases of B1 and A2 measured with

respect to A1 also describe the relative phases introduced on reflection and

transmission. The effect of the structure is described by some matrix M, such that

reflection and transmission coefficients can be described as:

⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

2

2

1

1 ˆBA

MBA

(1)

In the rest of this text, the method of calculating M will be described.

2. Definition of fields

The medium of propagation is invariant in the x and y direction. Fields will be

described for waves that have either the electric or magnetic fields oriented transverse

to the xy plane, as a summation of such plane waves can be used to describe incident

fields of interest, including other polarizations such as circularly polarized light, or

other beam profiles, such as Gaussian beams.

TE and TM positive field components are described by the labels given in the diagram

below. To describe what is meant by this, if the incident E field points in the same

direction as the component on the diagram, but the reflected E field points in the

opposite direction than the vector (in other words, 180deg out of phase), then the

reflection coefficient would be negative.

161

3. Relation of E&H fields

Consider Maxwell’s Equations relating E&H fields.

Faradays law:

HiBitBE ωμω −=−=

∂∂

−=×∇ (2)

Apply this to an electric field in the y direction, transverse to the xy plane (but not

necessarily in the z direction)

Regarding notation: E+ propagates forward (has a positive kz) and E- is backward

component of E field.

HiEzExE

zyxE yxyz

y

zyxy ωμ−=∂+∂−=∂∂∂=×∇ ˆˆ00

ˆˆˆ (3)

162

[ ] ( )[ ]( )yxxikzik

zzik

z EikzeeEikeEikxiH xzz −++−−= −−

−+ ˆˆ

ωμ (4)

For TE:

⎥⎦

⎤⎢⎣

⎡⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−=⎥

⎦

⎤⎢⎣

⎡BAkk

HE

zz

x

y

ωμωμ

11 (5)

This matrix converts Forward/Backward to transverse E&H for TE.

[ ]⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−≡

ωμωμzzTE

kktoEH11

(6)

Now TM:

Ampere’s law (no surface currents/charges)

EiDitDH ωεω ==

∂∂

=×∇ (7)

EiHzHxH

zyxH yxyz

y

zyxy ωε=∂+∂−=∂∂∂=×∇ ˆˆ00

ˆˆˆ (8)

[ ] ( )[ ]( )yxxikzik

zzik

z HikzeeHikeHikxiE xzz −++−−−= −−

−+ ˆˆ

ωε (9)

For TM:

⎥⎦

⎤⎢⎣

⎡⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−=⎥

⎦

⎤⎢⎣

⎡BA

kkHE

zzy

x ωεωε11

(10)

[ ]⎥⎥

⎦

⎤

⎢⎢

⎣

⎡−≡

zz

TMkk

toEH ωεωε11

(11)

Now the transverse components of E and H fields can be found from the forward and

backward wave amplitudes using these matrices. The total forward and backward

wave amplitudes are proportional to the transverse components, so they can be used

later (part 5) to back out the reflection and transmission coefficients. These equations

are self-consistent, though it is also possible to write the TM (or TE, but it would not

163

be common) case with the definition of a positive reflected H field pointing in the

same direction as the incident and transmitted vector. The changes in the matrices for

that definition are shown in part 7.

These matrices can be inverted.

[ ] [ ]⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡ −=≡ −

z

zTETE

k

ktoEHtoAB ωμ

ωμ

1

1

211 (12)

[ ] [ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−=≡ −

ωε

ωεz

z

TMTM k

k

toEHtoAB1

1

211 (13)

Example: For TM:

[ ] ⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡

y

xTE H

EtoAB

BA

(14)

4. Propagation matrix

A propagation matrix is used to describe the relation of forward and backward fields at

different points in a uniform medium. It is used to relate fields at one end to the other

end of a uniform region of a medium. Here are the names of the relative

phases/amplitudes within a single slab of the structure.

The propagation matrix can be found relating these fields:

⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡=⎥

⎦

⎤⎢⎣

⎡−

2

2

1

1

00

BA

ee

BA

dik

dik

z

z

(15)

Define P:

164

⎥⎦

⎤⎢⎣

⎡⋅=⎥

⎦

⎤⎢⎣

⎡←

2

221

1

1 ˆBA

PBA

(16)

5. Transfer matrix and calculation of reflection and transmission coefficients

The transverse E and H fields at one end of a material can be related to those at the

other end using the following conversions: (right to left, like matrix form, and like the

spatial relationship)

⎥⎦

⎤⎢⎣

⎡←⎥

⎦

⎤⎢⎣

⎡←⎥

⎦

⎤⎢⎣

⎡←⎥

⎦

⎤⎢⎣

⎡

2,

2,

2

2

1

1

1,

1,

t

t

t

t

HE

BA

BA

HE

(17)

This relation can be calculated with matrices:

[ ] [ ] ⎥⎦

⎤⎢⎣

⎡⋅⋅=⎥

⎦

⎤⎢⎣

⎡←

2,

2,21

1,

1, ˆt

t

t

t

HE

toABPtoEHHE

(18)

Define matrix T:

[ ] [ ]toABPtoEHT ⋅⋅≡ ←21̂ˆ (19)

For sections of length d:

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

−

−=

)cos()sin(

)sin()cos(ˆ

dkdkik

dkk

idkT

zzz

zz

z

TE

ωμ

ωμ

(20)

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=)cos()sin(

)sin()cos(ˆ

dkdkk

i

dkik

dkT

zzz

zz

z

TM ωεωε (21)

165

For whatever layers of material make up the entire structure, the T matrices can be

cascaded:

⎥⎦

⎤⎢⎣

⎡⋅⋅=⎥

⎦

⎤⎢⎣

⎡

outt

outtn

int

int

HE

TTTHE

,

,21

,

, ˆ...ˆˆ (22)

Forward and backward fields, and reflection and transmission coefficients can be

calculated:

[ ] [ ] ⎥⎦

⎤⎢⎣

⎡⋅⋅⋅⋅=⎥

⎦

⎤⎢⎣

⎡

out

outn

in

in

BA

toEHTTTtoABBA ˆ...ˆˆ

21 (23)

[ ] [ ] ⎥⎦

⎤⎢⎣

⎡⋅⋅⋅⋅=⎥

⎦

⎤⎢⎣

⎡01ˆ...ˆˆ

//1

21 toEHTTTtoABtrt

n (24)

Here, the reflection coefficients are defined in terms of the total E vector:

r=Ereflected/Eincident, and t=Etransmitted/Eincident (25) 6. How to choose the value of kz

The transverse wave vector (kx in diagrams here) remains constant between layers.

The total k-vector obeys:

ktot,nx2=kx

2+kz2 (26)

0

,2λπ x

xtotn

k = (27)

kz can be found by taking a square root. A square root has two solutions.

166

Propagating wave solution:

If a wave propagates from medium 1 to medium 2, kz2 can be found by taking the

positive solution of the square root:

0222,2, >−= xtotz kkk (28)

TIR solution:

If the wave is propagating in medium 1, and incident upon medium 2, and is totally

internally reflected at the interface, the wave envelope in medium 2 is a decaying

exponential. For this reason, kz,2 must choose the negative imaginary solution, since,

for positive a, exp(-ikzz)≡exp(-i*(-ia)z) is an exponential that decays with increasing z,

for positive a.

So, for TIR:

0, 22,

222,

22, >−−−= totxtotxz kkkkik (29)

Lossy material solution:

If a material is lossy, its index has a positive real and negative imaginary part:

nlossy=nr-ini, {nr,ni}>0. So, ktot advances in phase as it moves forward, and attenuates.

Ktot is in the 4th quadrant in a lossy medium. It borders on the 4th quadrant in the cases

of a propagating, lossless wave and TIR in the high index medium. If kx=0,

obviously, kz,2 should be chosen to be in the fourth quadrant, the same as ktot,2. If kx is

positive, and the solution is a propagating wave in the lossy medium, then by using the

equation for kz,2 and taking the solution in the 4th quadrant, it can be seen that by

increasing the incident angle, the attenuation in the z direction in medium 2 occurs in a

shorter distance, as one would expect.

167

Other common definition of TM (shown below:)

If TM is defined such that the positive transverse H vector in the incident, reflected,

and transmitted waves are all defined to be in the +y direction, then definitions of

toEHTM and toABTM are changed, while TTM stays the same. New definitions are:

[ ]⎥⎥

⎦

⎤

⎢⎢

⎣

⎡ −=

zz

TMkk

toEH ωεωε11

(29)

[ ]⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−=

ωε

ωεz

z

TM k

k

toAB1

1

21 (30)

Also, if reflection and transmission coefficients are still defined in terms of E (r=Er/Ei,

t=Et/Ei), then the way to calculate r also changes in this case:

[ ] [ ] ⎥⎦

⎤⎢⎣

⎡⋅⋅⋅⋅=⎥

⎦

⎤⎢⎣

⎡− 0

1ˆ...ˆˆ/

/121 toEHTTTtoAB

trt

n (31)

8. General advice

168

When writing a transfer matrix code, it is useful to test the simplest things you can

(reflection from a single interface) and build to more complex things. Use solutions in

textbooks for metals, TIR, lossy materials, etc., to check your results. Make sure that

solutions for oblique incidence obey the Frensnel equations. Try making

antireflection coatings, and make sure that power flux is conserved. Test to be sure

that your results obey boundary conditions, if your code allows you to do so. Make

sure that a simple Fabry-Perot cavity behaves as a Fabry-Perot cavity should, and use

equations from a textbook to make sure things are correct. When you have total faith

that your code can handle all the simple cases, you will be able to believe that it can

handle whatever more complicated structure you want to test.

169

Appendix B: Gaussian Beam Plane Wave Decomposition The transfer matrix technique is a way to simulate the response of materials varying in

only 1 dimension (as in dielectric stacks, epitaxial layers, mirrors, absorbers, etc) to

plane waves.

Excitation with other than plane waves can be accomplished with the method using a

representation of the exciting beam as a weighted sum of plane waves.

In the case of modulator designs, a Gaussian beam is focused onto or into the

modulator. A Gaussian beam can be represented as plane waves as follows.

From Siegman, Lasers, eq 17.1, the expression for a Gaussian beam field amplitude is:

( ) ( )( )( ) ( ) ( ) ⎟⎟

⎠

⎞⎜⎜⎝

⎛ +−

+−

Ψ+−=

zRyxjk

zwyx

zwzjjkzzyxu

2expexp2,,

22

2

22

π (1)

R(z) is the radius of curvature (R=infinity at the focus), w(z) is the Gaussian spot

radius at z, and ψ corresponds to the Gouy phase shift. Let z=0 correspond to the

minimum Gaussian spot radius, w0.

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛ += 2

0

22

0

exp120,,w

yxw

yxuπ

(2)

Now quote Siegman eq. 16.89 for the spatial frequency distribution, found by inverse

Fourier transforming an input field distribution at plane z0:

( ) ( ) ( )( )dxdyysxsjzyxuzssU yxyxPW ∫∫ += π2exp,,,, 00 (3)

170

To relate these spatial frequencies to plane waves, the equation which will be applied

is Siegman eq. 16.83:

0

sinλ

θ xx

ns = (4)

Now apply the inverse Fourier transform to get the spatial frequency distribution of

the Gaussian beam field distribution u(x,y,0):

( ) ( )( )dxdyysxsjw

yxw

ssU yxyxPW ∫∫ +⎟⎟⎠

⎞⎜⎜⎝

⎛ +−= π

π2expexp120,, 2

0

22

0

(5)

This integral can be separated:

( ) ( ) ( )∫∫ ⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟

⎟⎠

⎞⎜⎜⎝

⎛−= dyysj

wydxxsj

wx

wssU yxyxPW ππ

π2expexp2expexp120,, 2

0

2

20

2

0

(6)

Using the Mathematica-derived integrals.com website the following integral solution

can be found:

( )∫ ⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ +⎟⎟⎠

⎞⎜⎜⎝

⎛−−=+−

aiaxbiErf

ab

adxibxax

22

4exp

21exp

22 π (7)

Take the integral over all x:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−=+−∫

∞

∞− ab

adxibxax

4expexp

22 π (8)

Using this integral form for the dx integral component of UPW,

xsbw

a π2,12

0

== (9)

( ) ( )∫∞

∞−

−=⎟⎟⎠

⎞⎜⎜⎝

⎛− 2

022

020

2

exp2expexp wswdxxsjwx

xx πππ (10)

And solving for UPW,

( ) ( )( )2220

20 exp20,, yxyxPW sswwssU +−= ππ (11)

Now converting from units of sx, sy to θx, θy:

171

( ) ( )⎟⎟⎠

⎞

⎜⎜

⎝

⎛+−= yxyxPW

nwwU θθ

λπ

πθθ 222

20

20

2

0 sinsinexp20,, (12)

Since this will be used in software to do an integral over weighted small angles θx and

θy, and the integral would be closer to valid for sx and sy, it seems reasonable to drop

the sin2 and assume that θx and θy are proportional to sx and sy, giving the following

expression:

( ) ( )⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+−= 22

2

20

20

2

0 exp20,, yxyxPWnw

wU θθλ

ππθθ (13)

Also, since for oblique incidence in practical modulators, the variation in the normal

component of the wavevector is far more important in the plane defined by the normal

to the dielectric interface surface and the incident angle, so in practice only a 1D array

of incident plane waves are necessary. As the equation can be separated in θx and θy,

the integral over values of θy yields the same value for all values of θx, so the term can

be dropped. In software, the coefficient is dropped in favor of normalizing the total

intensity to 1, so the following expression is used:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛−= 2

0

2220

2

expλ

θπθ x

xPWnw

U (14)

Reference

Siegman, A.E., “Lasers”, University Science Books, New Edition (1986)

172

Appendix C: Matlab Software for Matching Transmission Experiments with Transfer Matrix Simulations A graphical user interface was designed in Matlab to simplify the plotting of

transmission data from optoelectronic modulators, and also to allow simple

comparison and hand-fitting of parameters for transfer matrix simulations to match the

experimental data. The window pane is shown below, followed by explanations for

the functions of different fields and buttons. The program currently assumes TE

incidence, though it can easily be changed to account for TM as well.

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Calculator

This feature is for determining parameters for modeling side-entry modulators. The

calculator allows for the input of the spot size diameter in air and the incident angle. It

outputs the beam angle in Si, the major axis of the elliptical Gaussian spot function in

Si, and the length of the projection of the spot on the mesa surface. It also calculates

the reflectivity of the air-Si interfaces in the optical path and reports the maximum

transmission for the incident angle used.

Absorption Data

The [Bkgnd] button loads the file with the background transmission through air, or

with the optical power measured where the sample is to be placed. The former is

required to normalize transmission measurements to calculate absorption coefficient,

and the latter is required to normalize photocurrent measurements. The program can

handle either.

[Transmission] loads photocurrent or transmission data from an optoelectronic

modulator, and the switch [T] chooses whether transmission or photocurrent data will

be used.

{Thickness nm} is the field where the thickness of the quantum well superlattice is

entered.

The [Use KK] toggle button determines whether the Kramers-Kronig relations will be

used to calculate a variable refractive index with wavelength/voltage, or whether the

index entered in {real n} will be used for all wavelengths/voltages. Pressing [n] after

pressing [Update+Plot] will show the real part of the refractive index.

[Update+Plot] plots the calculated absorption coefficient, and stores that data for use

in the simulated structure

174

Simulated Structure

In the fields {index} and {width}, the refractive indices and thicknesses in nm are

input for a dielectric stack with light incident from the first layer at the angle specified

in {angle from normal to mesa in Si deg.}. The {index} should have two values more

than the {width}, since the first and last indices are the material above and below the

structure, and do not need an associated width. A refractive index of -1 uses the real

and imaginary parts of the index from the Absorption Data section. In fact, the

incident material can be any material, not just Si. The spot size specified should be

that in the incident material, and the first entry in {index} should be the indicent

refractive index.

[Sim Update] calculates the transfer matrix results for reflection from the dielectric

stack, using voltages from {Use Voltages}, wavelengths from {Use wvlns nm}, the

spot size from {Spot diam. In Si um}, and the insertion loss from {% of light

transmitted through edges}.

[Plot Transmission] plots the percentage transmission through the device using

transfer matrix results.

[Plot CR] and [Plot CR Pair] plot contrast ratios as specified in {CR array spacings}

or {Array# pair}. Contrast ratios can be plotted as a ratio, or in decibels, selected

from the [ratio] [dB] toggle button.

When contrast ratios are plotted for a given array spacing, at each wavelength, the

program plots the data for the voltage swing specified by the array spacing, using the

bias voltage that maximize the contrast ratio for that wavelength.

Modulator Data

[Bkgnd] loads the detector current from a file for scanned wavelength, which is

normally from the light detected from a single reflection from the gold mirror in side-

entry modulator experiments. This is used to normalize the transmission data, and

175

find the fraction of light transmitted or reflected from a device at each wavelength and

voltage.

[Transmission] loads the detector current for scanned wavelength and voltage as

measured from transmission (reflection) from a modulator.

[Plot Transmission], [Plot CR Pair], and [Plot CR] plot transmission and contrast ratio

data using voltage and wavelength settings specified elsewhere in the Modulator Data

box. When contrast ratios are plotted for a given array spacing, at each wavelength,

the program plots the data for the voltage swing specified by the array spacing, using

the bias voltage that maximize the contrast ratio for that wavelength.

The two roughness settings can be used to do a weighted average of the reflectivity

from several different structures while changing the thickness of the bottom layer in

the structure, as if it had a Gaussian roughness profile. This model does not account

for incoherent scattering due to the rough surface.

Graph

On this graph, absorption coefficient data, transmission data, and contrast ratio data

are plotted for actual modulator data and simulated dielectric stacks using real

absorption coefficient data.

By hitting the [hold on] button, the graph can be set to hold its current contents when

the next successive plot command is executed, so that real and simulated data can be

overlaid.

The [New Fig] button plots the data currently on the graph to a separate window so it

can easily be exported for documentation.

176

Appendix D: Wafers Grown by Lawrence Semiconductor Research Laboratory Lawrence Semiconductor Research Laboratory was contracted to grow 12 wafers for

Stanford. Wafers were grown on 8” p-minus double side polished substrates

purchased from Silicon Quest. The final wafer was grown on a silicon on insulator

wafer from SOITec, with a 100 nm p-minus handle and 50 nm buffered oxide layer.

Wafer thickness specifications, with thicknesses in nm.

1-11 are on DSP wafers, 12 is on SOI. Spec T1 T1B T2 T3 T4 T5 T6 n:#QW 1 500 0 100 16 16 10 200 10 2 400 0 45 16 16 10 100 10 3 470 0 50 16 16 10 270 20 4 500 0 100 16 8 10 230 40 5 500 45 100 16 8 10 210 60 6 500 0 100 20 20 12.5 200 10 7 500 0 100 24 24 15 200 10 8 500 0 100 16 16 10 200 10 9 500 0 100 16 16 10 200 5 10 500 0 100 16 16 10 200 20 11 500 0 100 20 20 12.5 200 10 12*SOI 490 0 64 16 16 10 120 10

177

Nominal intended wafer use:

1. Baseline Yu-Hsuan Kuo structure replication/QW Physics

2. 10QW Oblique/Surface-normal/Waveguide modulator




6. 12.5nm QW Physics

7. 15nm QW Physics

8. For Yangsi Ge

9. For Yangsi Ge

10. For Yangsi Ge

11. For Yangsi Ge

12. 10QW Frustrated total internal reflection oblique modulator

178

Appendix E: Fabrication Recipes, Side Entry Modulator and Photocurrent Test Sample The two recipes in this appendix have a lot of overlap. Photocurrent test samples can use an

antireflection coating on the top (mesas) and bottom, while side-entry modulators do not have these AR

coatings. Side entry modulators may incorporate cavity tuning steps too.

WAFERS FROM LAWRENCE SEMI:

Substrate | Buffer | Quantum Wells | Cap|

Rough actual thicknesses in nanometers:

Wafer 1: B: 1000 | 10QW: 500 | Cap: 450

Wafer 2: B: 800 | 10QW: 500 | Cap: 300

Wafer 3: B: 900 | 20QW: 1000 | Cap: 550

Wafer 4: B: 1000 | 40QW: 2000 | Cap: 500

Wafer 5: B: 1000 | 60QW: 3000 | Cap: 450

Wafer 12: B: 1000 | 10QW: 500 | Cap: 300

Solvent cleaning is: Acetone, methanol, isopropanol, (followed by optional water, not normally used

on wafers), and immediately dry with nitrogen.

-Be careful about getting liquid stuck in tweezers that goes all over chips when you release them

-Solvent cleaning dissolves photoresist! Be careful...

-Keep solvents and acids apart from each other.

Standard SiGe wet etch (stops on Si) – From: D. J. Godbey, A. H. Krist, K. D. Hobart, and M. E. Twigg,

“Selective removal of Si1-xGex from (100)Si using HNO3 and HF,” J. Electrochem. Soc. 139, 2943-2947 (1992).

-Etches somewhere around 200nm / min -Mix a batch of dilute HF, 0.5%

-Right before you’re ready to use it:

-In a nalgene beaker, mix 35 parts nitric acid, 20 parts water, and 10 parts dilute HF.

-Stir it very well – this MAY avoid mask undercutting problems

-Hold the chip in the mixture using plastic tweezers. Give it a little whirl every 10 sec or so, as this

mixture does not stay mixed, and will otherwise etch faster in the top of the liquid than the bottom.

-The mixture seems to go bad! I only trust it for 20 minutes or so after mixing – The etch rate seems to

eventually slow down.

179

-You can keep a close eye on your chip and see when the edges go dark (reaching Si). Be aware that it

may etch faster right next to your photoresisted features, and you might not be able to see this without a

microscope! Etching the whole way down to Si will leave you with bad diode characteristics.

Dry Etch: Drytek4 in SNF.

-150mT, 100sccm SF6, 10sccm/50% O2, 100W, etches Si..1Ge..9 at 25nm/sec

-20 SECOND BURSTS MAX, long times make the PR get ugly.

-Not selective, won’t stop on Si, but it does avoid undercutting of the mask, since it’s not isotropic.

Procedure:

0 Preparation

-Look for a reservation on STS PECVD in CIS, see whether you’re at/near a clean cycle

(photocurrent test only)

-Check Tom Carver’s schedule or make a reservation on Metalica or Innotec (3-4hrs?), check

for availability of Ti & Al on those machines.

-Find some chunks of Si for testing in the nitride dep.

-Cleave pieces for fabrication. Label them carefully and record that you’re starting new pieces

and what the goal of the run is, so you can distinguish them from other fabbed pieces when

you’re partway done and/or testing

1 AR coat: ¼ wave thickness of nitride, on both sides. At 1450nm and index of 2, this

is 181 nm. -Nitride Deposition

-Use a blank piece of Si in the reactor to see the deposition rate. Test it on the nanospec

(or

ellipsometer)

-Keep in mind that the dep. rate changes as you deposit more

-People (Eric P) have told me that depositing the film in 2 stages (like, do 2/3 of

thickness, then measure dep rate and deposit last 1/3) can result in a lower quality film,

but I often do it anyway

-It’s normally purple when viewed from above, maybe yellow-purple. Try to correlate

your total dep thickness and the color.

-Recipes in STS: std1knit, rothnit. Modify your version for desired dep. time.

-You could use Ginzton spectrometer or possibly ellipsometer to see how good an AR

coat you made

-Lithography (for frontside AR coat)

- Clean, bake off solvents at 90’C for a few min

180

-@5000RPM,60sec: Spin on HMDS. Cover substrate, wait till it starts evaporating,

then go.

-Spin on SHIPLEY 4620 immediately after HMDS

-Bake 15min at 90’C

-Expose 17 sec 8.5mW/cm^2 or equivalent energy dosage

-Develop in our AZ400K (1:2?) for >90sec, stirring, then rinse well in DI water & dry

-NO SOLVENT CLEAN AFTER LITHO

-Backside protect with photoresist (bake on) so nitride on back

doesn’t etch off

-Etch off the nitride in BOE 6:1 for ~13-18min (give it a few mins extra to be sure

you got it all)

2 Mesa etch

-Litho



then go.





-NO SOLVENT CLEAN AFTER LITHO.

-Post-bake 15 min at 140’C

-Selective etch

-Use standard wet etch recipe given above, or use dry etch recipe (especially if

undercutting is a problem). If you dry etch, backside protect with photoresist first.

-Etch till the edges start to get dark colored (Si)

-Be careful if you try to etch multiple chips at once!

-Rinse, solvent clean,

-Consider measuring mesa height for max depth and uniformity using profilometer

3 Metal contacts

-Litho



then go.


181




-Metal contact evaporation (Tom Carver)

-Recipes that work:

: Substrate|10-15nmTi|200-500nmAl OR Substrate|10-

15nmCr|400nmAu

We’ve also done Ti/Au. The thin layer is intended to be a sticking layer. I think Al

and Au have high conductivity – for good current distribution?

-Liftoff in acetone – about 5 min

-possible bursts of ultrasound. Overkill can pull off metals

-Try not to let it dry out without being finished or metal bits might get permanently

glued to your chip. Consider pulling out 1 chip from acetone at a time and checking

under microscope

-Solvent clean

4 Electrical/optical testing (even if you’re going to do side-entry, you can test devices

electrically now)

5 Side polish (for side-entry only)

a. For these ~730 µm thick wafers you want pieces about 3.5 mm wide with devices

(big) in the middle to bounce the light off of

b. The total piece should be larger than these dimensions. Give the crystal shop explicit

instructions, and they can saw the wafers and polish the edges to the final size. A row

of device mesas should be in the middle of the piece gotten from the crystal shop.

c. Devices are ready for electrical/optical testing.

182

Appendix F: Matlab Software for Calculating Exciton Energy and Overlap Integrals A Matlab graphical user interface was designed to calculate the energy levels for

electron and hole states in quantum wells in the novel silicon germanium material

system. The program had the capability of specifying all the material properties for

the well and barrier and specifying quantum well and barrier thicknesses. It was

possible to plot and export the shift of the transition energies and change of overlap

integrals for different applied electric fields. A screenshot is given below, followed by

an explanation of some of the features.

183

1. Material Properties

The user may choose to use predetermined values for the effective masses, bandgaps,

or effective masses, or enter changes to the expected values manually.

2. Manual Entry of Material Properties.

3. Bandgaps/offsets

Based on the entered material properties, the bandgaps and offsets between four

specified materials (Buffer, Barrier, Well1, and Well2) can be plotted, on separate

axes for electrons and holes, or on the same axis.

4. Material Specification

The user can specify combinations of thicknesses of buffers, barriers, and well1 and

well2, to simulate structures including single quantum wells, coupled quantum wells,

or stepped quantum wells.

5. Update structure & Multi E-field

The user can calculate the energy transitions and bandgaps for a single electric field or

an array of electric fields, to be plotted below. The [Group] button joins values for the

same electric field so that the energy can be fit with a polynomial function. In the plot

below it is possible to click on points and lines in order to plot the associated wave

functions and report the energy values of the transition. The slider at the far right at

the panel can be used to continuously change the electric field across a group line.

6. Main plot window

This window can show structures with and without electric field applied, wave

functions, probability distributions, integration of the absorption function, and overlap

integrals between electrons and holes.

184

7. Text output

This button outputs data from the current simulation in a format amenable to

importation to Microsoft Excel.

185

Appendix G: Further information on MATLAB Codes This section provides information on code I wrote in Matlab which will be useful to

group members in the future. I describe a number of executable functions and

collections of functions, as well as the data file structure used for photocurrent data.

While group members will likely develop new data collection software in the future, it

is advisable to keep the data file structure backwards-compatible, to ensure

compatibility with other code including the ‘SIMGUI’ software described in Appendix

C.

Before graduation, I will place the latest copies of all code listed here in the Miller

group common hard drive in the directory \\isley\Group\CodeArchive. The attribute

of all code will be set to ‘read only’. The user should make his or her own copy

elsewhere to avoid accidentally corrupting the original file during use.

MatGPIB This code is a graphical user interface which collects photocurrent spectra,

reflection/transmission spectra, and files with names starting with ‘loss’ which

indicate the optical power hitting a sample. As a number of group members are

trained on this software, the most important element to document is the output file

structure, which is used by other programs for analysis. As stated above, for

compatibility with related software, it would be useful if future versions were

backwards-compatible with the output file structure described here.

An error was made in a number of codes here, though at present it does not affect the

results. It began in MatGPIB in the way the loss calibration data were saved, and was

propagated to the codes that calculated the absorption coefficient, including abscoeff

and simgui. When the loss structure is saved, the power measured at the detector is

186

average power, not peak power. The signal is modulated to be turned on 50% of the

time. The laser power is a peak power. Then the code which uses these data create a

value, ‘lossratio’, which is one of those numbers divided by the other. Then, when

absorption coefficient is calculated, the lockin reports photocurrent as an amplitude of

a sinusoid, while we initially expected to get a peak-to-peak value. In the end, the two

errors of a factor of 2 cancel one another. However, it is better to capture the loss data

with the modulation turned off, for stability. Though any reprogramming to caputure

loss data with modulation off should either divide the result by 2 when saving to

preserve the way things are currently calculated, or should change the downstream

data manipulation code to correctly account for the way photocurrent is reported as an

amplitude.

The loss*.mat files contain data for an array of wavelengths. The file is used to

determine the fraction of the light output by the laser which hits the sample. They

contain a structure called SystemLossData with the following elements:

laserID: The name the laser reports for itself over GPIB

msg: This message indicates that the amplitude modulation was on, which should halve the

power absorbed at the detector. We later discovered that if data were collected with amplitude

modulation off, it would have far less noise.

Wvln(wavelengtharray): Wavelengths (nm) addressed in the array of powlas and powdet

powlas(wavelengtharray): The output power of the laser at each wavelength.

powdet(wavelengtharray): This indicates the average power at the detector. If amplitude

modulation were on and all the light made it through the optics (with no beamsplitters),

powdet would be half of powlas. If amplitude modulation were off, powdet would equal

powlas. The ratio of powdet to powlas is a measure of the fraction of light from the sample

that gets to the laser.

timestamp: When the data were taken. This is important because often, it might be desirable

to collect loss data right before or after sample data, before any piece of the setup is

mechanically adjusted, potentially changing the loss numbers

187

polynum: There is an optional polynomial fit to the loss data, as an elementary noise

reduction technique. If polynum is ‘0’ the user did not desire to use the polynomial fit. If

polynum is an array, the fit values can be recovered using the form: SystemLossData.powdet=polyval(polyfit(SystemLossData.wvln,

SystemLossData.powdet, SystemLossData.polynum), SystemLossData.wvln)

The data files (*.mat) contain an array of photocurrent and/or reflectivity data for an

array of wavelengths and applied voltages. They contain a structure called

LasVScanDat with the following elements:

PreSensAPerV: Transimpedance Amplifier Multiplier (scalar)

LockinSensVper10V(wavelengtharray): The lockin output is on a -10V to +10V scale, as

measured through the front-panel analog output. The value measured by the parameter

analyzer (from that analog output) should be multiplied by LockinSensVper10V and divided

by 10V to get the photocurrent.

VM2Vper10V(wavelengtharray): This variable is the multiplier to convert the VM2 output

(typically reflection or transmission) to a voltage. Depending how you have the system set up,

the input to this lockin may be a current, and you may have the lockin set for current. In this

case, use the multiplier on the front of the instrument if you would like to know the actual

photocurrent instead of a voltage.

VM2(wavelengtharray,voltagearray): Raw data for reflection/transmission

VM1(wavelengtharray,voltagearray): Raw data for photocurrent

PhotocurrentA(wavelengtharray,voltagearray): Photocurrent. This data can also be extracted

from other variables by typing:

S=size(LasVScanDat.VM1)

PC=LasVScanDat.PreSensAperV*LasVScanDat.LockinSensVper10V'/10*ones(1,S(2)).*Las

VScanDat.VM1

PreampParams, li2Params: Parameters of the transimpedance amplifier and of Lockin 2. They

refer to the status of the settings of the instrument which can be set by the GUI’s front panel.

To see the meanings of each array element laid out, please look at the subfunctions ‘showli2’

and ‘showpre’. These variables are somewhat incomplete when it comes to recording this data

for future users, and they are also not ever used by the software after saving, so no future

188

versions of the program need to include them, or use this same system to record this type of

information. For a future version of the software, I would consider making a single variable

or structure which included all the relevant instruments’ status, such that settings could be

loaded and saved from a config file for faster set-up, and when appropriate, could be used to

set all the instruments at once.

wvln(wavelengtharray): The wavelengths used in the scan (nm)

Vs(voltagearray): The voltages used in the scan

powlas(wavelengtharray): The power the laser was set to (W).

wvlnrec(wavelengtharray): The value that the laser returned for the wavelength it was set to

(nm).

The data file contains either transmission/reflection data, photocurrent data, or both.

Depending which it contains some variables may be absent.

abscoeff This is a short, simple code to recover absorption coefficient data from data files. It

uses a user prompt to get the filenames to open.

Layerrtbothss This is a transfer matrix code to find reflection and transmission coefficients from

multilayered structures. One thing the present version does not do is give the field

amplitudes in each layer, though that function can be added without much difficulty.

This function calls a number of subfunctions. Certain things, like taking square roots,

must be done with care to be sure the proper square root is taken (as every number

has two square roots). The routine carried out in this function could be recoded in a

language like C in order to speed up optimization routines. Similar routines are also

used for quantum well transfer matrix codes, which could also be coded in C.

189

The function input is of the form: function out=layerrt2bothss(TETM,kt,wvlns,ns,wids)

TETM: ‘TE’ or ‘TM’

kt: array (can be 2D) of transverse wave vector components. Using a 2D kt allows for a beam

composed as a sum of plane waves, and allows an array of wavelengths all to be calculated in

parallel. Transverse wave vectors are calculated by 2*pi*n*sin(IncidentAngle)/wavelength.

wvlns: wavelengths (m) to simulate

ns: indices of refraction. The 1st value is the index in the space from which the beam is

incident.

wids: widths (m). The array length of wids is two shorter than the array length of ns, since the

starting and ending space do not need a width specified. If a single interface is being

specified, wids can be an empty array, indicated in Matlab by [].

The function output includes the variables:

r: complex reflection coefficient (for field amplitude)

t: complex transmission coefficient

Other output variables are derived from these ones.

UcallotofAngs This function does the Gaussian beam plane wave decomposition from Appendix B.

The important inputs are incang (incident angle radians), n (refractive index), w0

(spot size meters), and wvln (wavelength meters). The important output variables are

kts (transverse wave vector, for input to layerrt2bothss), and rowcomp. Rowcomp is

used to do a weighted sum of plane waves composing the Gaussian beam. The waves

can be added to have an amplitude of 1. Rowcomp obeys:

sum(out.rowcomp.^2)=1

For a future version of this code I would recommend spacing the array elements in

angle-space such that they were designed to cover the range of angles where there is

190

finite amplitude. Currently it sweeps out a fixed range in angle space, and some of the

angles included may contain insignificant data, lengthening the calculation time.

recolor This function changes the active plot’s colors, such that each trace is replotted on a

color scale including red, blue, and green. It also changes the line width used in the

plot. The function can be changed around to change line/point style of the plot and

the color scale used.

fresnel This function outputs the reflection and transmission coefficients at an interface

between indices n1 and n2 with incident angle ang1 (radians) on the n1 side.

NewtSiGe:

This function maximizes the contrast ratio of a modulator design using a modified

version of Newton’s method for finding the roots of a function. The routine optimizes

multiple variables at a time. It was more relevant during the design of the QWAFEM

than of the more recent structures, since the QWAFEM has more layer thicknesses to

optimize in parallel. Also, one must consider whether one is capable what precision

one can grow a wafer to in order to take advantage of a fully optimized design, and

also consider how well the refractive index of the material can be known. This

function calls define_paramsSiGe, and layerrt2bothss. define_paramsSiGe is a file

with an output of the format which was used by Noah Helman’s optimization and

E&M calculation software. The code can be modified to optimize some variable other

than contrast ratio.

191

onesscale This function prompts the user to choose a file representing photocurrent data, then

plots the data on a normalized scale which is useful to find the electron-hole transition

energies versus applied voltage.

CRGUI This is a simple graphical user interface which allows several pieces of contrast ratio

data (transmission or reflection) to be viewed in rapid succession.

measurespotsize

This routine is used to do a knife-edge measurement of spot size using the SR510

detector. It collects data points when a key is pressed, and the user can specify the

increment between adjacent points. The saved data can be compared to theory to find

the size of the Gaussian spot.

i ELECTROABSORPTION MODULATORS FOR CMOS …Optoelectronic modulators using this technology can be fabricated with conventional CMOS foundry processes, possibly on the same chips as

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