LINEAR ELECTRO-OPTIC CONVERSION OF SAMPLED SIGNALS …web.stanford.edu/group/dabmgroup/publications/t13.pdf · v Abstract The speed and capabilities of digital processing continue

LINEAR ELECTRO-OPTIC CONVERSION OF

SAMPLED SIGNALS FOR A PHOTONIC-ASSISTED

ANALOG-TO-DIGITAL CONVERTER

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

Henry Chin

June 2007

ii

© Copyright by Henry Chin 2007

All Rights Reserved

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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, Jr.




_________________________________

Shanhui Fan

Approved for the University Committee on Graduate Studies.

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v

Abstract

The speed and capabilities of digital processing continue to improve exponentially.

Analog-to-digital (A/D) conversion systems harness this computing power for

applications involving signals in the real world. When these real world signals have

bandwidths on the order of several tens of gigahertz – as can be the case for photonic

and wireless communication, high-speed instrumentation, and wideband radar –

suitably fast A/D technologies are needed.

However, conventional electronic A/D systems today are limited to resolutions of

4 to 8 bits for signal bandwidths of up to a few gigahertz. The sources of this

limitation include the aperture uncertainty (or jitter) and relatively low input

bandwidth of the front-end sampler. Incorporating a photonic-based sampling system

which exploits the low jitter of short-pulse lasers can help overcome such limitations.

We outline one proposed photonic-assisted analog-to-digital converter system.

Optical pulses from a mode-locked laser trigger photoconductive switches made from

metal-semiconductor-metal (MSM) devices based on low-temperature (LT) grown

GaAs. When excited by mode-locked laser pulses, these devices exhibit sampling

apertures on the order of a few picoseconds, thus enabling high-bandwidth sampling.

These sampled signals could then be digitized by CMOS circuits. A parallel, time-

interleaved architecture would utilize many switch/digitizer channels to increase the

aggregate sampling rate of the system.

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While the CMOS circuits can be directly solder-bonded to the photoconductive

switches, physically separating the circuits from the switches can be advantageous.

Reasons include electrical isolation, compact integration of the switches, and

improved digital data extraction from the circuits.

This dissertation focuses on the use of optical modulators to optically remote the

CMOS circuits from the photoconductive switches. These modulators are based on

GaAs/AlGaAs multiple quantum wells incorporated in a p-i-n diode structure. The

optical modulators linearly convert the sampled electrical signal to an optical one, thus

allowing the circuits to be placed on chips separate from the sampling switches.

We demonstrate the linearity of the modulators, and single-channel conversion

speeds on the order of 1 gigasample/second. By flip-chip bonding the sampling

switches to the modulators, we find that the linearity of the devices should allow for a

resolution of at least ~3.5 effective-number-of-bits (ENOB) for signals with 20 GHz

bandwidth.

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Acknowledgements

I would first of all like to thank Professor David Miller. I have of course learned a

tremendous amount from him on technical topics. Additionally, I feel that his

mentorship and respect for students fosters a wonderful sense of freedom and

creativity within the research group. I have also learned much from his strong

communication skills, which manifest themselves both in his teaching and in his

presentation of material orally and in writing.

I would also like to acknowledge Professor James Harris. His easy-going manner

makes him eminently approachable, and I greatly valued his sharing of technical

knowledge and insightful analysis during courses and meetings. Professor Shanhui

Fan graciously agreed to serve on my reading committee, providing feedback from a

perspective slightly outside the specific field of electroabsorption modulators.

Professor Roger Howe also kindly agreed to chair my committee on very short notice.

During my stay at Stanford I had the especial privilege of working closely with a

number of members of our research group. Petar Atanackovic, a visiting scholar,

patiently introduced me to working in an optics lab, a research environment which was

completely new to me. Gordon Keeler spearheaded much of the initial modulator

fabrication work, designing the wafer structure which I ultimately used in most of my

experiments. Both he and Noah Helman trained me in working in the clean room, and

were also very encouraging and helpful during the times when things didn’t go so well.

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Additionally, Mark Wistey in Professor James Harris’s group grew a GaAs modulator

wafer in support of some of this work.

Ryohei Urata’s phenomenally thorough studies of photoconductive sampling

switches allowed me to build on his research with relative ease. Kai Ma — also from

Professor Harris’s group — grew the GaAs wafers from which the switches were

fabricated. Without their contributions, none of the switch-related work in this

dissertation would have been possible.

I also benefited greatly from working with Ray Chen during my later years at

Stanford. His ability to focus on the most essential tasks necessary to achieve his

goals was a good example that I learned from. Ray also provided tremendous

assistance both in the clean room and in the optics lab.

In addition to these, I greatly enjoyed the general camaraderie with all the many

people in the group with whom I overlapped — not to mention all the additional

technical help that comes from discussions at the whiteboard, in the optics lab, or in

the clean room. And so I must also acknowledge Micah Yairi, Diwakar Agarwal, Vijit

Sabnis, Bianca Keeler, Helen Kung, Ellen Judd, Christof Debaes, Wei Zhou, H.

Volkan Demir, Ryo Takahashi, Timothy Drabik, Rafael Piestun, Martina Gerken,

Aparna Bhatnagar, Sameer Bhalotra, Yang Jiao, Michael Wiemer, Jonathan Roth,

Salman Latif, Onur Fidaner, Liang Tang, S. Ekin Kocabas, Shen Ren, Dany Ly-

Gagnon, Stephanie Claussen, Elizabeth Edwards, and Rebecca Schaevitz.

I must thank too the technical support staff at Stanford University. Pauline

Prather works late into the night to provide wire-bonding services for much of the

community. Her manual dexterity is unbelievable. Tom Carver was a dependably

cheery presence in the Ginzton Microfabrication Facility. It is amazing that he single-

handedly oversees all the equipment in the facility, and yet I could rely on him for

advice and metal deposition when needed. For the times when I needed to work in the

Stanford Nanofabrication Facility, I have also found the support staff there to be

incredibly helpful.

The Ginzton front office provided a vast array of services to support this work, as

did the staff of the Electrical Engineering department. And as the administrative

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assistant to Prof. Miller, Ingrid Tarien did a million things to help keep the group

functioning.

On a personal note, I would like to acknowledge my family — my parents, sister,

and grandparents — whose unflagging belief in me was a foundation on which I could

always rely. Also thanks to Thaddeus Ladd and Sharon Ungersma, especially for

providing a pair of friendly faces among a sea of strangers during my first few months

at Stanford. And last of all to Katie Greene, for all her support and encouragement

over the years.

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Contents

Abstract ................................................................................................................ v

Acknowledgements .....................................................................................................vii

Contents ............................................................................................................... xi

List of Tables .............................................................................................................. xv

List of Figures ...........................................................................................................xvii

Chapter 1 Introduction .......................................................................................... 1

1.1 Analog-to-Digital Conversion ...................................................... 1

1.2 Photonic A/D ................................................................................ 4

1.2.1 Limits from the Walden Wall ........................................... 4

1.2.2 Motivation......................................................................... 7

1.2.3 Approaches ....................................................................... 8

1.3 Photoconductive-sampling, Time-interleaved A/D Conversion. 11

1.4 Optical Remoting ........................................................................ 13

1.4.1 Differential Remoting ..................................................... 15

1.4.2 System Requirements...................................................... 16

1.5 Organization................................................................................ 17

1.6 Bibliography ............................................................................... 18

Chapter 2 Multiple Quantum Well Modulators ................................................ 21

2.1 Optical Absorption...................................................................... 22

2.1.1 Excitons........................................................................... 23

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2.1.2 Quantum wells ................................................................ 24

2.1.3 The Quantum Confined Stark Effect .............................. 27

2.1.4 Saturation ........................................................................ 29

2.2 Self-Linearization ....................................................................... 30

2.2.1 Basic Principles............................................................... 30

2.2.2 Ideal Current Source Bias and Equilibrium Stability ..... 33

2.2.3 First-order Block Diagram Model .................................. 36

2.2.4 Non-ideal Current Source ............................................... 39

2.2.5 Temporal Response to Pulsed Input ............................... 42

2.2.8 Input Range and Speed ................................................... 45

2.3 Differential Self-linearization ..................................................... 46

2.3.1 Equilibrium States........................................................... 47

2.3.2 Self-linearization with Constant Current ........................ 48

2.3.3 Block Diagram................................................................ 50

2.3.4 Impulse Response ........................................................... 52

2.3.5 Motivation....................................................................... 53

2.3.6 System Trade-offs........................................................... 57

2.4 System Requirements.................................................................. 58

2.4.1 Linearity.......................................................................... 59

2.4.2 Speed Issues .................................................................... 60

2.4.3 Noise ............................................................................... 62

2.4.5 Thermal noise.................................................................. 67

2.5 Preliminary Results..................................................................... 68

2.6 Conclusions................................................................................. 74

2.7 Bibliography ............................................................................... 75

Chapter 3 Pulsed Laser Experiments ................................................................. 77

3.1 Bell Laboratories Devices........................................................... 77

3.2 Initial Experiments...................................................................... 79

3.2.1 Experimental Setup......................................................... 79

3.2.2 Experimental Results ...................................................... 81

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3.3 Further Experiments.................................................................... 86

3.3.1 Setup ............................................................................... 87

3.3.2 High Current Injection .................................................... 88

3.3.3 High-Speed Conversion .................................................. 91

3.3.4 Linear Conversion........................................................... 91

3.3.5 Baseline Power................................................................ 93

3.4 Conclusions................................................................................. 96

3.5 Bibliography ............................................................................... 96

Chapter 4 Sampling Switches .............................................................................. 99

4.1 Low-Temperature Grown GaAs ................................................. 99

4.2 Annealed Low-Temperature Grown GaAs............................... 100

4.3 Metal-Semiconductor-Metal Structures.................................... 103

4.4 Fabrication ................................................................................ 106

4.5 Conclusions............................................................................... 109

4.6 Bibliography ............................................................................. 110

Chapter 5 Flip-Chip Bonded Devices ............................................................... 113

5.1 Fabrication and Processing ....................................................... 113

5.1.1 Epitaxial Structure ........................................................ 114

5.1.2 Electroabsorption Measurement ................................... 115

5.1.3 Modulator Processing ................................................... 116

5.1.4 Flip-Chip Solder Bonding............................................. 118

5.1.5 Substrate Removal ........................................................ 118

5.2 Quartz Carrier Die..................................................................... 119

5.2.1 Carrier Die .................................................................... 120

5.2.2 Experimental Results .................................................... 121

5.3 MSM Integration....................................................................... 126

5.4 DC Testing ................................................................................ 130

5.4.1 Single-ended operation ................................................. 130

5.4.2 Differential Mode.......................................................... 136

5.5 Dynamic Testing....................................................................... 139

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5.6 Conclusions............................................................................... 146

5.7 Bibliography ............................................................................. 147

Chapter 6 Conclusion ......................................................................................... 149

6.1 Summary ................................................................................... 149

6.2 Future Directions ...................................................................... 150

6.2.1 A/D System................................................................... 150

6.2.2 Device ........................................................................... 153

6.2.3 Other Applications ........................................................ 154

6.3 Bibliography ............................................................................. 155

Appendix A Quantization Noise Derivations....................................................... 157

A.1 Quantization Noise Power ........................................................ 157

A.2 Effective Number of Bits .......................................................... 158

Appendix B Fabrication Process Flow................................................................. 161

B.1 Lithography Procedures ............................................................ 161

B.1.1 Ginzton Microfabrication Facility ................................ 161

B.1.2 Stanford Nanofabrication Facility................................. 162

B.2 Modulator Process Steps........................................................... 162

B.2.1 N-holes.......................................................................... 162

B.2.2 N-contacts ..................................................................... 163

B.2.3 P-contacts...................................................................... 163

B.2.4 Capacitance Reduction.................................................. 164

B.2.5 Mesa Etch...................................................................... 164

B.2.6 Indium Deposition ........................................................ 165

B.2.7 Array Protection............................................................ 165

B.2.8 Carrier Die Preparation ................................................. 166

B.3 Flip-Chip Bonding .................................................................... 166

B.4 Substrate Removal .................................................................... 167

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List of Tables

Table 2.1 System parameters for three modulator configurations: (1) a base

case, (2) the base case with twice the area and optical input power,

and (3) a differential case using a pair of base case modulators............. 57

Table 2.2 Typical modulator device parameter values. .......................................... 66

Table 2.3 Epilayer wafer structure of modulators used in experiments. The

modulators were previously fabricated at Bell Laboratories. ................. 70

Table 4.1 Epilayer wafer structure for all photoconductive sampling switches

used in this work. .................................................................................. 106

Table 5.1 Epilayer wafer structure of modulators used in experiments.

Designed primarily by G. A. Keeler [1]. .............................................. 114

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List of Figures

Figure 1.1 Illustration of the analog-to-digital conversion process. Analog

signals are first sampled at discrete points in time. The sample

values are then quantized into discrete values, suitable for storing or

processing by digital systems.................................................................... 2

Figure 1.2 Survey of A/D performance (reproduced from [2]). SNR bits on the

vertical axis is equivalent to the effective number of bits ENOB............. 5

Figure 1.3 Survey of A/D performance, with degradation based on various

mechanisms with the listed parameter assumptions (reproduced from

[2]). The shape of the curve representing the highest sampling rates

appears to correspond to an aperture-jitter limitation, with the

reasonable rms jitter value of between 0.5 and 2 ps. ................................ 7

Figure 1.4 Impact of aperture jitter on A/D performance. The curves represent

the upper limit on A/D performance due to aperture jitter, as

calculated from (1.8). Jitter values of 2 and 0.5 ps are typical for

purely electronic sampling, while values of 0.1 and 0.01 ps have

been reported for mode-locked lasers. ...................................................... 8

Figure 1.5 A/D conversion based on phase-encoding (reproduced from [5]). A

Mach-Zehnder modulator phase-encodes the input signal, producing

two amplitude-modulated complementary outputs. These outputs

are eventually digitally processed to produce the final digital output. ..... 9

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Figure 1.6 Schematic of photonic-assisted A/D based on optical time-stretching

(reproduced from [8]). Fiber L1 chirps the pulse from a short-pulse

laser, and this chirped pulsed is modulated by the input electrical

signal. Fiber L2 further chirps the pulse, slowing it down so that it

can be detected and then converted to a digital output by a

conventional A/D. The actual setup requires erbium-doped optical

amplifiers at various stages in the process.............................................. 11

Figure 1.7 Schematic of time-interleaved A/D conversion based on

photoconductive sampling. The input waveform is demultiplexed

onto N parallel channels. CMOS A/D circuits quantize the signal

that has been sampled onto hold capacitors. Each channel operates

at a sampling frequency fsamp, for an aggregate sampling rate of N ×

fsamp.......................................................................................................... 12

Figure 1.8 A/D converter with optical remoting. The input electrical signal is

sampled onto the intrinsic capacitance of an optical modulator, and

the modulator converts the sample into optical form. An optical link

carries the amplitude of the sampled signal to a remote, isolated

subsystem consisting of a photodetector and CMOS A/D. Only one

channel is shown here for clarity. ........................................................... 14

Figure 1.9 A/D converter with differential optical remoting. A pair of

modulators converts the sampled electrical voltage into a differential

optical signal. Photodetectors can then receive this differential

signal, and the resultant electrical signal is quantized by CMOS

circuits..................................................................................................... 16

Figure 2.1 Illustration of conduction and valence bands in semiconductor. The

strongest optical absorption occurs at energies greater than Eg. ............. 22

Figure 2.2 Illustration of the lowest bound state for the exciton, corresponding

to n=1 (2.1) and zero in-plane momentum (k = 0). ................................ 23

Figure 2.3 A “quantum well” formed by layers of semiconductor material. The

well material has a smaller bandgap energy then the barrier material.

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In the case of GaAs and AlGaAs, the bands line up such that both

electrons and holes have lower energies in the well material. This is

referred to as “Type 1” band alignment. (Energy is shown “side-

ways”, i.e., along the horizontal axis, in the figure on the right.) ........... 25

Figure 2.4 Optical absorption in a quantum well. Absorption of a photon leads

to a transition of an electron from an energy level in the conduction

band to an energy level in the valence band. The quantum number n

for both conduction and valence bands must be equal in the

idealized infinite barrier case. This leads to the optical absorption

spectrum shown above, where the “corners” of the steps align with

the bulk absorption. Excitonic effects are ignored................................. 26

Figure 2.5 Sample absorption spectra for different applied voltages. These

curves were calculated based on photocurrent measurements for

fabricated quantum well samples............................................................ 28

Figure 2.6 Typical plot of absorbed optical power as a function of applied

voltage. The incident power is 0.90 mW, and the wavelength is 857

nm. .......................................................................................................... 31

Figure 2.7 Plot of absorbed power versus input current. This data and the data

from Figure 2.6 were collected at the same time Hence the optical

power and wavelength are the same: 0.90 mW and 857 nm. By

visual inspection, the set of points between 120 μA and 320 μA

indicates a linear relationship. The fitted line has a slope of 1.3 J/C,

closely matching the ideal unity quantum efficiency slope of 1.4 J/C. .. 32

Figure 2.8 An optical modulator diode biased with an ideal constant current

source Ibias. Vmod is the voltage that appears across the modulator,

and can be solved given Ibias and the modulator’s current-voltage

characteristic. The transient current source Inoise is used to illustrate

the feedback present in this system......................................................... 34

Figure 2.9 Load-line analysis for the circuit shown in Figure 2.8. The vertical

axis is the current through a circuit component, and the horizontal

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axis is Vmod. The blue, red, and green curves represent the behavior

of (1) the modulator, (2) an ideal current source of 170 µA, and (3)

an ideal current source of 300 µA, respectively. .................................... 35

Figure 2.10 Optoelectronic feedback loop linking optical absorption with current

and voltage. As long as the local slope of the electroabsorption

curve γ is positive, we realize a negative feedback loop. ....................... 37

Figure 2.11 Optical modulator diode biased by a voltage source with finite

output impedance R................................................................................. 39

Figure 2.12 An example of a load-line diagram for a modulator biased by finite-

resistance voltage source. To illustrate a situation with three

equilibrium points, we graphically solve the circuit with a 32.5 V

bias and a 90 kΩ output impedance. ....................................................... 40

Figure 2.13 Block diagram for the circuit of Figure 2.11. When Vmod increases,

it not only causes the modulator’s photocurrent to increase but also

reduces the current supplied by the voltage bias. Thus, the effect of

Vmod on the voltage source is to reduce Inode by Vmod/R. .......................... 41

Figure 2.14 Optical modulator biased with a constant current supply. The input

signal to the modulator is a time-dependent current Iin(t). The

capacitance C of the modulator is explicitly included. Qmod(t) is the

instantaneous amount of charge that passes through the modulator....... 43

Figure 2.15 Pulsed current input to a modulator with no bias. .................................. 44

Figure 2.16 Self-linearized modulators connected in a totem-pole topology.

Voltage sources of equal magnitude but opposite polarity bias the

modulator pair. Each modulator has an incident continuous-wave

beam. The input current signal is injected onto the node Vmod in

between the two modulators. .................................................................. 46

Figure 2.17 Load-line analysis for the circuit of Figure 2.16. The bias voltages

are ±3 V, and the input optical beams are 0.90 mW at 857 nm. The

sole equilibrium state occurs at the intersection of the two curves,

where the currents through both devices are identical due to current

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conservation in the steady state. Note that the zero-current

conditions occur near ±4 V rather than at the biases of ±3 V, since

even with no external voltage bias a modulator with incident light

produces a net current in the reverse-diode direction. ............................ 47

Figure 2.18 Load-line analysis calculated in the same way as Figure 2.17, except

that biases of ±6 V are used. Three possible equilibrium states result.

(a) and (c) are stable, while (b) is unstable. Note that a modulator

with no voltage bias across it still produces current when excited by

incident light. .......................................................................................... 48

Figure 2.19 Load-line analysis for the circuit in Figure 2.16, where we set Iin to

be a constant 100 μA. The blue curve represents the current leaving

Vmod through the modulators. The horizontal green curve is the

current supplied to Vmod from the current source. As before, the

circuit is in a stable state when the net current is zero at the

intersection of the two curves. ................................................................ 49

Figure 2.20 Block diagram of the circuit from Figure 2.16, using small-signal

(first-order) parameters of the circuit elements. In this case γ1 and γ2

are the local slopes of the electroabsorption curves for modulators 1

and 2........................................................................................................ 50

Figure 2.21 Differential modulator circuit, depicting the three possible current

paths for supply-line noise. For the three paths, the noise charge (1)

does not affect the optical response of either modulator, (2) leads to

an increase and then decrease in absorption in modulator 1, and (3)

causes both modulators to absorb extra optical energy. ......................... 54

Figure 2.22 Voltage bias dependence of the capacitance of a GaAs p-i-n diode.

Changing the reverse bias of the diode causes the depletion width in

the doped regions to vary, thus leading to changes in the device

capacitance. The vertical axis shows the capacitance as the

percentage deviation from the average capacitance. For an input

voltage range of 10 V, the single modulator exhibits a capacitance

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fluctuation of about ±3.5%, while the fluctuation is reduced to

±0.5% in the differential configuration. In this calculation, the built-

in voltage is assumed to be the bandgap voltage of 1.5 V. The

temperature is 300 K, the intrinsic region is 0.625 µm thick, and the

p and n regions are doped to 1×1019 and 5×1018 cm-3, respectively.

These device parameters are approximately those used for the wafer

structure processed for this work at Stanford University........................ 56

Figure 2.23 Plot comparing voltage-based and current-based operation of the

optical modulator with an ideal sinusoid. The simulation uses

experimental data from Figure 2.6 and Figure 2.7.................................. 60

Figure 2.24 Required modulator speed as a function of the resolution (2.63).

The vertical axis gives the number of time constants we must wait

for the modulator to finish the electro-optic conversion. We use a

first-order (small-signal) model of the modulator’s dynamics for this

analysis.................................................................................................... 62

Figure 2.25 Required input optical power as a function of A/D resolution. The

solid curve represents the needed power due to shot-noise

considerations, while the dashed curve is due to device speed

requirements. Only at high resolutions near 10 bits do shot-noise

considerations dictate the necessary optical power. The parameters

used for the plot are typical for the modulators used in this work and

shown in Table 2.2.................................................................................. 65

Figure 2.26 Minimum full-scale voltage needed to overcome shot noise. With a

capacitance of 40 fF, the thermal noise sets a minimum full-scale

voltage well below the typical modulator operating range of a few

volts......................................................................................................... 68

Figure 2.27 A reverse-biased photodetector can serve as a near-ideal current

source for the SEED. The magnitude of the input current is set by

the power of the light incident on the photodetector. The SEED

modulates the input power Pin. In the figure shown here the SEED

xxiii

operates in reflectance instead of transmissive mode, so that the

output power Pout exits the device on the same side as Pin...................... 69

Figure 2.28 LED drive voltage (top) and SEED output power (bottom) as a

function of time. When the LED drive voltage is high, the

photodetector outputs current to the SEED leading to higher

absorption and hence lower output power. The output power

changes with a time constant on the order of 100 ms. ............................ 71

Figure 2.29 Test circuit for operating the SEED under pulsed current conditions.

A pulsed HeNe beam incident on a photodetector creates the input

current pulses. An acousto-optic modulator (AOM) modulates the

HeNe laser. A square-wave function generator controls the

modulation of the AOM. When the AOM is on, the HeNe power is

diverted to the first diffractive order and triggers the photodiode.

When the AOM is off, the HeNe power passes straight through the

modulator. ............................................................................................... 72

Figure 2.30 Linear electro-optic conversion in SEED. As we increase the

number of electron-charges injected onto the device, the number of

photons absorbed from an input beam increases linearly. Slope of

linear fit is close to the ideal case, where a single electron-charge

leads to the absorption of a single photon............................................... 73

Figure 2.31 Plot as a function of time for power transmitted through the device

(top) under a pulsed input current (bottom). Both power and current

are plotted in units of number of particles per second. As expected,

when we feed current into the device the absorption increases and

the transmitted power decreases. The response time for this test

circuit is slow though, on the order of milliseconds. .............................. 74

Figure 3.1 Two series-connected modulators. The left device acts as a simple

photodetector. When excited by short pulses, this device produces

current pulses for the device on the right. This second device

modulates a CW input beam, and is the device we are testing for

xxiv

linearized electro-optic conversion. Such monolithically grown

structures allow for capacitances on the order of tens of femtofarads.... 78

Figure 3.2 Simplified schematic of optical setup. Lenses are not shown for

clarity. A polarizing beamsplitter (PBS1) combines the Ti:Sapphire

CW laser with the Ti:Sapphire mode-locked laser. (The mode-

locked laser output is first coupled into a fiber, and then coupled

back out into free space via lenses.) A non- polarizing beamsplitter

(NPBS) picks off both beams, allowing us to measure the input

power of either beam. (We choose which beam is measured by

simply blocking the other beam.) A second polarizing beamsplitter

(PBS2) picks of most of the reflected CW beam for monitoring by

an output photodetector. Enough of the CW power still passes

through PBS2 to allow us to view the position of the beam relative

to the device. Either a slow or a fast photodetector can be used to

measure the output power, thus allowing us to measure average or

time-dependent output. ........................................................................... 80

Figure 3.3 Circuit schematic of modulators in experiment. High-energy pulses

from an 80 MHz Titanium:Sapphire laser illuminate the upper

modulator (Device B), causing it to behave as a current source that

injects pulses of current onto the lower modulator (Device A).

Device A modulates a CW optical beam. The laser pulse’s time-

width δt is on the order of 200 fs. The average power of the pulsed

laser Ppulse, CW laser Pin, and modulated output Pout are all

monitored. The transient behavior of the output beam Pout(t) is also

measured. ................................................................................................ 81

Figure 3.4 Sample load-line diagram for modulator in series with photodiode.

When no light is incident on the photodiode, the voltage across the

modulator is given by the intersection point of the two curves, and

so the modulator is in slight forward bias............................................... 82

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Figure 3.5 Modulated output power as a function of time, normalized to

incident power. When a short pulse hits Device B of Figure 3.3, a

charge pulse is generated, the absorption of Device A increases, and

the output power drops. The increased absorption of A discharges

the charge pulse and the device recovers to its initial state. To the

first-order approximation, this recovery is an exponential curve.

The exponential fit has a time constant of 2 ns, close to the

calculated figure of 1.6 ns....................................................................... 83

Figure 3.6 Average absorbed optical power versus average power of the optical

pulses that drive the photodiode current source. For a certain range

of average pulse power, a linear relationship exists. This indicates

that there is a regime where an electrical signal is linearly converted

into an optical one................................................................................... 85

Figure 3.7 Normalized modulator power, with different input CW powers.

Higher CW powers result in faster recovery time. ................................. 85

Figure 3.8 Device recovery speed as a function of CW power. According to

the first-order formula Equation (3.1), the inverse of the time

constant is linearly proportional to the input CW power on the

modulator. Using the appropriate parameters the calculated slope

should be 5.0 × 10-4 (ns µW)-1. The best fit line has a slope of 5.2 ×

10-4 (ns µW)-1.......................................................................................... 86

Figure 3.9 Circuit diagram of experimental setup, with current preamplifier.

The current preamplifier provides an output voltage which indicates

the average current flowing I(t) through the devices. ............................. 88

Figure 3.10 Output power from modulator after current pulse injection. The two

curves correspond to two different levels of pulse power, and hence

two different amounts of charge injection. Under the larger

injection, the modulator’s initial voltage bias is pushed past the

voltage at which the first exciton peak lines up with the operating

xxvi

wavelength, and then the absorption peak passes through the

operating wavelength again during recovery.......................................... 90

Figure 3.11 Typical electroabsorption curve for optical modulator........................... 90

Figure 3.12 Output power of modulator with different amounts of current

injection. The incident CW power was 2.6 mW, and the device

dimensions were 20 µm × 20 µm. With these operating conditions

the device can meet the 1 GHz sampling frequency requirement of

the overall system. .................................................................................. 91

Figure 3.13 Absorbed optical energy versus input charge per period. A mode-

locked laser delivers optical pulses to a photodetector, thus

generating current pulses. These current pulses cause the modulator

to absorb optical energy. For a certain range of input pulses, we

observe a linear relationship between absorbed energy and input

charge. When plotted on axes with units of number of photons

versus number of electrons, the slope of approximately one indicates

near-unity quantum efficiency. ............................................................... 92

Figure 3.14 Baseline output power as a function of input current. The small spot

was 12 µm × 12 µm, and the large spot was 24 µm × 24 µm. The

baseline power is normalized for each curve by dividing by the

baseline power for the lowest input current data point. .......................... 95

Figure 4.1 Energy band diagrams for as-grown (left) and post anneal (right)

low-temperature grown GaAs. Defect densities decrease after

anneal. From [1] and [2]. ..................................................................... 101

Figure 4.2 MSM dimensions used to calculate capacitance. [9] uses the

variables a (half the width of a finger) and b (half the distance

between the top edge of two adjacent fingers). The capacitance

formula can be recast using finger width f and finger spacing s........... 105

Figure 4.3 Scanning electron micrograph (SEM) of fabricated MSM device.

The finger width and spacing are both 1 μm, and the device is

approximately 19 μm × 19 μm. ............................................................ 107

xxvii

Figure 4.4 Theoretical capacitance for MSM structure as calculated from (4.6),

as a function of finger spacing. For this plot the finger width is 1

μm, dielectric constant is 13, and device area is 19 μm × 19 μm......... 108

Figure 4.5 Schematic depicting how the temporal response of the MSM switch

can be measured. The device is connected in series with two

transmission lines. One line is terminated to a bias voltage, and the

other is terminated to ground. An optical pulse exciting the device

generates transient electrical waveforms. ............................................. 109

Figure 4.6 Temporal response of MSM switch after excitation with a short

optical pulse, indicating a full-width half-maximum (FWHM) of

about 2 ps. The pump pulse is produced by a Spectra Physics

Tsunami titanium:sapphire mode-locked laser, and has a FWHM of

approximately 200 fs and a center wavelength of approximately 850

nm. From [14]. ..................................................................................... 110

Figure 5.1 Mesa test structure for photocurrent measurements. Two ohmic

contacts provide electrical bias to the active quantum-well region. A

tunable Ti:Sapphire laser provides an input optical beam. The mesa

is 300 μm × 300 μm. ............................................................................. 115

Figure 5.2 Absorption coefficient versus input wavelength, for applied biases.

The absorption of bulk GaAs is also provided for reference [3]. ......... 116

Figure 5.3 Illustration of modulator structure after fabrication process flow.

The n-doped base region of the modulator is 40 μm × 80 μm. The

active area is formed by a reactive ion etch (RIE), with the gold

contact as a hard mask. We fabricated modulators with active areas

that ranged from 9 μm × 9 μm to 15 μm × 15 μm. ............................... 117

Figure 5.4 Scanning electron microscope (SEM) image of fabricated

modulators............................................................................................. 118

Figure 5.5 Metal mask layout for quartz carrier die. The metal pattern allows

us to perform a variety of experiments, including direct control of a

single modulator, single-ended testing using one modulator as a

xxviii

current source, and differential testing using one modulator as a

current source. The peripheral pads are for wire-bonding, and are

80 μm × 80 μm. Pads for solder-bonding to modulators are

approximately 15 μm × 15 μm.............................................................. 121

Figure 5.6 Single-ended modulator output as a function of time. .......................... 122

Figure 5.7 Photograph and equivalent circuit for differential testing of optical

modulators. Short pulses excite one of the modulators to generate

the input current. ................................................................................... 123

Figure 5.8 Optical power versus time, for the two outputs of the differential

modulator pair. Both signals have been vertically shifted so that 0

power represents the average output when no current is generated by

the third modulator. (This shift is necessary to compensate for slight

misalignment of the beams on the modulators.) Common mode

noise (which we attribute to a weak wire-bond contact) is clearly

apparent................................................................................................. 124

Figure 5.9 Differential output signal versus time. Again, the signal has been

vertically shifted so that zero output corresponds to no input current.

Much of the common mode noise has been cancelled out.................... 125

Figure 5.10 Optical energy in output pulse as a function of input charge. Units

of photons and electron charge are used, so that the fitted slope of 1

corresponds to unity quantum efficiency. When the input charge is

too high, the modulators are no longer able to completely discharge

the input node........................................................................................ 126

Figure 5.11 Metal mask layout for single-ended LT GaAs die. A 50-Ω coplanar

strip transmission line offers the opportunity to test the MSM and

modulator with high speed signals, though in actual experiments this

was used only for DC input voltages. ................................................... 127

Figure 5.12 Photograph of a section of a LT GaAs die. Extra indium bumps

have been deposited on all metal pads that will be bonded to the n-

contact of the modulator. ...................................................................... 128

xxix

Figure 5.13 Metal mask layout for differential LT GaAs die. A 50-Ω coplanar

strip transmission line offers the opportunity to test the MSM and

modulator with high speed signals. Differential modulators require

both positive and negative bias. The wire-bond pad for one of these

is placed within the transmission line, and the wire-bond must jump

over the CPS. ........................................................................................ 129

Figure 5.14 Photograph and schematic of MSM sampling and single-ended

modulator operation. Wire-bonds carry the DC input signal and

positive bias voltage. The pulse and CW input beams Ppulse and Pin

are incident on the sample at a normal angle........................................ 130

Figure 5.15 Modulator output power versus time. The behavior is marked by a

sharp initial drop when the MSM switch samples the input voltage,

and a subsequent exponential recovery. The input CW power is

about 0.5 mW........................................................................................ 131

Figure 5.16 Recovery speed as a function of input CW power. Using a first-

order approximation, the relationship should be linear, as the data

indicates. The calculated slope is 1.05, which matches the data well. 132

Figure 5.17 Absorbed power by modulator versus input current. Each curve

represents the response for a different incident pulse power. The

magnitude of the pulse power does not appreciably affect these

curves. Once the input charge is high enough to sufficiently reverse

bias the modulator, we see the linear conversion. Using units of

photons and electrons, the slopes of all three curves in the linear

region is about unity.............................................................................. 133

Figure 5.18 Absorbed power versus input voltage. The onset of the linear region

occurs at higher voltages when the pulse power is lower, since

linearity requires a minimum input current. ......................................... 134

Figure 5.19 Absorbed power versus input voltage, with different CW powers.

The curves have been offset in the vertical direction for clarity, since

the baseline absorption is naturally quite different for different CW

xxx

powers. For the pulse power used here, the behavior is similar when

the CW power is large enough. The range is quite limited when the

CW power is small................................................................................ 135

Figure 5.20 Scanning electron microscope (SEM) image of differential

modulator pair with MSM sampling switch. The MSM fingers and

spacings are both 1 μm in width, with a total switch size of 19 μm ×

19 μm. The modulators are 80 μm × 40 μm, though the active area

is on the order of 12 μm × 12 μm. ........................................................ 136

Figure 5.21 Photograph and schematic of MSM sampling and differential

modulator operation. A co-planar strip waveguide supplies the input

voltage Vin. The pulse and CW input beams Ppulse and Pin are

incident on the sample at a normal angle.............................................. 137

Figure 5.22 Linear differential electro-optic conversion. We plot the average

differential output power of the modulator pair, versus the input DC

voltage. The modulators were biased at ±3 V...................................... 138

Figure 5.23 Differential output versus time. For both positive and input voltages,

we see a recovery time of less than 100 ps. We obtain the

differential signals by separately measuring the response from each

modulator, and then numerically subtracting these. ............................. 139

Figure 5.24 Schematic of experimental setup for dynamic testing of differential

modulators. The MSM is triggered by a pulsed laser to sample a

high-frequency sinusoid that is synchronized to the laser. Slow

detectors and lock-in amplifiers measure the average output powers

from the differential modulator pair. A personal computer running a

custom LabVIEW program collects the data, and also introduces

successive phase shifts at the pulse generator to sample the entire

sinusoidal waveform. ............................................................................ 140

Figure 5.25 Differential output signal while sampling an 80 MHz sinusoid. The

data is not collected in real-time, since each data-point comes from a

measurement based on lock-in detection. The pulse power is 5.4

xxxi

mW, corresponding to a pulseenergy of 68 pJ. The linearity of the

conversion is 4.5 effective number of bits. ........................................... 141

Figure 5.26 Amplitude of differential modulator output versus pulse energy. As

the pulse energy increases, we approach full charge-up of the

sampled voltage. Assuming an RC-like mechanism, we can fit an

exponential decay to the data. The best fit curve a decay constant of

52 pJ, and the amplitude approaches 343 nW at large pulse energies.

Extrapolating from this curve, charging to 99% of the input voltage

would require a pulse energy of about 225 pJ. While full charge-up

may be desirable for increased robustness, it is not necessarily

required for linear operation. ................................................................ 143

Figure 5.27 Differential output signal for a sampled 2 GHz sinusoid, along with

its discrete Fourier transform (DFT)..................................................... 143


its discrete Fourier transform (DFT)..................................................... 144


its discrete Fourier transform (DFT). The lowest non-DC frequency

component is the 10 GHz sub-harmonic, and is not due to non-

linearity of the sampling or conversion process. The 20 GHz signal

is generated by doubling a 10 GHz signal, and a significant portion

of the 10 GHz power leaks through the doubler. .................................. 144

Figure 6.1 Photocurrent of MSM GaAs modulators versus optical power. The

linear relationship indicates constant responsivity. The active

material is a 1 μm thick layer of fully-depleted, undoped GaAs. The

MSM structure consists of 1 μm width fingers and spacings. .............. 151

Figure 6.2 Photocurrent versus bias voltage for MSM detector. A flat response

(as is evident for relatively large voltages) is desired to maintain a

constant responsivity............................................................................. 152

Figure 6.3 Demonstration of linear link between optical modulator and MSM

photodetector. The electrical output of the detector is plotted against

xxxii

the electrical input to the modulator. The two optoelectronic devices

perform E-to-O and then O-to-E conversion. ....................................... 152

1

Chapter 1

Introduction

In this chapter we introduce analog-to-digital conversion, describing its basic

principles and the mechanisms limiting performance. This motivates work on

photonic-assisted analog-to-digital converters, and we briefly discuss two approaches

to this before presenting the approach that our work supports.

We next explain the concept of “optical remoting” as applied to our converter

proposal, as this is the main topic of this dissertation. Finally, we point out some of

the advantages to this idea, and outline the remainder of this dissertation.

1.1 Analog-to-Digital Conversion

The performance of digital processing systems continues to improve exponentially, as

described by the often-mentioned Moore’s Law. However, signals in the real-world

are analog in nature – varying in amplitude and time in a continuous manner. High-

speed analog signals of particular interest include those related to communications or

sensing applications, such as cellular phone signals or radar. They may also include

the very voltage waveforms that physically exist on electronic circuits. Finally, high-

speed signals also arise in such research applications as particle accelerators [1]. In

2 CHAPTER 1. INTRODUCTION

order to harness the power of digital electronics to store and analyze such analog

signals, an analog-to-digital (A/D) converter system is required.

Since analog signals are continuous in both time and amplitude, the A/D system

must perform two basic functions to discretize both these properties (Figure 1.1). The

first function is to sample the analog signal, so that the analog values at discrete points

in time are stored (at least temporarily). The second function is to quantize these

analog values. In this way the analog values are assigned to discrete bins, so that the

value is approximated by a digital number with a finite number of bits.

tt tt tt

sampling quantization

Figure 1.1 Illustration of the analog-to-digital conversion process. Analog signals are first sampled at discrete points in time. The sample values are then quantized into discrete values, suitable for storing or processing by digital systems.

Corresponding to these two basic A/D functions are two basic measures of A/D

performance. One way to characterize the sampling performance is to measure the

rate at which the A/D can sample. To evaluate the quantization process, we can use

the concept of resolution. This tells us to what accuracy the A/D has quantized the

input signal.

The resolution of A/D converters can be described in a more precise way, through

the concept of effective number of bits (ENOB). Even an ideal A/D system will

always be inaccurate, by the very fact that it has quantized the original signal. The

noise causing this inaccuracy is termed “quantization noise”. For example, an ideal

12-bit A/D converter would be off by at most half the least significant bit (LSB), or

1/213 = 1/8192 of the full scale input signal.

1.1. ANALOG-TO-DIGITAL CONVERSION 3

The accuracy of real A/D converters is degraded by two primary factors:

distortion and noise. Distortion results from non-linearities in the quantization or

sampling process; if the input signal is a pure sinusoid with frequency f, distortion

leads to an output signal composed of signals at higher harmonics 2f, 3f, etc. One

metric for describing this is the spurious-free dynamic range (SFDR). This is the ratio

of the signal power to the power in the largest non-fundamental harmonic.

Noise on the other hand, at least in this context, refers to power in the output

signal at any other frequency. Generally, an A/D converter has been designed only to

convert signals up to a certain maximum frequency. Since any signal power above

this frequency will presumably be filtered out, only noise power that exists within the

bandwidth of the A/D contributes to performance degradation. The signal-to-noise

ratio (SNR) is used to quantify this effect, and refers to the ratio of the signal power to

the total noise power (within the A/D converter’s bandwidth) that does not belong to a

higher harmonic.

Ultimately, both non-linearity and noise hurt the resolution of the A/D. Hence,

the primary metric here is the signal-to-noise-plus distortion ratio (SNDR), which

compares the signal power to both distortion and noise power.

An alternate way to describe the resolution is by the effective number of bits, or

ENOB. The SNDR of an A/D can be directly converted to ENOB, and is defined in

the following way. Suppose a real converter has an ENOB of N, and that its

maximum input voltage range is the full-scale voltage VFS. This real converter has the

same SNDR as that of an ideal N-bit converter. As mentioned earlier, the only source

of noise or distortion in an ideal A/D is the quantization noise. We derive (1.1) in

Appendix A.

( ) bits02.6

76.1dBin −= SNDRENOB (1.1)


1.2 Photonic A/D

1.2.1 Limits from the Walden Wall

In a study published in 1999 [2], Robert Walden surveyed the performance of state-of-

the-art A/D converters at that time (Figure 1.2). Converters were plotted on a two-axis

graph: one axis represents the resolution performance in ENOBs (Walden used the

term SNR bits), and the other axis represent sampling rate. The survey revealed that

almost all converters fell below a straight line — the so-called “Walden Wall”. This

line indicated a clear trade-off between resolution and speed. Moreover, when

observed over time, this performance boundary appeared to improve at a rate

significantly slower than that of digital electronics — only about 1.5 bits over 8 years.

Walden presented a few basic mechanisms for this performance limitation. These

included thermal noise, aperture jitter, and comparator ambiguity. (In addition to

these, Walden also suggested a so-called Heisenberg limitation, which used the

Heisenbergy uncertainty principle that relates energy and time, and applied these to

resolution and sampling period.)

In Walden’s analysis, “thermal noise” actually referred to potential contributions

from many other noise sources, including shot noise and 1/f noise. After lumping all

these contributions together, he suggests an effective resistance Reff that is the source

of this equivalent thermal noise. Integrating the frequency-independent thermal noise

over the Nyquist band fsamp/2 leads to

242 sampeff

n

fkTRv = (1.2)

In order to derive the A/D resolution limit that (1.2) implies, we equate (1.2) with

the quantization noise of an ideal A/D with Bthermal bits of resolution. As derived in

Appendix A, this quantization noise is given by

122 22

2thermalB

FSQ

Vv

−⋅= (1.3)

where VFS is the maximum or full-scale voltage that the A/D can convert.

Equating (1.2) with (1.3) leads to

1.2. PHOTONIC A/D 5

16

log2 −⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

sampeff

FSthermal fkTR

VB (1.4)

Figure 1.2 Survey of A/D performance (reproduced from [2]). SNR bits on the vertical axis is equivalent to the effective number of bits ENOB.

The second mechanism, comparator ambiguity, refers to the finite speed of

comparator operation. Comparators are circuits which decide into which digital bin an

analog sample belongs. For example, for a 4-bit A/D, there may be one comparator

which decides whether a sample is 0101 or 0110 (under regular binary coding). The

probability of a comparator error decreases if the transistors used in the circuit are fast

(i.e. have a high characteristic frequency fT) and if there is a long time for the

comparator to make its decision (i.e. the sampling frequency is low). After making a

few reasonable assumptions as described in [2], the final result is

1.193.6

−=samp

Tambiguity f

fB π (1.5)


The last source of performance degradation is aperture jitter. This effect is due to

irregularity in the sampling events at the front-end of the A/D. We can think of the

sampling events as occurring at some time Δt, where Δt measures how much the time

of sampling deviated from the ideal case. Thus, Δt is a random variable, and the

probability distribution of Δt has a standard deviation which we call the rms jitter.

One way to characterize aperture jitter then is by using rms (root-mean-square) jitter τa.

Aperture jitter impacts A/D resolution; the worst case happens when the A/D

attempts to sample a signal when it has the highest possible slope with respect to time.

This occurs when sampling the maximum Nyquist frequency fsamp/2, right when the

sinusoid is crossing 0. The maximum slope is given by

( ) ( )

2

sin2 00

FSsamp

tsamp

FS

t

Vf

tfV

dtd

dttdv

π

π

=

⎥⎦⎤

⎢⎣⎡=

== (1.6)

For small Δt, the root-mean-square error in voltage is then the product of the

maximum slope (1.6) with the rms jitter τa

2aFSsamp

rms

Vfv

τπ= (1.7)

Again equating this to the quantization noise of an ideal A/D with a resolution of

Baperture bits (1.3) leads to

13

2log2 −⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

asamplaperture f

Bτπ

(1.8)

Walden overlaid the A/D performance survey with curves corresponding to these

mechanisms of performance degradation (Figure 1.3). Note in particular that the

shapes of these curves are different, since each of the three factors depends on the

sampling frequency fsamp in different ways. The primary conclusion from this work

was that aperture jitter was the primary phenomenon limiting A/D performance at the

time. The performance of most A/D converters fell below the curve representing an

aperture jitter of 2 ps, and all converters fell below 0.5 ps. Even in a more recent A/D

result from 2003 [3], researchers reported a converter with 5 bits resolution at a

1.2. PHOTONIC A/D 7

Nyquist sampling rate of 10 GS/s (giga-samples per second), which would still

correspond to an aperture jitter of greater than 0.5 ps.

Figure 1.3 Survey of A/D performance, with degradation based on various mechanisms with the listed parameter assumptions (reproduced from [2]). The shape of the curve representing the highest sampling rates appears to correspond to an aperture-jitter limitation, with the reasonable rms jitter value of between 0.5 and 2 ps.

1.2.2 Motivation

It is this realization — that aperture jitter is the primary limitation for the performance

of conventional A/D converters — that motivated much work into incorporating optics

into the system. Instead of using an electronic oscillator, an optical oscillator in the

form of a mode-locked laser can serve as the sampling reference. The pulsed output

of a mode-locked laser can exhibit very low jitter. Jitter below 0.1 ps is typical, and

researchers have even reported laser systems with jitter below 10 fs [4]. Figure 1.4

shows the A/D performance limitation imposed by such jitter figures. Note in

particular that an A/D converter with a sampling frequency of 100 GS/s requires an

aperture jitter of less than 0.5 ps, if we would like a resolution better than 2 bits.


Jitter-limited A/D Performance

0

12

3

45

6

7

89

10

0.1 1 10 100 1000Sampling Frequency (GS/s)

Res

olut

ion

(ENO

B)

20.50.10.01

RMS Jitter (ps)

Figure 1.4 Impact of aperture jitter on A/D performance. The curves represent the upper limit on A/D performance due to aperture jitter, as calculated from (1.8). Jitter values of 2 and 0.5 ps are typical for purely electronic sampling, while values of 0.1 and 0.01 ps have been reported for mode-locked lasers.

Work has progressed on a number of ideas exploiting this advantage of photonics

in A/D systems. We briefly describe just two of these, and then present the proposal

that our work supported.

1.2.3 Approaches

1.2.4 Optical Sampling with Phase Modulation

In this architecture [5], a Mach-Zehnder interferometer performs the front-end

sampling (Figure 1.5). The pulses from a mode-locked laser enter the interferometer,

which first splits the beam into two paths. The analog electrical input signal to be

converted provides a bias to the lithium niobate (LiNbO3) crystal in the interferometer.

This bias, due to the linear electo-optic effect in LiNbO3 [6], causes the beam in the

two branches to be phase-shifted with respect to each other. Re-coupling the two

beams via a waveguide-implemented beamsplitter leads to two optical outputs whose

amplitudes have now been modulated. The energies in these two outputs are given by

1.2. PHOTONIC A/D 9

( )⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛++= θπ

πVtV

CE

E INA

00 sin12

(1.9)

( )⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+−= θπ

πVtV

CE

E INA

00 sin12

(1.10)

where C is the modulator’s contrast ratio, Vπ is the voltage needed to produce π phase

shift, VIN(t0) is the voltage applied to the modulator at time t0, and θ is the phase shift

produced when VIN is 0.

Figure 1.5 A/D conversion based on phase-encoding (reproduced from [5]). A Mach-Zehnder modulator phase-encodes the input signal, producing two amplitude-modulated complementary outputs. These outputs are eventually digitally processed to produce the final digital output.

These complementary outputs are then fed into a pair of photodetectors, and the

resultant electrical signals are then quantized and sent to a digital signal processor

(DSP). The DSP calculates the original amplitude of the input signal VIN(t0) by

solving for the input signal from (1.9) and (1.10)

( ) ⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛+−

= − θπ

π

BA

BAIN EE

EEC

VtV 1sin 1

0 . (1.11)

Of note in (1.11) is that E0 does not appear in the formula. Hence, this scheme of

initially phase-encoding the signal results in a system that is relatively immune to

noise on the mode-locked laser.


The actual, implemented system is more complex than discussed here, since the

outputs from the sampling modulator are then demultiplexed and pass through various

fiber delay lines in order to be quantized by 16 63-MS/s quantizers. For the final

system, eight bit resolution at a sampling rate of 505 MS/s was reported, and the

system was projected to have the potential for 12 bits of resolution.

1.2.5 Optical Time-Stretching

In a somewhat different approach, researchers used time-stretch preprocessing to

achieve extremely high sampling rate for a buffered window in time [7][8]. In this

approach, the short-pulse from a mode-locked laser first passes through a dispersive

optical fiber. The original pulse is now stretched in time, but chirped so that the

higher-frequency components occur later in time during the pulse duration. An

electro-optic modulator then imprints the waveform of an input analog signal onto the

amplitude of the stretched pulse. A second spool of fiber further stretches the

modulated optical pulse. This stretched waveform is now slow enough that it can be

digitized by a conventional A/D converter.

In one implementation, researchers reported 5 bit conversion at an effective

sampling rate of 1 TS/s, where they used a 50× time-stretch factor [8]. One

disadvantage to this system is that it is only capable of capturing a fraction of the input

signal, where the fraction is at most the inverse of the time-stretch factor. In this case,

researchers captured a 1.1 ns window’s worth of input signal.

1.3. PHOTOCONDUCTIVE-SAMPLING, TIME-INTERLEAVED A/D CONVERSION 11

Figure 1.6 Schematic of photonic-assisted A/D based on optical time-stretching (reproduced from [8]). Fiber L1 chirps the pulse from a short-pulse laser, and this chirped pulsed is modulated by the input electrical signal. Fiber L2 further chirps the pulse, slowing it down so that it can be detected and then converted to a digital output by a conventional A/D. The actual setup requires erbium-doped optical amplifiers at various stages in the process.

1.3 Photoconductive-sampling, Time-

interleaved A/D Conversion

In the two approaches described above, as well as many other photonic A/D proposals,

the front-end sampling involves modulation of the laser pulses. In our approach, the

laser pulses merely serve to trigger electronic sampling switches. These

photoconductive switches are attached to a high-speed transmission line that carries

the input analog signal. Optical pulses staggered in time trigger the series of switches,

one after the other, sampling the signal onto hold capacitors. This simultaneously

samples and demultiplexes the electrical signal in time to each channel, so that the

sampled signal on each channel occurs at a slower rate than the aggregate sampling

rate. Since these channels carry slower signals, these sampled analog values can then

be quantized using more conventional CMOS A/D converters. Figure 1.7 is a

schematic of this architecture.


A/D A/D A/D

Digital Output

Staggered Optical Pulses

Input Electrical Signal

Photoconductive Sampling Switch

Hold Capacitor

Figure 1.7 Schematic of time-interleaved A/D conversion based on photoconductive sampling. The input waveform is demultiplexed onto N parallel channels. CMOS A/D circuits quantize the signal that has been sampled onto hold capacitors. Each channel operates at a sampling frequency fsamp, for an aggregate sampling rate of N × fsamp.

The goals for this proposal are to demonstrate the feasibility for sampling at

100 GS/s (giga-samples per second). At a Nyquist sampling rate, this implies an input

bandwidth of 50 GHz. Each channel would operate at 1 GS/s, so that 100 channels

would be required. We also target 3 – 5 bits of resolution. Excluding the time-stretch

approach which has an inherent limitation in the window it can sample, our proposal

targets a fast sampling rate at relatively low resolution when compared with other

proposals.

There are a few potential advantages to this system. The input electrical signal —

at least in high speed form — resides mainly in the electrical domain. Thus, much less

optical processing is required, obviating the need for bulky optical elements. This

system thus has the potential to be quite compact. Also, the sampling mechanism

involves simply charging up a capacitor. Assuming we can fully charge up this

1.4. OPTICAL REMOTING 13

capacitor, the system is relatively impervious to fluctuations in the power of the mode-

locked laser, or in misalignment of the pulsed beams. Further, this sampling

mechanism means that high-speed and highly-linear modulators are not needed.

Finally, by using relatively low-speed CMOS quantizers, we can achieve much lower

power consumption.

Since we do rely on distributing the high-speed signal electrically, reduced signal

integrity can be a disadvantage when compared with optical distribution. This could

especially be a problem when carrying signals from the sampling switches to the

CMOS quantizers. Moreover, the need for distributing on the order of 100 staggered

pulses to many switches still necessitates some potentially complex optical system.

Finally, the sampling mechanism does suffer from limited drive capabilities.

1.4 Optical Remoting

This dissertation focuses on a strategy for combating some of the disadvantages listed

above, at the cost of increased complexity. We call this concept “optical remoting”,

and it uses an optical link to connect the sampling switch with the CMOS quantizer,

thus allowing the two components to be placed remotely from each other. Figure 1.8

illustrates this idea. An optical modulator serves as the hold capacitor for the sampled

signal from the photoconductive switch. The modulator converts the sample analog

electrical signal into an optical one, by modulating an incident continuous-wave (CW)

beam. The modulated beam carrying the sampled signal is then detected by a

photodetector on another chip. The signal can then be integrated and passed on to the

quantizer.

One motivation for employing optical remoting is for noise-immunity purposes.

Optical remoting allows the quantizer to be placed far away from the sampling switch,

even on a separate die. This allows for complete electrical and thermal isolation

between the two components. The signals while they reside on the optical link are

also less susceptible to noise, thus potentially increasing signal integrity.


Figure 1.8 A/D converter with optical remoting. The input electrical signal is sampled onto the intrinsic capacitance of an optical modulator, and the modulator converts the sample into optical form. An optical link carries the amplitude of the sampled signal to a remote, isolated subsystem consisting of a photodetector and CMOS A/D. Only one channel is shown here for clarity.

If the quantizers were to be directly integrated with the switches, the large area of

the quantizers (on the order of 150 µm × 450 µm, not including output drivers [9])

would dictate the pitch of the sampling switches. Hence, ignoring the space occupied

by the drivers and global interconnects, 100 of these quantizers could optimistically fit

within an area of 2.6 mm × 2.6 mm. For architectures where we desire all sampling

switches to sample the same point on a high-speed transmission line, at 50 GHz this

implies that all switches must be located within 1 or 2 mm of each other. With optical

remoting, the sampling switches need only be integrated with modulators that are

small, whose active areas are on the order of 10 µm × 10 µm.

1.4. OPTICAL REMOTING 15

The use of optical remoting can also help solve the issue of how to extract the

large bandwidth of digital data coming from the A/D system. At 100 GS/s with 4 bits

of resolution, this would require the small chip to drive at least 400 Gb/s of data.

Squeezing such performance out of a small die can be problematic, especially from a

power perspective. Using optical remoting links allows us to place the quantizers on

one or more dies, thus making the extraction of large digital bandwidth from the A/D

system easier.

1.4.1 Differential Remoting

An additional option to the optical remoting scheme described above is to send the

optical signal differentially using a pair of optical modulators. This is illustrated in

Figure 1.9. Here the sampled signal is supplied to the center node in between two

series-connected modulators. The optical output signal is the difference between the

powers of the two beams.

We will go into more detail as to the benefits of a differential system in a later

chapter. As a quick preview though, one major advantage is rejection of common-

mode noise that might be present on the laser source supplying the CW input beam.

Other sources of common-mode noise that would be rejected include the voltage

supply lines and temperature. A second major advantage is the ability to work with

both positive and negative signals.


Figure 1.9 A/D converter with differential optical remoting. A pair of modulators converts the sampled electrical voltage into a differential optical signal. Photodetectors can then receive this differential signal, and the resultant electrical signal is quantized by CMOS circuits.

1.4.2 System Requirements

The performance goals for the A/D converter system place requirements on the

modulator. Of primary importance is that the modulator performs electro-optic

conversion in a linear manner. One goal for the overall A/D is that we minimize the

need for elements to correct for non-linearities in the system. Thus, with our target of

3–5 bits of resolution, the modulator must exhibit linearity of at least that much

resolution. Second, we are targeting an individual channel speed of 1GS/s. Thus, the

modulator must be able to match or surpass that conversion speed. Finally, the device

we use must fit into the overall architecture of the system. Thus, we require a device

with a small footprint that can be driven by the sampling switches, and a device which

can be scalable to on the order of 100 channels.

1.5. ORGANIZATION 17

At the outset of this work, we believed that multiple quantum-well modulators,

when operated in a “self-linearized” mode, could meet these requirements. The

purpose of this work was then to demonstrate this.

1.5 Organization

The scope of this dissertation is to study the behavior of multiple quantum-well

modulators for remoting an analog signal, in the context of a photonic-assisted analog-

to-digital converter. Previous work has verified self-linearized operation for DC and

slowly varying electrical inputs [11]. We examine whether this operation still works

for pulsed inputs, as would be the case from high-speed photoconductive sampling

switches.

In chapter 2, we explore the general principles behind the multiple quantum-well

modulator. We examine its speed of operation as well as the “self-linearized” mode,

both in its single-ended and differential configurations. Other system requirements are

considered, and we present some initial experimental results. Chapter 3 presents

further experiments that incorporate short-pulse lasers to explore the speed of these

devices. These results deal with work on devices that had previously been fabricated

at Bell Laboratories.

Chapter 4 switches focus to the operation of the photoconductive sampling

switches, as these are then considered in the subsequent chapter. Chapter 5 discusses

the fabrication of both the switches and modulators at Stanford University. We also

show experimental data from these integrated devices, ultimately presenting results

where a 20 GHz input voltage waveform is sampled and then converted into an optical

signal. Chapter 6 makes some general conclusions about this work, and points to

suggestions for further efforts on this research topic.


1.6 Bibliography

[1] I. Wilke, A. M. MacLeod, W. A. Gillespie, G. Berden, G. M. H. Knippels, and A.

F. G. van der Meer, “Single-shot electron-beam bunch length measurements,”

Physical Review Letters, vol. 88, pp. 124801/1–4 (2002).

[2] R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE Journal

on Selected Areas in Communications, vol. 17, pp. 539–550 (1999).

[3] K. Poulton, R. Neff, B. Setterberg, N. Wuppermann, T. Kopley, R. Jewett, J.

Pernillo, C. Tan, and A. Montijo, “A 20GS/s 8b ADC with a 1MB memory in

0.18µm CMOS,” IEEE International Solid-State Circuits Conference Technical

Digest, pp. 318–319 (2003).

[4] T.R. Clark, T.F. Carruthers, P.J. Matthews, and I.N. Duling III, “Phase noise

measurements of ultrastable 10 GHz harmonically-mode-locked fibre laser,”

Electronics Letters, vol. 35, pp. 720–721(1999).

[5] P. W. Juodawlkis, J. C. Twichell, G. E. Betts, J. J. Hargreaves, R. D. Younger, J.

L. Wasserman, F. J. O’Donnell, K. G. Ray, and R. C. Williamson, “Optically

Sampled Analog-to-Digital Converters,” IEEE Transactions on Microwave

Theory and Techniques, vol. 49, pp. 1840–1853 (2001).

[6] F. L. Pedrotti and L. S. Pedrotti, “Nonlinear optics and the modulation of light,”

Introduction to Optics, 2nd Ed., pp.541–567 (1993).

[7] F. Coppinger, A. S. Bhushan, and B. Jalali, “Photonic time stretch and its

application to analog-to-digital conversion,” IEEE Transactions on Microwave

Theory and Techniques, vol. 47, pp. 1309–1314 (1999).

[8] Y. Han, O. Boyraz, and B. Jalali, “Tera-sample per second real-time waveform

digitizer,” Applied Physics Letters, vol. 87, 241116/1–3 (2005).

[9] R. Urata, L. Y. Nathawad, R. Takahashi, K. Ma, D. A. B. Miller, B. A. Wooley,

and J. S. Harris, Jr., “Photonic A/D conversion using low-temperature-grown

GaAs MSM switches integrated with Si-CMOS,” Journal of Lightwave

Technology, vol. 21, pp. 3104–3115 (2003).

1.6. BIBLIOGRAPHY 19

[10] R. F. Pierret, “pn junction electrostatics,” Semiconductor Device Fundamentals

(1996).

[11] E. A. De Souza, L. Carraresi, G. D. Boyd, and D. A. B. Miller, “Self-linearized

analog differential self-electro-optic-effect device,” Applied Optics, vol. 33,

pp. 1492–1497 (1994).


21

Chapter 2

Multiple Quantum Well Modulators

In this chapter we introduce the basic principles that underlie the operation of multiple

quantum well optical modulators. We provide an overview of the quantum-confined

Stark effect (QCSE), which is the basic phenomenon that allows these devices to

convert signals from the electrical domain to the optical domain.

For analog-to-digital converter applications, linear modulation is of great

importance. We discuss how quantum well modulators can be operated in a “self-

linearized” mode due to an intrinsic negative feedback loop. We also explain how we

can perform electro-optic conversion in a differential fashion, and the benefits that

such a scheme brings.

The target performance for the overall A/D converter system imposes certain

requirements on the modulator device. These include specifications for linearity,

speed, and noise. Finally, we present some preliminary results based on devices

previously fabricated at Bell Laboratories.

22 CHAPTER 2. MULTIPLE QUANTUM WELL MODULATORS

2.1 Optical Absorption

The optical properties of semiconductor materials are primarily governed by the

electrons with the highest energies within the crystal. At absolute zero temperature in

purely intrinsic semiconductors, electrons completely fill up the valence band, which

is a virtually continuous range of allowable electron energies. In this simple model,

above the valence band is a range of energies called the bandgap energy which

electrons are forbidden from having. Above the bandgap is yet another band of

energies which are allowable called the conduction band (Figure 2.1). However, the

conduction band of pure semiconductors is completely free of electrons at zero

absolute temperature.

The strongest optical absorption for a material such as GaAs occurs near or above

the bandgap energy. For photons with energies less than the bandgap, there is

negligible absorption since there is no allowable energy state for an electron if it were

to absorb that low-energy photon. On the other hand, there are plenty of allowable

states for the electron if it absorbs a photon with energy higher than the bandgap.

Figure 2.1 Illustration of conduction and valence bands in semiconductor. The strongest optical absorption occurs at energies greater than Eg.

2.1. OPTICAL ABSORPTION 23

After an electron absorbs a single photon, the end result is an electron in the

conduction band and a “hole” in the valence band where the electron was previously.

2.1.1 Excitons

In the previous discussion, we treated the electrons and holes as completely

separate, non-interacting particles. In reality though, the two particles possess a

Coulombic attraction. This has the effect of modifying the Schrödinger equation that

describes the wavefunction of the two particles, introducing a Coulombic term that

depends on the relative position of the electron and hole. The solution to this modified

Schrödinger equation is mathematically equivalent to the hydrogen atom solution.

Such a solution is marked by two types of states, bound and un-bound.

The bound states are those with energies below the bandgap energy Eg, and

described by the equation 2/ nEEE Bg −= , (2.1)

where the binding energy EB is mathematically equivalent to the Rydberg energy of a

hydrogen atom (Figure 2.2). In GaAs, the exciton has a binding energy of

approximately 4 meV, which corresponds to a Bohr radius of approximately 15 nm.

Valence Band

Conduction Band

Eg En=1,k=0

EB

Figure 2.2 Illustration of the lowest bound state for the exciton, corresponding to n=1 (2.1) and zero in-plane momentum (k = 0).


The un-bound states are a continuum of states with energies above the bandgap

energy. As we consider unbound states with higher and higher energies, we approach

the limit of plane-wave electrons and holes when the Coulombic attraction can be

ignored.

The exciton has two effects on optical absorption that are worth mentioning here.

First, optical absorption occurs at energies slightly below the bandgap energy. This is

due to the bound exciton states1 that have energies below the bandgap energy. Second,

the strength of the optical absorption turns out to be proportional to the probability of

finding the electron and hole in the same unit cell. This probability can be particularly

large for bound exciton states, and still substantial even for unbound ones.

For bulk materials at room temperatures, excitonic resonances in the absorption

spectrum are difficult to resolve. In GaAs for example, the exciton binding energy is

4 meV, which is much lower than the room temperature thermal energy of 25 meV.

2.1.2 Quantum wells

A quantum well is a layer of semiconductor with a small bandgap, placed between two

layers of semiconductor with larger bandgap energies. The presence of the larger

bandgap material serves to confine the electron in the well material. This causes the

lowest possible energy state for the electron to be higher than for the bulk material

(Figure 2.3).

1 Here by “bound exciton” we mean the states of the electron-hole pair in which they are bound to one another.

The term “bound exciton” is also sometimes used to discuss excitons that are bound to impurities, but we do not use that meaning here.


Valence B

and

Conduction B

and

Eg

Figure 2.3 A “quantum well” formed by layers of semiconductor material. The well material has a smaller bandgap energy then the barrier material. In the case of GaAs and AlGaAs, the bands line up such that both electrons and holes have lower energies in the well material. This is referred to as “Type 1” band alignment. (Energy is shown “side-ways”, i.e., along the horizontal axis, in the figure on the right.)

The lowest quantized energy inside the well can be calculated using the

Schrödinger equation, given the potential profile of the quantum well. In fact,

typically several such quantized energy levels exist within the well, and these quantum

energy levels can be calculated as well. In the ideal case, for photon energies below

the lowest (n = 1) energy level, there is no optical absorption. The absorption then

increases in a step-like fashion for higher photon energies, where each step occurs

when the photon energy is equal to the next higher quantum well energy state (Figure

2.4).

Each step in the optical absorption corresponds to the transition from hole energy

n to electron energy n. (Strictly speaking, this is only true for quantum wells with

infinitely high barriers, where the hole and electron wavefunctions with different

energy quantum levels are orthogonal. As the barrier height decreases, this restriction

becomes less “strong,” so small intermediate absorption steps begin to occur.)

Additionally, each absorption step is constant as a function of energy, since the two-

dimensional density of states is independent of energy.


0 10 20 30 40 50 60 70 80 90 100

0

2

4

6

8

10

n=1n=2

n=3

ωh

Eg

n=1

n=2

n=3

Photon Energy

Figure 2.4 Optical absorption in a quantum well. Absorption of a photon leads to a transition of an electron from an energy level in the conduction band to an energy level in the valence band. The quantum number n for both conduction and valence bands must be equal in the idealized infinite barrier case. This leads to the optical absorption spectrum shown above, where the “corners” of the steps align with the bulk absorption. Excitonic effects are ignored.

In real devices, the optical absorption is dominated by excitonic effects. In

contrast to the bulk case, excitonic resonances in the optical absorption can be more

clearly resolved at room temperature. In quantum wells, the excitons can be

“squeezed” into a smaller volume than in bulk material. As noted earlier, excitons in

bulk GaAs have a Bohr radius of about 15 nm, or a diameter of 30 nm. If a quantum

well is fabricated to have a thickness of 10 nm, then the exciton diameter is squeezed

down to a similarly small size.

A smaller exciton will have a larger binding energy, resulting in a more clearly

resolvable peak in the optical absorption. Also, in a smaller-sized exciton the hole and

electron are more likely to be found in the same unit cell, resulting in a stronger

optical absorption.


2.1.3 The Quantum Confined Stark Effect

In a quantum well, optical absorption essentially begins when the photon energy

equals the lowest exciton energy level. If that lowest energy level can be changed

electrically, then we realize an electrically-controlled optical modulator.

The energy levels of the exciton do indeed shift with the introduction of an

electric field. In fact, the energy levels of the mathematically equivalent hydrogen

atom exhibit what is called a Stark shift. In the case of the exciton, we qualitatively

expect a red shift, or a shift to lower energies, in the presence of an electric field. This

is because the electron and hole of an exciton both have the opportunity to decrease

their energies: the electron by running against the direction of the electric field, and

the hole by running along the direction of the field.

If we expand the field dependence of the energy shift into a Taylor series, the

lowest order non-zero term is the quadratic term. This is because all the odd terms

must be zero due to the symmetry of the exciton. Otherwise, the polarity of the energy

level shift would be different depending on the direction of the applied field, which

cannot be the case in a symmetric structure. Since the energy shifts of both the

electron and hole energies depend quadratically on the applied field, the absorption

edge in photon energy also depends on the square of the applied field or voltage.

Assuming that the general shape of the absorption curve does not change too much

with applied voltage, this results in the electroabsorption (or absorption versus voltage

at a given wavelength) also being quadratic to lowest order.

The effects discussed so far are equally applicable to both bulk materials and to

quantum well devices. In bulk materials however, the Stark shift of the exciton’s

energy levels does not lead to the dominant electroabsorption effects that are observed.

At relatively low fields for bulk material, the excitons are quickly pulled apart by the

applied field. This results in a shortening of the exciton’s lifetime with applied

electric field. A stronger field thus tends to broaden the resonance of the exciton, and

it is this exciton broadening which explains the most prominent dependence of optical

absorption in bulk material on applied electric field [1].


A different situation exists in the quantum well case. When we apply an electric

field perpendicular to the well, the well barriers help keep the applied field from

ionizing the exciton. Moreover, if the well-layers are thin enough, the Coulombic

interaction between electron and hole is strong enough to retain bound excitonic states.

Thus, the quadratic Stark shift of the energy levels now explains the most prominent

electroabsorption characteristics of the optical absorption. This phenomenon is called

the quantum-confined Stark effect (QCSE) [2].

Figure 2.5 shows experimental data representing typical absorption curves for

GaAs/AlGaAs quantum wells. The details of the wafer and fabrication will be

described in a later chapter. The spectra shift to longer wavelengths with increasing

applied voltage. Included for comparison is the absorption for bulk GaAs taken from

the literature [3][4].

Absorption Spectra

0

2000

4000

6000

8000

10000

12000

14000

16000

820 830 840 850 860 870 880 890 900

Wavelength (nm)

Abs

orpt

ion

Coe

ffic

ient

(inve

rse

cm) 0

123456bulk GaAs

Applied Voltage

Figure 2.5 Sample absorption spectra for different applied voltages. These curves were calculated based on photocurrent measurements for fabricated quantum well samples.


2.1.4 Saturation

For low input optical powers, the absorbed optical power increases linearly with

incident power. When the incident power is high however, the modulator saturates

and begins to absorb less power than expected. This is largely due to the creation of

such large densities of excitons that they fill up the available states near the exciton

energy level. Due to the Pauli exclusion principle then, more excitons in the same

phase space cannot be created until these electron-hole pairs are removed [5].

We can express the photocurrent that arises from the absorbed power as

AePiω

ηh

= (2.2)

( )LeePi α

ωη −−= 1h

(2.3)

where P is the optical power that reaches the quantum wells, η is the quantum

efficiency, L is the thickness of the active region, A is the absolute absorption, and α is

the absorption coefficient. To account for saturation, we simply let α be a function of

the optical intensity I incident on the active region. This can be phenomenologically

expressed by [6]

( ) ( )satIII

/10

+=

αα (2.4)

where α0 is the absorption coefficient well below saturation, and Isat is a characteristic

saturation intensity at which the absorption coefficient is halved.

The saturation intensity Isat can be increased through thinner well barriers or

shallower wells. The saturation intensity also increases with larger applied fields [7].

In our work, we generally avoid saturating the modulators. However, note that for

high optical intensities, the optical absorption becomes smaller than expected. This

means that the derivative of absorption with respect to applied voltage

dVdA=γ (2.5)

also saturates. The importance of this parameter will become important later on.


2.2 Self-Linearization

As noted above, in quantum well structures the optical absorption tends to depend

quadratically on the electric field. For applications where we would prefer that the

absorption vary linearly with some electric input, a different class of operation must be

considered. In this section we discuss the “self-linearization” of quantum well

modulators. This type of behavior essentially results from considering a current input

to the device rather than a voltage input.

2.2.1 Basic Principles

The core basis for self-linearization rests on the fact that the leakage current of

quantum well diode modulators is negligible [8]. Current can pass through the

modulator only when the modulator has absorbed photons, as long as the diode is in

neither forward-bias nor extreme reverse-bias. Specifically, one electron-charge’s

worth of current can pass through the diode only if an electron-hole pair has been

generated. Moreover, an electron-hole pair generation is almost completely due to

photon absorption.

In Figure 2.6 we show a plot of the absorption versus voltage for a multiple

quantum well optical modulator. As we can see for low voltages below the first

exciton peak, the electroabsorption is not linear.

On the other hand, when we consider absorption as a function of current we

expect a linear relationship. Theoretically, we can derive this relationship by

assuming unity quantum efficiency. In other words, referring back to (2.2),

AePi i ωηh

= (2.6)

aPeiωh

= (2.7)

where Pi and Pa are the incident and absorbed powers, respectively, and we set the

quantum efficiency η equal to 1.

2.2. SELF-LINEARIZATION 31

Absorption vs. Voltage

0

0.1

0.2

0.3

0.4

0.5

0.6

0 5 10 15Voltage (V)

Abs

orpt

ion

(mW

)

Figure 2.6 Typical plot of absorbed optical power as a function of applied voltage. The incident power is 0.90 mW, and the wavelength is 857 nm.

This linear range of operation is determined by the requirement that each

absorbed photon results in the generation of a single electron/hole pair, and that this

carrier pair is swept out of the intrinsic region. With this assumption of unity quantum

efficiency, the theoretical slope is given by the photon energy divided by the electron

charge (a quantity that is numerically identical to the photon energy expressed in units

of electron-volts), or

edIdPa ωh= (2.8)

Figure 2.7 shows experimental data that illustrates the linearity between the

absorbed power and the input current. For this experiment, the wavelength is 857 nm,

yielding an ideal slope of 1.4 J/C. By visual inspection, the region of the plot shown

in Figure 2.7 is linear for input currents ranging from 120 µA to 320 µA. The linear

fit to this range is 1.3 J/C, reasonably closely matching the ideal unity quantum

efficiency slope.


Absorption vs. Current

00.10.20.30.40.50.60.7

0 100 200 300 400 500

Current (µA)

Abs

orpt

ion

(mW

)

Figure 2.7 Plot of absorbed power versus input current. This data and the data from Figure 2.6 were collected at the same time Hence the optical power and wavelength are the same: 0.90 mW and 857 nm. By visual inspection, the set of points between 120 μA and 320 μA indicates a linear relationship. The fitted line has a slope of 1.3 J/C, closely matching the ideal unity quantum efficiency slope of 1.4 J/C.

When the input current is either too small or too large, the device deviates from

this linear ideal. For a simple analysis of what leads the loss of linearity, consider an

equation representing the primary components of the current passing through a

modulator diode:

diffusionbreakdownlightdevice IIII −+= (2.9)

where Ilight is current due to photogenerated carriers (and is proportional to the optical

power absorbed), Ibreakdown is current due to impact ionization that occurs at large

reverse-bias voltages, and Idiffusion is the forward diffusion current present at forward-

bias. (Note that, because of the photocurrent Ilight behaving like a reverse current, a

photodiode can be in slight forward bias even if the actual current has the sign


corresponding to a current in reverse bias.) We set the signs of the terms in (2.9) such

that positive current occurs in the reverse-biased direction.

When the total current through the modulator is dominated by Ilight, then the

device operates within the linear range between 120 and 320 µA of Figure 2.7. When

we reduce the input current below that range (as indicated by the lowest data point),

Idiffusion becomes non-negligible. As we can see from (2.9), the total device current

thus becomes smaller in magnitude than what we would have expected for the amount

of power it is absorbing. Equivalently, the absorbed power is higher than expected.

On the other hand, if we raise the current to a value higher than 320 µA in this

particular experiment, Ibreakdown becomes non-negligible. Now, the total device current

is larger in magnitude than anticipated, so the absorbed power for high currents is

smaller.

To summarize, once the device has reached an equilibrium steady-state condition,

we achieve self-linearization so long as we bias the device such that

breakdownlight II >> (2.10)

and

diffusionlight II >> (2.11)

Incidentally, the plot in Figure 2.7 is obviously not a single-valued function. This

is because we varied the applied voltage to collect the data, and measured the current

to find the “input” current. In the electroabsorption curve of Figure 2.6, there are

clearly cases where two different voltages yield the same amount of current. Hence,

there are input currents for which the device could behave in either a linearized or a

non-linearized mode. The data points for which non-linearized behavior is evident

correspond to large input voltages, when the diode is in breakdown mode.

2.2.2 Ideal Current Source Bias and Equilibrium Stability

To illustrate the basic principles of self-linearization, we have explored the

device’s behavior when a voltage bias is applied, and considered what the measured

current would be. In actual operation, self-linearization is not necessarily


implemented with an ideal voltage source, and hence it is useful to consider how the

device behaves when biased with an electrical power source with finite (or even

virtually zero) output impedance. In particular, we will see that a non-stable operating

point may result, and that we must attain a negative feedback loop in order to achieve

stable self-linearization.

Suppose that we use an ideal current source to supply the electrical input to the

modulator diode (Figure 2.8). In practice, a reverse-biased photodiode with incident

light could be used to realize a near-ideal current source.

Vmod

Ibias

Inoise

modulator

Figure 2.8 An optical modulator diode biased with an ideal constant current source Ibias. Vmod is the voltage that appears across the modulator, and can be solved given Ibias and the modulator’s current-voltage characteristic. The transient current source Inoise is used to illustrate the feedback present in this system.

Assume for the moment that Inoise is zero. We would like to know where the

modulator will operate given some input current. We can graphically deduce this by

using a load-line analysis, overlaying the current-voltage relationship of an ideal

current source on top of that of the modulator. The x-axis now indicates the voltage

Vmod, and the y-axis is the current passing through a circuit component, whether it be

the modulator or the current source. Since the current source and modulator are

connected in series, the currents through both components must be equal. Hence, the


operating point of this circuit is indicated by the intersection of the curves, where both

currents are equal. Figure 2.9 shows the load-line analysis plot, incorporating the

modulator’s curve in blue along with those for two different possible current sources.

Load-line Analysis

050

100150200250300350

0 10 20 30

Vmod (V)

Cur

rent

(µA

)

a

bc

d

Figure 2.9 Load-line analysis for the circuit shown in Figure 2.8. The vertical axis is the current through a circuit component, and the horizontal axis is Vmod. The blue, red, and green curves represent the behavior of (1) the modulator, (2) an ideal current source of 170 µA, and (3) an ideal current source of 300 µA, respectively.

If a current source at, for example, 170 µA is used, the solution is simple: there is

only one point where the curves intersect, at the point labeled (a). Hence, the voltage

at Vmod would be about 1.5 V. For a current source of 300 µA however, we find three

intersection points: (b), (c), and (d) in Figure 2.9 .

With the current source of 300 µA, the second intersection point (c) is actually an

unstable equilibrium. Suppose that the devices were operating at this state, and a

small amount of noise were introduced into the system. This could be due to a

fluctuation in the current source or in the incident optical beam on the modulator. In


any case, we can imagine that a small amount of current noise might be removed from

the node at Vmod. This would then decrease the voltage Vmod, taking us away from the

equilibrium point.

If the voltage at the node is now slightly smaller, the absorption of the modulator

will increase, and the modulator’s current will increase as well. This is because the

local slope of the modulator’s curve at point (c) is negative. Since the ideal current

source continues to output the same amount of current into the node, there will now be

a net outflow of current away from the node. The voltage at the node will hence

decrease, exacerbating the movement of the circuit’s operation away from the

equilibrium state. The equilibrium point is hence an unstable one, and the state of the

circuit will continue to move until it reaches the first intersection point (b).

In contrast to the case just considered, this first intersection point (b) is a stable

one. Suppose now that some noise in the system momentarily decreases the voltage at

the node. Now the absorption of the modulator decreases, and the diode current will

also decrease. This means that there is a net inflow of current into the node, and the

voltage will rise again, recovering back to its initial state. A similar recovery would

happen if system noise pushed the node’s voltage higher. Moreover, these same

arguments can be applied to show that point (d) is also stable.

Incidentally, note that the system returns to its original stable equilibrium only if

it is not perturbed beyond the unstable state. For example, suppose the circuit starts at

state (b). If enough extra current noise were introduced that pushed Vmod all the way

past (c), the system would not return to (b) but instead move all the way to point (d).

Since the circuit is bistable, it can be used as a memory circuit: to set or reset the

memory, the circuit need only be pushed momentarily past the unstable point. A more

detailed exploration of this function is not relevant for our A/D application and beyond

the scope of this work.

2.2.3 First-order Block Diagram Model

To keep the equilibrium states stable, the circuit has a built-in negative feedback

loop. A block diagram illustrating this feedback loop is shown in Figure 2.10.


Analysis of this block diagram will reveal the conditions for stability as well as the

characteristic small-signal time constant for this first-order system.

Since Ibias is a constant current source, it does not appear in the block diagram.

We also use the variable γ to specify the local slope of the electroabsorption curve,

where

dVdA=γ , (2.12)

and A is the fraction of the input power P that is absorbed by the modulator, assuming

non-saturated operation. In other words, the absolute amount of optical power

absorbed the modulator is

APPabs = . (2.13)

Σ

—

Inode dV/dtInoise1/C 1/s

Vmod

γPPabs

ωheIphoto

Figure 2.10 Optoelectronic feedback loop linking optical absorption with current and voltage. As long as the local slope of the electroabsorption curve γ is positive, we realize a negative feedback loop.

In Figure 2.10, Inode is the total current flowing into the node at Vmod. As Inode

flows into the node, the voltage increases at a rate given by

CI

dtdV node= , (2.14)

where C is the total capacitance at the node Vmod.

The Laplace transform of the integral operation is then applied to dV/dt, in order

to recover the voltage at that node. Iphoto is the photogenerated current of the


modulator, and is subtracted from Inoise since Iphoto serves to discharge the node.

Clearly, as long as the electroabsorption slope γ is positive, we obtain a negative

feedback loop, giving us a stable equilibrium. More specifically, we can solve for the

transfer function of this system. By inspection,

CsI

V node=mod (2.15)

γω

PeVII noisenodeh

mod−= (2.16)

Substituting (2.16) into (2.15) and solving for Vmod, we find

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+=

CPesCI

V

noise γωh

11mod (2.17)

Equation (2.17) describes a classic system with an exponential response [9]. If

Inoise is an impulse input δ(t) with amplitude I0,

( )tII noise δ0= (2.18)then the system’s output is an exponential given by

( ) ( ) ( )tutCI

tVmod τ/exp0 −= (2.19)

where

γωτ

PC

eh= (2.20)

and u(t) is the Heaviside step function.

Note that (2.17) also tells us that the system is stable as long as

0>CPe γ

ωh. (2.21)

The condition of (2.21) then simplifies to

0>γ (2.22)since all other terms are always positive. This is consistent with the discussion earlier

in this section, when we observed that equilibrium points were stable whenever the

slope of the electroabsorption curve γ was positive.


Incidentally, note that for the block diagram of Figure 2.10, we make first-order

approximations in order to calculate the small-signal response to perturbations on

some steady-state solution previously determined by the biasing conditions. Hence, if

we expect the system to respond linearly to a small-signal input (such as a sinusoid),

then we must assume a linear electroabsorption response. However, the “self-

linearization” process explained in Section 2.2.1 does not require linear

electroabsorption. The modulator operates in a self-linearized mode as long as the

steady-state equilibrium is stable (2.22), and we bias the device such that we maintain

the criteria of (2.10) and (2.11). These conditions can be satisfied even if the

electroabsorption curve is non-linear over the range of operation.

2.2.4 Non-ideal Current Source

The analysis of Section 2.2.2 can apply even for current sources with non-zero

output impedance. We can generalize the circuit diagram of Figure 2.6 as shown in

Figure 2.11.

Figure 2.11 Optical modulator diode biased by a voltage source with finite output impedance R.


In this case, the load-line of the biasing source is not horizontal as in Figure 2.9,

but has a slope of 1/R with an x-intercept of Vbias. An example of this is shown in

Figure 2.12, where we overlay the current-voltage curve for the modulator with that of

a 32.5 V power supply that has an output impedance of 90 kΩ. In this case,

intersection point (b) is an unstable equilibrium, whereas points (a) and (c) are stable.

Load-line Analysis

050

100150200250300350

0 5 10 15

Vmod (V)

Cur

rent

(µA

) a b c

Figure 2.12 An example of a load-line diagram for a modulator biased by finite-resistance voltage source. To illustrate a situation with three equilibrium points, we graphically solve the circuit with a 32.5 V bias and a 90 kΩ output impedance.

For this circuit (Figure 2.11), the block diagram is similar to Figure 2.10 but must

now include the characteristics of the electrical bias, as shown in Figure 2.13. This is

because the amount of current sourced by the voltage supply is now no longer

independent of the voltage Vmod.


ωhe

Figure 2.13 Block diagram for the circuit of Figure 2.11. When Vmod increases, it not only causes the modulator’s photocurrent to increase but also reduces the current supplied by the voltage bias. Thus, the effect of Vmod on the voltage source is to reduce Inode by Vmod/R.

The transfer function for the block diagram in Figure 2.13 is

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎠⎞

⎜⎝⎛ ++

=

CPeRsCI

V

noise γωh

11mod (2.23)

The new transfer function of (2.23) introduces two changes to the ideal current

source case. First, the new time constant for the exponential step response is now 1−

⎟⎠⎞

⎜⎝⎛ +=

CPeR γ

ωτ

h. (2.24)

In other words, if R is large, then it will dominate the other term in (2.24), and the

system will respond very quickly to the injection of any current noise. The second

change is that the stability criterion is now

0>+CPeR γ

ωh (2.25)

or equivalently

PC

eR ωγ h−> . (2.26)


2.2.5 Temporal Response to Pulsed Input

Thus far in our analysis, we have focused on solutions in steady-state or in the Laplace

domain. We will now specifically look at the large-signal response of the modulator

in response to a pulsed current input. In particular, we verify that the self-linearization

evident in steady-state cases is also true for a pulse input, in the sense that the total

input charge is proportional to the total absorbed optical energy. We will first show

this to be the case when a current-bias source is present. Then we will show that this

is still the case without a current-bias.

2.2.6 Constant current bias

Consider the circuit in Figure 2.14. We supply an input current Iin(t) to a modulator

with a constant current bias Ibias. Assume that this current source biases the modulator

so that it satisfies three conditions, as long as Iin(t) is zero:

1. The modulator is in a stable equilibrium.

2. The modulator operates in the self-linearized mode.

3. If the voltage across the modulator increases to any value, the current will be

larger.

An example of a bias point that satisfies these three conditions would be point (a) from

Figure 2.9. Note that an alternative way to state condition 3 is that the circuit is never

pushed past an unstable equilibrium to settle in a different stable state. By specifying

this condition, we obtain the relationship

( ) biasmod ItI ≥ . (2.27)Hence, the modulator always serves to reduce Vmod(t) back to its initial state of Vmod(0).

Suppose that Iin(t) is a delta function, so that the total input charge is Qin. Also,

Qin is not so large that we push the modulator diode into the reverse breakdown region.

We would like to show that

( ) bmQdttP in

T

a +=∫0 (2.28)


where Pa(t) is the optical power absorbed by the modulator, m and b are constants

independent of Qin, and T is a sufficiently long enough time that we wait for the

modulator to return to its initial state. In other words, integrating the absorbed power

(which can be calculated by subtracting the output power from the input power) yields

a number that is linearly proportional to the input charge.

Figure 2.14 Optical modulator biased with a constant current supply. The input signal to the modulator is a time-dependent current Iin(t). The capacitance C of the modulator is explicitly included. Qmod(t) is the instantaneous amount of charge that passes through the modulator.

Because of our assumptions, the modulator’s breakdown and diffusion current are

always negligible and therefore the device satisfies the self-linearization conditions

(2.10) and (2.11). Hence, for all time t

( ) ( )

( ) ( )

( )[ ]

( )inbias

T

inbias

T

mod

T

a

moda

QTIe

dttIIe

dttIe

dttP

tIe

tP

+=

+=

=

=

∫

∫∫

ω

ω

ω

ω

h

h

h

h

0

00 (2.29)

In the last step, we make use of the fact that


( ) in

T

o in QdttI =∫ . (2.30)

This is true because at time t=T we have waited long enough for the circuit to return to

its initial stable state. Hence, Vmod has returned to its initial value, and all the charge

Qin that we had dumped into the node has been removed.

Since T and Ibias are both constants, we can conclude from (2.29) that the

integrated power is indeed linearly proportional to the input charge.

2.2.7 No current bias

Vmod

Iin(t)

modulator Imod(t)C

Figure 2.15 Pulsed current input to a modulator with no bias.

The linear relationship of (2.28) can actually hold true even if no current bias is

provided (Figure 2.15). In this case, when the initial input charge is injected on Vmod

the modulator will initially operate in a region where the self-linearization conditions

of (2.10) and (2.11) hold. However, at some point in time Vmod will drop to a level

when the diffusion current becomes significant. Let us call this voltage Vd, and define

td so that Vmod(td)=Vd. Then we can write

( ) ( ) ( )∫∫∫ +=T

t a

t

a

T

ad

d dttPdttPdttP00

(2.31)


The first integral term describes the modulator’s behavior until td, when self-

linearization still holds. We can thus write

( ) ( )∫∫ = dd t

mod

t

a dttIe

dttP00

ωh . (2.32)

This is simply the amount of charge that must be removed from Vmod in order to reach

Vd. Thus,

( ) ( )din

t

a CVQe

dttPd −=∫ωh

0 (2.33)

We can reasonably assume that after td, Vmod smoothly decreases back to

Vmod(0)=V0. Hence we can write

( ) ( )∫∫ = 0V

V modmod

moda

T

t add

dVdV

dtVPdttP . (2.34)

Since we have written (2.34) solely has a function of voltage, all of its terms are

independent of Qin. We can thus write (2.31) as

( ) ( ) ( )

constantQe

dVdV

dtVPCVQe

dttP

in

V

V modmod

modadin

T

ad

+=

+−= ∫∫ω

ω

h

h 0

0 (2.35)

We conclude then that the integrated absorbed optical power is still proportional

to input charge, even if no separate current bias is used, and even if that input charge is

provided from a pulsed source.

2.2.8 Input Range and Speed

The length of time it takes for the modulator to convert an input charge Qin can be

characterized by the time constant τ given by (2.20). Recall, however, that the

derivation of (2.20) was based on a small-signal analysis. This assumption can be

made only for cases where Vmod is below the first exciton peak Vpeak (about 5 volts in

Figure 2.9). When the input charge is larger than the value given by

peakin CVQ = , (2.36)

Vmod will be pushed past Vpeak, and the modulator’s conversion time will be much

longer than τ. In cases where the overall A/D system’s requirements call for


aggressively taking advantage of the modulator’s time constant τ, (2.36) effectively

sets an upper limit to the input range of the modulator.

2.3 Differential Self-linearization

Rather than using a single modulator to linearly convert an electrical signal, we can

instead employ a pair of modulators connected in series (Figure 2.16) [10][11]. The

current input is injected into the node in between the two modulators. Each modulator

has an incident CW optical beam. The output is the difference between the powers of

the two optical beams reflecting off the modulators. We will discuss the operation of

the self-linearized modulators in this differential mode, and hence see what advantages

we gain from such a scheme.

Figure 2.16 Self-linearized modulators connected in a totem-pole topology. Voltage sources of equal magnitude but opposite polarity bias the modulator pair. Each modulator has an incident continuous-wave beam. The input current signal is injected onto the node Vmod in between the two modulators.

2.3. DIFFERENTIAL SELF-LINEARIZATION 47

2.3.1 Equilibrium States

We first consider the bias state of the modulators when there is zero input current. We

can again use a load-line analysis to graphically solve for the modulators zero-input

state (Figure 2.17). The x-axis is the voltage Vmod, while the y-axis is the current

flowing through the device. For this sample circuit, the biases used are ±3 V.

Because of current conservation, in steady-state the circuit must operate at the voltage

where the two currents are equal. This occurs at Vmod = 0.

Load-line Analysis

050

100150200250300350

-10 -5 0 5 10

Vmod (V)

Cur

rent

(µA

) I1 I2

Figure 2.17 Load-line analysis for the circuit of Figure 2.16. The bias voltages are ±3 V, and the input optical beams are 0.90 mW at 857 nm. The sole equilibrium state occurs at the intersection of the two curves, where the currents through both devices are identical due to current conservation in the steady state. Note that the zero-current conditions occur near ±4 V rather than at the biases of ±3 V, since even with no external voltage bias a modulator with incident light produces a net current in the reverse-diode direction.

This equilibrium state happens to be a stable one. For example, if some amount

of noise causes I1 to be momentarily larger, then Vmod will increase. From the plot, if

Vmod is positive then I2 is larger than I1, leading to a net current flowing out of the node.

This causes Vmod to decrease, pushing the circuit back to its original state.


Now suppose we use a larger bias of ±6 V. This results in the load-line diagram

of Figure 2.18. Reminiscent of the load-line analysis of a single modulator with a

finite impedance bias (Figure 2.12), we are now faced with three possible equilibrium

states: (a), (b), and (c). Also as before, the middle state (b) is unstable. If Vmod is

perturbed to a higher voltage, I1 is now larger than I2. This leads to a net inflow of

current, so that Vmod keeps increasing away from its original state. On the other hand,

states (a) and (b) are stable, and the circuit recovers to those states when perturbed.

Load-line Analysis

050

100150200250300350

-10 -5 0 5 10

Vmod (V)

Cur

rent

(µA

) ab

cI1 I2

Figure 2.18 Load-line analysis calculated in the same way as Figure 2.17, except that biases of ±6 V are used. Three possible equilibrium states result. (a) and (c) are stable, while (b) is unstable. Note that a modulator with no voltage bias across it still produces current when excited by incident light.

2.3.2 Self-linearization with Constant Current

To verify that we retain self-linearization for this differential circuit with a constant

current input, consider (Figure 2.19). Here we have combined both modulators from

the circuit into a similar element, and plotted their combined current-voltage

relationship on a single curve. This represents the total current leaving Vmod due to the

modulators’ action. The second curve is that of the current source, which for this


illustrative example we set to 100 μA. Here we have returned to the lower biases of

±3 V, where only one stable equilibrium exists at Vmod=0 V.

Load-line Analysis

-350-250-150

-5050

150250350

-10 -5 0 5 10

Vmod (V)

Cur

rent

(µA

)

Figure 2.19 Load-line analysis for the circuit in Figure 2.16, where we set Iin to be a constant 100 μA. The blue curve represents the current leaving Vmod through the modulators. The horizontal green curve is the current supplied to Vmod from the current source. As before, the circuit is in a stable state when the net current is zero at the intersection of the two curves.

Knowing the state of the circuit for an input current of 100 μA, we see that Vmod is

about 1 V. This means that the biases across modulators 1 and 2 from Figure 2.16

are 5 V and 7 V, respectively. From the current-voltage (Figure 2.9) and absorption-

current (Figure 2.60) plots for this modulator, we see that the modulator remains in the

self-linearized region. However, by introducing a positive input current we have

decreased the absorption of modulator 1, and increased that of modulator 2. Thus, the

final output optical signal is given by the differential signal

12 absabsout PPD −= (2.37)

( ) ( )1122 outinoutinout PPPPD −−−= (2.38)If we supply the same input power to both modulators, we obtain


21 outoutout PPD −= . (2.39)From (Figure 2.17) it is clear that as we increase or decrease Vmod away from

equilibrium, it is the presence of forward diffusion current which first breaks the self-

linearization condition of (2.11). In practical applications of this differential circuit,

this implies that the one of the modulators is no longer self-linearized when Vmod

approaches either the positive or negative voltage bias. For any differential modulator

circuit then, we can determine the input current range once we know the current-

absorption-voltage relationships at a specific optical power and wavelength.

2.3.3 Block Diagram

Just as in the single-modulator case, we can use small-signal models of all circuit

components to model the system with a block diagram. As before, we can use this

block diagram to determine the stability criteria and the first-order time constant.

ωhe

ωhe

Figure 2.20 Block diagram of the circuit from Figure 2.16, using small-signal (first-order) parameters of the circuit elements. In this case γ1 and γ2 are the local slopes of the electroabsorption curves for modulators 1 and 2.

This block diagram is essentially identical to Figure 2.13, where we had modeled

the single modulator biased with a voltage source of impedance R. However, here we

have replaced R with a small signal model for modulator 1. Note the minus sign in

front of γ1, since an increasing Vmod serves to decrease the bias across the modulator.


The photocurrent of modulator 1 must be subtracted from that of modulator 2, since

the negative feedback path represents the net current flowing out of Vmod.

The transfer function for the block diagram is given by

( )⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

++=

22111

11

γγω inin

noise

mod

PPC

esCIV

h

. (2.40)

For a differential system, the modulators would typically be perfectly balanced. In

this ideal case, the input powers to both modulators would be equal and the

electroabsorption curves would also be identical:

21

21

γγγ ==== ininin PPP

(2.41)

In this case (2.40) simplifies to

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

+=

CPesCI

Vinnoise

mod

γω

211

h

. (2.42)

To obtain a stable equilibrium, we must satisfy the condition

0>γ , (2.43)and the time constant is given by

γωτ

inPC

e 2h= . (2.44)

While (2.44) appears to show a system twice as fast as the single modulator case, the

capacitance C will actually be increased by the presence of the second modulator. If

the capacitance at Vmod is dominated by the modulators then

mod2CC ≈ (2.45)and the speed of the differential conversion is actually the same as for the single

modulator case for the same input beam powers [12].


2.3.4 Impulse Response

Just as in the single-modulator case, we still retain self-linearized conversion of input

charge into absorbed optical energy. Suppose we have a current input such that Qin

charge is deposited onto Vmod. Assume that just before the input charge, the circuit is

in a stable state, and that at no time do we push the circuit past an unstable equilibrium.

If we wait a long enough time T for the circuit to recover to its initial state, then

referring again to the circuit from Figure 2.16 we have

( )∫ −=T

in dtIIQ0 12 . (2.46)

Define

( ) ( )02,12,12,1 ItII −=Δ (2.47)

( ) ( )02,12,12,1 PtPP −=Δ (2.48)

We then have

( )( ) ( )( )∫ Δ−−Δ−=T

in dtIIIIQ0 1122 00 (2.49)

In the initial state we were at steady-state equilibrium and so the currents were

identical. Moreover, we have assumed that during the conversion process we retain a

linear current-to-absorption relationship. Hence,

( )

( )

( )∫

∫

∫

Δ−Δ=

Δ−Δ=

Δ−Δ=

T

outout

T

absabs

T

in

dtPPe

dtPPe

dtIIQ

0 21

0 12

0 12

ω

ω

h

h (2.50)

Without assuming a balanced system, we see that we can linearly convert an input

charge into an integrated optical signal. Specifically, we would integrate the

perturbation of the output power away from steady-state for both modulators, and then

take the difference.

If on the other hand we did have a balanced system, then

( ) ( )00 21 outout PP = (2.51)and so


( )

∫

∫

=

−=

T

out

T

outoutin

dtDe

dtPPeQ

0

0 21

ω

ω

h

h (2.52)

2.3.5 Motivation

A primary motivation for using a balanced differential scheme is that it aids rejection

of common mode noise. Since the output signal is the difference between the outputs

of two modulators, then noise which is present on both modulators will be rejected if

the system has been perfectly balanced.

In a typical differential system, the two input powers Pin1 and Pin2 would be

derived from a single laser source using a 50/50 beam splitter. In this case, any noise

on the laser would be present to an equal degree on both Pin1 and Pin2. Since

( ) ( )2211 absinabsinout PPPPD −−−= (2.53)such laser noise would be subtracted out from the differential output.

A second possible source of noise might come from the voltage biases. In this

case a differential circuit would help reduce such noise. Suppose that noise on the

positive voltage bias injected extra charge onto the n-region of modulator 1 from

Figure 2.16. Assuming that this noise is small enough, it will not push the circuit to a

non-linearized region of operation, nor will it prevent the circuit from eventually

recovering to the same steady-state condition as before. In this case, the noise charge

Qnoise can only have taken one of three possible paths:

1. Return to the positive voltage source without entering the active region of

either modulator.

2. Travel through modulator 1 to Vmod and then returned back to the positive

bias through modulator 1 again.

3. Travel through both modulators and enter the negative voltage source.

(We assume here that the current signal input represents an ideal current source

that has infinite impedance.)


Figure 2.21 Differential modulator circuit, depicting the three possible current paths for supply-line noise. For the three paths, the noise charge (1) does not affect the optical response of either modulator, (2) leads to an increase and then decrease in absorption in modulator 1, and (3) causes both modulators to absorb extra optical energy.

In the case of path 1, the absorption of neither modulator is affected, and hence no

changes to Dout are introduced. In the case of path 2, the noise charge will result in a

momentary increase in Pabs1, such that the integrated optical energy noise is given by

noisenoise Qe

E ωh= . (2.54)

This is then followed by a decrease in integrated Pabs1 of equal magnitude in Enoise.

Finally, in the case of path 3, Qnoise causes the absorbed energy of both modulators 1

and 2 to increase by Enoise as given in (2.54).

For paths 2 and 3, Qnoise travels through a modulator’s active region twice. As

long as this happens within the sampling period T, the final integrated optical output

signal will not be affected. This effectively low-pass filters any noise in the lines

supplying electrical bias to the modulators.

Putting noise considerations aside, there are a few other advantages for employing

a differential system. For example, we now give ourselves the flexibility for having


negative input signals. This would have been difficult in the single-device case, since

the modulator must remain in reverse bias at all times. One workaround solution

would be to use a modulator in conjunction with an ideal current source as a biasing

mechanism, but we would then still need a second device without gaining the noise

immunity advantages discussed above.

Another benefit to differential operation is that this method can help mitigate non-

linear effects due to voltage-dependent variations in the modulator’s capacitance. The

modulator is able to linearly convert input charge to absorbed optical energy.

Sampling an input voltage implies that the voltage is multiplied by the input

capacitance before the signal can be converted by the modulator. Thus, if the input

capacitance is not constant, it will introduce some non-linearities. Increased reverse

bias on the p-i-n modulator can result in a slight change in capacitance as the depletion

width in the doped material increases.

On the other hand, when the input voltage of the differential pair increases, the

capacitance of the bottom modulator decreases, while that of the top modulator

increases. This effect does not completely cancel out the voltage-dependent

capacitance, since the dependence is not linear. However, it does help in reducing the

effect. Figure 2.22 shows the change in capacitance as a function of voltage. In this

simple calculation, we model the capacitance of the p-i-n device as a simple parallel-

plate capacitor

tAC ε= (2.55)

where A is the device area, ε is the dielectric constant of GaAs, and t is the thickness

of the intrinsic region and depletion widths. The total thickness of the depletion

widths in the p- and n-type regions depends on the applied forward bias voltage Va and

is given by

( )abiDA

DA VVNN

NNe

w −⎟⎟⎠

⎞⎜⎜⎝

⎛ += ε2 (2.56)

where e is the electron charge, NA and ND are the acceptor and donor doping

concentrations, and Vbi is the diode’s built-in voltage [10].


For the parameters used, we see that using the differential mode drastically

reduces the capacitance’s dependence on voltage bias. Of course, the percentage

deviation shown in Figure 2.22 is further mitigated by any capacitance that does not

come from the modulators (such as the sampling switches). Nevertheless, we see the

clear improvement that comes from moving from a single-ended to a differential mode.

Capacitance Dependence on Bias

-4%-3%-2%-1%0%1%2%3%4%5%

0 2 4 6 8 10

Reverse Voltage Bias (V)

Per

cent

age

Devi

atio

n of

Ca

pact

ianc

e (%

ΔC) Single Modulator

Differential Modulator

Figure 2.22 Voltage bias dependence of the capacitance of a GaAs p-i-n diode. Changing the reverse bias of the diode causes the depletion width in the doped regions to vary, thus leading to changes in the device capacitance. The vertical axis shows the capacitance as the percentage deviation from the average capacitance. For an input voltage range of 10 V, the single modulator exhibits a capacitance fluctuation of about ±3.5%, while the fluctuation is reduced to ±0.5% in the differential configuration. In this calculation, the built-in voltage is assumed to be the bandgap voltage of 1.5 V. The temperature is 300 K, the intrinsic region is 0.625 µm thick, and the p and n regions are doped to 1×1019 and 5×1018 cm-3, respectively. These device parameters are approximately those used for the wafer structure processed for this work at Stanford University.

A final advantage to the differential scheme involves the receiver circuits used to

detect the modulator outputs. Since typical circuits are designed for differential

operation, the use of differential optical beams can make receiver design a little easier.


2.3.6 System Trade-offs

As a final note, the use of differential modulators does not substantially affect the

system trade-offs that are present in the single modulator case. Suppose we have a

base case, where we use a single-ended modulator of size A and capacitance C. With

an input optical power of Pin, the time constant is τ and the modulator can accept input

currents ranging from Imin to Imax. Also, if we assume that the optical beam size fills

the device area A we have a saturation power of

AIP satsat = (2.57)where Isat is an intrinsic property defined in (2.4) that is independent of device size.

We compare this base case with two other situations: a single-modulator with

twice the area as the base case, and a differential scheme that uses two modulators

from the base case. Table 2.1 summarizes the results.

Parameter Single-ended 2 × Single-ended Differential

Size A 2A 2A

Capacitance C 2C 2C

Input Optical Power Pin 2Pin 2Pin

Speed τ τ τ

Input Range Imax–Imin 2 (Imax–Imin) 2 (Imax–Imin)

Saturation Power Psat 2Psat 2Psat

Table 2.1 System parameters for three modulator configurations: (1) a base case, (2) the base case with twice the area and optical input power, and (3) a differential case using a pair of base case modulators.


When the single-ended modulator is doubled in size, the capacitance also doubles.

If we now also double the input optical power, we can retain the same time constant τ

as before. Moreover, the optical power absorbed at the first exciton peak also doubles,

and so the input current range for the device increases twofold as well. Finally, with a

larger device area the saturation power also increases.

In the differential case, the size and capacitance increase because we are now

using two modulators. Two optical beams are needed, so the total input power is 2 Pin.

The time constant remains τ as shown from (2.44) and (2.45). The input current range

doubles since the input can be either negative or positive. Finally, the saturation

power has increased since it includes the power from both optical beams.

Of course, the differential circuit is not without some disadvantages. The primary

effect is increased optical system complexity, since twice the number of optical beams

must be imaged from the transmitter to the receiver. The need for an extra negative

voltage bias also increases the interconnect complexity on the modulator chip. Finally,

while the basic system trade-offs are not affected as shown in Table 2.1, certain more

fundamental restrictions do place limits on the trade-offs we can make. For example,

the diffraction-limited spot size effectively sets a minimum for the device area.

Fabrication practicalities also limit the minimum size of the devices. Thus, the single-

ended circuit can always achieve a smaller capacitance than is possible with the

differential scheme.

2.4 System Requirements

Consideration of the overall A/D converter system places certain requirements on the

SEED’s device performance. Most notably, these include the linearity of the

modulator’s electro-optic conversion process, speed of operation, shot noise, and

power required.

The SEED must be able to complete the electro-optic conversion of sampled

voltage quickly enough so that it is ready for the next sampling event on the channel.

Since the proposed channel speed is 1 gigasample/second, the SEED has at most 1 ns

2.4. SYSTEM REQUIREMENTS 59

to complete the conversion. (Of course, once the conversion process is completed the

optical signal must still be detected and processed by a detector and receiver circuit.)

2.4.1 Linearity

We have previously provided motivation for using the modulator in a self-linearized

mode because we are using the device for an analog-to-digital conversion application.

To provide a simple, more quantitative illustration, we can perform a simple

simulation using the data previously shown in Figure 2.6 and Figure 2.7.

In Figure 2.7 we see that a linear relationship exists for input currents ranging

between about 120 and 320 µA. This range of currents corresponds to a voltage range

of 0.5 to 4.0 V. We can thus compare the linearity of the absorbed power with respect

to either voltage or current for these ranges of operation. To do so, we posit a

sinusoidal input with a bias and amplitude that correspond to the ranges noted above.

Using Matlab, we then fit high-order polynomials to Figure 2.6 and Figure 2.7 to

create analytic functions, and then use these as transfer functions to convert electrical

input to optical output. The resulting optical output signals are shown in Figure 2.23,

overlaid on an ideal sinusoid.

Just from visual inspection it is clear that the current-based mode of operation

provides far more accurate, linear conversion than the voltage-based one. For the

time-discretization used in this particular simulation, we calculate the linearity for an

ideal analog-to-digital converter that utilizes these transfer curves. In this particular

case, the resolution for voltage-based operation is about 2 bits, while that for current-

based operation is about 5 bits. While the exact resolution given here is not

necessarily significant, the difference between the two indicates the vast resolution

improvement available when we use the modulators in a current-based, self-linearized

mode.


-3 -2 -1 0 1 2 3-1

-0.5

0

0.5

1

Input Signal

Out

put S

igna

lPerfectly LinearVoltage BasedCurrent Based

Figure 2.23 Plot comparing voltage-based and current-based operation of the optical modulator with an ideal sinusoid. The simulation uses experimental data from Figure 2.6 and Figure 2.7.

2.4.2 Speed Issues

As seen from section 2.2.3, to first order the modulator recovers exponentially to a

steady-state condition after a pulsed input. The time-constant associated with this

recovery tells us how much time the modulator needs to convert a sampled signal,

before it is ready to convert another sample. We present here a simple analysis using

the first-order model to derive the trade-off between resolution and speed. We

specifically do this for the single-ended modulator, though the analysis is equally

applicable to the differential case.

Mathematically, the temporal response for our model is a simple exponential

decay. The signal of interest is the integral of this temporal response. If we allow the

modulator an infinite amount of time to perform the conversion, then we recover the

full value of the sampled signal. Roughly speaking, we can cut short this conversion

time as long as we are within one-half of the least significant bit (LSB) of the full

value.


Assume that for a full-scale input, the modulator’s output as a function of time is

given by

( ) ( )⎩⎨⎧

≥<

−=

00

/exp0

tt

ttf

τ (2.58)

Hence, the actual output signal is the integral of this function

( )τ=

= ∫∞

0dttfg FS (2.59)

In the electro-optic conversion process, we incur an error because we cannot wait

forever for f(t) to return to zero. If we cut short the conversion at time t =T, then the

magnitude of the error is given by

( )( )ττ /exp T

dttfET

−=

= ∫∞

(2.60)

Suppose that we would like the resolution of this conversion to be N bits. We can

withstand an error of one-half the least significant bit (LSB/2). The full-scale signal is

τ as shown in (2.59), so setting the error equal to LSB/2 yields

1222

1

−−=

⋅=

N

NE

τ

τ. (2.61)

Setting (2.60) equal to (2.61),

( ) 12/exp −−=− NT τ (2.62)which gives

( ) 2ln1/ += NT τ . (2.63)Equation (2.63) roughly tells us how fast the modulator needs to be in order to

meet a resolution requirement. For the goals of our A/D proposal, the sampling period

is 1 ns and the desired resolution is about 3 to 5 bits. Using (2.63), this tells us that the

time constant of the modulator must be at least 4 times smaller than the sampling

period, or about 0.25 ns.

Figure 2.24 shows the trade-off between resolution and sampling rate. Note that

this is an upper bound on the sampling rate. The actual sampling rate will be lower,


since the other components of the overall analog-to-digital converter system will also

add errors to the conversion process.

Sampling Period vs. Resolution

0123456789

0 1 2 3 4 5 6 7 8 9 10

Resolution (in bits)

(Sam

plin

g Ti

me)

/ (T

ime

Con

stan

t)

Figure 2.24 Required modulator speed as a function of the resolution (2.63). The vertical axis gives the number of time constants we must wait for the modulator to finish the electro-optic conversion. We use a first-order (small-signal) model of the modulator’s dynamics for this analysis.

2.4.3 Noise

Another factor that can impact the resolution of the electro-optic conversion process is

the presence of noise in the system. While we did not explore this in depth

experimentally, we can consider the impact of shot noise and thermal noise in the

modulator’s conversion process.

2.4.4 Shot noise

Shot noise in a signal comes from the fact that the signal is composed of discrete

elements. Examples of this include photons in a beam of light or electrons in an


electrical current. The random arrivals of these discrete elements follows a Poisson

process, which essentially means that (1) the process has no memory and (2) the

probability of an arrival event during a small interval of time is proportional to the

length of that time interval.

In such a case, if we build a histogram representing the total number of arrivals

during some period of time, the histogram follows a Poisson distribution. The

variance of this distribution is simply equal to the mean, and so the standard deviation

is the square-root of the mean [14].

Our goal is to ensure that the signal-to-noise ratio (SNR) due to shot noise is

larger than the SNR required for an A/D conversion with resolution N bits. We

already know the latter SNR figure from Appendix A, which we convert here from

units of decibel to actual ratio for convenience: NSNR 602.0176.010 += . (2.64)

We now need to calculate the former, which we will call SNRshot.

The “signal” for SNRshot is the signal power contained in a full-scale input. In this

discussion we are interested in the capabilities of the optical modulator, so we will

consider what input signals the modulator is capable of converting. One parameter

used to characterize optical modulators for digital applications is the contrast ratio CR.

For our specific application, the maximum instantaneous absorbed power is equal to

the zero-input output power divided by CR. By making the small-signal assumption,

we can then use the characteristic time constant τ to describe the response of the

modulator to a full-scale input signal:

⎥⎦⎤

⎢⎣⎡ −−=

CRtPPout

)/exp(10τ (2.65)

where P0 is the output of the modulator with no input signal. As we can see from

(2.65), the peak absorbed power occurs at t=0 when Pout is P0/CR. The output signal

we are interested in is the integral of the optical output power. Equivalently, the

amplitude of the full-scale output signal is represented by the number of photons

absorbed by the modulator. Note that we are here considering single-ended operation,

though the analysis can easily be extended to the differential case.


The “noise” for SNRshot is the signal power contained in the shot noise when the

input signal is zero. The amplitude of this noise signal is the standard-deviation of the

total number of photons collected during a sampling period when the input signal is

zero. As discussed earlier, for this Poisson process the noise is then simply the square-

root of the total number of photons collected (on average) during the sampling

window. We can hence write an expression for SNRshot:

( ) ( )

( )

2

0 0

0 0

/

/

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡−

=

∫∫

ω

ω

h

h

T

T

out

shot

dtP

dtPPSNR (2.66)

In (2.66) both the numerator and denominator have units of (number of photons).

The number of photons is proportional to the amplitude of the original input signal.

Since SNR is the ratio of the signal-to-noise powers, we must square the expression

within the square-brackets to convert from amplitude ratio to power ratio. Equation

(2.66) simplifies to

( )[ ]22

0 /exp12

ττω

TT

PSNRshot −−⎟

⎠⎞

⎜⎝⎛=

h. (2.67)

As expected, the SNR power due to shot noise increases according to the background

power P0, since the relative amplitude of the noise increases according to the square-

root of the power.

Setting (2.64) to be greater than (2.67), we can solve for the minimum power, P0,

needed to overcome shot noise, given a desired A/D resolution of N bits:

( ) ( ) NTT

CRP 602.0176.02

0 10/exp1

1 +⋅⎥⎦

⎤⎢⎣

⎡−−

≥ ωττ

h . (2.68)

We can numerically evaluate (2.68) as a function of N¸ given a sampling period T

of 1 ns. The required time constant, τ, for the modulator is dictated by T and N, via

(2.63). However, the time constant τ is dependent on the input optical power, Pin, and

the background output power, P0, can be related to the input power as

00 RPP in= (2.69)


where R0 is the reflectivity of the modulator with zero input current. If the minimum

background power P0 from (2.68) does not imply a large enough Pin to give the

modulator the required speed, then we must use a higher input power.

Figure 2.25 plots the needed optical input power as a function of resolution in bits.

One curve shows the power needed to overcome shot noise, while the second shows

the power needed to make the modulator sufficiently fast. The actual power required

will then be the larger of the two. For this plot, we use parameters comparable to

those of devices actually tested in this work, as shown in Table 2.2.

Required Input Power Due to Shot Noise and Speed

1.0E-04

1.0E-03

1.0E-02

1.0E-01

1.0E+00

1.0E+01

0 1 2 3 4 5 6 7 8 9 10

Resolution (bits)

Inpu

t Pow

er (m

W)

Noise LimitedSpeed Limited

Figure 2.25 Required input optical power as a function of A/D resolution. The solid curve represents the needed power due to shot-noise considerations, while the dashed curve is due to device speed requirements. Only at high resolutions near 10 bits do shot-noise considerations dictate the necessary optical power. The parameters used for the plot are typical for the modulators used in this work and shown in Table 2.2.

As is evident from Figure 2.25 it is the required modulator speed, not the shot

noise requirement, which dictates the necessary power at low resolutions. Only at

high resolutions near 10 bits is the optical power set by noise considerations. For


operation at 6 bits of resolution, about 3 mW would be required — well below a

saturation power of ~20 mW. (We approximate this saturation power by using a pair

of optical beams with diameters of 12 μm, and assuming a saturation intensity of

about 10 kW/cm2 for our wafer structure and operating voltages [7].)

Figure 2.25 also seems to suggest that there is little penalty to using these

modulators at a resolution of 9 or 10 bits rather than the project goal of about 3 to 5

bits. However, the input power requirement, at least from a speed requirement, does

scale linearly with resolution in bits, as is apparent from (2.63). (This is not quite so

clear from Figure 2.25, since power is plotted on a logarithmic scale.) Furthermore,

noise from other components in the A/D system — such as the sampling switch, the

quantizer circuit, or the optical and electrical distribution networks — can limit the

overall performance.

Parameter Variable Value

Total Capacitance C 40 fF

Wavelength λ 850 nm

Sampling Period T 1 ns

Electroabsorption Slope γ 0.1

Maximum Contrast Ratio CR 2

Peak Reflectivity R0 0.7

Table 2.2 Typical modulator device parameter values.

The parameter values from Table 2.2 imply a full-scale input voltage of about 10

or 20 volts. This is a bit high, and a more reasonable full-scale voltage might be 4

times smaller. In such a case, the requirement of 6 bits of resolution at 20 volts


essentially converts to 8 bits of resolution at 5 volts. Even here, we are not limited by

shot noise, and the power required for a low enough device time constant increases

only to 4 mW.

In order to overcome shot effects, note that we can always increase the input

optical power and device size by the same amount. The larger optical power reduces

the effects of shot-noise. At the same time, by increasing the device area as well, we

maintain the same device speed and input intensity, thus avoiding hitting the saturation

intensity limit.

2.4.5 Thermal noise

Thermal noise is the cause of so-called “kT/C” noise that is present on voltage from

charge stored on a capacitor. It is due to the thermal noise present in a resistive

element through which current passes in order to charge up a capacitor. It is

independent of the resistor because even though the voltage noise power is

proportional to R, the noise bandwidth is inversely proportional to the RC time

constant [15].

In our case, the resistive element is the photoconductive sampling switch which

samples the input voltage onto the capacitance of the modulator. The thermal noise on

the sampling capacitance is simply given by

CkTVthermal =2 . (2.70)

We can thus write the signal-to-noise ratio due to thermal noise as

( )2/ thermalFSthermal VVSNR = . (2.71)

Setting this to be larger than (2.64), we find that

NthermalFS VV 602.0176.010 +≥ . (2.72)

Using (2.72) we plot the minimum full-scale voltage as a function of resolution in

Figure 2.26. As we can see, operating the modulator at a few volts implies negligible

effects from thermal noise.


Required Full-Scale Voltage Due to Thermal Noise

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0 1 2 3 4 5 6 7 8 9 10

Resolution (bits)

Full-

Scal

e Vo

ltage

(V)

Figure 2.26 Minimum full-scale voltage needed to overcome shot noise. With a capacitance of 40 fF, the thermal noise sets a minimum full-scale voltage well below the typical modulator operating range of a few volts.

2.5 Preliminary Results

Early work on the self-linearization of self-electrooptic effect devices (SEEDs)

demonstrated operation where the input current is a constant or DC current [8].

Subsequently, researchers modulated the input current in a sinusoidal fashion, and

showed that the linear response was still present for input frequencies below a

characteristic frequency [11]

CPe

f in

ωπγh2

= . (2.73)

This of course is simply the inverse of the time constant we derived in (2.20). Our

initial goal then is to demonstrate that linear conversion is retained, even in cases

where the input current has a bandwidth higher than the characteristic frequency.

Photodiodes represent a simple way of implementing a near-ideal current source.

A reverse-biased photodiode with incident light supplies a current that has a very high

2.5. PRELIMINARY RESULTS 69

differential resistance. Moreover, by modulating the incident light we can modulate

the input current into the SEED.

Figure 2.27 A reverse-biased photodetector can serve as a near-ideal current source for the SEED. The magnitude of the input current is set by the power of the light incident on the photodetector. The SEED modulates the input power Pin. In the figure shown here the SEED operates in reflectance instead of transmissive mode, so that the output power Pout exits the device on the same side as Pin.

In our first implementation of the circuit shown in Figure 2.27, we use a silicon

photodiode excited by a directly modulated red light emitting diode (LED) as our

current source. By switching the LED on and off, we can toggle the current that is fed

from the photodiode to the SEED. With a constant input power to the SEED, the

output power will then modulate accordingly.

Using external wires, we connect the photodiode to a SEED located on a separate

chip. The SEEDs used in these initial experiments were previously fabricated at Bell

Laboratories, and have the structure given in Table 2.3 [16].

V bias

+ -

ω h

Pin Pout

n-doped

intrinsic

p-doped

SEED


Description Material Thickness (Å) Dopant Type

cathode Al0.11Ga0.89As 3000 p = 1×1019/cm3

buffer Al0.11Ga0.89As 200 undoped

barrier/well stack 60 × Al0.3Ga0.7As/GaAs 60 × 60/100 undoped

first barrier Al0.3Ga0.7As 60 undoped

buffer Al0.11Ga0.89As 5000 undoped

anode Al0.11Ga0.89As 5000 n = 5×1018/cm3

reflector stack 15 × AlAs/ Al0.11Ga0.89As 15 × 723/599 undoped

Table 2.3 Epilayer wafer structure of modulators used in experiments. The modulators were previously fabricated at Bell Laboratories.

In Figure 2.28, two plots are shown, both versus time. The top shows the LED’s

drive voltage, which is a square wave that changes between 0 V and 1.6 V. The

bottom curve depicts the optical power reflected from the SEED. As expected, the

reflected power drops when the LED is on (since the LED provides a positive input

current). Conversely, when the LED is off, it supplies zero input current and the

SEED’s reflected power returns to its higher level.

While this preliminary experiment demonstrated the qualitative behavior of the

SEED under pulsed current conditions, the response time of the SEED was only on the

order of 100 ms. This slow speed was due to our use of a slow LED and large-area

photodiode. Hence, our next series of experiments employed a different method for

realizing a current source. We replaced the LED with a helium-neon (HeNe) laser and

we also switched to a smaller area photodiode to provide the input current to the

SEED (Figure 2.29).


Figure 2.28 LED drive voltage (top) and SEED output power (bottom) as a function of time. When the LED drive voltage is high, the photodetector outputs current to the SEED leading to higher absorption and hence lower output power. The output power changes with a time constant on the order of 100 ms.

In order to create pulsed input current, we modulate the HeNe beam that drives

the current-producing photodiode. This modulation is provided by an acousto-optic

modulator (AOM) manufactured by Brimrose Corporation. In an AOM, an acoustic

wave introduced to an optical material creates a periodic refractive index. This index

profile leads to a grating, so that almost all the power in an incident laser beam at the

appropriate angle will diffract to the first order. The acoustic waves of an AOM are

created by a piezo-electric material driven by a RF source. By turning this RF source

on and off, we can then modulate the optical output from the AOM to the first-order

diffractive angle.

To vary the total amount of charge injected onto the SEED, we can vary the duty

cycle of the square wave used to turn the AOM on and off. This allows us to test

whether the optical energy absorbed by the SEED is indeed linearly proportional to the

amount of charge that the silicon photodiode feeds to the device. In Figure 2.30, we

plot the number of photons absorbed by the SEED against the number of injected


electrons in a single cycle of the AOM’s control voltage. Not only do we see a linear

relationship, but we also see a near-unity slope when we plot absorbed photons versus

injected electrons. This supports the idea that each electron-charge placed on the

SEED can only be discharged by an electron-hole pair that has been generated by an

absorbed photon.

Figure 2.29 Test circuit for operating the SEED under pulsed current conditions. A pulsed HeNe beam incident on a photodetector creates the input current pulses. An acousto-optic modulator (AOM) modulates the HeNe laser. A square-wave function generator controls the modulation of the AOM. When the AOM is on, the HeNe power is diverted to the first diffractive order and triggers the photodiode. When the AOM is off, the HeNe power passes straight through the modulator.

V bias

+

–

n-doped intrinsic p-doped

SEED

helium-

neon laser

AOM

RF Driver

square-wave function

generator

Pin Pout


Absorbed Energy vs . Charge Injection

7.2E+12

7.4E+12

7.6E+12

7.8E+12

8.0E+12

8.2E+12

0.0E+00 2.0E+11 4.0E+11 6.0E+11 8.0E+11 1.0E+12 1.2E+12 1.4E+12

Injected Electrons

Abs

orbe

d Ph

oton

s

Data

Linear Fit (slope = 0.9)

Figure 2.30 Linear electro-optic conversion in SEED. As we increase the number of electron-charges injected onto the device, the number of photons absorbed from an input beam increases linearly. Slope of linear fit is close to the ideal case, where a single electron-charge leads to the absorption of a single photon.

While this result was very encouraging, the test circuit we used for this

demonstration was still much slower than that required by our ultimate A/D system.

Figure 2.31 shows a plot of the input current and output power as a function of time,

where the vertical axis has units of (number of particles)/sec. From the data, we see

that the time constant of the input current is on the order of milliseconds, while our

goal is to achieve speeds on the nanosecond timescale.

The primary factor limiting the speeds of our test circuits is the fact that the

current-producing photodiode and the SEED are connected via external cables. This

introduces an external capacitance that is quite large, thus severely slowing down the

operation of the devices. To overcome this limitation, we require that the photodiode

and SEED be integrated together, preferably on the same chip. Experiments with such

integrated devices will be detailed in subsequent chapters.


Injected electrons and transmitted photons versus time

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20

Time (ms)

Num

ber o

f par

ticle

s (1

0^14

) per

sec

Photons transmittedthrough deviceElectrons injected intodevice

Figure 2.31 Plot as a function of time for power transmitted through the device (top) under a pulsed input current (bottom). Both power and current are plotted in units of number of particles per second. As expected, when we feed current into the device the absorption increases and the transmitted power decreases. The response time for this test circuit is slow though, on the order of milliseconds.

2.6 Conclusions

Optical modulators based on the quantum-confined stark effect in multiple quantum

wells have been studied since the 1980’s. These devices provide for a convenient way

to encode electrical data onto optical beams. Waveguide-based devices provide a high

contrast ratio due to the long interaction length between the input beam and the

quantum wells, but surface-normal devices are more easily scalable to two-

dimensional arrays.

While most interest in optical modulators is for digital communication, certain

properties of these devices make them suitable for analog applications as well. In

particular, one class of modulators (the self electro-optic device or SEED) can exploit

an inherent negative-feedback loop to provide for a linear conversion of input current


into output optical power. Previous work in the literature centered on DC and low-

frequency operation, and linear conversion was verified only under DC conditions.

In our initial work, we verify the linearity of electro-optic conversion in SEEDs

under pulsed current conditions. Our test circuits exhibit time constants on the order

of milliseconds. For faster operation, we require circuits where the input current

source and optical modulator are integrated on a single chip [14].

2.7 Bibliography

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[2] D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H.

Wood, and C. A. Burrus, “Band-edge electroabsorption in quantum well

structures: the quantum confined Stark effect,” Physical Review Letters, vol. 53,

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[3] E. D. Palik, Handbook of Optical Constants of Solids, vol. 1, pp. 438–439 (1985).

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77

Chapter 3

Pulsed Laser Experiments

In the previous chapter, we discussed the basic principles of multiple quantum well

modulators, and how they could be used for an analog, linearized link. While our

initial experiments proved promising, they did not exhibit the speeds needed to satisfy

the overall goals of the proposed analog-to-digital converter system. In this chapter

we cover the experiments based on a pulsed laser in order to explore how fast we can

operate the optical modulators.

3.1 Bell Laboratories Devices

The key obstacle preventing fast operation in the experiment previously discussed is,

unsurprisingly, excess capacitance. Recall that the time constant for the modulator is

proportional to the capacitance:

γωτ

PC

eh= , (3.1)

where again P is the input optical power and γ is the electroabsorption slope with units

of inverse voltage. In those early experiments, we used external photodiodes to

implement the current sources that supplied input currents to the optical modulators.

78 CHAPTER 3. PULSED LASER EXPERIMENTS

This resulted in excess external capacitance. One option to reduce these external

capacitances is to use photodiodes wire-bonded to the modulator. With two separate

die placed in the same package, we can for example obtain capacitances on the order

of 1 pF [1]. A second option is to use a photodiode that has been monolithically

grown on the same substrate as the modulator. Fortunately, pre-existing structures

grown at Bell Laboratories [2] had this very structure, which simply consists of two

modulators connected in series. In this case then, one modulator would serve as the

photodiode supplying an input current, and the second modulator would be the actual

device under test. We would thus operate the second modulator as a self-linearized

modulator.

undoped GaAs substrate

Distributed Bragg Reflector

p Al0.11Ga0.89As

n Al0.11Ga0.89As

p Al0.11Ga0.89Asi MQW

ion-implant isolation

i MQW

SiO2

Gold

V–V+

Short PulseCW in Modulated out

Figure 3.1 Two series-connected modulators. The left device acts as a simple photodetector. When excited by short pulses, this device produces current pulses for the device on the right. This second device modulates a CW input beam, and is the device we are testing for linearized electro-optic conversion. Such monolithically grown structures allow for capacitances on the order of tens of femtofarads.

By minimizing the capacitance on the modulator, we enable the potential for fast

conversion of input current or charge. To conveniently characterize the speed of the

device though, we also need the input current signals themselves to have sharp edges.

If we want to observe time constants on the order of 1 ns, then the input signal itself

3.2. INITIAL EXPERIMENTS 79

should ideally be much faster than 1 ns. To produce such current signals, the optical

beam driving the photodiode also needs to be very fast. Mode-locked lasers provide a

convenient way to attain fast optical signals. Pulse widths on the order of 100 fs have

been measured for the mode-locked Spectra-Physics Tsunami laser used in our

experiments [3].

3.2 Initial Experiments

3.2.1 Experimental Setup

In our initial experiments, we provide a CW input laser beam using a Spectra-

Physics Titanium:Sapphire laser, pumped by a Coherent argon laser. Because the

mode-locked laser was located in a different room, we couple the pulsed beam into a

single-mode fiber, and bring the other end of the fiber to the same optical bench as the

CW laser and the modulators. After collimating the fiber output with a lens, the

pulsed and CW beams are then combined using a polarizing beam-splitter. A series of

lenses and mirrors then bring the beams to focused spots on the modulator and

photodiode. Figure 3.2 shows a schematic of this setup.

Because the pulsed beam and the CW beam are of orthogonal polarizations, we

can filter out the reflected pulse beam from the modulated CW output. This

modulated output represents the optical output of the modulator. We can measure the

output power with a high-speed detector and an oscilloscope in order to characterize

the temporal response of the modulator. We can also measure the output power using

a slow photodetector in order to find the average optical output power. The optical

system’s power losses are calibrated by substituting a near-infrared mirror that has a

reflectivity of over 99% for the wavelengths of interest.


Figure 3.2 Simplified schematic of optical setup. Lenses are not shown for clarity. A polarizing beamsplitter (PBS1) combines the Ti:Sapphire CW laser with the Ti:Sapphire mode-locked laser. (The mode-locked laser output is first coupled into a fiber, and then coupled back out into free space via lenses.) A non- polarizing beamsplitter (NPBS) picks off both beams, allowing us to measure the input power of either beam. (We choose which beam is measured by simply blocking the other beam.) A second polarizing beamsplitter (PBS2) picks of most of the reflected CW beam for monitoring by an output photodetector. Enough of the CW power still passes through PBS2 to allow us to view the position of the beam relative to the device. Either a slow or a fast photodetector can be used to measure the output power, thus allowing us to measure average or time-dependent output.


3.2.2 Experimental Results

The pulsed laser beam is incident on the modulator that is acting as a high-speed

photodetector. (We shall refer to this device as a photodetector for the rest of this

discussion.) The continuous wave (CW) beam is incident on the second device —

which we will refer to as the modulator — and it is the behavior of this device that is

of primary interest.

VbiasDC

Ppulse

Pin

Pout

I(t)

A

B

Figure 3.3 Circuit schematic of modulators in experiment. High-energy pulses from an 80 MHz Titanium:Sapphire laser illuminate the upper modulator (Device B), causing it to behave as a current source that injects pulses of current onto the lower modulator (Device A). Device A modulates a CW optical beam. The laser pulse’s time-width δt is on the order of 200 fs. The average power of the pulsed laser Ppulse, CW laser Pin, and modulated output Pout are all monitored. The transient behavior of the output beam Pout(t) is also measured.

Before a laser pulse hits the photodetector, the detector is in reverse bias.

However, the CW beam that is incident on the modulator causes this device to be in

slight forward bias. This is illustrated by the schematic load-line diagram (Figure 3.4),

where we see the intersection of the two current-voltage curves occurs below -1 V.


Load-line Analysis

-50

0

50

100

150

200

250

300

350

-2 -1 0 1 2 3 4 5 6

Vmod (V)

Curr

ent (

µA)

Figure 3.4 Sample load-line diagram for modulator in series with photodiode. When no light is incident on the photodiode, the voltage across the modulator is given by the intersection point of the two curves, and so the modulator is in slight forward bias.

When a pulse hits the photodetector, a short burst of current (or charge) is

generated. The reverse electrical bias then draws the charge down towards the second

device. Since the second device is reverse-biased, a negligible amount of this input

charge can flow through, except via photoabsorption processes. The electric field

across the intrinsic region of the modulator increases, and hence absorption increases.

This leads to a sharp drop in the output power of the modulator.

Figure 3.5 shows the modulated output power as a function of time. As we can

see, the output power indeed drops with a periodicity equal to that of the 80 MHz

repetition-rate laser. The increased absorption leads to photogeneration of carriers that

serve to discharge the injected charge. The bias across the modulator thus recovers to

its initial state.

The recovery time constant is given by (3.1). For the experiment whose results

are shown in Figure 3.5, we used a pair of devices that were each about 10 µm ×

20 µm with an intrinsic region whose thickness was approximately 1 µm, and thus

having a total capacitance of about 25 fF. The modulator’s electroabsorption curve


slope, γ, was about 0.1. The incident CW beam was 850 nm with 220 µW of power.

This yields a first-order time constant of about 1.6 ns, which is close to the fitted time

constant of 2.0 ns [4].

Figure 3.5 Modulated output power as a function of time, normalized to incident power. When a short pulse hits Device B of Figure 3.3, a charge pulse is generated, the absorption of Device A increases, and the output power drops. The increased absorption of A discharges the charge pulse and the device recovers to its initial state. To the first-order approximation, this recovery is an exponential curve. The exponential fit has a time constant of 2 ns, close to the calculated figure of 1.6 ns.

Once we verified that the device’s behavior in time is as expected, we then moved

to verifying the linearity of the electro-optic conversion process. From the derivation

in a previous chapter, we know this process ought to be linear (barring any constant

offsets to the conversion curve). To observe this, we would ideally like to directly

control the amount of charge injected onto the modulator, and measure the amount of

optical energy absorbed by the device.

Measuring the absorbed optical energy is fairly straightforward – as long as the

optical system is calibrated, we simply measure the output optical energy and subtract


this from the input energy. To simplify the measurement of optical energy, for the

purposes of the linearity experiment, we use a slow photodetector to measure the

average output power. Since the repetition rate of the pulsed-laser remains constant,

the difference between the average output power and the average input power tells us

the energy absorbed by the device.

On the other hand, when these early experiments were performed, we had not yet

devised a method for measuring (or directly controlling) the actual input charge to the

modulator being tested. Experimentally, the input charge was controlled by varying

the power of the pulsed laser used to drive the photodetector. To verify linearity in the

modulator’s charge-to-absorption conversion, we assume that the average input

current to the modulator is linearly proportional to the average power of the pulsed

laser beam used to generate current in the photodetector. To show linearity of the

charge-to-optical-energy conversion process then, we need to show a linear

relationship between the absorbed optical power and the power of the pulsed laser

beam.

Figure 3.6 shows this data. When the current produced by the photodetector is

high enough, we see a linear relationship between the absorbed optical power and the

power of the current-producing optical pulses.

A final point of interest with this experimental setup was to explore the speed of

the recovery time. From Equation (3.1), we see that the time constant is inversely

proportional to the CW optical power incident on the modulator. We thus repeated the

temporal experiment from Figure 3.5, though on a larger device (30 µm × 40 µm) and

with different CW powers. All other parameters remained the same. The result is

shown in Figure 3.7.


Figure 3.6 Average absorbed optical power versus average power of the optical pulses that drive the photodiode current source. For a certain range of average pulse power, a linear relationship exists. This indicates that there is a regime where an electrical signal is linearly converted into an optical one.

Normalized Modulator Recovery

0.4

0.5

0.6

0.7

0.8

0.9

1

0 2 4 6 8

Time (ns)

Nor

mal

ized

Out

put P

ower

481552646717788

Input CWPower (μW)

Figure 3.7 Normalized modulator power, with different input CW powers. Higher CW powers result in faster recovery time.

0 200 400 600 800 1000

170172174176178180182184186

Absorbed CW Power versusCarrier-Producing Pulse Power

Data Linear Fit

Abs

orbe

dC

W P

ower

(μW

)

Average Incident Pulse Power (μW)


We then fit an exponential curve to each of these plots to extract a fitted time

constant for each experimental condition. These time constants as a function of CW

power are shown in Figure 3.8. Even though we are using a rough first-order

approximation (which assumes a linear electroabsorption slope γ), the linear

relationship between the time constant and CW power can still be seen.

Device Speed vs. Incident CW Power

0.2

0.25

0.3

0.35

0.4

0.45

0.5

400 500 600 700 800 900

Incident CW Power (microwatts)

1 / τ

x 1

0^9

Figure 3.8 Device recovery speed as a function of CW power. According to the first-order formula Equation (3.1), the inverse of the time constant is linearly proportional to the input CW power on the modulator. Using the appropriate parameters the calculated slope should be 5.0 × 10-4 (ns µW)-1. The best fit line has a slope of 5.2 × 10-4 (ns µW)-1.

3.3 Further Experiments

The fastest conversion time we observed with the above set of experiments

corresponded to a time constant of about 2 ns. We could of course increase the CW

power further in order to achieve a faster conversion time. However, practically

speaking, at a certain point the current injection must also be increased when the CW

power is raised, so that we can still make sufficiently noise-free measurements.

However, we were restricted in the amount of pulsed laser power we could supply

to the photodetector device. The pulse power was limited by the fact that the mode-

3.3. FURTHER EXPERIMENTS 87

locked laser resided in a different room, and hence had to be coupled into a single-

mode fiber in order to bring the power to a different room. This coupling process

reduced the amount of power we could supply to the experiment.

A new optical setup was constructed for the experiments discussed below. This

new setup was placed on the same bench as the mode-locked laser, so that we could

realize higher current injection.

3.3.1 Setup

There are two primary differences between this setup and the previous one. First, the

free-space mode-locked laser output now directly feeds into our optical system.

Second, we now use a diode laser to supply the CW power, rather than the previous

Ti:Sapphire pumped by an Argon ion laser. While this latter change reduced the

maximum amount of CW power we could supply for our experiments, this was still

for the most part sufficient for our needs.

Beyond these changes, a small addition to the experimental setup is the placement

of a low-impedance current preamplifier (SR570 Low-Noise Current Preamplifier

from Stanford Research Systems) in series with the modulator and current-producing

photodetector. The low-impedance current pre-amplifier effectively monitors the

series current, and then supplies an output voltage that is proportional to the current.


VbiasDC

Ppulse

Pin

Pout

I(t)

A

B

Current Preamplifier

Vout(t) I(t)

Figure 3.9 Circuit diagram of experimental setup, with current preamplifier. The current preamplifier provides an output voltage which indicates the average current flowing I(t) through the devices.

3.3.2 High Current Injection

As stated earlier, one benefit to our new setup is that we can inject much higher

current into the modulator than was previously possible. This allows us to charge up

the modulator so that the operating wavelength can be well past the first exciton peak

(i.e., the operating wavelength is shorter than the wavelength of the exciton peak), and

then observe the modulator’s behavior as it recovers back to its initial state.

Figure 3.10 shows the modulated output power versus time, for two different

charge injections. (The legend shows the average current through the device, as

measured by the current pre-amplifier.) In the first curve with average input current of

243 µA, the modulator is initially charged up to a voltage just below the first exciton

peak of its electroabsorption curve at about 4 V (Figure 3.11). Then, as the modulator

recovers, its absorption monotonically decreases, and hence we see the output power

monotonically increase.


On the other hand, the average input current for the second curve is more than

double that of the first, and the modulator is initially charged up to a little past 8 V.

This occurs at approximately 218.6 ns on the time-axis of Figure 3.10. Hence, the

initial charging of the modulator’s input node occurs during the time between 217.8 ns

and 218.6 ns. The first dip in power at 218.2 ns shows the modulator being swept past

the first exciton peak during this initial charging. We presume that this trough in the

plot is not as low as it should be because of the limited speed of the 2.5 GHz optical

oscilloscope that we used. In reality, this initial dip in power is likely so sharp that its

full magnitude is not captured by our measurement.

Because we charge the modulator out to the second exciton peak at about 8 V

(Figure 3.11), we observe a very small dip in output power at 218.6 ns. The

modulator then recovers back to its initial state. This recovery is slow relative to the

initial charge-up, and so our oscilloscope is able to more accurately capture the

modulator’s behavior as it travels back through the initial exciton peak at 219.2 ns.

After this point, its recovery behavior is similar to the case of the low-current injection.

The most notable difference is that the two curves appear to be vertically offset by

about 0.4 mW, which we will discuss shortly.


Modulated Power vs. Time

2.5

3.0

3.5

4.0

4.5

5.0

5.5

216 217 218 219 220 221 222

Time (ns)

Opt

ical

Pow

er (m

w)

243502

Input Current (μΑ)

Figure 3.10 Output power from modulator after current pulse injection. The two curves correspond to two different levels of pulse power, and hence two different amounts of charge injection. Under the larger injection, the modulator’s initial voltage bias is pushed past the voltage at which the first exciton peak lines up with the operating wavelength, and then the absorption peak passes through the operating wavelength again during recovery.

Absorption vs. Voltage

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10 12 14

Voltage (V)

Abs

orpt

ion

(mW

)

Figure 3.11 Typical electroabsorption curve for optical modulator.


3.3.3 High-Speed Conversion

With the new setup, it was also possible to perform experiments with higher CW

powers, since as noted before we could now drive the device with higher current

injection. Figure 3.12 shows one example of this, where we use an input CW power

of 2.6 mW on a device with lateral dimensions of 20 µm × 20 µm. As we can see, it

was now possible to push the speed of the device so that it can satisfy the 1 GHz

sampling rate requirement for the overall system.

Modulated Power vs. Time

0.95

1.00

1.05

1.10

1.15

1.20

1.25

1.30

0 0.5 1 1.5 2 2.5 3Time (ns)

Opt

ical

Pow

er (m

w)

4316191121154

Average Input Current (μA)

Figure 3.12 Output power of modulator with different amounts of current injection. The incident CW power was 2.6 mW, and the device dimensions were 20 µm × 20 µm. With these operating conditions the device can meet the 1 GHz sampling frequency requirement of the overall system.

3.3.4 Linear Conversion

Including a current pre-amplifier allowed us to measure the average current that

passed through the device. In this way we can directly characterize the electro-optic

conversion characteristics of pulsed-mode operation. Just as in our average output-

power measurement, we simply measure the average current flowing through the

device.


Figure 3.13 shows a typical result when we measure the optical energy absorbed

by the modulator as a function of the amount of charge that we inject onto the device.

As before, we actually control the charge injection by changing the power of the short-

pulse laser incident on the photodetecting device. By simultaneously monitoring both

the average output power from the modulator, and the average current passing through

the device, we can construct the plot from Figure 3.13.

Absorbed Photons per Period vs. Injected Electrons

7.2E+07

7.4E+07

7.6E+07

7.8E+07

8.0E+07

8.2E+07

8.4E+07

8.6E+07

0.0E+00 5.0E+06 1.0E+07 1.5E+07 2.0E+07 2.5E+07

Input Charge / Period (electrons)

Abs

orbe

d En

ergy

/ Pe

riod

(pho

tons

)

slope ≈ 1

Figure 3.13 Absorbed optical energy versus input charge per period. A mode-locked laser delivers optical pulses to a photodetector, thus generating current pulses. These current pulses cause the modulator to absorb optical energy. For a certain range of input pulses, we observe a linear relationship between absorbed energy and input charge. When plotted on axes with units of number of photons versus number of electrons, the slope of approximately one indicates near-unity quantum efficiency.

Notably, for a large enough amount of input charge we experience a region where,

for every extra electron’s worth of charge injected on the modulator, the device

absorbs an extra photon’s worth of optical energy. With the axes of the plot in units of

number of photons versus number of electrons, we see a fitted line with a slope of

about one, which indicates unity quantum efficiency.


3.3.5 Baseline Power

Another area of investigation involves the phenomenon illustrated in Figure 3.10. As

we noted earlier, we see that as the pulsed power is increased, the “steady-state”

power which the modulator recovers to gradually decreases. In other words, we see a

lowering in the initial absorption by the modulator before the current injection. We

will refer to this initial output power as the “baseline” power.

One possible explanation for this behavior is that this is due to Joule heating in

the modulator. From a thermal perspective, the transient currents in the modulator are

fast enough that we need only consider the average current. Hence, with increased

average current running through the modulator as we increased the current injection,

the modulator may become hotter. Increased temperature reduces the bandgap of the

modulator, on the order of 4 meV / °C [13], and so the modulator absorbs more power

for a given wavelength. At 850 nm, this translates to a shift in wavelength of about

( )

Cnm/2

μm85.0μm24.1

CeV/004.0 2

°=

°=Δ

Δ=Δ

eV

EE

λ

λλ

(3.2)

The spot size of the incident CW beam was about 12 µm in diameter. The

modulator had dimensions of approximately 30 µm by 60 µm. As a rough

approximation then, we assume that Joule heating only occurs in the area where the

beam is incident on the modulator, and that this heat flows out to a room temperature

heat bath located an infinite distance away. In this case, the difference between the

temperature at the incident beam and the thermal bath is given by [6].

TD ZPT =Δ (3.3)where PD is the dissipated power, and ZT is the thermal impedance. For the

geometries described above, the thermal impedance is given approximately by

sZT ξ2

1= (3.4)


where s is the beam diameter, and ξ is the thermal conductivity of the material, which

is 0.45 W/(cm °C) for GaAs.

In the two curves of Figure 3.10, the difference in current is about 260 µA. Hence,

in the high-current case, the device would be heated by about 1°C. From (3.2), this

implies a bandgap shift of about 2 nm.

Since this rough estimate of the effects of Joule heating does not lead to an

obvious conclusion as to its impact on absorption, we performed an experiment where

we find the time-dependent absorption of the modulator with different input currents,

and then repeat this with a different beam spot size. A different beam spot size

changes the thermal impedance of (3.4), and we can observe whether this has an

impact on the absorption baseline.

However, even after we doubled the spot size of the beam from 12 µm to 24 µm

(by slightly defocusing the beam’s image on the modulator), we still observed the

same baseline power drop as before. Figure 3.14 shows the baseline output power as a

function of average current injection for the two spot sizes. While a small difference

for the two cases can be seen, our hypothesis cannot fully explain most of the

observed phenomenon.

An alternate hypothesis is that the larger pulse power incident on the current-

producing photodetector heats up this device. Moreover, some of this heating may be

due to pulse power that actually passes through the active region and is eventually

absorbed by the substrate material. While an increased temperature in the

photodetector and the substrate area underneath it would not directly lead to the

phenomenon that we observe, it could be heating up the neighboring modulator. The

hotter modulator thus exhibits slightly different absorption characteristics due to

bandgap narrowing, and higher “baseline” absorption is observed.

Because this heating effect is due to the way we experimentally produce a current

stimulus to the modulator, it is not a problem for the final devices that would be part

of the analog-to-digital converter system. Ultimately, current pulses will be supplied

by hitting photoconductive sampling switches with optical pulses. These optical

pulses do not change in power (since variations in the input signal are due to different


biases placed across the switch), and so there will be no thermal variations impacting

the baseline absorption. Note too that a differential scheme for electro-optic

conversion also mitigates any thermal effects, as long as the pair of devices are located

close enough together so that there is not an appreciable temperature gradient between

them.

Max Pout vs. Input Current

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

0 200 400 600 800 1000 1200 1400

Input Current (uA)

Base

line

(nor

m)

Large Spot Small Spot

Figure 3.14 Baseline output power as a function of input current. The small spot was 12 µm × 12 µm, and the large spot was 24 µm × 24 µm. The baseline power is normalized for each curve by dividing by the baseline power for the lowest input current data point.

Lastly, in the final converter system, there will likely be a minimum input signal

bandwidth that is greater than DC. If this minimum input signal bandwidth is faster

than then the time constants associated with these thermal effects, all time-dependent

thermal variations would be averaged out, leading to little impact on the modulators’

optical outputs.


3.4 Conclusions

In the experiments described here, we verified the linearity of the electro-optic

conversion process for optical modulators. Specifically, we use input signals

consisting of very sharp pulses of current. To supply these pulses, we drive a second

modulator with optical pulses from a mode-locked laser. Because this second

modulator is integrated with the device-under-test on the same die, we realize very

small capacitances.

This allowed us to verify linear operation, even when the current pulses have

widths much shorter than the first-order time constant of the modulator. We are thus

confident that the modulator can convert electrical pulses from a fast sampling switch

as would be needed at the front end of a sampling A/D converter.

We also conclude that the simple expression for the first-order time constant

describes the modulator’s behavior with reasonable accuracy. The calculated time

constants closely approximate the fitted exponential curves to the modulator’s

recovery behavior, even across a range of input CW powers.

Lastly, we observed certain thermal effects that cannot fully be explained by Joule

heating. However, such thermal effects should have little impact on the final analog-

to-digital converter system.

Thus far, all experiments were performed on devices previously fabricated at Bell

Laboratories. Later work focuses on the fabrication of devices at Stanford University.

This allows us fabricate smaller devices with lower capacitances (and hence faster

speeds), as well structures suitable for demonstrating differential conversion.

3.5 Bibliography

[1] A. V. Krishnamoorthy and K. W. Goosen, “Optoelectronic-VLSI: Photonics

Integrated with VLSI Circuits,” IEEE Journal of Selected Topics in Quantum

Electronics, vol. 4, pp. 899–912 (1998).


[2] A. L. Lentine, F. B. McCormick, R. A. Novotny, L. M. F. Chirovsky, L. A.

D’Asaro, R. F. Kopf, J. M. Kuo, and G. D. Boyd, “A 2 kbit array of symmetric

self-electrooptic effect devices,” IEEE Photonics Technology Letters, vol. 2, pp.

51–53 (1990).

[3] G. A. Keeler, D. Agarwal, C. Debaes, B. E. Nelson, N. C. Helman, H. Thienpont,

and D. A. B. Miller, “Optical Pump-Probe Measurements of the Latency of

Silicon CMOS Optical Interconnects,” IEEE Photonics Technology Letters, vol.

14, pp. 1214–1216 (2002).

[4] H. Chin, P. Atanackovic, D. A. B. Miller, “Optical Remoting of Ultrafast Charge

Packets Using Self-Linearized Modulation,” Conference on Lasers and Electro-

Optics Technical Digest, pp. 508-509 (2000).

[5] D. A. B. Miller, “Review of basic semiconductor physics,” Stanford EE243

Semiconductor Optoelectronics Devices Course Notes (1999).

[6] L. A. Coldren and S. W. Corzine, “A Phenomenological Approach to Diode

Lasers,” Diode Lasers and Photonic Integrated Circuits, pp. 55–57 (1995).


99

Chapter 4

Sampling Switches

High-speed optically triggered electrical switches are used to sample the analog input

signal for the overall analog-to-digital converter system. In this chapter we give a

brief overview of the low-temperature (LT) grown GaAs material of these switches.

We also discuss the metal-semiconductor-metal (MSM) structure used for the devices,

including the capacitance of such structures. Lastly we show that these switches do

indeed have a response time sufficiently fast for sampling high-bandwidth signals.

4.1 Low-Temperature Grown GaAs

Conventional GaAs epilayers are grown using molecular beam epitaxy (MBE) at

temperatures greater than 580°C. Such materials have low trap densities (< 1015 cm-3)

and hence have relatively long carrier lifetimes (≈ 1 ns). However, when GaAs is

grown at relatively low temperatures and under high arsenic pressure, excess As is

incorporated into the material. The temperatures used are usually between 190 °C

and 300 °C. At lower temperatures, materials with line defects or a polycrystalline

structure may result [1].

100 CHAPTER 4. SAMPLING SWITCHES

In low-temperature-grown GaAs (LT GaAs), excess As results in several types of

point defects, such as arsenic antisites ([AsGa]0), ionized arsenic antisites ([AsGa]+),

gallium vacancies (VGa) , and arsenic interstitials (Asi). (In the notation commonly

used, XY denotes that species X is located where one would normally find Y in a

perfect crystal. V represents a vacancy, while the subscript i represents an interstitial

location.)

[AsGa]0 has a group V element in place of a group III element, and hence is a

double-donor. These defects are located in the upper half of the bandgap and are

typically the most abundant type, with densities on the order of 1020 cm-3 (Figure 4.1).

A fraction of these [AsGa]0 defects are compensated by the VGa triple-acceptor defects

which have energies about 0.34 eV above the valence band [1], yielding the ionized

defect [AsGa]+. Both VGa and [AsGa]+ thus have identical densities on the order of 1018

cm-3. The actual densities have been observed to vary over an order of magnitude for

growth temperatures ranging from 200 °C to 280 °C, with higher growth temperatures

resulting in lower defect densities [2]. While the final type of defect Asi was

originally believed to be present in LT GaAs, more recent work has concluded that

these interstitials have negligible densities [3].

The [AsGa]+ and VGa defects act as electron and hole traps, respectively [4]. Any

carriers generated by a short optical pulse are quickly captured on a sub-picosecond

scale [5]. Hence, LT GaAs is a suitable material for high-speed photonic applications.

4.2 Annealed Low-Temperature Grown GaAs

Despite the advantages to LT GaAs described above, there remain two primary

problems with as-grown LT GaAs. First, even without photoexcitation the material

still exhibits non-negligible conductivity. The high density of antisite and vacancy

defects leads to a mini-band inside the bandgap. The possibility of “hopping”

conduction within this mini-band thus leads to resistivities as low as 10 Ω-cm [3][4].

Second, the electrons and holes in as-grown LT GaAs are captured by two

different types of defects. Hence, even though the trapping times are short the

4.2. ANNEALED LOW-TEMPERATURE GROWN GAAS 101

recombination times are long – on the order of 1 ns [5]. This means that even though

the material’s initial response after an optical pulse is quite fast, it subsequently

exhibits a much longer tail that limits its usefulness for sampling signals at a fast

repetition rate.

Due to these two characteristics — low resistivity and long carrier recombination

times — as-grown LT GaAs is not typically a good material for fast photoconductive

switches. However, annealing of LT GaAs after growth alleviates these two problems.

The primary effect of annealing at high temperatures is the formation of arsenic

precipitates or clusters. These clusters form when the excess As diffuses with

assistance from Ga vacancies [6].

The size of the As precipitates increases with higher anneal temperatures. Since

the total amount of arsenic atoms is conserved during the annealing process, the

increase in precipitate size results in both lower antisite defect density [2] and longer

inter-cluster distance [7]. For example, [2] reports that for a sample grown at 200°C,

[AsGa]0 starts at about 2×1020 cm-3 as-grown, but drops to 8×1019 cm-3 when annealed

at 500°C and then to 4×1019 cm-3 after a 600°C anneal.

Density of States

Ener

gy

Ev

EC

EF

0.34 eV

[AsGa]+~1018 cm-3

[AsGa]0~1020 cm-3

[VGa]~1018 cm-3

1.424 eV

Density of States

Ener

gy

Ev

EC

EF

0.34 eV

[AsGa]+~1017 cm-3

[AsGa]0~1019 cm-3

[VGa]~1017 cm-3

1.424 eV

post anneal as-grown

Figure 4.1 Energy band diagrams for as-grown (left) and post anneal (right) low-temperature grown GaAs. Defect densities decrease after anneal. From [1] and [2].


Because the arsenic defect concentration in annealed material is smaller, hopping-

conduction becomes less probable. It has also been proposed that the formation of

arsenic clusters creates metallic regions with Schottky barriers surrounding them [1],

depleting the free carriers around the clusters. When these depletion regions merge,

no free carriers remain in the material. The resistivity of annealed LT GaAs is then

increased compared to as-grown LT GaAs. A resistivity increase of five orders of

magnitude has been reported for an anneal temperature of 650°C [7].

With a reduction in defect density after post-growth anneal, the carrier trapping

times for LT GaAs increase rendering the material slower. Nevertheless, for anneal

temperatures of as high as 700°C, time constants of a few picoseconds are still

retained. Additionally, the newly formed As clusters are able to trap both electrons

and holes. Since the trapping sites for the two carriers are no longer spatially

separated, the recombination time is drastically reduced. In time-resolved data, a

single time-constant is evident in pump-probe measurements, with no separate, longer

time-scale behavior that would imply a longer recombination time [7].

In general then, higher anneal temperatures lead to higher resistivity at the cost of

longer carrier lifetimes. In almost all work in this field, the anneal temperature used is

typically above 500°C, with lifetimes on the order of one to several picoseconds.

More recent work [8] has shown that 100 fs lifetimes are possible with an anneal

temperature of 400°C, though the resistance is now about three orders of magnitude

less than for materials annealed at the typical high temperatures.

It has also been reported that defect concentrations reach an equilibrium value as

anneal duration is increased. Hence, the material properties do not change much with

varying anneal time, as long as this anneal time is long enough. An anneal time of 10

minutes is sufficient for temperatures above 300°C, and the equilibrium defect

concentration is reached earlier for higher anneal temperatures.

4.3. METAL-SEMICONDUCTOR-METAL STRUCTURES 103

4.3 Metal-Semiconductor-Metal Structures

A metal-semiconductor-metal (MSM) switch consists of two metal electrodes with

semiconductor material placed between them. As long as the semiconductor is not

highly doped, then there is no tunneling conduction at the metal contacts. Moreover,

the concentration of the antisite defects is high enough (~1017 cm-3 for growth

temperatures up to 400 °C) to compensate the material and pin the Fermi energy close

to midgap [2]. Hence, both metal contacts for the MSM device are Schottky diodes.

In a standard Schottky contact, the depletion width w is given by

( )eN

VVw bir −= 02 εε (4.1)

where rε is the relative permittivity of the semiconductor, biV is the built-in voltage,

V is the applied forward-bias voltage, and N is the net impurity concentration. In the

case of annealed LT GaAs, the ionized arsenic antisites are compensated by the

gallium vacancies, and so N is essentially given by the concentration of un-ionized

arsenic antisites, [AsGa]+.

Since the Fermi energy of annealed LT GaAs is near midgap, the built-in voltage

is small. Moreover, the density of the deep donor arsenic antisites is high (on the

order of 1018 or 1019 cm-3) [2]. Hence, the depletion width is small, and almost all of

the potential drop across a biased MSM will be across the highly resistive, annealed

LT GaAs material. Contrast this with MSMs constructed from regular GaAs, where

the more highly conducting GaAs means that most of the potential drop occurs at the

depletion region of the reverse-biased metal contact.

Upon optical excitation of the LT GaAs in the MSM device, carriers are generated

within the semiconductor material. The electric field in LT GaAs leads to carrier drift

to the electrodes of the devices. In a sample-and-hold configuration, drift-induced

transport will continue until the voltages are equalized, or the carriers are trapped

within the material.


The trapping time is set by anneal temperatures as discussed earlier. From a

systems design standpoint, the desired input bandwidth of the switch dictates the

maximum trapping time for the material. Hence, assuming ideal switch behavior, we

would like to make the time required to equalize the electrode voltages to be smaller

than this trapping time. This implies that we desire a large current through the MSM

for a given voltage bias. In general, we can achieve this by either increasing the

energy of the optical pulse excitation (and thereby increasing the carrier concentration),

or by increasing the mobility of the material.

The MSM device is realized using metal electrodes formed from interdigitated

fingers. Such structures have electrodes that are co-planar, leading to easier

integration with other devices via flip-chip solder bonding. Assuming infinitely many

but vanishingly thin fingers, we can calculate the capacitance for such structures from

[9], which derives a formula through a series of conformal mappings. The capacitance

Cfinger from a single finger to the equipotential plane halfway between two fingers is

given by

( ) ( )( )'

14 0

kKkKC r

fingerεε += (4.2)

where

∫ −=

2/

0 22 sin1

π

φφ

kdK , (4.3)

⎟⎠⎞

⎜⎝⎛=

bak4

tan2 π , (4.4)

21' kk −= , (4.5)

rε is the relative dielectric constant of the substrate, and a and b are MSM dimensions

as noted in Figure 4.2. Note that (4.3) is the complete elliptic integral of the first kind.

If we let f and s be the finger and spacing widths respectively, (4.2) yields the

capacitance per unit area for the entire MSM:

4.3. METAL-SEMICONDUCTOR-METAL STRUCTURES 105

( ) ( )( )'

10

kKkK

sfC r

++= εε , (4.6)

Note that in (4.6) we assumed that there is only air on top of the MSM device. If

instead the device is capped with a different dielectric with relative permittivity cε ,

then the expression rc εε + replaces rε+1 in (4.6).

Figure 4.2 MSM dimensions used to calculate capacitance. [9] uses the variables a (half the width of a finger) and b (half the distance between the top edge of two adjacent fingers). The capacitance formula can be recast using finger width f and finger spacing s.

The permittivity of annealed LT GaAs can potentially be affected by the presence

of arsenic precipitates. These precipitates can acquire multiple electron-charges of

either sign, and have the potential to increase the capacitance of any devices that

contain annealed LT GaAs.

A simple way of understanding this effect is to model the precipitates as a sheet of

metal with non-zero thickness inside a parallel plate capacitor. The capacitance per

unit area for a parallel-plate capacitor with a dielectric of thickness d and permittivity

ε and no precipitates is given by

dC /ε= (4.7)If the effect of the precipitates is to add a sheet of metal with thickness t, then the

capacitance per unit area is increased to ( )tdC −= /ε (4.8)

regardless of where inside the dielectric the sheet is positioned.

2a

2b

f

s


While this increased capacitance has indeed been measured, it is only significant

at low frequencies and high operating temperatures [10]. At high frequencies, the

charges in the precipitates and point defects do not have enough time to react to the

fluctuating electric field. The defects also are naturally more active at higher

temperatures. At 45°C, the permittivity of LT GaAs annealed at 700°C is measurably

larger only for frequencies below 10 kHz [10]. Since in our system all electrical nodes

will fluctuate at timescales of at least 1 GHz (and, in laboratory experiments, of at

least the repetition rate of the mode-locked laser of approximately 80 MHz), we can

safely assume for this work that the permittivity of annealed LT GaAs is not affected

by the presence of arsenic point defects or clusters. This is important not only because

the capacitance is smaller, but also because we can now operate in a regime where the

capacitance is independent of electrical signal frequency.

4.4 Fabrication

For this work all sampling switches were fabricated from a wafer with the layer

structure indicated in Table 4.1. This wafer was originally grown using molecular

beam epitaxy (MBE) for use in experiments involving direct integration of the

switches with a silicon CMOS buffer and quantizer [11]. The growth rate of the LT

GaAs was approximately 1μm/hour.

Description Material Growth Temperature (°C) Thickness (Å)

active material GaAs 250 600

etch stop layer Al0.6Ga0.4As 600 300

buffer layer GaAs 600 300

substrate SI GaAs — —

Table 4.1 Epilayer wafer structure for all photoconductive sampling switches used in this work.

4.4. FABRICATION 107

After growth of the epitaxial layers, the 2-inch wafer was diced into pieces with

dimensions of about 2 cm. We then annealed individual pieces in a rapid thermal

annealer (RTA), with a GaAs wafer placed on top of the epilayer to mitigate arsenic

diffusion via outgassing [12]. The MSM features were defined via contact

photolithography, after which 10 nm of titanium and 100 nm of gold were evaporated

onto the wafer (Figure 4.3).

Figure 4.3 Scanning electron micrograph (SEM) of fabricated MSM device. The finger width and spacing are both 1 μm, and the device is approximately 19 μm × 19 μm.

The MSM devices used in [11] demonstrated the ability to linearly sample

electrical signals with bandwidths of over 40 GHz. Consequently, for this work we

used the same anneal temperature and duration: 700°C for 1 minute. On the other

hand, though in [11] MSMs with a 2-μm finger spacing were used, we have in this

work used a 1-μm finger spacing. The smaller finger spacing yields better optical

responsivity, primarily because the electric field for a given voltage bias is naturally

larger with smaller spacing. In our case, because the optical modulators already have

high capacitance as compared to the switches, the increased capacitance of 1-μm


finger spacing MSMs did not appreciably increase the total capacitance at the

sampling node.

The theoretical capacitance as a function of finger spacing is shown in Figure 4.4.

We use a finger width of 1 μm since this is the smallest dimension that can be

conveniently and reliably fabricated at our facilities with contact photolithography.

The device area is 19 μm × 19 μm, as this was the area used for MSM devices so that

they could be integrated with the modulator array used in this work while at the same

time match the optical spot size in the experimental apparatus. Individual modulator

capacitances are 25 fF or greater. Moving from 2 μm to 1 μm finger spacing

consequently does not appreciably increase the total capacitance at the MSM output

node.

0 1 2 3 4 50

5

10

15

20

Finger Spacing (μm)

Cap

acita

nce

(fF)

MSM Capacitance

Figure 4.4 Theoretical capacitance for MSM structure as calculated from (4.6), as a function of finger spacing. For this plot the finger width is 1 μm, dielectric constant is 13, and device area is 19 μm × 19 μm.

The temporal response of the MSM devices can be characterized by fabricating

the device with a 50-Ω transmission line attached to each electrode [13]. One

4.5. CONCLUSIONS 109

transmission line is terminated to ground, while a DC bias is applied to the other.

Upon optical excitation of the switch with a titanium:sapphire mode-locked laser

“pump” beam (pulse width of ~200 fs FWHM, center wavelength ~850 nm), electrical

transients are generated and propagate along both transmission lines (Figure 4.5).

These transient waveforms generated in this fashion can then be detected using

electro-optic sampling with a “probe” beam incident on a lithium-tantalate crystal

placed on top of one of the transmission line. By varying the time-delay between the

“pump” and “probe” pulses, we can then trace out the transient voltage waveforms as

a function of time. Through such an experiment, it was verified that 1-μm MSM

devices fabricated from annealed wafers as described above have temporal responses

with a full-width half-maximum (FWHM) of about 2 ps (Figure 4.6). They are thus

suitable for high-bandwidth sampling.

50 Ω Transmission Line 50 Ω Transmission Line

Vbias

Ground

MSM

Short Optical Pulse

Figure 4.5 Schematic depicting how the temporal response of the MSM switch can be measured. The device is connected in series with two transmission lines. One line is terminated to a bias voltage, and the other is terminated to ground. An optical pulse exciting the device generates transient electrical waveforms.

4.5 Conclusions

From a review of the literature, we find that low-temperature-grown (LT) GaAs is a

good candidate for making high-speed optically triggered switches. The short carrier

trapping time is due to the presence of arsenic defects. As the growth temperature is

lowered, the defect concentration is increased. A post-growth anneal leads to fast


carrier trapping and recombination times, and at the same reduces the conductivity (or

dark current) of the material. The MSM structure using interdigitated fingers leads to

a low-capacitance device suitable for a high-speed sampling switch. Finally, the high

bandwidth of these switches has previously been verified, and it is from the same

wafer that we fabricate the devices used in this work.

0 10 20 30 40 500.4

0.5

0.6

0.7

0.8

0.9

Elec

tro-o

ptic

Sig

nal (

arb.

uni

ts)

Time (ps)

Figure 4.6 Temporal response of MSM switch after excitation with a short optical pulse, indicating a full-width half-maximum (FWHM) of about 2 ps. The pump pulse is produced by a Spectra Physics Tsunami titanium:sapphire mode-locked laser, and has a FWHM of approximately 200 fs and a center wavelength of approximately 850 nm. From [14].

4.6 Bibliography

[1] G. L. Witt, “LTMBE GaAs: present status and perspectives,” Materials Science

and Engineering B, vol. 22, pp. 9-15 (1993).

[2] X. Liu, A. Prasad, W. M. Chen, A. Kurpiewski, A. Stoschek, Z. Liliental-Weber,

and E. R. Weber, “Mechanism responsible for the semi-insulating properties of


low-temperature-grown GaAs,” Applied Physics Letters, vol. 65, pp. 3002–3004

(1994).

[3] X. Liu, A. Prasad, J. Nishio, and E. R. Weber, “Native point defects in low-

temperature-grown GaAs,” Applied Physics Letters, vol. 67, pp. 279–281 (1995).

[4] U. Siegner, R. Fluck, G. Zhang, and U. Keller, “Ultrafast high-intensity nonlinear

absorption dynamics in low-temperature-grown gallium arsenide,” Applied

Physics Letters, vol. 69, pp. 2566–2568 (1996).

[5] A. J. Lochtefeld, M. R. Melloch, J. C. P. Chang, and E. S. Harmon, “The role of

point defects and arsenic precipitates in carrier trapping and recombination in

low-temperature grown GaAs,” Applied Physics Letters, vol. 69, pp. 1465–1467

(1996).

[6] R. Yano, Y. Hirayama, S. Miyashita, N. Uesugi, and S. Uehara, “Arsenic

pressure dependence of carrier lifetime and annealing dynamics for low-

temperature grown GaAs studied by pump-probe spectroscopy,” Journal of

Applied Physics, vol. 94, pp. 3966–3971 (2003).

[7] J. K. Luo, H. Thomas, and D. V. Morgan, “Transport properties of GaAs layers

grown by molecular beam epitaxy at low temperature and the effects of

annealing,” Journal of Applied Physics, vol. 79, pp. 3622–3629 (1996).

[8] I. S. Gregory, C. Baker, W. R. Tribe, M. J. Evans, H. E. Beere, E. H. Linfield, A.

G. Davies, and M. Missous, “High resistivity annealed low-temperature GaAs

with 100 fs lifetimes,” Applied Physics Letters, vol. 83, pp. 4199–4201 (2003).

[9] Y. C. Lim and R. A. Moore, “Properties of alternately charged coplanar parallel

strips by conformal mappings,” IEEE Transactions on Electron Devices, vol. 15,

pp. 173–180 (1968).

[10] A. Vasudevan, S. Carin, and M. R. Melloch, “Permittivity of GaAs epilayers

containing arsenic precipitates,” Applied Physics Letters, vol. 73, pp. 671–673

(1998).






[12] J. K. Luo, H. Thomas, and D. V. Morgan, “Thermal annealing effect on low

temperature molecular beam epitaxy grown GaAs: Arsenic precipitation and the

change of resistivity,” Applied Physics Letters, vol. 64, pp. 3614–3616 (1994).

[13] D. H. Auston, “Picosecond photoconductivity: High-speed measurements of

devices and materials,” Measurement of High-Speed Signals in Solid State

Devices, ed. R. B. Marcus, vol. 28, pp. 85–134 (1990).

[14] R. Urata, R. Takahashi, K. Ma, D. A. B. Miller, and J. S. Harris, Jr.,

(unpublished).

113

Chapter 5

Flip-Chip Bonded Devices

In this chapter we explain the process flow for fabricating optical modulators. To

test these modulators, we then integrate them with separate carrier dies using a flip-

chip solder bonding technique. The carrier dies may have a quartz substrate when we

want to test various configurations of modulators. They may also have a low-

temperature-grown (LT) GaAs substrate when we test the modulators integrated with

metal-semiconductor-metal (MSM) sampling switches.

In addition to discussing the fabrication process, we present experimental results

that verify the devices’ ability to perform linear electro-optic conversion. In the last

set of data that we show, we demonstrate differential conversion of sampled high-

speed signals.

5.1 Fabrication and Processing

While the modulators fabricated at Bell Laboratories were very useful for initial

exploration, it was necessary to fabricate new devices at Stanford University in order

to perform all necessary experiments. This section outlines the fabrication process,

while detailed recipes are provided in Appendix B.

114 CHAPTER 5. FLIP-CHIP BONDED DEVICES

5.1.1 Epitaxial Structure

The epitaxial layers were grown via molecular beam epitaxy (MBE). The

specifications for this stack structure are shown in Table 2.3. While this design was

primarily for experiments that are not part of the work described here [1], they were

suitable for our purposes as well. The quantum well structure corresponds to peak

absorption at 850 nm for moderate bias voltages (~5 V), matching the wavelengths

from readily available diode lasers. The p-type GaAs cap inhibits the oxidation of the

cathode layer underneath. No reflector stack is necessary, since these devices will be

flip-chip bonded onto a separate die; the gold contact that will be deposited on the

cathode layer then acts as the reflector. On the other hand, it is necessary to remove

the opaque GaAs substrate, and hence the presence of a high aluminum-content etch

stop layer.

Description Material Thickness (Å) Dopant Type

cathode cap GaAs 100 [Be] = 1×1019/cm3

cathode Al0.3Ga0.7As 2030 [Be] = 1×1019/cm3

barrier/well stack 50 × Al0.3Ga0.7As/GaAs 50 × 30/95 undoped

first barrier Al0.3Ga0.7As 30 undoped

anode Al0.3Ga0.7As 5000 [Si] =4.4×1018/cm3

buffer GaAs 500 undoped

etch stop Al0.85Ga0.15As 2800 undoped

substrate GaAs [100] ~50000 undoped

Table 5.1 Epilayer wafer structure of modulators used in experiments. Designed primarily by G. A. Keeler [1].

5.1. FABRICATION AND PROCESSING 115

5.1.2 Electroabsorption Measurement

Once the epilayer stack was grown, we fabricated simple test structures in order to

characterize the absorption of the quantum wells as a function of both wavelength and

bias voltage. In these test structures, we deposit two ring contacts on a mesa structure

and then characterize the absorption simply by measuring the photocurrent (Figure

5.1).

P-doped GaAsIntrinsic quantum wells

N-doped GaAsGaAs substrate

input optical beam

ohmic goldp-contact

ohmic gold n-contact

Figure 5.1 Mesa test structure for photocurrent measurements. Two ohmic contacts provide electrical bias to the active quantum-well region. A tunable Ti:Sapphire laser provides an input optical beam. The mesa is 300 μm × 300 μm.

Knowing the input beam power and the photocurrent, we can find the absorption

coefficient α by making the following assumptions. We assume that 32% of the

incident beam power is reflected off the front surface, according to the formula [2] 2

11

⎟⎠⎞

⎜⎝⎛

+−=

nnR (5.1)

where the index of refraction n for GaAs is 3.6 [3] . Also, we assume that optical

power is only absorbed in the intrinsic region, and that all carriers generated in this

region are collected by the electrical contacts. The internal quantum efficiency is thus

1, so that the photocurrent is given by


( )( ) inL

photo PeReI α

ω−−−= 11

h (5.2)

where the thickness of the active region L is 628 nm from Table 2.3. Figure 5.2 shows

a typical electroabsorption curve for the wafer.

Absorption Spectra

0

2000

4000

6000

8000

10000

12000

14000

16000

820 830 840 850 860 870 880 890 900

Wavelength (nm)

Abs

orpt

ion

Coe

ffic

ient

(inve

rse

cm) 0

123456bulk GaAs

Applied Voltage

Figure 5.2 Absorption coefficient versus input wavelength, for applied biases. The absorption of bulk GaAs is also provided for reference [3].

5.1.3 Modulator Processing

The goal for this process flow is to form modulator structures suitable for flip-chip

solder bonding to a separate “carrier die”. While the exact carrier die will vary

depending on the desired experiment, it will have two coplanar contacts — one anode

and one cathode — for each modulator. Hence, our final modulator structure must

include isolated modulators with relatively coplanar contacts suitable for solder

bonding.

In the process flow that we used, we formed arrays of 20 rows (with a pitch of

62.5 μm) and 10 columns (with a pitch of 125 μm) of modulators. Each array is

suitable for solder bonding to a single carrier die. The modulators are isolated by

5.1. FABRICATION AND PROCESSING 117

etching trenches in both the horizontal and vertical directions, leaving behind mesas

that are 40 μm × 80 μm in the lateral dimensions. While the anode and cathode

contacts on these structures are not coplanar, the uneven height will be accommodated

by the indium solder bumps. Figure 5.3 illustrates the shape of the final modulator

structure, while in Figure 5.4 we show a scanning electron microscope (SEM) image

of the device.

P-doped GaAsIntrinsic quantum wellsN-doped GaAs

GaAs substrate

GoldP-doped GaAsIntrinsic quantum wellsN-doped GaAs

GaAs substrate

Indium

7-mask etching and metal deposition

process

Figure 5.3 Illustration of modulator structure after fabrication process flow. The n-doped base region of the modulator is 40 μm × 80 μm. The active area is formed by a reactive ion etch (RIE), with the gold contact as a hard mask. We fabricated modulators with active areas that ranged from 9 μm × 9 μm to 15 μm × 15 μm.


Figure 5.4 Scanning electron microscope (SEM) image of fabricated modulators.

5.1.4 Flip-Chip Solder Bonding

Once we have two dies — one with an array of 200 modulators, and the other with the

required carrier die (which will be discussed later) — we can solder bond them

together. A commercial flip-chip bonder (Research Devices M8-A) allows us to align

the two samples with a tolerance of about 2 μm, tilt them to a high degree of planarity,

and then press them together under a programmed pressure and temperature profile.

While the details are described in Appendix B, we typically used a pressure of 6 g per

~10 μm × ~10 μm indium solder bump, at a temperature of 140°C.

After bonding, we applied a few drops of low-viscosity epoxy (Tra-Bond 2113) to

the edge of the bonded dies. These epoxy drops wick into and fill up any empty space

between the two dies through capillary action. The epoxy cures after about a day,

forming a structurally stable device.

5.1.5 Substrate Removal

In the last stage of processing, we apply a wet etch to remove the opaque GaAs

substrate of the modulator die. We first use photoresist to temporarily fix the bonded

5.2. QUARTZ CARRIER DIE 119

dies to a glass cover slip. This cover slip allows the semiconductor material to be

etched in a more uniform manner in the later steps.

We first use a non-selective etch based on sulfuric acid to quickly remove much

of the GaAs substrate. During this etch we periodically measure the thickness of the

dies to ensure that we do not overetch the stack. Using a magnetic stir rod to agitate

the etchant improves the speed and uniformity of the etch. When only 50 to 100 μm

of GaAs are left, we switch to an etch based on citric acid and hydrogen peroxide,

which etches AlGaAs at a much slower rate than GaAs. (This selectivity is due to the

fact that oxidation of AlGaAs forms Al2O3 at the surface of the material. Aluminum

oxide, however, is insoluble in this mixture and blocks the etching mechanism [4]).

At this point the individual modulators of the array should be completely isolated,

and the top layer of material on all devices is the AlGaAs etch stop. (Incidentally, the

cured epoxy protects the modulators from being etched along the edge of the device.)

We now remove the AlGaAs etch stop with a mixture of water and hydrochloric acid.

In this case, the AlGaAs is etched more quickly since it oxidizes in the presence of

water much more easily than GaAs, and hydrochloric acid etches the oxidized material

[5].

Finally, we remove the cured epoxy using a reactive ion etch based on CHF3.

This is necessary since the epoxy often covers over the wire-bond pads. Then, after

removing the die from the glass cover slip, the chip can be epoxied and wire-bonded

to a package.

5.2 Quartz Carrier Die

Once we established the process flow for fabricating modulators, we turned our focus

to connecting these modulators in configurations and simple circuits which would

allow us to verify their operation with pulsed input currents. One configuration which

we had not originally been able to test is the differential mode, and is the main thrust

of this work.


5.2.1 Carrier Die

In order to perform differential testing, we designed a simple carrier die. This carrier

die provides for a structurally stable substrate to hold the modulators, since after

removal of the modulators’ GaAs substrate they become isolated islands. Furthermore,

a pattern of metal lines on the carrier die allows us to electrically connect the

modulators in whatever way we choose.

To make this carrier die we first lithographically define a pattern of photoresist

onto a quartz substrate. Then layers of first 100 Å of chromium and then 1000 Å of

gold are evaporated onto the substrate. The resist is removed through ultrasonic

stimulation of the wafer in an acetone bath, leaving behind the patterned metal.

Finally, the quartz wafer is diced into individual die suitable for flip-chip solder

bonding.

The gold provides a material that easily alloys with the indium solder, while the

chromium provides for a layer that easily adheres to quartz. We chose to use a quartz

substrate (which has a dielectric constant of about 4 — much less than that of GaAs)

in order to minimize parasitic capacitances. Figure 5.5 shows the single mask used for

this metal layout.

Our main interest is to test the modulators under differential operation. This

requires three modulators: one that is driven with laser pulses to provide pulsed

current input, and two more to perform differential modulation. Other connection

patterns are also provided for diagnostic purposes. Around the periphery of this layout

are 80 μm × 80 μm square pads that can be wire-bonded to a chip package. Since

these wire-bonded connections are only for providing DC voltage biases, we need not

be concerned with high-speed interconnects or packages. The only nodes which

fluctuate at high speeds are those that exist between two modulators; no external

connections are made to these nodes so that the capacitance is minimized, and is

dominated by the device capacitances.


p and n contacts for single modulator

two modulators connected in series for single-ended testing

three modulators connected for

differential mode

single modulator

testing

pad for wirebonding to chip package

Figure 5.5 Metal mask layout for quartz carrier die. The metal pattern allows us to perform a variety of experiments, including direct control of a single modulator, single-ended testing using one modulator as a current source, and differential testing using one modulator as a current source. The peripheral pads are for wire-bonding, and are 80 μm × 80 μm. Pads for solder-bonding to modulators are approximately 15 μm × 15 μm.

5.2.2 Experimental Results

To illustrate that this processing technique produced functioning devices, we repeated

the time-resolved experiments of the single-ended modulator. The results (Figure 5.6)

were as expected: the output power of the modulator dropped quickly when the second

modulator (functioning as a simple photodetector) was triggered with an optical pulse.

The modulated output then recovered to its original level. Note too that when we

apply a strong enough pulse to the photodetector, we can observe the modulator

traverse through the first exciton peak of the electroasborption curve.


Modulator Response vs. Time

0.30

0.35

0.40

0.45

0.50

0.55

0 5 10 15 20Time (ns)

Refle

cted

Pow

er (m

W)

26.8

33.3

Avg. Current (mA)

Figure 5.6 Single-ended modulator output as a function of time.

We can now perform experiments that seek to demonstrate differential conversion

of input charge, using a pair of modulators. Figure 5.7 shows a photograph of the

devices, along with an equivalent circuit diagram.


Vin

V+

gnd

differential modulator pair

input current generator

Vin

Ppulse

Pin1 Pout1

gndV+

Pout2Pin2

Figure 5.7 Photograph and equivalent circuit for differential testing of optical modulators. Short pulses excite one of the modulators to generate the input current.

In one experiment, the output powers of the modulator pair, when observed

individually, were rather noisy. We ascribe this to a wire-bond which did not form a

good contact to one of the pads on the chip, due to residue epoxy on the surface.

Hence, the DC voltage bias on the modulator pair was not completely stable, and so

each pulsed injection of current led to ringing on the supply line. We can see this in

Figure 5.8, where we presume the noise must be triggered by the pulsed laser since it

is synchronized with the pulses. (We recorded the data here with a sampling scope

after averaging, and so any noise not at the frequency of the laser’s repetition rate

would be averaged out.)


Complementary Outputs from Differential Pair

-8

-6

-4

-2

0

2

4

6

0 5 10 15 20

Time (ns)

Out

put P

ower

(μW

)(v

ertic

ally

offs

et)

Pout1Pout2

Figure 5.8 Optical power versus time, for the two outputs of the differential modulator pair. Both signals have been vertically shifted so that 0 power represents the average output when no current is generated by the third modulator. (This shift is necessary to compensate for slight misalignment of the beams on the modulators.) Common mode noise (which we attribute to a weak wire-bond contact) is clearly apparent.

However, once we take the difference of these two signals, we see that much of

the noise has been cancelled out (Figure 5.9). This is a clear demonstration of the

noise-immunity properties of the differential scheme. In this case, we were able to

reject noise on the voltage supply line. Moreover, this differential signal exhibits the

exponential recovery time that we expect. With a measured capacitance of 60 fF, an

absorption sensitivity of about 0.05 V-1, and a total CW input power of 1.3 mW, the

predicted time constant is on the order of nanoseconds and hence consistent with the

fitted time constant of 3.5 ns.


Time-Resolved Differential Output

-4

-2

0

2

4

6

8

10

12

0 5 10 15 20

Time (ns)

Diff

eren

tial O

utpu

t (μW

) DifferentialOutputExponential Fit(tau = 3.5 ns)

Figure 5.9 Differential output signal versus time. Again, the signal has been vertically shifted so that zero output corresponds to no input current. Much of the common mode noise has been cancelled out.

In addition to observing the output with respect to time, we also tested the

linearity of this conversion scheme. Again, we measure the average current supplied

by the modulator undergoing pulsed excitation, and also measure the average output

power of the modulators. Because of the sensitivity of the measurement we were

unable to take very many data points. Still, the general trend seems to support the

concept that we can indeed achieve linear signal conversion [6].

After completing these simple tests, we then turned our attention to experiments

that more closely match the configuration for our A/D converter system. We will now

use an actual photoconductive sampling switch as the source of the current pulses,

rather than the modulator that we had been using for convenience’s sake.


Linear Electrical-to-Optical Conversion

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Input Charge (10^6 electrons)

Diff

eren

tial S

igna

l per

C

harg

e Pu

lse

(10^

6 ph

oton

s)

Data

Linear fit(slope = 1)

Figure 5.10 Optical energy in output pulse as a function of input charge. Units of photons and electron charge are used, so that the fitted slope of 1 corresponds to unity quantum efficiency. When the input charge is too high, the modulators are no longer able to completely discharge the input node.

5.3 MSM Integration

In order to use the photoconductive metal-semiconductor-metal (MSM) sampling

switch as our current source, we replace our quartz carrier die with a low-temperature

grown GaAs (LT GaAs) die. This LT GaAs die has similar metal patterns as before in

order to connect the modulators as we wish. Additionally, the metal pattern also

includes interdigitated metal fingers, thus forming the MSM switch. The switches

have fingers and spacings that are 1 μm in width, and the total switch area is

19 μm × 19 μm. Figure 5.11 shows one example for a mask used to fabricate the

carrier die.

5.3. MSM INTEGRATION 127

Figure 5.11 Metal mask layout for single-ended LT GaAs die. A 50-Ω coplanar strip transmission line offers the opportunity to test the MSM and modulator with high speed signals, though in actual experiments this was used only for DC input voltages.

In addition to the MSM structure, we also added a coplanar strip (CPS) electrical

waveguide to the top and bottom of the layout. This waveguide gave us the option of

introducing a non-DC input signal to be sampled by the MSM. We ultimately did not

perform such dynamic-input experiments (saving these for our tests of the differential

mode), but we still used these CPS structures to supply DC input signals to the MSM

switches. We defined the dimensions of the CPS waveguides so that they formed 50-

Ω transmission lines when placed on a substrate with GaAs’s relative dielectric

constant of about 13 [7].

One issue that came up when we attempted to solder-bond modulators to the LT

GaAs die is that the n-contact of the modulator would often not form a good contact to

the other die. This was not surprising, since the n-contact was at a slightly lower

elevation than the p-contact (approximately 0.5 μm). While with previous solder-

bonding to the quartz dies the indium bumps were thick enough (3 – 5 μm) to


compensate for this height difference, it was unclear why the problem arose only when

we attempted to solder-bond to LT GaAs dies. In any case, we solved this problem by

depositing about 0.5 μm thick indium bumps on the p-contact of the LT GaAs dies, a

picture of which is shown in Figure 5.12.

n-contact with indium bump

p-contact without indium bump

MSM

Figure 5.12 Photograph of a section of a LT GaAs die. Extra indium bumps have been deposited on all metal pads that will be bonded to the n-contact of the modulator.

For testing the modulators in differential mode, we needed to supply an AC input

signal to one side of the MSM. The other side then connects to the center node

between a pair of series-connected modulators. The mask for these experiments is

shown in Figure 5.13.

5.3. MSM INTEGRATION 129

Figure 5.13 Metal mask layout for differential LT GaAs die. A 50-Ω coplanar strip transmission line offers the opportunity to test the MSM and modulator with high speed signals. Differential modulators require both positive and negative bias. The wire-bond pad for one of these is placed within the transmission line, and the wire-bond must jump over the CPS.

Because we were limited to a single metal layer, a “jumper” wire was needed in

order to accommodate the CPS waveguide while providing both positive and negative

biases to the differential modulator pair. Hence, only the top or bottom two rows of

modulators in the array could be tested in this manner. (For an actual system

implementation, using a second metal layer would allow all modulators in a 2D array

to be fully utilized. One way to do this is to deposit silicon nitride and then metal over

places that require a “jumper”.) In our test chip, these “jumpers” were formed by

using wire-bonds that connect from the bond pads (which are placed inside the CPS

waveguide) directly to the chip package. The CPS waveguide thus run underneath the

wire-bonds.

Other fabrication details pertaining to the MSM may be found in Chapter 4.


5.4 DC Testing

5.4.1 Single-ended operation

As before, we again would like to observe the modulator’s response versus time, and

verify linear electro-optic conversion. Figure 5.14 shows a photograph and circuit

schematic of the devices that we tested.

V+

Vin

Ppulse

Pin

Pout

MSM

modulator

Vin

V+

Figure 5.14 Photograph and schematic of MSM sampling and single-ended modulator operation. Wire-bonds carry the DC input signal and positive bias voltage. The pulse and CW input beams Ppulse and Pin are incident on the sample at a normal angle.

In one set of experiments, we observed the modulator’s behavior with time for

different input CW powers. Figure 5.15 shows one example of this.

5.4. DC TESTING 131

Figure 5.15 Modulator output power versus time. The behavior is marked by a sharp initial drop when the MSM switch samples the input voltage, and a subsequent exponential recovery. The input CW power is about 0.5 mW.

We can then repeat this measurement for different input CW powers, and fit an

exponential curve to each of the recovery waveforms. Recall that the time constant is

given by

CWPC

e γωτ h

=1 . (5.3)

Hence, there should be a linear relationship between the input CW power and the

inverse of the time constant, whose slope is defined by (5.3). Figure 5.16 shows the

result from our experiment.

0 2 4 6 8 10 12

7.0

7.5

8.0

8.5

9.0

Exp Fit (τ = 3.5 ns)M

odul

ator

Out

put

at P

hoto

dete

ctor

(μW

)

Time (ns)


Figure 5.16 Recovery speed as a function of input CW power. Using a first-order approximation, the relationship should be linear, as the data indicates. The calculated slope is 1.05, which matches the data well.

For the devices used here, each modulator had a capacitance of 15 fF, while the

MSM switch’s capacitance was 10 fF. With an electroabsorption slope γ of about

0.06 V-1, and operating at a wavelength of 850 nm, the calculated slope should be

1.05×1019 (s-mW)-1. This first-order approximation matches well with the result from

our data.

We also sought to verify linear conversion for this MSM/modulator device [8].

However, unlike previous experiments where we adjusted the pulse power incident on

a modulator to supply input current pulses with different amplitudes to the modulator,

in these experiments we changed the amplitude of the DC voltage which the MSM

switch sampled. We thus plot the average absorbed power’s dependence on the input

current by measuring the series current with a current preamplifier (Figure 5.17).

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

1

2

3

Response Speed vs. CW Power

slope = 1.07

1/τ

x 10

9

CW Optical Power (mW)

5.4. DC TESTING 133

Absorption vs. Input Current

1.48E+151.50E+151.52E+151.54E+151.56E+151.58E+151.60E+151.62E+151.64E+151.66E+15

-1.5E+14 -1E+14 -5E+13 0 5E+13 1E+14 1.5E+14 2E+14 2.5E+14

Input Current (electrons/s)

Abs

orbe

d Po

wer

(p

hoto

ns/s

)0.511.021.53

Pulse Power (mW)

Figure 5.17 Absorbed power by modulator versus input current. Each curve represents the response for a different incident pulse power. The magnitude of the pulse power does not appreciably affect these curves. Once the input charge is high enough to sufficiently reverse bias the modulator, we see the linear conversion. Using units of photons and electrons, the slopes of all three curves in the linear region is about unity.

As expected, we enter a linear conversion region (with a quantum efficiency of

approximately unity) once the input current is high enough. This threshold current

does not depend on the pulse beam power which triggers the sampling switch. From

the modulator’s point of view, it is able to perform linear conversion as long as a high

enough input current is supplied to cancel out the diode diffusion current in the

forward direction. A slight increase in the absorption can be seen as the pulse power

is increased; this is likely due to heat from the MSM diffusing to the neighboring

modulator and increasing its temperature.

Instead of plotting the absorbed power versus current, we can also plot the power

versus input voltage (which is the variable we are directly controlling). While the

curves in Figure 5.18 are similar to those of Figure 5.17, we see that the threshold

voltage for linearity decreases as the pulse power increases. For the pulse powers used

here, we are not fully charging up the modulator to the input voltage. Hence, to

achieve the required threshold current, a larger input voltage is needed when the pulse


power is low. Once we have exceeded the threshold voltage though, we again enter

the linear conversion regime.

Absorbtion vs. Input Voltage

0.3400.3450.3500.3550.3600.3650.3700.3750.3800.385

-5 0 5 10 15 20 25

Input Voltage (V)

Abso

rbed

Pow

er (m

W)

0.51

1.02

1.53

Pulse Power (mW)

Figure 5.18 Absorbed power versus input voltage. The onset of the linear region occurs at higher voltages when the pulse power is lower, since linearity requires a minimum input current.

In the last experiment we shall discuss here, we examine these linearity curves as

we change the input CW power. As shown in Figure 5.16, one effect of increasing

CW power is that we increase the speed of the device. However, an additional effect

we observe is that the input range of the device also increases (Figure 5.19).

As we change the CW power, the absolute absorbed power for low input voltages

is of course quite different. For clarity then, we have vertically shifted the curves so

that the absorbed power at low voltages is zero on this scale. The behavior is quite

similar when the CW power is large enough; when the input power is 0.61 mW and

0.92 mW, the modulator is able to provide linear conversion up to 25 V. However,

when the CW power is only 0.34 mW, the conversion abruptly saturates just below

20 V.

5.4. DC TESTING 135

Absorbed Power vs. Input Voltage(Offset to same baseline)

-0.005

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

-5 0 5 10 15 20 25Input Voltage (V)

Abs

orbe

d Po

wer

(mW

)

0.34

0.61

0.92

CW Power (mW)

Figure 5.19 Absorbed power versus input voltage, with different CW powers. The curves have been offset in the vertical direction for clarity, since the baseline absorption is naturally quite different for different CW powers. For the pulse power used here, the behavior is similar when the CW power is large enough. The range is quite limited when the CW power is small.

The amount of input charge the modulator can discharge is limited by the

maximum amount of optical energy it can absorb before it receives another charge

pulse. In the case of an input CW power of 0.34 mW, the modulator can not

completely discharge its input charge before the next sampling event. In other words,

the voltage across the MSM does not sufficiently “reset” after each laser pulse.

In the case of the higher CW powers, increasing the input voltage from 18 V to

19 V implies supplying an extra amount of charge Q to the modulator. For the low

CW power case, increasing the input voltage implies supplying less than Q extra

charge, because the modulator does not reset sufficiently. Consequently, the

conversion slope for low CW power in Figure 5.19 is smaller than the conversion

slopes for the higher CW powers.

We note too that the absorption curve begins to rise earlier when the CW power is

small. Again, because the modulator does not completely reset, it is charged up to a

higher voltage when compared with the other two cases. For a given input voltage to

the MSM then, the effective input voltage to the modulator is actually higher.


Lastly, we observe that the absorption curve appears to flatten out just below 20 V.

For other modulators on this die to which we could directly apply a voltage, many of

them exhibited a reverse breakdown voltage between 15 and 20 V. We suggest then

that the modulator’s response abruptly flattens at the observed input voltage because

the MSM has begun to (attempt to) charge the modulator past the reverse breakdown

voltage. The breakdown voltage serves as a clamp limiting the bias we can apply to

the modulator, and so leads to the behavior we see here.

5.4.2 Differential Mode

Armed with this understanding of the modulator’s behavior, we turn towards

experiments verifying differential mode operation. For these experiments, we use the

devices shown in the SEM image in Figure 5.20. Figure 5.21 is a photograph taken

through optical microscopy, along with the equivalent circuit.

Figure 5.20 Scanning electron microscope (SEM) image of differential modulator pair with MSM sampling switch. The MSM fingers and spacings are both 1 μm in width, with a total switch size of 19 μm × 19 μm. The modulators are 80 μm × 40 μm, though the active area is on the order of 12 μm × 12 μm.

5.4. DC TESTING 137

Figure 5.21 Photograph and schematic of MSM sampling and differential modulator operation. A co-planar strip waveguide supplies the input voltage Vin. The pulse and CW input beams Ppulse and Pin are incident on the sample at a normal angle.

As before, we are interested in whether the modulators can still perform linearized

electro-optic conversion when configured in a differential mode. Figure 5.22 shows

that this is indeed the case [9]. We also see a side benefit to the differential scheme:

we are now able to process both positive and negative input voltages. This means that

dynamic inputs can have a DC bias of 0 V, and still reside squarely in the middle of

the device’s operating range.


Linearized Differential Conversion

0.510.520.530.540.550.560.570.580.590.60

-30 -20 -10 0 10 20 30

Input Voltage (V)

Diffe

rent

ial O

utpu

t P

ower

(mW

)

Figure 5.22 Linear differential electro-optic conversion. We plot the average differential output power of the modulator pair, versus the input DC voltage. The modulators were biased at ±3 V.

Under ideal balanced conditions, the differential output power should be 0 mW

when the input voltage is 0 V. We were unable to produce such a result here, because

of limitations in our optical setup. The CW beam spot diameter of ~10 μm was about

equal to the nominal size of the modulators’ active area. Hence even slight

misalignment of the beams can lead to the vertical conversion offset seen in the data.

Note however that this did not detract from the linearity of the conversion. Also, it is

quite possible to obtain smaller spot sizes with the appropriate high-magnification

objective lens. We did not do so here because the working distance of the available

lenses were too small to accommodate the electrical probes in our setup.

When the input voltage was at +15 V and at -15 V, we also measured the

modulators’ response versus time. Since the signal is differential, we see that it can be

either positive or negative. Also, the 90 ps time constants of the exponential fits

match well with the calculated time constant of 100 ps, where the total input power is

4.2 mW, the capacitance is ~40 fF, and the electroabsorption slope γ is ~0.1.

5.5. DYNAMIC TESTING 139

0 1 2 30.80

0.85

0.90

0.95

1.00

1.05

Differential Output-15V Bias +15V Bias

Data Exp Fit (τ = 90ps)D

iffer

entia

l Sig

nal

(Nor

mal

ized

)

Time (ns)0 1 2 3

0.9

1.0

1.1

1.2

1.3 Data Exp Fit (τ = 90ps)

Figure 5.23 Differential output versus time. For both positive and input voltages, we see a recovery time of less than 100 ps. We obtain the differential signals by separately measuring the response from each modulator, and then numerically subtracting these.

The results discussed above prove that we are able to perform linear electro-optic

conversion, at sampling rates suitable for a channel speed of 1 GS/s. While previous

work had shown that the MSM switch can indeed sample high speed signals [11], we

would also like to demonstrate this capability when the MSM is driving a differential

modulator pair.

5.5 Dynamic Testing

In our final set of experiments, we introduce a sinusoidal input voltage to the MSM

switch. Ideally we would then want to sample these sinusoids with a mode-locked

laser with a repetition rate of many 10s of GHz. Since we had available to us only an

80 MHz laser, for experimental purposes we employed a sampling technique akin to

that implemented by sampling oscilloscopes.

Figure 5.24 is a schematic of the experimental setup. The mode-locked laser

provides the reference clock to which all other signals are synchronized. A

photodetector at the laser provides an 80 MHz periodic waveform that represents the

repetition rate of the laser. A pulse generator (HP 8133A) receives this waveform and


produces a clean 80 MHz square wave that is thus locked to the laser. We then use an

80 MHz filter to reject the higher odd harmonics of the square wave, producing an

80 MHz sine wave. An amplifier amplifies the 80 MHz signal to ~16 dBm, or about

1.4 V in amplitude. (Frequency multipliers may also be inserted here to produce

signals at higher frequencies.) Finally, to facilitate lock-in detection, an electronic

modulator (HP 11665B) mixes the amplified sine wave with a 5 kHz square wave

from an external signal generator. This modulated sine wave is applied to the input

node of the MSM, through the CPS electrical waveguide on the LT GaAs die.

Figure 5.24 Schematic of experimental setup for dynamic testing of differential modulators. The MSM is triggered by a pulsed laser to sample a high-frequency sinusoid that is synchronized to the laser. Slow detectors and lock-in amplifiers measure the average output powers from the differential modulator pair. A personal computer running a custom LabVIEW program collects the data, and also introduces successive phase shifts at the pulse generator to sample the entire sinusoidal waveform.


With the apparatus as described above, the MSM would continually sample the

same point on the input sinusoid. The differential modulator pair then produces a

differential optical signal representing this sampled electrical voltage. Slow

photodetectors measure the average output power, and lock-in amplifiers produce a

single datapoint that is collected by a computer running LabVIEW.

The LabVIEW program also controls the pulse generator, and introduces a small

phase shift between the synchronization waveform from the laser and the square wave

output. This causes the MSM switch to sample a different point on the sinusoidal

waveform. Hence, by successively shifting the phase of the pulse generator, we are

able to trace out the original sinusoid at the MSM’s input. Figure 5.25 shows one

result from this experiment.

Differential Conversion of 80 MHz Sinusoid

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0 2 4 6 8 10 12

Time (ns)

Diffe

rent

ial O

utpu

t (μW

)

Signalbest fit

Figure 5.25 Differential output signal while sampling an 80 MHz sinusoid. The data is not collected in real-time, since each data-point comes from a measurement based on lock-in detection. The pulse power is 5.4 mW, corresponding to a pulseenergy of 68 pJ. The linearity of the conversion is 4.5 effective number of bits.

In order to calculate the effective number of bits (ENOB) resolution for this data,

we perform an overlap integral of the data with both a sine and a cosine waveform at

the fundamental frequency of 80 MHz. Adding the results of these overlap integrals in


quadrature tell us how much of the signal’s power resides at the fundamental input

frequency. (The square-root of half the fundamental power also tells us the amplitude

of the best-fit sinusoid. The arctangent of the overlap integrals gives us the phase.)

Power at any other frequency, up to the Nyquist frequency of 50 GHz but ignoring DC,

then represents noise and distortion. Taking the ratio gives us SNDR and hence

directly leads to resolution in bits. For the data of Figure 5.25, we find that the ENOB

has a resolution of 4.5 bits. This satisfies the original project goal of achieving 3 to 5

bits of resolution in the A/D system.

The data collected in this way also allows us to evaluate the performance of the

MSM sampling switch. Specifically, we can observe to what extent it is able to charge

the modulators’ input node up to the input voltage. In Figure 5.26 we plot the

amplitude of the modulator’s sinusoidal output with respect to the energy of the laser

pulses that trigger the MSM. We see from the data that we have not been able to

completely charge the node up even with the highest pulse power that we used.

Assuming a simple RC-like charge-up, where the resistance of the switch is

proportional to the pulse energy, the data should follow an exponential decay. Such a

curve turns out to fit our data well, and we have an exponential decay constant of

52 pJ. This implies that, we would need pulse energies of above 225 pJ in order to

charge up the node to within 1% of the input voltage. Full charge-up is desirable,

since it increases the robustness of the system. For example, by ensuring full charge-

up we make the system less vulnerable to misalignment of the short pulses, or to

fluctuations in the pulse power. However, pulse energies above 225 pJ are rather high,

and point to the need for further work on the switch material in order to realize a more

robust converter system.


Saturation with Pulse Power

050

100150200250300350

0 20 40 60 80 100 120

Pulse Energy (pJ)

Opt

ical

Out

put

Am

plitu

de (n

W)

DataExp. Fit

Figure 5.26 Amplitude of differential modulator output versus pulse energy. As the pulse energy increases, we approach full charge-up of the sampled voltage. Assuming an RC-like mechanism, we can fit an exponential decay to the data. The best fit curve a decay constant of 52 pJ, and the amplitude approaches 343 nW at large pulse energies. Extrapolating from this curve, charging to 99% of the input voltage would require a pulse energy of about 225 pJ. While full charge-up may be desirable for increased robustness, it is not necessarily required for linear operation.

We also verify that this sampling and electro-optic conversion process can also

work at higher frequencies beyond 80 MHz. Using a series of frequency multipliers,

we test our devices with input signals at 2, 10, and 20 GHz. We then use the

commercial software tool MATLAB to find the discrete Fourier transform (DFT) of

this data. The results are shown in Figure 5.27 through Figure 5.29.

0 1 2 3 4 5x 10-10

-300

-200

-100

0

100

200

Time (s)

Diff

eren

tial O

utpu

t (nW

)

0 0.5 1 1.5 2

x 1011

0

50

100

Frequency (Hz)

Am

plitu

de (d

B)

Figure 5.27 Differential output signal for a sampled 2 GHz sinusoid, along with its discrete Fourier transform (DFT).


0 0.2 0.4 0.6 0.8 1x 10-10

-4000

-2000

0

2000

4000

Time (s)

Diff

eren

tial O

utpu

t (nW

)

0 0.5 1 1.5 2

x 1011

0

50

100

Frequency (Hz)

Am

plitu

de (d

B)

Figure 5.28 Differential output signal for a sampled 10 GHz sinusoid, along with its discrete Fourier transform (DFT).

0 0.2 0.4 0.6 0.8 1x 10-10

-200

-100

0

100

200

Time (s)

Diff

eren

tial O

utpu

t (nW

)

0 1 2 3 4

x 1011

20

40

60

80

Frequency (Hz)

Am

plitu

de (d

B)

Figure 5.29 Differential output signal for a sampled 20 GHz sinusoid, along with its discrete Fourier transform (DFT). The lowest non-DC frequency component is the 10 GHz sub-harmonic, and is not due to non-linearity of the sampling or conversion process. The 20 GHz signal is generated by doubling a 10 GHz signal, and a significant portion of the 10 GHz power leaks through the doubler.

Once we have the DFTs, we can then find the SNDR (and hence ENOB) by

summing the powers present at all non-DC frequencies within the Nyquist band. One

exception to this is our calculation for the 20 GHz case. In order to produce the 20

GHz signal, we used a frequency doubler (Marki Microwave ADA-0410) to process a

10 GHz sinusoid. However, the frequency doubler exhibited measurable leakage of

the 10 GHz signal, at about 20dB below the 20 GHz sinusoid. This 10 GHz signal

thus also appears at the modulator output, and to evaluate the performance of the

MSM and modulators we simply ignore that sub-harmonic when calculating the

resolution.

This leads to ENOB figures of 5.0, 4.3, and 4.2 for the 2 GHz, 10 GHz, and

20 GHz data, respectively. These results verify that our devices can meet the target

resolutions for the overall A/D system.


One notable point from these DFT plots is that the higher harmonics are typically

buried in the noise floor. This indicates that the resolution figures derived here are not

limited by non-linearity, but are instead limited by noise present in the system. Our

modulators thus exhibit the potential for performing electro-optic conversion at even

higher resolution.

Because of our use of lock-in techniques, most sources of noise (such as from the

supply lines or from the laser) should be filtered out. This fact suggested that the

noise originates with the input sinusoids before they are electrically chopped, or to

noise generated by the electronic modulator. Experimentally, we observed that the

noise seen at the output of the lock-in amplifiers dropped by an order of magnitude

when no pulse power was provided to the MSM. This seems to indicate that the

source of the noise does not come from the CW laser. The noise also virtually

disappears when we block the modulators’ optical outputs from hitting the

photodetectors; this would indicate that the noise is not coming from the

photodetectors or from the lock-in amplifiers.

These observations all seem to point towards the generated electrical input

waveforms as the root cause of the observed noise. Yet, when we measure these

electrical signals with a high-speed oscilloscope, we did not observe noise of the

magnitudes seen in the data.

However, in our experimental setup the signal lines were not properly terminated

with a 50-Ω load at the end of the transmission line. Moreover, the capacitances of

the linear array of MSM and modulator devices along the transmission line also lead

to a complicated impedance. Despite these non-ideal conditions, we managed to

obtain reasonable results even at high frequencies. This is probably because the

transmission line on our LT GaAs die is relatively short, and we can treat the line as a

lumped element. That said, the amplifiers, frequency multipliers, and electrical

modulators that we used were all designed to drive a 50-Ω load, so perhaps excess

noise is generated by these components in our experiments. Unfortunately, such noise

would of course not appear if we simply measure the generated waveform with a


suitably terminated oscilloscope. Further work using a more rigorously designed

microwave system could verify the hypotheses we suggest here.

5.6 Conclusions

We have developed a process flow suitable for fabricating modulators that can serve

as transmitters for an optical remoting link in a photonic-assisted A/D converter.

Initial test structures used the modulators themselves as photodetectors to provide

pulsed current inputs to the optical transmitter. Experimental results on such

structures indicated self-linearized operation in both single-ended and differential

modes.

We have also integrated modulators with the MSM photoconductive switches that

can sample the input waveforms for the A/D system. Using DC input voltages, we

verified our understanding of these modulators. We have also tested these modulators

with sinusoidal input signals in order to more closely emulate how such devices would

work in an actual system.

Our experiments demonstrated that these modulators are capable of performing

electro-optic conversion of at least 4 bits of resolution. This meets the target

resolution for the overall system. Moreover, the data indicate that the resolution is

likely not limited by non-linearities in the devices, but rather in noise in our

experiments. Finally, we also show that pulse energies greater than 200 pJ are

required if we want to fully transfer the input voltage to the modulators. While full

charge-up is not required for linear sampling and electro-optic conversion, it is

desirable in order to implement a more robust system.


5.7 Bibliography

[1] G. A. Keeler, “MQW Modulator Design, Fabrication, and Integration,” Optical

Interconnects to Silicon CMOS: Integrated Optoelectronic Modulators and Short

Pulse Systems, Ph.D. Dissertation, Stanford University (2002).

[2] F. L. Pedrotti, S.J, and L. S. Pedrotti, “Fresnel equations,” Introduction to Optics,

2nd Ed., pp. 407–425 (1993).

[3] E. D. Palik, Handbook of Optical Solids, vol. 1, pp. 438–439 (1985).

[4] T. Kitano, S. Izumi, H. Minami, T. Ishikawa, K. Sato, T. Sonoda, and M. Otsubo,

“Selective wet etching for highly uniform GaAs/Al0.15Ga0.85As heterostructure

field effect transistors,” Journal of Vacuum Science Technology B, vol. 15, pp.

167–170 (1997).

[5] M.-G. Kang, S.-H. Sa, H.-H. Park, K.-S. Suh, and K.-H. Oh, “The

characterization of etched GaAs surface with HCl or H3PO4 solutions,” Thin

Solid Films, vol. 308–309, pp. 634–642 (1997).

[6] H. Chin, G.A. Keeler, N.C. Helman, M. Wistey, D.A.B. Miller, and J.S. Harris,

Jr., “Differential optical remoting of ultrafast charge packets using self-linearized

modulation,” IEEE/LEOS Annual Meeting Conference Proceedings, pp. 467–468

(2002).

[7] C. P. Wen, “Coplanar waveguide: a surface strip transmission line suitable for

nonreciprocal gyromagnetic device applications,” IEEE Transactions on

Microwave Theory and Techniques, vol. 17, pp. 1087–1090 (1969).

[8] H. Chin, R. Urata, R. Chen, K. Ma, D.A.B. Miller, and J.S. Harris, Jr., “Linear

electro-optic conversion of sampled voltage signals using a low-temperature-

grown GaAs MSM and a multiple quantum well modulator,” CLEO 2005 Tech.

Digest, pp. 1718–1720 (2005).

[9] H. Chin, R. Urata, K. Ma, D.A.B. Miller, and J.S. Harris, Jr., “Linear differential

electro-optic conversion of sampled voltage signals using a MSM and multiple

quantum well modulators,” IEEE LEOS Tech. Digest, pp. 57–58 (2005).






149

Chapter 6

Conclusion

In this chapter we summarize the work presented in this dissertation. We also

offer suggestions on different avenues for future work from three different

perspectives: the overall A/D system, the switch and modulator devices, and other

potential applications.

6.1 Summary

In this dissertation we have explored the application of multiple quantum well optical

modulators to a photoconductive-sampling time-interleaved analog-to-digital

converter. The system overcomes the limitation of aperture jitter that appears to

plague many A/D converters by employing a sampling clock based on a mode-locked

laser. A high-bandwidth sampling switch using low-temperature-grown (LT) GaAs

allows for the sampling of high-frequency electrical waveforms.

Within the context of this proposed system, we suggest that an optical link that

isolates the sampling switches from the CMOS quantizer circuits may be of benefit.

This link requires a compact, low-capacitance device that can perform linear electro-

optic conversion at speeds greater than that of an individual channel.

150 CHAPTER 6. CONCLUSION

We have demonstrated that optical modulators operating in a “self-linearized”

mode offers great promise to satisfy that need. Our initial experiments began with

simple, pre-fabricated test circuits consisting solely of optical modulators. Eventually

they progressed to hybridly integrated modulators and metal-semiconductor-metal

(MSM) sampling switches that we fabricated in facilities at Stanford University.

Without resorting to exotic processing techniques, we produced research devices that

clearly demonstrate the capabilities of these devices.

A first-order model for the device’s temporal response proved to be a fairly

accurate one, and we saw the expected dependence of speed on input optical power.

We also showed some advantages to employing a differential scheme for self-

linearized optical modulation. Ultimately, we measured modulator time constants

down to 100 ps, and also linearity exceeding 4 effective bits of resolution for input

signals ranging from 80 MHz to 20 GHz. Our results also appear to indicate that

experimental noise is the limiting factor for this resolution, and not inherent non-

linearity in the modulator absorption process.

6.2 Future Directions

6.2.1 A/D System

One positive result from our dynamic tests is that the resolution does not appear to be

limited by non-linearity in the modulator. However, we were unable to definitively

identify the source of this noise. We suggested that the excess noise may be due to

non-ideal electrical loading on the amplifiers and other electronic components that

generated the input test waveforms. Experiments using a more carefully designed

high-speed electrical system could help bolster or counter this claim. Engineering

such a robust RF system would also be required in order to realize the full

implementation of our proposed A/D system. In particular, we would need to

demonstrate the feasibility of electrically demultiplexing high-bandwidth signals with

6.2. FUTURE DIRECTIONS 151

on the order of 100 individual channels. Efforts towards this would clearly be

beneficial.

Another important topic that was beyond the scope of this work involves the

receiver that would convert the modulators’ optical output back into the electrical

domain for quantization by CMOS circuits. We did conduct some initial

investigations, and a colleague, Ray Chen, designed a receiver circuit to amplify and

integrate-and-reset the output of a photodetector. We also fabricated MSM GaAs-

based detectors and solder-bonded these to the receiver circuit. Some initial

experimental results with the MSM photodetectors appeared promising.

For example, the photocurrent of our fabricated MSMs exhibited a linear

photocurrent-to-input power relationship (Figure 6.1). Such a constant responsivity is

important for maintaining the linearity of the optical link. The responsivity is also

fairly independent of bias voltage (for large enough bias), as seen in Figure 6.2.

Current vs. Optical Power

0

50

100

150

200

250

300

350

0 1 2 3 4

Optical Power (mW)

Curr

ent (

μA)

Figure 6.1 Photocurrent of MSM GaAs modulators versus optical power. The linear relationship indicates constant responsivity. The active material is a 1 μm thick layer of fully-depleted, undoped GaAs. The MSM structure consists of 1 μm width fingers and spacings.


Photocurrent vs. Voltage Bias

0

50

100

150

200

250

300

350

0 1 2 3 4 5

Voltage (V)

Pho

tocu

rren

t (μA

) 0.42 mW

0.82 mW

1.22 mW

1.95 mW

2.5mW

0 mW

Figure 6.2 Photocurrent versus bias voltage for MSM detector. A flat response (as is evident for relatively large voltages) is desired to maintain a constant responsivity.

In addition to characterizing the detectors, we also used these to detect the output

from the optical modulator when operating in self-linearized mode. These results

were also encouraging, since we observed a linear conversion starting from the

electrical input to the modulator and ending at the electrical output of the

photodetector (Figure 6.3).

Detector Output vs. Modulator Current

01234567

0 20 40 60 80 100 120 140 160

Avg. Input Current to Modulator Transmitter (uA)

Avg.

Cur

rent

at

Phot

odet

ecto

r (pA

)

Figure 6.3 Demonstration of linear link between optical modulator and MSM photodetector. The electrical output of the detector is plotted against the electrical input to the modulator. The two optoelectronic devices perform E-to-O and then O-to-E conversion.

6.2. FUTURE DIRECTIONS 153

While the results shown here are promising, much work remains in order to truly

demonstrate operation of the full optical link.

Another area for further study is operation of multiple modulator-based links in

parallel. Full implementation of the A/D system calls for 100 parallel channels.

Moreover, effective electrical sampling with the photoconductive switches likely

requires the use of a dummy switch [1]. Hence, even for a single A/D channel, we

would likely require two pairs of modulators — one differential pair for the signal

MSM, and another for the dummy MSM. Integration issues for such a multi-channel

system require further study.

Lastly, we were not able to perform all the linearity tests that are often performed

on A/D systems. While we did characterize much of the devices’ behavior through the

experiments described here, we were not able to measure the intermodulation

distortion of our device. Such distortion arises when two pure sinusoids are applied to

a system, and non-linear mixing produces tones at the sum and difference frequencies.

6.2.2 Device

Other topics for future study center on the actual optoelectronic devices.

Improvements on the photoconductive switch have been suggested [1], and a primary

target is for material with a higher responsivity that still maintains a large “OFF”

resistance and fast recombination rate.

A few avenues for work also exist for the optical modulators. For example, it

would be beneficial to enhance the device’s contrast ratio — the ratio of the output

power between the strongly absorbing state and the weakly absorbing state. This

would allow for operation at equivalent speeds but with lower incident power. The

recovery speed of the modulator depends on the electroabsorption slope γ and input

CW power. A high contrast ratio implies a large γ, and so a smaller CW power would

be needed to achieve a comparable speed.

One method for improving contrast ratio is to place the active quantum-well

region within a resonant optical cavity. This can greatly improve the contrast ratio at

the expense of optical bandwidth and temperature sensitivity [2]. While we did make


some attempts to do this in our work, the results were mixed due to processing and

optical test issues. Also, the resonant cavity’s effect on the linearity of the device

must be carefully considered. The self-linearization mode relies on having a

negligible (or at least constant) amount of power to be transmitted through the device

(as opposed to being absorbed or reflected). Using a gold reflector as we have done

here was sufficient to satisfy this requirement. However, operating with a resonant

cavity implies that the optical field inside the cavity can become quite high. If even a

small fraction of the extra optical power inside the cavity leaks through the back

reflector in a voltage-bias dependent fashion, we may observe intolerable degradation

of the modulator’s linearity. This potential problem may be overcome either with a

weakly resonant cavity (that still sufficiently boosts the contrast ratio), or with a very

highly reflective back reflector such as a distributed Bragg reflector (DBR).

A final way to improve device performance is to reduce the lateral dimensions,

and hence capacitance, of the modulator. The issues that set the minimum size of our

fabricated modulators are not insurmountable. From a process point of view, it was

difficult to use indium solder bumps that were much smaller than 6 μm × 6 μm, when

the height of these bumps was up to 5 μm. However, if we fabricate modulators with

coplanar contacts then we could use indium bumps that are shorter in height and hence

smaller in area. In fact, we may even be able to forego indium solder bumps

altogether and rely on gold-gold bonding [3].

From an optical testing point of view, we were limited to optical spots with

diameters on the order of 10 or 12 μm. This restriction was because only a low-

magnification microscope objection had a large enough working distance for us to fit

high-speed electrical probes onto our test samples. Redesigning the optical system

could easily allow for spot sizes down to 3 μm or less, as we observed such sizes with

high-magnification (but small working-distance) objective lenses.

6.2.3 Other Applications

The final area for future work involves exploring other applications for these devices

beyond A/D converters. There are a few applications that require analog optical links,


and such links may find self-linearized modulators to be beneficial. One example

involves radio-on-fiber, where optical fibers are modulated at radio frequencies, and

these radio frequencies themselves carry the signal of interest [4]. Such a technology

may be useful for broadband wireless distribution systems, as it allows widely

distributed antenna stations to be simpler and less expensive [5]. The necessary

complex portions of the system could then be concentrated at a central location. A

closely related application is for photonic distribution of cable television signals [6].

Another potential application for linearized modulators that may be considered

lies in multi-level signaling. Ultimately, we might think of analog waveforms as

simply signals with many discrete levels. One commonly studied encoding format is

PAM-4 — pulse amplitude modulation with 4 discrete levels (hence carrying two bits

of information). PAM-4 has been demonstrated in optical links [7], and linearized

modulators may offer the opportunity for encoding information with even more

discrete levels.

6.3 Bibliography

[1] R. Urata, Photonic A/D Conversion Using Low-Temperature-Grown GaAs MSM

Switches Integrated with Silicon CMOS, Ph. D. Dissertation, Stanford University

(2004).

[2] R. H. Yan, R. J. Simes, and L. A. Coldren, “Electroabsorptive Fabry-Perot

reflection modulators with asymmetric mirrors,” IEEE Phtonics Technology

Letters, vol. 1, pp. 273–275 (1989).

[3] T. S. McLaren, S. Y. Kang, W. Zhang, T.-H. Ju, and Y.-C. Lee, “Thermosonic

bonding of an optical transceiver based on an 8 × 8 vertical cavity surface

emitting laser array,” IEEE Transactions on Components Packaging and

Manufacturing Technology Part B Advanced Packaging, vol. 20, pp. 152–160

(1997).


[4] L. A. Johansson and A. J. Seeds, “36-GHz 140-Mb/s radio-over-fiber

transmission using an optical injection phase-lock loop source,” IEEE Photonics

Technology Letters, vol. 13, pp. 893–895 (2001).

[5] H. Ogawa, D. Polifko, and S. Banba, “Millimeter-wave fiber optics systems for

personal radio communication,” IEEE Transactions on Microwave Theory and

Techniques, vol. 40, pp. 2285–2293 (1992).

[6] R. Ohmoto, H. Ohtsuka, and H. Ichikawa, “Fiber-optic microcell radio systems

with a spectrum delivery scheme,” IEEE Journal on Selected Areas in

Communications, vol. 11, pp. 1108–1117 (1993).

[7] J. E. Cunningham, D. Beckman, X. Zheng, D. Huang, T. Sze, and A. V.

Krishnamoorthy, “PAM-4 signaling over VCSELs with 0.13μm CMOS chip

technology,” Optics Express, vol. 14, pp. 12028–12038 (2006).

157

Appendix A

Quantization Noise Derivations

We derive the average noise power that comes from quantization power. Using this

result, we then find the relationship between the effective number of bits (ENOB) and

the signal-to-noise-plus distortion ratio (SNDR).

A.1 Quantization Noise Power

Quantization implies assigning analog values to discrete bins. The quantization error

is the difference between the analog value and the digital value corresponding to the

assigned bin. We first make the reasonable assumption that, when averaged over the

entire full-scale analog input range VFS, all quantization error values are equally likely.

In this case, we have a random variable E representing the quantization error, and a

uniform probability density function (pdf) f(E) for this random variable given by

( )2/

2/2/2/

0/10

QEQEQ

QEQEf

>≤≤−

−<

⎪⎩

⎪⎨

⎧= (A.1)

158 APPENDIX A. QUANTIZATION NOISE DERIVATIONS

where Q is the magnitude of the least significant bit (LSB) for an N-bit A/D, and is

given by N

FSVQ 2/= . (A.2)

The limits of (A.1) come from the fact that in any digital bin, the maximum amplitude

of the error must be half the size of the bin. The magnitude of (A.1) comes from

normalizing the uniform pdf.

The average power of the error in E is found by averaging the square of the

magnitude. Thus, we have

( )

12

2

2/

2/

2

22

Q

dEQE

dEEfEE

Q

Q

=

=

=

∫

∫

−

(A.3)

Substituting (A.2) into (A.3) leads to

122 22

2N

FSVE

−⋅= (A.4)

A.2 Effective Number of Bits

Now that we know the power of the quantization noise from (A.4), we can derive the

formula linking the effective number of bits (ENOB) with the signal-to-noise-plus

distortion ratio (SNDR). For an ideal N-bit converter, the only source of noise and

distortion is the quantization noise power. The effective number of bits N is found by

equating the SNDR of a real converter with the SNDR of an ideal N-bit converter.

With a full-scale voltage range VFS, the largest sine wave that the ideal converter

can process has an amplitude of VFS/2. Since the power of a sine wave is given by half

the square of the amplitude, the SNDR is given by

A.2. EFFECTIVE NUMBER OF BITS 159

( )( )

N

NFS

FS

VV

SNDR

2

22

2

223

12/22/2/1

=

⋅=

− (A.5)

Converting (A.5) into decibels,

N

SNDR N

02.676.1

223log10dB)(in 2

10

+=

⎟⎠⎞

⎜⎝⎛= (A.6)

Solving for the effective number of bits N,

02.676.1dB)(in −

=SNDR

N (A.7)

160 APPENDIX A. QUANTIZATION NOISE DERIVATIONS

161

Appendix B

Fabrication Process Flow

This appendix includes details of the fabrication process flow. We cover both the

fabrication of the modulators, as well as the solder-bonding integration and wet-etch

removal of the GaAs substrate.

B.1 Lithography Procedures

B.1.1 Ginzton Microfabrication Facility

1. Clean with acetone, methanol, isopropanol, and water. Dry with nitrogen gun.

2. Bake for 10 minutes at 90°C on hot plate.

3. Spin HMDS adhesion promoter (5000 rpm for 40s).

4. Spin AZ4620 photoresist (PR) (5000 rpm for 40s).

5. Remove PR from backside of wafer.

6. Bake for 15 minutes at 90°C.

7. Align and expose on Karl Suss mask aligner at 9.11 intensity for 36 sec.

162 APPENDIX B. FABRICATION PROCESS FLOW

8. Develop in AZ400K developer (diluted at 1:4 in water) for ~3.5 min. Sample

should be checked under microscope to determine when the development has

finished.

9. Let sample sit in water for 10 to 15 minutes to help wash off any remaining

developer film.

B.1.2 Stanford Nanofabrication Facility

This recipe is similar to the Ginzton recipe. However, the 10 minute bake and

spinning of adhesion promoter is replaced with the programmed bake in the YES

prime oven. The PR process is to spin SPR 220-7 at 3500 rpm for 45 sec. Post-PR

bake is 5 min at 90°C. Expose 4 shots of 2 sec each. Develop in LDD26W for 90 sec.

The above recipe can be used for any of the typical lithography steps. The

exception is for definition of metals that contain photoconductive switches. Since the

metal layer is very thin in this case, a thin PR must be used: Shipley 3612 photoresist.

Use the same spin parameters, but bake for 60 sec instead of 5 min. Before exposure,

wipe the edges of the sample carefully with acetone-soaked wipe, to remove edge

bead. Expose for 2.1 sec. Develop in LDD26W for 20 sec.

B.2 Modulator Process Steps

B.2.1 N-holes

Lithography to open up n-holes for etchant to enter. Air bubbles can remain in the

holes during etching. To overcome this, spray water on the wafer with the water gun

for a while before trying to etch. Then put it into the etchant while wet so that air

bubbles do not reform. Once the sample has been placed in the etchant, vigorously

shake lthe wafer to remove the thin water film.

Wet Etch – Etch in H2SO4:H2O2:H2O (1:8:160). Calibrate the etch on a test piece

first. Time the etch so that it stops in the n-doped layer. Solvent clean and dry.

B.2. MODULATOR PROCESS STEPS 163

B.2.2 N-contacts

Lithography – makes holes for the n-ohmic deposition to stick to. Everything else lifts

off.

Plasma asher for 15 seconds to remove photoresist remnant film.

Oxide etch (1:1 HCl/water, 15 sec, DI rinse, N2 dry) to remove native oxide

formation.

N-contact deposition:

3000 Å Au

100 Å Ni

236 Å Au

63 Å Ge n-type ohmic contacts, no barrier

102 Å Au

108 Å Ge

substrate

Liftoff using acetone and ultrasound.

Rapid thermal anneal at 450˚C for 30 seconds.

B.2.3 P-contacts

Lithography – makes holes for the p-ohmic deposition to stick to. Everything else

lifts off. P-ohmics are not annealed, since we want to keep the reflectivity high.

Plasma asher for 15 seconds to remove PR remnant.

Reflective p-contact deposition with barrier layer. To maximize the reflectivity,

we use gold as the reflective surface, and therefore skip the Cr sticking layer which

would lower reflectivity. Also, we avoid annealing the wafer after the p-contact

deposition. Finally, the indium used for flip-chip solder could alloy with the gold,

again lowering the reflectivity. Therefore, we include a barrier layer, such as nickel or

copper, to stop indium diffusion. (Tests clearly show that gold and indium alloy into a

less-reflective conductive alloy.)


2000 Å Au

500 Å Cu p-type ohmic contacts, with In diffusion barrier

2000 Å Au

substrate

Liftoff (as above) using acetone and possibly ultrasound.

B.2.4 Capacitance Reduction

Lithography – opens up the p-contact area in order to etch off the p-region everywhere

except where the contact itself is. The contact itself protects the region below it, since

we use an anisotropic dry etch. This reduces the capacitance of the devices

significantly.

Affix sample to carrier wafer with a small piece of copper tape that ends up

completely concealed by the sample. (ie. No copper tape showing.) This tape

removes the requirement for a PR hard bake step and the resultant difficulty in

removing that PR.

PlasmaQuest RIE etch through the p-region at Stanford Nanofabrication Facility.

Parameters to use are as follows:

400 W ECR, 10 W RF

15 sccm Ar, 10 sccm BCl3 , and 3 sccm Cl2, though actual measured numbers

during run are 14, 10, and 1.5.

B.2.5 Mesa Etch

Lithography – covers both contacts and significant surrounding area. We etch

away everything else, down beyond the etch stop layer. Thus, following substrate

removal, only the mesas will remain on the chip.

Do a photoresist hardbake after developing. Using a hotplate, bake the PR mesas

at 140°C for 30 minutes.

Use copper tape to affix to carrier.

B.2. MODULATOR PROCESS STEPS 165

Dry etch with PlasmaQuest. Use anisotropic dry etch for GaAs/AlGaAs using

BCl3 and Cl2 as the active etchants and significant RF power for straight side-walls.

The same parameters as listed in the previous step are used.

Photoresist stripping – this step takes more time because of the hardbake and

plasma etching. Acetone alone will not work. Instead, use 1165 photoresist remover,

a.k.a. N-methyl-2-pyrrolidone. Remove the resist in a covered beaker of 1165 at 65°C

for 60 minutes. Give the beaker several seconds (~10 sec) of ultrasound agitation a

few times during the hour soak. A plasma ashing at the end may also prove quite

helpful.

B.2.6 Indium Deposition

Lithography – opens both contacts for indium solder bumps.

Deposit 3-6 microns of In.

Liftoff.

B.2.7 Array Protection

To avoid covering up the wire bonding pads on the carrier die, we must remove

the arrays of devices that surround the central array of devices. This can be done using

a large photoresist square to protect the main array. Also, overexpose the resist,

because it is likely to be extra thick at the edges and in between unwanted mesas (i.e.,

1813 with 40 second exposure, or 4620 with 45 seconds).

Etch away the unwanted stuff. Sulfuric acid:hydrogen peroxide:water (1:8:1) for 1

minute. This etch cannot be too long, or the later epoxy fill will be too thick. (If the

epoxy is too thick, it can expand during substrate removal and disconnect the

modulators from the carrier die.)

Solvent clean to remove the photoresist.

Cleave modulator arrays

Photoresist (especially hardbaked photoresist) will protect the indium bumps

during handling, so cleaving while covered with photoresist is usually preferable.


To cleave without damaging devices, hold the wafer by its edges with tweezers.

Carefully scribe a tiny mark (about 1 or 2 millimeters) at the edge of the sample,

where the cleave should occur. This may be done under a non-inverting microscope

for better precision. Place the wafer so that the scribed mark is over a thin piece of

metal, such as a paper clip or (even better) a sharp electrical probe that is used for

electrical testing of devices. Place a clean wipe on top of the resist-protected sample

and press down with your finger. The GaAs piece should snap neatly along a crystal

plane that matches the location of the scribed mark.

B.2.8 Carrier Die Preparation

The masks were described in Chapter 5. For the quartz die, typical deposition is first

15 nm of chromium followed by 200 nm of gold. LT GaAs preparation was described

in Chapter 4. The deposition is typically 10 nm of titanium followed by 100 nm of

gold, followed by a rapid thermal anneal.

B.3 Flip-Chip Bonding

Use the following steps on the Research Devices M8-A flip-chip bonder:

1. 1400 g pressure for 30 s at room temperature.

2. 1200 g pressure for 30 s at room temperature.

3. 1200 g pressure for 45 s at 140°C.

4. 1200 g pressure for 0 s at 65°C (ramp down as quickly as possible).

5. Release vacuum on the chucks holding either side of the now bonded sample..

Wick in epoxy. This provides additional mechanical strength for the modulators

after substrate removal, and stops any wet etchants from attacking the modulators

from the side during substrate removal. The epoxy type is TRA-BOND BA-2113.

Mix epoxy. Try to avoid introducing any bubbles. The best way is to skip the

mixing container altogether. Instead, cut both ends of the tube and squeeze it into a

small disposable dish, stirring gently.

B.4. SUBSTRATE REMOVAL 167

Apply dabs to edge of Si/GaAs interface. Use an optical fiber to collect a small

drop, and apply to the side of the modulator/carrier die bonded chip.

Cure for 4 hours at 65°C, or 24 hours at room temperature.

B.4 Substrate Removal

Non-selective removal: this is a fast wet etch to remove most of the substrate,

leaving about 50μm to remove selectively. Use photoresist to stick small chip pieces

onto larger glass slides. If the carrier die is GaAs, the sides of the sample must be

protected from the etch, and so photoresist should be applied to the edges of the chip.

This side-protection is not necessary if the carrier die is not etched by the acid

mixtures that will be used. This is the case for silicon, for example.

Place pieces into a basket, and put the basket into a tall beaker with a magnetic

stir-bar; the basket rests on top of a plastic spacer to leave room for the stir-bar.

Vigorously stir the etchant. This appears to make the GaAs etch more uniformly at a

fairly consistent rate of 10 microns/minute. Periodically measure the thickness with

the measurement tool in the clean room. When there is about 100 microns left, go

another 5 minutes and then stop. Do not use the measurement tool if there is less than

100 microns left, in case the GaAs breaks.

Selective etch: this should stop on the AlGaAs etch stop layer, leaving the

modulators behind on the carrier die. Use (citric acid:hydrogen peroxide) at (4:1).

Heating the citric to 40°C, which seems to etch the GaAs at about

1 micron/minute. Check the chips under a microscope every 3 minutes when we

approach the etch stop.

Remove the etch stop with HCl:water for 90 s. The colors of the modulators will

change: red-green-red-green-gray-gray-gray-gray.

Epoxy removal with drytek4 in Stanford Nanofabrication Facility. Parameters:

4sccm CHF3, 20 sccm (i.e. 100%) O2, Pressure = 150mtorr, RF = 100 W forward / 0

W reverse. Etch 5 minutes at a time to prevent overheating.


Remove sample from glass cover slip if necessary. The resist is often weakened

enough by the etch process that the chip can be removed if enough sideways force is

applied with tweezers.

Documents

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