Optoelectronic Integrated Circuit Design and Device Modeling

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Author: Jianjun Gao

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OPTOELECTRONIC INTEGRATED CIRCUIT DESIGN AND DEVICE MODELING

OPTOELECTRONIC INTEGRATED CIRCUIT DESIGN AND DEVICE MODELING Jianjun Gao East China Normal University, Shanghai, China

This edition first published 2011 Ó 2011 Higher Education Press, 4 Dewai Dajie, Xicheng District, Beijing, 100120, P.R. China. All rights reserved. Published by John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop, # 02-01, Singapore 129809, under exclusive license by Higher Education Press in all media and throughout the world outside the mainland of the People’s Republic of China. For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as expressly permitted by law, without either the prior written permission of the Publisher, or authorization through payment of the appropriate photocopy fee to the Copyright Clearance Center. Requests for permission should be addressed to the Publisher, John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop, #02-01, Singapore 129809, tel: 65-64632400, fax: 65-64646912, email: [email protected]. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The Publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Library of Congress Cataloging-in-Publication Data Gao, Jianjun, 1968Optoelectronic integrated circuit design and device modeling / Jianjun Gao. p. cm. Includes bibliographical references and index. ISBN 978-0-470-82734-5 (cloth) 1. Integrated optics. 2. Optoelectronic devices. I. Title. TA1660.G36 2011 621.3815–dc22 2010030422

Print ISBN: 978-0-470-82734-5 ePDF ISBN: 978-0-470-82735-2 oBook ISBN: 978-0-470-82736-9 ePub ISBN: 978-0-470-82838-0 Chinese ISBN: 978-7-04-031326-0 Typeset in 11/13pt Times by Thomson Digital, Noida, India. Not for sale within the mainland of the People’s Republic of China.

Contents Preface About the Author Nomenclature 1

Introduction 1.1 Optical Communication System 1.2 Optoelectronic Integrated Circuit Computer-Aided Design 1.3 Organization of This Book References

2

Basic Concept of Semiconductor Laser Diodes 2.1 Introduction 2.2 Basic Concept 2.2.1 Atom Energy 2.2.2 Emission and Absorption 2.2.3 Population Inversion 2.3 Structures and Types 2.3.1 Homojunction and Heterojunction 2.3.2 Index Guiding and Gain Guiding 2.3.3 Fabry–Perot Cavity Lasers 2.3.4 Quantum-Well Lasers 2.3.5 Distributed Feedback Lasers 2.3.6 Vertical-Cavity Surface-Emitting Lasers 2.4 Laser Characteristics 2.4.1 Single-Mode Rate Equations 2.4.2 Multimode Rate Equations 2.4.3 Small-Signal Intensity Modulation 2.4.4 Small-Signal Frequency Modulation 2.4.5 Large-Signal Transit Response 2.4.6 Second Harmonic Distortion

ix xi xiii 1 1 5 7 8 9 9 10 11 12 14 15 15 18 20 22 27 33 34 35 38 40 44 46 48

Contents

vi

2.4.7 Relative Intensity Noise 2.4.8 Measurement Technique 2.5 Summary References

51 55 58 58

3

Modeling and Parameter Extraction Techniques of Lasers 3.1 Introduction 3.2 Standard Double Heterojunction Semiconductor Lasers 3.2.1 Large-Signal Model 3.2.2 Small-Signal Model 3.2.3 Noise Model 3.3 Quantum-Well Lasers 3.3.1 One-Level Equivalent Circuit Model 3.3.2 Two-Level Equivalent Circuit Model 3.3.3 Three-Level Equivalent Circuit Model 3.4 Parameter Extraction Methods 3.4.1 Direct-Extraction Method 3.4.2 Semi-Analytical Method 3.5 Summary References

63 63 64 65 68 72 76 76 83 90 95 95 105 111 111

4

Microwave Modeling Techniques of Photodiodes 4.1 Introduction 4.2 Physical Principles 4.3 Figures of Merit 4.3.1 Responsivity 4.3.2 Quantum Efficiency 4.3.3 Absorption Coefficient 4.3.4 Dark Current 4.3.5 Rise Time and Bandwidth 4.3.6 Noise Currents 4.4 Microwave Modeling Techniques 4.4.1 PIN PD 4.4.2 APD 4.5 Summary References

113 113 114 116 117 118 119 119 121 122 122 124 129 145 145

5

High-Speed Electronic Semiconductor Devices 5.1 Overview of Microwave Transistors 5.2 FET Modeling Technique 5.2.1 FET Small-Signal Modeling 5.2.2 FET Large-Signal Modeling 5.2.3 FET Noise Modeling 5.3 GaAs/InP HBT Modeling Technique 5.3.1 GaAs/InP HBT Nonlinear Model

149 149 151 152 155 161 165 166

Contents

vii

5.3.2 GaAs/InP HBT Linear Model 5.3.3 GaAs/InP HBT Noise Model 5.3.4 Parameter Extraction Methods 5.4 SiGe HBT Modeling Technique 5.5 MOSFET Modeling Technique 5.5.1 MOSFET Small-Signal Model 5.5.2 MOSFET Noise Model 5.5.3 Parameter Extraction Methods 5.6 Summary References

168 170 171 175 176 177 181 181 183 183

6

Semiconductor Laser and Modulator Driver Circuit Design 6.1 Basic Concepts 6.1.1 NRZ and RZ Data 6.1.2 Optical Modulation 6.1.3 Optical External Modulator 6.2 Optoelectronic Integration Technology 6.2.1 Monolithic Optoelectronic Integrated Circuits 6.2.2 Hybrid Optoelectronic Integrated Circuits 6.3 Laser Driver Circuit Design 6.4 Modulator Driver Circuit Design 6.4.1 FET-Based Driver Circuit 6.4.2 Bipolar Transistor-Based Driver Integrated Circuit 6.4.3 MOSFET-Based Driver Integrated Circuit 6.5 Distributed Driver Circuit Design 6.6 Passive Peaking Techniques 6.6.1 Capacitive Peaking Techniques 6.6.2 Inductive Peaking Techniques 6.7 Summary References

187 187 188 190 191 194 195 197 199 205 207 215 221 222 224 225 226 229 229

7

Optical Receiver Front-End Integrated Circuit Design 7.1 Basic Concepts of the Optical Receiver 7.1.1 Signal-to-Noise Ratio 7.1.2 Bit Error Ratio 7.1.3 Sensitivity 7.1.4 Eye Diagram 7.1.5 Signal Bandwidth 7.1.6 Dynamic Range 7.2 Front-End Circuit Design 7.2.1 Hybrid and Monolithic OEIC 7.2.2 High-Impedance Front-End 7.2.3 Transimpedance Front-End 7.3 Transimpedance Gain and Equivalent Input Noise Current 7.3.1 S Parameters of a Two-Port Network

233 234 234 235 237 238 240 241 243 244 245 247 250 251

Contents

viii

7.3.2 7.3.3 7.3.4 7.3.5

Noise Figure of a Two-Port Network Transimpedance Gain Equivalent Input Noise Current Simulation and Measurement of Transimpedance Gain and Equivalent Input Noise Current 7.4 Transimpedance Amplifier Circuit Design 7.4.1 BJT-Based Circuit Design 7.4.2 HBT-Based Circuit Design 7.4.3 FET-Based Circuit Design 7.4.4 MOSFET-Based Circuit Design 7.4.5 Distributed Circuit Design 7.5 Passive Peaking Techniques 7.5.1 Inductive Peaking Techniques 7.5.2 Capacitive Peaking Techniques 7.6 Matching Techniques 7.7 Summary References Index

252 253 255 257 262 262 263 268 270 271 274 274 277 279 284 284 289

Preface This textbook is written for the beginning user of optoelectronic integrated circuit (OEIC) design. My purpose is as follows: . . .

To introduce the basic concepts of optoelectronic devices To describe the modeling technique for optoelectronic devices and electronic devices used in high-speed optical systems To provide advanced optical transmitter and receiver front-end circuit design techniques.

As we know, state-of-the-art computer-aided design (CAD) methods for OEICs rely heavily on models of real devices. When CAD tools are properly utilized, it is often possible to produce successful designs after only one design iteration. Given the considerable time and cost associated with unnecessary design revisions, CAD tools have proven themselves invaluable to electronic designers. Our primary objective with the present book is to bridge the gap between semiconductor device modeling and IC design by using CAD tools. Appropriate for electrical engineering and computer science, this book starts with an introduction of an optical fiber communication system, and then covers various lasers, photodiodes, and electronic devices modeling techniques, and high-speed optical transmitter and receiver design. Even for those without a good microwave background, the reader can understand the contents of the book. The presentation of this book assumes only a basic course in electronic circuits as a prerequisite. The book is intended to serve as a reference book for practicing engineers and technicians working in the areas of radio-frequency (RF), microwave, solid-state devices, and optoelectronic integrated circuit design. The book should also be useful as a textbook for optical communication courses designed for senior undergraduate and first-year graduate students. Especially in student design projects, we foresee that this book will be a valuable handbook as well as a reference, both on basic modeling issues and on specific optoelectronic device models encountered in circuit simulators. The

x

Preface

reference list at the end of each chapter is more elaborate than is common for a typical textbook. The listing of recent research papers should be useful for researchers using this book as a reference. At the same time, students can benefit from it if they are assigned problems requiring reading of the original research papers.

About the Author Jianjun Gao (M’05–SM’06) was born in Hebei Province, P.R. China, in 1968. He received BEng and PhD degrees from Tsinghua University, in 1991 and 1999, respectively, and an MEng degree from the Hebei Semiconductor Research Institute, in 1994. From 1999 to 2001, he was a Post-Doctoral Research Fellow at the Microelectronics R&D Center, Chinese Academy of Sciences, developing a PHEMT optical modulator driver. In 2001, he joined the School of Electrical and Electronic Engineering, Nanyang Technological University (NTU), Singapore, as a Research Fellow in semiconductor device modeling and wafer measurement. In 2003, he joined the Institute for HighFrequency and Semiconductor System Technologies, Berlin University of Technology, Germany, as a Research Associate working on the InP HBT modeling and circuit design for high-speed optical communication. In 2004, he joined the Electronics Engineering Department, Carleton University, Canada, as Post-Doctoral Fellow working on semiconductor neural network modeling techniques. From 2004 to 2007, he was a Full Professor with the Radio Engineering Department at Southeast University, Nanjing, China. Since 2007, he has been a Full Professor with the School of Information Science and Technology, East China Normal University, Shanghai, China. He has authored RF and Microwave Modeling and Measurement Techniques for Field Effect Transistors (USA SciTech Publishing, 2009). His main areas of research are characterization, modeling, and wafer measurement of microwave semiconductor devices, optoelectronic devices, and high-speed integrated circuit for radio-frequency and optical communication. Dr Gao is currently a member of the editorial board of IEEE Transactions on Microwave Theory and Techniques. Home page: http://faculty.ecnu.edu.cn/gaojianjun/info_eng.html.

Nomenclature Units nm mm fs ps ns GHz THz mW Mb/s Gb/s Tb/s c h k fF pF nF nH pH

nanometer, one-billionth of a meter (= 10 9 m) micrometer, one-millionth of a meter (= 10 6 m) femtosecond, one-millionth of a billionth of a second (= 10 15 s) picosecond, one-thousandth of a billionth of a second (= 10 12 s) nanosecond, one-billionth of a second (= 10 9 s) gigahertz, 1 billion vibrations per second (= 109 Hz) terahertz, 1000 billion vibrations per second (= 1012 Hz) milliwatt, one-thousandth of a watt (= 10 3 W) 1 million bits per second (= 106 bits per second) 1 billion bits per second (= 109 bits per second) 1000 billion bits per second (= 1012 bits per second) speed of light in vacuum, 300 million kilometers per second (= 3 108 m/s) Plank’s constant (= 6.626 10 34 J s) Boltzmann’s constant (= 1.38 10 23 J/K) femtofarad, one-billionth of a farad (= 10 15 F) picofarad, one-thousandth of a billionth of a farad (= 10 12 F) nanofarad, one-billionth of a farad (= 10 9 F) nanohenry, one-billionth of a henry (= 10 9 H) picohenry, one-thousandth of a billionth of a henry (= 10

Abbreviations 2-D AC

two-dimensional alternating current

12

H)

xiv

AGC AlGaAs APD BER BFL BH BJT CAD CPW CW DA DBR DC DCFL DFB DH DMUX DSM DWDM EA ECL ER FM FP GaAs GMIC GRIN-SCH HB HBT HEMT HOEIC HZ IL IM IMD IM-DD InP I/O ITS I–V laser LD

Nomenclature

automatic gain control aluminum gallium arsenide avalanche photodiode bit error rate/ratio buffered FET logic buried heterostructure bipolar junction transistors computer-aided design coplanar waveguide continuous wave distributed amplifier distributed Bragg reflector direct current direct-coupled FET logic distributed feedback lasers double heterojunction demultiplexer dynamic-single-mode dense wavelength division multiplexing electroabsorption emitter coupled logic extinction ratio frequency modulation Fabry–Perot gallium arsenide optoelectronic glass microwave integrated circuit graded index separate confinement heterostructure harmonic balance heterojunction bipolar transistor high electron mobility transistor hybrid optoelectronic integrated circuits high-impedance insertion loss intensity modulation intermodulation distortion intensity modulation direct-detection indium phosphide input/output intelligent transport system current–voltage light amplification by stimulated emission of radiation laser diode

xv

Nomenclature

LED LiNbO3 MBE MESFET MMAC MOCVD MOEIC MOSFET MQW MSM MUX M–Z NRZ OEIC PD P–I PIC QW RF RFIC RIN RMS RZ SAM SCFL SCH SCM SCR SDFL SI SiGe SLM SMSR SNR SPICE SQW TDM TEN TIA TJS TZ UV

light-emitting diode lithium niobate molecular beam epitaxy metal semiconductor field-effect transistor multimedia mobile access communication molecular organic chemical vapor deposition monolithic optoelectronic integrated circuit metal oxide semiconductor field-effect transistor multiquantum well metal–semiconductor–metal multiplexer Mach–Zehnder nonreturn-to-zero optoelectronic devices and integrated circuit photodiode/photodetector power-current photonic integrated circuits quantum-well radio-frequency radio-frequency integrated circuit relative intensity noise root mean square return-to-zero separate-absorption-and-multiplication source-coupled FET logic separate confinement heterojunction subcarrier multiplexing space-charge region Schottky diode FET logic semi-isolation silicon germanium single-longitudinal-mode submode suppression ratio signal-to-noise ratio simulation program with integrated circuit emphasis single quantum well time-division multiplexer terminal electrical noise transimpedance amplifier transverse junction stripe transimpedance ultraviolet

xvi

VCSEL VNA VSWR WDM

Nomenclature

vertical-cavity surface-emitting lasers vector network analyzer voltage standing wave ratio wavelength division multiplexing

1 Introduction The purpose of this chapter is to give an overview of the field of optical communications, and modeling and simulation methods of optoelectronic integrated devices and circuits. The first section of the chapter describes why there are fundamental reasons why optics is attractive for use in communications; the most important components such as the optical transmitter, fiber, and receiver are introduced briefly. In the second section, the conventional computer-aided design (CAD) methods for optoelectronic devices and integrated circuits (ICs) are introduced.

1.1 Optical Communication System The recent explosive growth of data traffic has stimulated the demand for highcapacity information networks. The data need to be transmitted from one place to another at high speed. There are essentially four possible methods to transmit these data [1, 2, 3]: 1. 2. 3. 4.

Free-space radio-frequency (RF) transmission Free-space optical transmission RF propagation over a fixed transmission line Optical propagation over a fixed fiber-optic transmission line.

Free-space RF transmission is flexible and cheap, but it cannot support large (10 Gb/s) bandwidths and requires fairly large power to transmit over long distances. It is also relatively easy to intercept the transmitted signal, although with sufficient encryption it can be essentially impossible to decode. Free-space optical transmission is also quite flexible, but the signal quality and propagation distance are weather-dependent. Standard RF signal propagation over coaxial cable is simple to integrate with standard electronics and is ideal for relatively short distances and low data rates. Fiber-optic links Optoelectronic Integrated Circuit Design and Device Modeling Jianjun Gao Ó 2011 Higher Education Press

Optoelectronic Integrated Circuit Design and Device Modeling

2

are being used increasingly to replace conventional guided-wave methods of conveying RF signals. Fiber-optical signal distribution is known to possess advantages over conventional signal distribution in cases where the signal must be transmitted over long distances, where signal security or low interference is desired, or where the size, weight, or cost of the distribution hardware is important. Fiber-optical transmission systems can replace normal coaxial or hollow waveguide signal distribution systems if the special characteristics of the electrooptical transducers can be tolerated. An additional advantage that makes millimeter-wave desirable for fiber radio systems is that these frequencies are highly attenuated by water molecules and oxygen in the atmosphere. This can be exploited to limit signal propagation to within the proximity of a picocell, as required for wireless secure communication and for frequency reuse. Fiber-optic communication is a method of transmitting information from one place to another by sending pulses of light through an optical fiber. The light forms an electromagnetic carrier wave that is modulated to carry information. Optical communication systems have been the mainstream information transmission systems in past decades and are still dominant today thanks to the invention and development of broadband semiconductor lasers, low-loss fibers, fast photodetectors, and other highquality optoelectronic components. The fiber-optic link has many advantages, which include tremendous available bandwidth (100 THz), very low transmission loss, immunity to electrical disturbance, and so on; all of this makes a fiber-optic link the preferred transmission solution in many applications. Figure 1.1 shows a possible scheme for a 40 Gb/s optical transmission system. It requires several high-speed ICs having a bit rate of 40 Gb/s. In the transmitter, a

Figure 1.1

Schematic diagram of 40 Gb/s optical fiber transmission configuration.

Introduction

Figure 1.2

3

Cross-section of optical fiber: (a) single mode; and (b) multimodel.

time-division multiplexer (MUX) combines several parallel data streams (four 10 Gb/s streams in Figure 1.1) into a single data stream with a high bit rate of 40 Gb/s. In the receiver, a demultiplexer (DMUX) splits the 40 Gb/s data stream back into the original four low bit rate streams. The MUX and DMUX are digital medium-scale ICs, which must achieve 40 Gb/s operation with suitably low power dissipation. In the receiver, the extremely small current signal generated by a photodiode is converted into a voltage signal and amplified by a low-noise preamplifier and succeeding main amplifiers having automatic gain control (AGC). The output voltage swing of the amplifier is kept constant, independent of the input signal level. Nevertheless, regeneration, performed by a decision circuit and a clock recovery circuit (composed of a differentiator, rectifier, microwave resonator, and limiting amplifier), is still needed to reduce the timing jitter produced by the cascaded amplifiers. The transmitter and receiver ICs, except for the clock recovery circuit, require broadband operation from near DC to the maximum bit rate with good eye openings. Compared to the conventional communication system, the difference here is that the communication channel is an optical fiber cable. Figure 1.2 shows the cross-section of single-mode and multimode optical fibres. The cable consists of one or more glass fibers, which act as waveguides for the optical signal (light). In its simplest form an optical fiber consists of a cylindrical core of silica glass surrounded by a cladding whose refractive index is lower than that of the core. Fiber optic cable is similar to electrical cable in its construction, but provides special protection for the optical fiber within. For systems requiring transmission over distances of many kilometers, or where two or more fiber optic cables must be joined together, an optical splice is commonly used. In multimode fiber, the light is guided by the almost perfect reflection at the interface between the core and cladding. Like multimode optical fibers, single-mode fibers do exhibit modal dispersion resulting from multiple spatial modes, but with narrower modal dispersion. Single-mode fibers are therefore better at retaining the fidelity of each light pulse over long distances than multimode fibers. For these reasons, single-mode fibers can have a higher bandwidth than multimode fibers. Multimode fiber has significantly higher loss (due to modal dispersion) than single-mode fiber and is therefore only used for short distance communications such as within a building or

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Optoelectronic Integrated Circuit Design and Device Modeling

on a corporate campus. All long-distance communications utilize single-mode fiber and laser light sources. In its simplest form an optical fiber consists of a cylindrical core of silica glass surrounded by a cladding whose refractive index is lower than that of the core. Advantages of the optical fiber are as follows: . . . . . . .

Low attenuation, large bandwidth allowing long distance (>100 km) at high bit rates (>10 Gb/s) Small physical size Low physical mass, low material cost Cables can be made nonconducting, thus eliminating electromagnetic interference and shock hazards and providing electrical isolation Negligible crosstalk between fiber channels in the same cable High security, since tapping is very difficult Upgrade potential to higher bit rates is excellent.

Because of the rapid growth of capacity requirement on long-distance transmission, fiber-optic telecommunications is advancing into high data rate and wavelength division multiplexing (WDM) [4, 5]. WDM, by which multiple optical channels can be simultaneously transmitted at different wavelengths through a single optical fiber, thus multiply the capacity of the link (as shown in Figure 1.3). The advantages of WDM systems are: transmission capacity increase per fiber, system cost reduction, simultaneous transmission of different modulation-scheme signals, and service channel expandability after fiber installation. These are the reasons why WDM technology is expected to be widely applied to systems in various fields of communications. In WDM system design, performance of optical multi/demultiplexers (MUX, DEMUX) should be the primarily consideration, together with fibers, light sources, and photodetectors.

Figure 1.3 Fundamental configuration for WDM transmission.

Radio-frequency (RF) or microwave subcarrier multiplexing has recently emerged as a potentially important multiplexing technique for future high-capacity lightwave systems. Optical subcarrier multiplexing (SCM) is a method for multiplexing many

Introduction

5

Figure 1.4 Basic SCM system configuration.

different fiber-optic-based communication links into a single uplink fiber [6]. SCM is a scheme where multiple signals are multiplexed in the radio-frequency (RF) domain and transmitted by a single wavelength. The basic configuration of an SCM system is shown in Figure 1.4. A number of baseband analog or digital signals are first frequency division multiplexed by using local oscillators (LOs) of different radio frequencies. The upconverted signals are then combined to drive a high-speed light source. The LO frequencies are the so-called subcarriers in contrast to the optical carrier frequencies. A significant advantage of SCM is that microwave devices are more mature than optical devices; the stability of a microwave oscillator and the frequency selectivity of a microwave filter are much better than their optical counterparts. In addition, the low phase noise of RF oscillators makes coherent detection in the RF domain easier than optical coherent detection, and advanced modulation formats can be applied easily.

1.2 Optoelectronic Integrated Circuit Computer-Aided Design Intense research to develop and expand the capabilities of fiber-optic technology is under way. The outstanding progress made in optical fiber transmission systems has been largely dependent on newly developed optical and electronic semiconductor devices. To realize high-bit-rate systems, high-speed transmitter and receiver circuits are in great demand, and the development of monolithic ICs, which have higher performances and multiple functions, is indispensable. The gigabit optical transmission systems must not only be high speed but also compact, cost effective, and highly reliable, and must minimize both power consumption and temperature rise, which increase with higher transmission speeds. One of the most effective ways to achieve such a system is with gigabit IC technology. Driver circuits and preamplifiers, which are directly connected to optical devices, are among the key components.

Optoelectronic Integrated Circuit Design and Device Modeling

6

The proliferation of optical and fiber-optic communications has created a need for efficient and accurate CAD tools for the design of optoelectronic integrated circuits and systems. In the electronic world, highly advanced CAD tools exist for the design, analysis, and simulation of nearly every aspect of integration, ranging from process to device to circuit to system. The application of modern CAD tools offers an improved approach. As the sophistication and accuracy of these tools improve, significant reductions in design cycle time can be realized. The goal is to develop CAD tools with sufficient accuracy to achieve first pass design. The CAD tools need to be improved until the simulated and measured RF performance of the component being designed are in good agreement. This will permit the design to be completed, simulated, and fully tested by an engineer working at a computer workstation before fabrication is implemented. In order to achieve this goal, improved accuracy CAD tools are required. The state of the CAD methods for active optoelectronic circuits rely heavily on models of real devices. There are two kinds of commercial optoelectronic device and integrated circuit CAD software: physical-based and equivalent-circuit-based CAD software. The physical-based CAD software, as a starting point of analysis, considers fundamental equations of transport in semiconductors. The equivalent-circuit-based CAD software addresses the issue of what needs to be known about the device in addition to its equivalent circuit to predict the performance. The model permits the RF performance of a device or integrated circuit to be determined as a function of process and device design information and/or bias and RF operating conditions. The equivalent circuit device models must be based upon accurate parameter extraction from experimental data. The model permits the RF performance of a device or integrated circuit to be determined as a function of process and device design information and/or bias and RF operating conditions. Figure 1.5 shows the flowchart for an ideal

Figure 1.5

A flowchart for ideal microwave and RF circuit simulator.

Introduction

7

optoelectronic circuit simulator. Such an integrated simulator allows both the active devices and passive elements to be optimized, based upon the parameters accessible in the fabrication process.

1.3 Organization of This Book We will spend the rest of this book trying to convey the basic operation mechanism of the key components of high-speed optical communication. The focus will be on how to build the linear, nonlinear, and noise models for optoelectronic devices (including lasers and photodiodes) using physical rate equations and how to design optimum laser/modulator driver and receiver front-end circuits using microwave matching techniques. In Chapter 2, the physical structure and basic concept of the most commonly used semiconductor laser diodes have been discussed. Based on the rate equations in the active region, the small signal modulation, large signal modulation, and noise performance of laser diode are formulated, and the corresponding measurement techniques are introduced. Chapter 3 presents the rate-equation-based modeling and parameter extraction techniques for semiconductor lasers. By using the microwave active device modeling concept, the rate equation model parameters can be determined. The standard double herojunction semiconductor lasers and single quantum-well lasers are used as examples. The model parameter extraction techniques for the extrinsic elements, intrinsic elements, and rate equations model parameters are described in more detail. In Chapter 4, we introduce the physical structure and operation concept of the commonly used photodiodes (such as PIN PD, APD, and MSM PD). The small-signal modeling and parameter extraction method are described. The high-speed electrical devices such as field effect transistor (FET), heterojunction bipolar transistor (HBT), and metal oxide semiconductor FET (MOSFET) are very attractive for a high-speed optoelectronic integrated circuit. In Chapter 5, the basic physical structures and operation concepts of various semiconductor devices are introduced, and the corresponding small-signal, large-signal, and noise modeling and parameter extraction methods are described briefly. The laser/modulator driver and receiver front-end are two key components of highspeed optical communication systems. Chapters 6 and 7 deal with the optimum design of 10 Gb/s to 40 Gb/s high-speed laser/modulator driver and receiver front-end integrated circuits based on different semiconductor technologies. The passive peaking techniques, which include inductance and capacitance techniques for extending bandwidth and minimizing the noise performance for the driver and receiver, are described in more detail.

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Optoelectronic Integrated Circuit Design and Device Modeling

References 1. Keijiro, H., Toshio, F., Koji, I., et al. (1998) Optical communication technology roadmap. IEICE Transactions on Electronics, E81-C(8), 1328–1341. 2. Shaw, N. and Carter, A. (1993) Optoelectronic integrated circuits for microwave optical system. Microwave Journal, 36(10), 90–100. 3. Loehr, J. and Siskaninetz, W.(April 1998) Optical communication systems for avionics. IEEE AES Systems Magazine, 9–12. 4. Ichino, H., Togashi, M., Ohhata, M., et al. (1994) Over-10-Gb/s ICs for future lightwave communications. IEEE Journal of Lightwave Technology, 12(2), 308–319. 5. Sano, E.(January 2001) High-speed lightwave communication ICs based on III–V compound semiconductors. IEEE Communications Magazine, 39(1), 154–158. 6. Way, W. I. (1989) Subcarrier multiplexed lightwave system design considerations for subscriber loop applications. IEEE Journal of Lightwave Technology, 7(11), 1806–1818.

2 Basic Concept of Semiconductor Laser Diodes 2.1 Introduction The key elements of microwave photonic systems are optical sources capable of fast modulation, suitable transmission media, and fast optical detectors or optically controlled microwave devices. The development of the first lasers, including in 1960 both the pulsed ruby laser at Hughes Research Laboratories and the continuously operating helium neon laser at Bell Laboratories, can be said to have started the optical communications era [1]. The theoretical and practical foundations for this development were made by the American Charles Townes and the Russians Alexander Prokhorov and Nikolay Basov, who shared the Nobel Prize for Physics in 1964 for their work. Most fiber-optic communication systems use semiconductor lasers (light amplification by the stimulated emission of radiations) as an optical source because of their superior performance compared with LEDs (light-emitting diodes). As the networks evolve in complexity and sophistication,these lasers must meet increasingly demanding performance specifications: lower power dissipation, higher bandwidth, lower chirp, greater tunability, less temperature sensitivity, and lower noise, wide range of wavelengths, and monolithic integration with other devices. Furthermore, semiconductor lasers are critical components in applications such as optical fiber communications, optical memories, sensors, printers, optical information processing, pumping sources, device processings, and medical inspection. Thus, semiconductor lasers exhibited versatile properties ranging from multimode laser structures mainly used for highpower applications to single-mode laser devices for information technologies [2, 3, 4, 5, 6, 7]. To design such lasers, it is important to understand better the physical device operation, and to be able to tailor and optimize design parameters. Commercial LEDs are only capable of 1 GHz maximum modulation speeds because of slow carrier recombination, limitingthem to applications in short-haul optical communication links. Optoelectronic Integrated Circuit Design and Device Modeling Jianjun Gao 2011 Higher Education Press

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Optoelectronic Integrated Circuit Design and Device Modeling

These lasers use semiconductors as the lasing medium and are characterized by specific advantages, such as the capability of direct modulation in the gigahertz region, small size and low cost, the capability of monolithic integration with electronic circuitry, direct pumping with conventional electronic circuitry, and compatibility with optical fibers. Laser diodes (LDs) are more powerful and operate at faster speeds than LEDs, and they can also transmit light farther with fewer errors, have a narrower spectrum, and can couple more power into a fiber. Table 2.1 shows the features comparison of LED and LD. Table 2.1 Comparison of LED and LD. Feature

LED

LD

Emitted light Optical spectrum Modulation speed Threshold current Transmission distance Output power Cost

Incoherent Wide (30–60 nm) Less than 1 GHz High Short Low Low

Coherent Narrow (2–4 nm) Up to 10–40 GHz Low Long High High

Depending on the application, it is preferable that laser diodes have some of the following features: 1. Operating at two low-absorption windows for long-distance communication (1.31 mm and 1.55 mm) 2. High output optical power 3. Low threshold current 4. Fast response time 5. High reliability and low cost 6. Easy-to-direct modulation and external modulation. In this chapter, we will introduce the basic concept of the laser diodes first and then the most commonly used semiconductor laser diodes, such as FP (Fabry–Perot) cavity lasers, QW (quantum-well) lasers, DFB (distributed feedback) laser, and VCSEL (vertical-cavity surface-emitting laser), have been introduced. The small signal modulation, large signal modulation, and noise performance of laser diodes are analyzed based on the rate equations.

2.2 Basic Concept Although there are various types of semiconductor diode laser, the basic concepts are similar. The first diode lasers were made in the early 1960s and were very similar to light-emitting diodes. However, whereas light from an LED is spontaneously emitted

Basic Concept of Semiconductor Laser Diodes

11

radiation, laser diodes emit light via stimulated emission [8, 9, 10, 11, 12, 13]. In this section, we will introduce three types of interaction between atom and photon: absorption, spontaneous emission, and stimulated emission.

2.2.1 Atom Energy As we know, all matter is made up of atoms, which essentially consist of a positively charged nucleus and negatively charged electrons round it in fixed orbits. The energy levels of atoms describe the quantum mechanical requirement that microscopic particles have discrete energy values. A given electron in an atom has an orbit of lowest energy that it can occupy, called the ground state. If it is in an orbit with a higher energy, it is said to be in an excited state. As the atoms are brought closer together their electron orbits overlap and hence the discrete energy levels of the free atoms turn into energy bands in the solid phase. The lowermost, almost fully occupied band is called the valence band; the uppermost band, completely empty or partially filled, is called the conduction band. In the semiconductor ground state, all of the available valence electrons share the valence band and none occupy the conduction band; the valence and conduction bands are separated by an energy gap Eg (as shown in Figure 2.1(a)). The difference between insulators and semiconductors is only the forbidden band gap between the valence band and conduction band. The term ‘band gap’ refers to the energy difference between the top of the valence band and the bottom of the conduction band; electrons are able to jump from one band to another (as shown in Figure 2.1(b)).

Figure 2.1 Energy bands in a semiconductor.

Under normal thermodynamic equilibrium, the populations of the energy level Ei will be governed by the Boltzmann relation Ei Ni ¼ N exp ð2:1Þ kT where Ni ði ¼ 1; 2; . . . ; nÞ is the population of level Ei , k ¼ 1:38 1023 J=K is the Boltzmann constant, and T is the temperature in kelvin. Figure 2.2 shows the

12

Optoelectronic Integrated Circuit Design and Device Modeling

Figure 2.2 The population distribution versus energy level.

population distribution versus energy level. It can be found that population decreases rapidly with an increase of the energy level. In equilibrium, the charge carriers occupy their lowest energy states, with electrons at the bottom of the conduction band and holes at the top of the valence band. In order to conduct electricity, electrons have to be excited from the valence band into the conduction band, and it requires a specific minimum amount of energy for the transition. The required energy differs with different materials.

2.2.2

Emission and Absorption

Absorption occurs when a photon of just the right energy for a particular transition encounters an atom in the ground state, and causes the atom (or, rather, one of the atom’s electrons) to jump into an excited state. The energy of the excited state E2 equals that of an electron in the ground state E1 plus that of the incident photon (as shown in Figure 2.3(a)). If the incident light energy is hc=l (where h is Plank’s constant, c is optical velocity, and l is optical wavelength), the energy of the excited state can be expressed as follows: E2 ¼ E1 þ hc=l

ð2:2Þ

Under these conditions, the population of level E2 is smaller than that of the ground state, level E1 . When a photon is incident on this material, it may either be absorbed or stimulated. The probability for these processes depends on the internal properties of the atoms, the intensity of the radiation, and the population difference between the two energy levels. Spontaneous emission is when an excited atom spontaneously returns to the ground state, emitting a photon in the process (as shown in Figure 2.3(b)). In the case of spontaneous emission, photons are emitted in random directions with no phase relationship among them. The properties of spontaneous radiation are as follows: wide spectral width, low intensity, poor directiveness, and incoherence, which make it impossible to use LEDs as light sources for long-distance communication links.

Basic Concept of Semiconductor Laser Diodes

Figure 2.3

13

Three types of interaction between the atom and photon: (a) absorption; (b) spontaneous

emission; and (c) stimulated emission.

When a photon of just the right energy hits an atom whose electron is in the excited state, it can induce the electron to jump down to the lower state, emitting another photon, which will be in phase with the incoming photon and traveling in the same direction (as shown in Figure 2.3(c)). This is called stimulated emission. The remarkable feature of stimulated emission is that the emitted photon matches

Optoelectronic Integrated Circuit Design and Device Modeling

14

the original photon not only in energy (or in frequency) but also in its other characteristics, such as the direction of propagation. Thus, in contrast to spontaneous radiation, stimulated radiation has narrow spectral width, high intensity (power), a high degree of directivity, and coherence. This is why laser diodes, which radiate stimulated light, find use in long-distance communication links.

2.2.3

Population Inversion

Population inversion is a dynamic, nonequilibrium situation in which there is a higher electron density in the conduction band than in the valence band. Let the numbers of atoms that have energies E1 and E2 be denoted by the level populations N1 and N2 , respectively. The ratio of the populations N1 and N2 can be expressed as follows: N2 E2 E1 ¼ exp ð2:3Þ N1 kT If the number N2 of excited atoms can be made larger than the number of N1 of atoms in the ground state, the condition N2 > N1 is called population inversion (as shown in Figure 2.4), or sometimes as a negative-temperature condition, since application of Boltzmann’s law (see Equation (2.1)) implies T negative. The population inversion can be achieved for energy levels E1 and E2 by experiments that make use of other energy levels of the atoms.

Figure 2.4

Population inversion in a semiconductor.

Population inversion is a necessary condition to create a lasing effect because the greater the number of excited electrons, the greater the number of stimulated photons that can be radiated. In order to overcome the loss (which stems mainly from the absorption and transmission of the stimulated photons), an optical cavity or optical resonator is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain

Basic Concept of Semiconductor Laser Diodes

15

medium and providing feedback of the laser light. If we choose the material correctly (for example direct bandgap material, good crystalline quality, and so on), the probability of radiative recombination will be large. Therefore a large number of photons can be obtained, which, in turn, will stimulate other excited electrons to emit light. If the injected electron and hole population is large enough, stimulated emission can exceed the absorption and other losses in the material, so that optical gain can be achieved in the active region. The optical gain alone is not enough for laser operation. The other necessary ingredient is optical feedback – it converts an amplifier into an oscillator. In most lasers the feedback is provided by placing the gain medium inside a Fabry–Perot (FP) cavity formed by using two mirrors. Taking all the above considerations into account, the three necessary conditions to create a lasing effect are as follows: population inversion, stimulated emission, positive feedback, and optical gain.

2.3 Structures and Types Semiconductor injection lasers are highly efficient light sources with typical dimensions of 300 mm 500 mm, compact and compatible with the size of optical fibers. They can be directly modulated by the injection current at frequencies higher than 10–40 Gb/s, and produce powers over 100 mW. The principal difference between an edge-emitting LED and the edge-emitting laser is that, in the laser, the active region is thinner vertically and narrower horizontally. In addition, multilayer reflectors are added to the ends of the structure to provide optical feedback.

2.3.1 Homojunction and Heterojunction Figure 2.5 shows the basic structure of a semiconductor laser with a Fabry–Perot cavity. The active region (thickness 0.1 mm) is the media to provide optical gain sandwiched between the p- and n-type semiconductor materials. The resulting p–n junction is forward-biased through metallic contacts. The laser light is emitted from the two cleaved facets. The early laser diodes were homojunction broad area devices made by diffusion of impurities to form the p–n junction in the bulk single crystals. However, the action of these lasers can be established only at low temperatures where phonon scattering in the semiconductor in small, typically <100 K around 0.85 mm. Because of the large electron diffusion length (several micrometers) the threshold current densities were in the order of 1 105 A=cm2 at room temperature; thus the required current to reach the threshold was too high to permit continuous operation. The reasons for the inefficiency and the very large threshold currents are related to the lack of confinement of the charge carriers (electrons, holes) and of photons around the active region.

Optoelectronic Integrated Circuit Design and Device Modeling

16

Figure 2.5

Basic structure of a laser diode.

To improve the efficiency of diode lasers, it is necessary to confine the current carriers (electron and holes) and the photons to the active region of the junction area. This can be achieved in layer structures called double heterostructures. It is known that probably the most significant step in optical source and detector technology occurred in the late 1960s. This followed on from Kroemer’s suggestions [14] in 1963 that additional semiconductor layers with wider bandgaps and a lower refractive index could be included in laser structures to provide better carrier and optical confinement, Alferov et al. [15] and Hayashi et al. [16] both showed how it was possible to grow lattice-matched heterojunctions of AlGaAs on GaAs that exhibited true heterojunction properties – that is the interfaces were not controlled by defects resulting from poor morphology and lattice mismatch. The homojunction is a junction (interface) between the same kind of semiconductors, whose materials have equal bandgaps but typically have different doping (semiconductors). For example, a junction between an n- and a p-type GaAs is a homojunction, while a junction between a GaAs and an InP material is called a heterojunction. A heterojunction is the interface that occurs between two layers or regions of dissimilar crystalline semiconductors. These semiconducting materials have unequal band gaps as opposed to a homojunction. For example, one of the most common heterojunction lasers is based on a double heterostructure between GaAs and AlGaAs. In this laser a thin (for example 0.2 mm) GaAs layer is sandwiched between thicker (for example 1 mm) AlGaAs layers. Figure 2.6 shows the comparison of a GaAs homojunction and heterojunction p–n junction laser diode. In a heterojunction p–n junction structure, it can be found that a layer of low bandgap material is sandwiched between two high bandgap layers. One

Basic Concept of Semiconductor Laser Diodes

Figure 2.6

17

Comparison of homojunction and heterojunction p–n junction laser diode.

commonly used pair of materials is gallium arsenide (GaAs) with aluminum gallium arsenide (AlGaAs). Each of the junctions between different bandgap materials is called a heterostructure, and hence the name ‘double heterostructure laser’ or DH laser. Double heterojunctions are used to confine both the charge carriers and the optical fields in the vertical direction. The losses due to absorption outside the active region are greatly reduced because the laser beam is confined to the active region and the bandgap of the n and p layers is wider so that the light of the lasing-supported wavelength cannot be absorbed. The free electrons and holes exist simultaneously and the active region is confined to the thin middle layer. This means that many more of the electron–hole pairs can contribute to amplification – not so many are left out in the poorly amplifying periphery. The physical reasons for the reduction of threshold current density with the DH laser diodes are twofold: (1) the large bandgap of the cladding layers confines the injected carriers inside the active layer of the small bandgap to produce high gain and (2) the higher index of refraction in the active layer of the DH structure also forms a planar waveguide that confines the optical field close to the active layer. The optical confinement significantly reduces the internal loss that would otherwise occur in the absence of waveguiding due to spreading of the optical field in the lossy medium. The threshold current density reduces proportionally to the thickness of the active layer.

18

2.3.2

Optoelectronic Integrated Circuit Design and Device Modeling

Index Guiding and Gain Guiding

Although the junction properties and configuration can be manipulated to confine the diode laser beam to the plane of the junction, other modifications in wafer geometry are often employed to restrict the beam further. Various laser cavity structures have been successfully introduced to stabilize the laser transverse mode. Diode lasers may be broadly divided into two general classes depending on the mechanism providing optical waveguidance in the lateral direction parallel to the p–n junction. One type utilizes the real refractive index waveguidance; the other more conventional lasers are said to employ ‘gain’ guiding. Index guiding and gain guiding are two methods by which the lasing action is confined to a narrow strip or portion of the semiconductor material: 1. Gain-guided devices, whereby lateral mode control is obtained by the injected carrier profile 2. Index-guided devices, whereby lateral mode control is obtained by a built-in dielectric waveguide. In gain-guided lasers, the confinement minimizes absorption in the nonactive region of the active layer. The mechanism of providing lateral waveguiding with the change in the refractive index caused by the current carriers is called gain guiding. The confinement is achieved in the index-guided lasers by changing the refractive index along the active material. They have lower threshold current and better efficiency compared to gain-guided lasers. An example of gain guiding is the strip-geometry laser, in which the laser beam lateral profile is controlled by the gain (or the imaginary part of the refractive index). Figure 2.7 shows the cross-section of the strip-geometry laser structures used to design gain-guided semiconductor lasers. In the emitting region under the strip, the index of refraction is slightly higher than the laterally adjacent regions, because of the presence of the current carriers in that region. This slight rise in the refractive index forms a lateral waveguiding structure. (The vertical waveguide structure is formed by the heterojunction materials.) Current flows only through the central region and is blocked elsewhere because of the reversebiased nature of the p–n junction. Gain-guided semiconductor lasers solve the lightconfinement problem by limiting current injection over a narrow strip. Such lasers are also called strip-geometry semiconductor lasers. Gain guiding occurs when the gain rather than the refractive index influences the field distribution. A dielectric (SiO2) layer is deposited on top of the p layer with a central opening through which the current is injected. Examples of index guiding include the buried heterostructure (BH) laser and transverse junction strip (TJS) lasers. In the commonly used buried heterostructure index-guided devices the active layer is surrounded on all sides by a lower index, higher bandgap material leading to current confinement as well as lateral mode

Basic Concept of Semiconductor Laser Diodes

19

Figure 2.7 Cross-section of the strip-geometry laser structures used to design gain-guided semiconductor lasers.

stabilization. However, these devices require sophisticated fabrication techniques such as regrowth over an etched mesa. To avoid high-order lateral modes, the active-region width is generally limited to 2 mm. Figure 2.8 shows a typical BH laser where the p-type GaAs active emitting region is surrounded to the left and right by n-type GaAlAs. The change in material is

Figure 2.8 Cross-section of index-guided semiconductor lasers: BH lasers.

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Optoelectronic Integrated Circuit Design and Device Modeling

accompanied by a step change in the refractive index providing the lateral waveguide. The vertical waveguide structure is again done by the heterojunctions. In the BH diode lasers shown in Figure 2.8, both the current and the beam are also confined laterally, so that, for lasing beams, their active regions become the three-dimensional dielectric optical waveguides. The stabilization or the simplification of the lateral modes in such diode lasers is an important problem to obtain the low threshold and the stable beam or to improve the modulation characteristics. In telecommunication systems the Fabry–Perot (FP) lasers, quantum-well (QW) lasers, and the distributed feedback (DFB) laser are the most commonly used lasers. In data communication systems, such as gigabit Ethernet, the FP laser and the verticalcavity surface-emitting laser (VCSEL) are preferred because of their lower cost. The commonly used lasers mentioned previously will be introduced in the next sections.

2.3.3

Fabry–Perot Cavity Lasers

In most lasers the feedback is provided by placing the gain medium inside an FP cavity formed by using two mirrors. When the mirrors are aligned perfectly parallel to each other, the reflections of the light waves between the two mirrors interfere constructively and destructively, giving rise to a standing wave pattern between the mirror surfaces. Figure 2.9 shows a typical basic structure of an FP laser. The typical dimensions for FP lasers are as follows: height 0.1–0.2 mm, length 250–500 mm, and width 5–15 mm. The distance between the two facets, the cavity length, determines the wavelengths at which the laser can operate. If the cavity contains a whole number of wavelengths and the net optical gain is larger than one, lasing occurs. Since the facets are many wavelengths apart, there are multiple modes satisfying the cavity constraint.

Figure 2.9 Basic structure of an FP laser.

In the case of semiconductor lasers, external mirrors are not required as the two cleaved laser facets act as mirrors whose reflectivity is given by R¼

ðng nÞ2 ðng þ nÞ2

ð2:4Þ

Basic Concept of Semiconductor Laser Diodes

21

where ng is the refractive index of the semiconductor and n2 is the refractive index of the sounding medium (usually n2 ¼ 1 for air). For example, in the case of GaAs, the refractive index is 3.6, resulting in 32 % facet reflectivity; in the case of GaAsP, the refractive index is 3.7, resulting in 33 % facet reflectivity. This reflectivity is normally high enough to eliminate the need for mirrors; however, the back surface of the laser is frequently coated with a multilayer, 100 % reflecting surface, resulting in emission from the front surface only. For higher-power lasers the front surface is also coated with a partially transmitting coating to protect the surface from forming defects due to ambient moisture. Light reflects back and forth between the mirrors, and one or both transmit a fraction of the resonant frequency. All optical fields inside the cavity that experience a roundtrip phase equal to some multiple of 2p will oscillate when the lasing threshold is reached. This gives rise to the longitudinal modes of the Fabry–Perot cavity laser. These modes are at wavelengths satisfying the equation lm ¼

2ng L m

ð2:5Þ

where L is the FP cavity length and m is the mode number (an integer). The spacing between adjacent modes is Dlm ¼ lm þ 1 lm ¼

l2m 2ng L

ð2:6Þ

that is Dfm ¼ fm þ 1 fm ¼

c 2ng L

Each mode, starting with the spontaneous emission into the mode, grows as the optical gain increases. Because of the parabolic density of states, the gain for each mode can be approximated by [5] ðlp lm Þ 2 ð2:7Þ gm ¼ gp Go where lp is the wavelength at the gain peak, gp , and Go characterizes the width of the gain curve. The steady-state photon-flux density of each mode can be expressed by [17] Sm ¼

gN=t ðc=ng Þ½ac Ggm

ð2:8Þ

where c is the velocity of the light, g is the spontaneous emission factor, ac is the cavity loss per unit length, t is the carrier lifetime, and N is the injected electron density. Figure 2.10 shows the corresponding spectral distribution and gain curve for FP lasers.

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Optoelectronic Integrated Circuit Design and Device Modeling

Figure 2.10 Spectral distribution and gain curve for FP lasers.

The power of each mode depends inversely on the difference of the loss and the modal gain, ac Ggm ; the closer the gain is to the loss, the higher is the mode power. An FP semiconductor laser generally emits light in several longitudinal modes of the cavity. The optical gain spectrum of semiconductor lasers is wide enough (bandwidth 10 THz) that many longitudinal modes of the FP cavity experience gain simultaneously. The mode closest to the gain peak becomes the dominant mode.

2.3.4

Quantum-Well Lasers

It is well known that electronic and optical properties can be altered by using heterostructures and the most widely used heterostructures in semiconductors are quantum wells. In a quantum well, a single layer of one narrow-gap semiconductor is sandwiched between two layers of a wider-gap material. Conventional semiconductor lasers are made of DH, as described previously. Although the active layer in a DH laser is thin enough (100–300 nm) to confine electrons and the optical field, the electronic and the optical properties remain the same as in the bulk material. In a quantum-well laser, on the other hand, the active layer is made thinner than 10 nm so that the electronic and the optical properties change drastically due to the reduced dimensionality of freeelectron motion from three to two dimensions. Improvements in fabrication technology now allow the thickness in the active layer of the diode structure to be as small as 5–10 nm with smooth, defect-free interfaces. With this new tool the research community went to work and the first conceptual breakthrough was that of quantum-well lasers.

Basic Concept of Semiconductor Laser Diodes

23

Quantum-well (QW) lasers, lasers with active layer thicknesses on the order of 10 nm, resulted in a number of advantages, including a dramatic reduction in threshold current, a reduction in the free carrier loss, and a reduction in the temperature sensitivity of the threshold current. All of these effects increased the efficiency of the laser and the ability to make lasers with longer cavities and therefore lower thermal resistance. Therefore, multiple quantum well (MQW) laser diodes are expected to exhibit several advantages compared to conventional DH laser diodes with an active bulk layer, such as lower threshold current density, improved temperature behavior, frequency response, spectral linewidth, and chirping. These improved properties have been demonstrated successfully on short- and long-wavelength lasers. The QWs are usually surrounded by an optical waveguide structure so as to confine the photons to near the quantum well. The multilayer arrangement results in a waveguide structure that confines the photons to a region near the quantum well, while the quantum well itself confines the charge carriers. This type of arrangement, where the optical field and the charge carriers are separately confined, is known as a separate confinement structure laser. The comparison of conceptual energy band diagrams between bulk and quantumwell lasers is shown in Figure 2.11 [18]. In a bulk laser (Figure 2.11(a)), carriers are

Figure 2.11 Comparison of conceptual energy band diagrams between bulk and quantum-well lasers.

24

Optoelectronic Integrated Circuit Design and Device Modeling

injected directly into the gain region where they interact with photons, so that the carriers and the optical mode are confined to the same region in space. In contrast, the gain region in a QW laser is embedded inside a larger optical confinement region. Carriers are injected at the ends of that confinement region and have to affect the gain in the quantum wells, which are located at a different point in space (as shown in Figure 2.11(b)). Quantum-well laser diodes are available with the following structures: single quantum well (SQW), multiple quantum well (MQW), and graded-index separate confinement heterostructure (GRIN-SCH). Figure 2.12 shows the InGaAs/InGaAsP/GaAs SQW laser structure, the layer structure for the 0.98 mm emitting aluminum-free laser employs 8.5 nm thick InGaAs QW with 1.62 eV InGaAsP barriers and waveguide [19]. Electron and hole transport from the doped cladding layers to the quantum well consists of two parts. First is the transport across the SCH. This is governed by the classical current continuity equations, which describe the diffusion, recombination, and, in the presence of any electric field, drift of carriers across the SCH. The second part is the carrier capture by the quantum well. This is a quantum mechanical problem, which has to take into account the relevant dynamics of the phonon-scattering mechanism that mediates this capture. This scattering process is a function of the initial and final state wavefunctions, the coupling strength of the transition, and the phonon dispersion in the material.

Figure 2.12 InGaAs/InGaAsP/GaAs SQW laser structure.

Figure 2.13 shows the separate confinement heterostructure multiple quantum well (SCH-MQW), where four quantum wells of GaInAs with GaInAsP barrier

Basic Concept of Semiconductor Laser Diodes

25

Figure 2.13 InGaAs/InGaAsP/InP MQW laser structure: (a) cross-section; and (b) band gaps schematic.

layers are sandwiched between the InP layers to form a waveguide with a step index change [20]. Figure 2.14 shows the threshold current change as a function of the number of quantum wells with the various total losses, where the total loss includes the loss in the active region and cladding layer [21]. This figure indicates that when the total loss is low, the SQW structure is optimum, whereas the optimum number is larger than 1 for higher loss. Thus the gain saturation, which is enhanced in an SQW structure, causes a significant dependence of the optimum well number on the total loss for

26

Optoelectronic Integrated Circuit Design and Device Modeling

Figure 2.14 Threshold current change as a function of the number of quantum-wells with the various total losses.

reducing the threshold current. Strained-layer multiple quantum well (MQW) structures have been used to obtain wide bandwidth modulation of semiconductor lasers due to their enhanced high-speed performance over unstrained single QW structures. The differential gain increases with the number of QWs because of the reduced carrier density per well, and the state-filling effect due to the carrier population in optical confinement layers is less severe for an MQW structure than a single QW structure. Figure 2.15 shows a graded-index separate confinement heterostructure (GRINSCH) where a graded index of the waveguide is accomplished by several small stepwise increases of the bandgap energies of multiple cladding layers [22]. This structure consists of: (1) an n-type InP buffer layer; (2) a lower optical confinement layer of undoped GRIN-SCH GaInAsP layers with a step-like decreasing bandgap; (3) undoped GaInAs quantum wells separated by GaInAsP barriers; (4) an upper optical confinement layer of undoped GRIN-SCH GaInAsP layers with a step-like increasing bandgap; (5) a p-type InP cladding layer and a p-type GaInAsP contact layer. The GRIN-SCH structure confines both the carriers and the optical field more effectively than the SCH structure, and consequently leads to a lower threshold current density. The use of a GRIN-SCH in QW lasers has been demonstrated to be effective in the reduction of threshold current in the GaAs/AlGaAs system, which is due to the fact that the GRIN-SCH structure enhances the confinement of both the carriers and the optical field into the quantum wells.

Basic Concept of Semiconductor Laser Diodes

27

Figure 2.15 The structure of graded index separate confinement heterostructure (GRIN-SCH) MQW laser.

2.3.5 Distributed Feedback Lasers The optical coherent transmission systems are very attractive because of their essential ability to achieve marked receiver sensitivity improvement to direct detection systems. The use of conventional FP semiconductor lasers as light sources in the wavelength region of 1.5–1.6 mm degrades the transmission bandwidth of conventional singlemode optical fibers due to the effect of chromatic dispersion influenced by dynamic spectral broadening of the lasers. Such broadening of the spectral width, due to multimode oscillation with the intensity fluctuations of each longitudinal mode, causes pulse broadening of transmitted light and the mode partition noise in the detected signal. Since a broad spectral linewidth induces optical receiver sensitivity deterioration, as the light sources for coherent transmission systems, a single frequency operation (that is a single longitudinal mode, SLM) with a narrow spectral line width is necessary [23, 24, 25]. Figure 2.16 shows the comparison of power output and mode spectrum for (a) multimode and (b) SLM lasers

Figure 2.16 Comparison of power output and mode spectrum for (a) multimode and (b) SLM lasers.

28

Optoelectronic Integrated Circuit Design and Device Modeling

Figure 2.17 Relative side-mode intensity.

Single-frequency oscillation can be obtained by integrating a frequency-selective grating element inside the laser cavity. The significance of the single-mode property of SLM lasers is expressed by a factor called a submode suppression ratio (SMSR), which is an intensity ratio of the main lasing mode Pmm to the nonlasing side mode Psm under continuous wave (CW) operation (as shown in Figure 2.17), given as follows [26, 27]: Pmm ð2:9Þ SMSRðdBÞ ¼ 10 log10 Psm and SMSR can also be expressed as a function of the injection current [24]: Z Da I SMSR ¼ d 1 ð2:10Þ xCs asm Ith where Zd is an external differential quantum efficiency of the laser cavity, x an optical confinement factor of the active region, asm the mirror loss of the nonlasing mode, and Cs the spontaneous emission factor, respectively. The ratio of the time-averaged photon density of the nonlasing mode to that of the lasing main mode can be calculated and is characterized in terms of the mirror loss difference Da between that of the submode and the main lasing mode, which is expressed as 1 1 1 1 ð2:11Þ Daðcm Þ ¼ up tps tpm where tps and tpm are the photon lifetimes of the nonlasing and the lasing main mode, respectively, and up is the phase velocity of the lasing main mode.

Basic Concept of Semiconductor Laser Diodes

29

From Equations (2.9) to (2.11), it can be found that the SMSR increases with the increase of the mirror loss difference Da, and a mirror loss difference larger than a few tens cm1 is required for an SMSR larger than 30 dB, which is regarded as an SLM laser. An FP laser with a reasonable length (200–300 mm) usually has a small gain suppression comparable to Da around 1 cm1 , which is not sufficient for SLM operation. Examples of dynamic single-mode (DSM) or SLM lasers include distributed Bragg reflector (DBR) lasers and distributed feedback (DFB) lasers for single-wavelength operation [28, 29, 30, 31, 32]. These lasers have been successfully applied to high-bitrate/long-distance optical communications. The most attractive type of laser diodes for monolithic integration of photonic integrated circuits (PICs) can be limited to DBF/ DBR LDs because of their promising features of (1) facetless cavity structure and (2) a stable single longitudinal-mode operation with an accurate determination of lasing wavelength compared with other types of LDs. Currently, DFB lasers are available from 760 nm up to 2300 nm with almost no gap in the spectral coverage. DFB lasers offer a significant advantage in comparison with external cavity diode lasers. The wavelength of each individual DFB laser can be tuned mode-hop free over a total tuning range of 1 nm without any moving mechanical parts. The lack of mechanical parts qualifies DFB lasers especially for field deployment and space applications. DFB and DBR lasers should show the lowest threshold and the largest wavelength selectivity when they operate at the Bragg wavelength, since the Bragg reflection occurs most effectively at the Bragg wavelength. In the DFB laser, the grating region is built in a waveguide layer adjacent to the active layer, the grating is formed on the guiding layer contacting the active layer, and the grating provides frequency-selective feedback to allow oscillation at one dominant mode in the laser cavity. In a DBR laser, the grating region is outside the active region along the length of the cavity (as shown in Figure 2.18). The operation of the DBR laser is understandable by considering that the reflection is enhanced at the wavelength lB , known as the Bragg wavelength, which is related to the period of the grating lB ¼

2ne L ðm ¼ 1; 2; 3; . . .Þ m

ð2:12Þ

where ne is the effective refractive index in the waveguide for the mode under consideration, L is the grating spacing, and m is the integer order of the grating. The mode at the Bragg wavelength, which has the lowest loss and thus the lowest threshold gain, will lase predominantly. Although the grating is capable of reflecting many different longitudinal modes, corresponding to the various values of m, usually only one mode will lie within the gain bandwidth of the laser. There are several parameters that determine the performance of the DFB/DBR lasers: (1) grating height; (2) composition or refractive index of the guiding layer; (3) grating shape; and (4)

30

Optoelectronic Integrated Circuit Design and Device Modeling

Figure 2.18 Conventional structures of DFB and DBR.

distance between the active layer and the grating. Among the parameters mentioned above, grating height is the most important one for controlling the coupling constant. Another advantage of the SLM laser is the potential for wavelength-tunable operation, which is attractive for wavelength division multiplexing (WDM), coherent optical communication systems, and optical measurements. It is desirable that the wavelength tuning range of a single laser covers as many channels as possible. For example, if the channel spacing is 10 GHz and the channel number is 100, the tuning range of 1000 GHz, which is equivalent to about 8 nm at the 1.55 pm center wavelength range, is required for the local laser. In a single-electrode DFB laser operated above threshold, most injected carriers recombine to produce photons, resulting in a very small increase in carrier density, which in turn leads to a small change in lasing wavelength. The range of wavelength tuning can be improved by using two- or threeelectrode DFB/DBR lasers, with a large current applied to one electrode and a small current to the other. The various kinds of wavelength-tunable lasers grouped into three categories: 1. Active tuning: The gain medium is separated into multisections such as a two- or three-section DFB laser. To control the lasing wavelength in wavelength-tunable

Basic Concept of Semiconductor Laser Diodes

31

lasers, which are composed of a multisection gain medium, injection current into every section should be controlled at the same time for a constant output operation. 2. Passive tuning: The wavelength tuning without both a severe change of output nonlinear power and hysteresis can be done by separating the index tuning region from the gain medium. 3. Bragg wavelength tuning and phase tuning: These kinds of tuning are a combination of active and passive tuning, and give a larger tuning range than that of active and passive tuning, because the lasing wavelength deviation from the Bragg wavelength can be adjusted by phase control. Figure 2.19 shows the structure of three-electrode DFB and DBR wavelengthtunable lasers. A phase shift of p=2 or l=4 is necessary to ensure single-mode operation and to enhance side-mode rejection. Multiple electrodes permit tailoring of the carrier

Figure 2.19 Structure of three-electrode wavelength tunable lasers: (a) DFB; (b) DBR.

Optoelectronic Integrated Circuit Design and Device Modeling

32

density in the active region to improve the static linewidth or to change the lasing wavelength. The DBR laser is similar to the DFB laser, but the grating is not distributed along the length of the active region. Instead, the grating is placed at one end of the active region to act as a frequency selective mirror. In this case, the separate electrodes may be used to control the optical frequency, phase, and power characteristics of the laser. In order to explain the working principle for the wavelength-tunable lasers having multiple sections, two simple model configurations for three-electrode DFB/DBR lasers is shown in Figure 2.20. A roundtrip phase change of optical field in the cavity is written as [33] f¼2

3 X

bi Li ¼ 2ðb1 L1 þ b2 L2 þ b3 L3 Þ

ð2:13Þ

i¼1

with bi ¼

2pneq;i l

ði ¼ 1; 2; 3Þ

Figure 2.20 Analytical model of three-electrode wavelength tunable lasers: (a) DFB; (b) DBR.

Basic Concept of Semiconductor Laser Diodes

33

where l is the lasing wavelength, bi the propagation constant, Li the subsection length, and neq;i the equivalent refractive index of each subsection. In the subsection including the grating, Li should to be replaced with Leff ;i , which is the equivalent section length. The lasing modes must satisfy the phase matching condition described as f ¼ 2mp

ðm ¼ 1; 2; 3; . . .Þ

ð2:14Þ

From Equations (2.13) and (2.14), the wavelength of the mth (m is an integer) longitudinal mode is expressed as lm ¼

3 2X 2 neq;i Li ¼ ðneq;1 Leff ;1 þ neq;2 Leff ;2 þ neq;3 Leff ;3 Þ m i¼1 m

ð2:15Þ

A shift of longitudinal model Dlm , which is caused by the change of equivalent refractive index of each subsection, can be expressed as 3 X

ðDneq;i Leff ;i Þ Dneq;1 Leff ;1 þ Dneq;2 Leff ;2 þ Dneq;3 Leff ;3 Dlm i¼1 ¼ ¼ 3 X lm neq;1 Leff ;1 þ neq;2 Leff ;2 þ neq;3 Leff ;3 ðneq;i Leff ;i Þ

ð2:16Þ

i¼1

The maximum tuning range is obtained when the indexes of all sections are changed maximally to the same direction. Because it is generally difficult to change the index of all sections to the maximum simultaneously, the tuning range becomes smaller than the maximum.

2.3.6 Vertical-Cavity Surface-Emitting Lasers Vertical-cavity surface-emitting lasers (VCSELs) are interesting light sources for future massively parallel optical interconnects [34, 35, 36, 37]. Their potential advantages include ultralow-threshold operation, easy fabrication of two-dimensional (2-D) arrays, and easy coupling to optical fibers. Compared with edge-emitting semiconductor lasers, VCSELs offer a variety of advantages. The main advantages of the VCSELs are an inherent single longitudinal mode, a small divergence angle, a low threshold current, the capability of ultrahigh bit rate modulation, ease of forming a two-dimensional (2-D) laser array, and good scalability and integrability with other optoelectronic components. In a typical VCSEL, an optical cavity is formed along the device’s growth direction, with distributed Bragg reflectors (DBRs) typically forming the cavity mirrors. The

34

Optoelectronic Integrated Circuit Design and Device Modeling

many advantages of VCSELs can be related to this simple design. First, because the cavity length is typically very short, the correspondingly large mode spacing limits the optical output to a single longitudinal mode. Second, a VCSEL’s planarity allows symmetric transverse cross-sections, thereby resulting in circular output beams. Figure 2.21 shows the schematic structure of selectively oxidized top-emitting GaAs VCSELs for ultrahigh-speed optical interconnections. The laser resonator consists of two DBR mirrors parallel to the wafer surface with an active region consisting of one or more QWs for the laser light generation in between. The planar DBR mirrors consist of layers with alternating high and low refractive indices. The current is injected through the upper Bragg reflector either by a ring contact for the topemitting devices or by a full contact for the bottom-emitting devices. Both mirrors consist of quarter-wavelength pairs of GaAs–AlGaAs stacks and are optimized for low series resistance.

Figure 2.21 Schematic structure of a high-bandwidth single-mode top-emitting GaAs VCSEL.

2.4 Laser Characteristics In this section, we will introduce the rate equations, which describe the injected carrier and photon densities for the single and multiple longitudinal mode lasers, and give an overview of the direct modulation performance of high-speed semiconductor lasers. The direct frequency modulation capability of a semiconductor laser through an injection current modulation is promising for the application to the coherent transmission system. The principal attraction of the direct modulation technique is its simplicity. With the laser biased above threshold and a modulation signal superimposed on the drive current, the output optical power of the laser is an analog of the modulation waveform. Based on the rate equations mentioned above, the general form of the response characteristics is described and the main factors limiting the high-speed performance are identified. The dynamic characteristics of semiconductor lasers include amplitude modulation (that is small signal intensity modulation), frequency

Basic Concept of Semiconductor Laser Diodes

35

modulation (laser chirping), large signal switching transients, and relative intensity noise. These dynamic properties of the active region can be studied by using the rate equations. The rate equations may be solved by numerical integration to obtain a timedomain solution or used to derive a set of steady-state or small-signal equations to help in further understanding the static and dynamic characteristics of semiconductor lasers.

2.4.1 Single-Mode Rate Equations The distributions of photon density SðxÞ and electron density NðxÞ in the active region can be determined by the following rate equations for a laser [38]: L2eff @ 2 NðxÞ @Nt ðxÞ JðxÞ NðxÞ ¼ GðxÞSðxÞ þ @t qd tn tn @x2

ð2:17Þ

@St ðxÞ SðxÞ NðxÞ þb ¼ GðxÞSðxÞ @t tp tn

ð2:18Þ

where St ðxÞ ¼ photon density in the active region (m3 ) Nt ðxÞ ¼ electron density in the active region (m3 ) JðxÞ ¼ injected drive current density (A=m2 ) GðxÞ½G ¼ go ðNNom Þ ¼ optical gain (s1 ) go ¼ gain slope coefficient (m3 =s) Nom ¼ electron density at which the optical gain is zero (m3 ) tn ¼ carrier spontaneous recombination lifetime (ns) tp ¼ photon lifetime (ps) b ¼ fraction of spontaneous emission coupled into the lasing mode d ¼ thickness of the active region (mm or m) q ¼ electron charge ð¼ 1:6 1019 AsÞ The first term JðxÞ=qd in Equation (2.17) describes the pumping of carriers in the laser active region. The second term on the right-hand side describes phenomenologically the spontaneous decay of the inversion. The third term accounts for the spatial diffusion of the carriers in terms of an effective carrier diffusion length Leff in the active layer. This term describes lateral diffusion in the active layer, and also includes the effects of drift in the passive region due to the lateral electric field associated with nonuniformities in the junction voltage. The last terms describe the loss of inversion due to the stimulated emission of photons in the laser.

36

Optoelectronic Integrated Circuit Design and Device Modeling

In Equation (2.18), on the right-hand side, the first term expresses the photon generation rate in the active region; the second term describes the spontaneous decay of the inversion; and the third term describes the carrier spontaneous emission coupled into the lasing mode. The distributions of the photon and electron densities along the lateral direction can be assumed to be [39] St ðxÞ ¼ 2 S cos2 ðpx=WÞ

ð2:19Þ

Nt ðxÞ ¼ NN1 cosð2px=WÞ

ð2:20Þ

where S is the average photon density over the volume of the active region, N is the average electron density over the volume of the active region, N1 is a parameter that describes the deviation of carrier density from a uniform distribution, and W is the width of the active layer. These distributions are illustrated in Figure 2.22. The assumed photon density distribution falls to zero at x ¼ W=2. Substituting Equations (2.19) and (2.20) into (2.17) and (2.18), and with both sides of Equations (2.17) and (2.18) integrated over the active layer, two coupled rate equations are obtained by simplifying the three position-independent rate equations [40] dN IA N ¼ go ðNNom Þð1xSÞS dt a tn

ð2:21Þ

Figure 2.22 Distribution of photon density and electron density across the active layer.

Basic Concept of Semiconductor Laser Diodes

37

dS S N ¼ Ggo ðNNom Þð1xSÞS þ Gb dt tp tn

ð2:22Þ

where IA ¼ current injected into the active layer (A) a ¼ volume of the active region multiplied by the electronic charge (A m3 s) G ¼ optical confinement factor given by the ratio of the active region volume to the modal volume x ¼ gain compression factor For narrow-strip devices, the maximum variation of junction voltage Vj across the active layer is of the order of a few millivolts. Thus, the average junction voltage can be written as Vj ¼

nkT lnðN=Ne Þ q

ð2:23Þ

where Ne is the equilibrium electron density for n 2 AlGaAs devices. The output optical power can be expressed as P¼

ZhgSa 2qGtp

ð2:24Þ

The two coupled position-independent rate equations mentioned previously are very popular to study the dynamics of the electron and photon populations in lasers. The active region is modeled here in terms of a pair of single-mode rate equations that incorporate an optical field-dependent gain saturation or compression. The inclusion of gain compression is a phenomenological approach that can represent a number of mechanisms, including spatial hole burning and lateral carrier diffusion, spectral hole burning, and other nonlinearities. It is noted that in order to simplify the completed rate equations (2.17) and (2.18), six basic assumptions are used as follows: 1. The carrier and photon densities N and S are assumed to be constant across the active layer. 2. The current injected into the active layer is assumed to be constant across the active layer. 3. The active layer is assumed to be narrower than the effective electron diffusion, that is W=Leff < 1. 4. The deviation of carrier density N1 is assumed to be constant, that is N1 =dt ¼ 0. 5. The optical gain is assumed to be a linear function of carrier density N and independent of the photon density S.

Optoelectronic Integrated Circuit Design and Device Modeling

38

6. The laser is assumed to be operated at single frequency and nearly single frequency, and biased close to or above threshold. Although the rate equations are suitable for the single-mode semiconductor lasers only, they also serve as a useful guide to the modulation behavior of multimode devices. Under the steady-state condition, the time rates of changes of carrier density and photon density are zero (dN=dt ¼ 0 and dS=dt ¼ 0) and the steady-state carrier density and photon density No and So can be determined from Equations (2.21) and (2.22).

2.4.2

Multimode Rate Equations

Much work has been done on the issue of modeling semiconductor lasers with many different techniques being developed. The use of the laser rate equations has been one of the most popular modeling methods. The multimode version of the rate equations were found to be necessary for predicting the performance of the multimode semiconductor lasers [41, 42]. The first equation, which describes the carrier number in the active region, is X dN IA GGi ðN; li ÞSi ¼ RðNÞ dt q i

ð2:25Þ

The remaining rate equations describe the total photon number in each mode i, where the equation for mode i is dSi Si ¼ GGi ðN; li ÞSi þ bi ðli ÞBN 2 dt tp

ð2:26Þ

where N ¼ carrier number in the active region Si ¼ photon number in ith laser longitudinal mode R(N) ¼ recombination term that accounts for radiative and nonradiative recombination Gi(N) ¼ optical gain for the ith laser longitudinal mode and is a function of electron density bi ðli Þ ¼ fraction of spontaneous emission coupled into each lasing mode B ¼ band-to-band recombination coefficient li ¼ wavelength of ith laser longitudinal mode A parabolic dependence of optical gain with wavelength is assumed. The peak gain is taken to be directly proportional to the electron density. The expression for Gi(N), the

Basic Concept of Semiconductor Laser Diodes

39

optical gain for the ith laser longitudinal mode, is given by " # li lp 2 Gi ðN; li Þ ¼ go ðNNom Þ 12 ð1xStot Þ Dlg

ð2:27Þ

where lp ¼ wavelength of peak gain Dlg ¼ full-width half-maximum (FWHM) wavelength of the parabolic gain curve Stot ¼ sum of the photons in all the modes, with gain saturation effects taken into account by using the gain compression factor x The rate of carrier recombination is denoted by RðNÞ in Equation (2.25) and is given by [43] RðNÞ ¼ AN þ BN 2 þ CN 3

ð2:28Þ

where A ¼ a constant describing recombination via traps C ¼ Auger recombination constant Only the second term, which contains B, represents radiative recombination. A and C are constants that represent nonradiative recombination processes where an electron–hole pair recombine without emitting a photon. The spontaneous emission coefficient bi in Equation (2.26) for the ith mode is given by [17] bi ¼

bo 4ðli lp Þ2 2 1þ i Dl2s

ð2:29Þ

where Dls is the width of the spontaneous emission spectrum (FWHM) and bo is the spontaneous emission coefficient at the center wavelength. Its value can be determined from bo ¼

l4o 8p2 ng n2r Dls Vact

ð2:30Þ

where ng is the group refractive index, nr is the refractive index, lo is the center wavelength, and Vact is the mode volume of the active region. Comparing multimode rate equations with the single-mode rate equations mentioned previously, it can be found that the carrier density rate equations are similar except that, in the multimode case, the stimulated current component is divided into

Optoelectronic Integrated Circuit Design and Device Modeling

40

different nodes. Thus, the optical section consists of the same number of branches as the number of modes considered. The photon density rate equation for each mode is identical to the single-mode rate equations. Hence, individual branches of the optical section differ only in the gain constant and the spontaneous emission coupling coefficient. Figure 2.23 shows the relationship between multimode and single-mode rate equations.

Figure 2.23 Relationship between multimode and single-mode rate equations.

2.4.3

Small-Signal Intensity Modulation

Since Equations (2.21) and (2.22) are nonlinear, exact analytical solutions are difficult to obtain. However, an approximation can be used to calculate the small-signal modulation response of the lasers. The small-signal intensity modulation (IM) is defined as the ratio of small-signal output optical power to the modulating injected electric current: Mð joÞ ¼

pð joÞ iA ð joÞ

ð2:31Þ

When a small-signal modulation current at angular frequency o is superimposed on a DC bias current, then IA ¼ IAo þ iA ejot

ð2:32Þ

Similarly, for carrier and photon density, we have N ¼ No þ ne jot

ð2:33Þ

S ¼ So þ se jot

ð2:34Þ

Basic Concept of Semiconductor Laser Diodes

41

Substituting Equations (2.32) to (2.34) into (2.21) and (2.22), the transfer function for the IM response (normalized to the response at zero frequency) can be calculated as follows [44]: Mð joÞ ¼ Mð0Þ

ð joÞ2 þ jo

b0 1 þ þ So So tn

bo2o ð2:35Þ e b0 b þ eSo 2 go þ þ þ boo þ tp tn Sp tn tp

with b0 ¼

bGIth a

b ¼ 1eSp o2o ¼

go So tp

The zero-frequency (DC) IM response is Mð0Þ ¼

pð0Þ Zhv ¼ iA ð0Þ 2q

ð2:36Þ

where Ith is the threshold current and Z is the quantum efficiency of the intrinsic laser. Figure 2.24 illustrates the general form of the normalized IM response (magnitude and phase) against frequency. The frequency of the resonance peak is op , the height of the peak is Mðjop Þ=Mð0Þ, and the 3 dB roll-off frequency is o3db . Above the resonance peak, the magnitude of the transfer function approaches asymptotically a slope of 40 dB/decade. The phase of the IM response is zero at low frequencies, but undergoes a p radian shift near the resonance frequency. For QW lasers, an additional rate equation is needed to describe the carrier transport in the SCH region. The three-rate equation system typically used to describe the dynamics of the well and barrier/SCH carrier populations is given by [45] dNS I NS NW ðaW =aS Þ þ ¼ aW tS te dt

ð2:37Þ

dNW NS ðaS =aW Þ NW NW GðNW ; SÞS ¼ tS 1 þ xS dt tn te

ð2:38Þ

Optoelectronic Integrated Circuit Design and Device Modeling

42

Figure 2.24 Normalized IM response (magnitude and phase) against frequency.

dS GGðNW ; SÞS S ¼ dt 1 þ xS tp

ð2:39Þ

where NS ¼ carrier density in the SCH region NW ¼ carrier density in the well region aS ¼ volumes of the SCH region multiplied by electron charge aW ¼ volumes of the active region multiplied by electron charge tnS ¼ time constants for the spontaneous recombination process in the SCH te ¼ thermionic emission lifetime

Basic Concept of Semiconductor Laser Diodes

43

The small-signal IM response is obtained by linearizing Equations (2.37), (2.38) and (2.39) with the time-varying variables split into DC and AC components as follows: NW ¼ NWo þ nw e jot

ð2:40Þ

NS ¼ NSo þ ns e jot

ð2:41Þ

G ¼ GAo þ ga nw e jot

ð2:42Þ

S ¼ So þ s e jot

ð2:43Þ

Substituting Equations (2.40), (2.41), (2.42), and (2.43) into (2.37), (2.38), and (2.39), the steady-state quantities are set to zero and the resulting small-signal equations are as follows: i ns nw ðaW =aSCH Þ þ ð2:44Þ jons ¼ aSCH ts te jonw ¼

ns ðaW =aSCH Þ nw nw ga So Go nw s ts tn te 1 þ eSo ð1 þ eSo Þ2 jos ¼

Gga So s s nw þ tp ð1 þ eSo Þ tp 1 þ eSo

The IM response is given by [45] sðoÞ Gga So 1 ¼ MðoÞ ¼ i A0 þ jA1 oA2 o2 jA3 o3 aw with ga So e 1þ A0 ¼ ga tn tp ts eSo ts ts 1 A1 ¼ ga So 1 þ 1þ þ þ þ ð1 þ eSo Þ tn tp tp te tn ts ts eS0 ts þ ga S0 t s þ A2 ¼ ð1 þ eSo Þ 1 þ þ te tn tp A3 ¼ ts ð1 þ eSo Þ

ð2:45Þ

ð2:46Þ

ð2:47Þ

44

2.4.4

Optoelectronic Integrated Circuit Design and Device Modeling

Small-Signal Frequency Modulation

The common modulation formats presently used are IM for direct detection systems and frequency modulation (FM) for heterodyne systems. The direct current modulation of single-longitudinal mode semiconductor lasers causes a dynamic shift of the peak emission wavelength. From a physical standpoint, the strong nonlinear coupling that exists between photons and carriers in semiconductor diode lasers produces simultaneous IM and FM under direct injection current modulation. The intensitymodulated laser in a direct detection system experiences FM or frequency chirp, which can give rise to a dispersion penalty loss in a fiber-based system. This linewidth broadening or chirping combines with the chromatic dispersion characteristics of single-mode optical fiber to disperse intensity-modulated pulses when the laser emission wavelength is displaced from the zero dispersion wavelength of the fiber. The seriousness of the chirping-induced performance degradation increases with the transmission bit rate and can ultimately limit achievable system performance. Frequency modulation can be included through the additional rate equation df 1 1 ¼ Gae go ðNNom Þ ð2:48Þ dt 2 tp The optical frequency shift Dv (in hertz) due to a change DN in the active layer electron density is given by 1 df ae Ggo DN ð2:49Þ Dv ¼ 2p dt 4p where the linewidth enhancement factor ae is the ratio of the real part to the imaginary part of a change in the active region refractive index due to a change in electron density: ReðDne Þ ae ¼ ð2:50Þ ImðDne Þ where ImðDne Þ is the deviation of the imaginary part of the refractive index from its steady-state value. The change in ImðDne Þ is caused by a change in carrier density, which will also alter the real part of the refractive index ReðDne Þ. A change in ReðDne Þ during a limited period of time results in an additional phase shift of the laser field and in additional line broadening. Typical values of ae for InGaAsP lasers are in the range 4–8, depending on the operating wavelength. Lower values of ae occur in MQW lasers, The small-signal FM is defined as the ratio of the small-signal component of Dv to the modulating injected electric current [46]: Fð joÞ ¼

dvð joÞ iA ð joÞ

ð2:51Þ

Basic Concept of Semiconductor Laser Diodes

45

The transfer function for the IM response (normalized to the response at zero frequency) can be calculated as follows (b ¼ 1eSo ¼ 0 and b ¼ 0) [44]: om jo 2 þ 1 FðjoÞ oo 2 Fð0Þ jo jo þ1 þ oo om

ð2:52Þ

with o2o ¼

g0 Sp tp

om ¼ go =e Fð0Þ ¼

ae Ge 4pa

The magnitude of the FM transfer function against frequency is illustrated in Figure 2.25. The frequency of the resonance peak is op , the height of the peak is Mð jop Þ=Mð0Þ. Above the resonance peak, the magnitude of the transfer function approaches asymptotically a slope of 20 dB/decade.

Figure 2.25 Normalized FM response against frequency.

46

Optoelectronic Integrated Circuit Design and Device Modeling

The ratio of the FM to IM for small-signal injection current modulation or the chirpto-modulated power ratio (CPR) provides a direct comparison between IM and FM for a given laser. The CPR, which has units of GHz/mW, indicates how much frequency chirp to expect for a given level of power modulation or, conversely, indicates the power change to expect for a given frequency deviation. The CPR can be experimentally determined from small-signal IM and FM measurements, and can be expressed as follows [46]: dvðjoÞ a o2o ð2:53Þ jo þ ¼ CPR ¼ pðjoÞ 4pPo om where Po is the steady-state output power. The magnitude of the CPR is independent of frequency at low frequencies and the low-frequency phase shift is zero.

2.4.5

Large-Signal Transit Response

The small-signal analysis, although useful for a qualitative understanding of the modulation response, is not generally applicable to optical communication systems where the laser is typically biased close to threshold and modulated considerably above threshold to obtain optical pulses representing digital bits. In this case of largesignal modulation, the rate equations should be solved numerically. Large-signal behavior has been investigated for a variety of modulation schemes including shortpulse generation by gain-switching and conventional pulse code modulation for highbit-rate data communication. Therefore, the large-signal models are required for predicting the turn-on delay of the laser in response to input pulses. The rate equations describe the interaction between the carrier density and the photon field in the laser cavity. In intensity modulation direct-detection (IM-DD) systems the laser output power is a replica of the modulation waveform when a laser biased above threshold is modulated. The modulated envelope of the carrier signal contains the information to be transmitted. An important effect that arises from the nonlinearity of the laser is that the output optical frequency varies in response to variations in the drive current, known as frequency chirp. In high-bit-rate IM-DD systems this frequency chirp leads to a dispersion penalty. The rate equations can be used to model large-signal modulation dynamics, but the complexity of the largesignal waveforms will often necessitate a numerical solution technique. In the following, the transit response and frequency chirp will be discussed based on the numerical analysis results of the rate equations. Figure 2.26 shows the large-signal response simulation diagram, where the modulation current Im is generated by a random pattern generator and the current drive levels for a logic 0 and a logic 1 are specified by level 0 and level 1, respectively. The DC drive current is injected by using a bias-tee, that is a ‘tee’ in which the capacitor in the left

Basic Concept of Semiconductor Laser Diodes

47

Figure 2.26 Large-signal response simulation diagram.

Step input current and optical response

arm acts as a DC block/high-pass filter. When the rate equations that model parameters have been determined and are used in computer simulations, the large-signal modulation of the laser can be predicted. Figure 2.27 shows the idealized step input current drive waveform and the resulting large-signal response, where the variables in the figure are defined as follows: Ion

Drive current

Pp Pon Optical power Ioff

Poff ton Time

Figure 2.27 Step input current drive waveform and the resulting large-signal response for the onlevel average output optical power Pon (or the rise time measured between 10 and 90 % of the steadystate values for logic 0 and logic 1).

Ioff ¼ off-level drive current (logic 0 state) Poff ¼ off-level output optical power (logic 0 state) Ion ¼ on-level drive current (logic 1 state) Pon ¼ on-level average output optical power (logic 1 state) Pp ¼ peak value of optical power ton ¼ turn-on time, defined here as the time taken for the output power to be reached The turn-on time is an important parameter affecting the maximum achievable bit rate in digital systems, and influences the chirp characteristics. A simple expression for ton is given by [47]

48

Optoelectronic Integrated Circuit Design and Device Modeling

ton

pﬃﬃﬃ Pon 1=2 2 ¼ ln Poff oon

with oon

ð2:54Þ

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ go Son ¼ tp

Figure 2.28 shows the simulated modulation response of a BH semiconductor laser to 2 Gb/s rectangular current pulses with a different bias and modulation current level. The magnitude of the relaxation oscillations is governed by the gain saturation parameter x. The frequency of the relaxation oscillations is that of the resonant peak exhibited by the small-signal modulation response. When the bias level (off state) is above threshold, the relaxation oscillations are significantly damped with the increase of bias and modulation current level. Once the laser is biased below threshold, the magnitude of the relaxation oscillations begins to grow significantly. The dashed curves in Figure 2.28 show the frequency chirp across the optical pulse. The mode frequency shifts toward the blue side near the leading edge and toward the red side near the trailing edge of the optical pulse. Such a frequency shift implies that the pulse spectrum is considerably broader than that expected in the absence of frequency chirp. It also can be found that the frequency chirp increases with the increase of bias and modulation current level.

2.4.6

Second Harmonic Distortion

In subcarrier multiplexed (SCM) optical systems, where baseband signals from different channels are transmitted by a number of high-frequency carriers, the intrinsic nonlinearity of the semiconductor laser is an important limiting performance factor, especially second-order harmonic distortion, which is generally caused by the combination of a number of distortion mechanisms. In this application it is essential to keep the noises and distortions originating from laser nonlinearity as small as possible. Very often, it is highly desired to develop linearization techniques to compensate for the nonlinear distortions using only one laser diode. In the next section, the second harmonic distortion will be analyzed based on the rate equations [48, 49]. Limiting the analysis to second order and replacing the carrier and photon density by N ¼ No þ nejot ¼ No þ n1 ejot þ n2 ej2ot

ð2:55Þ

S ¼ So þ sejot ¼ So þ s1 ejot þ s2 ej2ot

ð2:56Þ

where n1 and s1 are the fundamental AC components of carrier and photon densities, respectively, and n2 and s2 are the second-order AC components of carrier and photon densities, respectively.

Basic Concept of Semiconductor Laser Diodes

49

Figure 2.28 Simulated modulation response of a BH semiconductor laser to 2 Gb/s rectangular current pulses. Solid curve shows the pulse shape and the dashed curve shows the frequency chirp imposed on the pulse.

Optoelectronic Integrated Circuit Design and Device Modeling

50

Substituting Equations (2.32), (2.55), and (2.56) into (2.21) and (2.22), the rate equations become dn i ¼ þ An þ Bs þ Esn þ Fs2 dt a

ð2:57Þ

ds ¼ Cn þ DsGEsnGFs2 dt

ð2:58Þ

The corresponding small-signal rate equations for fundamental frequency can be obtained as follows: jon1 ¼

i þ An1 þ Bs1 a

ð2:59Þ

jos1 ¼ Cn1 þ Ds1

ð2:60Þ

From the above linear equations, fundamental AC components n1 and s1 can be expressed as follows: s1 ¼

i C a ð joÞ2 joðA þ DÞ þ ADBC

ð2:61Þ

n1 ¼

i joD a ð joÞ2 joðA þ DÞ þ ADBC

ð2:62Þ

with A ¼ go So ð1xSo Þ

1 tn

B ¼ go ðNo Nom Þð12xSo Þ C ¼ Ggo So ð1xSo Þ þ

b tn

D ¼ Ggo ðNo Nom Þð12xSo Þ

1 tp

The small-signal IM response can be derived from Equations (2.59) and (2.60), in which pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ the relaxation oscillation frequency is jADBCj and the damping factor is A þ D. Similarly, the small-signal rate equations for second-order frequency can be obtained as follows:

Basic Concept of Semiconductor Laser Diodes

51

j2on2 ¼ An2 þ Bs2 þ En1 s1 þ Fs21

ð2:63Þ

j2os2 ¼ Cn2 þ Ds2 GEn1 s1 GFs21

ð2:64Þ

with E ¼ go ð12xSo Þ F ¼ xgo ðNo Nom Þ Combining Equations (2.59) to (2.64), the ratio of second harmonic distortion P2o to the fundamental output power Po can be obtained as follows: P2o s2 GEð joEÞ=DGF ¼ ¼ s1 Po s1 jo MCD

ð2:65Þ

with M¼

j2oðGB þ DÞ j2oG þ ðGA þ CÞ

2.4.7 Relative Intensity Noise When considering noise and distortions in optical fiber communication systems, the semiconductor laser emitter must be considered in addition to the receiver. It must be taken into account that noise and distortions of the semiconductor laser are altered considerably due to the interaction of the semiconductor laser with the optical fiber. In addition, mode partition noise will cause timing jitter at the receiver for high bit rates, and pulse broadening will occur due to the effective low-pass filtering of the fiber and the receiver. Intrinsic intensity fluctuations in semiconductor laser diodes are caused by quantum-statistical photon generation and electron–hole recombination within the lasing medium. These intrinsic intensity fluctuations are usually very small and the noise performance of an optical communication system is normally determined by the receiver, but in some specific applications the quantum noise may significantly reduce the signal-to-noise ratio (SNR). For example, when laser light distributed on several modes is transmitted through a dispersive fiber, the signals emitted in different modes will be delayed relative to each other and the fluctuations on the total output signal will increase with increasing dispersion. In addition, mode partition noise will cause timing jitter at the receiver for high bit rates and pulse broadening will occur due to the effective low-pass filtering of the fiber and the receiver.

52

Optoelectronic Integrated Circuit Design and Device Modeling

The performance of optical communication systems, especially subcarrier multiplexed (SCM) transmission systems, is strongly affected by the source laser’s relative intensity noise (RIN), which is known to be a critical factor in determining the system’s signal-to-noise ratio. The spectral density of a diode laser’s intrinsic RIN peaks at the device’s relaxation oscillation or resonance frequency, a resonance arising from the interaction between the injected carrier density and the cavity photon density. The RIN decreases both below and above the resonance frequency. The RIN is related to the signal-to-noise ratio (SNR), and is defined as the ratio of the mean square intensity fluctuation spectral density of the optical output, hSn ðf Þ2 i, to the square of the average output optical power, S2o : hSðoÞ2 i RIN ¼ 2 So Df

ð2:66Þ

where Df is the noise bandwidth when the RIN is given in units of dB/Hz, which is defined as " # hSðoÞ2 i RINðdB=HzÞ ¼ 10 log10 S2o Df " # hSðoÞ2 i ¼ 10 log10 10 log10 ½ Df S2o Df

ð2:67Þ

¼ RINðdBÞ10 log10 ½Df ðHzÞ Another noise measure for lasers is the terminal electrical noise (TEN) voltage, which is defined as the contribution of all the noise sources to the input electrical port. TEN can be used for characterization and in situ diagnostics of laser diodes. Many important laser parameters and characteristics can be determined from TEN measurements. Among these are the relaxation frequency, the threshold current, the spectral lineshape and linewidth, optical feedback properties, and mode hopping behavior. The noise performance (including TEN and RIN) may be predicted by solving the rate equations with Langevin noise terms and is characterized either in the frequency domain by relative intensity noise spectra or in the time domain by probability distributions for the mode intensities. The spectral intensity of the quantum fluctuations of the photon and electron population can be found by adding to the familiar rate equations Langevin source terms for electrons and photons, assumed to have shot noise character [50]: dNt IA Nt ¼ ðECV EVC ÞSt þ fN dt q tn

ð2:68Þ

Basic Concept of Semiconductor Laser Diodes

53

dSt Nt St ¼ ðECV EVC ÞSt þ b þ fS dt ts tp

ð2:69Þ

where Nt and St are the total number of electrons in the gain medium and photons in the single lasing mode, fN is the Langevin noise source describing the fluctuation in the carrier density, and fS is the Langevin noise source describing the photon density fluctuation; the time average values of fN and fS are zero. The gain can also be expressed as the net rate of stimulated emission per photon: G ¼ ECV EVC ¼ go ðNNom Þ

ð2:70Þ

where ECV and EVC are the stimulated emission and absorption rates per photon, respectively. Following the treatment of reference [50], each change in the photon or electron population is associated with a noise impulse of unit integrated intensity. Figure 2.29 shows the inspection of the particle rates entering and leaving the electron and photon reservoir. The spectral intensities of the Langevin noise sources fN and fS are given by [51] hFN2 ð f Þi ¼ EVC Sto þ ECV Sto þ

hFS2 ð f Þi ¼ b

Nto IAo þ 2EVC Sto ¼ tn q

Nto Sto Sto þ EVC Sto þ ECV Sto þ ¼2 þ 2EVC Sto tn tp tp

ð2:71Þ

ð2:72Þ

Figure 2.29 The inspection of the particle rates entering and leaving the electron and photon reservoir.

Optoelectronic Integrated Circuit Design and Device Modeling

54

Nto Sto hFs ð f ÞFN ð f Þi ¼ EVC Sto þ b þ ECV Sto ¼ þ 2EVC Sto tn tp

ð2:73Þ

where Nto and Sto are the steady-state numbers of carrier and photon, respectively, and hi denotes the average value. The multimode version of the rate equations with Langevin source terms can be described as follows [52]: X dN IA GGi ðN; li ÞSi þ fN ðtÞ ¼ RðNÞ dt q i

ð2:74Þ

dSi Si ¼ GGi ðN; li ÞSi þ bi ðli ÞBN 2 þ fSi ðtÞ dt tp

ð2:75Þ

where the optical gain for the ith mode can be expressed as i i Evc GGi ðN; li Þ ¼ Ecv i i where Ecv and Evc are the stimulated emission and absorption rates per photon for mode ith, respectively. The spectral intensities of the Langevin noise terms have an average of zero and, furthermore, can be expressed as

hFN ðtÞFN ðt0 Þi ¼ 2DNN dðtt0 Þ

ð2:76Þ

hFSi ðtÞFSj ðt0 Þi ¼ 2Dij dij dðtt0 Þ

ð2:77Þ

hFN ðtÞFSi ðt0 Þi ¼ 2DNi dðtt0 Þ

ð2:78Þ

Here, dij is the kronecker detla and dðtÞ is the Dirac delta function. The factor dij in Equation (2.77) indicates that there is no direct correlation between events in different modes. The diffusion coefficients DNN , Dii , and DNi are as follows: DNN ¼

X IA i i ðEcv þ Evc ÞSi þ RðNÞ þ q i

ð2:79Þ

Si þ bi ðli ÞBN 2 tp

ð2:80Þ

i i Dii ¼ ðEcv þ Evc ÞS þ

i i DNi ¼ ½ðEcv þ Evc ÞSi þ bBN 2

ð2:81Þ

Basic Concept of Semiconductor Laser Diodes

55

with i i Ecv þ Evc ¼ 2bBN 2 GGi ðN; li Þ

The RIN spectrum has a maximum that appears at a frequency that increases when increasing the injected current, as can be seen in Figure 2.30. In the multimode laser, the main mode gain is reduced in the presence of the side modes and RIN for the dominant mode is higher than the total RIN. Partition noise is the dominant limitation on a system error rate for single-mode fiber laser transmission systems.

-175

Drive current

2

RIN dB (V /Hz)

-160

-190 -205 -220 1.0E+08

1.0E+09

1.0E+10

Frequency (Hz)

Figure 2.30 RIN spectra for a single fundamental mode.

2.4.8 Measurement Technique Microwave and optical measurement techniques are the basis of characterization of the semiconductor lasers. The optoelectronic integrated circuits (OEICs) also need verification by using microwave and optical measurements. It is noted that unlike the coarse measurement, the microwave and optical measurement techniques are the highaccurate measurements; for example, a small error will cause the large discrepancy for semiconductor device modeling and parameter extraction, and the corresponding OEICs designed by using the device model mentioned above. Because of this chapter’s focus on semiconductor device modeling and parameter extraction, the most commonly used four measurements for laser diodes are as follows: 1. 2. 3. 4.

S-parameter measurement technique Noise measurement technique Distortion measurement technique Large-signal measurement technique.

The S-parameter measurement includes the microwave reflection coefficient S11 and IM response S21 . The typical experimental arrangement used to measure the reflection

56

Optoelectronic Integrated Circuit Design and Device Modeling

coefficient and intensity modulation frequency response for the lasers is shown in Figure 2.31 [53]. Traditionally, measurements of the intensity modulation frequency response can be made using a broadband optical receiver in conjugation with a microwave vector network analyzer. The devices are mounted in a 50 O microstrip test fixture. The reflection coefficient data ðS11 Þ referred to the device terminals are obtained using a vector network analyzer. The intensity modulation frequency response can also be measured using the network analyzer ðS21 Þ. For this measurement, the lasers are driven from the 50 O internal resistance of the network analyzer reflection port and the light output was detected with a high-speed photodetector and a broadband amplifier. The components in the dashed box in Figure 2.31 can be regarded as the device under test (DUT) in the S-parameter measurement system. To achieve accurate laser modulation bandwidth measurement results, the frequency response of the highspeed photodetector must be well characterized and compensated for in the overall measurement.

Figure 2.31 Experimental arrangement for reflection coefficient measurements and frequency response measurements.

The RIN is measured by using a photodiode to detect the optical output of the lasers and the corresponding electrical output of the photodiode is often amplified. The experimental setup for measurements of both the TEN and the optical intensity noise is shown in Figure 2.32 [54]. The laser is temperature controlled to within 0:01 C using a Peltier cooler. To avoid undesired optical feedback to the left laser facet as shown in Figure 2.32, a tilted optical attenuator was inserted in the optical path. A monochromator is simultaneously used to study the longitudinal mode behavior. The noise is amplified by a low-noise wideband amplifier and displayed on a spectrum analyzer, and the amplifier gain must be large enough and its noise figure low enough in relation to the spectrum analyzer to provide adequate sensitivity to make these noise measurements. Calibration measurements were performed where a precision signal generator replaced the laser. The measurement setup of intermodulation distortion levels of the lasers is shown in Figure 2.33 [55]. Three subcarriers, output from signal generators, were combined

Basic Concept of Semiconductor Laser Diodes

57

Figure 2.32 RIN and TEN measurement setups.

and used to modulate the laser diode. The optical power is detected and amplified by the lightwave converter, the output of which is connected to the spectrum analyzer. An optical isolator can be placed between the laser and the photodetector to reduce reflections back to the laser, which can cause ripples in the modulation response. It is noted that the temperature of the laser should be kept constant. The experimental setup used for the measurements of transit response measurement is shown in Figure 2.34 [56]. A pigtailed optical isolator is used to provide isolation to

Figure 2.33 Distortion measurement setup for lasers.

Optoelectronic Integrated Circuit Design and Device Modeling

58

Figure 2.34 Transit response measurement setup for lasers.

the laser diode. The fiber coupling mechanism to the laser diode is a drawn taper with a formed hemispherical lens. The optical return loss is estimated to be better than 60 dB. Therefore, optical feedback will not influence the experimental data. The pattern generator output was fed directly into the digital sampling oscilloscope. This enabled direct measurement of the rise time, fall time, duty-cycle distortion, signal amplitude, standard deviation of noise, and the bandwidth of the output waveform.

2.5 Summary In this chapter, the basic concept of the most commonly used semiconductor laser diodes, such as FP (Fabry–Perot) cavity lasers, QW (quantum-well) lasers, DFB (distributed feedback) lasers, and VCSELs (vertical-cavity surface-emitting lasers) have been introduced. Based on the rate equations in the active region, the small-signal modulation, large-signal modulation, and noise performance of the laser diode are formulated, and the corresponding measurement techniques are discussed.

References 1. Seeds, A. J. and Williams, K. J. (2006) Microwave photonics. IEEE Journal of Lightwave Technology, 24 (12), 4826–4641. 2. Kressel, H. and Butler, J. K. (1977) Semiconductor Lasers and Heterojunction LEDs, Academic, New York. 3. Botez, D. (1985) Laser diodes are power-packed. IEEE Spectrum, 22(6), 43–53.

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4. Botez, D. (1987) Recent developments in high-power InGaAsP lasers. Laser Focus, 23(3), 69–79. 5. Lee, T. P. (1991) Recent advances in long-wavelength semiconductor lasers for optical fiber communication. Proceedings of the IEEE, 79(3), 253–276. 6. Bowers, J. E., Koch, T. L., Hemenway, B. R. et al. (1985) 8-GHz bandwidth 1.52 lm vapor phase transported InGaAsP lasers. In Proceedings of the IEEE/OSA Conference on Lasers and Electro-Optics (Baltimore, MD), pp. 88–90. 7. Bowers, J. E., Hemenway, B. R., Gnauck, A. H. et al. (1985) High-frequency constricted mesa lasers. Applied Physics Letters, 47(7), 78–80. 8. Kerser, G. (2000) Optical Fiber Communications, 3rd edn, McGraw-Hill Companies. 9. Mynbaev, D. K. and Scheiner, L. (2002) Fiber-Optic Communication Technology, Prentice Hall. 10. Agrawal, G. P. (2002) Fiber-Optics Communication Systems, John Wiley & Sons, Inc., New York. 11. Lee, T. P. and Dentai, A. J. (1978) Power and modulation bandwidth of GaAs–AlGaAs high radiance LEDs for optical communication systems. IEEE Journal of Quantum Electronics, 14(3), 150–159. 12. Namizaki, H., Nagano, M., and Nakahara, S. (1974) Frequency response of GaAlAs light emitting diodes. IEEE Transactions on Electron Devices, 21, 688–691. 13. Morthier, G. and Vankwikelbcrge, P. (1997) Handbook of Distributed Feedback Lasers, Artech House, Boston. 14. Kroemer, H. (1963) A proposed class of heterojunction injection lasers. Proceedings of the IEEE, 51(12), 1782–1783. 15. Alferov, Zh. I., Andreev, V. M., Portnoi, E. L., and Trukan, M. K. (1969) AlAs–GaAs heterojunction injection lasers with a low room-temperature threshold. Fizika i Tekhnika Poluprovodnikov, 3, 1328–1332. 16. Hayashi, I., Panish, P. B., Foy, P. W., and Sumski, S. (1970) Junction lasers which operate continuously at room temperature. Applied Physics Letters, 17(3), 109–111. 17. Lee, T. P., Bums, C. A., Copeland, J. A., et al. (1982) Short cavity InGaAsP injection lasers: dependence of mode spectra and single-longitudinal-mode power on cavity length. IEEE Journal of Quantum Electronics, QE-18, 1101–1113. 18. Tessler, N. and Eisenstein, G. (1993) On carrier injection and gain dynamics in quantum well lasers. IEEE Journal of Quantum Electronics, 29(6), 1586–1595. 19. Tsvid, G., Kirch, J., Mawst, L. J., Kanskar, M., et al. (2008) Spontaneous radiative efficiency and gain characteristics of strained-layer InGaAs–GaAs quantum-well lasers. IEEE Journal of Quantum Electronics, 44(8), 732–739. 20. Koren, U., Miller, B. I., Su, Y. K., et al. (1987) Low internal loss separate confinement heterostructure InGaAs/InGaAsP quantum well laser. Applied Physics Letters, 51(21), 1744–1746. 21. Arakawa, Y. and Amnon, A. (1985) Theory of gain, modulation response, and spectral linewidth in AlGaAs quantum well lasers. IEEE Journal of Quantum Electronics, 21(10), 1666–1674. 22. Kasukawa, A., Murgatroyd, I. J., Imajo, Y., et al. (1989) 1.5 pm GaInAs/GaInAsP graded index separate confinement heterostructure multiple quantum well (GRIN-SCH-MQW) laser diodes grown by metal organic chemical vapor deposition (MOCVD). Electronics Letters, 25, 659–661. 23. Koch, T. L. and Koren, U. (1990) Semiconductor lasers for coherent optical fiber communications. IEEE Journal of Lightwave Technology, 8(3), 274–293. 24. Suematsu, Y. and Iga, K. (2008) Semiconductor lasers in photonics. IEEE Journal of Lightwave Technology, 26(9), 1132–1144. 25. Sumatsu, Y. and Arai., S. (1987) Integrated optics approach for advanced semiconductor lasers. Proceedings of IEEE, 75(11), 1472–1487. 26. Koyama, F., Suematsu, Y., Arai, S., and Tanbun-Ek, T. (1983) 1.5–1.6 lm GaInAsP/InP dynamic-singlemode (DSM) lasers with distributed Bragg reflector. IEEE Journal of Quantum Electronics, QE-19(6), 1042–1051. 27. Komori, K., Tohmori, Y., Arai, S., and Suematsu, Y. (1985) Bundle integrated guide (BIG) DBR type dynamic-single-mode laser with short active region. Transactions of the Institute of Electronics and Communication Engineers of Japan, E68(11), 742–743.

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28. Kogelnik, H. and Shank, C. V. (1972) Coupled-wave theory of distributed feedback lasers [J]. Journal of Applied Physics, 43(5), 2327–2335. 29. Ghafouri-Shiraz, H. and Lo, B. S. K. (1995) Distributed Feedback Laser Diodes: Principles and Physical Modeling, John Wiley & Sons, Inc., New York. 30. Akiba, S., Usami, M., and Utaka, K. (1987) 1.5-mm l/4 shifted InGaAsP DFB lasers. IEEE Journal of Lightwave Technology, 5(11), 1564–1573. 31. Whitesway, J. E. A., Thompson, G. H. B., Collar, A. J., and Armistead, C. J. (1989) The design and assessment of k/4 phase-shifted DFB laser structures. IEEE Journal of Quantum Electronics, 25(6), 1261–1279. 32. Smith, G. M., Hughes, J. S., Lammert, R. M. et al. (1996) Very narrow linewidth asymmetric cladding InGaAs–GaAs ridge waveguide distributed Bragg reflector lasers. IEEE Photonics Technology Letters, 8 (4), 476–478. 33. Kotaki, Y. and lshikawa, H. (1991) Wavelength tunable DFB and DBR lasers for coherent optical fibre communications. IEE Proceedings – Journal of Optoelectronics, 138(2), 171–177. 34. Sale, T. E. (1995) Vertical Cavity Surface Emitting Laser, John Wiley & Sons, Inc., New York. 35. Hadley, G. R., Lear, K. L., Warren, M. E., et al. (1996) Comprehensive numerical modeling of verticalcavity surface-emitting lasers [J]. IEEE Journal of Quantum Electronics, 32(4), 607–615. 36. Margalit, N. M., Zhang, S. Z., and Bowers, J. E. (1997) Vertical cavity lasers for telecom applications [J]. IEEE Communications Magazine, 35(5), 164–170. 37. Chow, W. W., Choquette, K. D., Crawford, M. H., et al. (1997) Design, fabrication, and performance of infrared and visible vertical-cavity surface-emitting lasers. IEEE Journal of Quantum Electronics, 33(10), 1810–1824. 38. Kobayashi, S., Yamamoto, Y., Ito, M., and Kimura, T. (1982) Direct frequency modulation in AlGaAs semiconductor lasers. IEEE Journal of Quantum Electronics, QE-18, 582–595. 39. Fumya, K., Suematsu, Y., and Hong, T. (1978) Reduction of resonancelike peak in direct modulation due to carrier diffusion in injection laser. Applied Optics, 17(6), 1949–1952. 40. Tuker, R. S. and Pope, D. J. (1983) Circuit modeling of the effect of diffusion on damping in a narrow-stripe semiconductor laser. IEEE Journal of Quantum Electronics, 19(7), 1179–1183. 41. Jensen, N. H., Olesen, H., and Stubkjaer, K. E. (1987) Partition noise in semiconductor lasers under CWand pulsed operation. IEEE Journal of Quantum Electronics, QE-23, 71–80. 42. Byme, D. M. (1992) Accurate simulation of multifrequency semiconductor laser dynamics under gigabitsper-second modulation. Journal of Lightwave Technology, 10, 1086–1096. 43. Olshansky, R., Su, C. B., Manning, J., and Powazinik, W. (1984) Measurements of radiative and nonradiative recombination rates in InGaAsP and AlGaAs light sources. IEEE Journal of Quantum Electronics, QE-20, 838–854. 44. Tuker, R. S. (1985) High-speed modulation of semiconductor lasers. IEEE Journal of Lightwave Technology, 3(6), 1180–1192. 45. Nagarajan, R., Ishikawa, M., Fukushima, T., et al. (1992) High speed quantum-well lasers and carrier transport effects. IEEE Journal of Quantum Electronics, 28(10), 1990–2007. 46. Bowers, J. E., Tsang, W. T., Koch, T. L., et al. (1985) Microwave intensity and frequency modulation of hetero-epitaxial-ridge- overgrown distributed feedback lasers. Applied Physics Letters, 46, 233–235. 47. Tucker, R. S. (1984) Large-signal switching transients in index-guided semiconductor lasers. Electronics Letters, 20, 802–803. 48. Kuo, C. Y. (1992) Fundamental second order nonlinear distortions in analog AM CATV transport systems based on single frequency semiconductor lasers. Journal of Lightwave Technology, 10, 235–243. 49. Lin, H.-T. and Kao, Y.-H. (1996) Nonlinear distortions and compensations of DFB laser diode in AM-VSB lightwave CATV applications. Journal of Lightwave Technology, 14(11), 2561–2574. 50. McCumber, D. E. (1966) Intensity fluctuations in the output of cw laser oscillators. Physical Review, 141, 306–322. 51. Harder, C., Katz, J., Margalit, S., et al. (1982) Noise equivalent circuit of a semiconductor laser diode. IEEE Journal of Quantum Electronics, 18(3), 333–337.

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52. Jensen, N. H., Olesen, H., and Stubkjaer, K. E. (1987) Partition noise in semiconductor lasers under CWand pulsed operation. IEEE Journal of Quantum Electronics, QE-23, 71–80. 53. Tuker, R. S. and Pope, D. J. (1983) Microwave circuit models of semiconductor injection lasers. IEEE Transactions on Microwave Theory and Techniques, 31(3), 289–294. 54. Andrekson, P. A., Abdersson, P., Alping, A., et al. (1986) In situ characterization of laser diodes from wide band electrical noise measurements. Journal of Lightwave Technology, 4(7), 804–811. 55. Salgado, H. M. (1997) Member, IEEE, J. M. Ferreira and J. J. O’Reilly, Extraction of semiconductor intrinsic laser parameters by intermodulation distortion analysis. IEEE Photonics Technology Letters, 9(10),1331–1333. 56. Byme, D. M. (1992) Accurate simulation of multifrequency semiconductor laser dynamics under gigabitsper-second modulation. Journal of Lightwave Technology, 10, 1086–1096.

3 Modeling and Parameter Extraction Techniques of Lasers 3.1 Introduction High-speed semiconductor lasers continue to be important for both analog microwave and millimeter wave fiber optical links, as well as higher data rate digital lightwave transmission systems in phased array radar and signal processing systems. In many radar and signal processing systems applications, the microwave and millimeter wave signals to be transmitted fall in the 8–12 GHz range. Thus, the semiconductor lasers should have a direct modulation bandwidth significantly greater than the carrier frequency of the microwave and millimeter wave signals. The semiconductor lasers for application in high-speed digital transmissions must also exhibit low power penalties, low relative intensity noise (RIN), and high linearity. A detailed analysis of the microwave operating characteristics of semiconductor lasers is crucial to the design of high-speed optical links. Traditionally, the microwave modulation response of the laser has been determined using a direct solution of the rate equations. This method of analysis has several disadvantages: it requires specialized software, it is not suited to the inclusion of package parasitic elements, and device– circuit interactions are not easily taken into account. An alternative approach is to transform rate equations to an equivalent circuit model that includes an electronic part and an optical part, and the corresponding DC, small-signal, and large-signal performance can be obtained by using general circuit simulators (such as SPICE) [1, 2, 3, 4, 5, 6, 7, 8]. Figure 3.1 shows the flowchart for a semiconductor laser equivalent circuit simulator, all equivalent circuit models including small-signal, large-signal, and noise models being based on the physical rate equations. To save time, state-of-the-art computer-aided design (CAD) simulators such as SPICE are all based on the device empirical equivalent model, and the model parameters can be determined from various microwave and radio-frequency (RF) performance measurements. Optoelectronic Integrated Circuit Design and Device Modeling Jianjun Gao Ó 2011 Higher Education Press

Optoelectronic Integrated Circuit Design and Device Modeling

64

Figure 3.1

A flowchart for a semiconductor laser’s equivalent circuit simulator.

When microwave frequency measurements are made, signals are brought to the laser by a transmission line, the source impedance, and cavity impedance, and parasitic effects due to the chip and package geometry will have significant effects on the measured results. The parasitic elements and rate equation model parameters can be obtained from the reflection coefficient, modulation response, and the relative noise intensity measurements by using numerical optimization techniques. Since the accuracy of the results strongly depends on the parameters of the equivalent circuit model, a good circuit model is not only useful for predicting the microwave performance but also the convenience for parameters extraction. In this chapter, we will introduce small-signal modeling, large-signal modeling, noise modeling, and the parameter extraction technique for semiconductor lasers. The standard double herojunction semiconductor lasers and single quantum-well lasers are used as examples. The parameter extraction includes pad capacitances, extrinsic inductances, extrinsic resistances, intrinsic elements and rate equation model parameter extractions.

3.2 Standard Double Heterojunction Semiconductor Lasers Standard double heterojunction semiconductor lasers include gain-guided semiconductor lasers and index-guided semiconductor lasers (for example ridge waveguide lasers and buried heterostructure lasers). The corresponding intrinsic small-signal, large-signal, and noise-equivalent circuit models can be obtained from the physical rate equations directly.

Modeling and Parameter Extraction Techniques of Lasers

65

3.2.1 Large-Signal Model A rigorous derivation of the rate equations generally starts from Maxwell’s equations together with a quantum-mechanical approach for the induced polarization. The rate equations can also be written heuristically by considering various physical phenomena through which the carrier density and photon density change with time inside the active region [3, 4]: dN IA N ¼ go ðNNom Þð1xSÞS dt a tn

ð3:1Þ

dS S N ¼ Ggo ðNNom Þð1xSÞS þ Gb dt tp tn

ð3:2Þ

where S is the photon density averaged over the nominal modal volume, N is the electron density averaged over the volume of the active region, G is the optical confinement factor, go is the gain slope coefficient given by go ¼ aug and ug is the group velocity, and Nom is the electron density at which the net gain is zero; tn is the spontaneous recombination lifetime, tp is the photon lifetime, b is the fraction of spontaneous emission coupled into the lasing mode, a is the volume of the active region multiplied by the electronic charge ða ¼ qVact Þ, IA is the current injected into the active region, and x is the nonlinear gain compression factor. Figure 3.2 shows the large-signal circuit model of active region. The model has been obtained from Equations (3.1) and (3.2) using a simplified version of the method described in detail in reference [3]: IA ¼ Ispon þ

dIspon þ Istim dt

Istim þ bIspon ¼ Cch

dS S þ dt Rch

Figure 3.2 Large-signal equivalent circuit model of the active region.

ð3:3Þ ð3:4Þ

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Optoelectronic Integrated Circuit Design and Device Modeling

It is noted that the rate equations are just valid under the bias close to or above the threshold conditions. Under these conditions the electron density is almost constant and spontaneous recombination is approximated by the N=tn term. The static power–voltage (I–V) characteristic of the heterojunction is modeled by the simple Shockley diode in Figure 3.2, and the diode current can be expressed as follows: Isp ¼

aN ¼ IS expðqVj =ZkTÞ tn

ð3:5Þ

where Isp is the spontaneous recombination current, IS is the heterojunction saturation current, Z is an empirical heterojunction ideality factor, k is Boltzmann’s constant, and Vj is the junction voltage. The current generator Istim models the stimulated emission current, In is proportional to the time derivative of Ispon , which models the charge storage in the active region, and Ip is the spontaneous emission. The above-mentioned current generators can be expressed as Istim ¼ ago ðNNom Þð1xSÞS

ð3:6Þ

dIsp dt

ð3:7Þ

Ip ¼ bIspon

ð3:8Þ

In ¼ tn

The photon loss and storage are modeled by resistance Rch and capacitance Cch , respectively. These elements are given by tp aSn

ð3:9Þ

Cch ¼ aSn

ð3:10Þ

Rch ¼

where Sn is the normalization constant that is used to avoid the numerical overflow problem that occurs in the general circuit simulator. The voltage at the output port of the model is an analog of the photo density S and is, therefore, proportional to the large-signal light output intensity: Pout ¼ 0:5SVZo hg=ðGtP Þ

ð3:11Þ

where h is Plank’s constant, g is the optical frequency, and Zo is the quantum efficiency. Table 3.1 summarizes the rate equations model parameters for three different buried heterostructure (BH) lasers (Ortel LS-620, Laser Diode Labs LCW-10, and Hitachi HLP-3400) [4, 5, 6]. The power–current (P–I) curve, current–voltage (I–V) curve,

Modeling and Parameter Extraction Techniques of Lasers

67

Table 3.1 Rate equation model parameters for three commercial BH lasers. Parameters

Units

Ortel SL-620

a b Nom go G tn tP x

A m3 s — m3 m3 =s — ns ps m3

1:44 1035 1 103 4:6 1024 1 1012 0.646 3.72 2 3:8 1023

Laser Diode Labs LCW-10

Hitachi HLP-3400

2:3 1034 1:86 104 1:07 1024 9:21 1013 — 3.95 1.28 —

1:58 1035 1 105 9:26 1023 8:69 1013 — 1.49 3.89 7:44 1024

small-signal and large-signal responses, and harmonic distortion performance can be obtained using the large-signal equivalent circuit model with the corresponding model parameters. The photon–current (S–I) curve characterizes the emission properties of a semiconductor laser, as it indicates not only the threshold level but also the current that needs to be applied to obtain a certain amount of power. Figure 3.3 shows the S–I curve of an Ortel SL-620 laser diode at room temperature, where the threshold current is reached near 20 mA. For I > Ith, the photon density S increases linearly with current I as Pout / ðIIth Þ.

Photo density (1/m3)

600 450 300 150 0

0

20

40

60

80

100

Current (mA)

Figure 3.3 The S–I curve of the Ortel SL-620 laser diode at room temperature.

As we know, the high signal-to-noise ratio (SNR) is a major requirement from a microwave analog fiber-optic transmission system. For multichannel transmission, good system linearity is important to prevent nonlinear distortions of signals. However, to achieve high SNR usually requires large-signal modulation of the laser diode, which in turn results in degradation of the linearity performance. Based on the large-signal equivalent model, the harmonic distortion and intermodulation distortion (IMD) can

Optoelectronic Integrated Circuit Design and Device Modeling

68

be predicted [6]. Figure 3.4 shows the power ratio of second harmonics and fundamentals as a function of bias current. The modulation signal powers are 1 dBm and 3 dBm, and the corresponding frequencies are 1 and 2 GHz, respectively. Pf and P2f are the received power of the fundamental carrier and second-order harmonics, respectively. Figure 3.5 shows the power ratio of third-order intermodulation to the fundamental carrier as a function of bias current. Two equal-amplitude sinusoidal or cosinusoidal signals at 4 and 4.04 GHz, each with an input power of 1 dBm, are used to examine third-order intermodulation products at 3.96 and 4.08 GHz.

P2f / Pf (dB)

0 -12 f=2GHz

-24 -36 f=1GHz

-48

1

1.5

2

2.5

3

I / Ith (a)

Pin = − 1dBm

P2f / Pf (dB)

0

-12 f=2GHz

-24 f=1GHz

-36

-48

1

1.5

2

2.5

3

I / Ith (b)

Pin = + 3dBm

Figure 3.4 The power ratio of second harmonics and fundamentals as a function of bias current: (a) Pin ¼ 1 dBm; (b) Pin ¼ þ 3 dBm.

3.2.2

Small-Signal Model

The corresponding small-signal equivalent circuit model can be obtained from the steady-state analysis by using the direct transform of rate equations and Fourier

Modeling and Parameter Extraction Techniques of Lasers

69

PIM3 / Pf (dB)

-16

-32

-48

-64

1

1.5

2

2.5

3

I / Ith

Figure 3.5 The power ratio of third-order intermodulation to the fundamental carrier as a function of bias current.

transform of the linear rate equations with the time-varying variables split into DC and AC components as follows [5]: IA ¼ IAo þ iejot Vj ¼ Vjo þ vj ejot N ¼ No þ nejot

ð3:12Þ

S ¼ So þ sejot where IAo is the DC component of the total driver current, Vjo is the DC junction voltage, and No and So are the steady-state carrier density and photon density, respectively. Under the steady-state condition, the time rates of changes of carrier density and photon density are zero (that is dN=dt ¼ 0 and dS=dt ¼ 0); thus the rate equations (3.1) and (3.2) become IAo No ¼ þ go ðNo Nom Þð1xSo ÞSo a tn

ð3:13Þ

So No ¼ Ggo ðNo Nom Þð1xSo ÞSo þ Gb tp tn

ð3:14Þ

Substituting Equations (3.12) through (3.14) into (3.1) and (3.2), the rate equations are easily linearized. Since the incremental terms are small, products of the incremental terms are also very small and can be neglected. Thus, the rate equations reduce to [3] vj ¼ iðRs1 þ Rs2 þ joLs Þ

ð3:15Þ

i ¼ vj ð1=R1 þ joCt Þ þ is

ð3:16Þ

70

Optoelectronic Integrated Circuit Design and Device Modeling

where 2kT qIth

ð3:17Þ

Rd 1 þ go tn So

ð3:18Þ

xRd go tn

ð3:19Þ

bGRd tp Ith ago tn S2o

ð3:20Þ

tn Rd

ð3:21Þ

Rd tp go t n So

ð3:22Þ

Rd ¼

R1 ¼

Rs1 ¼

Rs2 ¼

Cd ¼ Ls ¼

where the threshold current of the active layer is given by a 1 Ith ¼ þ Nom tn tp Ggo

ð3:23Þ

and the steady-state photon density is given by So ¼

Gtp ðIA Ith Þ a

ð3:24Þ

The corresponding small-signal circuit model of the laser follows directly from Equations (3.15) and (3.16), and is shown in Figure 3.6 [5], where the space-charge capacitance of the heterojunction is modeled by Csc. In this model, charge storage in the active layer is modeled by the diffusion capacitance Cd and small-signal photon storage is modeled by the inductance L. The small-signal photon density s is

Figure 3.6 Small-signal equivalent circuit model of the laser active region.

Modeling and Parameter Extraction Techniques of Lasers

71

proportional to the current is in the inductive branch of the model. Thus, is can be used as the output variable representing the optical output intensity or intensity modulation (IM) response. Alternatively, the output voltage vs across Rs2 can be used as a measure of optical density. The small-signal modulation response can be predicted by using the small-signal equivalent circuit model of a laser diode. Figure 3.7 shows the small-signal modulation responses, and it can be found that the well-known relaxation oscillation resonance peak moves to higher frequencies as the bias level is increased.

Modulation response (dB)

4

I=1.75Ith 0

-4

I=1.25Ith I=2.5Ith

-8

0

2

4

6

8

10

Frequency (GHz)

Figure 3.7 Small-signal modulation response of the Ortel SL-620 laser diode.

It is noted that the high-level injection effects are neglected in the rate equations (3.1) and (3.2), that is xS ¼ 1. To take in the high-level injection effects, the previously mentioned rate equations should be modified as follows: dN IA N xS ¼ go ðNNom Þ 1 S ð3:25Þ dt 1 þ 2xS a tn dS xS S N ¼ Ggo ðNNom Þ 1 S þ Gb dt 1 þ 2xS tp tn

ð3:26Þ

Although the small-signal model remains invariant, the expressions of the elements become 2xSo is ¼ ago ðNo Nom Þ 1 ð3:27Þ ð1 þ 2xSo Þð1 þ xSo Þ Rj ¼ Rd 1 þ go tn So 1

xSo 1 þ 2xSo

1

ð3:28Þ

Optoelectronic Integrated Circuit Design and Device Modeling

72

Ls ¼ GGo

Rd ¼ 2tn KT=ðqaNo Þ

ð3:29Þ

Cd ¼ tn =Rd

ð3:30Þ

Rd 2xSo xSo 1 b þ go tn So 1 ð1 þ 2xSo Þð1 þ xSo Þ 1 þ 2xSo Rs1 ¼ GxGo So

1xSo Ls ð1 þ 2xSo Þð1 þ xSo Þ

Rs2 ¼

3.2.3

GbNo Ls tn So

ð3:31Þ

ð3:32Þ

ð3:33Þ

Noise Model

The performance of optical communication systems, especially subcarrier multiplexed (SCM) transmission systems, is strongly affected by the source laser’s relative intensity noise (RIN). By equivalent circuit modeling of noise, one can calculate the component noise and hence the system noise. The rate equations can be used to study laser noise by adding a noise term, known as the Langevin force, to each of them [7, 8, 9, 10, 11]. Equations (3.1) and (3.2) then become dN IA N ¼ go ðNNom Þð1xSÞS þ fN ðtÞ dt a tn

ð3:34Þ

dS S N ¼ Ggo ðNNom Þð1xSÞS þ Gb þ fS ðtÞ dt tp tn

ð3:35Þ

Langevin noise source terms due to carrier generation and recombination fN ðtÞ and emission and absorption of photons fS ðtÞ have been added and are assumed to have a short noise character. The expressions for the time-averaged spectral intensities of Langevin sources can be expressed by the following [11]: 2 FN ðoÞ ¼ IA =q þ 2So go Nom a=q

ð3:36Þ

2So a 1 þ Ggo Nom Fs ðoÞ ¼ Gq tp

ð3:37Þ

2

Modeling and Parameter Extraction Techniques of Lasers

So a 1 * Fs ðoÞFN ðoÞ ¼ þ 2Ggo Nom Gq tp

73

ð3:38Þ

The noise-equivalent circuit model can be derived directly from Equations (3.34) and (3.35), and is shown in Figure 3.8. A noise current source and a noise voltage source (in and vn in Figure 3.8(a)) or two noise current sources (in1 and in2 in Figure 3.8(b)) are used to represent the noise behavior of a laser diode active region. The fluctuation of the photon population is due mainly to the short noise of the gain mechanism, that is due to the voltage noise source vn (or noise current source in2 ). The noise sources in and vn (or in1 and in2 ) are partially correlated due to the coupled rates. The self-spectral intensities and their cross-spectral intensity are given by [7]

Figure 3.8 Noise-equivalent circuit model of the laser diode: (a) in and vn ; (b) in1 and in2 .

2 2 2 2 mqVt in1 =Df ¼ 2Cd FN ðoÞ ¼ 2qIo þ 4qgo Nom So a aNo

ð3:39Þ

2 in2 =Df ¼ 2ðLs =Rs Þ2 ðaGo Þ2 FS2 ðoÞ ¼4

ðmVT Þ2 ½1=ðGtp Þ þ go Nom qSo ½No ðgo So þ b=tn ÞRs 2 a

ð3:40Þ

Optoelectronic Integrated Circuit Design and Device Modeling

74

2mVT q½1=ðGtp Þ þ 2go No * =Df ¼ in1 in2 So No ðgo So þ b=tp ÞRs

ð3:41Þ

with No m ¼ 2 þ pﬃﬃﬃ ðNV þ NC Þ 2 2 where NV and NC are the effective valence and conductance band densities, k is Boltzmann’s constant, and T is the absolute temperature. To obtain values for the circuit elements (include the capacitances, resistances, inductance, and noise sources) in the small-signal noise model, it is necessary to determine the DC terms No and So (steady-state carrier density and photon density, respectively). Solutions for these variable are obtained from Equations (3.13) and (3.14). Thus, No 2 ð1bÞ½1 þ x=ðgo tn Þ No ½1=ðGtp go Þ þ IA tn =a þ ð1bÞNom þ ð2bÞxIA =ðgo aÞ

ð3:42Þ

þ ½1=ðGtp go Þ þ Nom þ xIA =ðgo aÞIA tn =a ¼ 0 In general, there will be two real solutions for No, one of which is nonphysical. The correct solution is the smaller of the two: No ¼ Nom þ 1=ðGtp go Þ þ xIo =ðgo aÞ

ð3:43Þ

The corresponding output optical density can be expressed as No a 1 So ¼ IA =a ð1bÞ tp G þ Nom tn tp Ggo tn

ð3:44Þ

Based on the noise-equivalent model, the TEN (terminal electrical noise) and RIN can be calculated as follows: TEN ¼

RIN ¼

2 2 2 2 * 2 in1 ½Rs þ ðoLs Þ2 þ in2 Rs þ 2 in1 in2 Rs ðLs Ct qGo Þ2 DD*

2 2 2 * in1 þ in2 Rs ½1=R2d þ ðoCt Þ2 2 in1 in2 Rs =Rj ðLs Ct qGo So Þ2 DD*

ð3:45Þ

ð3:46Þ

Modeling and Parameter Extraction Techniques of Lasers

75

with

1 Rs Rs 1 2 o þ jo 1þ þ D¼ Ls Ct Rj Ct Rj Ls Go ¼ go ðNo Nom Þ Figures 3.9(a) and (b) show the frequency dependence of TEN and RIN spectra as a function of the normalized bias current, respectively, and the corresponding rate equation model parameters are as follows: a ¼ 6:56 1036 Am3 s; b ¼ 2 104 ; go ¼ 1:2 1012 s1 m3 ; G ¼ 0:17; tn ¼ 2:0 ns; tP ¼ 1:2 ps; Nom ¼ 1:45 1024 m3

TEN dB (V2/Hz)

-100 -120 -140

Io /Ith=1.0 Io /Ith=1.5

-160 Io /Ith=2.0 -180 1.0E+08

1.0E+09

1.0E+10

Frequency (Hz) (a)

RIN dB (V2/ Hz)

-160 Io/I th=1.5 -180 -200

I/I th=2.0 I o/I th=1.0

-220 -240 1.0E+08

1.0E+09

1.0E+10

Frequency (Hz) (b)

Figure 3.9 current.

Frequency dependence of TEN and RIN spectrum as a function of the normalized bias

76

Optoelectronic Integrated Circuit Design and Device Modeling

Depending on the structural parameters of the device, the RIN has been attributed to both the spontaneous emission and carrier recombination processes. Typically, analyses and measurements have shown that the intensity noise increases with rising injection current and optical power, reaches a maximum at threshold, and then decreases as the injection current is increased above threshold. The TEN voltage is measured at the modulation input terminal and is determined by the intrinsic junction voltage noise filtered through the parasitic elements of the laser chip and package.

3.3 Quantum-Well Lasers Semiconductor quantum-well lasers have a low threshold current, high intrinsic modulation bandwidth, narrow linewidth, and large photon gain, and are the important light sources for a high-bit-rate lightwave communication system. A detailed analysis of the microwave operating characteristics of semiconductor lasers is crucial to the design of high-speed optical links. Based on the number of rate equations, the commonly used equivalent circuit models can be categorized as one-level, two-level, and three-level equivalent circuit models [12, 13, 14, 15, 16, 17, 18]. The one-level equivalent circuit model is based on two coupled rate equations, which describe the relation between the carrier density and photon density in a QW active region; the two-level equivalent circuit model is based on three coupled rate equations, which take into account the effect of the separate confinement heterostructure (SCH) the three-level equivalent circuit model is based on four coupled rate equations, which includes the effects of the gateway state and SCH.

3.3.1

One-Level Equivalent Circuit Model

The conventional one-level equivalent circuit models for QW lasers consist of two parts: the electronic part and the optical part. The model parameters of the electronic part can be determined from the static I–V characteristic and model parameters of the optical part can be extracted from the static P–I characteristic and theoretically the modulation response. However, it is difficult to distinguish the electronic part and the optical part from each other by using a conventional modeling technique; the model parameters of the electronic part and the optical part cannot be determined directly from DC characteristics and intensity modulation response, respectively. Moreover, these models have been found to be unsatisfactory for accuracy of the input reflection coefficients and intensity modulation response, especially in the low-frequency range at a low biased condition [16]. The main reason is that the effect of the heterojunction at the input port has not been taken into account in the conventional circuit model. In order to overcome the limitations of previous literature, we have developed a compact nonlinear equivalent circuit model for the QW lasers. An independent Schockley diode has been used to model the static current–voltage characteristics.

Modeling and Parameter Extraction Techniques of Lasers

77

A full analytical and accurate method for extracting the small-signal and large-signal model parameters is given also. The extraction procedure allows direct and fast calculation of a unique physically meaningful set of parasitic elements by using a set of closed-form expressions based on the input reflection coefficients and modulation responses on wafer measurements. Figure 3.10(a) shows the conventional rate equations based on the large-signal model of a laser diode The corresponding small-signal equivalent circuit model can be obtained from the steady-state analysis by using the direct transform of rate equations and Fourier transform of the linear rate equations, as shown Figure 3.10(b). A typical parasitic network model includes a pad capacitance Cp , a series inductance Lp representing the feedline, a shunting capacitance Cs representing the contact capacitance, a series resistance Rs representing the contact resistance, and the space-charge capacitance of the heterojunction modeled by Csc. In the conventional circuit models for QW lasers, it is difficult to distinguish the electronic part and the optical part from each other (as shown in Figure 3.10(a)). An accurate parameter extraction for static current–voltage (I–V) characteristics becomes very difficult due to the optoelectronic interaction. Moreover, these models have been found to be unsatisfactory for accuracy of input reflection coefficients and intensity modulation response, especially in the low-frequency range at the low biased condition.

Figure 3.10 Conventional circuit model of the laser diode: (a) large-signal model; (b) small-signal model.

Figure 3.11(a) shows an improved large-signal circuit model for a QW laser [19]. The proposed small-signal equivalent circuit model can be obtained by linearizing the

78

Optoelectronic Integrated Circuit Design and Device Modeling

Figure 3.11 Proposed circuit model of the QW laser: (a) large-signal model; (b) small-signal model.

large-signal model (as shown in Figure 3.11b). An independent Schockley diode Dsc has been used to model the static current–voltage (I–V) characteristics. Iin is the current injected into the active region, which is equal to the current passed through the diode Dsc , and can be expressed as qVj 1 ð3:47Þ Iin ¼ Isco exp nkT with Vj ¼ VIin Rs where Isco is the heterojunction saturation current, n is an empirical heterojunction ideality factor, k is Boltzmann’s constant, and Vj and V are the internal and external junction voltages, respectively. After de-embedding the effects of CP , Lp , Rs , and Cs , the heterojunction resistance Rsc and capacitance Csc can be determined from microwave reflection coefficients under above-threshold bias conditions: Rsc ¼

1 A

Re Y11

A

Im Y11 Csc ¼ o

ð3:48Þ

ð3:49Þ

Modeling and Parameter Extraction Techniques of Lasers

79

Subscript A denotes one-port Y parameter under above-threshold biased condition, and o is the angular frequency. For the forward-bias value of space-charge capacitance Csc , the well known junction capacitance formula has been used: Csc ¼

Csco ð1Vj =Vbi ÞM

ð3:50Þ

where Vbi ¼ 1:65 V is the heterojunction built-in potential, Csco is the zero-bias spacecharge capacitance, and M is the grading coefficient. The DC model parameters of the heterojunction (Isco and n) can be carried out by fitting the static current–voltage (I–V) characteristic. The nonlinear capacitance model parameters Vbi and M can be carried out by fitting Csc at different junction voltages or by using the iteration method in which different values of Vbi and M are tried until the plot of Csc versus ð1Vj =Vbi ÞM is a straight line. In contrast with the conventional rate-equations-based equivalent circuit model, the proposed model has the following advantages: 1. The electronic part can be distinguished from the optical part and the corresponding DC model parameters (Isco and n) can be extracted from the static I–V measurement without the effect of the output optical power. 2. The parasitic elements can be extracted from the microwave reflection coefficient measurement ðS11 Þ without any assumption and the intrinsic response of QW lasers can be determined directly after de-embedding the parasitic elements. 3. The model parameters of the optical part can be directly determined from the intrinsic small-signal intensity modulation response measurement ðS21 Þ. To illustrate the above model, a high-speed quantum-well laser diode has been characterized. The active region consists of six 7 nm quantum wells in an InGaAsP separate confinement heterostructure (SCH) region, operating at 1310 nm with Ith ¼ 4:4 mA (ambient temperature). The measurements were carried out with the laser mounted in the microstrip test fixture and the light output detected using a highspeed photodiode. A network analyzer was used to determine the transfer function of the laser–photodiode combination. The S-parameter measurements for model extraction and verification are made on a wafer measurement. The extracted heterojunction dynamic resistance Rsc at different biased currents (IA ¼ 10; 20; and 30 mA) in the low-frequency range is shown in Figure 3.12. The magnitude variation of Rsc is very small and almost negligible, and can be considered to be independent of bias. Figure 3.13 shows the extracted results of heterojunction space charge capacitance Csc at different biased currents (IA ¼ 10; 30; and 50 mA). A remarkable flat frequency response can be observed in the middle-frequency range. This is due to the accurate

Optoelectronic Integrated Circuit Design and Device Modeling

80 2.2 1.9 R sc (Ω)

IA=10mA 1.6

IA=20mA IA=30mA

1.3 1.0 0.0

0.3

0.6

0.9

1.2

1.5

Frequency (GHz)

Figure 3.12 Extracted resistance Rsc versus frequency. 80

IA=10mA IA=30mA IA=50mA

CSC (pF)

60 40 20 0 5

6

7

8

9

10

Frequency (GHz)

Figure 3.13 Extracted capacitance Csc versus frequency.

extraction of all extrinsic elements and reflects the physical situation. From Figure 3.14, it can be found that the extracted Csc closely agrees with the modeled data calculated by using (3.50). Figure 3.15 shows the comparison of measured and simulated static I–V characteristics, and good agreement is observed. The improved model is also compared with the conventional model; it can be found that the new model is more accurate than the conventional one. The main reason is that the output optical power has an effect on the static I–V characteristics in the conventional model while the proposed model overcomes this problem. The extracted DC and capacitance model parameters are summarized in Table 3.2 and the rate equation parameters are summarized in Table 3.3. Figures 3.16 to 3.18 compare the measured and modeled microwave reflection coefficient S11 for a QW laser in the frequency range of 0.1–26 GHz under different biased conditions (IA ¼ 10; 20; and 30 mA). Excellent agreement over the whole frequency range is obtained. The proposed model is also compared with the conventional model, and it can be clearly observed that the proposed model is more accurate

Modeling and Parameter Extraction Techniques of Lasers

81

60 Extracted

Csc (pF)

50

Simulated

40 30 20 0.8

0.9

1.0

1.1

1.2

Vj (V)

Figure 3.14 Extracted and simulated capacitance Csc .

1.2

Vj (V)

1.1 1.0 0.9 Measured

0.8 0.7 0

10

20

30

40

IA (mA)

Figure 3.15 Measured and simulated I–V characteristics. Table 3.2 DC and capacitance model parameters. DC parameters Capacitance elements

Isco n Csco Vbi M

6 1.25 6.5 1.65 2.2

fA pF V

than the conventional one, especially for the magnitude of the microwave reflection coefficient S11 in the low-frequency ranges. Figure 3.19 shows the comparison of measured and simulated small-signal modulation responses at the 15 mA bias condition. Good agreement is obtained. The improved model also compares well with the conventional model and conventional model with Lc (Lc represents the inductance of the cable between the source and

Optoelectronic Integrated Circuit Design and Device Modeling

82

Table 3.3

Rate equation model parameters.

Parameters

Units

Values

a b G x tn tp go Nom

A m3 s — — m3 ns ps m3 =s m3

2:624 1036 4:0 103 0.075 5:5 1024 0.85 6.0 4:7 1012 0:95 1024

0.95 Conventional model Proposed model Measured

Mag (S11)

0.90

0.85

0.80

0.75 0

7 14 Frequency (GHz)

21

28

21

28

(a) 200

Phase (S11)

150 100 50 Conventional model Proposed model Measured

0 -50 0

7

14 Frequency (GHz) (b)

Figure 3.16 Comparison of measured and modeled reflection coefficient for the QW laser; bias current: I ¼ 10 mA.

Modeling and Parameter Extraction Techniques of Lasers

83

0.95 Conventional model Proposed model Measured

Mag (S 11)

0.90

0.85

0.80

0.75 0

7

14

21

28

21

28

Frequency (GHz) (a) 200

Phase (S 11)

150 100 50 Conventional model Proposed model Measured

0 -50 0

7

14 Frequency (GHz) (b)

Figure 3.17 Comparison of measured and modeled reflection coefficient for the QW laser; bias current: I ¼ 20 mA.

microstrip line on the test fixture) proposed in reference [18]. It can be found that the accuracy can be improved in the low-frequency ranges by adding the inductance Lc for the conventional model, but a large ripple will be caused in the high-frequency ranges. Measured and modeled small-signal frequency responses for the QW laser at three different bias currents above the threshold are shown in Figure 3.20. Good agreement is obtained between simulated and measured modulation response data over a wide range of bias points.

3.3.2 Two-Level Equivalent Circuit Model Figure 3.21 shows a typical separate confinement heterostructure (SCH) SQW. Electron and hole transport from the doped cladding layers to the quantum well

Optoelectronic Integrated Circuit Design and Device Modeling

84 0.95

Conventional model

0.90

Proposed model

Mag (S11)

Measured

0.85

0.80

0.75 0

7

14 Frequency (GHz)

21

28

(a)

200

Phase (S11)

150 100 50 Conventional model Proposed model Measured

0 -50 0

7

14 Frequency (GHz)

21

28

(b)

Figure 3.18 Comparison of measured and modeled reflection coefficient for the QW laser; bias current: I ¼ 30 mA.

consists of two parts. First is the transport across the SCH. This is governed by the classical current continuity equations, which describe the diffusion, recombination, and, in the presence of any electric field, drift of carriers across the SCH. The second part is the carrier capture by the quantum well. The next transport mechanism, which is significant in devices operating at room temperature, is the thermally activated carrier escape from the quantum well or thermionic emission. The rate equations for the carrier density in the quantum well ðNW Þ and the separate confinement heterostructure (SCH) layer ðNS Þ and the photon density in the

Modeling and Parameter Extraction Techniques of Lasers Proposed model

85 Measured

12 Modulation response (dB)

Conventional model 0

Conventional model with "Lc"

-12 -24

-36 -48 0

5

10 15 Frequency (GHz)

20

25

30

Figure 3.19 Comparison of measured and modeled modulation response for the QW laser; bias: I ¼ 15 mA.

Modulation response (dB)

5

-5

-15 I =10mA, 20mA, 30mA -25 Measured Modeled

-35

-45 0

1

10

100

Frequency (GHz)

Figure 3.20 Comparison of measured and modeled modulation response for the QW laser at different bias conditions.

cavity (S) are written as [20] dNS IA NS NW ðaW =aS Þ ¼ þ te dt aW tS

ð3:51Þ

dNW NS ðaS =aW Þ NW NW GðNW ; SÞS ¼ tS 1 þ xS dt tn te

ð3:52Þ

86

Optoelectronic Integrated Circuit Design and Device Modeling

Figure 3.21 Schematic diagram of a single quantum-well laser with a separate confinement heterostructure.

dS GGðNW ; SÞS S NW ¼ þ Gb dt 1 þ xS tp tn

ð3:53Þ

where NS and NW represent the carrier density in the SCH region and the well region, respectively; aS and aW are the volumes of the above regions multiplied by electron charge, respectively; tnS is the time constant for the spontaneous recombination process in the SCH; te is the thermionic emission lifetime; tn is the nonradiative carrier lifetime; tp is the photon lifetime; G is the optical confinement factor; x is the gain compression factor; and b is the spontaneous emission factor. The optical gain GðNW ; SÞ is a function of both the electron and hole carrier densities within the quantum well. Since charge neutrality has been assumed, the electron and hole densities are equal to one another in the quantum well. The peak optical gain GðNW ; SÞ variation with carrier density has been implemented with the following expression [16]: go ðNW Nom Þ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ GðNW ; SÞ ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ NW =1024 m3 þ Nom =1024 m3

ð3:54Þ

where the go is the optical gain coefficient and Nom is the carrier density for transparency. To test the validity of the above experiential formula, we have compared simulation results with experimental data in Figure 3.22 [21]. It can be found that the simulated data agree well with the measured results. Here the group velocity of light in the active region is 7:8 107 m=s. Figure 3.23 shows the large-signal circuit model of the active region. The model is obtained from Equations (3.51), (3.52) and (3.53) using a simplified version of the

Modeling and Parameter Extraction Techniques of Lasers Measured

87

Modeled

Peak gain (/cm)

2000 1500 1000 500 0 0

1

2

3

Carrier density

4 (1018

5

6

cm-3)

Figure 3.22 The peak optical gain variation with carrier density of QW lasers.

Figure 3.23 Large-signal equivalent circuit model of SQW LD based on two-level rate equations: (a) SCH model; (b) active region model.

method described in detail in reference [3]: tn VS dVS Isp ¼ þ Csch te Rsch dt

ð3:55Þ

dIsp VS tn þ Istim Isp ¼ In þ tn Rsch te dt

ð3:56Þ

IA þ IS ¼

Istim ¼

S dS þ Cch þ bIsp Rch dt

ð3:57Þ

88

Optoelectronic Integrated Circuit Design and Device Modeling

where the spontaneous recombination current Isp and the simulated emission current Istim can be expressed as Isp ¼ aNW =tn ¼ IS eqVj =ZkT

ð3:58Þ

Istim ¼ GaW GðNW ; SÞSn S

ð3:59Þ

The carrier loss and storage are modeled by resistance Rsch and capacitance Csch in the SCH regions, and the photon loss and storage are modeled by resistance Rch and capacitance Cch in the active region. These elements are given by Rsch ¼

qtS a S Cn

Csch ¼

Cn qaS

Rch

tP ¼ aW Sn

ð3:60Þ

Cch ¼ aW Sn with VS ¼

qNS Cn

Under the steady-state condition, the time rates of changes of carrier density and photon density are zero (that is dN=dt ¼ 0 and dS=dt ¼ 0). Thus the rate equations (3.51), (3.52) and (3.53) become IAo NSo NWo ðaW =aS Þ þ ¼0 te aW tS

ð3:61Þ

NSo ðaS =aW Þ NWo NWo GðNWo ; So ÞSo ¼0 tS tn te 1 þ xSo

ð3:62Þ

GGðNWo ; So ÞSo So NWo þ Gb ¼0 1 þ xSo tp tn

ð3:63Þ

The small-signal solution of the equations is done by making the following substation: IA ¼ IAo þ iejot , NS ¼ NSo þ nS ejot , NW ¼ NWo þ nW ejot , S ¼ So þ sejot , and G ¼ Go þ g0o ejot . For the small-signal carrier density variation nW , it is noted that g0o is a constant because the steady-state value carrier density in the quantum well is clamped at the steady-state value of NWo . The g0o is different for different values of NWo ,

Modeling and Parameter Extraction Techniques of Lasers

89

and this accounts for the saturation of the gain at high carrier densities in quantum-well lasers. After the small-signal quantities are substituted into Equations (3.51), (3.52) and (3.53), the steady-state quantities are set to zero. The resulting small-signal equations are as follows: i ¼ joCsch vs þ is0

ð3:64Þ

vj ¼ is ðRs þ joLs Þ

ð3:65Þ

is ¼ aW Go s=ð1 þ xSo Þ2

ð3:66Þ

is0 ¼ vs =Rsch

tn vj te

ð3:67Þ

is0 ¼ vj ð1=RT þ joCT Þ þ iS

ð3:68Þ

Ls ¼ RD tP ð1 þ xSo Þ2 =ðg0o So tn Þ

ð3:69Þ

Rs ¼ xSo LS =tP ð1 þ xSo Þ

ð3:70Þ

RT ¼ RD =½1 þ g0o So tn =ð1 þ xSo Þ

ð3:71Þ

CT ¼ tn =RD

ð3:72Þ

RD ¼ 2tn kT=ðqaW NWo Þ

ð3:73Þ

with

The corresponding small-signal equivalent circuit model for the QW laser is shown in Figure 3.24. From Figures 3.23 and 3.24, it can be found that three additional

Figure 3.24 Small-signal equivalent circuit model of SQW LD.

Optoelectronic Integrated Circuit Design and Device Modeling

90

elements (resistance Rsch , capacitance Csch , and a controlled current source) are used to model the carrier behavior of the SCH region.

3.3.3

Three-Level Equivalent Circuit Model

A schematic representation of the dynamical processes occurring within a QW laser possessing gateway states is given in Figure 3.25 [13]. Briefly, the gateway states can be viewed as a temporary storage location for carriers that are supplied from the SCH at a rate / 1=tD .

Figure 3.25 Schematic of the dynamical processes occurring within the QW laser.

The three charge-continuity equations, taking into account stimulated emission, and augmented by a fourth equation describing the photon dynamics, lead to the three-level rate equations for a laser operating in the single mode [22], namely dNS IA NS NS NG ðaG =aS Þ ¼ þ tG dt aS tnS tD

ð3:74Þ

dNG NS ðaS =aG Þ NG NG NG NW ðaW =aG Þ þ ¼ tD te dt tG tnG tC

ð3:75Þ

dNW NG ðaG =aW Þ NW NW ug GðNW ÞS ¼ tC 1 þ xS dt te tn

ð3:76Þ

Modeling and Parameter Extraction Techniques of Lasers

dS Gug GðNW ÞS S NW ¼ þ Gb dt 1 þ xS tp tn

91

ð3:77Þ

where NS , NG , and NW represent the carrier density in the SCH region, the gateway region of the well, and the well region respectively; aS , aG , and aW are the volumes of the above region multipied by electron charge; tnS and tnG are time constants for the spontaneous recombination process in the SCH and gateway regions; tG is a time constant associated with the lifetime of the carriers in the gateway states; tD is the diffusion time constant across the SCH region; tC is the ambipolar capture time constant; te is the thermionic emission lifetime;tn is the nonradiative carrier lifetime; tp is the photon lifetime; G is the optical confinement factor; x is the gain compression factor; and b is the spontaneous emission factor. By using a simplified version of the method, the rate equation becomes [16] IA þ

aG Cn VS VS dVS VG ¼ þ þ Csch qtG Rschs Rschd dt

ð3:78Þ

VS a G Cn tn VG VG dVG VG þ Isp ¼ þ þ Cg Rschd qtG te Rgg Rgc dt

ð3:79Þ

VG tn Isp ¼ Isp þ In þ Istim Rgc te

ð3:80Þ

Istim ¼

S dS þ Cch Rch dt

ð3:81Þ

The carrier loss and storage in the SCH region are modeled by two resistances, Rschs and Rschd , and a capacitance, Csch , respectively. These elements are given by Rschs ¼

qtS aS Cn

ð3:82Þ

Rschd ¼

qtD aS Cn

ð3:83Þ

Csch ¼

aS Cn q

ð3:84Þ

The carrier loss and storage in the gateway region are modeled by RSCHS, RSCHD , and CSCH , respectively. These elements are given by

Optoelectronic Integrated Circuit Design and Device Modeling

92

Rgc ¼

qtC aG Cn

ð3:85Þ

Rgg ¼

qtnG a G Cn

ð3:86Þ

Cg ¼

aG Cn q

ð3:87Þ

where the voltage VS at the SCH region is equal to qNS =Cn , the voltage VG at the gateway region is equal to qNG =Cn , and both Cn and Sn are the normalization constants. Figure 3.26 shows the large-signal circuit model of the active region based on Equations (3.78) through (3.81). The model is based on the three-level rate equations, which include, in their characterization of charge dynamics, the role of gateway states at the quantum well.

Figure 3.26 Large-signal equivalent circuit model of SQW LD based on three-level rate equations.

By linearizing the rate equations (3.74) to (3.77), the rate equations become [17] iA þ

aG Cn vS vS dvS vG ¼ þ þ Csch qtG Rschs Rschd dt

ð3:88Þ

vS aG Cn tn vG vG dvG vG þ vj ¼ þ þ Cg Rschd qtG te Rgg Rgc dt

ð3:89Þ

vg tn vj ¼ vj ð1=RT þ joCT Þ þ ip Rgc te

ð3:90Þ

vj ¼ iP ðRS þ joLS Þ

ð3:91Þ

iP ¼ aW Go s=ð1 þ xSo Þ2

ð3:92Þ

Modeling and Parameter Extraction Techniques of Lasers

93

The small-signal equivalent circuit model of an SQW LD based on the three-level rate equations is illustrated in Figure 3.27, where vSCH , vG , and vj are small-signal junction voltages in the SCH region, gateway state region, and active region, respectively.

Figure 3.27 Small-signal equivalent circuit model of SQW LD based on three-level rate equations.

Figures 3.28 and 3.29 show the measured and modeled small-signal modulation responses of 76 nm SCH and 300 nm SCH QW lasers, respectively. The QW lasers with a cavity length of 300 mm, 2.5 mmwide, and an 8 nm quantum well are used for the modulation bandwidth measurement. The simulation results are compared with experimentally obtained data, and agreement is obtained consistently on a separate confinement SCH of different sizes. Table 3.4 lists the corresponding model parameters of QW lasers used in the simulation [13, 20, 21]. Modeled

Measured

10 3.1mW 8.0mW

1.3mW

Response (dB)

5

20.9mW 43.3mW

0

-5 0.4mW

-10

0

4

8

12

16

20

Frequency (GHz)

Figure 3.28 Simulated and measured modulation response for 76 nm SCH laser.

Figure 3.30 shows the turn-on delay and the on/off aspect ratio as a function of bias current resulting from transient simulation. Accordingly, the DC bias current Ib is varied up to 2Ith and the injection pulse current amplitude Ip ¼ 1:5Ith , which is excited

Optoelectronic Integrated Circuit Design and Device Modeling

94

Measured

Modeled 10 0.9mW

2.4mW 7.4mW

Response (dB)

5 13.4mW

0

30.0mW 42.7mW

-5

-10 0

4

8

12

16

Frequency (GHz)

Figure 3.29 Simulated and measured modulation response for 300 nm SCH laser. Table 3.4 Values of the model parameters for different SCH-sized QW lasers. Parameters

Unit

Values SCH ¼ 76 nm

aW aS aG tnS tnG tG tD tC te tn tp G x go b Nom

3

Am s A m3 s A m3 s ns ns ps ps ps ns ns ps m3 m3 =s m3

37

9:6 10 9:1 1036 9:6 1037 1 1 1 3.1 0.18 0.2 0.13 2 0.029 3 1023 2:34 1011 1 104 1 1024

SCH ¼ 300 nm 9:6 1037 3:6 1035 9:6 1037 1 1 1 48.3 0.18 0.2 0.35 3 0.019 1 1023 1:05 1011 1 104 1 1024

by a 200 Mb/s pulse train with a 50 % duty cycle. DC simulation revealed the threshold current Ith to be about 24 mA and 13 mA for lasers with 76 nm and 300 nm SCH lengths. As the biased current Ib becomes larger than the threshold current, the turn-on delay and the on/off aspect ratio decrease quickly. In order to obtain the small turn-on delay and the large on/off aspect ratio, increasing the pulse amplitude Ip is the only approach.

Modeling and Parameter Extraction Techniques of Lasers SCH=76nm

1.00

9

0.75

7

0.50

5

0.25

3

0.00 0.0

Aspect ratio

Turn-on delay (ns)

SCH=300nm

95

1 0.5

1.0 1.5 Biased current (Ib/Ith)

2.0

Figure 3.30 The dependence of turn-on delay and on/off aspect ratio on the biased current amplitude ratio (Ib =Ith ).

3.4 Parameter Extraction Methods Accurate extraction of the small-signal and large-signal equivalent circuits for laser diodes is extremely important for optimizing the device performance. When microwave frequency measurements are made, signals are brought to the laser by a transmission line, and the source impedance, cavity impedance, and parasitic effects due to the chip and package geometry will have significant effects on the measured results. The parasitic elements and rate equation model parameters can be obtained from the reflection coefficient, modulation response, and the relative noise intensity measurements by using numerical optimization techniques [23, 24, 25, 26, 27, 28]. However, the accuracy of the numerical optimization methods that minimize the difference between measured and modeled data can vary depending upon the optimization method and starting values, while the analytical methods allow us to extract the equivalent circuit model parameters in a straightforward manner. In order to overcome these difficulties, the full analytical method and semianalytical method for extracting the small-signal and large-signal model parameters will be introduced in the next sections [18, 29].

3.4.1 Direct-Extraction Method The direct-extraction procedure allows direct and fast calculation of a unique physically meaningful set of parasitic elements by using a set of closed-form expressions based on the input reflection coefficients and modulation responses on wafer measurements. First, the parasitic elements including pad capacitance, series wire inductance, and chip parasitic elements can be extracted from the input reflection coefficient on wafer measurements. After de-embedding the effects of parasitic

96

Optoelectronic Integrated Circuit Design and Device Modeling

elements, the intrinsic small-signal model parameters can be obtained from the smallsignal modulation response. The rate equation model parameters are extracted from the intrinsic small-signal model parameters at multiple bias points to verify the validity of this approach. 3.4.1.1 Equivalent Circuit Model To illustrate the method described next, we present the extracted model parameters for several quantum-well laser diodes. The active region consists of six 7 nm quantum wells in an InGaAsP separate confinement herostructure (SCH) region, operating at 1310 nm with Ith ¼ 4:4 mA (ambient temperature). A typical parasitic network model (as shown in Figure 3.31) includes a pad capacitance Cp , a series inductance Lp representing the wirebond, a shunting capacitance Cs representing the contact capacitance, a series resistance Rs representing the contact resistance, and the space-charge capacitance of the heterojunction modeled by Csc . RIN is the source impedance and Lc represents the inductance of the cable between the source and microstrip line on the test fixture. The intrinsic small-signal equivalent circuit model of the laser diode can be obtained from the steady-state analysis by using the direct transform of rate equations and Fourier transform of the linear rate equations.

Figure 3.31 Small-signal model of the QW laser diode, including parasitic elements.

To calculate the normalized small-signal modulation response of the laser, we must take into account both the photo response and the effect of the parasitic elements. The total small-signal normalized response TðoÞcan be expressed as TðoÞ ¼

HðoÞ FðoÞ Hð0Þ Fð0Þ

ð3:93Þ

where HðoÞ is the small-signal current transformation function of the parasitic network: HðoÞ ¼

Z1 Z3 Z5 Z2 Z4 Rs

ð3:94Þ

Modeling and Parameter Extraction Techniques of Lasers

97

with Z1 ¼

Rs 1 þ joRs Cs

Z2 ¼ joLp þ Z1 Z3 ¼

Z2 1 þ joZ2 Cp

Z4 ¼ joLc þ Z3 Z5 ¼

Z4 RIN Z4 þ RIN

The small-signal current transformation function of the intrinsic network can be determined from the rate equation description of the dynamics: FðoÞ ¼

R1 þ joðL þ R1 R2 Ct Þ

R1 þ R2 o2 LR1 Ct

ð3:95Þ

where Ct ¼ Csc þ Cd 3.4.1.2 Extrinsic Parameter Extraction Procedure The internal resistance of the modulation source RIN is usually known and is typically 50 O, and the cable inductance Lc can be obtained from S-parameter measurement of the cable. The values of the other parasitic elements (including CP , Lp , Rs , and Cs ) can be obtained from measurements of the microwave reflection coefficient under zerobiased and above-threshold-biased conditions. Under the above-threshold-biased condition ðI Ith Þ, the space-charge capacitance of the heterojunction has low impedance and low junction dynamic resistances shorting it. The input impedance of the laser diode is very small and can be modeled by using a short circuit. Therefore, the equivalent circuit becomes much simpler, the Y parameter being Y11 ¼

1 þ joRs Cs þ joCp Rs ð1o2 Cs Lp Þ þ joLp

Rs can be extracted directly as follows at low frequency: 1 Rs ¼ A Re Y11 o!0

ð3:96Þ

ð3:97Þ

Optoelectronic Integrated Circuit Design and Device Modeling

98

Lp and Cp can be expressed as 1 Lp ¼ o

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ R s A R2s Re Y11

A

Im Y11 LP Cp ¼ þ 2 2 o o Lp þ R2s

ð3:98Þ

ð3:99Þ

After de-embedding the effects of the parasitic elements (Cp , Lp , and Rs ), the contact capacitance Cs and the zero-bias space-charge capacitance Csco can be determined from the zero-biased condition Y parameter: sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ O

Re Y11 1 ð3:100Þ Csco ¼ o Rs ½1Rs ReðY11 Þ Cs ¼

1 joCsco O Im Y11 o 1 þ joRs Csco

ð3:101Þ

A O where Y11 and Y11 represent the one-port Y parameter under above-threshold-biased and zero-biased conditions, respectively. After obtaining the intrinsic modulation responses, R2 =R1 and R1 Cd can be determined as follows: vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ﬃ ! u 2 2 2 u R2 t 1 o or o ¼ 2 2 þ 2 1 ð3:102Þ 2 2 2 G Gp or or o R1 or

R1 1 R1 Cd ¼ 2R2 or

sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ! 2 2 1 R2 1 1 R2 R1 4 G2p or G2p R1 R1 R2 o2r

ð3:103Þ

where G represents the small-signal frequency response and GP is the peak response at the resonant frequency or. With Equations (3.18) and (3.21) substituted in (3.103), we have 1 1 ¼ þ o2r tp R1 Cd tn

ð3:104Þ

where tn and tp can be obtained from the plot of 1=ðR1 Cd Þ versus fr2 , the interception would gives the value of the t1n , and the slope would gives the value of 4p2 tp . Therefore, all intrinsic elements can be determined from Equations (3.21), (3.102) and (3.103).

Modeling and Parameter Extraction Techniques of Lasers

99

The extracted contact resistance Rs at different biased current I in the low-frequency range is shown in Figure 3.32. The magnitude variation of Rs is very small (less than 8 % from the middle value) and almost negligible, and can be considered to be independent of bias. Figures 3.33 and 3.34 show the extracted parasitic elements Lp and Cp . Cs and Csco can be extracted with the de-embedding procedure, as shown in Figures 3.35 and 3.36. Rather constant values can be observed. 12

RS (Ω)

9

I=80mA

I=90mA

0.2

0.4 0.6 Frequency (GHz)

I=100mA

6 3 0 0.0

0.8

1.0

Figure 3.32 Extracted Rs versus frequency under the above-threshold-biased condition (I Ith ).

0.5

LP (nH)

0.4

I=80mA

I=90mA

10

15 20 Frequency (GHz)

I=100mA

0.3 0.2 0.1 5

25

30

Figure 3.33 Extracted Lp versus frequency under the above-threshold-biased condition (I Ith ).

3.4.1.3 Intrinsic Parameter Extraction Procedure From Equations (3.1) and (3.2), it can be found that there are eight model parameters in the rate equations (a, b, G, tn , tp , go , Nom , and x), and all are bias independent. The parameters a can be calculated from known device dimensions and G can be calculated using the three-dimensional equivalent refractive index method [30]. Then go , Nom , x, and b can be determined in sequence:

Optoelectronic Integrated Circuit Design and Device Modeling

100 0.4

CP (pF)

0.3

I =80mA

I =90mA

I =100mA

0.2 0.1

0.0 10

15

20

25

30

35

40

Frequency (GHz)

Figure 3.34 Extracted Cp versus frequency under the above-threshold-biased condition (I Ith ).

4

CS (pF)

3

2

1

0 0

5

10

15

20

Frequency (GHz)

Figure 3.35 Extracted Cs versus frequency under the zero-biased condition.

20

CSCO (pF)

15

10

5

0 0

5

10

15

20

Frequency (GHz)

Figure 3.36 Extracted Csco versus frequency under the zero-biased condition.

Modeling and Parameter Extraction Techniques of Lasers

101

Since the space-charge capacitance Csc is smaller when compared with Cd , the relaxation oscillation resonance frequency can be expressed approximately as 1 1 fr ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2p 2p ðCd þ Csc ÞL

rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Ggo ðIIth Þ a

ð3:105Þ

that is go ¼

ao2r GðIIth Þ

ð3:106Þ

Nom can be determined directly from the threshold current measurement: Nom ¼

Ith tn 1 Ggo tp a

ð3:107Þ

It is found that R2 is almost a constant under the high current bias condition, and can be expressed as xRd go t n

ð3:108Þ

go tn R2 Rd

ð3:109Þ

R2 ¼ that is x¼

The spontaneous emission factor b can be determined at the lower bias condition: b¼

xRd atn o4r tp R2 go tn Ggo Ith Rd

ð3:110Þ

This method also can be considered as an initial method of an optimization procedure for a more complete model. The extracted radio of R2 and R1 versus frequency at three different bias conditions is shown in Figure 3.37, where constant values are observed over a wide frequency range. Figure 3.38 shows the plot of 1=ðR1 Cd Þ versus fr2 . The extracted spontaneous recombination lifetime tn and photon lifetime tp are 0.84 ns and 6.0 ps, respectively. It can be found that the measured data in the low bias condition region with low resonant frequency or is very useful to improve the extraction accuracy of tn and tp . The extracted intrinsic small-signal parameters are summarized in Table 3.5. It is noted that

Optoelectronic Integrated Circuit Design and Device Modeling

102 0.20

I =25mA

I =35mA

I =45mA

R2 /R1

0.15

0.10

0.05

0.00 1

3

5

7

Frequency (GHz)

Figure 3.37 Extracted R2 =R1 versus frequency under three different biased conditions.

×10 9 40

1/R1 Cd

30 20 10

0 0

40

80 fr

2

120

160

2

(GHz)

Figure 3.38 Plot of 1=ðR1 Cd Þ versus fr2 .

Table 3.5 Extracted intrinsic elements. Bias current (mA)

R1 (O)

R2 (mO)

Cd (pF)

L (pH)

15 20 25 30 35 40 45 50 55

1.5 1.366 0.826 0.713 0.587 0.553 0.496 0.437 0.401

50 47 25 20 17 17 17 16 16

71 71 71 71 71 71 71 71 71

10 7 5.4 4.3 3.8 3.4 3 2.6 2.4

Modeling and Parameter Extraction Techniques of Lasers

103

we have assumed a linear relationship between gain and carrier density in the active region, and a sublinear relationship caused by the size quantization effect in the QW is neglected (typically a logarithmic formula has been chosen based on phenomenological considerations). 3.4.1.4 Measurement Procedure The measurements were carried out with the laser mounted in the microstrip test fixture and the light output detected using a high-speed photodiode. A network analyzer was used to determine the transfer function of the laser–photodiode combination. The S-parameter measurements for model extraction and verification were made up to 40 GHz on wafer using Cascade Microtech’s Air-Coplanar Probes ACP50-GSG-100, with all instruments under IC CAP software control. Figure 3.39 shows the microstrip test fixture with the laser mounted.

Figure 3.39 Laser diode test structure.

Figure 3.40 compares the measured and modeled S parameters for the laser diode in the frequency range of 1–40GHz under two different bias conditions (I ¼ 80 mA and I ¼ 0 mA). A good agreement over the whole frequency range is obtained. The measured and modeled small-signal frequency response for the QW laser is shown in Figure 3.41 at four different bias currents above thethreshold, and a comparison between modeled and measured resonance frequency versus bias current is given in Figure 3.42. Good agreement is obtained between simulated and measured modulation response data over a wide range of bias points. The discrepancy between measured and modeled small-signal frequency responses may be due to the assumption of a linear relationship between gain and carrier density in the active region, while a sublinear relationship caused by the size quantization effect in QW is neglected.

Optoelectronic Integrated Circuit Design and Device Modeling

104

Figure 3.40 Comparison of modeled and measured S parameter for the laser diode; bias currents: (a) I ¼ 80 mA; (b) I ¼ 0 mA. Measured

Modeled

Modulation response (dB)

10 35mA

0 -10

45mA

-20 15mA

25mA

-30 0

5

10 Frequency (GHz)

15

20

Figure 3.41 Comparison of modeled and measured modulation responses. Measured

Modeled

Resonant frequency (GHz)

12

9

6

3

0 0

10

20

30

40

50

60

Bias current (mA)

Figure 3.42 Comparison of modeled and measured resonant frequency versus bias currents.

Modeling and Parameter Extraction Techniques of Lasers

105

3.4.2 Semi-Analytical Method By assuming that the input impedance of intrinsic laser diode is very small and can be modeled by using a short circuit under an above-threshold-biased condition, a fully analytical approach was developed in references [18], [19], and [29]. Actually, only under a very high current bias condition does the input impedance satisfy the assumption, approximately. The accuracy has been found to be not satisfactory under a lower above-threshold-biased condition. An improved method for the extraction of the extrinsic elements of the quantum-well laser diode based on a combination of numerical optimization and direct extraction methods is developed [31]. There are three aspects that are new here: 1. The parasitic pad capacitance and feedline inductance are determined by using an input reflection coefficient on the wafer measurement under the above-thresholdbiased condition. The influence of the intrinsic elements on the input impedance measurement has been taken into account. 2. The analytical method can be considered as an initial guess of a subsequent optimization procedure leading to the final model parameters. The extrinsic contact resistance and capacitance are described as functions of the pad capacitance and feedline inductance. 3. The proposed method is suitable for any above-threshold-biased condition, not only under a very high current bias condition. The complete laser diode small-signal equivalent circuit model under the abovethreshold-biased condition is shown in Figure 3.43. The typical parasitic network model includes a pad capacitance Cp , a series inductance Lp representing the feedline, a shunting capacitance Cs representing the contact capacitance, a series resistance Rs representing the contact resistance, and Zin representing the input impedance of the active layer.

Figure 3.43 Small-signal equivalent circuit model of the QW laser under the above-thresholdbiased condition.

The QW laser small-signal equivalent circuit model under the cutoff-biased condition is shown in Figure 3.44. The cutoff bias condition for lasers is defined as the condition when the current injected into the laser is less than the threshold current or is zero biased. Under such a condition, the output optical power is zero, and hence

Optoelectronic Integrated Circuit Design and Device Modeling

106

Figure 3.44 Small-signal equivalent circuit model of the QW laser under the cutoff-biased condition.

the intrinsic part can be modeled by using zero-biased space-charge capacitance Csco and the device behaves like a passive component. Under the above-threshold-biased condition (I >> Ith ), the input impedance of the intrinsic part is very small and can be modeled by the real part of Zin . Therefore, the equivalent circuit becomes much simpler and the Y parameter is A ¼ Y11

1 þ joR0s Cs þ joCp R0s ð1o2 Cs Lp Þ þ joLp

ð3:111Þ

The superscript A denotes a one-port Y parameter under the above-threshold-biased condition, o is the angular frequency. R0s is the sum of Rs and ReðZin Þ, and can be extracted directly as follows at low frequency: R0s ¼ Rs þ ReðZin Þ ¼

1 A

Re Y11

ð3:112Þ

By neglecting the small high-order terms of frequency, Lp and Cp can be expressed as approximately sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 R0 s A R02 ð3:113Þ Lp s o Re Y11 A

Im Y11 LP þ 2 2 Cp o o Lp þ R02 s

ð3:114Þ

After de-embedding the effects of the pad capacitance and feedline inductance (Cp and Lp ), the contact resistance and capacitance can be determined from the o : zero-biased condition one-port Y parameter Y11

o

2 oCsum Im Y11 Rs ¼ n 2 o

2 o o o Re Y11 Re Y11 þ oCsum Im Y11

ð3:115Þ

Modeling and Parameter Extraction Techniques of Lasers

o 2 o

2 Re Y11 þ oCsum Im Y11 o

Cs ¼ Csum o oCsum Im Y11

107

ð3:116Þ

where Csum is the sum of the zero-bias space-charge capacitance Csco and contact capacitance Cs , and can be obtained from Y-parameter at low frequency: o

Im Y11 ð3:117Þ Csum ¼ Cs þ Csco ¼ o Also, the extracted parasitic pad capacitance and feedline inductance (Cp and Lp ) can be considered as an initial guess of an optimization procedure, and the contact resistance and capacitance (Cs and Rs ) determined by using the analytical method are described as functions of Cp and Lp . The optimization procedure is then used to optimize only the parasitic pad capacitance and feedline inductance with very small dispersions of initial values. A flowchart of the iterative process is shown in Figure 3.45, where e is the error function criterion and can be expressed as

Figure 3.45 Algorithm.

Optoelectronic Integrated Circuit Design and Device Modeling

108

e¼

N1 1 X Sm Sc j2 N1 i¼0 11 11

ð3:118Þ

Subscript c denotes the modeled S parameter, m is the measured S parameter, and i ¼ 0; . . . ; N1 is the number of sampling points. Figure 3.46 shows the S-parameter measurement system. Figure 3.47 shows the extracted resistance R0s versus frequency with different injection current Ib . It can be observed that R0s decreases when Ib increases. The reason is that the real part of intrinsic input impedance Zin decreases quickly when Ib increases. Furthermore, it is difficult to determine the contact resistance Rs from R0s directly. Figure 3.48 shows the extracted and optimized values of Lp and Cp versus bias current. It can be observed that the discrepancy between extracted and optimized data decreases when Ib increases, which means that if the bias current is infinite, the optimized data will be consistent with the directly extracted data.

Figure 3.46 S-parameter measurement system for lasers.

6.0 Ib=20mA

Rs + Re (Z in) (Ω)

5.5

Ib=40mA

5.0

Ib=60mA Ib=80mA

4.5

Ib=100mA

4.0 3.5 0.0

0.2

0.4 0.6 0.8 Frequency (GHz)

1.0

1.2

Figure 3.47 Extracted resistance R0s versus frequency.

Modeling and Parameter Extraction Techniques of Lasers

109

Extracted

Optimized

Lp (nH) and Cp (pF)

0.5 Lp

0.4 0.3

Cp 0.2 0.1 0.0 0

20

40

60

80

100

Bias current (mA)

Figure 3.48 Extracted resistance LP and CP versus bias current.

8

RS (Ω)

6 4 2 0 0

5

10 15 20 Frequency (GHz)

25

30

Figure 3.49 Extracted Rs versus frequency under the cutoff-biased condition.

CSCO and CS (pF)

10 CSCO

8 6 4

CS

2 0 0

5

10 15 20 Frequency (GHz)

25

30

Figure 3.50 Extracted Cs and Csco versus frequency under the cutoff-biased condition.

Optoelectronic Integrated Circuit Design and Device Modeling

110

Table 3.6 Extracted parasitic elements. Cp (pF) 0.15

Parameters Units Values

Lp (nH) 0.28

Rs (O) 3.90

Measured

Cs (pF) 0.70

Csco (pF) 6.45

Modeled

1.0

Real (S11)

0.5 0.0 -0.5 -1.0 0

10

20

30

40

Frequency (GHz)

Measured

Modeled

1.0

Imag (S11)

0.5 0.0 -0.5 -1.0 0

10

20

30

40

Frequency (GHz)

Figure 3.51 Comparison of modeled and measured S parameter under the cutoff-biased condition.

After de-embedding the pad capacitance and feedline inductance LP and CP , the contact resistance Rs and capacitance Cs can be determined from the zero-biased condition. The extracted Rs , Cs , and Csco versus frequency are shown in Figures 3.49 and 3.50. The magnitude variations of Rs , Cs , and Csco are very small and almost negligible (less than 8 % of magnitudes), and the above model parameters can be considered to be constants. The extracted parasitic elements are summarized in Table 3.6, while Figure 3.51 compares the measured and modeled S parameter for the QW laser diode in the

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frequency range of 50 MHz–40 GHz under cutoff bias conditions. A good agreement over the whole frequency range is obtained with an error that is less than 1 %.

3.5 Summary In this chapter, the small-signal modeling, large-signal modeling, noise modeling, and parameter extraction techniques for semiconductor lasers is introduced. The standard double heterojunction semiconductor lasers and single quantum-well lasers are used as examples. The model parameter extraction techniques for the extrinsic elements, intrinsic elements, and rate equation model parameters are described in more detail.

References 1. Katz, J., Margalit, S., Harder, C., et al. (1981) The intrinsic electrical equivalent circuit of a laser diode. IEEE Journal of Quantum Electronics, 17(1), 4–7. 2. Tuker, R. S. (1981) Large-signal circuit model for simulation of injection laser modulation dynamics. IEE Proceedings – I Communications Speech and Vision, 128(5), 180–184. 3. Tuker, R. S. and Kaminow, I. P. (1984) High-frequency characteristics of directly modulated InGaAsP ridge waveguide and buried heterostructure lasers. Journal of Lightwave Technology, 2(4), 385–393. 4. Tuker, R. S. (1981) Circuit model for double-heterojunction laser below threshold. IEE Proceedings – I Communications Speech and Vision, 128(3), 101–106. 5. Tuker, R. S. and Pope, D. J. (1983) Microwave circuit models of semiconductor injection lasers. IEEE Transactions on Microwave Theory and Techniques, 31(3), 289–294. 6. Way, W. I. (1987) Large signal nonlinear distortion prediction for a single-mode laser diode under microwave intensity modulation. Journal of Lightwave Technology, 5(3), 385–393. 7. Harder, C., Katz, J., Margalit, S., et al. (1982) Noise equivalent circuit of a semiconductor laser diode. IEEE Journal of Quantum Electronics, 18(3), 333–337. 8. Andrekson, P. A., Abdersson, P., Alping, A., et al. (1986) In situ characterization of laser diodes from wide band electrical noise measurements. Journal of Lightwave Technology, 4(7), 804–811. 9. Orsal, B., Signoret, P., Peransin, J.-M., et al. (1994) Correlation between electrical and optical photocurrent noises in semiconductor laser diode. IEEE Transactions on Electron Devices, 41(11), 2151–2160. 10. Bich-Ha, T. T. and Mollier, J. (1997) Noise equivalent circuit of a two-mode semiconductor laser with the contribution of both the linear and the nonlinear gain. IEEE Journal of Selected Topics in Quantum Electronics, 3(4), 304–308. 11. Mortazy, E., Ahmadi, V., and Moravvej-Farshi, M. K. (2002) An integrated equivalent circuit model for relative intensity noise and frequency noise spectrum of a multimode semiconductor laser. IEEE Journal of Quantum Electronics, 38(10), 1366–1371. 12. Gao, D. S., Kang, S. M., Bryan, R. P. et al. (1990) Modeling of quantum-well lasers for computer-aided analysis of optoelectronic integrated circuits. IEEE Journal of Quantum Electronics, 26(7), 1206–1215. 13. Tsou, B. P. C. and Pulfrey, D. L. (1997) A versatile SPICE model for quantum-well lasers. IEEE Journal of Quantum Electronics, 33(2), 246–254. 14. Ahn, D. and Chuang, S.-L. (1990) Optical gain and gain suppression of quantum-well lasers with valence band mixing. IEEE Journal of Quantum Electronics, 26(1), 13–22. 15. Lu, M. F., Deng, J. D., Juang, C., et al. (1995) Equivalent circuit model of quantum-well lasers. IEEE Journal of Quantum Electronics, 31(8), 1418–1421. 16. Gao, J., Gao, B., and Liang, C. (2003) Large signal model of quantum-well lasers for spice. Microwave and Optical Technology Letters, 39(4), 295–298.

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17. Gao, J., Gao, B., and Liang, C. (2001) A small-signal equivalent circuit model of quantum-well lasers based on three-level rate equations. Microwave and Optical Technology Letters, 30(4), 270–271. 18. Gao, J., Li, X., Flucke, J., and Boeck, G. (2004) Direct parameter-extraction method for laser diode rate equation model. Journal of Lightwave Technique, 22(6), 1604–1609. 19. Gao, J. (2008) Microwave modeling and parameter extraction method for quantum-well lasers. Journal of Lightwave Technique, 26(14), 2245–2251. 20. Nagarajan, R., Ishikawa, M., Fukushima, T., et al. (1992) High speed quantum-well lasers and carrier transport effects. IEEE Journal of Quantum Electronics, 28(10), 1990–2007. 21. Ahn, D. and Chuang, S.-L. (1990) Optical gain and gain suppression of quantum-well lasers with valence band mixing. IEEE Journal of Quantum Electronics, 26, 13–22. 22. Mcdonald, D. and O’Dowd, R. F. (1995) Comparison of two-level and three-level rate equations in the modeling of quantum-well lasers. IEEE Journal of Quantum Electronics, QE-31, 1927–1934. 23. Cartledge, J. C. and Srinivasan, R. C. (1997) Extraction of DFB laser rate equation parameters for system simulation purposes. IEEE Journal of Lightwave Technology, 15, 852–860. 24. Bruensteiner, M. and Papen, G. C. (1999) Extraction of VCSEL rate-equation parameters for low-bias system simulation. IEEE Journal of Selected Topics in Quantum Electronics, 5(3), 487–494. 25. Majewski, M. L. and Novak, D. (1991) Method for characterization of intrinsic and extrinsic components of semiconductor laser diode circuit model. IEEE Microwave Guided Wave Letter, 1(9), 246–248. 26. Lee, J., Nam, S., Lee, S. H., and Jeong, Jichai (2002) A complete small-signal equivalent circuit model of cooled butterfly-type 2.5 Gbps DFB laser modules and its application to improve high frequency characteristics. IEEE Transactions on Advanced Packaging, 25(4), 543–548. 27. Zhu, N. H., Hou, G. H., Huang, H. P., et al. (2007) Electrical and optical coupling in an electro-absorption modulator integrated with a DFB laser. IEEE Journal of Quantum Electronics, 43(7), 535–544. 28. Minoglou, K., Kyriakis-Bitzaros, E. D., Syvridis, D., and Halkias, G. (2004) A compact nonlinear equivalent circuit model and parameter extraction method for packaged high-speed VCSELs. IEEE Journal of Lightwave Technology, 22(12), 2823–2827. 29. Gao, J., Gao, B., and Liang, C. (2002) An approach to determining parasitic elements for laser diodes. Microwave and Optical Technology Letters, 34(3), 191–193. 30. Shimizu, J., Yamada, H., Murata, S., Tomita, A., et al. (1991) Optical-confinement-factor dependencies of the K factor, differential gain, and nonlinear gain coefficient for 1.55 lm InGaAs/InGaAsP MQW and strained-MQW lasers. IEEE Photo Technology Letter, 3(9), 773–776. 31. Gao, J. and Li, X. (2007) A semianalytical method to determine parasitic elements of quantum-well laser. Journal of Lightwave Technique, 25(10), 3078–3081.

4 Microwave Modeling Techniques of Photodiodes 4.1 Introduction The semiconductor laser diodes convert an electrical signal into light and launch it into the optical fiber serving as a communication channel. At the end of an optical transmission line (fiber), there must be a receiving device, which interprets the information contained in the optical signal carrier by the fiber. The first element of this receiver is the photodetector. The photodetector senses the luminescent power falling upon it and coverts the variation of this optical power into a correspondingly varying electronic current. Of the semiconductor-based photodetectors, the photodiode is used almost exclusively for fiber-optic systems because of its small size, suitable material, high sensitivity, and fast response time. Thus, the function of a photodiode is just the opposite: to convert light into electricity through the photoelectric effect. Thus, the principle of operation of a photodiode (PD) can be explained simply as operating in a manner exactly the opposite to the way a laser works. Conventionally, photodetectors based on different absorption materials are used for a corresponding spectral range. For instance, in the visible wavelength region, Si-based photodetectors are preferred, while in the ultraviolet (UV) wavelengths, the III–V nitrides are the promising materials. It is also well known that the GaAs has superior performance for detection in the 600–900 nm wavelength range [1, 2, 3, 4, 5, 6, 7]. Proper design of a demodulation system for optical signals requires specially designed photodetectors that are efficient and fast. The major requirements imposed on photodetectors and detection systems for optical communication applications thus include:

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1. A large response to the incident optical signal 2. Sufficient instantaneous bandwidth to accommodate the information bandwidth of the incoming signal 3. A minimum of noise added by the demodulation process. Additionally, the photodetectors would be small, electronically compatible with integrated circuits, reliable, and inexpensive. These requirements are best met by photodetectors made of semiconductor materials. As we know, the computer simulations of optical fiber systems are useful in predicting system behavior at the design stage [8, 9, 10]. Both the model and the parameters must be sufficiently accurate if the simulation results are to be useful. For enhancing the performance, optoelectronic integrated circuits (OEICs) must be accurately designed and device characteristics improved. Circuit simulation of electronic circuits, laser diodes, optical fibers, and photodetectors must be conducted to ensure that optical transmission characteristics are taken into account. In Chapters 2 and 3, basic physical principles, and modeling and parameters extraction techniques have been introduced for semiconductor laser diodes. In this chapter, we will introduce the basic physical principles, figures of merits, and microwave modeling techniques for the commonly used photodiodes. The p-i-n photodiode, avalanche photodiode (APD), and metal–semiconductor–metal (MSM) photodiode are used as examples.

4.2 Physical Principles The light carried by a fiber is converted to an electrical signal at the receiver end by means of a photodiode. Various properties of photodiodes affect the sensitivity and speed of the front end. Actually, the reverse-biased p–n junction is the simplest photodiode. Figure 4.1 shows the p–n junction photodiode with an external load and Figure 4.2 shows the generation of an electron–hole pair by means of a photon. The incident light must penetrate into the depletion region of the p and n material where the free carriers have been removed. When the incident light energy is greater or equal to the bandgap energy of the semiconductor material ðEg Þ, the photons can give up their energy and excite the electrons from the valence band to the conduction band, leaving holes in their place in the valence band (see Figure 4.2). If the incident light energy is hc=l (where h is Plank’s constant, c is optical velocity, and l is optical wavelength), the maximum optical wavelength requires lmax ¼

hc Eg

ð4:1Þ

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Figure 4.1 Reverse-biased p–n junction photodiode with an external load.

Figure 4.2 Generation of an electron–hole pair by means of a photon.

Therefore, the incident light wavelength must fall below a threshold lmax to stimulate carrier generation. Table 4.1 summarizes the bandgap energies and operation wavelength at 300 K for representative photodiode materials. It can be found that silicon has 1.1 micrometers (Eg ¼ 1:14 eV) and is a suitable detector material for the short-wavelength but not for the long-wavelength sources. The generated electron–hole pairs will be separated by the electronic field existing across the depletion region and swept to the opposite sides of the depletion region. If an external circuit is connected between p and n regions, electrons will flow away from the n region and holes will flow away from the p region toward the opposite electrodes. These electrons and holes generating a current flow in a semiconductor are called the carriers. Figure 4.3 shows the photocurrent versus reverse bias voltage for different

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Table 4.1 Bandgap energies and operation wavelength at 300 K for representative photodiode materials. Materials

Bandgap energies eV

Short wavelengths less than 1.31 mm

Long wavelengths 1.31–1.55 mm

1.43 1.35 1.15 1.15 1.14 0.75 0.73 0.67 0.35

H H H H H H H H H

H H H H

GaAs InP GaAs0.88Sb0.12 In0.14GaAs0.86 Si In0.53GaAs0.47 GaSb Ge InAs

Figure 4.3

Photocurrent versus reverse-bias voltage for different incident light power.

incident light power, and it can be found that the photocurrent increases with the increase of the incident light power.

4.3 Figures of Merit The most important figures of merit for common photodiodes are as follows: . . .

Responsivity Quantum efficiency Absorption coefficient

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Dark current Rise time and bandwidth Noise currents.

We will introduce the definitions and expressions for the basic concepts mentioned above that are common to all photodetectors and are needed later in this chapter.

4.3.1 Responsivity The responsivity of the photodiode is a measure of the sensitivity to light; in other words, this characteristic shows how efficiently a photodiode does its main job – converting light into an electrical signal (see Figure 4.4). It is defined as the ratio of the photocurrent Ip to the incident light power Pin at a given wavelength: R¼

Figure 4.4

Ip Pin

ð4:2Þ

Basic concept of photocurrent.

where R is called ‘responsivity.’ Typical values of R range from 0.5 A/W to 1.0 A/W. For example, some photodiodes exhibit a responsivity of 0.8 A/W; that is when the photodiode is illuminated by 1mW of light, a current of 1 mA will be produced. Since the value of R is provided by photodiode manufacturers, the output photocurrent with the given light-input power can be calculated. Responsivity varies with the wavelength of the incident light (see Figure 4.5) as well as applied reverse bias and temperature. This is due to a decrease or increase of the bandgap, because of an increase or decrease in the temperature, respectively. This results in an apparent shift of the responsivity curve toward higher wavelengths. Figure 4.5 shows the typical spectral dependence of the response of photon detectors, where it can be found that responsivity increases with increasing wavelength until the cutoff wavelength is reached. At that point it drops rapidly to zero. The photodiode

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should ideally be operated in a spectral region that is not far below the highest possible value, because this leads to the lowest possible diction noise and thus a high signalto-noise ratio (SNR) and high sensitivity.

Figure 4.5

4.3.2

Typical spectral responsivity of the photodiode.

Quantum Efficiency

Quantum efficiency of the photodiode is also a measure of the sensitivity to light and can be expressed as the ratio of the electron generation rate and photon incidence rate: Z¼

Ip =q Ip =q ¼ l Pin =hg Pin =hc

ð4:3Þ

where Z is the quantum efficiency and l and g are the optical wavelength and frequency, respectively. Substituting Equation (4.3) into (4.2), we have R¼

Zq Zl hg 1:24

ð4:4Þ

The responsivity of a photodetector is in proportion to quantum efficiency and optical wavelength. The relationship between responsivity, quantum efficiency, and optical wavelength is shown in Figure 4.5 for a GaAs-based photodiode. The

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device exhibits a quantum efficiency higher than 90 % in the 400–750 nm wavelength range.

4.3.3 Absorption Coefficient The penetration of the light down into the depletion region of the photodiode is governed by the absorption properties of the material. The quantum efficiency Z depends on the absorption coefficient of the material and the thickness of the absorbing material. Assuming no reflection of light from the surface of the photodetection material, if the photon power at the surface is Pin , then the electron–hole pair generation rate at a depth W from the illuminated side of the semiconductor layer (the depletion region in a junction-based device, as shown in Figure 4.6) is given by Po ¼ Pin eaW

ð4:5Þ

Figure 4.6 Variation of optical power inside the photodiode.

where a is the absorption coefficient and is a strong function of wavelength and varies greatly depending on the material. The absorbed power in the depletion region can be written as Pa ¼ Pin ð1eaW Þ

ð4:6Þ

Assuming each absorbed photon creates an electron–hole pair, the quantum efficiency is given by Z¼

Pa ¼ 1eaW Pin

ð4:7Þ

4.3.4 Dark Current The dark current is the leakage current that flows when the photodiode is in the absence of any optical signal and originates from thermally generated electron–hole pairs,

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while a reverse voltage is applied across the junction. The dark current is a result of four major effects, including diffusion current, generation recombination, surface current, and avalanche current. The current–voltage characteristics of a photodiode with no incident light is similar in nature to the normal p–n junction. When the photodiode is forward biased, there is an exponential increase in the current. When a reverse bias is applied, a small reverse saturation current appears. The dark current can be expressed as follows: qV 1 ð4:8Þ Id ¼ Is exp nkT where Id is the photodiode dark current, Is is the reverse saturation current, q is the electron charge, V is the applied bias voltage, k is the Boltzmann constant, and T is the absolute temperature. For a qualified photodetector, the dark current should be negligible (Id < 10 nA). The dark current of a GaAs p-i-n photodetector is usually too low to have any significant influence on receiver sensitivity. The photodiode device produces a total current that is a sum of the photocurrent Ip and a dark current Id , and can be expressed by

qV It ¼ Is exp 1 Ip nkT

ð4:9Þ

where Ip is the photocurrent and It is the total current across the junction. Figure 4.7 shows the characteristic I–V curves of the photodiode. It can be found that the generation of electron–hole pairs (photocurrent) in a p–n junction shifts the reverse ‘breakdown’ characteristic toward the origin when illuminating the photodiode with

Figure 4.7

Characteristic I–V curves of the photodiode.

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optical radiation. As the applied reverse bias increases, there is a sharp increase in the photodiode current. The applied reverse bias at this point is referred to as breakdown voltage (also known as maximum reverse voltage). The photodiode should be operated below the maximum applied reverse bias.

4.3.5 Rise Time and Bandwidth The rise time tr is a time constant (in seconds) that expresses the time required for a photodetector to go from 10 % to 90 % of its final response state, as shown in Figure 4.8. Clearly, tr will depend on the time taken by electrons and holes to travel to the electrical contacts. Photodiodes have a photoabsorption layer that converts input light into carriers such as electrons and holes. For an ultra-wideband response, the carrier transit time in the photoabsorption layer should be much shorter than the required system response.

Figure 4.8 Optical response of the photodiode.

The rise time tr also depends on the response time of the electrical circuit used to process the photocurrent, that is the RC time constant tRC of the circuit. The RC time constant is the capacitance C of the photodiode junction multiplied by the load resistance R (usually a small resistor placed in parallel with the detector or the smallsignal resistance of the photodetector device itself), and can be represented as RC. The corresponding 3 dB electrical bandwidth, which is limited by the carrier transit time and RC time constant of the circuit, can be expressed by BW3dB ¼

1 2pðtRC þ tr Þ

ð4:10Þ

For lightwave systems operating at bit rates of 10 Gb/s or more, the sum of rise time tr and RC time constant tRC should be less than 10 ps.

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4.3.6

Noise Currents

In high-speed optical fiber communication systems, the photodiode is generally required to detect very weak optical signals. It is necessary that noises in photodiodes should be kept as low as possible. The shot noise is the major noise source that is related to the statistical fluctuation in both the photocurrent and the dark current. These two noise sources are characterized by their mean quadratic value in a bandwidth Df centered on the frequency f, and can be given by the following expressions: 2 id ¼ 2qId Df

ð4:11Þ

D E ip2 ¼ 2qIp Df

ð4:12Þ

where hid2 i and hip2 i are the mean-square dark noise current and photodiode noise current, respectively. The root mean square (RMS) of total noise current hit i can be calculated by hit i ¼

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2qðIp þ Id ÞDf

ð4:13Þ

4.4 Microwave Modeling Techniques State-of-the-art computer-aided design (CAD) methods for active optoelectronic integrated circuits rely heavily on models of real devices. Modeling of photodetectors is very important for a careful analysis of their performance and design issues, since they are the key components of the photoreceivers. Figure 4.9 shows the commonly used modeling methods for photodiodes. There are three kinds of modeling methods for various photodiodes, that is the physics-based model (see ! 1 in Figure 4.9), the equivalent circuit model (see ! 2 in Figure 4.9), and the semi-analytical model (see ! 3 in Figure 4.9). The physics-based models are based on the behavior of photo-generated carriers and electric fields in photodiodes, and are obtained by numerically solving basic semiconductor device physical equations. The physical simulation of the photodiode device is based on the Poisson equation, current continuity equation, and rate equations for charged traps in two or three dimensions. This kind of physical model accounts for process-related parameters (geometry, recess depth, material parameters, doping profile, and so on), surface depletion effects, substrate conduction, contact resistivities, and avalanche breakdown. The difficulty in applying physical device models to microwave CAD simulators is the large execution times required. The physical models solve the semiconductor device equations using some form of numerical technique such as finite differences or finite elements. Due to lengthy execution times,

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Figure 4.9 Modeling methods for photodiodes.

however, the operation of the models is usually limited to DC solutions and parasitic elements cannot be taken into account. Equivalent-circuit-based models are commonly used to investigate large-signal and small-signal device performance. However, these models require extensive characterization of the device after fabrication, as well as some knowledge of process variation statistics. For the well-proven physical model used here, there is no need for an extensive series of measurements since all the data are provided from the process parameters and physical structure of the device. Equivalent circuit models also suffer from problems associated with curve-fitting errors and discontinuous or inaccurate high-order derivatives in current and voltage expressions, leading to inaccurate predictions of intermodulation distortion (IMD). Equivalent circuit models of an active device (such as laser, photodiode, and so on) are the backbone of the OEIC CAD simulator software. All commercially available software includes one or more of each type of device model. The modeling concept is that the complex active device is represented using the basic resistances, capacitances, and control sources. The difference in the various models is the expression used to characterize the drain current generator. The semi-analytical models are based on the combination of physical equations and the equivalent circuit and overcome the drawbacks of the physics-based models and equivalent-circuit-based models, while retaining their advantages. The circuit simulators are used to solve the physical equations and parasitic elements can be taken into account. Table 4.2 gives a comparison of the three kinds of microwave modeling techniques for photodiodes.

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Table 4.2 Comparison of microwave modeling techniques for photodiodes. Parameters

Physical-based models

Equivalent circuit models

Semi-analytical models

Speed Accuracy Physical meaning

Slow High Excellent

Fast Medium Medium

Fast High Good

The most commonly used photodiodes are the p-i-n photodiode (PIN PD), avalanche photodiode (APD), and metal–semiconductor–metal photodetector (MSM PD). The basic mechanism and microwave modeling will be introduced in more detail as follows.

4.4.1

PIN PD

4.4.1.1 Basic Concept The bandwidth of p–n photodiodes is limited by the presence of a diffusive component in the photocurrent. Electron–hole pairs created outside the depletion region cause a slow response component because these carriers propagate to the electrodes very slowly by diffusion. By increasing the depletion region width and decreasing the widths of the p and n regions, the bandwidth can be improved. This is the major reason for adopting the PIN PDs, shown schematically in Figure 4.10 [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]. The device structure consists of p and n regions separated by a very light n-doped intrinsic region. This architecture effectively increases the depletion width, which results in a higher collection efficiency since incoming photons are more likely to generate collected electron–hole pairs. It also lowers the junction capacitance and increases the transit time. Although less junction capacitance reduces the RC time constant of the device, however, the longer transit time limits the overall time response of the device. Therefore, the width W of the intrinsic layer controls the trade-off between efficiency and speed of the photodiode.

Figure 4.10 Reverse-biased PIN PD with an external load.

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Because of its intrinsic nature, the middle intrinsic layer (I region) offers a high resistance, and most of the voltage drop occurs across it. As a result, a large electric field exists in the middle intrinsic region. The double heterostructure design can be used to improve the performance of PIN PD [16]. The heterojunction photodiode involves combining different semiconductor materials with different bandgaps in order to optimize a particular feature; normally the semiconductor material of the intrinsic layer is different from the p-type and n-type layers. The incident light is absorbed only in the middle intrinsic layer, while the absorption coefficients are near zero in the p-type and n-type layers. The schematic cross-section of a typical double heterojunction PIN PD is shown in Figure 4.11 (InGaAs is used for the middle intrinsic layer and InP for the p-type and n-type layers).

Figure 4.11 Schematic cross-section of a double heterojunction InP/InGaAs PIN PD.

4.4.1.2 Equivalent Circuit Model The rate equations for electrons and holes in the absorption region are written as follows [10, 12]: dN N Pin N þZ ¼ dt tnt hg tnr

ð4:14Þ

dP P Pin P ¼ þZ dt tpt hg tpr

ð4:15Þ

where N and P are the electron and hole numbers, respectively. The quantum efficiency is Z ¼ ð1RÞð1eaW Þ, where R is the facet reflectivity, a is the absorption coefficient, W is the depletion region width, Pin is the power of incident light, and hg

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is the photon energy; also tnr and tpr are the recombination lifetimes of the electron and hole in the depletion region, respectively, while tnt and tpt are the electron and hole transit time through the absorption region, which can be expressed as follows: tnt ¼ W=nn

ð4:16Þ

tpt ¼ W=np

ð4:17Þ

where nn and np are the electron and the hole drift velocities, respectively. For different materials, the dependences of electron and hole drift velocities on the electric field are different. The carriers are separated by the electric field, assuming that they reach immediate thermal equilibrium; the velocities of the electron and hole can be calculated by using the following empirical equations for III–V compound semiconductor materials [11]: vn ðEÞ ¼ ðmn E þ bVnL En Þ=ð1 þ bEn Þ

ð4:18Þ

vp ðEÞ ¼ VpL tanhðmp E=Vpl Þ

ð4:19Þ

with E ¼ ðV þ Vbi Þ=W where E is the electric field in the middle intrinsic layer, V is the reverse-biased voltage, Vbi is the built-in potential, mn and mp are the electron and hole mobilities, respectively, VnL and Vpl are the high field velocities of the electron and hole, respectively, and b and n are the fitting factors. Figure 4.12 shows the typical electron and hole drift velocities versus electric field. It can be found that the electron and hole drift velocities will remain invariant when the electric field is higher than a certain threshold electric field.

8

3

6 Electron

2

4 Hole

1 0

0

20

40

2

60

80

Hole velocity (106 cm/s)

Electron velocity (107cm/s)

4

0 100

E (kV/cm)

Figure 4.12 The electron and hole drift velocities versus electric field.

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The total current through the PIN PD can be expressed as follows: Ip ¼ Id þ

q ðNvn þ Pvp Þ W

ð4:20Þ

Substituting Equations (4.14) and (4.15) into (4.20), the total current can be expressed as [12] Ip ¼ gm Pin þ Id

ð4:21Þ

with 1

0 gm ¼

qZo B B nn hg @W

1 1 jo þ tn

þ

t0n ¼

tnt tnr tnt þ tnr

t0p ¼

tpt tpr tpt þ tpr

np W

C C 1A jo þ tp 1

Therefore, the photocurrent can be represented by using a linear controlled current source with a complex transconductance or by using a noiseless two-port network with S parameters as follows [12]: 2 3 1 0 5 S ¼ 4 2gm ð4:22Þ 1 Yo Figures 4.13 and 4.14 show the small-signal and noise-equivalent circuit models and the large-signal equivalent circuit model, respectively, where Cj is the junction capacitance of the device, gd is the conductance under the dark condition, hitPIN i is the total shot noise as described in Equation (4.13), and the noise source hiR2 S i represents the noisy behavior of the access resistance RS and is simply given by D E 4 KT iR2 s ¼ Df Rs

ð4:23Þ

where q is the electronic charge, k is Boltzmann’s constant, and T is absolute temperature.

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Figure 4.13 Small-signal and noise-equivalent circuit models.

Figure 4.14 Large-signal equivalent circuit model of a PIN PD.

These models can be used to simulate the small-signal response, large-signal response, and noise performance using a circuit simulator. Figure 4.15 shows the input optical power and output electric current of an InP/InGaAs PIN PD, where it can be found that the magnitude of the output electric current is 0.77 mA and the corresponding quantum coefficient is 73 %. The model parameters are summarized in Table 4.3 [11, 12] and the input optical power can be expressed as follows: Pin ¼ Po ð1 þ m sin 2pf Þ

Output electric current

2.0

2.0

1.5

1.5

1.0

1.0

0.5

0.5

0.0 0.0

0.2

0.4

0.6

0.8

1.0

0.0

Output electric current (mA)

Input optical power (mW)

Input optical power

ð4:24Þ

Time (ns)

Figure 4.15 Input optical power and output electric current of an InP/InGaAs PIN PD.

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Table 4.3 PIN PD model parameters. Parameters

Description

Values

W (mm) tnr (ps) tpr (ps) mn ðcm2 =VSÞ mp ðcm2 =VSÞ VnL (cm=S) Vpl (cm=S) b n ao (mm1) RS (O) CS (pF) Po (dBm) f (GHz) m RL (O)

Absorption layer width Electron recombination lifetime Hole recombination lifetime Electron mobility Hole mobility Electron high field velocity Hole high field velocity Fitting factor Fitting factor Absorption coefficient Access resistance Parasitic capacitance Input optical power Signal frequency Modulation coefficient Load resistance

1 50 50 10 500 420 6 106 4:8 106 7:4 1010 2.5 1 30 0.2 0 5 0.5 50

Table 4.4 gives a comparison of simulated and numerical calculated output electric current harmonics for the InP/InGaAs PIN PD, where good agreement is obtained to verify the accuracy of the model. Table 4.4 Comparison of simulated and numerical calculated output electric current harmonics for an InP/InGaAs PIN PD. Input optical power Output electric power

Fundamental Second harmonic Third harmonic

Simulated Calculated Simulated Calculated Simulated Calculated

0

2.5

5.0

7.5

10.0

24.5 26.0 61.0 64.0 64.0 77.0

29.0 32.0 66.0 78.0 69.0 100.0

35.0 37.0 72.0 92.0 75.0 < 100.0

40.0 42.0 76.0 < 100 80.0 < 100

44.5 47.0 81.0 < 100 84.0 < 100

4.4.2 APD For high-bit-rate long-haul fiber-optic systems, the avalanche photodiode (APD) is usually the photodetector of choice owing to its internal gain, which provides higher sensitivity than PIN photodiodes [22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33]. It is important to achieve high sensitivity in order to maximize the separation between optical repeaters and, thus, reduce the overall system cost. APDs can achieve

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Optoelectronic Integrated Circuit Design and Device Modeling

sensitivity of 5–10 dB better than PINs, provided that the multiplication noise is low and the gain–bandwidth product of the APD is sufficiently high. The multiplication region of an APD plays a critical role in determining the gain, the multiplication noise, and the gain–bandwidth product. As previously mentioned, operation of the PIN PD is based on the generation of one electron–hole pair for each photon entering the lattice. The responsivity R of PIN PDs is limited by Equation (4.4) and takes its maximum value R ¼ q=ðhgÞ for Z ¼ 1. To improve the responsivity R of PDs, the APDs, which are based on the avalanche effect (the generated electrons and holes carry so much energy that they can stimulate other electrons and holes), become another good choice for weak optical power detection. Figure 4.16 shows the APD structure together with the variation of electric field in various layers. Compared with the PIN PD, the p-type and n-type regions are all heavily doped in the APD structure. APDs are p-i-n diode structures that are operated at large reverse-bias voltages. Under reverse bias, a high electric field exists in the p-type layer sandwiched between i-type and n þ -type layers. This layer is referred to as the multiplication layer, since secondary electron–hole pairs are generated here through impact ionization. The i layer still acts as the depletion region in which most of the incident photons are absorbed and primary electron–hole pairs are generated. Signal multiplication is obtained when photogenerated carriers gain enough energy from the electric field to generate secondary carriers through impact ionization. These secondary carriers are also accelerated by the electric field and generate other electron–hole pairs. The output current is the primary photocurrent multiplied by the avalanche current.

Figure 4.16 APD structure and electric field distribution.

The multiplication factor is defined as the ratio of the output current with multiplication current IM and output current without multiplication IP :

Microwave Modeling Techniques of Photodiodes

M¼

131

IM IP

ð4:25Þ

Figure 4.17 shows the schematic representation of ionization layer [22], the continuity equations in the ionization layer are as follows:

Figure 4.17 Schematic representation of the ionization layer.

1 qInm qInm þ ¼ aInm þ bIpm dx un dt

ð4:26Þ

1 qIpm qIpm ¼ aInm þ bIpm up dt dx

ð4:27Þ

where a and b are the electron and hole ionization rates, respectively, and Inm and Ipm are the multiplication electron and hole currents, respectively. Under the steady-state condition, the time rates of changes of multiplication electron and hole currents are zero (that is qInm =dt ¼ 0 and qIpm =dt ¼ 0), and thus the continuity equations (4.26) and (4.27) become qInm aInm bIpm ¼ 0 dx

qIpm aInm bIpm ¼ 0 dx

ð4:28Þ

ð4:29Þ

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Optoelectronic Integrated Circuit Design and Device Modeling

Substituting boundary conditions In ð0Þ ¼ Ins and Ip ðlÞ ¼ Ips into Equations (4.28) and (4.30), we have eðabÞx 1 abeðabÞl

ð4:30Þ

eðabÞl eðabÞx abeðabÞl

ð4:31Þ

Inm ðxÞ ¼ Ins þ ðaIns þ bIps Þ

Ipm ðxÞ ¼ Ips þ ðaIns þ bIps Þ

Therefore, the multiplication factor can be obtained as follows: 8 ðaIns þ bIps Þ eðabÞl 1 > > 1þ ; < Inm ðxÞ þ Ipm ðxÞ Ins þ Ips abeðabÞl ¼ M¼ > Ins þ Ips > : 1 ; 1al

a„b

ð4:32Þ

a¼b

Because of the small difference between the hole and electron ionization coefficients in III–V semiconductors, conventional InGaAs APDs have a limited gain– bandwidth product and a poor noise figure. Si-based APDs are well known for a low excess noise and a high gain–bandwidth product due to the large difference between the hole and electron ionization coefficients. However, the quantum efficiency of Si APDs is negligible at 1.3–1.55 mm, making them unusable for fiber communication systems. The requirements for high-performance APDs include high quantum efficiency, high speed, low dark current, a high gain–bandwidth product, and low multiplication noise. Resonant-cavity separate absorption and multiplication (SAM) APDs have been shown to achieve all of these properties [27, 29]. The SAM structure has separate high-field multiplication and absorption regions. Another benefit of the SAM APD structure is that only a single type of carrier is injected into the multiplication region, which is a well-known requirement for reducing the multiplication noise that arises from the stochastic nature of the multiplication process. The schematic cross-section of the InP/InGaAs-based SAM APD is shown in Figure 4.18. Light is coupled into the APD through the InP layer to the absorption region, which has a lower bandgap than that of InP. The i layer still acts as the depletion region in which most of the incident photons are absorbed and primary electron–hole pairs are generated. The electron–hole pairs generated in this absorption region are first separated by the high field that exists here and the separated carriers are then transported by the field to the p þ n junction where avalanche multiplication of carriers takes place. By separating the absorption and multiplication regions the leakage current found in a reverse-biased junction of narrow gap materials is greatly reduced. Secondary electron–hole pairs are created when accelerated carriers collide with the lattice of the semiconductor, thereby setting free valence electrons.

Microwave Modeling Techniques of Photodiodes

133

Figure 4.18 Schematic cross-section of an InP/InGaAs SAM APD.

Figure 4.19 shows the one-dimensional model of an SAM-APD [26], where Wa is the thickness of the absorption layer, Wm is the thickness of the multiplication layer, and DWm is the effective multiplication plane (all the secondary charges are generated at this plane). The total photocurrent can be written as Ip ¼

q ðNðtÞvn þ PðtÞvp þ Ns ðtÞvn þ Ps ðtÞvp Þ Wd

with Wd ¼ Wa þ Wm

Figure 4.19 One-dimensional model of an SAM-APD.

ð4:33Þ

134

Optoelectronic Integrated Circuit Design and Device Modeling

where NðtÞ, PðtÞ, Ns ðtÞ, and Ps ðtÞ are the total number of uncollected photogenerated primary electrons, primary holes, secondary electrons, and secondary holes in the depletion region, respectively. The corresponding equivalent circuit model of APD is similar to the PIN PDs model (see Figure 4.20). The major difference between them is the total noise current hit i. In APDs, the secondary electron–hole pairs are generated through the process of impact ionization. Since such pairs are generated at random times, an additional contribution is added to the shot noise associated with the generation of primary electron–hole pairs. The root mean square (RMS) of the total noise current hit i can be calculated by

Figure 4.20 Equivalent circuit model of an APD.

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ APD it ¼ M FðMÞ itPIN

ð4:34Þ

PIN qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ¼ 2qðIp þ Id ÞDf it

ð4:35Þ

where the excess noise factor of the APD and is given by

1 FðMÞ ¼ kM þ 1 ð1kÞ M

ð4:36Þ

4.4.2.1 MSM PD Metal–semiconductor–metal photodetectors (MSM PDs) have attracted a great deal of attention for optoelectronic integrated circuits, because of their high operating speed and ultra-low intrinsic capacitance and compatibility with high-performance field effect transistor technology [34, 35, 36, 37, 38, 39, 40, 41, 42, 43]. These features are essential for building high-speed, high-sensitivity, and ultra-wide bandwidth optoelectronic integrated circuit (OEIC) receivers, which include monolithically integrated MSM PD and MESFET (HEMT) preamplifiers. For very high-speed applications, the MSM PD has an advantage over the PIN PD since the real capacitance of an MSM PD is lower than that of a comparably sized p-i-n

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135

photodiode due to its interdigitated electrode geometry. As a result, very large bandwidths can be achieved with MSM PDs without resorting to the use of very small lateral detector dimensions. The MSM PDs have inherent ultra-low capacitance compared to conventional PIN diodes, which have a capacitance that is typically 10–20 times higher than that of MSM PDs. Furthermore, the low capacitance per unit area allows use of a detector with a relatively large area, which is essential for the alignment tolerance in the optoelectronic interconnections. Most of the beneficial properties of the MSM PD stem from its lateral planar geometry. The planner MSM PD is illustrated schematically in Figure 4.21. It consists of numbers of semiconductor layers and a pair of interdigitated electrodes formed on the top surface of a semiconductor layer [35, 36]. The interdigitated electrodes, connection patterns, and bond pads were formed by standard lift-off techniques. The cap layer is used to increase the surface Schottky barrier height. Thus the dark conduction current can be reduced drastically. The absorption layer thickness is chosen as a compromise between responsitivity and bandwidth. The buffer layer reduces the propagation of defects from the substrate to the absorption layer.

Figure 4.21 Schematic of a conventional MSM PD.

Light incident on the top surface of the MSM structure is absorbed within the underlying semiconductor, resulting in the creation of electron–hole pairs. The application of a bias to the metallic fingers creates an electric field within the underlying semiconductor, which acts to sweep the photogenerated carriers out of the device. How fast these carriers are collected and how many of them actually survive to the contacts within a particular collection time determine the speed and the responsivity, respectively, of the detector. Carriers generated deep within the semiconductor must traverse a greater distance before they are collected at the contacts compared to those generated near the surface. Figure 4.22 shows the schematic representation of current flow paths, which correspond to both hole and electron transport paths in opposite directions.

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Optoelectronic Integrated Circuit Design and Device Modeling

Figure 4.22 Schematic representation of current flow paths, which correspond to both hole and electron transport paths in opposite directions.

The response speed of the MSM PD is largely limited by the transit time of the photogenerated carriers and thus the interelectrode spacing should be small. Scaling down the distance between the interdigital contacts and overall dimensions of the MSM detector has been the most common way to increase the detector speed of response. The MSM photodetector consists essentially of two Schottky contacts, connected back-to-back. When a bias is applied, one of the Schottky contacts is forward- and the other is reverse-biased. Only the reverse current–voltage (I–V) characteristics of these Schottky contacts can be measured. The voltage increases until the forward-biased contact meets the reverse-biased contact at the depletion region. In this case the reach-through voltage VRT is defined and the total width is W. The voltage increases further and eventually the energy band of the forward-biased contact become flat. In this case the biased voltage is named flat-band voltage VFB and is defined as [35, 36] pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð4:37Þ VRT ¼ VFB 2 VFB VD VFB ¼ q

NL2 2x

ð4:38Þ

where VD is Schottky barrier height, q is electronic charge, L is electrode spacing, N is active region carrier density, and x is the permittivity of the semiconductor. 4.4.2.2 Semi-Analytical Model To understand the behavior of photo-generated carriers and electric fields in MSM PDs, Poisson’s equation, the current-continuity equations, and a rate equation for charged traps are numerically solved in two dimensions, such as finite differences or finite elements. In order to apply physical device models to microwave CAD

Microwave Modeling Techniques of Photodiodes

137

simulators, the semi-analytical model based on a combination of the physical equations and equivalent circuit modeling techniques is a good choice. The semi-analytical model for MSM PDs in the time domain consists of a conductance in parallel with a capacitance (as shown in Figure 4.23). The conductance, which is dependent on the incident optical power, can be expressed as follows [37]:

Figure 4.23 Semi-analytical model for MSM PDs.

gðtÞ ¼

qaFg ½nðtÞvn ðaFg Þ þ pðtÞvp ðaFg Þ þ gd Vg2

ð4:39Þ

where Vg is the gap voltage, Fg is the average electronic field in the gap (Fg ¼ Vg =Lg ), Lg is the gap length between the positive electrode (anode) and grounded electrode (cathode), and n and p are the total numbers of electrons and holes, respectively, given by (in the finite difference form) Dt PðtDtÞ Dt ð4:40Þ þ nðtÞ ¼ nðtDtÞexp tn ðtDtÞ hg pðtÞ ¼ pðtDtÞexp

Dt PðtDtÞ Dt þ tp ðtDtÞ hg

ð4:41Þ

where Dt is the time interval of circuit simulation, PðtDtÞ is the optical power incident upon the substrate, and tn and tp are the electron and hole transit times. Carrier velocity dependence on the local electric field F is expressed as vn ðFÞ ¼

mn F þ usn ðF=Fth Þ4

vp ðFÞ ¼

1 þ ðF=Fth Þ4 mp F 1 þ ðmp F=usp Þ

ð4:42Þ

ð4:43Þ

where mn and mp are the electron and hole mobilities, respectively, and usn and usp are the electron and hole saturation drift velocities, respectively.

138

Optoelectronic Integrated Circuit Design and Device Modeling

The formation of the space-charge capacitance is as follows: CðtÞ ¼

Cgc ðtÞCga ðtÞ þ Cdark Cgc ðtÞ þ Cga ðtÞ

ð4:44Þ

where the first term represents the increase in capacitance due to the formation of space-charge regions and the second term is the gap capacitance under dark conditions. Similar to the capacitances in the metal–semiconductor junction, Cgc ðtÞ and Cga ðtÞ can be calculated as follows: Cga ðtÞ ¼ bAa

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qnðttd Þxs =Vg ðtÞ

ð4:45Þ

Cgc ðtÞ ¼ bAc

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ qpðttd Þxs =Vg ðtÞ

ð4:46Þ

where Aa and Ac are the anode and cathode areas, n(t) and p(t) are the average electron and hole concentrations, td is the time required for the space-charge region to form, and b is a fitting parameter.

4.4.2.3 Empirical Equivalent Circuit Model As previously mentioned, the empirical equivalent circuit model is based on the device port performance (that is DC, small-signal, and large-signal responses). This kind of model is suitable to be implemented into the circuit simulator to perform various analyses of MSM PDs. In this section, we will introduce the experience formulas of DC characteristics and intrinsic capacitance–voltage characteristics. The corresponding model parameters are obtained from DC and C–V measurement data by using the curve-fitting technique. Simulated results are compared with experimentally obtained data, and excellent agreement is obtained consistently on MSM PDs of different sizes [40]. Figure 4.24(a) shows the DC characteristics of an MSM PD with a 2 mm finger width and spacing on a 50 mm by 50 mm InGaAs active area (that is a 2 2 MSM PD) [3]. Figure 4.24(b) shows the DC characteristics of MSM PDs with a 3 mm finger width and spacing on a 100 mm by 100 mm GaAs active area (that is a 3 3 MSM PD) [4]. At the voltage below the reach-through voltage VRT , the MSM PD is not fully depleted and the potential barrier at the positive contact limits the current so that the photocurrent is very small. When the voltage bias is in excess of the reach-through voltage VRT but below the flatband voltage VFB , the photocurrent increases quickly since the potential barrier at the positive contact disappears. At a voltage in excess of the flatband voltage, the active region below the electrodes is completely depleted and the electronic field

Microwave Modeling Techniques of Photodiodes

139

everywhere is negative. In this case the velocity of carriers attains the saturation and the photocurrent is nearly constant. Measured

Modeled

Photocurrent (mA)

2.0 1.5

2.0mW 1.5mW

1.0 1.0mW 0.5 0.0

0.6mW

0

2

4

6

8

10

Bias voltage (V) (a) 2 × 2 MSM PD Measured

Modeled

Photocurrent (uA)

8 30µW

6

20µW

4

2

0

10µW

0

2

4

6

8

10

12

14

16

18

Bias voltage (V) (b) 3 × 3 MSM PD

Figure 4.24 DC performance of different-sized MSM PDs: (a) 2 2 MSM PD; (b) 3 3 MSM PD.

The I–V characteristic shape of an MSM PD is similar to that of a GaAs MESFET [41], so the following DC experiential formula can be used: ( 0; when V < VRT ð4:47Þ Isp ¼ bðPin =Po Þ½1 þ lðVVRT Þtanh½aðVVRT Þ; when V VRT where Isp is the photocurrent, Pin is the input optical power, Po is the normalized constant, and V is the bias voltage. The meaning of the model parameters are discussed in the following.

Optoelectronic Integrated Circuit Design and Device Modeling

140

In the case of the voltage in excess of the flatband voltage (that is V VFB ), the photocurrent can be approximately estimated by the following due to tanh½aðVVRT Þ 1: Isp bPin =Po

ð4:48Þ

As a result we define b as the saturation responsitivity parameter and its unit is A/W. After the active region is depleted and the carriers attain the saturation velocity, the DC characteristic is expected to be independent of the bias voltage. However, the data show an increase of the current as the voltage increases beyond the flatband voltage, which shows the existence of the internal current gain. As a result, we define l as the internal current gain coefficient and its unit is V1 . When the flatband voltage VFB is large, the photocurrent Isp reaches the saturation slowly. Otherwise, if the flatband voltage is small, the photocurrent reaches the saturation quickly. The function of the parameter 1=a is similar to VFB , and a can be determined by the value of VFB directly. Therefore, a is defined as the flatband voltage parameter with its unit V1 . To test the validity of the proposed model, we have compared simulation results with experimental data in Figures 4.24(a) and (b). It can be found that the results agree well with the measured results. The corresponding model parameters are extracted by using the curve-fitting technique. The physical meanings and values of model parameters are given in Table 4.5.

Table 4.5 Meanings and values of DC characteristic model parameters. Parameter

Meaning

Unit

Value 22

b l a VRT Po

Saturation responsitivity parameter Internal current gain coefficient Flatband voltage parameter Reach-through voltage Normalized constant

A=W V1 V1 V

33 4

7:11 10 8:5 1012 0.563 0:75 1

1:0 103 0.390 0.078 0 10

The dark current characteristic can be represented by using the following experimental formula: ( 0; when V < VRT ð4:49Þ Id ¼ bd ½1 þ ld ðVVRT Þtanh½ad ðVVRT Þ; when V VRT

Microwave Modeling Techniques of Photodiodes

141

where bd is the dark current transconductance parameter, ld is the internal current gain coefficient, and ad is the flatband voltage parameter in the condition of the dark current. For the same device, ld and ad should be equal to l and a, respectively, but band bd will be different under illumination and dark because the dark current is much smaller than the photocurrent. Figure 4.25(a) shows the DC characteristics for a 2 2 MSM PD. Figure 4.25(b) shows the DC characteristics of an MSM PD with a 3 mm finger width and 2 mm spacing on a 100 mm by 100 mm GaAs active area (that is 3 2) [36, 43].

Measured

Modeled

Dark current (µA)

40

30

20

10

0

0

2

4

6

8

10

Bias voltage (V) (a) 2 × 2 MSM PD Modeled

Measured

Dark current (mA)

1.5

1.0

0.5

0.0

0

2

4

6

8

10

12

Bias voltage (V) (b) 2 × 3 MSM PD

Figure 4.25 Dark current performance of different sized MSM PDs: (a) 2 2 MSM PD; (b) 3 2 MSM PD.

Optoelectronic Integrated Circuit Design and Device Modeling

142

The simulation results agree well with the measured results in Figures 4.25(a) and (b). The corresponding model parameters are extracted by using curve fitting. The physical meanings and values of model parameters are summarized in Table 4.6.

Table 4.6 Physical meanings and values of dark current characteristic model parameters. Parameter

Meaning

Unit

Value 22

bd ld ad VRT

Dark current transconductance parameter Internal current gain coefficient Flatband voltage parameter Reach-through voltage

A=W V1 V1 V

32 8

3:2 10 8:5 1012 0.28 0.8

1:01 107 0.390 2.0 0

The intrinsic capacitance of an MSM PD is composed of two components, depletion-layer capacitance and charge storage capacitance. The depletion-layer capacitance results from the changing width of the depletion layer and the charge storage capacitance is used to model transit time. Since the current shows little variation after the flatband voltage, the charge storage capacitance can be neglected under illumination. Figure 4.26(a) shows a plot of measured intrinsic capacitance for a 2 2 MSM PD under illumination. Figure 4.26(b) shows a plot of measured intrinsic capacitance for a 1 3 MSM PD under illumination [6]. It is observed that the capacitance decreases rapidly with increasing bias voltage below the flatband voltage, and decreases slowly at a higher voltage. This is because at zero bias the capacitance is determined by the built Schottky barrier region, which increases its width with reverse bias, resulting in a decreasing capacitance. This process continues until the region between the electrodes is completely depleted, after which the capacitance becomes essentially constant. The intrinsic capacitance can be modeled by using the conventional reverse-biased diode capacitance formula: C¼

Cjo VVRT m 1 Vj

ð4:50Þ

where Cjo is the capacitance at V ¼ VRT bias condition, Vj is the built-in potential, m is the junction capacitance grading coefficient, and V is the total positive voltage across the terminals. The simulation results agree well with the measured results in Figures 4.26(a) and (b), and verify the accuracy of the above formulas. The physical meanings and values of the model parameters are given in Table 4.7.

Microwave Modeling Techniques of Photodiodes

143

Measured

Modeled

Capacitance (pF)

0.3

0.2

0.1

0

5

10

15

20

Bias voltage (V) (a) 2 × 2 MSM PD Measured

Capacitance (pF)

4

Modeled

3 2 1 0

0

2

4

6

Bias voltage (V) (b) 2 × 3 MSM PD

Figure 4.26 Capacitance-voltage characteristic of different sized MSM PDs: (a) 2 2 MSM PD;

(b) 3 2 MSM PD.

Table 4.7 Physical meanings and values of intrinsic capacitance model parameters. Parameter

Cjo Vj m VRT

Meaning

Capacitance at V ¼ VRT bias Built-in potential Junction capacitance grading coefficient Reach-through voltage

Unit

pF V V

Value 22

13

1.38 3.0 2.4 0.8

1.024 0.8 0.64 0.75

Figure 4.27 shows a large-signal equivalent circuit model, where a diode is used to model intrinsic capacitance and resistance of the active area. A small-signal equivalent circuit model is obtained by linearizing the large-signal equivalent circuit model in Figure 4.28, where gm is the differential gain coefficient of the photocurrent, gsp and gd

Optoelectronic Integrated Circuit Design and Device Modeling

144

Figure 4.27 Large-signal equivalent circuit model of PIN PD.

Figure 4.28 Small-signal equivalent circuit model of PIN PD.

represent conductance of the photocurrent and dark, respectively, and are given by gm ¼

gd ¼

ð4:51Þ

dIsp ¼ bðPin =Po Þ l tanh½aðVVRT Þ þ a½1 þ lðVVRT Þsec h2 ½aðVVRT Þ dV ð4:52Þ

dIdark ¼ bD l tanh½aD ðVVRT Þ þ a½1 þ lD ðVVRT Þsec h2 ½aD ðVVRT Þ dV ð4:53Þ V=2.8V

Frequency response (dB)

gsp ¼

dIsp ¼ bð1=Po Þ½1 þ lðVVRT Þtanh½aðVVRT Þ dPin

V=4.8V

V=6.8V

0

-2

-4

-6

0

2

4

6

8

10

Frequency (GHz)

Figure 4.29 Frequency response of a 2 2 MSM PD at different bias levels.

Microwave Modeling Techniques of Photodiodes

145

The large-signal equivalent circuit model is accomplished in the circuit simulation program SPICE, a high-frequency response of a 2 2 MSM PD at different bias levels with a 50 O load is simulated, and results are shown in Figure 4.29. It is shown that the 3 dB bandwidth increases with the increase of the bias voltage. The major reason is the variation of the intrinsic capacitance with respect to the bias voltage.

4.5 Summary The basic physical principles and figures of merit are described first in this chapter, and in sequence microwave modeling techniques for the common photodiodes (such as PIN PD, APD, and MSM PD) have been introduced.

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18. Wang, G., Tokumitsu, T., Hanawa, I., et al. (2002) Analysis of high speed p-i-n photodiodes S-parameters by a novel small signal equivalent circuit model. IEEE Microwave and Wireless Components Letters, 12(10), 378–380. 19. Wang, G., Tokumitsu, T., Hanawa, I., et al. (2003) A time-delay equivalent-circuit model of ultrafast p-i-n photodiodes. IEEE Transactions on Microwave Theory and Techniques, 51(4), 1227–1233. 20. Malyshev, S. A. and Chizh, A. L. (2004) P-I-N photodiodes for optical control of microwave circuits. IEEE Journal of Selected Topics in Quantum Electronics, 10(4), 679–685. 21. Wu, M.-C., Huang, Y.-H., and Ho, C.-L. (2007) High-speed InGaP/GaAs p-i-n photodiodes with wide spectral range. IEEE Electron Device Letters, 28(9), 797–799. 22. Fisher, S. T. (1967) Small-signal impedance of avalanching junctions with unequal electron and hole ionization rates and drift velocities. IEEE Transactions on Electron Devices, 14(6), 313–322. 23. Teich, M. C., Matsuo, K., and Saleh, B. E. A. (1986) Excess noise factors for conventional and superlattice avalanche photodiodes and photomultiplier tubes. IEEE Journal of Quantum Electronics, 22(8), 1184–1193. 24. Chen, W. and Liu, S. (1996) PIN avalanche photodiodes model for circuit simulation. IEEE Journal of Quantum Electronics, 32(12), 2105–2111. 25. Xiao, Y. G. and Deen, M. J. (2001) Temperature dependent studies of InP/InGaAs avalanche photodiodes based on time domain modeling. IEEE Transactions on Electron Devices, 48(4), 661–670. 26. Wu, W., Hawkins, A. R., and Bowers, J. E. (1996) Frequency response of avalanche photodetectors with separate absorption and multiplication layers. Journal of Lightwave Technology, 14(12), 2778–2785. 27. Shiba, T., Ishimura, E., Takahashi, K., et al. (1988) New approach to the frequency response analysis of an InGaAs avalanche photodide. Journal of Lightwave Technology, 6(10), 1502–1506. 28. Anselm, K. A., Nie, H., Hu, C., et al. (1998) Performance of thin separate absorption, charge, and multiplication avalanche photodiodes. IEEE Journal of Quantum Electronics, 34(3), 482–490. 29. Ghose, A., Bunz, B., Weide, J., and Kompa, G. (2005) Extraction of nonlinear parameters of dispersive avalanche photodiode using pulsed RF measurement and quasi-DC optical excitation. IEEE Transactions on Microwave Theory and Techniques, 53(6), 2082–2087. 30. Bandyopadhyay, A., Jamal Deen, M., Tarof, L. E., and Clark, W. (1998) Simplified approach to timedomain modeling of avalanche photodiodes. IEEE Journal of Quantum Electronics, 34(4), 691–699. 31. Shi, J.-W., Wu, Y.-S., Li, Z.-R., and Chen, P.-S. (2007) Impact-ionization-induced bandwidth-enhancement of a Si–SiGe-based avalanche photodiode operating at a wavelength of 830nm with a gain-bandwidth product of 428GHz. IEEE Photonics Technology Letters, 19(7), 474–476. 32. Moloney, A. M., Morrison, A. P., Jackson, J. C., et al. (2002) Small signal equivalent circuit for Geigermode avalanche photodiodes. Electronics Letters, 38(6), 285–286. 33. Campbell, J. C. (2007) Recent advances in telecommunications avalanche photodiodes. Journal Lightwave Technology, 14(5), 109–121. 34. Chou, S. Y. and Liu, M. Y. (1992) Nanoscale Tera-Hert metal-semiconductor-metal photodetectors. IEEE Journal of Quantum Electronics, 28(10), 2358–2368. 35. Se, S. M., Coleman, D. J., and Loya, A. (1971) Current transport in metal–semiconductor–metal (MSM) structure. Solid-State Electronics, 14(14), 1209–1218. 36. Song, K. C., Matin, M. A., Robinson, B., et al. (1996) High performance InP/InGaAs-based MSM photodetector operating at 1.3–1.5 mm. Solid-State Electronics, 39(9), 1283–1287. 37. Sano, E. (1990) A device model for metal–semiconductor–metal photodetectors and its applications to optoelectronic integrated circuit simulation. IEEE Transactions on Electron Devices, 37(9), 1964–1968. 38. Lu, J., Surridge, R., Pakulski, G., et al. (1993) Studies of high speed metal–semiconductor–metal photodetector with a GaAs/AlGaAs/GaAs heterostructure. IEEE Transactions on Electron Devices, 40(6), 1087–1091. 39. Xiang, A., Wohlmuth, W., Fay, P., et al. (1996) Modeling of InGaAs MSM photodetector for circuit-level simulation. Journal Lightwave Technology, 14(5), 716–723. 40. Gao, J., Gao, B., and Liang, C. (2000) Modeling of MSM PD for SPICE. Microwave and Optical Technology Letters, 26(6), 390–394.

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41. Statz, H., Newman, P., Smith, I. W., et al. (1984) GaAs device and circuit simulation in SPICE. IEEE Transactions on Electron Devices, 34(2), 160–169. 42. Sugeta, T., Urisu, T., Sakata, S., et al. (1980) Metal–semiconductor–metal photodetector for high speed optoelectronic circuits. Japanese Journal of Applied Physics, 19(Supplement), (19–1), 459–464. 43. Li, Z., Wang, Q., and Shi, C. (1992) Study on GaAs MSM PD optoelectronic performance. Research and Progress of Solid State Electronics, 12(3), 225–229.

5 High-Speed Electronic Semiconductor Devices The long-haul optical communication systems have shown increased data rates up to 40 Gb/s. To realize such systems, high-speed transmitter and receiver circuits are in great demand, and the development of monolithic integrated circuits (ICs) is indispensable. The high-speed electronic semiconductor devices are very attractive for ultra broadband optoelectronic IC design. Before introducing the analysis and optimum design of the optical transmitter and receiver, it is necessary to understand the operation mechanism of various high-speed electronic semiconductor devices. Several competing semiconductor device technologies serve as the backbone in the making of RF transceivers in current wireless systems. They range from silicon-based to compound-semiconductor-based devices. In the chapter, we will introduce the basic concept of modeling and parameter extraction methods for commonly used silicon-based and III–V compound semiconductor devices, such as MESFET, HEMT, HBT, and MOSFET. These devices are commonly discussed technologies of choice with higher RF performance for highspeed optical transmitters and receivers.

5.1 Overview of Microwave Transistors Semiconductor material systems can be categorized into silicon-based and III–Vcompound-semiconductor-based devices. Silicon-based semiconductor devices, with their low-cost, high-volume production, have improved frequency response significantly as the channel length is made smaller and up to 45 nm. In contrast, compoundsemiconductor-based devices take advantages of their intrinsic material properties and offer superior device performance in high-frequency applications such as monolithic microwave integrated circuits (MMICs). The III–V semiconductor industries have Optoelectronic Integrated Circuit Design and Device Modeling Jianjun Gao Ó 2011 Higher Education Press

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also increased their production yield and integration scale in response to the increasing demand of RF circuits in terrestrial and mobile wireless communications [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. Alternatively, in terms of transistor operation principles, semiconductor transistor technologies can be categorized into two major types depending on their physical carrier transportation mechanisms: field effect transistors (FETs) and bipolar junction transistors (BJTs). Table 5.1 shows the comparison of some device parameters for both FET and bipolar transistor devices. FET devices are also referred to as unipolar devices because the majority carriers are in principle responsible for the transport characteristics. Drain current in an FET is modulated by gate voltage through a channel width modulation scheme. The amplification process in the FET is characterized by a transconductance to assess the controllability of the gate voltage modulation over the output drain current. On the other hand, carrier transportation mechanisms in bipolar transistors involve both electrons and holes. The collector current is modulated by the minority current injection from the base. BJT is equivalent to a current amplifier as the input base current is ‘amplified’ by a factor of current gain through the transistor and the output current is ‘collected’ at the collector end. Table 5.1 gives the comparison of a FET and bipolar transistor. Table 5.1 Comparison of FET and bipolar transistor. Parameters

FET/HEMT

BJT/HBT

Physical dimension limitation Turn-on characteristics Output current density Input impedance controller Noise source

Gate length Gate threshold voltage Medium Gate voltage Gate induced noise Channel current noise Low-frequency noise Gate leakage current noise Medium

Base and collector thickness Base–emitter voltage High Base current

Processing complexity

Shot noise Low-frequency noise High

There are wide varieties of the solid-state device technologies available for implementation of optoelectronic integrated circuits (OEICs). The commonly used semiconductors are as follows: 1. 2. 3. 4.

Silicon-based bipolar junction transistors (BJTs) Silicon-based metal oxide semiconductor field effect transistors (MOSFETs) Silicon germanium-based heterojunction bipolar transistors (SiGe HBTs) Gallium arsenide-based metal semiconductor field effect transistors (GaAs MESFETs) 5. Gallium arsenide-based high electron mobility transistors (GaAs HEMTs) 6. Gallium arsenide-based heterojunction bipolar transistors (GaAs HBTs)

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7. Indium phosphide-based high electron mobility transistors (InP HEMTs) 8. Indium phosphide-based heterojunction bipolar transistors (InP HBT). The high-speed ICs in optical transmitters and receivers require different transistor parameters. For example, the drivers of lasers and optical modulators use transistors with higher power densities and optical preamplifiers employ transistors with lownoise characteristics. In most designs, the minimum noise figure, maximum power gain, stability factor voltage standing wave ratio (VSWR) usually do not occur at the same input/output impedance in the Smith chart. Therefore, the selection of bias point and input/output impedance is determined by the special requirements of each component.

5.2 FET Modeling Technique In a compound semiconductor, GaAs MESFET technology is the most widely used III–V semiconductor device for high-frequency applications. A typical device crosssectional view of an n-channel MESFET is shown in Figure 5.1. The gate Schottky

Figure 5.1

MESFET device structure.

barrier forms a depletion region in the channel under the gate area. When positive potential is applied to the drain, electrons flow from the source to the drain through the channel. The active channel can be formed either by ion implantation followed by anneal or by doped epitaxial growth. The drain current is modulated by the gate potential due to the modulation in the channel width with the gate voltage. The derivative device technologies of GaAs MESFETs is HEMT. The HEMT utilizes advanced epitaxial material growth technology, such as molecular beam epitaxy (MBE) or molecular organic chemical vapor deposition (MOCVD), and bandgap engineering techniques to achieved high-speed and low-noise performance. A typical device structure is shown in Figure 5.2. A large-bandgap doped material (such as AlGaAs) is grown heteroepitaxially on an undoped lower bandgap material (such as

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Figure 5.2 HEMT device structure.

GaAs). The undoped GaAs provides a high-mobility two-dimensional (2-D) channel for carriers supplied from AlGaAs. An undoped AlGaAs layer is used to avoid electronic interaction and to increase mobility. Compared with MESFET, HEMT devices have a higher cutoff frequency and lower noise performance, and are more suitable for the high-speed transmitter and receiver at over 40 Gb/s.

5.2.1

FET Small-Signal Modeling

In the high-frequency characterization of microwave transistors, small-signal models are often used to parameterize complicated behaviors with relatively simple equations. A small-signal model is preferably designed so that the model parameters represent something physical in the transistor. This can provide important information to optimize the test structures layout, in order to perform the simulation of the complete structure using an equivalent circuit [15, 16, 17, 18, 19, 20, 21, 22]. Figure 5.3 shows the small-signal equivalent circuit model for FETs. This equivalent circuit model can be divided into two parts:

Figure 5.3 Small-signal equivalent circuit model for PHEM.

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1. The intrinsic elements that consist of gm , gds , Cgs , Cgd , Cds , Ri , and t 2. The extrinsic elements that consist of Lg , Ld , Ls , Rg , Rs , Rd , Cpg , Cpd , and Cpdg . The various components in the model are defined in the following list: Cpg Cpd Cpgd Lg Ld Ls Rg Rd Rs gm gds Cgs Cgd Cds Ri t

gate pad capacitance drain pad capacitance isolation capacitance between the gate and drain pads inductance of the gate feedline inductance of the drain feedline inductance of the source feedline distributed gate resistance drain-to-channel resistance, including contact resistance source-to-channel resistance, including contact resistance transconductance drain conductance gate-to-source capacitance gate-to-drain capacitance drain-to-source capacitance channel resistance time delay associated with transconductance

The intrinsic part is characterized by the Y parameters: 3 2 joCgs þ joCgd joCgd 7 6 1 þ joRi Cgs 7 6 YINT ¼ 6 7 5 4 gm ejot joCgd gds þ joðCds þ Cgd Þ 1 þ joCgs Ri

ð5:1Þ

The PAD capacitances are determined by measuring an open structure that consisted of only the pads. Measurements of the open test structure are modeled as a PI network of capacitances. Figure 5.4 shows the open test structure layout with the corresponding

Figure 5.4 (a) Open test structure and (b) equivalent circuit model.

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equivalent circuit model. The pad capacitances Cpg , Cpd , and Cpgd can be directly obtained: 1 open open Im Y11 þ Y12 o 1 open open ¼ Im Y22 þ Y12 o 1 open 1 open ¼ Im Y12 ¼ Im Y21 o o

Cpg ¼

ð5:2Þ

Cpd

ð5:3Þ

Cpgd

ð5:4Þ

The parasitic device connection impedances can be determined by measuring a test pattern, which consists of the pads, the device feeds, and a short replacing the transistor. The shorted test structure is modeled as a T-network of series resistors and inductors. Figure 5.5 shows the shorted test structure and corresponding equivalent circuit model. The extrinsic inductances and feedline losses can be directly determined from Z parameters of the short test structure:

Figure 5.5 (a) Short test structure and (b) equivalent circuit model.

1 short 1 short Im Z12 ¼ Im Z21 o o 1 short short Z12 Z Lg ¼ o 11 1 short short Ld ¼ Z Z12 o 22 Ls ¼

ð5:5Þ ð5:6Þ ð5:7Þ

Once the extrinsic elements are obtained, the intrinsic elements are determined as follows: dðoi Þ ¼

Re½Y11 ðoi Þ þ Y12 ðoi Þ Im½Y11 ðoi Þ þ Y12 ðoi Þ

ð5:8Þ

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cðoi Þ ¼ ½Y21 ðoi ÞY12 ðoi Þ½1 þ eoi dðoi Þ

ð5:9Þ

Cgs ðoi Þ ¼

1 þ d 2 ðoi Þ Im½Y11 ðoi Þ þ Y12 ðoi Þ ðoi Þ

ð5:10Þ

Ri ðoi Þ ¼

d 2 ðoi Þ ½1 þ d 2 ðoi ÞRe½Y11 ðoi Þ þ Y12 ðoi Þ

ð5:11Þ

Im½Y12 ðoi Þ oi pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ gm ðoi Þ ¼ c2 ðoi Þ 1 tðoi Þ ¼ tan1 fIm½cðoi Þ; Re½cðoi Þg oi gds ðoi Þ ¼ Re½Y22 ðoi Þ þ Y12 ðoi Þ Cgd ðoi Þ ¼

Cds ðoi Þ ¼

Im½Y22 ðoi Þ þ Y12 ðoi Þ oi

ð5:12Þ ð5:13Þ ð5:14Þ ð5:15Þ ð5:16Þ

where oi is the angular frequency and ið¼ 0; . . . ; N1Þ is the number of sampling points.

5.2.2 FET Large-Signal Modeling State-of-the-art computer-aided design (CAD) methods for active microwave circuits rely heavily on models of real devices. The commonly used nonlinear FET models are the physical-based nonlinear model, table-based nonlinear model, and empirical equivalent-circuit-based model. The physical-based models are derived from solutions of the basic semiconductor device equations of the basic semiconductor device equations. The physical simulation of the FET device is based on four semi-classical semiconductor equations (Poisson equation, current continuity equation, and energy and momentum equations) with analytical expressions for the FET channel. The difficulty in applying physical device models to microwave CAD simulators is the large execution times required. The physical models solve the semiconductor device equations using some form of numerical technique such as finite differences or finite elements. Table-based models are highly accurate and device independent and they expedite simulations because they are based directly on the measured data. Performance between measured points is interpolated with spline functions and these functions should be differentiable to a high order of derivatives in order to ensure a correct description of harmonics and convergence within harmonic balance (HB) simulations. Equivalent-circuit-based models are commonly used to investigate

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large-signal device performance. However, these models require extensive characterization of the device after fabrication, as well as some knowledge of process variation statistics. Equivalent circuit models of an active device (such as FET, HBT, and so on) are the backbone of the nonlinear microwave CAD simulator software. All commercially available software includes one or more of each type of device model. The modeling concept is that the complex active device is represented by using basic resistances, capacitances, and control sources. 5.2.2.1 Relationship Between Small-Signal and Large-Signal Models The basic nonlinear equivalent circuit model for microwave and RF FETs is shown in Figure 5.6. The model only contains elements considered to be of first-order importance to device operation. There are seven nonlinear elements: three current generators, three charges, and a nonlinear input resistance.

Figure 5.6 Basic nonlinear equivalent circuit model for microwave and RF FETs.

The various components in the model are defined in the following list: Ids ðVin ; Vout Þ Idg ðVout Vin Þ Igs ðVin Þ Qgs ðVin ; Vout Þ Qgd ðVin ; Vout Þ Qds ðVout Þ

gate-to-source and drain-to-source voltage-controlled drain current source drain-to-gate voltage-controlled current source gate-to-source voltage-controlled current source gate-to-source and drain-to-source voltage-controlled gate-tosource charge storage gate-to-source and drain-to-source voltage-controlled gate-todrain charge storage drain-to-source voltage-controlled charge storage

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Rin ðVin ; Vout Þ

157

gate-to-source and drain-to-source voltage-controlled intrinsic resistance

It can be observed that the main nonlinearity is the drain source current Ids . The nonlinear current sources Igs and Igd are used to represent forward conduction of the gate source and reverse breakdown of the gate–drain Schottky barrier diodes. Figure 5.7 shows the relationship between nonlinear and linear equivalent circuit elements, where gm ¼

qIds qVgs

qIds qVds qQgs qQgd þ Cgs ¼ qVgs qVgs gds ¼

Cgd ¼

ð5:17Þ ð5:18Þ ð5:19Þ

qQgs qQgd þ qVgd qVgd

ð5:20Þ

qQds qVds

ð5:21Þ

Cds ¼

Figure 5.7 Relationship between nonlinear and linear equivalent circuit elements.

5.2.2.2 Statz Model The Statz model is a popular nonlinear FET model that is available in most large-signal circuit simulation packages used by microwave engineers [23]. The model can be

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divided into two shells: an inner shell represents the intrinsic FET device, while an outer shell represents the device parasitic elements. The drain current can be expressed as follows: Ids ¼

bðVgs VTO Þ2 ð1 þ lVds ÞtanhðaVds Þ 1 þ bðVgs VTO Þ

ð5:22Þ

In this equation, the model parameters are defined in the following list: Ids VTO b a l b

drain current (A) threshold voltage (V) transconductance parameter (A/V2) saturation voltage parameter (determine the voltage that Ids saturates) (V1) channel length modulation parameter (V1) fitting parameter that controls the Ids Vgs characteristic transition from quadratic to linear behavior (V1)

The tanh function in Equation (5.6) consumes considerable computer time and can be further approximated below saturation by a simple polynomial Kt of the form 1ð1aVds =3Þ3 ; 0 < Vds < 3=a ð5:23Þ Kt ¼ tanhðaVds Þ ¼ 1; Vds 3=a It can be found that in the saturation region (Vds 3=a), the tanh function is replaced by unity. The corresponding transconductance and output conductance can be expressed as follows: b Vgs VTO ½2 þ bðVgs VTO Þ ð1 þ lVds ÞKt ð5:24Þ gm ¼ ½1 þ bðVgs VTO Þ2 i bðVgs VTO Þ2 h gds ¼ lKt þ ð1 þ lVds Það1aVds =3Þ2 ð5:25Þ ½1 þ bðVgs VTO Þ In the Statz MESFET model, the dependence of intrinsic capacitances Cgs and Cgd on the intrinsic terminal voltages are given by Cgso 1 1 Cgs ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð1 þ k1 Þð1 þ k2 Þ þ Cgdo ð1k2 Þ 4 2 1 VVnew bi

ð5:26Þ

Cgso 1 1 Cgd ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð1 þ k1 Þð1k2 Þ þ Cgdo ð1 þ k2 Þ 4 2 1 VVnew bi

ð5:27Þ

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where Vnew

Veff 1

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 ¼ Veff 1 þ VTO þ ðVeff 1 VTO Þ2 þ d2 2 qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 ¼ Vgs þ Vgd þ ðVgs Vgd Þ2 þ a2 2 Veff 1 VTO k1 ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ðVeff 1 VTO Þ2 þ d2 Vgs Vgd k2 ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ðVgs Vgd Þ2 þ a2

where Cgs and Cgd are the gate-to-source and gate-to-drain capacitances, respectively. Cgso and Cgdo are the corresponding zero-bias gate–source and gate–drain capacitances. The d parameter models the behavior of Cgs and Cgd around and below pinchoff. 5.2.2.3 Curtice Nonlinear Model The most commonly used Curtice models are the Curtice quadratic model [24] and the Curtice cubic model [25]. Curtice Quadratic Model The quadratic dependence of the drain current with respect to the gate voltage is calculated using the following expression in the region Vds 0: Ids ¼ bð1 þ lVds ÞðVgs VTO Þ2 tanhðaVds Þ

ð5:28Þ

Assuming symmetry, in the reverse region, the drain and source swap roles and the expression becomes Ids ¼ bð1 þ lVds ÞðVgs VTO Þ2 tanhðaVds Þ

ð5:29Þ

The drain current is set to zero in the case where the gate-to-source junction voltage Vgs drops below the threshold voltage VTO . In order to model the non-square-law performance for Ids, an advanced Curtice quadratic model is available in the commercial software. The corresponding drain current is expressed as follows: Ids ¼ bn ð1 þ lVds ÞðVgs Vton ÞQ tanhðaVds Þ

ð5:30Þ

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with bn ¼

b 1 þ UðVgs VTO Þ

ð5:31Þ

Vton ¼ VTO þ gVds where Q, g, and U are the fitting factors. Curtice Cubic Model By using a cubic approximation, drain current in the Curtice cubic model is calculated with the following expression: Ids ¼ ðA0 þ A1 V1 þ A2 V12 þ A3 V13 Þtanh½gVds ðtÞ

ð5:32Þ

where V1 is the input voltage: o Vds ðtÞg V1 ¼ Vgs ðttÞf1 þ b½Vds

ð5:33Þ

where

b is the coefficient for pinchoff change o is the output voltage at which A0 , A1 , A2 , and A3 are evaluated Vds t is the internal time delay of FET. The coefficients A0 , A1 , A2 , and A3 can be evaluated from data in the saturation region. One disadvantage of the cubic relationship is that, unlike the quadratic, a pinchoff voltage may result with current zero or transconductance zero, but not both. Figure 5.8 shows the Curtice nonlinear equivalent circuit model, which is available in the commercial software. A shunt network (Cf and Rc ) in parallel with the output port is used to model frequency-dependent output conductance.

Figure 5.8

Curtice nonlinear equivalent circuit model.

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In this model, the drain–gate avalanche current Idg is taken to be 8 < Vdg ðtÞVB ; Vdg > VB Idg ¼ : 0; R1 Vdg < VB

161

ð5:34Þ

where VB ¼ VBO þ R2 Ids , R1 is the approximate breakdown resistance, and R2 is the resistance relating the breakdown voltage to channel currents. VBO is the gate–drain junction reverse-bias breakdown voltage. The forward-bias gate current Igs is taken to be 8 < Vgs ðtÞVbi ; Vgs > Vbi ð5:35Þ Igs ¼ : 0; RF Vgs < Vbi where Vbi is the built-in voltage and RF is the effective value of forward-bias resistance.

5.2.3 FET Noise Modeling Low noise design is one of the key issues in most optical receiver circuits. The complete characterization of the transistor in terms of noise and scattering parameters is necessary for the computer-aided design (CAD) of a low-noise amplifier. Therefore, accurate modeling of high-frequency noise is indispensable to develop a low-noise amplifiers (LNAs) with a short development time. The ‘PRC’ model [26, 27] has emerged as one of the most accurate and convenient ways to obtain the noise model parameters for FETs in microwave simulators. Following these pioneering works, Pospieszalski proposed an alternative highfrequency noise model. In the following, two commonly used FET noise models are described briefly. 5.2.3.1 Pucel Noise Model The Pucel noise model, also called the PRC noise model (as shown in Figure 5.9), the gate induced noise current ig2 and drain channel current noise id2 are expressed as follows: 2 ig2 ¼ 4kTDf o2 Cgs R=gm

ð5:36Þ

id2 ¼ 4kTDfgm P

ð5:37Þ

The cross-correlation between ig2 and id2 can be expressed as qﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃ ig* id ¼ C ig2 id2 ¼ 4kTDf oCgs C PR

ð5:38Þ

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Figure 5.9 FET noise equivalent circuit model: (a) extrinsic part; (b) intrinsic part.

where R and P are the gate and drain noise model parameters, C is the correlation coefficient, k is the Boltzmann constant, T is the absolute temperature (normally 290 K), and Df is the bandwidth. The corresponding noise parameters can be expressed as follows [28]: ﬃ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃﬃ f PRð1C 2 Þ pﬃﬃﬃﬃﬃﬃ ð5:39Þ gm ðRs þ Rg Þ þ Fmin ¼ 1 þ 2 P þ R2C PR fc P þ R2C PR 2

pﬃﬃﬃﬃﬃﬃ f gn ¼ gm P þ R2C PR ð5:40Þ fc vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ u ugm ðRs þ Rg Þ þ PRð1Cp2 Þﬃﬃﬃﬃﬃ t P þ R2C PR 1 pﬃﬃﬃﬃﬃﬃ ð5:41Þ Ropt ¼ oCgs P þ R2C PR pﬃﬃﬃﬃﬃﬃ 1 PC PR pﬃﬃﬃﬃﬃﬃ Xopt ¼ ð5:42Þ oCgs P þ R2C PR In several commercial software such as the SPICE circuit simulator, gate induced noise current ig2 has been neglected, that is R ¼ 0. Equations (5.39) to (5.42) can be

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simplified as follows: pﬃﬃﬃ f qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ gm ðRs þ Rg Þ Fmin ¼ 1 þ 2 P fc 2 f gn ¼ Pgm fc Ropt

rﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ gm ðRs þ Rg Þ 1 ¼ P oCgs Xopt ¼

1 oCgs

Here fc is the cutoff frequency, and is expressed as follows: gm fc ¼ 2pCgs

ð5:43Þ ð5:44Þ

ð5:45Þ ð5:46Þ

ð5:47Þ

According to reference [21], the parameter P can be approximated for operating points below the onset of saturation by P¼

Ids Ec Lgm

ð5:48Þ

In this expression, Ids is the DC drain current, Ec the critical field, L the gate length, and gm the transconductance.

5.2.3.2 Pospieszalski Noise Model The Pospieszalski noise model is shown in Figure 5.10 [29]. The thermal noise voltage sources generated by extrinsic resistances Rg , Rd , and Rs are as follows: e2g ¼ 4kTa Rg Df

ð5:49Þ

e2d ¼ 4kTa Rd Df

ð5:50Þ

e2s ¼ 4kTa Rs Df

ð5:51Þ

where Ta is the ambient temperature. The two uncorrelated current noise sources e2gs 2 represent the internal noise sources of the intrinsic FET. These two noise and ids sources are characterized by their mean quadratic value in a bandwidth Df centered on the frequency f, and can be given by the following expressions:

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Optoelectronic Integrated Circuit Design and Device Modeling

Figure 5.10 (a) Pospieszalski noise model and (b) intrinsic part.

e2gs ¼ 4kTg Rgs Df

ð5:52Þ

2 ¼ 4kT g Df ids d ds

ð5:53Þ

e*gs ids ¼ 0

ð5:54Þ

where Tg and Td are the equivalent noise temperatures of the intrinsic resistance Rgs and output conductance gds , respectively. In the Pospieszalski noise model, the elements of the noise correlation matrix are [30] 2 joC gs i12 ¼ 4kTg DfRgs ð5:55Þ 1 þ joCgs Rgs 2 ! T g d m ð5:56Þ i22 ¼ 4kDf þ Tg Rgs Rds 1 þ joCgs Rgs i1 i2* ¼ 4kTg Df

g*m oCgs Rg j1 þ joCgs Rgs j2

ð5:57Þ

In the lower drain current ranges, Tg equals the ambient temperature and Td increases with the increase of drain current.

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Once the small-signal elements are extracted from the S-parameter measurements, the extraction of the four unknown noise model parameters can be carried out using the procedure based on the noise correlation matrix technique as follows [31]: 1. Calculation of the chain noise correlation matrix for FET: 2 3 Fmin 1 * Rn Yopt 7 6 Rn 2 CAT ¼ 4kT 4 F 1 5 min Rn Yopt Rn jYopt j2 2

ð5:58Þ

Transformation of the chain noise correlation matrix to the admittance noise correlation matrix and subtraction of pad capacitances (Cpg , Cpd , and Cpgd ). Because of the pad network is a noiseless network, the admittance noise matrix remains invariant. 2. Transformation of the admittance noise correlation matrix to the impedance noise correlation matrix and subtraction of extrinsic inductances and resistances. 3. Transformation of the impedance noise correlation matrix to the impedance noise correlation matrix. Then the noise model parameters can be determined as follows: P¼ R¼

CY22 4kTgm Df

CY11 2aqIgL 4kTðoCgs Þ2 Df

C¼

ð5:59Þ gm

ImðCY12 Þ pﬃﬃﬃﬃﬃﬃ 4kToCgs PR

ð5:60Þ ð5:61Þ

5.3 GaAs/InP HBT Modeling Technique III–V compound heterojunction bipolar transistors (HBTs) largely retain the advantages of their Si predecessors, but extend them to higher frequencies. Additionally, a variety of disadvantages of Si bipolar transistors can be overcome. HBTs in the AlGaAs/GaAs material system have been the first beneficiaries of the improved materials. These devices are now becoming available commercially, and are poised for application in a wide variety of high-performance circuits. HBTs enjoy several advantages over their conventional silicon cousins. These include: .

A thinner base and lower base resistance, which yields higher gain, cutoff frequency, and maximum oscillation frequency

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166 . . .

High breakdown voltage Low parasitic elements High power density.

A cross-section of a simple HBT is shown in Figure 5.11. In a single-heterojunction device, the base, collector, and subcollector will all be of the same material, such as GaAs, while, in the AlGaAs system, for example, a small mole fraction of aluminum is added to the emitter to increase the bandgap. HBT operation involves the following three steps [14]: (1) minority carrier injection from emitter to base, (2) carrier transport in the base region, and (3) carrier collection at the base–collector (B–C) junction. In normal operation (forward bias), electrons are injected from the emitter into the base crossing over the heterostructure barrier. For an abrupt heterojunction barrier, the electron injection is due to thermionic emission, while for a graded emitter–base (E–B) junction the electrons diffuse to the base. The C–B junction is reverse biased and the high electric field present in the space-charge region is responsible for collection of electrons in the collector terminal.

Figure 5.11 Cross-section of a typical heterojunction bipolar transistor with a single emitter finger, two base contacts, and two collector contacts.

5.3.1

GaAs/InP HBT Nonlinear Model

Although the HBT is a relatively new type of device, there are no fundamental differences in its basic operating principles compared to the normal homojunction bipolar transistor (BJT). On this basis, many designers have directly used conventional BJT models such as the Ebers–Moll or Gummel–Poon for circuit designs incorporating the HBT. Nevertheless, the models that result are usually only useful in restrictive areas of application because HBTs exhibit several significant differences in electrical performance compared to Si BJTs, which cannot be adequately represented by traditional BJT models. Figure 5.12 shows the HBT large-signal equivalent circuit model based on the BJT Gummel–Poon model [32, 33, 34, 35, 36, 37]. The base current is represented by two sets of parallel diodes. One set corresponds to the base–emitter junction and the other set corresponds to the base–collector junction. The use of two parallel diodes to simulate each junction makes it possible to account for the bias dependence of current

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167

Figure 5.12 HBT large-signal equivalent circuit model.

gain. One diode in each set corresponds to the current due to the recombination in the space-charge region (SCR) primarily at low bias voltages. This current component is represented by the ideality factor ne for the forward operation and is generally close to 2. The other diode in each set is directly proportional to one of the components of the current source between the emitter and the collector. This diode simulates an ideal, constant current gain, and a region of operation for the BJTwhere both the base and the collector currents have the same ideality factor and are essentially parallel to each other on a log plot. The collector current is represented by the ideality factor nf in the forward operation. Since the collector current of a BJT is the result of diffusion-driven injection of electrons into the base, nf is generally very close to unity. The ibc1 represents the constant current gain region of the HBT, with an ideality factor nr, which is close to 1. The ibc2 represents the current due to recombination and generation mechanisms in the space-charge region, with an ideality factor nc that is close to 2. The four currents in Figure 5.12 can be expressed as follows: qVbe Ibe1 ¼ Isf exp 1 ð5:62Þ nf kT qVbe 1 ð5:63Þ Ibe2 ¼ Ise exp ne kT qVbe Ibc1 ¼ Isr exp 1 ð5:64Þ nr kT qVbc Ibc2 ¼ Isc exp 1 ð5:65Þ nc kT where nf and nr are the forward and reverse current emission factors, respectively; ne and nc are base–emitter and base–collector leakage emission coefficients, respectively; Isf and Isr are the forward and reverse transport saturation currents and Ise and Isr are base–emitter and base–collector leakage saturation currents, respectively; bf and br are the forward and reverse current gains.

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Optoelectronic Integrated Circuit Design and Device Modeling

The base, collector, and emitter currents are given by Ib ¼ areaðibe1 =bf þ ibe2 þ ibc1 =br þ ibc2 Þ

ð5:66Þ

Ic ¼ areaðibe1 =qbibc1 =qbibc1 =br ibc2 Þ

ð5:67Þ

Ie ¼ areaðibe1 =qbibc1 =qbibe1 =bf ibe2 Þ

ð5:68Þ

where qb is the normalized base hole charge and area is the emitter area. Compared with the static model, the large-signal model also includes the base–emitter and base–collector junction capacitance models. CDF is the diffusion capacitance of the charge due to the forward active current, CDR is the diffusion capacitance of the charge due to the reverse active current, and Cje and Cjc are the intrinsic base–emitter and base–collector junction capacitances, and can be expressed as CjE0 mjE 1 VVBE jE

ð5:69Þ

CjC0 mjC CjC ðVBC Þ ¼

1 VVBE jC

ð5:70Þ

CjE ðVBE Þ ¼

Compared with the BJT model, it is noted that the base–collector junction capacitance is split into two portions. While the intrinsic portion remains at the original location, an extrinsic portion of the capacitance Cjcx now bypasses the base resistance and directly connects the base to the collector terminals.

5.3.2

GaAs/InP HBT Linear Model

Two well-known basic small-signal equivalent circuit models based on the conventional physical-based T-type model and hybrid PI-type model are shown in Figure 5.13, where Rbi is the intrinsic base resistance, Rc and Re are the collector and emitter resistances, and Cex is the extrinsic base–collector capacitance. In the T-type model (as shown in Figure 5.13(a)), Cbc is the base–collector capacitance, and Rbe and Cbe are the base–emitter dynamic resistance and capacitance, respectively. Assuming a single-pole approximation, the transport factor can be written a¼

ao ejotT 1 þ jo=oa

ð5:71Þ

where ao denotes the intrinsic current gain at low frequency, oa is the 3 dB roll-off frequency, and tT is the transit time delay.

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169

Figure 5.13 HBT small-signal equivalent circuit models: (a) T-type model; (b) PI-type model.

In the PI-type model (as shown in Figure 5.13(b)), Rm and Cm are the base–collector dynamic resistance and capacitance, respectively, and Rp and Cp are the base–emitter dynamic resistance and capacitance, respectively. The transconductance gm is given by gm ¼ gmo ejotp

ð5:72Þ

where gmo denotes the intrinsic transconductance at low frequency and tp is the transit time delay. The PI- and T-type equivalent circuit models are compatible with each other only at low frequencies. The relationship between PI- and T- type equivalent circuit models at low frequencies can be written as follows:

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Optoelectronic Integrated Circuit Design and Device Modeling

gmo ¼

ð5:73Þ

tp ¼ tT

ð5:74Þ

Cp ¼ Cbe þ gmo tp

ð5:75Þ

Rp ¼

5.3.3

ao Rbe

Rbe 1gmo Rbe

ð5:76Þ

GaAs/InP HBT Noise Model

The complete HBT small-signal and noise-equivalent circuit model is shown in Figure 5.14. Figure 5.14(a) shows the extrinsic and Figure 5.14(b) the intrinsic network, respectively. The circuit model comprises the well-known T-type small-

Figure 5.14 Noisy small-signal equivalent circuit model of GaAs/InP HBT: (a) extrinsic part; (b) intrinsic part.

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171

signal equivalent circuit and six noise sources e2bx , e2bi , e2c , e2e , ib2 , and ic2 . Since the Tshaped equivalent circuit is more closely related to the original derivation of the common base Y parameters of bipolar transistors and involves the less simplifying assumption than the p equivalent circuit, it is usually employed in the literature for the purpose of small-signal modeling of HBTs. The two correlated current noise sources ib2 and ic2 represent the internal noise sources of the intrinsic HBT. These two noise sources are characterized by their mean quadratic value in a bandwidth Df centered on the frequency f, and can be given by the following expressions: ib2 ¼ 2qIb Df

ð5:77Þ

ic2 ¼ 2qIc Df

ð5:78Þ

where q is the electronic charge and Ib and Ic are the base and collector currents, respectively. The cross-correlation between ib2 and ic2 can be expressed [4, 6] as ib* ic ¼ 2qIc ðejot 1ÞDf

ð5:79Þ

The four noise sources e2bx , e2bi , e2c , and e2e represent the noisy behavior of access resistances Rbx , Rbi , Rc , and Re and are simply given by e2i ¼ 4kTRi Df ði ¼ bx; bi; c; eÞ

ð5:80Þ

where k is Boltzmann’s constant, T is the absolute temperature, and Ri is the resistance value

5.3.4 Parameter Extraction Methods The complete hybrid T-type small-signal equivalent circuit model is shown in Figure 5.15. The open-circuit Z parameters ZINT of the small-signal equivalent circuit can be expressed [38, 39] as Z11 ¼

½ð1aÞZBC þ ZEX Rbi þ ZBE þ ZE þ ZB ZBC þ ZEX þ Rbi

ð5:81Þ

ð1aÞZBC Rbi þ ZBE þ ZE ZBC þ ZEX þ Rbi

ð5:82Þ

½aZEX þ ð1aÞRbi ZBC þ ZBE þ ZE ZBC þ ZEX þ Rbi

ð5:83Þ

ð1aÞZBC ðZEX þ Rbi Þ þ ZBE þ ZE þ ZC ZBC þ ZEX þ Rbi

ð5:84Þ

Z12 ¼ Z21 ¼ Z22 ¼

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172

Figure 5.15 Complete small-signal equivalent circuit for HBT.

where ZB ¼ Rbx þ joLb ; ZC ¼ Rc þ joLc ; ZE ¼ Re þ joLe ZBC ¼

1 1 RBE ; ZEX ¼ ; ZBE ¼ joCbc joCex 1 þ joRBE CBE

The small-signal equivalent circuit model for HBT under the cutoff bias condition is shown in Figure 5.16. The cutoff bias condition for HBTs is defined as the condition when both junctions are zero biased (or reverse biased). Under such a condition, the DC current is zero, and hence a would be extremely small and the device behaves like a passive component (Z12 ¼ Z21 ). Therefore, the equivalent circuit becomes much simpler and the Z parameters are

Figure 5.16 Small-signal equivalent circuit for InP HBT under the cutoff condition.

High-Speed Electronic Semiconductor Devices

Z11 Z12 ¼ Z12 ¼ Z21 ¼ Z22 Z12 ¼

173

ZEX Rbi þ ZB ZBC þ ZEX þ Rbi

ð5:85Þ

ZBC Rbi þ ZBE þ ZE ZBC þ ZEX þ Rbi

ð5:86Þ

ZBC ZEX þ ZC ZBC þ ZEX þ Rbi

ð5:87Þ

The pad capacitances can be determined by measuring an open structure that consists of only the pads. The parasitic device-connection inductances are determined by measuring a test pattern that consists of the pads, the device feedlines, and a short replacing the HBT. The series emitter resistance RE can be extracted by the method that considers the variation of the real part of Z12 versus the reciprocal emitter current. The interception of the plot ReðZ12 Þ versus 1=IE gives the value of RE . After determination of the pad capacitances, series inductances, and emitter resistance, the extrinsic base and collector resistances can be determined from Z parameters under the cutoff bias condition, where the base–collector and base–emitter junctions are in the reverse condition. Once the extrinsic elements are known, the intrinsic elements under the normal condition (Figure 5.14) can be determined by using direct parameter extraction techniques: 1 1 ð5:88Þ Cbc þ Cex ¼ Im o Z22 Z21

1 1 Re Re Z22 Z21 Z11 Z12 1

Cex ¼ 2 ð5:89Þ 1 o Im Z22 Z21

1 Im Z22 Z 21

Rbi ¼ 1 oCbc Re Z11 Z 12 Z12 Z21 ao ¼ jaðoÞjjo ! 0 ¼ Z22 Z21 o ! 0 ojaðoÞj ﬃ oa ¼ qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ a2o aðoÞj2

Z12 Z21 Im Z22 Z21 1 1 o Þ þ arctg t ¼ arctgð

Z Z o o oa Re Z1222 Z2121

ð5:90Þ

ð5:91Þ ð5:92Þ

ð5:93Þ

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174

Rbe ¼

0

1

1

ð5:94Þ

1

A Re@ ex Rbi Z12 ðCbc þ ð1aÞC Cex Þ þ joCbc Cex Rbi 0 1 1 1 A Cbe ¼ Im@ ð1aÞC ex Rbi o Z12

ð5:95Þ

ðCbc þ Cex Þ þ joCbc Cex Rbi

The DC model parameters can be determined from forward and reverse measurements of I–V characteristics. Figure 5.17 shows the forward and reverse measurements for extraction of HBT DC model parameters.

Figure 5.17 Forward and reverse measurements for extraction of HBT DC model parameters.

For the forward active operation, when Vbc is set to zero (as shown in Figure 5.17(a)), the base and collector currents are expressed as qVbe Ib ¼ Isf exp 1 ð5:96Þ nf kT Ic qVbe þ Ise exp Ic ¼ 1 ð5:97Þ bf ne kT For the reverse active operation, when Vbe is set to zero (as shown in Figure 5.17(a)), the base and collector currents are expressed as Ie qVbc Ib ¼ þ Isc exp 1 ð5:98Þ br nc kT

High-Speed Electronic Semiconductor Devices

Ie ¼ Isr

qVbc exp 1 nr kT

175

ð5:99Þ

All the DC model parameters can be determined from Equations (5.96) to (5.99) by using the linear least square fit method.

5.4 SiGe HBT Modeling Technique The addition of Ge into the bipolar junction transistor (BJT) creating a heterojunction bipolar transistor, or HBT, enabled higher performance. Incorporation of substitutional Ge into the crystal lattice of the silicon creates a compressive strain in the material (because the Ge atom requires a larger atomic separation) and, as a result, reduces the bandgap of the material. Figure 5.18 shows the schematic diagram of the Ge concentration and associated band structure illustrating this concept. The Ge provides a lower barrier to injection from the emitter to the base as well as an accelerating field through the base. The electrons are injected from the emitter of the device, having a reduced barrier to injection because of the small Ge content at the junction, and then experience an accelerating field from the increasing Ge content deeper into the device [40].

Figure 5.18 Ge concentration (bottom) and band structure (top) of an SiGe heterojunction transistor.

Figure 5.19 shows the SiGe HBT small-signal equivalent circuit model. Compred with the III–V-based HBT model, two additional resistances have been used to model substrate losses. The pad parasitic elements can be determined from Y parameters

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Optoelectronic Integrated Circuit Design and Device Modeling

Figure 5.19 SiGe HBT small-signal equivalent circuit model.

Yijopen ði; j ¼ 1; 2Þ of the open test structure: Cpb ¼

1

oIm Y open þ1 Y open

ð5:100Þ

1

ð5:101Þ

11

Cpc ¼ oIm

open Y22

12

1 open þ Y12

open ImðY12 Þ o 1 Rpb ¼ Re open open Y11 þ Y12 1 Rpc ¼ Re open open Y22 þ Y12

Cpbc ¼

ð5:102Þ ð5:103Þ ð5:104Þ

5.5 MOSFET Modeling Technique The deep submicrometer metal oxide semiconductor field effect transistors (MOSFETs) have shown excellent microwave and noise performance and are very attractive for radio-frequency integrated circuit (RFIC) design. Compared to the III–V compound semiconductor devices (such as PHEMTand HBT), the silicon-based MOSFET offers the advantages of low cost, high integration, and the possibility of a single-chip solution. Nevertheless, the design of radio-frequency (RF) circuits for real products remains a challenge due to strong constraints on power consumption and noise that leave very little margins for the RFIC designers. Therefore, it is crucial to be able to predict accurately the performance of MOS RF circuits in order to reduce design cycles and have first-time success.

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177

Compared with the MOSFET modeling for digital and low-frequency analog applications, the high-frequency modeling of MOSFETs is more challenging. All of the requirements for a MOSFET model in low-frequency application, such as continuity, accuracy, and scale ability of the DC and capacitance models, should be maintained in an RF model.

5.5.1 MOSFET Small-Signal Model Figure 5.20 shows the conventional schematic layout and I/O pads (Figure 5.20(a)) for MOSFET, which consists of a single cell only; in order to minimize the bulk resistance, the guard ring around the device is needed [10, 11]. The corresponding conventional small-signal model is shown in Figure 5.20(b), where Lg , Ld , and Ls represent the inductances of the gate, drain, and source feedline, respectively. The parasitic elements of the pad due to substrate losses are modeled by the capacitors Coxg and Coxd in series with the resistors Rpg and Rpd . Rg models the distributed effect at the gate, while the source and drain resistances Rs and Rd are dominated by the resistance of the lightly doped extensions of the source and drain diffusions. The capacitor Cgs is composed of

Figure 5.20 (a) Conventional schematic layout and (b) small-signal model for MOSFET.

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178

the gate–channel capacitance and the capacitance of the gate–source overlap, whereas the gate–drain capacitance Cgd is mainly due to the gate–drain overlap. Cds is the drainto-source capacitance, gm is the transconductance, gds is the drain conductance, and t is the time delay associated with transconductance. In order to take into account the influence of the lossy Si well/substrate region beneath the drain–bulk junction in Si MOSFETs, a coupling network consisting of a series connection of Cjd and Rsub between the drain and lossy substrate is needed. For 0 V bulk bias, the source and bulk are tied to the ground from the small-signal point of view, and therefore the coupling network is connected between the drain and source. It is also noted that the gate–bulk capacitance is incorporated into the intrinsic gate–source capacitance Cgs . The open-circuit Z parameters of the small-signal equivalent circuit for a single elementary cell can be expressed as follows: Z11 ¼

INT Z11 þ Rs þ Yjd N þ joðLg þ Ls Þ þ Rg INT þ Rs ÞYjd 1 þ ðZ22

ð5:105Þ

Z12 ¼

INT Z12 þ Rs þ joLs INT 1 þ ðZ22 þ Rs ÞYjd

ð5:106Þ

Z21 ¼

INT Z21 þ Rs þ joLs INT 1 þ ðZ22 þ Rs ÞYjd

ð5:107Þ

Z22 ¼

INT Z22 þ Rs þ joðLd þ Ls Þ þ Rd INT 1 þ ðZ22 þ Rs ÞYjd

ð5:108Þ

with Yjd ¼

joCjd 1 þ joRsub Cjd

INT INT INT INT INT INT INT INT N ¼ Z11 Z22 Z12 Z21 þ Rs ðZ11 þ Z22 Z12 Z21 Þ

where ZijINT ði; j ¼ 1; 2Þ are the Z parameters of the intrinsic part (dashed box in Figure 5.21) and can be expressed as INT ¼ Z11

gds þ joðCgd þ Cds Þ M

ð5:109Þ

INT Z12 ¼

joCgd M

ð5:110Þ

INT Z21 ¼

gm ejot þ joCgd M

ð5:111Þ

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179

Figure 5.21 Small-signal equivalent circuit model of MOSFET under the cutoff bias condition: (a) at high frequency; (b) at low frequency.

INT Z22 ¼

joðCgs þ Cgd Þ M

ð5:112Þ

with M ¼ o2 ðCgs Cds þ Cgs Cgd þ Cgd Cds Þ þ jo½gm ejot Cgd þ gds ðCgs þ Cgd Þ The cutoff bias condition for MOSFETs is defined as the condition when gate-tosource and drain-to-source voltages are zero (that is Vgs ¼ 0 and Vds ¼ 0). Under such conditions, the DC current is zero, and hence gm would be extremely small and the device behaves like a passive component (Z12 ¼ Z21 ). Therefore, the equivalent circuit becomes much simpler and the Z parameters are as follows: Z11 ¼

joðCgd þ Cds Þ þ Mc Rs þ Yjd ½1 þ joRs ðCgs þ Cds Þ þ joðLg þ Ls Þ þ Rg Mc þ Yjd ½ joðCgd þ Cgs Þ þ Mc Rs ð5:113Þ

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180

joCgd þ Mc Rs þ joLs Mc þ Yjd ½ joðCgd þ Cgs Þ þ Mc Rs

ð5:114Þ

joðCgd þ Cgs Þ þ Mc Rs þ joðLd þ Ls Þ þ Rd Mc þ Yjd ½ joðCgd þ Cgs Þ þ Mc Rs

ð5:115Þ

Z12 ¼ Z21 ¼

Z22 ¼ with

Mc ¼ o2 ðCgs Cds þ Cgs Cgd þ Cgd Cds Þ After de-embedding the pad parasitic elements, the intrinsic part of the MOSFET equivalent circuit of Figure 5.22 exhibits a pure capacitive behavior at low frequency, with also a corresponding equivalent circuit model.

Figure 5.22 MOSFET small-signal and noise-equivalent circuit model: (a) intrinsic part; (b) extrinsic part.

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5.5.2 MOSFET Noise Model The complete MOSFET small-signal and noise-equivalent circuit model is shown in Figure 5.22 [41]. Figure 5.22(a) shows the intrinsic and Figure 5.22(b) the extrinsic network, respectively. The circuit model comprises the well-known small-signal equivalent circuit and eight noise sources e2pg , e2pd , e2sub , e2g , e2d , e2s , e2gs , 2 . The two uncorrelated current noise sources 2 and i2 represent the internal and ids ds egs

noise sources of the intrinsic MOSFET. These two noise sources are characterized by their mean quadratic value in a bandwidth Df centered on the frequency f, and can be given by the following expressions: e2gs ¼ 4kTg Rgs Df

ð5:116Þ

2 ¼ 4kT g Df ids d ds

ð5:117Þ

where Tg and Td are the equivalent noise temperature of the intrinsic resistance Rgs and output conductance gds , respectively. The six noise sources e2pg , e2pd , e2sub ,e2g , e2d , and e2s represent the noisy behavior of the access resistances Rpg , Rpd , Rsub , Rg , Rd , and Rs , and are simply given by e2i ¼ 4kTo Ri Df ði ¼ pg; pd; sub; g; d; sÞ

ð5:118Þ

where q is the electronic charge, k is Boltzmann’s constant, To is the ambient temperature, and Ri is the resistance value.

5.5.3 Parameter Extraction Methods Accurate extraction of the small-signal equivalent circuit for deep submicrometer MOSFET is extremely important for optimizing the device performance. However, it is not easy to adapt the conventional small-signal models of the III–V compound semiconductor devices and parameter extraction method to MOSFET devices because the substrate is resistive [42]. It is well known that the intrinsic elements can be determined directly after all the extrinsic elements are obtained. However, sometimes only S parameters of the device are available; it is difficult to extract all the extrinsic elements according to the methods mentioned above. Under such a case, a semi-analysis method is very useful [43, 44, 45], where the intrinsic elements are determined by described functions of extrinsic elements. Assuming that the equivalent circuit composed of lumped elements is valid over the whole frequency range of the measurements, the extrinsic elements are iteratively determined using the variance of the intrinsic elements as an optimization

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Optoelectronic Integrated Circuit Design and Device Modeling

criterion. The more detailed procedure follows: 1. Set up the initial value of extrinsic elements. 2. Calculate the intrinsic elements, which can be expressed as the functions of the extrinsic elements as well as frequency: Cgs ¼ f1 ðCoxg ; Cpd ; Coxd ; Lg ; Ld ; Ls ; Rg ; Rd ; Rs ; Rpg ; Rpd Þ

ð5:119Þ

Cgd ¼ f2 ðCoxg ; Cpd ; Coxd ; Lg ; Ld ; Ls ; Rg ; Rd ; Rs ; Rpg ; Rpd Þ

ð5:120Þ

Cds ¼ f3 ðCoxg ; Cpd ; Coxd ; Lg ; Ld ; Ls ; Rg ; Rd ; Rs ; Rpg ; Rpd Þ

ð5:121Þ

gm ¼ f4 ðCoxg ; Cpd ; Coxd ; Lg ; Ld ; Ls ; Rg ; Rd ; Rs ; Rpg ; Rpd Þ

ð5:122Þ

t ¼ f5 ðCoxg ; Cpd ; Coxd ; Lg ; Ld ; Ls ; Rg ; Rd ; Rs ; Rpg ; Rpd Þ

ð5:123Þ

Ri ¼ f6 ðCoxg ; Cpd ; Coxd ; Lg ; Ld ; Ls ; Rg ; Rd ; Rs ; Rpg ; Rpd Þ

ð5:124Þ

gds ¼ f7 ðCoxg ; Cpd ; Coxd ; Lg ; Ld ; Ls ; Rg ; Rd ; Rs ; Rpg ; Rpd Þ

ð5:125Þ

For convenience, the function f can be expressed as follows: fk ¼ fk ðoi ; Zext Þ

ði ¼ 0; 1; . . . ;7Þ

ð5:126Þ

where Zext represent the extrinsic elements, oi is the angular frequency. Setup error criteria are as follows: 2 N 1 N 1 X X 1 k fk ðoi ; Zext Þ e1 ðZext Þ ¼ fk ðoi ; Zext Þ N1 i¼0 i¼0 2 XXX c m e2 ðZext Þ ¼ Wpq Spq ðoi ; Zext ÞSpq ðoi Þ ðp; q ¼ 1; 2Þ

ð5:127Þ

ð5:128Þ

where Scpq ðoi ; Zext Þ represent the calculated S parameters and Sm pq ðoi Þ represent the measured S parameters. 3. If error criteria are small enough, the iterative process will be over. Although all the extrinsic and intrinsic elements can be determined from full-analysis methods, the extracted elements still may have a small variation with respect to frequency due to measurement and numerical calculation errors. In order to obtain the optimum values, constrained optimization is needed. First, initial extrinsic elements are extracted from the pinchoff condition S parameters; then the values of intrinsic elements are determined from Y parameters that subtracted extrinsic elements. The

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above element values are regarded as the initial values for optimization, and the variations range of elements is a dispersion of the initial values.

5.6 Summary In this chapter, we introduced the basic physical structure and operational concept of FET, HBT, and MOSFET devices. The small-signal, large-signal and noise modeling and parameter extraction methods are described.

References 1. Washio, K. (1999) SiGe HBTs and ICs for optical-fiber communication systems. Solid-State Electronics, 43, 1619–1625. 2. Lunardi, L. (1999) Herterostructure circuit applications in optical communications. Solid-State Electronics, 43, 1627–1632. 3. Emura, K. (1999) Technologies for making full use of high-speed IC performance in the development of 40 Gb/s optical receiver. Solid-State Electronics, 43, 1613–1618. 4. Feng, M., Shen, S.-C., Caruth, D. C., and Huang., J.-J. (2004) Device technologies for RF front-end circuits in next-generation wireless communications. Proceedings of the IEEE, 92(2), 354–375. 5. Burns, L. M. (1995) Application for GaAs and silicon integrated circuit in next generation wireless communication systems. IEEE Journal of Solid-State Circuits, 30, 1088–1095. 6. Esson, S. D. (1996) SiGe stretches limits of silicon application. Microwave and RF, 35(12), 89–96. 7. Halchin, D. and Golio, M. (1997) Trends and portable wireless applications. Microwave Journal, 40(1), 62–68. 8. Bailey, M.J. (1997) PHEMT devices offer high power density and efficiency. Microwave & RF, 32(6), 61–70. 9. Case, M. (1997) SiGe MMIC and flip-chip MICs for low cost microwave systems. Microwave Journal, 40(5), 264–276. 10. Lum, E. J. (1997) GaAs technology rides the wireless wave. IEEE GaAs IC Symposium, 11–14. 11. Moniz, J. M. (1997) Is SiGe the future of GaAs for RF application? IEEE GaAs IC Symposium, 229–232. 12. Wang, N. L. (1998) Transistor technology for RFICs in wireless application. Microwave Journal, 41(2), 98–110. 13. Larson, L. E. (1998) Integrated circuit technology options for RFICs present status and future directions. IEEE Journal of Solid-State Circuits, 33(5), 387–399. 14. Kobayashi, K. W. (1998) InP-based HBT technology for next-generation lightwave communications. Microwave Journal, 41(6), 22–38. 15. Costa, D., Liu, W. U., and Harris, J.S. (1991) Direct extraction of the AlGaAs/GaAs heterojunction bipolar transistors small-signal equivalent circuit. IEEE Transactions on Electron Devices, 38(9), 2018–2024. 16. Gao, J., Li, X., Wang, H., and Boeck, G. (2005) A new method for determination of parasitic capacitances of PHEMTs. IOP Semiconductor Science and Technology, 20(6), 586–591. 17. Gao, J., Law, C. L., Wang, H., and Aditya, S. (2002) An approach for extracting small signal equivalent circuit of double heterojunction d-doped PHEMTs for millimeter wave applications. International Journal of Infrared and Millimeter Wave, 23(3), 345–364. 18. Gao, J., Law, C. L., Wang, H., and Aditya, S. (2002) An improved pinchoff equivalent circuit model for determining small-signal model paremeters of double heterojunction-doped pHEMTs. International Journal of Infrared and Millimeter Waves, 23(11), 1611–1626.

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19. Gao, J., Law, C. L., Wang, H., and Aditya, S. (2002) An approach to linear scalable DH-PHEMT model. International Journal of Infrared and Millimeter Waves, 23(12), 1787–1801. 20. Gao, J. (2005) An approach for determining PHEMT small-signal circuit model parameters up to 110GHz. International Journal of Infrared and Millimeter Waves, 16(7), 1017–1012. 21. Gao, J., Law, C. L., Wang, H., and Aditya, S. (2003) A submicron PHEMT nonlinear model suitable for low current amplifier design. International Journal of Electronics, 90(7), 433–443. 22. Gao, J., Law, C. L., Wang, H., et al. (2003) A new method for PHEMT noise parameter determination based on 50-O noise measurement system. IEEE Transactions on Microwave Theory and Techniques, 51(10), 2079–2089. 23. Statz, H., Newman, P., Smith, I. W., et al. (1987) GaAs FET device and circuit simulation in SPICE. IEEE Transactions on Electron Devices, 34(2), 160–169. 24. Curtice, W. R. (1980) A MESFET model for use in the design of GaAs integrated circuits. IEEE Transactions on Microwave Theory and Techniques, 28(5), 448–456. 25. Curtice, W. R. and Ettenberg, M. (1985) A nonlinear GaAs FET model for use in the design of output circuits for power amplifiers. IEEE Transactions on Microwave Theory and Techniques, 33(12), 1383–1394. 26. van der Ziel, A. (1962) Thermal noise in field-effect transistor. Proceedings of the IRE, 50, 1808–1812. 27. Pucel, R. A., Haus, H. A., and Statz, H. (1975) Signal and noise properties of GaAs microwave FET, in Advances in Electronics and Electron Physics, vol. 38 (ed. L. Morton), Academic Press, New York. 28. Cappy, A. (1988) Noise modeling and measurement technique. IEEE Transactions on Microwave Theory and Techniques, 36(1), 1–10. 29. Pospieszalski, M. W. (1989) Modeling of noise parameters of MESFETs and MODFETs and their frequency and temperature dependence. IEEE Transactions on Microwave Theory and Techniques, 37(9),1340–1350. 30. Heymann, P. (1999) Experimental evaluation of microwave field-effect-transistor noise models. IEEE Transactions on Microwave Theory and Techniques, 47(2), 156–163. 31. Li, X., Gao, J., and Boeck, G. (2006) Microwave noise modeling for A1GaAs/InGaAs/GaAs PHEMTs. Microwave Journal, 49(12), 94–106. 32. Liu, W. (1998) Handbook of III–V Heterojunction Bipolar Transistors, John Wiley & Sons, Inc. 33. McMacken, J., Nedeljkovic, S., Gering, J., and Halchin, D. (2008) HBT modeling. IEEE Microwave Magazine, 48–72. 34. Tiwari, S. and Frank, D. J. (1989) Analysis of the operation of GaAlAdGaAs HBTs. IEEE Transactions on Electron Devices, 36(10), 2105–2121. 35. Dikmen, C. T., Dogan, N. S., and Osman, M. A. (1994) DC modeling and characterization of AlGaAs/GaAs heterojunction bipolar transistors for high-temperature applications. IEEE Journal of Solid-State Circuits, 29(2), 108–106. 36. Hafizi, M. E., Crowell, C., and Grupen, M. E. (1990) The DC characteristics of GaAs/AlGaAs heterojunction bipolar transistors with application to device modeling. IEEE Transactions on Electron Devices, 37(10), 2121–2129. 37. Gao, J., Li, X., Wang, H., and Boeck, G. (2004) Microwave noise modeling for InP/InGaAs HBTs. IEEE Transactions on Microwave Theory and Techniques, 52(4), 1264–1272. 38. Gao, J., Li, X., Wang, H., and Boeck, G. (2005) An approach for determination of extrinsic resistances for metamorphic InP/InGaAs HBT equivalent circuit model. IEE Proceedings – Microwaves, Antennas and Propagation, 152(2), 195–200. 39. Gao, J., Li, X., Wang, H., and Boeck, G. (2005) An improved analytical method for determination of small signal equivalent circuit model parameters for InP/InGaAs HBTs. IEE Proceedings – Circuit, Device and System, 152(6), 661–666. 40. Dunn, J. S., Ahlgren, D. C., and Coolbaugh, D. D. (2003) Foundation of RF CMOS and SiGe BiCMOS technologies. IBM Journal of Research and Development, 47(2/3), 101–137. 41. Gao, J. and Werthof, A. (2009) Scalable small-signal and noise modeling for deep-submicrometer MOSFETs. IEEE Transactions on Microwave Theory and Techniques, 57(4), 737–744.

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42. Gao, J. and Werthof, A. (2009) Direct parameter extraction method for deep submicrometer metal oxide semiconductor field effect transistor small signal equivalent circuit. IET Microwaves Antennas and Propagation, 3(4), 564–571. 43. Shirakawa, K., Oikawa, H., Shimura, T., et al. (1995) An approach to determining an equivalent circuit for HEMTs. IEEE Transactions on Microwave Theory and Techniques, 43(3), 499–503. 44. Yanagawa, S., Ishihara, H., and Ohtomo, M. (1996) Analytical method for determining equivqlent circuit parameters of GaAs FETs. IEEE Transactions on Microwave Theory and Techniques, 44(10), 1637–1641. 45. Wang, Q. and Gao, J. (2008) An approach for determination of MOSFET small signal model. Microwave Journal, 51(10), 128–136.

6 Semiconductor Laser and Modulator Driver Circuit Design In high-speed optical communication systems, the laser diode and modulator driver is one of the key components in the transmitter, where it performs the interface between high-speed electronics and the laser diode or modulator. In this chapter, we will introduce the basic concepts of the transmitter, which includes the optical modulation and optical transmission; the emphasis will be the integrated circuit design techniques of the laser diode and modulator driver for the direct modulation and external modulation systems.

6.1 Basic Concepts The simple schematic diagram in Figure 6.1 consists of an optical transmitter and receiver connected by a length of optical cable in a point-to-point link. The optical transmitter converts electronic signal voltage into optical power, which is launched into a fiber by a light-emitting diode (LED) and laser diode (LD). Semiconductor lasers or light-emitting diodes are used as optical sources because of their compatibility with the optical fiber communication channel, as discussed in detail in Chapters 2 and 3. In optical fiber communication systems, data are transmitted as light energy over optical fibers. Figure 6.1 shows the signal transmission in the optical transmitter, where the electrical pulse signal (bit rate is 1=Tb ) is the input of the transmitter and an attenuated signal with distortion will arrive at the end of the optical fiber.

Optoelectronic Integrated Circuit Design and Device Modeling Jianjun Gao Ó 2011 Higher Education Press

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Figure 6.1 Signal transmission in optical transmitter.

6.1.1

NRZ and RZ Data

In principle, the capacity of optical communication systems can exceed 10 Tb/s (1 T ¼ 1012 b/s) because of the large frequency associated with the optical carrier. In practice, the bit rate is limited by the dispersive and nonlinear effects and by the speed of electronic components for single-channel transmission. Therefore, normally, the optical transceiver begins with a high-speed multiplexer (MUX), used to concentrate a number of lower speed signals into one high-speed bit stream. For instance, a 40 Gb/s channel would be implemented by multiplexing four existing 10 Gb/s channels together into a 40 Gb/s data stream; an OC-192 (10 Gb/s) channel would be implemented by multiplexing four existing OC-48 (2.5 Gb/s) channels together into a 10 Gb/s data stream (see Figure 6.2). Channel multiplexing can be achieved in the time or the frequency domain through time-division multiplexing (TDM) and

Figure 6.2

A 4 : 1 high-speed multiplexer for (a) 10 Gb/s and (b) 40 Gb/s transmission.

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frequency-division multiplexing (FDM) or wavelength-division multiplexing (WDM), respectively. In order to convey information on an optical wave, it is necessary to modulate a property of the wave in accordance with the information signal. The wave property may be its intensity, frequency, polarization, or direction. Both analog and digital formats are suitable for optical modulation. In this manner, digital signals, which are subjected to intensity modulation (IM), are simply differentiated as ones having intensity higher than a predetermined reference level and ones having intensity lower than the predetermined reference level. Most deployed fiber-optic systems in telecommunications use simple binary amplitude modulation, otherwise known as ON-OFF keying (OOK); that is the data are represented by ‘1’s and ‘0’s. In this scheme every digit ‘1’ is represented by a highamplitude value of the carrier and every digit ‘0’ by a zero amplitude of the carrier. There are two choices for the modulation format of the resulting optical bit stream: return-to-zero (RZ) and nonreturn-to-zero (NRZ) formats. In the NRZ modulation format, a sequence of ‘1’s is transmitted without the light level falling back to its zero level in between each bit. Return-to-zero (RZ) does exactly what it says – with the light level always falling back to its zero level in between bits, even in a succession of ‘1’s. One of the major differences between the NRZ and RZ pulse sequences is the bandwidth requirement. In contrast to NRZ data, RZ waveforms occupy about twice as much bandwidth as NRZ data (as shown in Figure 6.3). The bandwidth requirements for NRZ and RZ data can be expressed approximately as

Figure 6.3

NRZ and RZ formats and their spectra.

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BW

1=Tb ; 2=Tb ;

NRZ RZ

ð6:1Þ

Thus, the bandwidth requirements for RZ are more severe than those for NRZ, which is also expected since pulses in the RZ format are narrower than pulses in the NRZ format. For example, a 10 Gb/s system would need 20 GHz in the RZ format, whereas the same signal would require only 10 GHz in the NRZ format. Most fiberoptic communication systems today use NRZ schemes for communication.

6.1.2

Optical Modulation

There are two methods and three types of device available for the transmission of 10–40 Gb/s data over optical fiber: direct modulation with laser diodes and indirect modulation (also called external modulation) with either electroabsorption (EA) or Mach–Zehnder (M–Z) modulators. Direct modulation is used predominantly for single-channel time-division multiplexing (TDM) transmission over relatively short distances, whereas indirect modulation is required for dense wavelength-division multiplexing (DWDM), due to the lower spectral width that can be achieved. The M–Z modulator provides the best performance in this respect, but is also the most costly of the three devices. Direct optical modulators modulate the optical wave as it is generated at the source. In direct modulation, a current that activates a semiconductor laser is turned on and off directly by the ‘0’s and ‘1’s of a data signal to control the emission and extinction of the laser beam. At bit rates of 10 Gb/s or higher, the frequency chirp imposed by direct modulation becomes large enough that direct modulation of semiconductor lasers is rarely used. When chirping is caused by direct modulation, propagation velocity fluctuates, waveforms are distorted during propagation through the optical fiber, and it becomes difficult to perform long-distance transmission and transmission at high speed. This increase is not very significant at bit rates of 2.5 Gb/s, but for higher bit rates, such as 10 and 40 Gb/s, it can affect the repeater spacing considerably. The external optical modulation by an optical modulator, such as an electroabsorption modulator, is emerging as a promising scheme for long-haul optical transmission, because it has smaller optical frequency chirping characteristics than the direct modulation using a laser diode and has a large tolerance for optical fiber dispersion. In external modulation, a laser diode emits light continuously and the emitted light is turned on and off by the ‘1’s and ‘0’s of data using an external modulator. With external modulation, the optical source is operated continuously and its output light is modulated using an optical external modulator. The basic link topologies using direct and external (or indirect) modulation are shown in Figure 6.4. Table 6.1 gives the comparison of direct and external modulations. In direct modulation, the RF signal modulates the intensity of the optical output

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Figure 6.4 Direct and external modulation configurations: (a) direct modulation; (b) external modulation. Table 6.1 Comparison of direct and external modulations. Parameters

Direct modulation

External modulation

Optical source External modulator Bit rate Chirp Output of driver Complexity and cost

Yes No Low Large Current signal Low

Yes Yes High Small Voltage signal High

of the laser directly. All directly modulated links use diode lasers, since this is the only type that at present offers sufficient bandwidth in a simple modulation interface. In an externally modulated link, the laser operates continuous wave (CW), with the intensity of its optical output modulated by the application of the RF signal to the modulator. Since modulation does not occur at the laser, in theory any laser of the appropriate wavelength can be used as a source.

6.1.3 Optical External Modulator The main requirements of an optical modulator in a optical fiber communications system are [1]:

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Low insertion loss Broad modulation bandwidth Low drive voltage Large extinction ratio (ratio between intensity when light ON and light OFF) Low wavelength chirp.

In a 40 Gb/s optical communications system, the broad modulation bandwidth and low chirp characteristics are especially important. The optical modulator is an optoelectronic device that provides a modulated optical signal at the output driven by an electrical command when a continuous input beam is provided at the input. Performances of different optical modulators can be compared in terms of the insertion loss (IL) and extinction ratio (ER), given by the following relations PIN, PON, and POFF, defined in Figure 6.5 [2]: PON IL ¼ 10 log ð6:2Þ PIN PON ER ¼ 10 log POFF

ð6:3Þ

Figure 6.5 Optical external modulator operating principle.

Figure 6.6 shows an application map in terms of the transmission distance and system capacity (that is the product of the channel rate and the channel number) for the three conventional types of optical modulators: the directly modulated distributedfeedback laser diode (DFB-LD), the EA external modulators, and the lithium niobate (LiNbO3) M–Z external modulators [3]. These modulators’ application areas are determined by their bandwidth, chirping, and wavelength-dependence characteristics. The EAMs can be used for 2.5 or 10 Gb/s systems over distances of several hundred kilometers, while the M–Z modulators can generate high-bit-rate signals with low chirp. In the following, the operation mechanism of M–Z modulators will be briefly introduced.

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Figure 6.6

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Application map for optical modulators.

The M–Z modulator consists of an input Y-branch, two arms with independent drive electrodes, and an output Y-branch; the corresponding structure is shown in Figure 6.7. The two single-mode waveguides usually have one arm (arm one) under no electric field and the other arm (arm two) under an electric field. The electric field is often applied in the transverse direction because the longitudinal electric field requires a much higher magnitude to achieve the switching operation. The refractive index of electrooptical materials such as LiNbO3 can be changed by applying an external voltage. In the absence of external voltage (that is 0 V, as shown in Figure 6.7(a)), the optical fields in the two arms of the M–Z interferometer experience identical phase shifts and interfere constructively. The additional phase shift introduced in one of the arms through voltage-induced index changes destroys the constructive nature of the interference and reduces the transmitted intensity. In particular, no light is transmitted when the phase difference between the two arms equals p, because of destructive interference occurring in that case (as shown in Figure 6.7(b)). As a result, the electrical bit stream applied to the modulator produces an optical replica of the bit stream. The expression for the output light intensity, Po , as a function of the driving voltage, V, is [4] j 2 pV Po ¼ Pi cos þ ð6:4Þ 2Vp 2 where Pi is the input optical power, Vp ¼ p=ðklÞ is the voltage required to change Po from its maximum value to its minimum value, l is the active electrode length, k is

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Figure 6.7 M–Z modulator operating principle: (a) no electric field is applied on the electrodes; (b) maximum electric field is applied on the electrodes.

a constant representing the electrooptical coefficient, wavelength dependence, refractive index, and other geometrical constants, and j is a static phase shift that may be present due to slight asymmetry in the interferometer arms. Typically, for EA modulators, the required drive level is 3.5 Vp-p, for GaAs-based M–Z modulators, the drive level is 5 V, and a typical drive level for LiNbO3 modulators may be as high as 6 V.

6.2 Optoelectronic Integration Technology Technologies for integrating optoelectronic devices and electronic circuitry can be classified as either hybrid or monolithic, that is monolithic optoelectronic integrated

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circuits (MOEICs) and hybrid optoelectronic integrated circuits (HOEICs). Both technologies are playing an important role in optical communication systems, signal processing, and sensing.

6.2.1 Monolithic Optoelectronic Integrated Circuits MOEICs incorporate electronic circuits and optical devices (such as lasers, photodetectors, and modulators) on a single semiconductor chip. There are a variety of advantages of the OEIC with respect to existing discrete elements [5, 6, 7, 8, 9, 10, 11]: 1. OEICs can integrate a large number of elements and so show the feasibility of incorporating complicated signal processing functions and by extension to multiplying those circuit channels on a single chip. The ease of arranging these circuits and devices on a single chip can open an opportunity of applying optoelectronic devices to multichannel systems. 2. The speed and noise performance of optoelectronic devices can be significantly improved by the integration due to the reduction of parasitic reactances. These parasitic elements can be eliminated by the integration, and a flat response characteristic up to the limit of the laser relaxation oscillation frequency can be realized. Furthermore, the reliability of the finished components is enhanced over hybrid versions as the number of wire bonds and related mechanically weak points in the circuit are reduced. 3. The chip size can be significantly reduced. This advantage is truly important for applications where optoelectronic components are required or where the highspeed capabilities of optoelectronic devices allow for significant reduction of interconnect lines, which also results in lower packaging costs and improved noise immunity. There are two types of commonly used OEIC: GaAs-based OEIC and InP-based OEIC. The GaAs-based OEIC uses GaAs as a substrate and has been studied for short-wavelength (0.8–0.9 mm) systems. The InP-based OEIC is the choice for longwavelength (1.3–1.6 mm) systems and uses an InP substrate. Figure 6.8 shows an example of the monolithic integration of a MESFET and an ion-implanted laser on a semi-isolation (SI) GaAs substrate [12]. The transistor is formed on an n-type GaAs layer, which has been epitaxially grown on an SI substrate. Current flows through the laser and the transistor, which are connected in series, and is modulated by the gate voltage. The MESFET can be used to modulate an injection laser simply by connecting the two in series and applying a driving signal to the Schottky gate electrode. Figure 6.9 shows another example of the monolithic integration of on an SI–GaAs substrate [13]. This circuit incorporates a laser and three field effect transistors (FETs), one of which is used as a photodetector. These works are the earliest ones to demonstrate the feasibility

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Figure 6.8 Monolithic integration of a Be-implanted laser and a MESFETon the same SI substrate.

Figure 6.9

Optical repeater monolithically integrated on an SI-GaAs substrate.

of the OEIC approach to add more sophisticated functions than simply converting optical signals into electrical ones and vice versa. The commonly used integration formats of high-speed electronic transistors and optical devices for a high-speed transmitter are as follows: 1. Buried heterostructure semiconductor lasers with MESFETs 2. Buried heterostructure semiconductor lasers with HBTs

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3. Quantum lasers with MESFETs 4. Quantum lasers with HEMTs 5. Quantum lasers with HBTs.

6.2.2 Hybrid Optoelectronic Integrated Circuits Although monolithic integration offers significant advantages over hybrid circuits in compactness, reliability, possible performance improvements resulting from reduced parasitics, and potentially significant reductions in cost, particularly in the case of arrays. However, OEICs are more complex than monolithic microwave integrated circuit (MMICs), because the structures of optical components; lasers, LEDs, and photodetectors are quite different and not compatible with the requirements for other electronic devices (such as field effect transistors and bipolar transistors). They require planar and vertical structures; hence multistep wafer processing is necessary and this leads to high costs and low yields. OEICs are also limited in their uses, since nonsemiconductor components cannot be incorporated monolithically. In contrast, HOEICs offer the option of combining optoelectronic, electronic, and optical components that are optimized with the most efficient design in the most appropriate material. The substrate typically is ceramic or silicon, with conductive patterns formed by electroplating, deposition, or other techniques. Unlike OEICs, hybrid designs do not constrain the subsystem designer to work within one material system and can incorporate nonsemiconductor components such as optical fibers, interconnection components, microlenses, and so on. Hybrid integration offers an immediate solution to certain OEIC needs, and it may always be the technology of choice when many different kinds of devices need to be combined. The commonly used hybrid integration techniques involve the following [9, 14]: 1. Wire bonding technology 2. Microsolder bump bonding technology 3. Microwave photonic multichip module technology. Wire bonding is widely used in the hybrid integration of optical and electrical devices. Figure 6.10 shows a typical construction of hybrid integration by conventional wire bonding. However, the bonding wires have prevented these devices from achieving their full potential because the large inductance of the wire limits the modulation rate of the LDs. For example, when the laser is wire-bonded in a conventional package, it suffers from having an inductance of 1–3 nH and a capacitance of 0.01–0.1 pF, which produce a resonant blocking of the signal for driving the laser in the gigahertz region.

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Figure 6.10 Conventional structure of a hybrid integration of LD and driver.

One way to overcome this problem is microsolder bump bonding technology. Figure 6.11 shows the corresponding structure for integration of an LD and driver. The LD chip and a driver chip are bonded on to the substrate by the microsolder bumps. The electrical interconnection is achieved by the bumps and the microstrip on the substrate.

Figure 6.11 Integration of LD and driver using microsolder bump bonding.

Figure 6.12 shows a conceptual diagram of an optical transceiver module using the microwave photonic multichip module technology known as opto-GMIC (optoelectronic glass microwave integrated circuit) [14]. The glass layer serves as the microwave dielectric, while the silicon layer provides the necessary mechanical support and creates an integral carrier. A gold film between the two carries the ground currents to minimize losses. Semiconductors can be mounted to the silicon through holes in the thin glass layer. Opto-GMIC can accommodate optical, optoelectronic, and microwave components, along with passive matching and bias networks on a single glass silicon platform. GMIC offers a high level of integration and can greatly improve the device density of the integrated circuit, using traditional hybrid techniques to simply combine packaged devices on a ceramic substrate.

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Figure 6.12 Transceiver concept using microwave photonic multichip module technology.

Laser driver ICs for driving a laser diode with a large current swing were reported using GaAs MESFETs, AlGaAs/GaAs doped-channel hetero-MISFETs (DMTs), high electron mobility transistors (HEMTs) and InP/InGaAs heterojunction bipolar transistors (HBTs). The laser driver can be operated at 2.5 Gb/s and 5 Gb/s using MOEIC technology and 6–10 Gb/s for HOEIC technology. Table 6.2 shows the comparison of the MOEIC and HOEIC laser drivers under direct modulation [15, 16, 17, 18].

Table 6.2 Comparison of MOEIC and HOEIC transmitter design. Optical device

Transistor

Integration

Bit rate

MQW LD DFB-LD MQW-LD FP-LD DFB-LD

GaAs MESFET GaAs MISFET GaAs HBT HBT IC GaAs MESFET

MOEIC MOEIC MOEIC HOEIC HOEIC

2 Gb/s 4 Gb/s 5 Gb/s 6 Gb/s 10 Gb/s

6.3 Laser Driver Circuit Design Among the elements consisting of optical systems, a laser driver (LD) is one of the key components needed to generate the high-current, high-speed signal required for driving a transmitter. The laser driver is actually an optical modulation circuit for the laser, but of course it should be in the direct modulation system. The optical signal generated by a laser can be modulated by the RF signal through the laser driver. The laser driver must provide a large modulation current, together with fast rise and fall times. For the development of the high-speed driver, a differential topology was employed to stabilize current ripple in the power supply lines, which would otherwise

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corrupt the laser output. The differential design minimizes the simultaneous switching noise by using parallel but inverted signal paths with subsequent subtraction of the two signals. The most commonly used laser driver circuits are emitter-coupled logic (ECL) for a bipolar transistor and source-coupled FET logic (SCFL) for field effect transistors. ECL using bipolar technology is generally used in applications where switching speed is more important than power dissipation and cost. With the achievement of low power, high speed, as well as high density, ECL technology is expected to be used widely in various high-performance digital circuits. A key advantage of the ECL circuit configuration is its ability to operate reliably at low voltage swings. High-speed operation is featured in the SCFL due to the following reasons [19, 20]: 1. The gate–drain capacitance is essentially small because the drain voltage at the ‘on’ state is designed to be higher than for any other logic (such as buffered FET logic (BFL), Schottky diode FET logic (SDFL), and direct-coupled FET logic (DCFL)). 2. The cascade of differential pairs can be directly connected to one another without interstage coupling capacitors. 3. The discharging time of the differential amplifier outputs is short because the discharging current is dominated by the current in the saturation region of the FET. 4. The fanout capability is excellent because the source–follower buffers enable quick charging-up into the load capacitors. 5. The nonuniformity of the threshold voltage of the FET across the wafer can be ignored by controlling the input and reference voltages. Figure 6.13 shows the typical laser driver schematic circuit diagram using SCFL and ECL. With the constant-current source as shown, the laser can be placed arbitrarily in the drain (or collector) lead. The peak modulation current is set by Vp and the base voltage marked Vb can be used for DC biasing the laser. The laser current is the sum of the drain (or collector) currents of transistor Q2 (drive current) and transistor Q4 (the bias). Since Q1 and Q2 form a nonsaturating currentrouting switch, Q2 is always in its active region and its switching action is unaffected by the presence of Q3 . When the input voltage Vsig is applied to Q1 in the differentia1 amplifier, the voltage Vsig is compared to the fixed reference voltage Vref (Vref normally sets the logic threshold level) applied to Q2 , so that either Q1 or Q2 can turn ‘on’ in a current mode depending on whether Vsig is higher or lower than the reference voltage Vref ; that is, when Vsig is higher than Vref , the current mostly flows through Q1 , when Vsig is lower than Vref , the current mostly flows through Q2 , and when Vsig is equal to Vref , the same magnitude of the current flows through Q1 and Q2 . The corresponding current through

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Figure 6.13 Typical laser driver schematic circuit diagram: (a) SCFL; (b) ECL.

the laser can be expressed as follows: 8 Ip þ Ib ; > > < I Im ¼ Ib þ p ; > 2 > : Ib ;

Vsig < Vref Vsig ¼ Vref

ð6:5Þ

Vsig > Vref

As mentioned in Chapters 2 and 3, the frequency chirp increases with the increase of bias and modulation current level. Therefore the bias current of the laser should be closed to threshold, 1.0–1.1 Ith (as shown in Figure 6.14). At the input the laser diode driver interfaces to gigabit electronics, for which ECL levels (0.9 V, 1.8 V) and SCFL levels (0 V, 1 V) are the most widely accepted input/output (I/O) levels, normally a pair of buffers are necessary to adjust the voltage levels to optimize the bias point. At the output the laser diode driver interfaces to a laser diode, and by making the modulation current adjustable in the 0–60 mA range most commercially available laser diodes capable of operating at gigabit per second bit rates

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Figure 6.14 Idealized laser input and output waveforms: (a) input pulse of laser (or driver output); (b) output of laser.

can be modulated to utilize the maximum available optical on/off ratio. Therefore, the laser driver must be designed to drive different laser modules with different modulation currents. Traditionally, the laser diode can be connected directly to a differential pair due to the fact that the small signal impedance of the intrinsic laser is very small and can be regarded as a short circuit (for example FP, DFB, and QW lasers). However, as the modulation frequency extends into the upper microwave and millimeter-wave frequencies, the feeding transmission lines and parasitic effects due to the chip and package geometry of the laser module will have a significant influence on the impedance, and cause the differential driver to no longer be symmetrical and the bandwidth of the circuit to be limited. This makes the differential driver difficult to handle short electrical pulses in timescales of pico- or femtoseconds, as required for high-speed optoelectronics. Therefore, matching the circuit between the laser driver and driver is necessary, especially at high frequencies. One way to achieve the matching is to match the laser diode to a 50 O system. Four kinds of matching network have been developed to match the impedance to the low laser impedance: 1. Series resistor matching network. In order to minimize spurious reflections, it is common practice to introduce a 45–48 O resistor physically close and in series with the laser, matching the impedance of the load but dissipating most of the available electrical power (as shown in Figure 6.15(a)). For example, if the input impedance of the laser is 2 O, the series resistance is 48 O. The power delivered to the laser diode is less than 4 % of the input drive, which is a large loss of power. 2. Chebyshev bandpass matching network [21]. Chebyshev impedance transforming networks employ low-pass elements designed to provide a pseudo-bandpass response. The lowpass topology of these networks provides a distinct advantage for laying out microwave lumped and semi-lumped bandpass filters (as shown in Figure 6.15(b)). It is noted that lumped elements are used for frequencies up to 3–5 GHz. 3. Transmission line matching network [22]. Matching circuits may be composed of either lumped or distributed elements. Distributed circuit elements are suitable

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203

Figure 6.15 Impedance matching circuits of laser diode for a 50 O system: (a) series resistor; (b) lumped elements network; (c) transmission line; and (d) coplanar waveguide.

for high-frequency ranges while the lumped network for low-frequency ranges. For a wider bandwidth, Butterworth and Chebyshev polynomials are the common choice of approximation functions to realize multisection or taper matching transformers. Figure 6.15(c) shows a three-step Chebyshev transformer that

204

Optoelectronic Integrated Circuit Design and Device Modeling

matches 50 O to 2 O at a center frequency of 10.5 GHz with a bandwidth of about 9 GHz. In order to avoid making the transmission line very wide, two additional capacitances are needed. 4. Coplanar waveguide (CPW) matching network [23]. The matching network is formed by different coplanar waveguide configurations (as shown in Figure 6.15 (d)). At the input end, a standard 50 O CPW is used. The separation between the center strip and the semi-ground planes is reduced along the structure in order to obtain a 5 O impedance at the output end. Compared with the series resistor matching network, clearly the other three passive matching networks should be very advantageous to drive the laser in an impedance matched circuit and make full use of the electrical power available. Alternatively, matching between the driver and laser diode can be achieved by using a 25 O subsystem [24]. The 25 O subsystem means that the output impedance of the driver and the input impedance of laser module (which is composed of the matching network and laser diode) are equal to 25 O. The interconnection scheme between the driver and laser is shown in Figure 6.16. The LD is driven through the transmission line with the impedance matching load; the bias current is also supplied through it. The LD driver has a dummy load consisting of a series load and biased level shift diodes.

Figure 6.16 Interconnection scheme between LD and LD driver.

The different semiconductor technologies (such as MESFETs, HEMTs, HBTs, and Si-BJTs) can be used to achieve the high-bit-rate laser driver. Table 6.3 gives a summary of the driver and compares the corresponding figures of merit such as bit rate, modulation current, and rise/fall time [24, 25, 26, 27, 28, 29, 30, 31].

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Table 6.3 High-bit-rate laser driver using different semiconductor technologies. Semiconductor technology Si-BJT IC HBT IC HFET IC MESFET IC

Bit rate (Gb/s)

Modulation current (mA)

Rise/fall time (ps)

3 5 10 10

50 35 60 80

200 100 40 50

6.4 Modulator Driver Circuit Design Unlike laser driver ICs for driving a laser diode with a large current swing, the function of a modulator driver is to provide the required voltages for external modulation. It must have both high-speed operation and a large drive voltage swing to ensure a sufficient extinction ratio. Furthermore, the external modulators are inherently nonlinear devices with input impedance dependent on the operating conditions. In order to prevent multiple reflections, which can affect both extinction ratio and jitter, the output impedance of the driver should closely match that of the transmission line connecting the driver to the modulator. Figure 6.17 shows a block diagram of the modulator driver IC, which mainly consists of an input buffer stage, differential amplifier stage, and output buffer stage. It is noted that the differential amplifier stage could be cascaded, with AC coupling, to produce a multistage amplifier with higher gain. However, for an SCFL circuit, the bandwidth would be reduced substantially due to the heavy capacitive loading of the succeeding stage’s gate capacitance. The capacitive loading is greatly reduced by use of a buffer circuit, as shown in Figure 6.18(a). In addition to the buffering provided by the source follower FET, the level shifting is provided by several diodes and their associated series resistance (no level shifting occurs in the source–follower, since it is the same size as the current source and thus operates Vgs ¼ 0 V).

Figure 6.17 Block diagram of the modulator driver IC.

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Optoelectronic Integrated Circuit Design and Device Modeling

Figure 6.18 Buffer/level shift circuit and equivalent circuit model: (a) buffer/level shift circuit; (b) equivalent circuit model at low-frequency ranges.

The corresponding equivalent circuit model of a buffer circuit neglecting the effect of the diode at low-frequency ranges is shown in Figure 6.18(b). The gain of the buffer/level-shift stage is roughly approximated by the usual source–follower formula [32]: Gbuf ¼

gm gm þ 2gds

ð6:6Þ

The voltage gain of the buffer circuit is less than unity because the denominator of the expression is larger than the numerator. When the input voltage changes, the output voltage changes by almost the same amount and in the same direction; therefore the buffer circuit is noninverting. In general, the output impedance of the buffer circuit is much lower and the input impedance is much higher than those of other FET single stages. Therefore it can be used as an isolation stage between amplifier stages. The high-speed optical modulator driver IC can be fabricated in many different semiconductor process technologies. The published studies of the noise properties of the modulator driver IC may be divided into three distinctive groups: 1. FET-based modulator driver IC. This kind of IC is based on a III–V compound semiconductor MESFET and HEMT device. 2. Bipolar transistor-based modulator driver IC. The corresponding semiconductor processes include a Si-BJT, SiGe HBT, and III-V compound semiconductor HBT. 3. MOSFET-based modulator driver IC. With deep submicrometer CMOS technology, these devices have a cutoff frequency exceeding 100 GHz. To obtain sufficient switching characteristics of an optical signal, driver circuits for the modulator are normally required to supply a voltage swing greater than 3 Vp-p. There is also a strong demand for driver ICs with low power dissipation to enable the design of an air-cooled system.

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6.4.1 FET-Based Driver Circuit With fast growth in the RF wireless communications market, the demand for highperformance but low-cost RF solutions is rising. This advanced performance of FETs (for example MESFET and HEMT) is attractive for high-frequency circuit design in view of a system-on-a-chip realization, where digital, mixed-signal baseband, and RF transceiver blocks would be integrated on a single chip. Compared with most other III-V device technologies, which require advanced epitaxial growth technologies, GaAs MESFETs can be fabricated using a direct ion-implantation approach, which is a common practice in silicon technology. In a compound semiconductor, GaAs MESFET technology is the most widely used III–V semiconductor device for highfrequency applications. The HEMT technology in principle is similar to the MESFET structure. An HEMT IC can operate on a lower supply voltage than HBT or Si-bipolar ICs, so it has the advantage of a higher cutoff frequency, lower noise figure, and low power dissipation. 6.4.1.1 Basic Concept Figure 6.19 shows the typical FET-based modulator driver IC, which operates at 10–20 Gb/s [33, 34]. The driver IC consists of three parts as follows: 1. Input buffer stage. The buffer circuits (source followers) at the data inputs allow DC coupling between ICs, since high-speed ICs in broadband communication systems require not only operation at high speed but also down to very low frequencies. 2. Pre-driver stage. In order to obtain a high-voltage gain and to compensate the high-frequency degradation of the output driver, a two-stage differential amplifier acting as a pre-driver is used in front of the output driver stage. The first stage of the pre-driver provides single ended-to-differential conversion. 3. Output driver stage. The output buffer is composed of an open drain switch with large gatewidth FETs for a large output voltage swing.

Figure 6.19 Typical FET-based modulator driver IC.

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208

Some popular design rules are as follows: 1. A 50 O resistor is used at the inputs for matching the transmission lines and suppressing the potential instability of the source–follower inputs. 2. In front of each amplifier, the cascaded source–follower pairs should be used for level shifting and impedance transformation. 3. The load resistor of the succeeding amplifier stage should be smaller than that in the previous amplifier stage to increase the driving capability. 4. The device gatewidth of the succeeding amplifier stage should be larger than that in the previous amplifier stage to increase the driving capability. The most important is to optimize the output driver device gatewidth to make the input logic swing as small as possible. 5. The FET device in the differential amplifier stage should be operated at around the cutoff frequency. Table 6.4 shows the comparison of a modulator driver IC using III-V compound HEMT device technologies. The ranges of bit rate are 10 Gb/s to 40 Gb/s, drive voltages are 2–4 V, and the rise/fall times are roughly 30 % of the input signal pulse width. It is noted that the gradual rise of the leading edge of the driver IC transit response is quantified by giving the rise time, which is the time interval between the point at which the driver achieves 10 % of the eventual output amplitude and the point at which the output is 90 % of the final value. Table 6.4 Comparison of HEMT modulator driver ICs. Year

Bit rate (Gb/s)

Modulation voltage (V)

1992 1996 1997 1998 1999 2000 2001 2005

10 10 10 25 10 10 10 40

4 2.5 3.0 3.3 2.5 3 14 2

Rise/fall time (ps) 35–40 40 40 13 40 20 40 NA

Reference [35] [36] [33] [34] [37] [38] [39] [40]

6.4.1.2 Optimum FET Device Model Parameters In this section, the optimum nonlinear model parameters of the FET device will be discussed. The Statz nonlinear model is used here as an example to develop the optimum ranges of the model parameters to meet the requirements of the 10 Gb/s driver IC [41]. The nonlinear model parameters include:

Semiconductor Laser and Modulator Driver Circuit Design

1. 2. 3. 4. 5.

209

Saturation voltage parameter a Threshold voltage VTO Transconductance coefficient b Zero-bias gate–source capacitance Cgso Zero-bias gate–drain capacitance Cgdo .

Saturation Voltage Parameter a In SCFL circuits, the output logic swing is limited by supply voltage and drainto-source knee voltage because differential switching transistors must operate in the current saturation region for high-speed operation. The drain-to-source voltage Vknee is an important parameter in high-speed IC design, because FET devices with low drain-to-source knee voltage are effective for reducing supply voltage. The drain-to-source voltage Vknee is the voltage at which the I–V curves transition from the linear region to the saturation region. In the Statz nonlinear model, the drain-to-source voltage Vknee is determined by the saturation voltage parameter a directly (Vknee 3=a). From the circuit diagram of the single differential pair stage shown in Figure 6.20, the high-level VH and low-level VL of the input logic swing are described by the following formulas: VH ðVout þ Vknee Þ þ Vgs

on

VL VSS þ Vknee

Figure 6.20 Circuit diagram of single differential pair stage.

with Vknee 3=a

ð6:7Þ ð6:8Þ

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210

where Vout is the output voltage swing required, Vgs on is the gate-to-source voltage necessary to make modulation current flow across external load resistor, and VSS is the supply voltage. The maximum input logic swing can be expressed as follows: VSW Vgs

on ðVout

þ VSS þ 6=aÞ

ð6:9Þ

Assuming that the parameters Vgs on , Vout , and VSS are 0, 3, and 5.2 V, Figure 6.21 shows the variation of maximum input logic swing VSW versus a. It is observed that the maximum input logic swing VSW increases with the increase of a. 1.6

VSW (V)

1.2 0.8 0.4 0.0

2

3

4

5

6

7

α

Figure 6.21 Variation of VSW versus a.

The power dissipation of single differential pair stage can be expressed as follows: PD ¼ Vss IS

ð6:10Þ

Vss ðVout þ 6=aÞ

ð6:11Þ

where PD is the power dissipation and IS is the total current. Figure 6.22 shows the variation of PD versus a (IS ¼ 300 mA), where it is observed that the power dissipation PD decreases rapidly when a is below 6 and decreases slowly when a is larger than 6; therefore the optimum value for a is a 6. That means in order to increase output logic swing of the pre-driver and decrease power dissipation of the driver IC, Vknee should be kept as small as possible. Threshold Voltage V TO The input signal Vin is the ECL level (1.7 V to 0.9 V) and the reference voltage Vref is 1.3 V. If the output voltage swing required is 3 Vp-p the voltage gain of the

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211

1.60

PD (W)

1.45 1.30 1.15 1.00

2

3

4

5

6

7

α

Figure 6.22 Variation of PD versus a.

whole driver IC (Figure 6.19) can be written as follows: Vout G ¼ 20 log ¼ 12 dB VIN

ð6:12Þ

In Figure 6.19, there are three amplifier stages totally. Assuming that the voltage gains of these differential amplifier stages are 2 dB, 2 dB, and 8 dB, respectively, the corresponding output voltage swings of each stage are 1 V, 1.2 V, and 3.0 V. Assuming the FET Q1 is on-state and the FET Q2 is off-state (as shown in Figure 6.20), the following equations can be used: Ids

Q1 Ids Q2

Ids

Q2

Vout =RL

Imax

ð6:13Þ ð6:14Þ

where Ids Q1 and Ids Q2 are the drain-to-source currents of Q1 and Q2 , respectively, and can be expressed based on the Statz model: Ids

Ids

Q1

Q2

bWð0Vto Þ2 ð1 þ lVds ÞtanhðaVds Þ 1 þ bð0Vto Þ

ð6:15Þ

bWðVin Vto Þ2 ð1 þ lVds ÞtanhðaVds Þ 1 þ bðVin Vto Þ

ð6:16Þ

¼

¼

where Vin is the input signal voltage, RL is the load resistor, W is the gatewidth of the FET device, and Imax is the maximum current for the off state. For the first differential amplifier stage, let W ¼ 100 mm; Vin ¼ 0:8 V; Vout ¼ 1:0 V; RL ¼ 150 O

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212

For the second differential amplifier stage, let W ¼ 200 mm; Vin ¼ 1:0 V; Vout ¼ 1:2 V; RL ¼ 100 O For the third differential amplifier stage, let W ¼ 500 mm; Vin ¼ 1:2 V; Vout ¼ 3:0 V; RL ¼ 50 O The variation ranges of the threshold voltage can be derived from Equations (6.15) and (6.16) with b ¼ 0 and l ¼ 0. Table 6.5 gives the threshold voltage VTO versus transconductance parameter b for each amplifier stage and whole driver IC. Table 6.5 The variation ranges of VTO versus b. b VTO VTO VTO VTO

for for for for

first stage second stage third stage whole driver

350 mA=V2 mm

450 mA=V2 mm

550 mA=V2 mm

0.93 to 0.45 1.4 to 0.57 1.4 to 0.58 0.9 to 0.58

0.9 1.3 1.4 0.9

0.82 to 0.33 1.3 to 0.54 1.4 to 0.47 0.82 to 0.54

to 0.4 to 0.55 to 0.5 to 0.55

It is observed that the optimum variation ranges of the threshold voltage can be written as 0:9 Vto 0:6 Transconductance Parameter b Since the voltage gain of the output driver is the highest one among three stages, the corresponding transconductance parameter b required is higher than any pre-driver stage. The output driver design target for the output voltage swing is 3 Vp-p and the corresponding modulation current Im is equal to 60 mA. The transconductance parameter b can be determined as follows: b¼

Im ½1 þ bðVgs

on Vto Þ WðVgs on Vto Þ2

ð6:17Þ

Figures 6.23 and 6.24 show the plots of transconductance parameter b versus threshold voltage VTO , gate-to-source voltage Vgs on , and doping tail extending parameter b. It can be found that the required b for the output driver current of 60 mA of the modulator driver increases with the increase of VTO , Vgs on , and b. Therefore, VTO , Vgs on , and b should be kept as small as possible to reduce the requirement of the FET device transconductance parameter b.

Semiconductor Laser and Modulator Driver Circuit Design

213

β (mA/V2/mm)

800

Vgs_on = 0 V

b=0

600

Vgs_on = -0.1 V

400

Vgs_on = -0.2 V

200 0 -1

-0.9

-0.8

-0.7 -0.6 VTO (V)

-0.5

-0.4

Figure 6.23 Plot of transconductance parameter b versus threshold voltage VTO and gateto-source voltage Vgs on . 800 β (mA/V2/mm)

b=2 600

b=1

400

b=0

200 0

-1

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

VTO (V)

Figure 6.24 Plot of transconductance parameter b versus threshold voltage VTO and doping tail extending parameter b.

Based on the analysis above, the optimum variation ranges of the transconductance parameter b can be written as 350 mA=V2 mm b 650 mA=V2 mm Zero-Bias Gate–Source Capacitance Cgso and Gate–Drain Capacitance Cgdo Figure 6.25 shows the plot of the 3 dB bandwidth of the output driver versus Cgso and Cgdo . It can be observed that the bandwidth decreases quickly with increases of Cgso and Cgdo . The optimum ranges for 10 Gb/s operation are as follows: Cgso 2 pF mm; Cgdo 0:3 pF mm Figure 6.26 shows the plot of the 3dB bandwidth of the three differential amplifier stages (gatewidths are 100 mm, 200 mm, and 500 mm, respectively) against the FET device cutoff frequency fT ( fT ¼ gm =2pðCgs þ Cgd Þ). It is observed that the 3dB bandwidth is limited mainly by the output driver; therefore two very useful conclusions can be drawn as follows:

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214

3 dB bandwidth (GHz)

20 16

Cgdo=0.2,0.4,0.6 pF·mm

12 8 4

0

0

1

2

3

4

5

Cgso (pF·mm)

Figure 6.25 Plot of 3 dB bandwidth of output driver versus Cgso and Cgdo .

3 dB bandwidth (GHz)

W=100 μm

W=200 μm

W=500 μm

16 12 8 4 0

0

15 30 45 Cutoff frequency (GHz)

60

Figure 6.26 Plot of 3 dB bandwidth of the three differential amplifier stages against the FET device cutoff frequency.

1. The cutoff frequency of the FET device ( fT ) should be above 12 GHz for the 2.5 Gb/s modulator driver IC design. 2. The cutoff frequency of the FET device ( fT ) should be above 50 GHz for the 10 Gb/s modulator driver IC design. Several HEMT driver ICs for 10 Gb/s have been reported, and the corresponding device characteristics are given [2, 3, 4, 5]. To test the validity of our calculated method, we have compared calculated results with experimental data in Table 6.6. It is observed that the predicted results agree well with the experimental results extracted from references. 2.5 Gb/s and 10 Gb/s Modulator Driver IC Design Figures 6.27(a) and (b) show computer simulated output simulation for a 2.5–10 Gb/s driver IC. By using the previously discussed model parameters (see Table 6.7), a good eye opening is observed and sensitivity for the input voltage swing in single-operation is as low as 0.4.

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215

Table 6.6 HEMT model parameters of a 10 Gb/s modulator driver. Model parameter

a b VTO (V) fT (GHz)

Predicted result

6 350 b 650 0.9 to 0.6 45

Experimental data extracted from references Ref [35]

Ref [33]

Ref [42]

6 350 0.6 51

6 650 0.8 67.5

6 350 0.6 50

Ref [36] na na 0.9 55

Figure 6.27 Simulated output eye diagram for 2.5 Gb/s and 10 Gb/s drivers.

6.4.2 Bipolar Transistor-Based Driver Integrated Circuit 6.4.2.1 Basic Concept Based on the different substrates, the bipolar device can be categorized into the following: 1. Silicon-based BJTs 2. Silicon germanium (SiGe)-based HBTs

Optoelectronic Integrated Circuit Design and Device Modeling

216

Table 6.7 HEMT model parameters of a 2.5–10 Gb/s modulator driver. Parameters

Physical meaning

2.5 Gb/s

10 Gb/s

a b b Vto l Rs RD Cgs Cgd fT

Saturation voltage parameter Transconductance coefficient Doping tail extending parameter Threshold voltage Channel-length modulation Source ohmic resistance Drain ohmic resistance Zero-bias gate–source capacitance Zero-bias gate–drain capacitance Cutoff frequency

6 350 mA=V2 mm 1 0.9 0.02 1 O mm 1 O mm 4 pF=mm 1:5 pF=mm 15 GHz

1:0 pF=mm 0:3 pF=mm 54 GHz

3. Gallium arsenide (GaAs)-based HBTs 4. Indium phosphide (InP)-based HBTs. Compared with high-speed driver ICs in III–V technologies, such as GaAs, silicon bipolar ICs still have a superior yield, which, together with the cheaper basic material, results in lower cost. The Si-BJTs normally are suitable for low-speed driver IC design, while HBTs are suitable for high-speed (more than 10 Gb/s) modulator driver IC design. InP-based bipolar transistors offer the advantages over GaAs–AlGaAs HBTs of a lower turn-on voltage, higher electron mobility, better thermal dissipation, and better microwave performance, while still obtaining a high collector-to-base breakdown voltage. SiGe HBT technology has become an important semiconductor technology for wireless telecommunications and optical communication applications because SiGe HBTs with a sub-10 ps emitter-coupled logic (ECL) gate delay and cutoff frequency above 100 GHz were demonstrated and can be fabricated by the well-established Si process, which is fully compatible with the CMOS process. By employing bandgap engineering, SiGe HBTs outperform Si BJTs in nearly every important performance metric and, in several areas, provide improved performance over the III–V HBTs. One of the areas in which SiGe HBTs exceed GaAs HBTs is in low-noise corner frequency. Compared with FET devices, the HBT has several advantages as follows [43]: 1. Higher transconductance per unit area allowing high integration density 2. Excellent device matching resulting in low offset differential circuits 3. Reduced low-frequency noise enabling very low phase noise oscillators. Figure 6.28 shows the typical bipolar transistor-based modulator driver IC, which operates at 10Gb/s. Similar to the FET-based driver IC, the bipolar transistor-based driver consists of three parts:

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217

Figure 6.28 Typical bipolar transistor-based modulator driver IC.

1. Input buffer stage. The emitter followers are required for level shifting and impedance transformation. 2. Pre-driver stage. Due to the high gain of the HBT, only one differential amplifier stage is needed, while two differential amplifier stages are necessary in front of the output driver stage for the FET-based driver IC. Therefore the schematic configuration for the HBT driver IC is simpler than the FET-based driver IC. 3. The output driver stage is composed of a differential amplifier stage and is similar to the FET-based driver IC. Table 6.8 shows the comparison of the modulator driver IC using HBT device technologies, which operates at 10 Gb/s. Table 6.8 Comparison of modulator driver IC using HBT device technologies. Semiconductor technology GaAs HBT InP DHBT SiGe HBT SiGe HBT

Bit rate (Gb/s)

Modulation voltage (V)

Rise/fall time (ps)

Reference

10 12 10 10

3 2.5 3.3 9

38 50 42 29

[44] [45] [46] [47]

6.4.2.2 Optimum HBT Device Model Parameters Three important HBT model parameters for the modulator driver design will be discussed in the following: the knee voltage, the intrinsic base–emitter capacitance, and the base–collector capacitance.

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218

Knee Voltage To realize a high-efficiency IC, it is essential to select a transistor that has a low saturation (or knee) voltage with respect to the supply voltage. For a bipolar transistor, this knee voltage is most dependent on the parasitic collector and emitter resistances and the offset voltage within the device. Many points of efficiency are lost when the supply voltage approaches the transistor saturation voltage. Figure 6.29 gives the I–V characteristics showing the definition of knee voltage; the knee voltage is the collector–emitter voltage at which the collector current reaches roughly its maximum value. The power supply of the whole driver IC is mostly determined by the knee voltage.

Figure 6.29 I–V characteristics showing the definition of knee voltage.

Based on the expressions of the base–emitter and base–collector voltage [48]: VBE

Zf kT IE aR IE ¼ ln þ IB RB þ IE RE q IES ð1 aF aR Þ

ð6:18Þ

VBC

Zr kT aF IE IC ¼ þ IB RB IC RC ln ICS ð1 aF aR Þ q

ð6:19Þ

The knee voltage can be determined approximately as follows: Vknee ¼ VCEðsatÞ

Zf kT IE aR IE Zr kT aF IE IC ¼ ln ln q q IES ð1aF aR Þ ICS ð1aF aR Þ

ð6:20Þ

þ IE RE þ IC RC By neglecting the extrinsic resistance and assuming that Zbe ¼ Zbc ¼ 1, a simple expression can be obtained:

Semiconductor Laser and Modulator Driver Circuit Design

Vknee

219

kT ICS ðIE aR IE Þ ln q IES ðaF IE IC Þ

ð6:21Þ

where Zf and Zr are the forward and reverse current emission factors, respectively; IES and ICS are base–emitter and base–collector leakage saturation currents, respectively; aF ð¼ bF =ð1 þ bF Þ, where bF is the ideal maximum forward current gain); and aF and aR are the common base forward and reverse current transfer ratios, respectively. Figures 6.30 to 6.32 show the plots of knee voltage Vknee versus forward current gain bF , extrinsic resistance RE (or RC ), and the forward current emission factor Zf . It can be observed that Vknee increases with the increase of the collector current, extrinsic resistance, and the forward current emission factor Zf . Therefore, in order to reduce Vknee , the extrinsic resistance and the forward current emission factor Zf should be kept as small as possible. For the GaAs-based HBT, the base–emitter threshold voltage is roughly 1.1 V and the corresponding Vknee will be around 1.1 V; similarly, for the InP-based HBT, the base–emitter threshold voltage is roughly 0.75 V and the corresponding Vknee will be around 0.75 V.

1.50 Vknee (V)

Ic=80mA 1.25 Ic=60mA 1.00

Ic=40mA

0.75 40

60

80

100

120

βF

Figure 6.30 Knee voltage Vknee versus forward current gain bF .

2.0 Ic=80mA

Vknee (V)

Rc=5 1.5

Ic=60mA Ic=40mA

1.0 0.5

0

2

4

6

8

10

12

14

RE ( or RC)(Ω)

Figure 6.31 Knee voltage Vknee versus extrinsic resistance RE (or RC ).

Optoelectronic Integrated Circuit Design and Device Modeling

220 1.50

Vknee (V)

1.25

Ic=80mA

Rc =5 RE=5

Ic=60mA

1.00 Ic=40mA 0.75 0.50 0.9

1

1.1

1.2

1.3

1.4

nf Figure 6.32 Knee voltage Vknee versus forward current emission factor Zf .

Intrinsic Base–Emitter Capacitance and Base–Collector Capacitance Figure 6.33 shows the 3 dB bandwidth versus intrinsic capacitance for the signal differential amplifier stage; the 3 dB bandwidth decreases with the increase of base–emitter and base–collector capacitances. Figure 6.34 shows the plot of the 3 dB bandwidth versus HBT cutoff frequency for the driver IC. It can be observed that the device cutoff frequency should be more than 35 GHz for the driver IC, which operates

25 fT (GHz)

20

CjE=150 f F

15 10

CjE=180 fF

5 40

80

120 CjC (f F)

160

200

3 dB bandwidth (GHz)

Figure 6.33 3 dB bandwidth versus HBT intrinsic capacitance for the signal differential amplifier stage.

25 20 15 10 5 20

30

40 50 f T (GHz)

60

70

Figure 6.34 3 dB bandwidth versus HBT cutoff frequency for the driver IC.

Semiconductor Laser and Modulator Driver Circuit Design

221

at 10 Gb/s, and the device cutoff frequency should be more than 60 GHz for the driver IC, which operates at 20 Gb/s. Figure 6.35 shows the simulated output pulse response for the HBT driver IC using the schematic shown in Figure 6.28. The output voltage swing of the pre-driver is 1 V (1 V to 0 V) while the input pulse width is 100 ps and the output voltage swing of the pre-driver is 3 V (3 V to 0 V); therefore the driver IC can be operated at 10 Gb/s.

Figure 6.35 Simulated output eye diagram for a 10 Gb/s HBT driver IC.

6.4.3 MOSFET-Based Driver Integrated Circuit Porting optical and optoelectronic devices to silicon within a commercially deployed and high-yielding CMOS process is very attractive to achieve low cost, and it reduces the size and power dissipation while simultaneously achieving all the benefits of integration. CMOS processing technology has continued to reduce the minimum channel length of the MOS device and, to date, silicon CMOS-based laser drivers with operation bit rates up to several gigabits per second for low-cost and low-power consumption implementations have been reported [49]. Figure 6.36 shows a 10 Gb/s MOSFET-based modulator driver IC, where the driver circuit comprises a differential cascode output stage and a feedback network. To generate a higher voltage swing, the transistor Q1 should be a high-voltage device sustaining a higher voltage swing, while the transistor Q2 is a low-voltage device sustaining a lower voltage swing for a smaller Miller effect. Table 6.9 summarizes the modulator driver IC operating at 10 Gb/s by using CMOS device technologies. It can be found that the output modulation voltage is higher than a III–V compound semiconductor-based driver IC.

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Figure 6.36 10 Gb/s MOSFET-based modulator driver IC.

Table 6.9 Comparison of modulator driver IC using CMOS device technologies. Semiconductor technology

Bit rate (Gb/s)

Modulation voltage (V)

Rise/fall time (ps)

Reference

0.18 mm CMOS 0.18 mm CMOS 0.18 mm CMOS

10 10 10

5 8 6.8

32 40 40

[50] [47] [47]

6.5 Distributed Driver Circuit Design High-speed IC technologies with 40 Gb/s data rates are required for both wavelengthdivision multiplexing (WDM) and time-division multiplexing (TDM) systems, and ICs with various semiconductor technologies have been developed for practical use. At present 10 Gb/s (OC-192/STM-64) is the highest electrical data rate being installed in commercial systems. The next step will be the deployment of systems operating at 40 Gb/s electrical data rates (OC768/STM-256). The input 40 Gb/s data include various frequency components, and a bandwidth of over 40 GHz and a flat gain are required to amplify this waveform accurately. In the case of 40 Gb/s systems, the modulator driver is very challenging because it simultaneously has to achieve a high output voltage swing and a bandwidth exceeding 30 GHz. The distributed amplifier (DA) is recognized as one of the most popular and well-established broadband amplifier configurations. In particularly, good wideband performance has been demonstrated with compact, low-cost, and highly reliable microwave distributed amplification. Its main advantages are uniform gain, group delay, noise figure, and a low voltage standing wave ratio (VSWR) performance over a wide frequency band, making possible its utilization for a low-noise millimeter-wave receiver for digital optical communication and other pulse applications.

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Traditional distributed amplifiers have demonstrated ultra-wide bandwidths, but they suffer from low gain and need bias-tees and/or DC blocks, increasing size and cost. Therefore, combining a differential configuration with a distributed amplifier has potential to fulfil all the driver requirements. Figure 6.37 shows the block diagram of the 40 Gb/s distributed modulator driver, which consists of a lumped-element differential pre-driver followed by a differential distributed amplifier. The pre-driver is required because the differential distributed amplifier does not provide enough gain by itself. The circuit is DC coupled and no bias-tee or DC block is needed. The predriver consists of several differential amplifier and buffer stages. To avoid multiple reflections between the pre-driver output and the termination of the distributed amplifier input line, the output current switch has load resistors (RL ) that approximately match the image impedance of the input artificial lines of the distributed output stage.

Figure 6.37 Block diagram of the 40 Gb/s distributed modulator driver.

There are two kinds of commonly used distributed amplifiers: .

.

Single ended input/single ended output distributed amplifier. A schematic of the amplifier is given in Figure 6.38. It consists of several identical gain cells with their input and output ports connected by transmission lines. Artificial transmission lines (low-pass filter networks) at the input (gate line) and output (drain line) are formed using inductive elements and capacitive elements of the active transistors. The lines are terminated in the loads Rg and Rd . Resistive elements short the drain-line inductive elements to improve the high-frequency circuit stability. The resistors ensure that the transistors do not see the high impedance presented by the artificial transmission line at the upper frequency band edge. Differential input/differential output distributed amplifier(as shown in Figure 6.39). The distributed output stage consists of several identical differential amplifier cells

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Figure 6.38 Single-ended input/single-ended output distributed amplifier.

Figure 6.39 Differential input/differential output distributed amplifier.

separated by microwave transmission lines. Different circuit design techniques can be used to extend the bandwidth of the distributed amplifier. Table 6.10 gives a comparison of the distributed modulator driver IC. The transmission rate can be achieved to at least 40 Gb/s and up to 80 Gb/s, and the modulation voltage can be achieved to more than 10 V. The most commonly used semiconductor technologies are the GaAs-based PHEMT and the InP-based HBT.

6.6 Passive Peaking Techniques Traditionally, the bit rate of the laser/modulator driver IC can be increased by using higher cutoff frequency semiconductor devices, for example, deep submicrometer (0.1–0.2 mm) gate-length HEMT devices can be used to design more than 40Gb/s driver IC. However, reducing the device gate length may increase the difficulties in fabrication process. The passive peaking techniques are a simple way to enhance the bandwidth of driver IC and thereby push the performance limits of the semiconductor

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Table 6.10 Comparison of distributed modulator driver ICs. Semiconductor technology

fT (GHz)

Bit rate (Gb/s)

Output Vpp (V)

Rise/fall time (ps)

Reference

GaAs PHEMT GaAs PHEMT GaAs PHEMT GaAs PHEMT GaAs PHEMT GaAs PHEMT InP HBT InP HBT InP HBT InP HBT InP HBT

55 100 90 90 95 100 150 160 200 200 150

40 40 40 40 40 40 40 40 40 80 40

5 3 6.6 6.3 7.5 1.5 2.7 3.0 5.1 2.6 11.3

9 9 9 9 9 9 10 8.6 9 na 8

[51] [52] [53] [54] [55] [56] [57] [58] [59] [59] [60]

devices. An attractive feature of this technique is that the bandwidth enhancement comes with no additional power dissipation. Meanwhile, it can have a relatively flat frequency response similar to LC-ladder filters. The most common used passive peaking techniques are capacitive peaking technique and inductive peaking technique.

6.6.1 Capacitive Peaking Techniques The capacitive peaking techniques are use to improve the buffer circuit performance normally. In order to eliminate the effect of the series resistances of level shifted diodes, an additional capacitance is necessary in parallel with the level shifted diodes. The inserted capacitors do not significantly degrade the gain, frequency response flatness, or noise characteristics of the circuit. Figure 6.40 shows the buffer circuit with capacitive peaking element and corresponding equivalent circuit model and the corresponding 3 dB bandwidth versus peaking capacitance for buffer circuit is shown in Figure 6.41. It can be observed that

Figure 6.40 Buffer circuit with capacitive peaking: (a) schematic; (b) equivalent circuit model.

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3 dB bandwidth (GHz)

18 15 12 Optimum value 9 6 0.0

0.5

1.0

1.5

2.0

2.5

3.0

C (pF)

Figure 6.41 Plot of 3 dB bandwidth versus peaking capacitance for the buffer circuit.

the 3-dB bandwidth increases with the increase of peaking capacitance rapidly before the peaking capacitance is less than optimum values. Employing a proper capacitance, the 3 dB bandwidth of the buffer circuit can be extended up to two times than that without inserting capacitance approximately.

6.6.2

Inductive Peaking Techniques

This method usually places inductors in a strategic location of the amplifier circuit, resulting in a resonance with parasitic capacitances, which broadens the bandwidth of the driver IC. The inductor loading of the gate and drain terminals of the FET are most effective from the viewpoint of wide bandwidth. Inductor peaking shows no reduction of gain at low frequencies compared with non-peaking. Figure 6.42 shows the schematic of differential amplifier stage with gate inductive peaking, and the 3dB bandwidth versus peaking inductance for differential amplifier stage is shown in Figure 6.43. The peaking inductances are placed on the gate of differential FET devices, and the 3 dB bandwidth can be extended up to twice of bandwidth of differential amplifier without peaking technique.

Figure 6.42 Differential amplifier stage with gate inductive peaking.

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3 dB bandwidth (GHz)

7 6 5 4

Optimum value

3 2

0

1

2

3

4

5

L (nH)

Figure 6.43 3 dB bandwidth versus peaking inductance for the differential amplifier stage.

Figure 6.44 shows the schematic of differential amplifier stage with drain inductive peaking, and 3 dB bandwidth versus peaking inductance for differential amplifier stage is shown in Figure 6.45. To have a better speed performance, an inductor is inserted between the load and the power supply for peaking. Employing a proper inductance value with an acceptable overshoot peaking, it can be found that the 3-dB bandwidth of the proposed topology is 4 times than that without inserting inductors.

Figure 6.44 Differential amplifier stage with drain inductive peaking.

Figure 6.46 shows the 10 Gb/s modulator driver HEMT IC design with passive peaking techniques, and corresponding output eye diagram is shown in Figure 6.47. The model parameters used to design 10 Gb/s modulator driver HEMT IC are as follows:

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228

3 dB bandwidth (GHz)

DC parameters: a ¼ 3; b ¼ 350 mA=V2 =mm; b ¼ 1Vto ¼ 0:9 V; l ¼ 0:02 Capacitance parameters: Cgs ¼ 1:5 pF=mm; Cgd ¼ 0:5 pF=mm Cutoff frequency: fT ¼ 35 GHz. 20 16 12 8

Optimum value

4 0

0

1

2

3

4

5

L (nH)

Figure 6.45 Plot of 3 dB bandwidth versus peaking inductance for the differential amplifier stage.

Figure 6.46 10 Gb/s modulator driver HEMT IC design with passive peaking techniques.

Figure 6.47 Simulated output eye diagram for a10 Gb/s HEMT driver IC with passive peaking techniques.

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Compared with 10 Gb/s modulator driver HEMT IC without passive peaking techniques, the cutoff frequency of the device can be reduced from 45 GHz to 35 GHz using passive peaking techniques. That means the requirement of semiconductor device can be decreased for high-speed modulator drive IC design by using passive peaking techniques.

6.7 Summary In this chapter, we have introduced the basic concepts of the optical modulation and optical transmission for optical transmitter firstly, 10 Gb/s40 Gb/s high-speed modulator driver IC based on different semiconductor technologies are described. Sequentially, the passive peaking techniques are introduced for extending the bandwidth of driver IC.

References 1. Nagai, K. and Wada, H. (2002) 40 Gb/s EA modulator. OKI Technical Review, 190, 69(2), 6–67. 2. M-Morini, D., Vivien, L., and Rasigade, G. (2009) Recent progress in high-speed silicon-based optical modulators. Proceedings of the IEEE, 97(7), 1199–1215. 3. Mochida, Y., Yamaguchi, N., and Ishikawa, G. (2002) Technology-oriented review and vision of 40-Gb/sbased optical transport networks. IEEE Journal of Lightwave Technology, 20(12), 2272–2281. 4. Becker, R. A. (1984) Broad-band guided-wave electrooptic modulators. IEEE Journal of Quantum Electronics, QE-20(7), 723–727. 5. Wada, O., Sakurai, T., and Nakagami, T. (1986) Recent progress in optoelectronic integrated circuits (OEICs). IEEE Journal of Quantum Electronics, 22(6), 805–821. 6. Horimatsu, T. and Sasaki, M. (1989) OEIC technology and its application to subscriber loops. IEEE Journal of Lightwave Technology, 7(11), 1612–1622. 7. Bar-Chaim, N., Margalit, S., Yariv, A., and Ury, I. (1982) GaAs integrated optoelectronics. IEEE Transactions on Electron Devices, ED-29(9), 1372–1381. 8. Dagenais, M., Leheny, B. F., Temkin, H., and Bhattacharya, P. (1990) Applications and challenges of OEIC technology: a report on the 1989 Hilton Head Workshop. IEEE Journal of Lightwave Technology, 8(6), 846–862. 9. Hayashi, T., Katsura, K., and Tsunetsugu, H. (1994) New hybrid integrated laser diode–drivers using microsolder bump bonding: SPICE simulation of high-speed modulation characteristics. IEEE Journal of Lightwave Technology, 12(11), 1963–1970. 10. Koren, U., Margalit, S., Chen, T. R., et al. (1982) Recent developments in monolithicintegration of InGaAsP/InP optoelectronic devices. IEEE Journal of Quantum Electronics, QE-10, 1653–1662. 11. Shaw, N. and Carter, A., (1993) Optoelectronic integrated circuits for microwave optical system. Microwave Journal, (10), 90–100. 12. Wilt, D., Bar-Chaim, N., Margalit, S., et al. (1980) Low threshold Be implanted (GaAl)As laser on semiinsulating substrate. IEEE Journal of Quantum Electronics, QE-16, 390–391. 13. Yust, M., Bar-Chaim, N., Izadpanah, S. H., et al. (1979) A monolithically integrated optical repeater. Applied Physics Letters, 35, 795–797. 14. Iezekiel, S., Soshea, EricA., O’Keefe, M. F., and Snowden, C. M. (1995) Microwave photonic multichip modules packaged on a glass-silicon substrate. IEEE Transactions on Microwave Theory and Techniques, 43(9), 2421–2427.

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15. Matsueda, H. (1987) AlGaAs OEIC transmitters. IEEE Journal of Lightwave Technology, 5(10), 1382–1390. 16. Wada, O., Nobuhara, H., Sanada, T., et al. (1989) Optoelectronic integrated four-channel transmitter array incorporating AlGaAs/GaAs quantum well lasers. IEEE Journal of Lightwave Technology, 7(1), 186–197. 17. Forrest, S. R. (1985) Monolithic optoelectronic integration: a new component technology for lightwave communications. IEEE Journal of Lightwave Technology, 3(6), 1248–1263. 18. Liang, C. and Yang, R. (1994) Development of optoelectronics and photonics integrations abroad. Semiconductor Information, 31(2), 27–37. 19. Katsu, S., Nambu, S., Shimano, A., and Kano, G. (1985) A source coupled FET logic – a new current-mode approach to GaAs logics. IEEE Transactions on Electron Devices, 32(6), 1114–1118. 20. Idda, M., Takada, T., and Sudo, T. (1984) Analysis of high-speed GaAs source-coupled FET logic circuits. IEEE Transactions on Microwave Theory and Techniques, 32(1), 5–10. 21. Goldsmith, C. L. and Kanack, B. (1993) Broad-band reactive matching of high-speed directly modulated laser diodes. IEEE Microwave and Guided Wave Letters, 3(9), 336–338. 22. Ghiasi, A. and Gopinath, A. (1990) Novel wide-bandwidth matching technique for laser diodes. IEEE Transactions on Microwave Theory and Techniques, 38, 673–675. 23. Cristina, M., Carvalho, R., Margulis, W., and Souza, J. R. (1992) A new, small-sized transmission line impedance transformer, with applications in high-speed optoelectronics. IEEE Microwave and Guided Wave Letters, 2(11), 428–430. 24. Miyamoto, Y., Hagimoto, K., Ohhata, M., et al. (1994) 10 Gb/s strained MQW DFB-LD transmitter module and superlattice APD receiver module using GaAs MESFET ICs. IEEE Journal of Lightwave Technology, 12(2), 332–341. 25. Ueda, D., Shimano, A., and Otsuki, T. (1985) A GaAs laser–driver operating up to 2 Gb/s data rate. IEEE GaAs IC Symposium, 103–106. 26. Suzuki, Y., Hida, H., Fujita, S., et al. (1989) A 10 Gb/s laser driver IC with I-AlGaAs/n-GaAs dopedchannel hetero-MISFETs (DMTs). IEEE GaAs IC Symposium, 129–132. 27. Rein, H.-M. (1988) Multi-gigabit-per-second silicon bipolar ICs for future optical-fiber transmission systems. IEEE Journal of Solid-State Circuits, 23(3), 664–675. 28. Liou, K.-Y., Chandrasekhar, S., Dentai, A. G., et al. (1991) A 5 Gb/s monolithically integrated lightwave transmitter with 1.5 mm multiple quantum well laser and HBT driver circuit. IEEE Photonics Technology Letters, 3(10), 928–930. 29. Berroth, M., Hurm, V., Lang, M., et al. (1992) 10–20 Gb/s GaAs/AlGaAs HEMT ICs for high speed data links. IEEE GaAs IC Symposium. 30. Riish, J. (1993) 2.5 Gb/s laser-driver GaAs IC. IEEE Journal of Lightwave Technology, 11(7), 332–341. 31. Derksen, R. H. and Wernz, H. (1993) Silicon bipolar laser driving IC for 5 Gb/s and 45 mA modulation current and its application in a demonstrator system. IEEE Journal of Solid-State Circuits, 28(7), 824–828. 32. Hornbuckle, D. P. and Van Tuyl, R. L. (1981) Monolithic GaAs direct-coupled amplifiers. IEEE Transactions on Electron Devices, 28(2), 175–182. 33. Miyashita, M., Yoshida, N., Kojima, Y., Kitano, T., et al. (1997) AnAlGaAs/InGaAs pseudomorphic HEMT modulator driver IC with low power dissipation for 10-Gb/s optical transmission systems. IEEE Transactions on Microwave Theory and Techniques, 45(7), 1058–1064. 34. Lao, Z., Hurm, V., Thiede, A., et al. (1998) Modulator driver and photoreceiver for 20 Gb/s optic-fiber links. Journal Lightwave Technology, 16(8), 1491–1497. 35. Suzuki, Y., et al. (1992) Pseudomorphic 2DEG FET ICs for 10-Gb/s optical communication systems with external optical modulation. IEEE Journal of Solid-State Circuits, 27, 1342–1346. 36. Demange, D., Billard, M., Devaux, F., and Lefkvre, R. (1996) High-performance and low-consumption 10 Gb/s GaAs PHEMT driver for external modulation transmitter. IEEE Photonics Technology Letters, 8(8), 1029–1031. 37. Nishino, A., Ohshima, T., Tsunotani, M., et al. (1999) A low power electroabsorption modulator driver IC for 10 Gbps optical transmitter. In Optical Fiber Communication Conference, 1999, and the International

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38.

39.

40.

41. 42. 43. 44.

45.

46. 47. 48. 49.

50. 51. 52.

53. 54.

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Conference on Integrated Optics and Optical Fiber Communication. OFC/IOOC ’99. Technical Digest, vol. 2, pp. 365–367. Ransijn, H., Salvador, G., Daugherty, D., and Gaynor, K. (2000) A 10 Gb/s, 120/60 mA laser/modulator driver IC with dual-mode actively matched output buffer. In Proceedings of the 26th European Solid-State Circuits Conference, pp. 464–467. Carroll, J. M. and Campbell, C. F. (2001) A 14-Vpp 10 Gbit/s E/O modulator driver IC. In Gallium Arsenide Integrated Circuit (GaAs IC) Symposium, 2001. 23rd Annual Technical Digest, 2001, pp. 277–279. Kerherve, E., Moreira, C. P., Jarry, P., and Courcelle, L. (2005) 40-Gb/s wide-band MMIC pHEMT modulator driver amplifiers designed with the real frequency technique. IEEE Transactions on Microwave Theory and Techniques, 53(6), 2145–2152. Gao, J., Gao, B., and Liang, C. (2002) Model device parameters for a 10-Gb/s HEMT modulator driver IC. Microwave and Optical Technology Letters, 35(5), 357–360. Clci, A., Sainson, S., Feuillade, M., et al. (1993) GaAs on InP MESFETs and circuits for OEICs. GaAs IC Symposium, 201–204. Baeyen, Y., Georgiou, G., Weiner, J. S., et al. (2002) InP D-HBT ICs for 40-Gb/s and higher bit rate lightwave transceivers. IEEE Journal of Solid-State Circuits, 37(9), 1152–1159. Wong, T. Y. K., Freundorfer, A. P., Beggs, B. C., and Sitch, J. E. (1995) A 10 Gb/s AlGaAs/GaAs HBT high power fully-differential limiting distributed amplifier for III–V Mach–Zehnder modulator. Gallium Arsenide Integrated Circuit (GaAs IC) Symposium, 201–204. Bauknecht, R., Schneibel, H. P., Schmid, J., and Melchior, H. (1996) A 12 Gb/s laser and optical modulator driver circuit with InGaAs/InP double heterostructure bipolar transistors. Indium Phosphide and Related Materials, 61–63. Sanduleanu, M. A. T. and Stikvoort, E. (2005) A 10 Gb/s, 3.3 V, laser/modulator driver with high power efficiency. In Proceedings of the 31st European Solid-State Circuits Conference, ESSCIRC, pp. 427–430. Li, D.-U. and Tsai, C.-M. (2006) 10-Gb/s modulator drivers with local feedback networks. IEEE Journal of Solid-State Circuits, 41(5), 1025–1030. Liu, W. (1998) Handbook of III–V Heterojunction Bipolar Transistors, John Wiley & Sons, Inc. Sialm, G., Krome, C., Ellinger, F., et al. (2006) Design of low-power fast VCSEL drivers for highdensity links in 90-nm SOI CMOS. IEEE Transactions on Microwave Theory and Techniques, 54(1), 65–73. Galal, S. and Razavi, B. (2003) 10 Gb/s limiting amplifier and laser/modulator driver in 0.18 mm CMOS technology. In IEEE International Solid-State Circuits Conference (ISSCC), pp. 188–189. Long, A., Buck, J., and Powell, R. (2002) Design of an opto-electronic modulator driver amplifier for 40-Gb/s data rate systems. Journal of Lightwave Technique, 20(12), 2015–2021. McPherson, D. S., Pera, F., Tazlauanu, A., and Voinigescu, S. P. (2002) A 3-V fully differential distributed limiting driver for 40 Gb/s optical transmission systems. In Gallium Arsenide Integrated Circuit (GaAs IC) Symposium, pp. 95–98. Virk, R. S., Camargo, E., Hajji, R., et al. (2002) 40-GHz MMICs for optical modulator driver applications. IEEE MTT-S International Microwave Symposium Digest, 91–94. Yuen, C., Laursen, K., Chu, D., and Mar, K. (2002) 50 GHz high output voltage distributed amplifiers for 40 Gb/s EO modulator driver application. IEEE MTT-S International Microwave Symposium Digest, 481–484. Mouzannar, W., Jorge, F., Vuye, S., et al. (2002) 40 Gbit/s high performances GaAs pHEMT high voltage modulator driver for long haul optical fiber communications. Gallium Arsenide Integrated Circuit (GaAs IC) Symposium, 163–166. Radisic, V., Yu, M., Lao, Z., et al. (2003) 40 Gb/s differential traveling wave modulator driver. IEEE Microwave and Wireless Components Letters, 13(8), 332–334. Hafele, M., Schworer, C., Beilenhoff, K., and Schumacher, H. (2003) AGaAs PHEMT distributed amplifier with low group delay time variation for 40 GBit/s optical systems. European Microwave Conference, 1091–1094.

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58. Krishnamurthy, K., Vetury, R., Xu, J., et al. (2003) 40 Gb/s TDM system using InP HBT IC technology. IEEE MTT-S International Microwave Symposium Digest, 1189–1192. 59. Schneider, K., Driad, R., Makon, R. E., et al. (2005) Comparison of InP/InGaAs DHBT distributed amplifiers as modulator drivers for 80-Gbit/s operation. IEEE Transactions on Microwave Theory and Techniques, 53(11), 3378–3387. 60. Baeyens, Y., Weimann, N., Roux, P., et al. (2004) High gain–bandwidth differential distributed InP D-HBT driver amplifiers with large (11.3Vp-p) output swing at 40 Gb/s. IEEE Journal of Solid-Sate Circuits, 39(10), 1697–1704.

7 Optical Receiver Front-End Integrated Circuit Design In the intensity-modulation/direct-detection (IM-DD) system, the intensity modulation means that information is carried only by the intensity or power of the transmitted lightwave, not by its frequency or phase. The term direct detection refers to the receiver configuration, where the received signal is applied directly to a photodetector (PD). The optical receiver is a combination of the optical detector, electronic preamplifier, and the electronic processing elements that recover information sent on the optical signal. The role of an optical receiver is to convert the optical signal back into electrical form and recover the data transmitted through the lightwave system. It should have high sensitivity, fast response, low noise, low cost, and high reliability. Its size should be compatible with the fiber-core size. The most important part in an optical receiver is the front-end circuit, which consists of a PD and transimpedance preamplifier. Figure 7.1 shows the signal transmission in an optical front-end circuit. An attenuated optical signal modulated with an electrical pulse signal (bit rate is 1=Tb ) is the input of the optical receiver and the optical signal will be transformed to an electric signal current by a photodiode and then amplified by a transimpedance preamplifer before passing through electronic processing elements for regeneration. The optical receivers have key roles in high-speed optical fiber communications, in high-speed chip-to-chip interconnections in computers, efficient networking between computers, and in other diverse areas such as medical imaging. Recent trends in optical fiber communication systems experimentation have been towards a 10–40 Gb/s channel bandwidth. This has increased the emphasis on receiver performance. Particular requirements include ultra-wide bandwidth, high sensitivity, and a large dynamic range for use with unbounded line codes [1, 2, 3, 4, 5, 6, 7, 8]. Ultra-wide bandwidth optical receivers are critical components for multi-gigabit/s direct detection transmission systems, as well as for future subcarrier-multiplexed or coherent

Optoelectronic Integrated Circuit Design and Device Modeling Jianjun Gao 2011 Higher Education Press

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234

Figure 7.1 Signal transmission in an optical front-end circuit.

communications systems. One of the most critical building blocks in an optical link system is the front end, which consists of a photodiode (PD) and a preamplifier. The performance of such a receiver is determined to a large extent by the front-end circuit. An integrated front-end photoreceiver consists of a photodetector and an amplifier fabricated on a single chip. In this chapter, we will introduce the basic concept of a high-speed receiver, the integrated circuit (IC) technique of the front-end. Subsequently, passive peaking techniques for a preamplifier are described.

7.1 Basic Concepts of the Optical Receiver This section introduces basic concepts such as signal-to-noise ratio (SNR), bit error ratio (BER), sensitivity, bandwidth, and dynamic range. To understand these figures of merit is very useful for designing an optimum front-end optical receiver.

7.1.1

Signal-to-Noise Ratio

In optical communication systems, the SNR of the receiver is a measure of signal strength relative to background noise at the input port, expressed as a simple arithmetic ratio or in decibels: Ip2 Signal power at the input port ¼ 2 ð7:1Þ Noise power at the input port hN i where Ip2 is the average power of the photocurrent and N 2 is the average power of the equivalent input noise current for the optical receiver. N 2 consists of the shot SNR ¼

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235

2 noise generated by PD NPD and preamplifier noise NA2 , and can be expressed as follows: 2 2 2 N ¼ NPD þ NA

ð7:2Þ

Based on the PIN PD and APD PD noise model described in Chapter NaN, the shot 2 can be expressed as: noise generated by PD NPD 2 NPD ¼ 2qðIp þ Idark ÞDf for PIN PD ð7:3Þ

2 NPD ¼ 2qM 2 FðMÞðIp þ Idark ÞDf

for APD PD

ð7:4Þ

where Df is the noise-effective bandwidth and can in turn be determined by the transfer function of the receiver: ð¥ 1 ð7:5Þ B¼ jHð f Þj2 df 2 jHð0Þj 0 where Hð0Þ is the asymptotic value of the transfer function Hðf Þ at low frequencies. The previously described receiver noise can introduce serious degradations in the system bit error ratio and must be strongly suppressed in high-speed optical systems.

7.1.2 Bit Error Ratio The goal of any digital transmission system is to deliver error-free information reliably and economically from one location to another. Therefore, the quality of transmission systems can be evaluated using the bit error ratio (BER). A digital receiver must take a weak optical signal and convert it into an electrical signal, and the decision circuit determines if a bit is a zero or a one by comparing the output voltage to the threshold voltage, which is located at the midpoint between zero and one, and finally generate an electronically compatible voltage representative of the logic state. The performance criterion for digital receivers is governed by the BER, defined as the number of bits received in error divided by the number of bits transmitted, which equals the error count in a measurement period divided by the product of the bit rate and the measurement period. The BER can be expressed as follows: BER ¼

Ne Ne Tb Ne ¼ ¼ Nt Bt t

ð7:6Þ

where Ne is the bits of incorrect identification, Nt is the total transmission bits, B is the bit rate, and Tb ¼ 1=B is the pulse width. A commonly used criterion for digital optical

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receivers requires the BER to be below 109, corresponding to an average of 1 error per billion bits. Figure 7.2 shows the probability density curves for a logical 1 and a logical 0. The total probability of making an error is the sum of the probability of deciding 0 when 1 is received and the probability of deciding 1 when 0 is received; therefore, the BER can be expressed as follows: BER ¼ Pð1ÞPð0=1Þ þ Pð0ÞPð1=0Þ

ð7:7Þ

where Pð1Þ and Pð0Þ are the probabilities of receiving bits 1 and 0, respectively, Pð0=1Þ is the probability of deciding 0 when 1 is received, and Pð0=1Þ is the probability of deciding 1 when 0 is received [1].

Figure 7.2 Probability density curves for a logical 1 and a logical 0.

When average and variance values are I1 and hN1 i for 1 and average and variance values are I0 and hN0 i for 0, the BER can be expressed in terms of I1 , I0 , hN1 i, and hN0 i as follows: 1 Q expðQ2 =2Þ pﬃﬃﬃﬃﬃﬃ BER ¼ erfc pﬃﬃﬃ ð7:8Þ 2 2 Q= 2p with Q¼

I1 I0 hN1 i þ hN0 i

where the complementary error function is defined as ð¥ 2 erfcðxÞ ¼ pﬃﬃﬃ expðy2 Þdy p x

ð7:9Þ

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Table 7.1 shows how the BER varies with the Q parameter; it can be found that the requirement of Q is more than 6 for BER less than 109 . When hN1 i ¼ hN0 i, Ith ¼ ðI1 þ I0 Þ=2, which corresponds to setting the decision threshold in the middle. The BER can be simplified as follows [2]: ! pﬃﬃﬃﬃﬃﬃﬃﬃﬃ 1 I1 1 SNR pﬃﬃﬃ ¼ erfc BER ¼ erfc pﬃﬃﬃ 2 2 2 2hN1 i 2 2

ð7:10Þ

Table 7.1 BER versus Q. Q

BER

Q

BER

0.0 3.090 3.719 4.265 4.753 5.199 5.612

0.5 103 104 105 106 107 108

5.998 6.361 6.706 7.035 7.349 7.651 7.942

109 1010 1011 1012 1013 1014 1015

7.1.3 Sensitivity An important performance measure for optical receivers is receiver sensitivity. To allow large repeater separations in an optical communication system, therefore, receivers have been designed to have good sensitivity, that is to require only a very low level of mean received optical power while operating within the maximum specified BER necessary to achieve a BER of 109 . In addition to direct measurement of the sensitivity through BER measurements, the sensitivity of a photoreceiver can be estimated from the analog noise performance. A simple analysis that considers only noise and finite bandwidth contributions to BER results is given in the following expression for the sensitivity: qﬃﬃﬃﬃﬃ hu 2 ð7:11Þ P ¼ SNRmin iin Zq where Z u h q

¼ ¼ ¼ ¼

photodiode external quantum efficient frequency of the incident light Planck’s constant electronic charge

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SNRmin ¼ minimum signal-to-noise ratio required to achieve the desired bit error ratio 2 iin ¼ mean square noise current at the input of the receiver This expression assumes that the detector bandwidth is sufficiently large so that the detector responsivity can be assumed to be constant for the frequencies of interest and that the amplifier exhibits a single-pole low-pass frequency response. Receiver sensitivity is determined by the SNR and the noise current at the input to the decision circuit in the regenerator. Optical receivers that employ an APD generally provide a higher SNR for the same incident optical power. The improvement is due to the internal gain, which increases the photocurrent by a multiplication factor M. Table 7.2 shows the comparison of typical PIN and APD receiver sensitivity. It can be found that sensitivity of the APD receiver is higher by 10 dB than the PIN receiver when the multiplication factor M is 10. Table 7.2

Typical PIN/APD receiver sensitivity.

Bit rate Noise current of preamplifier PIN receiver APD receiver

7.1.4

2.5 Gb/s

10 Gb/s

400 nA 24.3 dBm 34.3 dBm

1.2 mA 19.5 dBm 29.5 dBm

Eye Diagram

High-speed optical transmission systems often suffer serious impairment due to lowprobability phenomena such as modulation fluctuation and spectrum fluctuation of lasers. Degradation of quality occurs in each process: modulation, transmission, and detection. The eye pattern of the receiving amplifier output contains all the information concerning the degradation of quality. Therefore, the analysis of the eye pattern is important in analyzing the degradation mechanism. The eye diagram can be applied to many types of investigation, for example modulation characteristics and transmission characteristics of laser diodes, analysis of noise, jitter, intersymbol interference, and estimation of eye margin [3, 4, 9]. The eye diagram is formed by superposing 2–3 bit-long electrical sequences in the bit stream on top of each other. The resulting pattern is called an eye diagram because of its appearance. The best sampling time corresponds to maximum opening of the eye. Eye patterns can be observed using an oscilloscope. The oscilloscope is synchronized so that the pulses overlap on the screen. Since the bit pattern is random, if we consider a 4-bit pattern, the combinations can be only the following: 0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111

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Since 0 represents no light pulse and 1 represents the presence of a light pulse, an overlap of all the pulses is shown in Figure 7.3. The figure formed by the overlapping pulses is the eye diagram and the center is called the eye.

Figure 7.3 Eye pattern formed by overlapping the random pulse sequence. In this case the eye is open.

The resulting eye diagram contains a number of easily observed information about the digital transmission characteristics of the optical receiver (as shown in Figure 7.4): 1. Rise time and fall time of bit transition. The rise/fall time (20–80 %) is an analog parameter of fundamental importance in a high-speed optical receiver, since it is a measure of the ability of a circuit to respond to fast input signals. 2. Extinction ratio. The extinction ratio is an important specified test parameter for high-speed transmission systems and is typically defined as: ER ¼ 10 log

P1 P0

ð7:12Þ

where P1 and P0 are the mean or average optical power level of the logic 1 level and logic 0 level, respectively. 3. Jitter at the transition point. As shown in Figure 7.4, jitter can be measured in the eye diagram by computing a histogram of the time points when the signal crosses a

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Figure 7.4 Representative eye diagram.

reference voltage, that is the width of the threshold crossing (‘C’ on the figure). This voltage is set to the eye crossing point where the histogram has the tightest distribution. Many sampling oscilloscopes have the capability to calculate and display such histograms. From Figure 7.4, it can be found that the eye pattern when the pulses have suffered dispersion and have some jitter (that is the time interval between adjacent pulses does not remain constant but keeps changing randomly). The timing jitter is defined as (in %) Timing jitterðin %Þ ¼

Dt 100 % Tb

ð7:13Þ

where Tb is the bit spacing in the data stream. This jitter is an indication of the timing accuracy of received pulse as modified by the receiver. 4. Eye opening height. This height is a measure of the amplitude distortion of the signal; the extinction ratio increases with the increase of eye opening height. 5. Eye opening width. This width gives the optimum sampling time interval for the received signal to be sampled without error from intersymbol interference. 6. Noise level. The noise level of the output signal of the receiver can be determined from the spacing of ‘A’ and ‘B’ on the figure.

7.1.5

Signal Bandwidth

In this section, we will introduce how to determine the optimum signal bandwidth of the receiver. Figure 7.5 shows the normalized spectrum of the NRZ code. It is obvious that the signal bandwidth of the receiver should be equal to the bit rate in order to cover the frequency occupied by the NRZ code. However, due to the fact that most frequency spectrums (more than 90 %) concentrate on the frequency 0–0.8B, it is usually

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Figure 7.5 Normalized spectrum of the NRZ code.

common to design the receiver, with a bandwidth of 80 % of the data rate. This means that BWR 0:8B ¼

0:8 Tb

ð7:14Þ

Therefore, the bandwidth requirement of the high-speed optical receiver is 80 % of the required bit rate; that is, for a 10 Gb/s optical receiver design, an 8 GHz signal bandwidth is enough. Similarly, a 32 GHz signal bandwidth is enough for a 40 Gb/s optical receiver design. Figure 7.6 shows the eye diagram of the output signal with different bandwidths of the optical receiver [7], where it can be seen that the rise/fall times and noise level increase with the decrease of the bandwidth.

7.1.6 Dynamic Range Dynamic range is defined as the difference between the maximum and minimum signal levels that the system can accommodate. The maximum and minimum levels are sometimes defined rather arbitrarily; the minimum signal level is often defined as the sensitivity. The dynamic range of the receiver can be expressed as Dynamic range ¼ Pmax P

ð7:15Þ

242

Figure 7.6

Optoelectronic Integrated Circuit Design and Device Modeling

Eye diagram of the output signal with different bandwidths of the optical receiver:

(a) BWR ¼ B; (b) BWR ¼ 0:7B; and (c) BWR ¼ 0:5B.

Figure 7.7 shows the eye diagram of the output signal with different input power of a 10 Gb/s optical receiver [10]. It is seen that well-opened eye diagrams are obtained for a wide input dynamic range.

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Figure 7.7 Eye diagram of the output signal with different input power of the optical receiver: (a) Pin ¼ 20 dBm; (b) Pin ¼ 10 dBm; and (c) Pin ¼ 0 dBm.

7.2 Front-End Circuit Design An integrated lightwave receiver front-end is made of two basic elements: the PD and the electronic amplifier. The choice of optical device technology for the PD and electronic device technology are based on three criteria: performance (sensitivity,

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frequency response, and noise), ease of monolithic integration, and maturity of technology. The noise performance of the electronic devices is important at high bit rates, because the device noise dominates the input equivalent noise of the receiver.

7.2.1

Hybrid and Monolithic OEIC

The monolithic optoelectronic integrated circuits (MOEICs) and hybrid optoelectronic integrated circuits (HOEICs) are two kinds of technologies for integrating optoelectronic devices and electronic circuitry. High-performance PDs commonly used for high-speed optical fiber communication are the avalanche photodiode (APD), PIN, or metal–semiconductor–metal (MSM) PD. While APDs are attractive for highsensitivity applications, the other two photodetectors are more suitable for OEICs. The state-of-the-art active devices for very high-speed amplifiers are heterojunction bipolar transistors (HBTs) and high electron mobility transistors (HEMTs). Figure 7.8 shows the commonly used hybrid optoelectronic integrated optical receivers, where a matching network is normally necessary between the PD and preamplifier.

Figure 7.8

Hybrid optoelectronic integrated optical receivers.

In order to maximize the speed of a photoreceiver front end, minimization and careful control of the interconnect parasitics between the PD and the electrical amplifier is essential. One attractive approach for reducing these interconnect parasitic elements is to integrate the PD monolithically with active electrical devices on a common substrate. Among the MSM- and PIN-based integrated photoreceivers, MSM-HEMT and PIN-HBT are two popular choices of system designers because of its mature technology (as shown in Figure 7.9):

Figure 7.9 Monolithic optoelectronic integrated optical receivers.

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245

1. In the shared-layer integration scheme for PIN/HBT photoreceivers, the PIN layers are grown simultaneously with the growth of the epitaxial layers of HBTs. This type of integration has the advantages of one-step epitaxy, simplicity of fabrication, and possibly higher reliability. 2. Most of the beneficial properties of the MSM PD stem from its lateral planar geometry and compatibility with high-performance field-effect transistor technology and MSM PD is easily integrable with HEMT. The MSM PD and HEMT devices are integrated vertically in a stacked-layer structure. The HEMT epilayers were grown first, followed by a barrier layer of semi-insulating ferrous-doped InP. The growth of the MSM PD structure completes the growth sequence. The design of the receiver is much more demanding than the design of the transmitter. The sensitivity of the receiver is dominated by the noise sources at the front-end and hence the design of a low-noise preamplifier is very important. The preamplifier has the following basic requirements: 1. The transimpedance gain is high enough to override the noise of subsequent circuits. 2. Wide frequency band. 3. Low noise. 4. The input impedance is low enough to avoid degrading the frequency band with photodiode capacitance. 5. Wide dynamic range. The two basic front-end topologies commonly used for integrated photoreceivers are: (1) the high-impedance (HZ) design and (2) the transimpedance (TZ) design [11, 12].

7.2.2 High-Impedance Front-End Figure 7.10(a) shows the block diagram of the HZ front-end. The HZ amplifier design achieves low noise by using a large detector biasing resistor Rb. The input admittance of the amplifier is therefore dominated by the total input capacitance, and the input signal tends to be integrated by this capacitance. The HZ amplifier is used in combination with an equalizer to compensate for the distortion caused by the limited bandwidth of the high input admittance. Figure 7.10(b) shows the equivalent circuit model of the HZ front-end, where the HZ preamplifier is modeled by an arbitrarily large, noiseless, fixed gain A. The PD is modeled by a shunt current source for the signal current ip and a shunt capacitance Cd . The input impedance of the amplifier is modeled by the parallel combination of resistance Ra and capacitance Ca . An equivalent series voltage noise source en and an

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Figure 7.10 Block diagram and equivalent circuit model of the HZ front-end: (a) block diagram; (b) equivalent circuit model.

equivalent shunt current noise source in are used to model the noisy two-port network of the preamplifier. The front-end also includes the input bias resistor Rb with its equivalent thermal noise current ib . The signal transfer function for the HZ front end is HHZ ðoÞ ¼

vo ART ¼ ip 1 þ oRT CT

ð7:16Þ

The corresponding 3 dB bandwith of the signal transfer function can be determined directly from Equation (7.16): BWHZ ¼

1 2pRT CT

ð7:17Þ

where CT ¼ Cd þ Ca ; RT ¼ Ra ==Rb ¼

Ra Rb Ra þ Rb

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The mean square of equivalent input circuit current can be expressed as follows: 2 d iHZ d id2 d ib2 d in2 ¼ þ þ df df df df ð7:18Þ 2 2 d en d eno 1 2 þ þ þ ðoCT Þ df A2 R2T where heno i is the noise voltage contributed by the succeeding circuit after the preamplifier. Although the HZ amplifier is capable of giving the absolute minimum noise and has demonstrated exceptional bandwidth, it suffers from several shortcomings. First, the amplifiers may have to be individually equalized due to their sensitivity to device and temperature variations. Furthermore, the HZ front-end reduces the dynamic range of the amplifier compared to the TZ front-end.

7.2.3 Transimpedance Front-End The TZ amplifier or shunt feedback amplifier is the most commonly used design in OEIC receivers due to its wide bandwidth and dynamic range compared to the HZ front-end. The amplifier consists of an inverting voltage amplifier with resistive feedback from output to input. In practice, the noise performance of the TZ amplifier is not as good as that achieved with the HZ amplifier, but at high bit rates, this noise performance gap decreases. With proper design the TZ amplifier can almost match the noise performance of the HZ amplifier. Figure 7.11(a) shows the block diagram of the TZ front-end and Figure 7.11(b) shows the corresponding equivalent circuit model, where the noise current if is generated by feedback resistance Rf . The signal transfer function for the TZ front-end can be expressed as follows: HTZ ðoÞ ¼

Rf 1 þ 1=A þ Rf =ðART Þ þ joRf CT =A

ð7:19Þ

Note that lim HTZ ðoÞ ¼ Rf

A!¥

ð7:20Þ

As shown in Equations (7.19) and (7.20), the feedback resistance determines the transimpedance, and thus the sensitivity of the amplifier. Larger feedback resistances increase the sensitivity of the amplifier, but simultaneously reduce the amplifier bandwidth.

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Figure 7.11 Block diagram and equivalent circuit model of the TZ front-end: (a) block diagram; (b) equivalent circuit model.

The corresponding 3 dB bandwidth of the signal transfer function can be determined directly from Equation (7.19): BWTZ ¼

1 þ Rf =ð1 þ AÞ=RT 1 2pCT Rf =ð1 þ AÞ 2pCT Rf =ð1 þ AÞ

ð7:21Þ

The mean square of equivalent input circuit current can be expressed as follows: D E 2 2 2 2 d if2 d iTZ d id d ib d in ¼ þ þ þ df df df df df # 2 " 2 2 d en d eno A 2 þ þ ðoCT Þ þ df A2 R2f

ð7:22Þ

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with D E d if2 df

¼

4kT Rf

Figure 7.12 shows the frequency response of the HZ and TZ front-ends, where it is obvious that the TZ front-end has a lower gain of transfer function and wide bandwidth. The ratio of gains of the HZ and TZ front-ends and the ratio of bandwidths of the HZ and TZ front-ends can be expressed as follows: Rgain ¼ lim

o!0

RBW ¼

HHZ ðoÞ RT ¼A 1 HTZ ðoÞ Rf

BWTZ ðoÞ ð1 þ AÞRT ¼ 1 BWHZ ðoÞ Rf

ð7:23Þ

ð7:24Þ

Figure 7.12 Frequency response of the HZ and TZ front-ends.

The difference of equivalent input noise current densities of the TZ and HZ frontends can be expressed as # 2 2 " d iTZ d iHZ d e2no A2 1 4kT 4kT ¼ þ ð7:25Þ df df A2 Rf Rf R2f R2T Table 7.3 summarizes the comparison of the HZ and TZ front-ends, showing that there is a trade-off between the bandwidth and the noise (speed versus sensitivity) of a

250

Optoelectronic Integrated Circuit Design and Device Modeling

Table 7.3 Comparison of optical HZ and TZ front-ends. Front-end

HZ

TZ

Result

Gain at low frequencies

ART

Rf

HZ

Bandwidth

1 2pRT CT

1 2pCT Rf =ð1 þ AÞ

TZ

Input impedance

RT 1 þ joRT CT

Rf 1 þ A þ joRf CT D E 2 d if2 d iHZ þ df df

Input noise current

2 d iHZ df

TZ

HZ

TZ front-end. Additionally, the dynamic range of the TZ front-end is greater than that of the HZ front-end; for a given preamplifier, the improvement in dynamic range will be approximately the ratio of the open- and closed-loop gains.

7.3 Transimpedance Gain and Equivalent Input Noise Current The major design goals of the front-ends are the transimpedance gain and equivalent input noise current density. The transimpedance gain of front-ends must be large enough to overcome the noise of the subsequent stage, typically a 50O driver or a limiting amplifier. The equivalent input noise current density determines the minimum input current that yields a given bit error ratio, directly impacting the link budget. Unfortunately the transimpedance gain and equivalent input noise current density cannot be measured directly from microwave and noise equipments, while the S parameters and noise figure of front-ends can be measured from a vector network analyzer (VNA) and noise figure meter in a straightforward manner. Therefore a fast transformation between S parameters/noise figure and transimpedance gain/equivalent input noise current density is needed. Although analytical expressions for transimpedance gain and equivalent input noise current of optical receivers have been derived in reference [13], simple expressions for the relationship between the transimpedance gain and Z parameters is given in reference [14]. However, the expressions mentioned above are not universally valid, and the transimpedance gain and equivalent input noise current density cannot be accurately calculated directly from S parameters and noise figure measurement data. A simple but efficient transformation technique for front-ends will be introduced in this section, and the analytical expressions for the relationships between the transimpedance gain and S parameters, equivalent input noise current density and the noise figure for high-speed optical transimpedance preamplifier design are derived. This technique is based on the signal-and-noise equivalent circuit model of the optical receiver front-end.

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Compared with previous publications, this method has the following advantages: 1. The transimpedance gain can be directly derived from S parameters for arbitrary source and load impedance, and simplified expressions for two special cases (source impedances are zero and 50 O) are also given. 2. The equivalent input noise current density can be determined from the noise figure measurement without four noise parameters (minimum noise figure, noise resistance, and optimum source reflection coefficient) of the transimpedance amplifier (TIA) in 50 O and non-50 O systems.

7.3.1 S Parameters of a Two-Port Network The S parameter characterization of two-port networks are based on exciting the network by the incident waves at the input port and output port. In this case a1 and a2 are the independent variables and b1 and b2 are the dependent variables. The network operation can be described by two equations: b1 ¼ S11 a1 þ S12 a2

ð7:26Þ

b2 ¼ S21 a1 þ S22 a2

ð7:27Þ

where ½S is called the scattering matrix of a two-port network. Sij ði; j ¼ 1; 2Þ are known as the scattering parameters of the two-port network. Since the units of the incident and reflected waves are the same, scattering parameters must be dimensionless. As already mentioned above, the S parameters can only be determined under conditions of perfect matching on the input or output side. For instance, in order to record S11 and S21 we have to ensure that on the output side the line impedance Zo is matched for a2 ¼ 0 to be enforced. Figure 7.13 shows the block diagram for

Figure 7.13 Block diagram for calculation of S parameters: (a) block diagram for calculation of S11 and S21 ; (b) block diagram for calculation of S12 and S22 .

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calculation of S11 and S21 (as shown in Figure 7.13(a)) and the block diagram for calculation of S12 and S22 (as shown in Figure 7.13(b)) [15]. The definition equations and physical meaning of the S parameters are summarized in Table 7.4 [16]. Table 7.4 Definition of S parameters. Parameters S11 S21 S12 S22

7.3.2

Definition equation b1 2V1 ¼ 1 a1 a2 ¼0 VS b2 2V2 ¼ a1 a2 ¼0 VS b1 2V1 ¼ 0 a2 a1 ¼0 VS b2 2V2 ¼ 0 a2 a1 ¼0 VS

Physical meaning Input reflection coefficient when output port is terminated in a matched load Forward transmission coefficient when output port is terminated in a matched load Reverse transmission coefficient when input port is terminated in a matched load Output reflection coefficient when input port is terminated in a matched load

Noise Figure of a Two-Port Network

The noise figure (or noise factor) is a figure of merit quantitatively specifying how noisy a component or system is. The most basic definition of the noise figure F is the ratio of the signal-to-noise power ratio at the input to the signal-to-noise power ratio at the output, as shown in Figure 7.14: F¼

SNRin Si =Ni ¼ SNRout So =No

ð7:28Þ

Figure 7.14 Noise figure of a two-port network.

where SNRin and SNRout are the available signal-to-noise ratios at the input and output ports, respectively, Si and Ni are the available signal and noise power at the input port, respectively, and So and No are the available signal and noise power at the output port, respectively. Assuming the available signal and noise power of the two-port network are G and Na , the available noise power at the output port can be expressed as follows:

Optical Receiver Front-End Integrated Circuit Design

No ¼ Na þ GNi

253

ð7:29Þ

With Equation (7.29) substituted in Equation (7.28), we have F¼

Si =Ni No Si =Ni Na þ GNi ¼ ¼ ¼ So =No GNi GSi =ðNa þ GNi Þ GNi

ð7:30Þ

or F ¼ 1þ

Na kT0 BG

ð7:31Þ

7.3.3 Transimpedance Gain The schematic of the optical receiver front-end circuit is shown in Figure 7.15, where YS is the photodiode (PD) input admittance. Typically this will be that of the PIN/APD and is almost completely capacitive (that is YS ¼ poCpd ). YL is the load admittance, which is generated mainly by input admittance of the next stage (typically the admittance should be 20 mS for an impedance of 50 O, that is YL ¼ Yo ¼ 20 mS).

Figure 7.15 Simplified model of the optical receiver front-end.

The transimpedance is defined as the magnitude of the ratio of output voltage V2 at a load impedance and photocurrent through the photodiode is . Based on the small-signal circuit model analysis for an optical receiver front-end in Figure 7.15 and applying Kirchhoff’s current law, the transimpedance gain of the optical receiver front-end can be expressed as ZT ¼

V2 Y21 ¼ is ðYS þ Y11 ÞðYL þ Y22 ÞY21 Y12

ð7:32Þ

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The relationship between the S parameters and Y parameters can be expressed as Y11 ¼ Yo

ð1 þ S22 Þð1S11 Þ þ S12 S21 ð1 þ S22 Þð1 þ S11 ÞS12 S21

ð7:33Þ

Y12 ¼ Yo

2S12 ð1 þ S22 Þð1 þ S11 ÞS12 S21

ð7:34Þ

Y21 ¼ Yo

2S21 ð1 þ S22 Þð1 þ S11 ÞS12 S21

ð7:35Þ

Y22 ¼ Yo

ð1 þ S11 Þð1S22 Þ þ S12 S21 ð1 þ S22 Þð1 þ S11 ÞS12 S21

ð7:36Þ

where Yo (¼ 20 mS) is the characteristic admittance of the system. Substituting Equations (7.33) through (7.36) into Equation (7.32), we have ZT ¼

V2 2S21 ¼ is Yo A þ YL B þ YS C þ YS YL D=Yo

ð7:37Þ

with A ¼ ð1 S11 Þð1 S22 Þ S12 S21 B ¼ ð1 S11 Þð1 þ S22 Þ þ S12 S21 C ¼ ð1 þ S11 Þð1 S22 Þ þ S12 S21 D ¼ ð1 þ S22 Þð1 þ S11 Þ S12 S21 If source impedance is infinite (that is YS ¼ 0) and the output end of the TIA is connected to a matched load (that is YL ¼ Yo ¼ 20 mS), the corresponding transimpedence gain of the receiver front-end can be simplified as follows: ZTT ¼

S21 Yo ð1S11 Þ

ð7:38Þ

When the TIA is operated in a 50 O system (that is YL ¼ YS ¼ Yo ¼ 20 mS), the transimpedence gain can be written as ZT50 ¼

S21 2Yo

ð7:39Þ

The transimpedance gain versus YS and YL are summarized in Table 7.5 [17], where it can be observed that the transimpedance 3 dB bandwidth can be determined from the

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Table 7.5 Transimpedance gain versus YS and YL . Source and load impedances

Transimpedance gain

Physical meaning

Arbitrary YS and YL

ZT

Receiver front-end (PD þ TIA)

YL ¼ Yo ;

ZTT

TIA only

ZT50

Power gain S21 of TIA

YS ¼ 0

YL ¼ YS ¼ Yo

forward transmission coefficient S21 only when the input and output ports are terminated in the matched loads. The physical meanings of the three transimpedance gains mentioned above are as follows: ZT is the transimpedance gain of the whole optical receiver front-end (PD þ TIA), ZTT is the transimpedance gain of the TIA, and ZT50 is proportional to the power gain S21 of the TIA.

7.3.4 Equivalent Input Noise Current 7.3.4.1 Equivalent Input Noise Current Density of the TIA Figure 7.16 shows the noise model of the noise figure measurement system for the optical preamplifier. It is noted that 50 O standard resistances have been used for the source and load impedances (that is ZS ¼ ZL ¼ Zo ¼ 50 O). ZiT and ZoT are the input and output impedances of the TIA, respectively, vno is the total output noise voltage T is the equivalent input noise current density of the TIA. density, and iin

Figure 7.16 Noise model of the 50 O noise figure measurement system for the optical preamplifier.

The noise figure of the TIA can be expressed as follows: F50 ¼ 1 þ

v2no 4kT A2v jZo

ð7:40Þ

that is v2no ¼ 4kT A2v jZo ðF50 1Þ

ð7:41Þ

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where Av is the voltage gain and can be expressed as Av ¼

V2 S21 ZT ¼ ¼ T T Vs 2 Zi þ Zo

ð7:42Þ

where ZTT is the transimpedance gain of the TIA ðZTT ¼ V2 =I1 Þ. The corresponding T can be derived as follows: equivalent input noise current density of the TIA iin pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ðF50 1Þ4kT0 Zo v no T ¼ ð7:43Þ ¼ iin Zo þ Z T j jZTT j i With ZiT ¼ Zo (1 þ S11)/(1 S11) substituted in Equation (7.43), we have sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ T ¼ vno ¼ j1S j ðF50 1ÞkT0 ð7:44Þ iin 11 jZTT j Zo

7.3.4.2 Equivalent Input Noise Current Density of the Front-End Figure 7.17 shows the noise model of a typical optical receiver front-end in a non-50 O R is the total equivalent input noise current density and v is the total system, where iin no output noise voltage density of the receiver front-end. It is noted that the input port of the TIA is connected to the PD, not the matched load. Therefore the expression (7.44) is only valid for the TIA design, not the whole receiver front-end.

Figure 7.17 Noise model of the optical receiver front-end.

Assuming that the total output noise voltage density vno is composed mainly of the TIA (here the noise contribution of the PD is neglected), the equivalent input noise R can be expressed as follows: current density of the receiver front-end iin R ¼ iin

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ vno 1 ¼ jYo A þ YL B þ YS C þ YS YL D=Yo j kTo Zo ðF50 1Þ jZT j 2

ð7:45Þ

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Traditionally, the output end of the TIA is connected to a matched load (that is R can be rewritten as YL ¼ Yo ¼ 20 mS) and iin sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ R ¼ vno ¼ j1S þ ð1 þ S ÞY =Y j kTo ðF50 1Þ ð7:46Þ iin 11 11 S o Zo jZT j When the TIA is operated in a 50 O system (that is YL ¼ YS ¼ Yo ¼ 20 mS), the equivalent input noise current density can be simplified to sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ kTo ðF50 1Þ 50 ð7:47Þ iin ¼2 Zo It is noted that expression (7.47) is the conventional formula for predicting the 50 equivalent input noise current density for the TIA IC, and the iin is dependent on the noise figure only and independent of the S parameters of the TIA. The equivalent input noise current density versus YS and YL are summarized in Table 7.6 [17]. Table 7.6 Equivalent input noise current density versus YS and YL . Source and load impedances

Input noise current density

Physical meaning

Arbitrary YS and YL

R iin

Receiver front-end (PD þ TIA)

YL ¼ Yo ; YS ¼ 0

T iin

TIA only

YL ¼ YS ¼ Yo

50 iin

Only dependent on noise figure of TIA

7.3.5 Simulation and Measurement of Transimpedance Gain and Equivalent Input Noise Current In order to demonstrate the expressions derived in Sections 7.3.3 and 7.3.4 for the TIA, a HEMT-based TIA which operates at 10 Gb/s has been designed using a 0.2 mm PHEMT process [18]. Figure 7.18 shows a schematic of the developed TIA IC by using both enhancement- and depletion-mode (E–D) transistors. This IC consists of three parts: a parallel-feedback amplifier core, a source–follower buffer, and an output match stage. The source–follower buffer improves the flatness of the gain–frequency characteristics by separating the parallel-feedback loop from the large input capacitance of the output buffer (that is eliminates the Miller capacitance loading to the previous stages). The output stage is designed for a 50 O output impedance match. Figure 7.19 shows the experimental setup for S parameters and noise figure measurement. All measurements were carried out on wafer using air-coplanar probes.

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Optoelectronic Integrated Circuit Design and Device Modeling

Figure 7.18 Schematic of the 10 Gb/s HEMT-based TIA IC.

Figure 7.19 Experimental setup for S parameters and noise figure measurement.

The wafer probes were calibrated using the line-reflect-match (LRM) calibration method for S-parameter measurement. The noise parameter measurement method here has been tested on wafer up to 26 GHz. Figure 7.20 shows the measured magnitudes and phases of the S parameters of the TIA IC. A high gain jS21 j of 25 dB and a broad 3 dB bandwidth over 10.8 GHz have been obtained. Good matching has also been achieved; jS11 j is below 10 dB and jS22 j is below 7 dB for the whole frequency range. The corresponding noise figure versus frequency is shown in Figure 7.21. The transimpedance gain (TG) and equivalent input noise current density (EINCD) can be obtained from AC and noise signal analysis by using commercial circuit design tools (such as SPICE), but it is difficult to measure

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259

Magnitudes of S parameters (dB)

30 S21 15

0

S22

S11

-15 f3dB

-30 0

3

6 9 12 Frequency (GHz)

15

18

(a)

Phases of S parameters ( degree )

200

S22

100 S11

0 S21

-100

-200 0

3

6

9

12

15

18

Frequency (GHz)

(b) Figure 7.20 S parameters of the 10 Gb/s HEMT-based TIA IC: (a) magnitudes; (b) phases.

Noise figure (dB)

8 6 4 2 0 0

2

4

6

8

10

12

14

16

18

Frequency (GHz)

Figure 7.21 Measured noise figure of the 10 Gb/s HEMT-based TIA IC.

Optoelectronic Integrated Circuit Design and Device Modeling

260

directly using conversional microwave signal and noise measurement system. Alternatively, they can be calculated from S parameters and noise figure measurements by using the proposed transformation expressions. Figure 7.22 shows the transimpedance gain that is derived from the measured S parameters of the 10 Gb/s TIA and the corresponding 3 dB bandwidth versus capacitance of the PD is shown in Figure 7.23. It can be found that a 3 dB bandwidth of TIA transimpedance gain is 11.5 GHz roughly, and the corresponding optical receiver front-end 3 dB bandwidth decreases with the increase of PD capacitance (YS ¼ joCpd ). As long as the capacitance of the PD is less than 0.6 pF (the 3 dB bandwidth is above 8 GHz), the proposed TIA can be operated at 10 Gb/s. Figure 7.24 shows the comparison of the predicted transimpedance gain for a 10 Gb/s TIA by using expressions (7.38) and (7.39). It is obvious that the gain and bandwidth predicted by Equation (7.38) is better than that of the TIA operating in a matching system. That means the transimpedance gain will be underestimated using the conventional formula. 64

TG (dBΩ)

57 50 43

Cpd=0.1, 0.3, 0.6 pF

36 0

3

6

9

12

15

18

Frequency (GHz)

Figure 7.22 Plot of transimpedance gain versus frequency for the 10 Gb/s TIA.

Bandwidth (GHz)

14 12 10 8 6 0.0

0.2

0.4

0.6

0.8

Capacitance (pF)

Figure 7.23 The 3 dB bandwidth of transimpedance gain versus PD capacitance.

Figure 7.25 shows the equivalent input noise current density (EINCD) derived from the measured noise figure of the 10 Gb/s TIA and the corresponding average values

Optical Receiver Front-End Integrated Circuit Design

261

64

TG (dBΩ)

57 50 43

Conventional Proposed

36 0

3

6 9 12 Frequency (GHz)

15

18

Figure 7.24 Comparison of transimpedance gain for the 10 Gb/s TIA by using predicted data from Equations (7.38) and (7.39).

EINCD

(pA/Hz 1/2 )

60 Cpd=0.1, 0.3, 0.6 pF 45 30 15 0 0

2

4

6

8

10

12

14

16 18

Frequency (GHz)

Figure 7.25 Equivalent input noise current density (EINCD) versus frequency for the 10 Gb/s TIA.

versus PD capacitance is shown in Figure 7.26. It can be found that the equivalent input noise current density increases with the increase of PD capacitance (YS ¼ joCpd ). As long as the capacitance of the PD is less than 0.3 pF, the equivalent input noise current pﬃﬃﬃﬃﬃﬃ density of the TIA is below 20 pA= Hz. Figure 7.27 shows the comparison of the EINCD (pA/Hz 1/2 )

40 30 20 10 0 0.0

0.2

0.4

0.6

0.8

Capacitance (pF)

Figure 7.26 Equivalent input noise current density (EINCD) versus PD capacitance.

Optoelectronic Integrated Circuit Design and Device Modeling

262

EINCD (pA/Hz 1/2 )

60 Conventional Proposed

45 30 15 0 0

2

4

6

8

10

12

14

16

18

Frequency (GHz)

Figure 7.27 Comparison of equivalent input noise current density (EINCD) for the 10 Gb/s TIA: predicted data from the proposed expression (7.44) and the conventional expression (7.47).

predicted equivalent input noise current density for the 10 Gb/s TIA. By using the proposed expressions (7.44) and the conventional formula (7.47), it is obvious that the equivalent input noise current density predicted by Equation (7.44) is better than that predicted by the conventional formula. This means that the equivalent input noise current density will be overestimated using the conventional formula.

7.4 Transimpedance Amplifier Circuit Design In the receiver front-end of an optical fiber communication system, transimpedance amplifiers (TIAs) are widely used as the first active building block to convert the photodiode current to an amplified voltage for data recovery. Since the system specifications such as sensitivity, speed, and signal-to-noise ratio are strongly influenced by the TIA, tremendous design efforts are required in determining the circuit parameters for optimum performance. The high-speed TIAs can be fabricated by various semiconductor techniques, such as silicon, GaAs, and InP, and so on. The speed of a TIA based on a silicon BJT can be achieved up to 10 Gb/s. Based on GaAs MESFET, HEMT, and HBT devices, the TIA can be operated at 10–40 Gb/s. In order to achieve over 40 Gb/s, state-of-art InP HEMT and HBT should be used.

7.4.1

BJT-Based Circuit Design

The basic elementary of a BJT-based TIA includes the common-emitter inverter stage and emitter followers mainly (as shown in Figure 7.28) [19, 20, 21, 22, 23, 24, 25]. The emitter followers are used for level shifting between the amplifier cells. Moreover, they are required for improving the mismatch between the amplifier stages (impedance transformation) and can be used for gain peaking at high frequencies.

Optical Receiver Front-End Integrated Circuit Design

263

Figure 7.28 Basic elements of a BJT-based TIA.

Traditionally, in BJT-based TIA circuit design, single-feedback and dual-feedback techniques are commonly used to improve bandwidth and noise performance. Figure 7.29 shows the single-feedback techniques in the BJT-based TIA, where the output signal can be fed back into the input port using either local stage feedback or feedback from succeeding buffer stage techniques. Figure 7.30 shows the dual-feedback loop in a BJT-based TIA, where the gain stage design is based on a dual-feedback loop circuit having both current feedback RF1 and voltage feedback RF2 [22]. For the preamplifier, the input noise of the circuit is mainly due to thermal noise in the current feedback resistor RF1. Increasing the resistance value of RF1 is very effective for reducing input noise. However, a large resistance of RF1 causes a bandwidth degradation. The dual-feedback configuration aids in producing a wide bandwidth amplifier with a large current feedback resistor RF1 value. Table 7.7 summarizes the comparison of the performance of BJT-based TIAs.

7.4.2 HBT-Based Circuit Design Heterojunction transistors (HBTs) extend the advantages of a silicon bipolar transistor to significantly high frequencies. For high-speed applications requiring a high-current drive, high transconductance, high-voltage handing capability, low-noise oscillator, and uniform threshold voltage, HBTs have been a natural choice at frequencies from 1 to 100 GHz. Based on the substrate material, HBTs have three categories: GaAs HBT, InP HBT, and SiGe HBT. The SiGe base, adopting a Ge graded profile, reduces the base transit time due to the presence of a drift field. Therefore, the SiGe-base bipolar transistor provides a faster maximum cutoff frequency than a conventional Si-bipolar transistor. The commonly used HBT-based high-speed TIAs will be introduced in the following list [33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49]. 1. Darlington feedback amplifier: Darlington transistors contain two transistors connected in an emitter–follower configuration, while sharing the same collector

264

Optoelectronic Integrated Circuit Design and Device Modeling

Figure 7.29 Single feedback techniques in a BJT-based TIA: (a) feedback from the local stage; (b) feedback from the succeeding buffer stage.

contact. The key advantage of the Darlington configuration is that the total current gain of the circuit equals the product of the current gain of the two devices. The disadvantage is the larger saturation voltage. Figure 7.31 shows the configuration of the Darlington feedback amplifier. This direct-coupled amplifier topology consists of two gain stages. The first stage is a common-emitter amplifier and the second stage is a feedback amplifier comprised of Darlington connected transistors, Q2 and Q3. The first stage acts as a low-noise common-emitter amplifier stage that determines the noise figure of the overall twostage amplifier. The second-stage Darlington feedback amplifier provides wideband gain and output drive capability. The feedback resistor Rf 2 is used to control the noise figure as well as input return-loss performance.

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265

Figure 7.30 Dual-feedback loop in a BJT-based TIA. Table 7.7 BJT-based TIA. ft (GHz) 12 15 28 40 — 23 23 35

Bandwidth (GHz)

TG (dB O)

pﬃﬃﬃﬃﬃﬃ EINCD (pA= Hz)

Power (mW)

Ref.

2.2 1.67 5.1 11.2 9 7.8 9 10.5

55 70 50 53 45 57 57 60

18 3.5 9.5 — — 9 10 12

— 170 — — 400 143 215 450

[26] [27] [28] [29] [30] [31] [31] [32]

2. Differential feedback amplifier: Figure 7.32 shows the configuration of the differential feedback amplifier. The differential operation mode reduces noise problems, typical in amplifiers with high gain and operating speed. The amplifier consists of a differential TIA stage, followed by two emitter followers (2EF), a transadmittance stage (TAS), and a transimpedance stage (TIS) to give high bandwidth through the impedance mismatch. The negative-feedback resistor is only used in the first stage to extend the bandwidth and improve the dynamic range. 3. Cascode feedback amplifier: The cascode is a two-stage amplifier composed of a transconductance amplifier followed by a current buffer. Compared to a single amplifier stage, this combination may have one or more of the following advantages: higher input–output isolation, higher input impedance, higher output impedance, higher gain, or higher bandwidth. In the case of transistors, the gain device can be operated in common-emitter or common-collector modes, which utilize a second transistor in the common base

266

Optoelectronic Integrated Circuit Design and Device Modeling

Figure 7.31 Configuration of the Darlington feedback preamplifier.

Figure 7.32 Configuration of the differential feedback amplifier.

mode whose emitter is connected to the collector of the gain transistor. The cascode improves input–output isolation as there is no direct coupling from the output to input. This eliminates the Miller effect and thus contributes to a higher bandwidth. Figure 7.33 shows the configuration of the cascode feedback amplifier. In order to reduce the capacitance and high shot noise current at the input due to the large DC base current of the transistor, the small emitter-area HBTs for the input cascodedpair stage should be used, followed by a two-step emitter-follower involving one small and one large emitter-area HBT.

Tables 7.8 to 7.10 summarize the performance of GaAs-, InP-, and SiGe-based HBT TIAs. It is obvious that the transmission bit rate can be greatly improved compared with a BJT-based TIA.

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267

Figure 7.33 Configuration of the cascode feedback amplifier. Table 7.8 GaAs HBT-based TIA. ft (GHz) 24 41 70 70

Bandwidth (GHz)

TG (dB O)

pﬃﬃﬃﬃﬃﬃ EINCD (pA= Hz)

Power (mW)

Ref.

9.1 12.7 27 40

53 50 53 50

<12 — — —

53 — 102 280

[33] [34] [35] [35]

Bandwidth (GHz)

TG (dB O)

pﬃﬃﬃﬃﬃﬃ EINCD (pA= Hz)

Power (mW)

Ref.

10 14 32 40 47 26.7

40 45 32 45 56 48.9

— 10 — — 35 25

84 34.3 — 130 457 26.5

[39] [40] [41] [42] [43] [44]

Bandwidth (GHz)

TG (dB O)

pﬃﬃﬃﬃﬃﬃ EINCD (pA= Hz)

Power (mW)

Ref.

19 9 5.5 50

38 45 43 49

95 77 — 200

[45] [46] [47] [48]

Table 7.9 InP HBT-based TIA. ft (GHz) 54 67 80 125 160 120

Table 7.10 SiGe HBT-based TIA. ft (GHz) 60 52 18 200

— 20 30

268

7.4.3

Optoelectronic Integrated Circuit Design and Device Modeling

FET-Based Circuit Design

Compared with HBT devices, the FET devices (including MESFET and HEMT) have the lowest noise performance; therefore, they are more suitable for optical preamplifier design. A common-source FET is chosen as the basic amplifying element since it provides voltage and current gain along with reverse isolation, a combination not available from common-gate or common-drain configurations. An active-load FET is used rather than a resistor load because it results in better large-signal performance for a given small-signal gain. With the active load it is possible to choose a quiescent operating point nearly half of the saturation current of the common-source FET. The circuit, which consists of a common-source FET and an active-load FET, is called an inverter, as a basic elementary cell for high-speed optical preamplifier design [58]. Figure 7.34 shows the inverter circuit and corresponding equivalent circuit model at low-frequency ranges. The gain of the inverter circuit can be calculated as follows: AV ¼

gm 2 gm ¼ gd þ gd =2 3 gd

ð7:48Þ

Figure 7.34 (a) Inverter circuit and (b) equivalent circuit model at low-frequency ranges.

where gm and gd are the transconductance and output conductance of the commonsource FET, respectively. The gain is independent of the inverter FET gate width, so long as the active-load FET remains half the width of the inverter FET, as assumed for this calculation. The inverter circuit of Figure 7.34(a) could be cascaded, with AC coupling, to produce a multistage amplifier with higher gain. However, the bandwidth would be reduced substantially due to the heavy capacitive loading of the succeeding stage’s gate capacitance. Therefore, a buffer circuit is necessary to insert between the inverter circuits. The combination of an inverter and a buffer circuit will be referred to as a single amplifier stage, although they could, as well, be treated as two stages: common source followed by common drain. The configurations of commonly used FET-based high-speed TIAs are shown in Figure 7.35. The resistive feedback, active feedback, and cascade are three popular

Optical Receiver Front-End Integrated Circuit Design

269

Figure 7.35 Configurations of the commonly used FET-based TIAs: (a) passive feedback; (b) active feedback; and (c) cascade with active feedback.

choices for FET-based TIAs. Tables 7.11 and 7.12 summarize the performance of MESFET- and HEMT-based TIAs. For the cascode configuration, it consists of a common-source stage M1/M2 (inverting), followed by a common-gate stage M3/M4 (noninverting). The total gain of an FET cascode circuit is approximately as follows [59]: Acascode ¼

gm1 1 gd4 1 þ ð1 þ gd3 =gd4 Þðgd1 þ gd2 Þ=gm3

ð7:49Þ

Optoelectronic Integrated Circuit Design and Device Modeling

270

Table 7.11 GaAs MESFET-based TIA. ft (GHz) -/0.3 40/-/13/1.0 -/0.5

Bandwidth (GHz)

TG (dB O)

pﬃﬃﬃﬃﬃﬃ EINCD (pA= Hz)

Power (mW)

8.6 13 3.5 7.6 12

55 54 59 67 44

20.9 15 12 — 12.6

95 — 800 — —

Table 7.12 GaAs/InP HEMT-based TIA. ft (GHz) 35 85 60 170

Bandwidth (GHz)

TG (dB O)

pﬃﬃﬃﬃﬃﬃ EINCD (pA= Hz)

Power (mW)

10 8.0 18 43

55 63.3 41.8 48.2

13.5 6.5 20 20

— 465 — 350

Reference [49] [50] [51] [52] [53]

Reference [54] [55] [56] [57]

where gm1 and gm3 are the transconductances of FET M1 and M3, respectively; gdi ði ¼ 1;:::;4Þ is the output conductance of FET Mj ðj ¼ 1;:::;4Þ.

7.4.4

MOSFET-Based Circuit Design

Due to the inherently high-speed and low-noise characteristics, III–V compound semiconductor devices have been dominantly utilized to realize such amplifiers. With the continuous scaling of transistor feature size, fully integrated TIA designs using submicrometer CMOS technologies have attracted great attention due to the low implementation cost and high integration level. Figure 7.36 shows the cutoff frequency

Figure 7.36 Cutoff frequency versus gate length for MOSFET.

Optical Receiver Front-End Integrated Circuit Design

271

versus gate length for a MOSFET. It can be seen that as the CMOS technology is downscaled to gate lengths of 90 nm and less, current state-of-the art 70–45 nm CMOS devices have achieved performances similar to III–V devices or Si-Ge bipolar transistors, but at a lower cost [60, 61]. The peak transit frequency of an NMOS transistor is pushed to over 100 GHz. Therefore, the design of circuits in CMOS technology operating over 10 GHz should be straightforward. Figure 7.37 shows the schematic of a conventional single-stage resistive shunt feedback TIA in the common-source configuration, and Table 7.13 summarizes the performance of MOSFET-based TIAs.

Figure 7.37 Schematic of a conventional resistive shunt feedback TIA in the common-source configuration. Table 7.13 MOSFET-based TIA. Process (mm) 0.08 0.08 0.18 0.18 0.18 0.18 0.18 0.18 0.25

Bandwidth (GHz)

TG (dB O)

pﬃﬃﬃﬃﬃﬃ EINCD (pA= Hz)

Power (mW)

Ref.

19 20 6 7.2 7.6 7.9 8 9.2 9

45 52 53 61 52 90 53 54 55

— 50 — 8.2 — — 18 — 9.5

6.5 2.2 88 70 34 199 25 55 140

[62] [63] [64] [65] [66] [67] [67] [68] [69]

7.4.5 Distributed Circuit Design In future optical transmission systems, data rates of more than 40 Gb/s are expected. Millimeter-wave wireless technology will be used in such future applications as

272

Optoelectronic Integrated Circuit Design and Device Modeling

multimedia mobile access communication (MMAC) and intelligent transport systems (ITSs). A wide-bandwidth baseband amplifier is a key component for developing such systems. Baseband amplifiers are used as preamplifiers in optical receivers and as data signal amplifiers in optical communication systems. Distributed circuit-design amplifiers have been used in approaches to obtain bandwidths extending into the millimeter-wave frequency range [70, 71, 72, 73, 74, 75, 76, 77]. The schematic circuit of a conventional distributed amplifier is depicted in Figure 7.38. It has artificial input and output lines that are constructed with a series of transmission lines and the parasitic capacitances of the transistors. These lines have very high cutoff frequencies and cancel out the effects of parasitic capacitances. Thus, these amplifiers inherently have wideband characteristics.

Figure 7.38 Schematic circuit of a conventional distributed amplifier.

The gate extrinsic inductors Lg and gate–source capacitance Cgs of the gain cells (FET device) form an input artificial transmission line. The input line has impedance given by qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð7:50Þ Zpg ¼ Lg =Cgs The drain extrinsic inductors Ld and drain–source capacitance Cds of the gain cells (FET device) form an input artificial transmission line. The output line has impedance given by pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ Zpd ¼ Ld =Cds ð7:51Þ The gate and drain lines are matched with the terminating resistors, equal to Zpg and Zpd , so that input and output impedances of the preamplifier remain constant over a

Optical Receiver Front-End Integrated Circuit Design

273

large frequency bandwidth. The magnitude of the transimpedance in the passband is given by n jZTf j ¼ gm Zpg Zpd 2

ð7:52Þ

where gm is the transconductance of the FET and n is the number of FETs in the distributed preamplifier structure. Bandwidth is a high priority in transimpedance amplifiers. Unlike conventional microwave amplifiers, these amplifiers have to maintain an acceptable response down to very low frequencies and still perform satisfactorily at high frequencies. The lowfrequency response must extend as close as possible to zero Hz. However, with conventional design techniques, gain and noise performance are low at relatively low frequencies. This makes it very difficult to produce a baseband amplifier for optical transmission systems. By using frequency-dependent drain termination and active gate termination, a 0 Hz-to-millimeter-wave bandwidth with a low noise figure is achieved (as shown in Figures 7.39 and 7.40). Table 7.14 summarizes the performance of the distributed circuit design amplifiers.

Figure 7.39 Schematic gate termination circuits of distributed amplifiers: (a) resistor termination; (b) active termination.

Figure 7.40 Schematic drain termination circuits of distributed amplifiers: (a) conventional resistor termination; (b) frequency-dependent termination.

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274

Table 7.14 Distributed TIA. ft (GHz) 43 (MESFET) 20 (MESFET) 40 (MESFET) 80 (HBT) 147 (HBT) 167 (HEMT)

Bandwidth (GHz)

TG (dB O)

pﬃﬃﬃﬃﬃﬃ EINCD (pA= Hz)

Power (mW)

Ref.

0.5–30 0.5–8 DC–36 0.055–55 0.05–50 0.1–49

41 45 41 38 53 52

30 8 20 — — —

— — 1000 82 240 520

[70] [71] [72] [73] [74] [75]

7.5 Passive Peaking Techniques The bandwidth of a high-speed optical receiver front-end is normally determined by the cutoff frequency of the semiconductor device. In order to overcome the limitations of semiconductor technology (such as CMOS, FET, and HBT), the passive peaking techniques can be used to extend circuit bandwidth significantly without the penalty of power consumption. Meanwhile, it can have a relatively flat frequency response similar to LC-ladder filters.

7.5.1

Inductive Peaking Techniques

Although inductors are commonly associated with narrowband circuits, they are useful in broadband circuits as well. There are many different methods of broadband amplifier design; one of the most extensively used is inductive peaking. This method involves placing inductors in strategic locations so that they resonate with parasitic capacitances and, consequently, broaden the bandwidth. Inductive peaking offers an advantage over conventional microwave design techniques in that it allows for an increase in bandwidth without sacrificing low-frequency gain [78, 79, 80, 81, 82, 83]. There are five types of inductive peaking techniques that are commonly used as follows: a. Gate inductive peaking technique out of the feedback loop b. Gate inductive peaking technique in the feedback loop c. Drain inductive peaking technique out of the feedback loop d. Drain inductive peaking technique in the feedback loop e. Feedback inductive peaking technique. Figure 7.41 shows the reduced circuit configurations of preamplifier with various inductive peaking techniques. Conventionally, the planar inductors are fabricated by forming a dielectric on a semiconductor substrate such as Si and GaAs, on printed circuit boards, and on hybrid integrated circuit substrates, and then depositing metal in a spiral geometry directly on the dielectric. To improve the performance of spiral

Optical Receiver Front-End Integrated Circuit Design

275

Figure 7.41 Circuit configurations of a preamplifier with inductive peaking techniques.

inductors, airbridges, rather than a dielectric, can be used to separate the metal from the substrate. The nonidealities of on-chip inductors present several challenges for implementing monolithic gigahertz circuitry. In shunt-peaking applications, the biggest issue is the reduction in bandwidth improvement because of the additional parasitic capacitance introduced by the on-chip inductor. Figure 7.42 shows the configuration of a square spiral inductor with the corresponding equivalent circuit model.

Figure 7.42 Configuration of a square spiral inductor with an equivalent circuit model.

Figures 7.43 to 7.45 show the effects of gate (a and b), drain (c and d), and feedback inductor peaking on the 3 dB bandwidth, gain peaking, and equivalent input noise current density (EINCD). It can be seen that gate inductor peaking is especially useful for high bandwidths and EINCD, whereas drain inductor peaking is good for high bandwidths. Figures 7.46 and 7.47 show the typical FET-based TIA and MOSFET-based TIA designs using gate and drain peaking inductors. It is well known from circuit theory that excessive gain peaking can lead to system instability; therefore, the peaking inductor value is limited by the stability factor of the amplifier.

Optoelectronic Integrated Circuit Design and Device Modeling

276 16 3 dB bandwidth (GHz)

b 12

a

d

e

8

c 4 0

1

2

3

4

5

Inductance (nH)

Figure 7.43 3 dB bandwidth of a TIA versus a peaking inductor.

Gain peaking (dB)

30

d

20

b c

10

a

e 0 0

1

2

3

4

5

Inductance (nH)

Figure 7.44 Gain peaking of a TIA versus a peaking inductor.

30 EINCD (pA/Hz 1/2 )

e d

20

c

b 10 a 0 0

5

10

15

20

Frequency (GHz)

Figure 7.45 EINCD of a TIA versus peaking inductor.

25

Optical Receiver Front-End Integrated Circuit Design

277

Figure 7.46 Typical FET-based TIA design with gate and drain peaking inductors.

Figure 7.47 Typical MOSFET-based TIA design with gate peaking inductors.

7.5.2 Capacitive Peaking Techniques As previous mentioned, the bandwidth and noise performance can be improved using inductive peaking techniques. This method usually places inductors in a strategic location of the amplifier circuit, resulting in a resonance with parasitic capacitances, which broadens the bandwidth of the amplifier. However, there are several issues that need to be overcome: 1. The stray capacitances of the inductor often cause a bandwidth degradation rather than an improvement. To overcome this problem, the size of the inductor must be as small as possible to reduce the stray capacitance effect.

278

Optoelectronic Integrated Circuit Design and Device Modeling

2. It is difficult to fabricate the on-chip inductors with a high-quality factor on the silicon-based substrate, resulting in worse noise. 3. The area of the chip increases with the increase in the number of on-chip inductors, resulting in a larger die area and high cost. Instead of inductive peaking, capacitive peaking can be used to increase the bandwidth of a TIA. Because the size of a capacitor is relatively smaller than an inductor, the parasitic effect can also be reduced. Figure 7.48 shows the typical FET-based TIA design with peaking capacitors, and the corresponding frequency response is shown in Figure 7.49 [84]. To deliver proper DC bias to the next stage, three-level shift diodes are inserted in the source follower. Diodes are attained by connecting the source and the drain of an FET produced using the conventional GaAs process. Resistance components of the diodes degrade the frequency performance of the SF. To overcome this problem, a capacitor is inserted in parallel with the diodes so that AC signals

Figure 7.48 Typical FET-based TIA design with peaking capacitors.

Figure 7.49 Frequency response of TIA with peaking capacitor.

Optical Receiver Front-End Integrated Circuit Design

279

bypass the diodes. This arrangement permits an increase in high-frequency gain and expansion of the bandwidth.

7.6 Matching Techniques Optical receivers for direct detection are required to operate at over several decades of frequency span with flat gain. However, conventional microwave design techniques are not generally applicable for operation from nearly DC to gigahertz frequencies. For this reason, wideband receiver front-ends are generally based on a mismatched TIA amplifier and PD configuration. Therefore, it is difficult to achieve the optimum noise and gain design for an ultra-wideband front-end using conventional microwave lownoise amplifier design rules. However, by inserting a matching network between the TIA amplifier and PD, the equivalent input noise current density can be minimized for a certain frequency range (passband). This kind of optical front-end is called a tuned front-end. The use of front-end tuning in optical receivers can provide a significant improvement in the noise performance of certain optical communication links. Schemes such as subcarrier multiplexing (SCM) particularly benefit as the information to be transmitted is frequency translated before optical modulation. The basic concept behind SCM is borrowed from microwave technology, which employs multiple microwave carriers for transmission of multiple channels over optical fiber. With such a modulation scheme the optical receiver only has to operate over a restricted bandwidth and as such allows tuned front-end techniques to be employed. A tuned front-end receiver not only provides the required passband response but minimizes the noise contribution of the receiver [85, 86]. The noise behavior of a linear noisy two-port network (TIA) can be characterized by the four noise parameters, Fmin , Rn , Gopt , and Bopt , as follows: F ¼ Fmin þ

i Rn h ðGs Gopt Þ2 þ ðBs Bopt Þ2 Gs

ð7:53Þ

Rn Ys Yopt j2 Gs

ð7:54Þ

or F ¼ Fmin þ

where F is the noise figure, Ys ¼ Gs þ jBs is the source admittance, Fmin is the minimum noise figure, Rn is the noise resistance, and Yopt ¼ Gopt þ jBopt is the optimum source admittance. It is obvious that in order to obtain the optimum noise figure, it is necessary to match the source admittance of the TIA (looking into the output of the matching network) to the impedance of the optimum source admittance. Figure 7.50 shows the configuration of a tuned optical front-end and Figure 7.51 shows the noise-equivalent circuit model of an FET-based tuned front-end. The two

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Optoelectronic Integrated Circuit Design and Device Modeling

Figure 7.50 Configuration of a tuned optical front-end.

Figure 7.51 Noise-equivalent circuit model of an FET-based tuned front-end.

current noise sources ig2 and ig2 represent the internal noises of the FET device; these noise sources are correlated. It is noted that two input noise voltages e2n and currents in2 are used to represent the noise property of the noisy two-port TIA. The corresponding admittance noise correlation matrix of the FET can be expressed as 2 pﬃﬃﬃﬃﬃﬃ 3 ðoCgs Þ2 R=gm joCgs C PR 5 ð7:55Þ CY ¼ 4kT 4 pﬃﬃﬃﬃﬃﬃ joCgs C PR gm P where gm is the transconductance, Cgs is the gate-to-source capacitance, R and P are the gate and drain noise model parameters, and C is the correlation coefficient.

Optical Receiver Front-End Integrated Circuit Design

281

The input noise voltage e2n and current in2 can be determined by using noise matrix techniques: e2n ¼

in2

CY22 jY21 j2

ð7:56Þ

en in * ¼

CY21 Y11 * þ CY22 Y21 j2 Y21

ð7:57Þ

en *in ¼

CY21 Y11 * þ CY22 Y21 j2 Y21

ð7:58Þ

Y11 Y11 Y11 * þ CY22 j2 ¼ CY11 CY21 CY12 Y21 * Y21 Y21

ð7:59Þ

The equivalent input noise current density of the PD and TIA (without a tuned network) can be expressed in terms of the input noise voltage e2n and current in2 : 2 iin ¼ ½en Yin ðoÞ þ in ½en Yin ðoÞ þ in * ¼ e2n jYin ðoÞj2 þ en in* Yin ðoÞ þ e*n in Yin* ðoÞ þ in2

ð7:60Þ

where Yin ðoÞ is the input admittance of the TIA. The equivalent input noise current density of the complete tuned front-end is given by 2 4KT GðZ22 Þ iin ¼ gm Z21 j2

ð7:61Þ

where k is the Boltzmann constant, T is the absolute temperature (normally 290 K), Z21 and Z22 are the Z parameters of the input network (as shown in Figure 7.51), and GðZ22 Þ is the noise factor of the front-end, given by pﬃﬃﬃﬃﬃﬃ gm 2ð1 þ PÞ 2 GðZ22 Þ ¼ P þ ðoCgs Þ R þ Re½Z22 jZ22 j2 2C PRðoCgs Im½Z22 Þ þ Rf Rf For the untuned case, it is obvious that the noise factor GðZ22 Þ is constant and that the correlation term is additive so that GðZ22 Þ is increased. For the tuned case, GðZ22 Þ in general becomes frequency dependent. In order to minimize the equivalent input noise

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Optoelectronic Integrated Circuit Design and Device Modeling

current density of the complete tuned front-end, two conditions should be satisfied for the Z parameter of the input network: 1. The real part of Z22 is zero, that is Re½Z22 ¼ 0. The tuned network should be a lossless network. 2. The imaginary part of Z22 should be larger than zero, that is Im½Z22 > 0. The noise factor GðZ22 Þ can be regarded as a quadratic polynomial; therefore optimum values can be determined from GðZ22 Þ:

Im½Z22 opt ¼

pﬃﬃﬃﬃﬃﬃ C PRðoCgs Þ ðoCgs Þ2 R þ gm=Rf

ð7:62Þ

Substituting Equation (7.62) into (7.61), the optimum noise factor is given by " # ðoCgs Þ2 RC2 ð7:63Þ GðZ22 Þmin ¼ P 1 ðoCgs Þ2 R þ gm=Rf It is very common to use reactive components to achieve this impedance transformation, because they do not absorb any power or add noise. Thus, series or parallel inductance or capacitance can be added to the circuit to provide an impedance transformation. Figure 7.52 shows the typical narrowband inductor tuning networks: parallel tuning, T-type tuning, and Pi-type tuning. Figure 7.53 shows the gain and noise performance of a tuned receiver front-end using three typical narrowband inductor tuning networks. By using a single inductor tuning network, the noise factor of the front-end can be minimized at a single frequency point. When broader noise tuning bandwidths are required, multielement tuning networks that provide a noise match across the desired frequency band are required. For tuning bandwidths of around an octave, transformer tuning is a popular method used. The two equivalent circuit representations of a transformer, namely T-type and Pi-type, are used when analyzing and designing transformer tuned front-ends.

Figure 7.52 Typical narrowband inductor tuning network: (a) parallel tuning; (b) T-type tuning; and (c) Pi-type tuning.

Optical Receiver Front-End Integrated Circuit Design

283

55

TG (dBΩ)

50

b

d

45 a

40

c 35 0

5

10 Frequency (GHz)

15

(a) Gain

EINCD (pA/Hz 1/2 )

40 30 a

20

b 10 c

d 0 0

5

10

15

Frequency (GHz)

(b) Noise

Figure 7.53 (a) Gain and (b) noise performance of a tuned receiver front-end using the three typical narrowband inductor tuning networks.

Of course, the tuned optical receiver front-end using a narrowband inductor tuning network is suitable for an SCM system only. In the case of broadband optical receivers, the noise-matching network must be synthesized to satisfy the network requirements over a wide frequency range. The commonly used noise-matching network between

Figure 7.54 Broadband noise-matching network.

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Optoelectronic Integrated Circuit Design and Device Modeling

Figure 7.55 Noise performance of a tuned receiver front-end using a broadband noise-matching network.

the PD and TIA is shown in Figure 7.54. By using a high-order low-pass filter-type network as the noise-matching network, the equivalent input noise current density of a completely tuned front-end can be reduced,as shown in Figure 7.55 [87, 88].

7.7 Summary In this chapter, the basic concept of a high-speed receiver, the integrated circuit (IC) design technique of the front-end, has been introduced. The passive peaking techniques, which include inductance and capacitance techniques for extending bandwidth and minimizing the noise performance of transimpedance preamplifier designs, are described in more detail.

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Index above-threshold bias condition, 78, 97, 106 absolute temperature, 74 absorption coefficient, 119, 125 absorption rate, 53 absorption region, 125 active layer, 35 active region, 35 active tuning, 30 ambient temperature, 79 analytical method, 105 atom energy, 11 avalanche multiplication, 132 band gap, 11, 117 bandwidth, 121 base-collector junction capacitance, 220 base-emitter junction capacitance, 220 bit error ratio, 234 Boltzmann’s constant, 66 built-in potential, 79 buried heterostructure, 18 capacitance-voltage characteristics, 138 capacitive peaking technique, 225, 277 carrier density, 26, 42 carrier transport, 41, 166 cascode feedback amplifier, 265 channel length modulation parameter, 158 channel resistance, 153 charge storage, 66

charge storage capacitance, 142 chirping, 44 compound-semiconductor-based device, 149 conduction band, 11 contact resistance, 77 coplanar waveguide, 204 correlated current noise sources, 171 cross spectral intensity, 73 Curtice-cubic model, 160 cutoff bias condition, 179 dark current, 119, 140 Darlington feedback amplifier, 263 DC model parameters, 174 de-embedding, 78, 98 depletion region, 119 depletion width, 124 depletion-layer capacitance, 142 differential feedback amplifier, 265 diffusion capacitance, 70 direct modulation, 190 direct-coupled FET logic, 200 distortion measurement, 57 distributed amplifier, 222 distributed Bragg reflector, 29 distributed feedback laser, 27 double heterojunction, 17 drain channel current noise, 161 drain pad capacitance, 153

Optoelectronic Integrated Circuit Design and Device Modeling Jianjun Gao Ó 2011 Higher Education Press

290

drain-bulk junction, 178 drain-to-source capacitance, 153 driver circuit, 199 dynamic range, 241 dynamic resistance, 97 electrical signal, 114 electro-absorption modulator, 190 electron density, 35 electron mobility, 150 electron-hole pair, 39, 114 electronic field, 115 electronic part, 79 emitter coupled logic, 200 empirical equivalent circuit model, 138 energy band, 11 equilibrium electron density, 37 equivalent circuit model, 63 equivalent input circuit current, 247–248 equivalent noise temperature, 164 external modulation, 191 extinction ratio, 239 eye diagram, 238 Fabry-Perot cavity lasers, 20 fall time, 239 FET modeling technique, 151 fiber-optic links, 1 finite-difference form, 137 flat-band voltage, 136 forward-bias, 79 Fourier transform, 77 frequency chirp, 46 frequency modulation, 34, 44 front-end circuit design, 243 gain compression factor, 37, 65 gain slope coefficient, 65 gain-guided, 18 gap capacitance, 138 gap voltage, 137 gate induced noise current, 161 gate pad capacitance, 153 gate-to-drain capacitance, 153 gate-to-source capacitance, 153

Index

gateway state, 76 grounded electrode, 137 harmonic balance, 155 harmonic distortion, 48 HBT modeling, 165 HEMT, 151 heterojunction, 15 high impedance front-end, 245 hole mobility, 129 homojunction, 15 hybrid optoelectronic integrated circuits, 197, 244 incident light power, 116 index guiding, 18 inductive peaking technique, 226, 274 input logic swing, 209 input reflection coefficient, 95 insertion loss, 192 intensity modulation direct-detection, 46 interdigitated electrode, 135 intermodulation distortion, 56 intrinsic region, 124 inverter circuit, 268 ionization layer, 131 junction capacitance, 127 knee voltage, 217 Langevin noise, 52 large signal model, 65, 168 large signal transit response, 46 large-signal circuit model, 65 large-signal modulation, 46 laser driver, 199 lateral planar geometry, 135 level shift circuit, 206 linear model, 168 linewidth enhancement factor, 44 Mach–Zehnder, 190 matching network, 202 measurement procedure, 103

291

Index

measurement technique, 55 MESFET, 152 microsolder bump bonding, 197 microstrip test fixture, 103 microwave modeling technique, 114 millimeter-wave, 1 modulation response, 48 modulator driver, 205 monolithic optoelectronic integrated circuit, 195, 224 MOSFET, 176 MSM PD, 134 multi quantum well, 24 multimode fiber, 3 multimode rate equations, 38 multiplexer, 188 multiplication noise, 130 multiplication region, 132 noise bandwidth, 52 noise correlation matrix technique, 165 noise current source, 73 noise effective bandwidth, 235 noise figure, 252 noise measurement technique, 55 noise model, 161, 163, 170, 181 noise performance, 52 nonlinear equivalent circuit model, 76 nonradiative recombination, 39 non-return-to-zero, 189 normalization constant, 66 normalized small signal modulation response, 96 one-level, 76 on/off aspect ratio, 93 open test structure, 153 operating wavelength, 44 optical cavity, 14, 33 optical communication system, 1 optical confinement factor, 37 optical external modulator, 191 optical fiber, 3–4 optical modulation, 190

optical receiver, 234 optical transmitter, 188 parameter extraction method, 95, 171, 181 parasitic effects, 95 parasitic element, 79 passive peaking technique, 224, 274 passive tuning, 31 phase tuning, 31 photocurrent, 127 photo-generated carrier, 122 photon density, 36 photon lifetime, 35 PIN PD, 124 PI-type model, 168 population distribution, 12 population inversion, 14 positive electrode, 137 positive feedback, 14 Pospieszalski noise model, 163 power dissipation, 210 Pucel noise model, 161 quantum efficiency, 66, 116 quantum well lasers, 22 radio frequency, 1 rate equation, 35 reach-through voltage, 138 receiver sensitivity, 238 relationship, 156 relative intensity noise, 51,72 relaxation oscillation, 48 responsivity, 116 return-to-zero, 198 reverse-bias, 115 ridge-waveguide laser, 64 rise time, 47, 117, 239 room temperature, 67 saturation drift velocity, 137 saturation voltage parameter, 209 Schottky barrier, 136 Schottky contact, 136 second-order harmonic distortion, 48

292

semi-analysis method, 105, 181 semiconductor laser, 10 separate absorption and multiplication, 132 separate confinement structure laser, 23 separate-confinement heterostructure, 24 series inductance, 77 short noise, 73 shunting capacitance, 77 SiGe, 175 signal bandwidth, 240 signal transfer function, 247 signal-to-noise ratio, 238 silicon-based device, 149 single mode fiber, 3 single quantum well, 24 single-longitudinal mode semiconductor laser, 44 single-mode rate equations, 35 small signal frequency modulation, 44 small signal intensity modulation, 34, 40 small signal model, 68, 152, 177 source-coupled FET logic, 200 space-charge capacitance, 70, 97, 138 space-charge region, 167 spontaneous emission, 12, 35, 66 Statz model, 157 steady state carrier density, 38 steady-state analysis, 68 steady-state condition, 38, 69, 88 stimulated emission, 13 stripe-geometry laser, 18 subcarrier multiplexed, 52

Index

submode suppression ratio, 28 supply voltage, 210 terminal electrical noise, 52, 74 thermal equilibrium, 126 thermionic emission lifetime, 42, 86 three-level, 76 three-level equivalent circuit model, 90 threshold current, 70 threshold voltage, 209 time-varying variable, 43, 69 timing jitter, 240 transconductance parameter, 141, 212, 213 transfer function, 45 transimpedance front-end, 247 transimpedance gain, 250 transit response, 46 transit response measurement, 58 transit time, 124 transverse junction stripe, 18 T-type model, 168 turn-on delay, 94 turn-on time, 47 two-level, 76 two-level equivalent circuit model, 83 two-port network, 251 valence band, 11 vertical cavity surface emitting laser, 33 voltage standing wave ratio, 222 wire bonding, 197