Novel Heterostructure Metal-Semiconductor-Metal (HMSM) Photodetectors with

Resonant Cavity for Fiber Optic Communications

A Thesis

Submitted to the Faculty

of

Drexel University

by

Xiying Chen

in partial fulfillment for the

requirements for the degree

of

Doctor of Philosophy

June 2002

ii

Dedications

I would like to dedicate this work to my father Lieyi Chen, my mother Lili Shen, and my

sister Xueying Chen, for their continuous support, love and belief in me.

iii

Acknowledgements

I would like to thank Dr. Bahram Nabet for his tireless motivation, continuous

guidance, and neverending support of my work. I am also extremely grateful to Dr.

Richard L. Coren, Dr. Steward D. Personick, and Dr. M. El-Sherif for their support to my

education, and Dr. Peter Herczfeld and Dr. Afshin Daryoush for their encouragement to

my research.

I would also like to thank Dr. Afshin Daryoush and Dr. Warren Rosen for helping

design the distributed Bragg reflector (DBR), Dr. Fabio Quaranta for fabricating the

devices, Dr. Adriano Cola for assisting to analyze the experimental data and making

photocurrent spectral response and current-voltage measurements, Dr. Marc Currie for

lending me a hand in waveguide transmission line designs and for making the time

response measurement, and Mr. Eric Gallo for editing the whole thesis.

Many thanks to Dr. Amro Anwar, Dr. Hujie Chen, Dr. Xueshi Yang, and Dr.

Francisco Castro for their valuable discussions, to Mr. Eric Gallo, Ms. Athena Bauerle,

and Mr. Hungjen Huang for their helpful arguments, and Mr. Liming Zhou, Mr. Yuankai

Zhou, Mr. Qiliang Zhang and Ms. Hongyuan Shi for their friendship and support of my

graduate study.

iv

Table of Contents

LIST OF TABLES........................................................................................................... viii LIST OF FIGURES ............................................................................................................ix ABSTRACT.......................................................................................................................xv 1. INTRODUCTION ...................................................................................................1

1.1 The Need for Fiber-Optic Communication Systems ...................................1 1.2 Fiber-Optic Communication Systems..........................................................2 1.3 Optical Photodetectors .................................................................................3

1.3.1 PIN photodiode ................................................................................5 1.3.2 Avalanche photodiods (APDs) ........................................................7 1.3.3 Metal-Semiconductor-Metal (MSM) photodiodes ..........................8

1.4 Photodetectors for Different Transmission Windows..................................9 1.4.1 Transmission characteristic of the optical fiber .............................10 1.4.2 Transmission in the 0.85 µm optical window................................12

1.4.2.1 Si photodiodes..............................................................13 1.4.2.2 GaAs photodiodes........................................................14

1.4.3 Transmission in the 1.3 µm optical window..................................18 1.4.4 Transmission in the 1.55 µm optical window................................18

1.4.4.1 Ge infrared (IR) photodiodes .......................................19 1.4.4.2 In0.53Ga0.47As infrared (IR) photodiodes......................20

1.5 Objective and Scope of the Thesis.............................................................23 1.6 Literature Review.......................................................................................26

2. RESONANT CAVITY ENHANCED DEVICES .................................................34

2.1 Introduction................................................................................................34 2.2 Theoretical Analysis of Planar Mirror Resonators ....................................36 2.3 Formulation of Quantum Efficiency for RCE Photodetectors...................39

2.3.1 Formulation of the quantum efficiency for RCE photodetectors ................................................................................40

2.3.2 Formulation of the reflectivity of the two mirrors .........................43 2.3.3 Numerical calculation of RCE quantum efficiency .......................44 2.3.4 Standing wave effect......................................................................47

2.4 Formulation of Reflection Coefficient of Mirrors .....................................50 2.4.1 Reflection coefficient calculated from transmission line

analogue .........................................................................................50 2.4.2 Multiple reflection viewpoint ........................................................53

2.5 Formulation Modified at Oblique Incidence..............................................56

v

3. A CLOSED-FORM EXPRESSION TO ANALYZE ELECTRONIC PROPERTIES IN DELTA-DOPED HETEROSTRUCTURES............................60 3.1 Introduction................................................................................................61 3.2 Closed-form Expression for Delta Doped Modulation

Heterostructures .........................................................................................63 3.3 Closed-form Model of Electric Field and Potential ...................................68 3.4 Numerical Model Based on Schrödinger and Poisson Equations..............69 3.5 Calculation Scheme for Numerical Model Based on Schrödinger

and Poisson Equations ...............................................................................71 3.6 Results and Discussion ..............................................................................73 3.7 Conclusions................................................................................................78

4. III-V MATERIAL BASED DOPED HMSM PHOTODETECTOR

DESIGN WITH RESONANT CAVITY FOR OPTICAL COMMUNICATIONS ..........................................................................................79 4.1 Introduction................................................................................................80 4.2 Material Selection ......................................................................................83

4.2.1 III-V material parameters’ calculation...........................................84 4.2.1.1 Ternary (GaAl)As system............................................85 4.2.1.2 Quaternary (GaIn)(AsP) and (Al,Ga,In)As

systems.........................................................................88 4.2.2 Absorption layer.............................................................................89

4.2.2.1 Absorption materials for 800-900 nm optical window.........................................................................89

4.2.2.2 Absorption materials for 1550 nm optical window.........................................................................90

4.2.3 Barrier enhancement layer .............................................................91 4.2.3.1 Barrier enhancement layer for GaAs based

photodetectors ..............................................................91 4.2.3.2 Barrier enhancement layer for InP based

photodetectors ..............................................................93 4.2.4 Distributed Bragg reflector ............................................................94

4.2.4.1 DBR for GaAs based photodetectors...........................94 4.2.4.2 DBR for InP based photodetectors ..............................95

4.3 Selection of Structure Parameters..............................................................96 4.3.1 The grown RCE heterojunction MSM...........................................96

4.3.1.1 GaAs based photodetector structures...........................97 4.3.1.2 InP based photodetector structures ..............................98

4.3.2 Dispersion relation expression.......................................................99 4.3.2.1 Dispersion relation in ternary (GaAl)As system..........99 4.3.2.2 Dispersion relation of quaternary (GaIn)(AsP),

(Al,Ga,In)As system ..................................................101 4.3.3 Reflectivity from the bottom mirror ............................................102

4.3.3.1 Reflectivity from the bottom mirror in GaAs based PD ....................................................................103

4.3.3.2 Reflectivity from the bottom mirror in InP based PD ..............................................................................104

vi

4.3.4 Quantum efficiency......................................................................106 4.3.4.1 Quantum efficiency in GaAs based PD .....................106 4.3.4.2 Quantum efficiency in InP based PD.........................107

4.3.5 Sheet charge density ....................................................................108 4.3.6 Electric field.................................................................................110

4.3.6.1 Electric field profile in GaAs based PD.....................110 4.3.6.2 Electric field profile in InP based PD ........................112

4.4 Conclusions..............................................................................................114 5. PERFORMANCE CHARACTERISTICS OF ALGAAS/GAAS DELTA

DOPED HMSM PHOTODETECTOR WITH RESONANT CAVITY FOR SHORT HAUL COMMUNICATIONS .....................................................118 5.1 Wavelength Selectivity, High Sensitivity, and High Speed ....................119

5.1.1 Wavelength selectivity.................................................................120 5.1.2 Sensitivity, light response ............................................................122 5.1.3 High speed (time domain)............................................................124 5.1.4 High speed (frequency domain)...................................................126 5.1.5 Long trace of time response.........................................................128 5.1.6 Capacitance measurement............................................................129

5.2 Improvement of MSM Photodetector using Delta-doped AlGaAs/GaAs Heterostructure ................................................................131 5.2.1 Band bending profile....................................................................131 5.2.2 Current-voltage comparison.........................................................133

5.2.2.1 Experimental data ......................................................133 5.2.2.2 Thermionic emission theory ......................................134 5.2.2.3 Discussions ................................................................138 5.2.2.4 Potential distribution in 2DEG ..................................139

5.2.3 Comparison of current voltage at different temperature..............141 5.2.4 Comparison of capacitance- voltage measurements ....................144 5.2.5 Time response comparison ..........................................................145 5.2.6 Discussion of time response.........................................................147

5.2.6.1 Comparison of temporal response (short trace) .........148 5.2.6.2 Comparison of temporal response (long trace)..........153

5.3 Further Comparison of Undoped and Delta-doped Devices....................156 5.3.1 TEM (transmitted electron microscopy) structure.......................157 5.3.2 Comparison of the reflectivities between two devices ................159 5.3.3 Simulation results of the reflectivity spectrum ............................161 5.3.4 Comparison of the internal quantum efficiency...........................163

5.4 Conclusions..............................................................................................165 6. CONTRIBUTIONS AND FUTURE DIRECTIONS ..........................................167

6.1 General.....................................................................................................167 6.2 Contributions............................................................................................167 6.3 Future Work .............................................................................................170

6.3.1 ISE-TCAD simulation .................................................................170 6.3.2 Dynamic behavior........................................................................172 6.3.3 Electro-Optic measurement of microwave circuits......................174

vii

6.3.4 HEMT design...............................................................................176 LIST OF REFERENCES.................................................................................................184 APPENDIX A: TRANSMISSION LINE DESIGN ........................................................197

A1 Requirements of Geometry of Structure ..................................................197 A2 Formula for Calculation...........................................................................198 A3 Simulation Results ...................................................................................201

VITA ..............................................................................................................................205

viii

List of Tables

Table 1. 1 Typical characteristics of p-i-n and avalanche photodiodes [5, 6]. .............9 Table 1. 2 Comparison of characteristics of Si and GaAs photodiodes for 0.85

µm [5, 6, 20-26]. ........................................................................................17 Table 1. 3 Progress in trans-Atlantic-transmission (TAT) capacity. ..........................29 Table 4. 1 Lattice constant, gap energy, and electron affinity for a selected

number of III-V binary compounds [125] [126]........................................84 Table 4. 2 AlxGa1-xAs material information................................................................87 Table 4. 3 Material parameters of quaternary (GaIn)(AsP) and (Al,Ga,In)As

systems.......................................................................................................88 Table 4. 4 Optical and electrical characteristics of GaAs and Si. ...............................89 Table 4. 5 Optical and electrical characteristics of In0.53Ga0.47As and Ge..................90 Table 4. 6 Performance of barrier enhancement layer structure above

In0.53Ga0.47As active layer [85, 47, 134-136]. ............................................93 Table 4. 7 Electronic parameters for GaAs, AlAs, and AlxGa1-xAs..........................101 Table 4. 8 Parameters used in the calculation of ε1(ω). ............................................101 Table 5. 1 Measured and theoretical capacitance values. .........................................145

ix

List of Figures

Figure 1. 1 Conventional fiber optic communication link, showing a fiber optic connecting an optical transmitter and a receiver passing by a repeater, adapted from [2]............................................................................3

Figure 1. 2 Block diagram of an optical receiver, consisting of a photodetector

and an amplifier. ..........................................................................................4 Figure 1. 3 Optical receiver equivalent circuit. ..............................................................4 Figure 1. 4 Layer and functional structure of a PIN photodiode....................................6 Figure 1. 5 p-i-n photodiode: (a) front-illuminated PD; (b) fear-illuminated

PD; (c) edge-illuminated PD........................................................................6 Figure 1. 6 Functional structure of an APD photodiode. ...............................................7 Figure 1. 7 A top-view for the Metal-Semiconductor-Metal photodetector

planar interdigitated structure. .....................................................................8 Figure 1. 8 Attenuation as a function of wavelength[7]...............................................10 Figure 1. 9 Typical dispersion vs. wavelength curve[8]. .............................................11 Figure 1. 10 Absorption coefficients of important semiconductor materials

versus wavelength [9]. ...............................................................................12 Figure 1. 11 Schematic cross section of a Si pin photodiode.[10]. ................................13 Figure 1. 12 Cross-section of a Si APD with a so-called pπpπn structure (π

standing for low p- doping level).[10]........................................................14 Figure 1. 13 Integration schemes for integrated photoreceivers: (a) pin-HBT;

(b) pin-FET on a planar substrate; (c) pin-FET on a recessed substrate [10]..............................................................................................15

Figure 1. 14 Devices for monolithic photoreceiver integration. One should

notice the similarity of MSM and FET structures. [10].............................16 Figure 1. 15 Ge photodiode on SiGe/Si [34]..................................................................20 Figure 1. 16 Example of an InGaAs photodiode with back-illumination.[10]...............21

x

Figure 1. 17 Fundamental device structure of III-V MESFET and heterostructure HEMT. ..............................................................................23

Figure 2. 1 Two-mirror planar resonator (Fabry-Perot Mirror). ..................................36 Figure 2. 2 Schematic diagram of resonant-cavity-enhanced heterojunction

photodetector..............................................................................................40 Figure 2. 3 Wavelength dependence of η for RCE detectors having various top

mirror reflectivities for fixed L1=550Å, L2=1175 Å, R2=0.9, and αL2=0.1. .....................................................................................................45

Figure 2. 4 Frequency dependence of η for RCE detectors having various top

mirror reflectivities for fixed L1=550Å, L2=1175 Å, R2=0.9, and αL2=0.1. .....................................................................................................46

Figure 2. 5 SWE as a function of wavelength for four different active layer

thicknesses: L2a=1175 Å (solid), L2b=2306 Å (dash), L2c=3438 Å (dot), L2d=4569 Å (dash dot) for a cavity with R2=1, ψ2=-π, and the material refractive index will not change with the wavelength. (a) in wavelength spectrum; (b) in frequency spectrum..................................49

Figure 2. 6 Discontinuity between two different transmission lines is

analogues to that between two dissimilar media........................................51 Figure 2. 7 Equivalent electric circuit for photodetector shown in Fig. 2.2.................52 Figure 2. 8 Multiple reflection analysis of the RCE photodetector. ............................55 Figure 2. 9 A wave is (a) perpendicularly polarized when its E field is

perpendicular to the plane of incidence and (b) parallel polarized when its E field lies in the plane of incidence. ..........................................57

Figure 3. 1 Schematic diagram of conduction band of a modulation doped

heterojunction. ...........................................................................................64 Figure 3. 2 Flow chart diagram of computer program. E is electric filed, E1

and E2 are two energy level, n1 and n2 are 2DEG concentration at E1 and E2, respectively, V is static potential. .............................................72

Figure 3. 3 Schematic diagram of delta-doped AlGaAs/GaAs heterostructure. ..........74 Figure 3. 4 Simulation of nso against AlGaAs delta doping concentration at

300K for various spacer layer thickness. ...................................................75 Figure 3. 5 Simulation of nso against AlGaAs delta doping concentration at

300K for various spacer layer thickness. Also shown are numerical results of analytical expressions for nso. ....................................................76

xi

Figure 3. 6 Comparison of electric field strength profile by using Eq. (3.13) and modified Shrödinger and Poisson model 300K for various spacer layer thickness. ...............................................................................77

Figure 4. 1 Energy band diagrams showing existence of a conduction-band-

edge discontinuity at interface between semiconductors with different values of electron affinity............................................................87

Figure 4. 2 Device structure of GaAs based resonant-cavity-enhanced HMSM

photodetector..............................................................................................97 Figure 4. 3 In0.52Al0.48As/In0.53Ga0.47As/InP HMSM RCE-PD schematic

diagram. .....................................................................................................98 Figure 4. 4 Reflectivity of bottom mirror vs wavelength for different numbers

of quarter wave pairs. N is the number of quarter wave pairs. +: N=10; ×: N=15; • : N=20; ∗ : N=30. (GaAs based PD) .............................103

Figure 4. 5 Reflectivity of bottom mirror vs wavelength for different numbers

of quarter wave pairs. N is the number of quarter wave pairs. +: N=10; • : N=15; ×: N=20; ∗ : N=30. (InP based PD).................................105

Figure 4. 6 Quantum efficiency of entire structure vs wavelength for different

thickness of absorption layer (number of quarter wave pairs is fixed as N=20). m represents thickness of GaAs absorption layer. • : m=1; +: m=2; ×: m=3; ∗ : m=4. (GaAs based PD)................................106

Figure 4. 7 Quantum efficiency of entire structure vs wavelength for different

thickness of absorption layer (number of quarter wave pairs is fixed as N=15). m represents thickness of InGaAs absorption layer. +: m=1; • : m=2; ×: m=3; ∗ : m=4. (InP based PD) ...................................108

Figure 4. 8 Simulation of nso against AlGaAs delta doping concentration at

300K for various thickness of spacer layer. (GaAs based PD)................109 Figure 4. 9 Comparison of electric field strength profile by using closed-form

expression and modified Schrödinger and Poisson model 300K for various spacer layer thickness (GaAs based PD).....................................110

Figure 4. 10 Drift velocity in GaAs material [144]......................................................111 Figure 4. 11 The electric field strength profile by using closed-form expression

and modified Schrödinger and Poisson model 300K. (InP based PD) ...........................................................................................................113

Figure 4. 12 Drift velocity of electrons and holes in In0.53Ga0.47As [145] ...................114 Figure 4. 13 Top view and schematic cross-section of GaAs based PD. .....................116

xii

Figure 4. 14 InP based PD diagram..............................................................................117 Figure 5. 1 Simulation results for quantum efficiency of layered structure as a

function of wavelength for two different incident angles........................120 Figure 5. 2 Photocurrent spectral response of resonant-cavity-enhanced

HMSM photodetector measured at 10V reverse bias. (Data courtesy of IME-CNR, Lecce, Italy)........................................................121

Figure 5. 3 Photoresponse of resonant-cavity-enhanced HMSM photodetector

measured at 20V reverse bias at different incident light power. (Data courtesy of IME-CNR, Lecce, Italy)..............................................124

Figure 5. 4 Schematic of high-speed time response measurements setup..................125 Figure 5. 5 Temporal response of photodetector with 1 µm finger and 4 µm

gap with a 0.1 mW incident power at 5V reverse bias. ...........................126 Figure 5. 6 Calculated frequency response from Fig. 5.5. .........................................127 Figure 5. 7 Long trace time response with 1 µm finger and 4 µm gap with a

0.1 mW incident power at 5V reverse bias. .............................................129 Figure 5. 8 C-V curves for four different interdigital structures of delta doped

devices. (Data courtesy of IME-CNR, Lecce, Italy)................................130 Figure 5. 9 Schematic diagram of energy band of devices: (a) undoped device;

(b) doped device.......................................................................................133 Figure 5. 10 Comparison of I-V of undoped and δ-doped devices. ο: undoped

device; • : doped device (Data courtesy of IME-CNR, Lecce, Italy). ......134 Figure 5. 11 Potential profile at zero bias of undoped and δ-doped devices. (a):

undoped device; (b): doped device. .........................................................135 Figure 5. 12 Potential profile at V=V1+V2 bias of undoped and δ-doped devices.

(a): undoped device; (b): doped device....................................................136 Figure 5. 13 Simplified model of 2D electron gas p-type semiconductor

junction. ...................................................................................................140 Figure 5. 14 Current-voltage measurement under different temperature for

GaAs based devices. empty symbols: undoped device; solid symbols: doped device. (Data courtesy of IME-CNR, Lecce, Italy). ......142

Figure 5. 15 Ln(I) vs 1/kT at 5V, 10V, and 15V for GaAs based. empty

symbols: undoped device; solid symbols: doped device. (Data courtesy of IME-CNR, Lecce, Italy)........................................................143

xiii

Figure 5. 16 C-V curves GaAs based.photodetectors, empty symbols: undoped

device; solid symbols: doped device. (Data courtesy of IME-CNR, Lecce, Italy). ............................................................................................145

Figure 5. 17 Comparison of temporal response of undoped and doped devices

under a bias of 5V; insert shows comparison of their calculated frequency response. ο: undoped device; • : doped device........................146

Figure 5. 18 Comparison of temporal response (short trace) at the different bias.

Empty symbols: undoped devices; solid symbols: doped devices. and : W1G2; and : W2G2; ∆ and : W1G4; and : W2G4.......................................................................................................149

Figure 5. 19 Comparison of temporal response (long trace) at the different bias.

Empty symbols: undoped devices; solid symbols: doped devices. and : W1G2; and : W2G2; ∆ and : W1G4; and : W2G4.......................................................................................................154

Figure 5. 20 TEM picture for DBR layer. (a) undoped device, Al0.9Ga0.1As:

(67±1) nm, Al0.24Ga0.76As: (61±1) nm. (b) doped device, Al0.9Ga0.1As: (67±2) nm, Al0.24Ga0.76As: (60±2)nm (Data courtesy of IME-CNR, Lecce, Italy). .....................................................................157

Figure 5. 21 Comparison of contrast line scan profiles (a) undoped device, (b)

doped device (Data courtesy of IME-CNR, Lecce, Italy). ......................158 Figure 5. 22 Comparison of reflectivity spectrum between undoped device and

doped device. ο: undoped device; • : doped device (Data courtesy of IME-CNR, Lecce, Italy). .....................................................................160

Figure 5. 23 Interfaces for light to be reflected. (a) bottom mirror, (b) top

mirror. ......................................................................................................161 Figure 5. 24 Comparison of reflectivity spectrum between undoped device and

doped device. (a) undoped device, solid line: experimental data, dashed line: simulation results; (b) doped device, solid line: experimental data, dashed line: simulation results. .................................162

Figure 5. 25 Comparison of simulation results of quantum efficiency between

undoped device and doped device. ο: undoped device; • : doped device. (a) incident angle is 0o; (b) incident angle is 50o.........................164

Figure 6. 1 HMSM typical device structure. ..............................................................171 Figure 6. 2 Cross section of simulated device: X is carrier transport direction,

Z is growth direction; device is biased at V volts. ...................................173

xiv

Figure 6. 3 Electro-optic sampling system schematic [151]. .....................................175 Figure 6. 4 External electro-optic sampling scheme[151]. ........................................176 Figure 6. 5 Series of GaAs based heterostructure RCE devices. ...............................180 Figure 6. 6 Series of InP based heterostructure REC devices. ...................................183

xv

Abstract Novel Heterostructure Metal-Semiconductor-Metal (HMSM) Photodetectors with

Resonant Cavity for Fiber Optic Communications Xiying Chen

Bahram Nabet

Monolithically integrated photoreceivers, optoelectronic integrated circuit

photoreceivers (OEIC), are important components for fiber optic communications. Two

novel delta modulation doped HMSM photodetectors with resonant cavities have been

designed with improved performance in terms of responsivity, speed, sensitivity, and

wavelength selectivity to fulfill the increasingly more stringent requirements of

transmission systems. The major contributions of the author during the Ph.D. period are

as follows: 1. A closed-form model was developed to describe the electronic properties of

delta modulation doped heterostructures, which has been compared with a modified self-

consistent method of solving Schrödinger and Poisson equations. 2. A GaAs based and an

InP based delta modulation doped HMSM photodetectors with a resonant cavity have

been designed for short haul and long haul optical communications, respectively. 3. Two

different groups of GaAs based devices with various geometries have been fabricated and

characterized: one with the delta modulation doped structure, the other without this

doping. Delta doped photodetector shows wavelength selectivity at 850 nm, with 9.2

fA/µm2 dark current, 0.08 A/W average photo responsivity, less than 30 fF capacitance,

10.6 ps full width at half maximum, 9 ps rise time, and 18.4 ps fall time. 4. The most

important feature of the delta doped GaAs based device is its improvement of the optical

and speed response: its dc photocurrent increases by a factor of 1.6 while the dark current

reduces by a factor of 7.8 under 4V bias and a 7 GHz expansion of the 3dB bandwidth

xvi

under 5V bias compared to the undoped device. The mechanism responsible for the

reduction of dark current is enhancement of the cathode metal-semiconductor barrier due

to the confined electron cloud, as well as band bending in the anode that reduces hole

current flow. The increase in responsivity and speed of response is attributed to the

vertical electric field and suitable potential profile in the direction of growth. The device

designed, analyzed, characterized, and presented here is an excellent candidate for optical

detection purpose, especially for fiber optic communications.

1

1. Introduction

1.1 The Need for Fiber-Optic Communication Systems

The most important characteristic of a telecommunication system is

unquestionably its information-carrying capacity, but there are many other important

characteristics such as security and speed. According to the Shannon-Hartley theorem,

the information-carrying capacity is limited by

)1(log 2 SNRBWC ci +×= , (1.1)

where Cci is the information-carrying capacity (bits/sec), BW is the link bandwidth

(Hz=cycles/sec), and SNR is the signal-to-noise power ratio.

The Shannon-Hartley theorem states that information-carrying capacity is

proportional to channel bandwidth. Using a rule of the thumb estimation, the bandwidth

is approximately 10 percent of the carrier-signal frequency, which means that the

frequency of the carrier signal limits channel bandwidth. Optical fiber has emerged as an

excellent medium in view of its tremendous bandwidth potential (50 THz), which permits

high data transmission, thus satisfies the demands of the emergence of high-speed

applications such as video-conferencing and the rapid growth in the number of networked

users. Besides the benefits from the information-carrying capacity, optical fiber is

difficult to tap, thus providing a higher degree of security than possible with copper wire;

immunity to electromagnetic interference reduces bit error rate and eliminates the need

for shielding within or outside a building; the low attenuation of glass fiber permits

2

extended cable transmission distances; light as a transmission medium provides the

ability to use optical fiber in dangerous environments; as well as light weight and small

diameter of fiber permit high capacity through existing conduits.

Over the past decades, the growth of optical-fiber technology in undersea,

terrestrial long-haul interoffice trunklines and cable television (cable TV) systems has

been explosive. At present, single-mode fiber is the preferred transmission medium for

long-distance, point-to-point links such as telephone company intercity trunks. Although

it is still unclear what role photonics technology will play in short-hop applications such

as local area networks (LANs) and telephone subscriber loops [1], visionaries predicted

that fiber’s fingers would touch every home, ultimately replacing coaxial cables and

twisted-pair copper wires for telephone and cable television communications.

1.2 Fiber-Optic Communication Systems

A modern fiber-optic communications system consists of many components

whose functions and technical implementation vary. However, regardless of the

sophistication of a network, the features of a fiber-optic communication system can be

seen in Fig. 1.1, which includes three main constituent parts: the optical transmitter, the

fiber optic channel and the receiver. The major part of the optical transmitter is a light

source, whose function is to convert an information signal from its electrical form into

light. There are two sources for the fiber-optic communications systems, either light-

emitting diodes (LEDs) or laser diodes (LDs). The transmission medium is an optical

fiber, which guides light from a transmitter to a receiver. The optical fiber is made from a

3

type of glass called silica. The heart of an optical receiver is its photodetector, which is

used to convert an optical information signal back into an electrical signal. The

photodetector in fiber-optic communications systems is semiconductor photodiode.

Two novel photodetector designs will be discussed in detail in this thesis: one is

for short haul communication, and the other is aimed for long haul communication.

Electricalinputsignal

Drivecircuit

Lightsource

TransmitterFiberflylead

OpticalspliceConnector Optical

fiber

Opticalcoupler

Signalrestorer

Electriclsignalout

Amplifier

Photo-detector

Opticaltransmitter

Electronics

Opticalreceiver

Repeater

Receiver

OpticalAmplifier

Electrical signal

Optical signal

Figure 1. 1 Conventional fiber optic communication link, showing a fiber optic connecting an optical transmitter and a receiver passing by a repeater, adapted from [2].

1.3 Optical Photodetectors

At the receiving end, an optical receiver converts the modulated optical signal

back into electrical form, thus closing the optical path for information traveling along the

fiber-optic communications link. An optical receiver consists of a photodetector, an

4

amplifier, and some related matching circuit. A generic photo-receiver with a

photodetector is shown as Fig. 1.2 and its equivalent circuit as Fig. 1.3. A photodiode is

the heart of a receiver in the same manner as an LED or an LD is the heart of a

transmitter. Only miniature semiconductor photodiodes are employed in fiber-optic

communications technology to detect an optical signal.

AMP

Photodiode

Bias voltage

Output

RL

Figure 1. 2 Block diagram of an optical receiver, consisting of a photodetector and an amplifier.

Rs

AMP CD RD Ra Ca

Photo-diode

Equivalent photo-diode circuit

(Ideal)

Ls

Figure 1. 3 Optical receiver equivalent circuit.

5

1.3.1 PIN photodiode

A PIN photodiode (PD) is basically a reverse biased p-n (or p-i-n, with i standing

for intrinsic or undoped) semiconductor junction, which is sensitive to incident light

through the absorption of photons, and generates a photocurrent imitating this photon

flux. The major feature of this photodiode is that it consists of a thick, lightly doped

intrinsic layer sandwiched between thin p and n region. The basic structure of a p-i-n PD

is shown in Fig. 1.4. There are three major types of p-i-n photodiodes: front-illuminated

PD (Fig. 1.5 [a]), end-illuminated PD (Fig. 1.5 [b]), and edge-illuminated PD (Fig. 1.5

[c]).

In a front-illuminated PD, light enters the active region through the top contact.

To reduce the backreflection of the incident light, the active surface is covered by an

antireflective coating. The light passes through the thin p region and generates electron-

hole pairs in the thick intrinsic layer. In a rear-illuminated PD, light enters the active

region through a heavily doped n+ layer, which is transparent to the incident light, due to

its energy band gap is larger than the incident photon energy. The other processes are

similar to those that take place in the front-illuminated PD. In an edge-illuminated PD,

the incident light doesn’t impinge to the junction perpendicularly; the junction is

illuminated in parallel. A large interest in exploiting the specific features of edge-

illuminated pin photodiodes has developed since the late 1980’s to solve the limited

bandwidth-responsivity product, lack of compatibility with semiconductor laser geometry

and limited saturation power in the conventional PIN diodes [3, 4].

6

P

n

N + P+

Figure 1. 4 Layer and functional structure of a PIN photodiode.

A p-i-n photodiode is the most commonly employed light detector in today’s

fiber-optic communications systems because of its ease of fabrication, high reliability,

low noise, low voltage, and relatively high bandwidth.

P

n

i

Metal contact Metal contact

Antireflection coating

Metal contact

n+

p

i

n

Antireflection coating

Metal contact Metal contact

Metal contact

(a) (b)

Metal contact

n

i

p

Metal contact

(c)

Figure 1. 5 p-i-n photodiode: (a) front-illuminated PD; (b) fear-illuminated PD; (c) edge-illuminated PD.

7

1.3.2 Avalanche photodiods (APDs)

The basic diagram of an APD is shown in Fig. 1.6, which indicates there is an

avalanche effect in the photodiode. When the reverse bias on a semiconductor diode is set

close, but not quite up to Zener breakdown level, there is strong acceleration of free

electrons and holes by large electric fields in the depletion region. These highly energized

charges and semiconductor atoms can generate secondary electron-hole pairs through a

process known as “impact ionization”, which increases the external current by a factor of

G defined by

pIIG = (1.2)

n+p+pi

Elec

tric

field

Depletion region

Figure 1. 6 Functional structure of an APD photodiode.

APD is at least 10 times more sensitive than a p-i-n PD with comparable

bandwidth, which implies a 10-times-longer fiber-optic span between a transmitter and a

receiver. But this advantage almost vanishes if one recalls that an APD requires relatively

high reverse voltage.

8

1.3.3 Metal-Semiconductor-Metal (MSM) photodiodes

An MSM (metal-semiconductor-metal) is another type of photodetector used in

fiber-optic communications. The basic structure of an MSM photodetector is shown in

Fig. 1.7. Photons generate electron-hole pairs whose flow creates current.

A set of flat metal contacts is deposited on the surface of a semiconductor, which

are called fingers. They are biased alternately so that a relatively high electric field exists

between the fingers. Photons strike the semiconductor material between the fingers and

create electron-hole pairs, which are separated by the electric field.

Metal Semiconductor Metal

Figure 1. 7 A top-view for the Metal-Semiconductor-Metal photodetector planar interdigitated structure.

Since both electrodes and a photosensitive region are fabricated on the same side

of the semiconductor, this structure is called planar. The advantage of this photodetector

is that planar structure results in low capacitance, thus high bandwidth, and in ease of

9

fabrication. However, a drawback to an MSM photodetector is its relatively low

responsivity, which ranges from 0.4 to 0.7 A/W.

Table 1.1 summarizes the typical characteristics of p-i-n and avalanche

photodiodes [5, 6] for three semiconductor materials.

Table 1. 1 Typical characteristics of p-i-n and avalanche photodiodes [5, 6].

Material Parameter Symbol Unit Type Si Ge InGaAs Wavelength λ nm 0.4-1.1 0.8-1.8 1.0-1.7 Responsivity R A/W p-i-n 0.4-0.45 0.8-0.87 0.5-0.95 Quantum Efficiency

η % p-i-n 75-90 50-55 60-70

APD gain M - APD - 50-200 10-40 Dark Current Id nA p-i-n 1-10 50-500 1-20 APD 0.1-1 50-500 1-5 Bandwidth BW GHz p-i-n 0.125-1.4 0-0.0015 0.0025-40 APD - 1.5 1.5-3.5 Bit rate BR Gbit/s p-i-n 0.01 - 0.1555-53 APD - - 2.5-4 Reverse voltage

V V p-i-n 50-100 6-10 5-6

APD 200-250 20-40 20-30 k-factor kA - APD 0.02-0.05 0.7-1.0 0.5-0.7

1.4 Photodetectors for Different Transmission Windows

The transmission characteristics of the optical fiber are of utmost importance for

optical telecommunication systems. When incident light propagates along the fiber link,

the optical signal experiences all types of losses, which demand the use of a repeater.

When short optical pulses are used, a pulse broadening effect arising from dispersion

must be accounted for.

10

1.4.1 Transmission characteristic of the optical fiber

The key optical performance parameters are attenuation and dispersion.

Attenuation is the reduction of signal strength or light power over the distance, whose

unit is decibels per kilometer (dB/km). Attenuation of an optical signal varies as a

function of wavelength (see Fig. 1.8) [7]. Attenuation is very low, as compared to other

transmission media (i.e., copper, coaxial cable, etc.), with a typical value of 0.35 dB/km

at 1300 nm. Attenuation at 1550 nm is even lower with a typical value of 0.25 dB/km.

This gives an optical signal, transmitted through fiber, the ability to travel more than 100

km without regeneration or amplification.

Figure 1. 8 Attenuation as a function of wavelength[7].

Dispersion is the time distortion of an optical signal that results from the many

discrete wavelength components traveling at different rates and results in pulse

broadening, whose unit is picosecond per nanometer per kilometer (ps /nm-km). In digital

transmission, dispersion limits the maximum data rate, the maximum distance, or the

information-carrying capacity. In analog transmission, dispersion can cause a waveform

11

to become significantly distorted and can result in unacceptable levels of composite

second-order distortion (CSO). Fiber dispersion varies with wavelength and is controlled

by fiber design (see Fig. 1.9) [8]. The wavelength at which dispersion equals zero is

called the zero-dispersion wavelength (λ0). This is the wavelength at which fiber has its

maximum information-carrying capacity. For standard fibers, this is in the region of 1310

nm.

Figure 1. 9 Typical dispersion vs. wavelength curve[8].

During the evolution of optical transmission, there have been two major basic

fiber optic types: single mode and multimode developed. The multimode fibers operate at

0.8 ~ 0.9 µm (short wavelength) and 1.25 ~ 1.35 µm (long wavelength) while single

mode fibers are qualified at two primary regions from 1.2 to 1.6 µm and from 1.60 to

1.65 µm.

12

Figure 1. 10 Absorption coefficients of important semiconductor materials versus wavelength [9].

1.4.2 Transmission in the 0.85 µm optical window

Although optical fiber provides its lowest attenuation in the third optical window

at 1.55 µm, 0.85 µm is used for some short-haul transmission due to the availability of

very low cost components for this wavelength.

From the absorption spectrum of semiconductor materials (see Fig. 1.10) [9],

excluding In0.53Ga0.47As and 6H-SiC, the other materials are appropriate for the visible

and near infrared spectral range, which is the 0.85 µm optical window. But Si and GaAs

are cheaper than other semiconductor materials and also their processing is more mature

when compared to the other materials.

13

1.4.2.1 Si photodiodes

The absorption of Si is one or two orders of magnitude lower than that of the

direct semiconductor in this spectral range. For Si detectors, a much thicker absorption

layer is needed than for the direct semiconductor. However, silicon is economically the

most important semiconductor in integrated circuits in spite of the nonoptimum optical

absorption of silicon. Benefiting from the well-established microelectronics technology,

pin photodiodes operating at 0.85 µm have been available for a long time, with a planar

technology on n-type substrate, as sketched in Fig. 1.11 [10]. To achieve a good

responsivity, a specific characteristic of the wafers for the photodiodes operating at 0.85

µm is a thick (20-50 µm) non-intentionally doped epitaxy layer.

n-

n+

p+ ARC

contact

Figure 1. 11 Schematic cross section of a Si pin photodiode.[10].

A Si APD photodiode has other advantages over Si pin photodiodes, such as low

noise and large gain-bandwidth. To cope with the low absorption coefficient and with the

requirement of pure electron injection in the multiplication region, which is necessarily

14

situated close to the surface at the p-n junction, the structure has to be complex. pπpπn

structure is the one designed for Si APD (see Fig. 1.12. [10]). To withstand the high

avalanche electric field, very good material quality for both the substrate and the epitaxy

layer is mandatory.

p-(π)

p+

ARC

contactn

n+ p π

Figure 1. 12 Cross-section of a Si APD with a so-called pπpπn structure (π standing for low p- doping level).[10].

1.4.2.2 GaAs photodiodes

In optoelectronics, III-V semiconductor materials are typically used when speed

and quantum efficiency of a photodetector are necessary. This is due to low electron

mobility in Si, a factor of six lower than that of GaAs, and its indirect band gap,

providing a low absorption coefficient.

In the past decade, manufacturability and reliability of avalanche photodiodes was

the main issue. More recently, speed and power handling capability have received much

15

more attention. At the same time, avalanche multiplication has lost part of its importance

with the development of optical amplifiers.

Also, short-haul communications are attracting research groups’ concentration

more and more as computer processor speeds continue to reach the giga-hertz regime, as

introduction of video on demand (VoD) influences the demand for transmission capacity,

and also as the transmission rate of data continues to expand [11]. Fiber optics is

progressing from point-to-point links to optical networks. The trend towards optical

computer networking creates a need for the emergence of high-speed optical components.

A compact, low-loss, low-cost optical photodetector whose performance reaches multi-

Gigabyte/s levels is rapidly becoming very attractive [12 - 15].

substrate

pin HBT

(a)

substrate

pin FET

(b) (c)

substrate

pin FET

Figure 1. 13 Integration schemes for integrated photoreceivers: (a) pin-HBT; (b) pin-FET on a planar substrate; (c) pin-FET on a recessed substrate [10].

Optoelectronic integrated circuits (OEICs) are the key technology for advanced

optical storage systems and for the enhancement of their speed and data rate. The trend

towards monolithic optoelectronic integrated circuits (OEIC) motivates appreciable

research activity directed towards the employment of planar photodetectors, which can be

easily fabricated and are compatible with the field effect transistor (FET) process. OEIC

16

photoreceivers incorporating pin photodiodes and metal semiconductor field effect

transistors (MESFET) pioneered the recessed substrate approach to planarize the wafer

and ease the processing. Integration schemes for integrated photoreceivers with pin

photodiodes are shown in Fig. 1.13 [10].

Planar metal-semiconductor-metal photodetectors (MSM-PD’s) are good

candidates for such OEIC receivers [16, 17] since these devices can be fabricated in a

GaAs buffer layer (or semi-insulating undoped substrate) and there is no additional cost

to deposit MSM electrodes, they can be deposited at the same time as the gate electrodes.

Since the introduction of MSM device in 1979 by Sugeta [18, 19], several experimental

investigation were reported for the utilization of MSM in high-speed receivers [20-26].

The devices for monolithic photoreciever integration can be shown in Fig. 1.14 [10].

n

n+

S.I.

p+ n

n+

S.I.

pn+

B E C

n or p

S.I.

n

S.I.

buffer n-, p-

D GSPhotodiode bipolar transistor

M.S.M. diode FET

Figure 1. 14 Devices for monolithic photoreceiver integration. One should notice the similarity of MSM and FET structures. [10].

17

For the first generation fiber optic links, GaAs based MSM PDs were used in the

0.85 µm wavelength range. The second and third generation fiber optic links shift from

the 0.85 µm window to the 1.3 µm window where minimum dispersion in fibers occurs

and the 1.55 µm window where minimum attenuation occurs.

For the detection of the 1.3 µm and 1.55 µm lightwaves, GaAs can not be used

any more due to its cutoff wavelength and other ternary semiconductor compound

materials are utilized to obtain acceptable responsivity.

Table 1. 2 Comparison of characteristics of Si and GaAs photodiodes for 0.85 µm [5, 6, 20-26].

Material Parameter Symbol Unit Type Si GaAs Wavelength λ nm 0.4-1.1 0.6-0.9 Responsivity R A/W p-i-n 0.4-0.45 MSM 0.35-0.45 Quantum Efficiency

η % p-i-n 75-90

MSM 100 Dark Current Id nA p-i-n 1-10 MSM < 1nA Bandwidth BW GHz p-i-n 0.125-1.4 MSM > 10GHz Bit rate BR Gbit/s p-i-n 0.01 MSM > 2.5 Gbits/s Reverse voltage V V p-i-n 50-100 MSM

18

1.4.3 Transmission in the 1.3 µm optical window

For the 1.3 µm optical transmission window, both single mode fiber and multi-

mode fiber are qualified in this wavelength region. For standard single-mode fibers, 1.31

µm has the lowest dispersion.

From the absorption spectrum of Fig. 1.10, In0.53Ga0.47As and Ge cover the widest

range including the wavelengths 1.3 and 1.55 µm which are used for long distance optical

data transmission via optical fibers.

Also, chromatic dispersion consists of two kinds of dispersion. Material

dispersion refers to the pulse spreading caused by the specific composition of the glass.

Waveguide dispersion results from the light traveling in both the core and the inner

cladding glasses at the same time but at slightly different speeds. The two types can be

balanced to produce a wavelength of zero dispersion anywhere within the 1.31 µm to

1.65 µm operating window. Thus, optical fiber can be manufactured to have the zero

dispersion wavelength in the 1.55 µm region, which is also the point where silica-based

fibers have inherently minimal attenuation.

In0.53Ga0.47As and Ge photodiodes will be discussed in the next section; they are

suitable for transmission in the 1.55 µm optical window, since both of them can operate

at that wavelength.

1.4.4 Transmission in the 1.55 µm optical window

The dispersion-shifted fibers have low dispersion and low attenuation in the 1.55

µm optical window, which are used in long-distance applications at high bit rates. For

19

applications utilizing multiple wavelengths, it is undesirable to have the zero dispersion

point within the operating wavelength range and fibers known as nonzero dispersion-

shifted fiber (NZDSF) are most applicable. NZDSF fibers with large effective areas are

used to obtain greater transmission capacity over longer distance than would be possible

with standard single-mode fibers. These fibers are able to take advantage of the optical

amplifier technology available in the 1.53 to 1.6 µm operating window while mitigating

nonlinear effects that can be troublesome at higher power levels.

1.4.4.1 Ge infrared (IR) photodiodes

The developments of long haul communications systems have stimulated a great

deal of research towards the fabrication of low-cost optical receivers for the infrared

photodiodes. The integration of optoelectronic devices on the silicon chips has been

demonstrated as one of the applicable approaches. Due to the SiGe process’s

compatibility with complementary metal oxide semiconductor (CMOS) technology, and

also a lower bandgap of Ge enabling Si-based detectors for 1.3 µm and to a somewhat

less advantageous extent for 1.55 µm [27-30], many research groups have concentrated

on integrating SiGe photodiodes on silicon [31-32]. The challenge is to solve the lattice

mismatch between Si and Ge of about 4%. The most effective way to fabricate high-

quality SiGe and Ge layers on Si substrates is to implement graded composition buffer

layers [33]. The reduction in threading dislocation density has led to a low dark current

density of 0.15 mA/cm2 in Ge mesa photodiodes shown in Fig. 1.15 [34].

Still, there is some difficulty in integrating a Ge photodiode on Si substrate. With

a layer thickness of the buffer shown in Fig. 1.15, there is a height of 9.2 µm plus 1.5 µm

20

for the top n+ and p+ layers. Metal interconnects from the Ge photodiode to circuits on the

Si substrate, therefore, cause significant problems. Also, this structure is contrary to the

trend towards planarization.

(001) Si substrate offcut 6o to in-plane <110>

Relaxed graded buffer 10% Ge µm-1 750oC, 250 mT

Relaxed graded buffer 10% Ge µm-1 750oC, 250 mT

Relaxed graded buffer 10% Ge µm-1 750oC, 250 mT

Uniform n+ Ge cap layer, 550oC, 30mT

hν

CMP 50% Ge

76% Ge

92% Ge

n+ Ge

Figure 1. 15 Ge photodiode on SiGe/Si [34].

1.4.4.2 In0.53Ga0.47As infrared (IR) photodiodes

While Ge photodiodes were the components of choice for earlier fiber

transmission at 1.3 µm, their poor performance at 1.55 µm and the development of an

InP-based optoelectronic technology lead In0.53Ga0.47As photodiodes to meet most

demands of long haul communications (long wavelength transmission). Also, its high

electron mobility (~12,000cm2V-1s-1 at 300K) and high saturation velocity

21

(~2.5x107cm/s) make lattice-matched growth of In0.53Ga0.47As on InP substrate to be of

great promise for receivers used in the 1.55µm and 1.3µm fiber bands of importance to

high bit rate, long fiber-link communications [35-40].

n-

n

n+

p+

InP

InGaAsP InGaAs

InGaAsP

Figure 1. 16 Example of an InGaAs photodiode with back-illumination.[10].

Conventional InGaAs pin photodiodes have taken the specific features of the InP

heterostructure technology as described in the following: the front layer is wide bandgap

material, which is transparent to the incident light, thus it improves both responsivity and

response time, while at the same time, it decreases the leakage current; semi-insulating

substrates allow for the fabrication of low-capacitance bonding pad; InP’s transparent

substrate offer the possibility of illumination through the substrate, which is the way to

improve the bandwidth without compromising the responsivity since light crosses the

active region two times due to the reflection provided by the front metallization (see Fig.

1.16 [10]). Some sophisticated structures have been investigated to overcome the

responsivity-bandwidth limitation of the conventional InGaAs pin photodiodes, such as

22

edge-illuminated InGaAs pin photodiode [41], resonant-cavity photodetector [42], and

double-heterostructure multimode photodiodes [43]. Recent developments have further

improved the performance of edge-illuminated photodiodes in terms of bandwidth or

power handling capability: traveling wave photodiodes and uni traveling carrier

photodiodes.

Due to its low bandgap and direct type transition, InGaAs is not suited as

avalanche multiplication material. In fact, the tunneling current is greater than 1 A/cm2

when avalanche occurs. A very sophisticated structure has been developed, called

separate absorption and multiplication (SAM) –APDs, in which absorption takes place in

the InGaAs region while multiplication occurs in another material. Such APDs are

interesting for applications in the 622 Mbit / s- 10Gbit / s range. To extend to bit rates

higher than 10 Gbit / s, much more complicated designs have to be implemented.

MSM PDs can be easily integrated with high electron mobility transistor (HEMT)

based amplifiers and have much lower capacitance per unit area than the best p-i-n

diodes. Receivers for operating at a bit rate over 10 Gb/s have been fabricated by using

MSM PD with HEMT technology [44,45]. Figure 1.17 shows the device structure of III-

V MESFET and heterostructure HEMT. Several techniques have been used to improve

performance of InGaAs MSM photodetectors, such as responsivity enhancement with

nanometer fingers [46] or with semi-transparent Schottky contacts [47], speed increasing

with He-plasma assisted MBE grown InGaAsP [48], and dark current reduction with

coplanar waveguide transmission lines [49].

23

HEMT MESFET

Gate

SI Substrate

narrow band gap material

2DEG

wide band gap material

Figure 1. 17 Fundamental device structure of III-V MESFET and heterostructure HEMT.

1.5 Objective and Scope of the Thesis

The main objective of this dissertation is to design a novel photodetector for the

fiber optical communications applications.

Since the early 1980s, monolithically integrated photoreceivers have been

identified as important components for optical fiber communications due to their

compactness, lower cost, increased sensitivity, and flat response in the case of very large

bandwidth photoreceiver [50,51]. Planar metal-semiconductor-metal photodetectors

(MSM-PD’s) are good candidates for such OEIC receivers since they are easily

fabricated, and are compatible with the FET technology [16, 17]. The latter itself is

strongly affected by progress in heterojunction-based devices that take advantage of the

reduced dimensionality regime of conduction. This has motivated the development of

heterojunction based photodetectors that enjoy better conduction while being compatible

with HEMT technology [16]. Heterostucture metal-semiconductor-metal photodetectors

(HMSM-PD’s) have demonstrated much less dark current than conventional MSM due to

24

both the two-dimensional electron gas (2DEG) and the effect of barrier enhancement due

to the wide-gap material [52-54]. Delta modulation doped technology has been employed

due to its high channel electron density, reduced trapping effects, and improved threshold

voltage as well as high breakdown characteristics [55-59], thus providing the means to

make a high speed device. A resonant cavity is another technology used to solve the trade

off between high quantum efficiency and high speed while, at the same time, offering

narrow spectral bandwidth detection useful in wavelength-division multiplexing (WDM)

applications [60].

In this dissertation, design, fabrication, characterization and analysis of two high-

speed, resonant-cavity-enhanced (RCE), HMSM photodetectors with a distributed Bragg

reflector (DBR) operating at certain wavelength will be reported.

As fiber optics is progressing from point to point links to optical networks, the

short haul communications in the Gigabit region is receiving increased attention.

Multimode fiber operating at 0.85 µm is used primarily in a LAN environment since it

has large bandwidth capability and low costs although the attenuation level is higher

compared to a single-mode fiber.

We have designed a GaAs-based high-speed, resonant-cavity-enhanced,

heterostructure metal-semiconductor-metal photodetector with Al0.24Ga0.76As/

Al0.9Ga0.1As distributed Bragg reflector operating around 0.85 µm for the short haul

communications. The photocurrent spectrum shows a clear peak at this wavelength with

full width at half maximum (FWHM) of around 30 nm. At resonance wavelength, a

seven-fold increase can be achieved in quantum efficiency compared to a detector of the

same absorption depth. The top reflector is a delta modulation doped Al0.24Ga0.76As that

25

also acts as the barrier enhancement layer thus providing a 9.2 fA/µm2 low dark current

values. The breakdown voltage is above 20 V. Time response measurements show rise

time, fall time and FWHM of 9 ps, 18.4 ps, and 10.6 ps, respectively, giving a 3-dB

bandwidth of about 33-GHz. Photo response shows 0.08 A/W average photo responsivity

and capacitance-voltage measurements indicate less than 30 fF capacitance value.

Delta doping of the top AlGaAs layer produces a confined electron cloud and an

associated electric field. The delta doped device shows a factor of 7.8 reduction in dark

current and a factor of 1.6 increase in DC photocurrent with a 4 volts bias, and about 7

GHz expansion of the 3dB bandwidth under 5V bias compared to an undoped device. We

propose that the mechanism responsible for the reduction of dark current is enhancement

of the cathode metal-semiconductor barrier due to the confined electron cloud, as well as

band bending in the anode that reduces hole current flow. The increase in responsivity

and speed of response is attributed to the vertical electric field and suitable potential

profile in the direction of growth.

As stated earlier, the dispersion-shifted fibers have low dispersion and low

attenuation in the 1.55 µm optical window, which are used in long-distance applications

with high bit rates. A InP-based high-speed, RCE, In0.52Al0.48As/In0.53Ga0.47As HMSM

photodetector with InP/In0.527Al0.144Ga0.329As DBR operating around 1.55 µm has been

designed for long haul communications. The devices have been made, while the

measurements are still in progress.

To understand delta modulation-doped heterostructures’ electronic behavior and

the underlying device physics, a closed-form model has been developed to describe the

electronic properties for delta modulation doped heterostructures, particularly the 2DEG

26

sheet charge density and the electric field distribution in the direction of growth. The

model includes the effects of real-space charge transfer and carrier degeneracy. The

electron transfer and quasi-equilibrium condition in the growth direction have been used

in order to express the 2DEG sheet charge density that is only a function of material

parameters and constants. An empirical constant, corresponding to quantized energy

states, has been employed to further simplify this description and to arrive at a closed

form expression. Results from the analytical expressions are shown to agree well with

numerical simulations based on a self-consistent solution of modified Schrödinger and

Poisson equations.

To overcome the limitation of the time response of the measurement systems, a

coplanar stripe transmission line (CPS) and a coplanar waveguide (CPW) transmission

line have been designed for the high speed testing.

1.6 Literature Review

High sensitivity (large signal to noise ratio, which also means low dark current),

high responsivity, and high speed are goals for future photodetectors. Good power

handling devices lost part of their importance due to the development of optical

amplifiers. Wavelength selectivity and agile photodetectors are expected to become

important devices for future work. The knowledge of material physics, bandgap

engineering, and integration technology should be involved in designing novel devices

for fiber optical communications of the future.

27

Fiber optical communications are experiencing a shift from point-to-point link to

optical networks. Data transmission rate and cost play more important roles than

attenuation in short haul optical communications. Fast speed and low cost are high

priorities to be satisfied when an optical component device is to be designed. The optical

transmission window for short haul communications is in the 0.85 µm region based on

the above consideration. The adoption of 0.85 µm short wavelength permits the

integration of low capacitance MSM photodetector and the conventional electronic circuit

onto a single chip [61].

A 1 Gbit/s OEIC receiver for fiber-optic data link application has been reported

by using the conventional GaAs MSM photodetector [61]. To further increase time

response, a GaAs based fully integrated HMSM optoelectronic receiver with HEMT

technology has demonstrated a data transmission rate beyond 20 Gbit/s [62].

AlGaAs/GaAs heterostructure metal-semiconductor-metal photodetectors (HMSM-PD’s)

have much less dark current than conventional MSM due to both the two-dimensional

electron gas (2DEG) and the effect of barrier enhancement due to the wide-gap material

[52-54]. Also, it takes advantages of 2DEG effects and space separation between the

ionized donors in AlGaAs materials and the electrons in the GaAs side to remove

scattering effects, thus achieving a high speed device. Such high speed and low current

photodetectors based on uniformly modulation-doped technology have been

demonstrated in our previous work [52-54].

Uniformly modulation-doped field-effect transistors (U-MODFETs) in

optoelectronic applications have been limited by the occurrence of persistent

photoconductivity, threshold voltage shift, and collapse of voltage characteristics due

28

largely to effects caused by DX centers and surface states [63-65]. Using a delta (δ)

doping technique as an alternative choice for selectively doped heterostructure transistors

results in the optimization of its electronic properties. Its high channel electron density,

reduced trapping effects, and improved threshold voltage as well as high breakdown

characteristics [55-59], have been used to design high speed optoelectronic devices.

To better understand the underlying operation mechanisms, extensive exploitation

of modulation-doped heterostructure in the novel high-speed devices has motivated the

development of theoretical expressions that reveal and help understand the underlying

device physics [58,59,66-71]. Specifically, a simplified analytical tool has been

developed for carrying out most calculations in terms of sheet carrier density (nso) level in

uniformly modulation-doped heterostructure, which is a closed form expression

[69,72,73]. Also, a description of the electric field profile can be expressed through the

application of Gauss’s Law [74]. A closed-form model to describe the electronic

properties for delta modulation doped heterostructures has been developed based on the

background mentioned in the above, particularly the 2DEG sheet charge density and the

electric field distribution in the direction of growth.

A common problem with planar as well as vertical, photodetectors is the trade-off

between speed and quantum efficiency. A resonant cavity technique offers the possibility

to balance such conflict between fast speed and sensitivity [75]. Resonant cavity (RC)

technology has been exploited in the design of active optical components as light

emitting diodes [76,77] and vertical cavity surface emitting lasers (VCSELs) [78,79].

Recently, it has extended in the design of passive optical components, such as p-i-n

29

heterojunction photodiodes, Schottky barrier internal emission photodiodes, and quantum

well infrared photodetectors [80-82].

There are at least three reasons for Al0.24Ga0.76As to be selected as the top layer

above GaAs absorption layer: the first is that its lattice constant matches with the

substrate material, which prevents imperfections that might result from the bonding

process from affecting the quality of the devices; the second is that its Schottky barrier

height with metal is 0.8 eV, which is high enough to form a very good Schottky contact;

the third is that the conduction band discontinuity is high enough to make a good

heterojunction between Al0.24Ga0.76As and GaAs.

Based on the above research background, we designed a GaAs-based high-speed,

resonant-cavity-enhanced, heterostructure metal-semiconductor-metal photodetector with

Al0.24Ga0.76As / Al0.9Ga0.1As distributed Bragg reflector operating around 850 nm.

Combination of low dark current, fast response, wavelength selectivity, and compatibility

with high electron mobility transistors makes this device especially suitable for short haul

communications purposes.

Table 1. 3 Progress in trans-Atlantic-transmission (TAT) capacity.

Year 1956 1963 1970 1976 1988 1997 2001 Medium Coaxial Coaxial Coaxial Coaxial Fiber

(1.3 µm) Fiber (1.55 µm)

Fiber (1.55 µm)

Voice channels

84 128 720 4000 40,000 60,000 (5Gbit/s)

≈120,000

While for long haul communication, fiber optics is on the road to becoming the

key technology of information superhighways offering ultrahigh bit rate transmission.

Typical point-to-point links are the telephone company intercity trunk. Typically these

30

links operate at data rates between 45 Mbit/s and 565 Mbit/s, but now, 1.6 Gbit/s to 1.7

Gbit/s (USA) and 2.4 Gbit/s to 2.5 Gbit/s (Europe) systems are available in most places.

Table 1.3 shows the progress in trans-Atlantic-transmission (TAT) capacity.

The dispersion-shifted fibers have low dispersion and low attenuation in the 1.55

µm optical window, which are used in long-distance applications with high bit rates.

While Ge photodiodes were the components of choice for the earlier fiber transmission at

1.3 µm, their degraded performance at 1.55 µm and the development of an InP-based

optoelectronic technology lead In0.53Ga0.47As photodiodes to dominate the market of the

long haul communications (long wavelength transmission).

There are several advantages for InGaAs over the other III-V semiconductor

materials: its high electron mobility and high saturation velocity promise a high speed

device, its lattice-matched growth of In0.53Ga0.47As on InP substrate result in no stress

within the entire structure, and also its aborption region from 1.0-1.6 µm makes it

suitable for either 1.3 µm or 1.55 µm fiber optical communications.

Receivers for operating with bit rate over 10 Gb/s have been fabricated by using

MSM PD with HEMT technology [44,45]. Nanometer fingers or semi-transparent

Schottky contacts to enhance the responsivity, He-plasma assisted MBE grown InGaAsP

to increase the speed, and CPW transmission lines to reduce dark current have been

employed to improve the performance of InGaAs HMSM PDs [46-49].

High-speed monolithically integrated InAlAs/InGsAs/InP HMSM/HEMT

photoreceivers have been reported [83]. A packaged receiver has been tested at 5 Gbit/s

and an open eye pattern has been obtained. Another research group developed a

31

monolithic receiver by using HMSM structure with a pseudomorphic In0.25Ga0.75As

channel with delta doping to acquire 13.5 GHz bandwidth [84].

We have developed a novel design including a delta modulation doping structure,

HMSM, and RCE for the InGaAs photodetectro used for the long haul communication.

However, low Schottky barrier height (~0.2eV) on n- In0.53Ga0.47As causes excessive

leakage current [85]. A lattice-matched material In0.52Al0.48As has been used as a barrier

enhancement layer on the top of In0.53Ga0.47As to limit the leakage current to an

acceptable value, which has been demonstrated by several groups [86-88].

Based on the background mentioned above, an InP-based high-speed, RCE,

In0.52Al0.48As/In0.53Ga0.47As HMSM photodetector with InP/In0.527Al0.144Ga0.329As DBR

operating around 1.55 µm is proposed in this thesis.

Testing of high speed photodetectors presents a challenge in its own right. We

have used femtosecond pulses for excitation of detectors and extracted the response using

microwave probes. This limits the resolutions of measurement. To overcome the

limitation of the time response of the measurement systems, a coplanar stripe

transmission line (CPS) and a coplanar waveguide (CPW) transmission line have been

designed for the high speed testing.

This dissertation is arranged in the following manner. In Chapter 2, a formulation

of resonant cavity enhanced photodetectors derived from the theoretical analysis of

planar mirror resonator is presented to calculate the quantum efficiency, finesse, and free

spectral range of an arbitrary RCE detector structure. A simplified transmission line

model is applied to compute reflection coefficients of two mirrors that form resonant

cavity of our detector in terms of the parameters of materials and structures.

32

Since a distinguishing feature of our devices developed here is delta-doping

technique, whose advantages are demonstrated in chapter 5, a closed-form model has

been developed to describe the electronic properties for delta modulation doped

heterostructures, particularly the 2DEG sheet charge density and the electric field

distribution in the direction of growth in Chapter 3.

Two complete designs are presented in Chapter 4. One is a GaAs-based high-

speed, RCE, HMSM photodetector with Al0.24Ga0.76As/ Al0.9Ga0.1As DBR operating

around 0.85 µm, which will be employed for short haul optical communications. The

other is InP-based high-speed, RCE, HMSM photodetector with

InP/In0.527Al0.144Ga0.329As DBR operating around 1.55 µm, which will be used for long

haul optical communications.

In Chapter 5, the experimental results of GaAs-based photodetectors are

presented. First, the performance characteristics of GaAs-based high-speed, RCE,

HMSM photodetector with Al0.24Ga0.76As/ Al0.9Ga0.1As DBR are listed; then, the effect of

delta doping that is employed in the top AlGaAs layer are investigated by comparing

current-voltage, current-votage variation with temperature, capacitance-voltage, and

temporal response measurements of doped and undoped devices. Finally, further

comparison between the delta-doped and undoped device are discussed, which includes

structures from transmitted electron microscope (TEM) pictures and the reflectivity for

the light incident on the top surface of the devices from the reflectivity spectrum.

In Chapter 6, the contributions of this dissertation are reiterated and future work

related to these designs is discussed. Commercial software will be used for simulating the

static electronic properties of the specific structures; a model based on Ramo’s theory

33

will be employed to describe the dynamic behavior of the photogenerated carriers in

those devices; and the mechanism of the electro-optic measurement will be described.

34

2. Resonant Cavity Enhanced Devices

Importance for the design and understanding of RCE based devices is the

development of an analytical mathematical model describing the behavior of an active

absorption (or gain) region inside a Fabry-Perot resonator. Below, the theoretical analysis

of a planar mirror resonator is presented first. Then, a formulation of resonant cavity

enhanced photodetectors derived from the theoretical analysis of planar mirror resonator

allows the calculation of the quantum efficiency, finesse, and free spectral range of an

arbitrary RCE detector structure. The dependence of RCE detector properties on the

placement of the active layer within the cavity and the angle of incidence of the detected

radiation is also considered in the following analysis. A simplified transmission line

model is applied to compute reflection coefficients of two mirrors that form resonant

cavity of our detector in terms of the parameters of materials and structures. The

simulation results and discussions in this chapter help design the resonant cavity part of

the devices used for the short haul and long haul communications in Chapter 4, and

characterize the optical properties of those optoelectronic devices.

2.1 Introduction

High speed and high sensitivity photo-receivers are the key components in high-

bit-rate and low cost fiber optic communication systems. For some of the applications

that employ wavelength division multiplexing (WDM), it would be advantageous to

35

combine wavelength selectivity with detection. A family of optoelectronic devices

emerged over the past twenty years whose performance is improved by placing the active

device structure inside a Fabry-Perot resonant micro-cavity. Such resonant cavity

enhanced (RCE) devices derive advantages from the wavelength selectivity and the large

increase of the resonant optical field resulting from the resonant microcavity. The

increased optical field allows photodetctors to be made thinner and therefore faster, while

at the same time, increasing the quantum efficiency at the resonant wavelength. Off-

resonant wavelengths are rejected by the microcavity, thus making it suitable for the low

cross-talk WDM applications. The resonant cavity structure alleviates the well-known

bandwidth/quantum efficiency tradeoff as well as to provide a narrow spectral response

in p-i-n photodiodes [89, 90], elemental semiconductor (Si and Ge) and compound

semiconductor APDs [91 - 93], and MSM photodiodes [36, 38]. The enhanced

performance of the semiconductor devices resulting from the resonant cavity in the

optoelectronic applications has also been demonstrated in numerous active optoelectronic

devices: vertical resonant cavity surface emitting lasers (VCSEL’s) decreased the

threshold current densities [94], light emitting diodes (LED’s) improved their spectral

purity and directivity, as well as optical modulator operated at lower voltages.

This chapter provides an overview of RCE passive optoelectronic devices,

including theoretical analysis of RCE photodetectors parameters in Section 2.3 and

design criteria for RCE photodetectors in Section 2.4. The formula in the first 3 sections

are employed in the normal incident case; while in Section 2.5, the oblique incidence are

discussed and the formula are modified to be used in this case based on those of the

previous sections.

36

2.2 Theoretical Analysis of Planar Mirror Resonators

For the purpose of the design and understanding of RCE-based photonic devices,

an analytical mathematical model describing the behavior of an active absorption (or

gain) region inside a Fabry-Perot resonator has to be developed. Several research groups

have contributed to this endeavor [95 - 99].

A resonator is constructed of two parallel, highly reflective, flat mirrors separated

by a distance d (Fig 2.1).

r1r2e-jΨ + E0 E

E1=r1r2e-jΨE0

(a) (b)

Mirror 2 Mirror 1

E3

E2

E1

E0

t1 r1 r2 t2d

z=0

Figure 2. 1 Two-mirror planar resonator (Fabry-Perot Mirror).

Resonator modes are the standing waves. A monochromatic wave of frequency f

has a wavefunction,

37

)2exp()(),( tfjrEtrE π= rr (2.1)

which represents the transverse component of the electric field. The complex amplitude

)(rE r should satisfy the Helmholtz equation,

0)()( 22 =+∇ rErE rr β (2.2)

where β=2π f/up is the wave number and up is the speed of light in the medium. The

modes of a resonator are the basic solutions of the Helmholtz equation subject to the

appropriate boundary conditions, which require that )(rE r equals zero at z=0 and z=d

plane. This restricts β to the values d

mm

πβ = , which also means that the frequency f is

limited to the discrete values d

umf p

m 2= . Thus, the adjacent resonance frequencies are

separated by a constant frequency difference d

uff pmm 21 =−+ .

The resonator modes can alternatively be determined by following a wave as it

travels back and forth between the two mirrors (Fig. 2.1(a)). The phase difference

imparted by a single propagation round trip is

λd4π

udf4πd2βΨ

p=== , (2.3)

where λ is the wavelength in the medium. When the mirrors are not perfect, which means

that reflectivity is not 1, the phasors are not of equal magnitude. The relation between the

two consecutive phasors can be expressed as

ijΨ

211i EerrE −+ = (2.4)

38

As shown in Fig. 2.1(b), r1 and r2 are the reflection coefficients of the two

mirrors, respectively. If the phasor Ei+1 is related to Ei by a complex factor jΨerrh −= 21 .

The net result is the superposition of an infinite number of waves

jΨ21

0

i i

ii

err1E

hE

hEE

EEEE

−

∞

=

∞

= −=

−===

+++=

∑ ∑ 1

....

0

0 00

210

. (2.5)

Therefore, the wave intensity in the resonator is found to be

)cos(21

1

1

212121

0

2

21

0

2

21

02

21

ΨΨΨ

ΨΨΨ

Ψ

++−+=

−=

−==

−−−

−

RRRRI

eeReRE

errE

EI

jjj

j

(2.6)

where R1 and R2 are the reflectivities of the two mirrors, respectively, and Ψ1 and Ψ2 are

phase shifts introduced by the front and the back mirrors. Here 200 EI = is the intensity

of the initial wave, and 21

2/121

1)(

RRRR

F−

π= is the finesse of the resonator. The intensity, I,

can be maximized when )cos( 21 ΨΨΨ ++ equals unity, which

requires π=++ mΨΨΨ 21 2 . If F is large, which requires that the mirrors have large

reflectivities, then I has sharp peaks centered at the values π=++ mΨΨΨ 21 2 .

In the above derivation, we only considered the losses arising from imperfect

reflection at the mirrors. There are other sources of resonator loss due to absorption and

scattering in the medium between the mirrors. The round trip power attenuation factor

associated with these processes is )2exp( dα− , where α is the absorption coefficient of the

39

material. Then, the complex factor h relating the phasor Ei+1 to Ei should include this

effect, which can be rewritten as exp(-αd)r1r2e-jΨ. Thus, Eq. 2.6 is modified to the

following

)cos(21

1

212

21

0

2

21

021

21dd

jjjd

ΨΨΨeRReRRI

eeReReE

I

++−+=

−=

α−α−

−−−α− ΨΨΨ (2.7)

Also, the finesse F can be expressed as a function of the effective loss coefficient

αr

)exp(1)2/exp(

ddF

r

rα

απ−−

−= , (2.8)

where αr can be calculated from the formula

)1ln(21

21RRdr +=αα . (2.9)

Based on the above theoretical analysis, a formulation of the quantum efficiency

for RCE photodetectors can be derived as follows.

2.3 Formulation of Quantum Efficiency for RCE Photodetectors

The content covered in this section is arranged as the following description. A

formula of quantum efficiency for the resonant-cavity-enhanced heterojunction

photodetector shown as Fig. 2.2 is derived at first. The formulation of the reflectivity of

the two mirrors is described in terms of material parameters in the next part. The

40

numerical calculation results are discussed as the next following. The standing wave

effect involved in the quantum efficiency will be depicted as the last part.

2.3.1 Formulation of the quantum efficiency for RCE photodetectors

incident light

Ei

Ef

Eb

t1√R1e-jΨ1 L1

L2

DBR reflector

Barrier enhancement layer

absorption layer √R2e-jΨ

2

Z=0

Figure 2. 2 Schematic diagram of resonant-cavity-enhanced heterojunction photodetector.

A typical RCE photodetector is made of a Fabry-Perot cavity, with a mirror on

each end, whose length determines the resonant frequency. In practice, the bottom mirror

consists of quarter-wave stacks of two different materials forming a distributed Bragg

reflector (DBR). The top mirror can be the interface between the native semiconductor

and air due to the large difference in their refractive index. The active layer, where the

absorption occurs, is placed between the two mirrors. Here we use a delta-doped

heterojunction to achieve better photon reflection as well as other important electronic

functionalities. These include decreasing the dark current due to an enhancement of

41

Schottky barrier height, modulating the two dimensional electron gas density in the

triangular quantum well at the narrow gap material side, adjusting the electric filed

profile distribution in the growth direction, thus controlling the carriers' behavior, and

more as will be detailed in Chapter 4 and Chapter 5.

Figure 2.2 shows a simplified structure of our RCE photodetector, where L1 is the

non-absorbing barrier enhancement layer. Re-circulation of photons from the top of this

layer and the bottom DBR, allows a thin absorption layer L2 to be used to minimize the

response time without hampering the quantum efficiency. R1 and R2 are the reflectivity of

top mirror and bottom mirror respectively, α is the absorption coefficient of the

absorption layer, Ψ1 and Ψ2 are phase shifts introduced by top and bottom mirrors due to

light penetration into the mirrors, and β1 and β2 are the propagation constants in these two

materials.

The transmitted component of the incident light wave electrical field (Ein) equals

t1Ein. In the cavity, the forward traveling wave is composed of these transmitted waves

and the feedback as a result of internal reflections at the mirrors. Thus, the forward

traveling wave Ef at z=0 can be obtained through a self-consistent consideration, i.e., Ef is

the sum of the transmitted field and the feedback after a round trip in the cavity:

injjjLf

f

Lλ

Lλ

jjjL

in

fL2βL2βjjjL

in

fjjjL

inf

EeeReRe

tE

EeeReReEt

EeeReReEt

EeeReReEtE

21

2211

ΨΨΨ

ΨΨ

ΨΨ

ΨΨΨ

−−−α−

π+π−−−α−

+−−−α−

−−−α−

−=⇒

+=

+=

+=

212

21212

212

212

21

1

)2222(

211

)(211

211

1

(2.10)

42

The backward traveling wave Eb, i.e., electric field at z=L1+L2, can be found from

Ef through the detector region:

fLβLβjjL

fjjL

b

EeeRe

EeeReE

2211 )(2

2/

2/2

2/

22

22

+−−α−

−−α−

=

=Ψ

ΨΨ

(2.11)

The optical power inside the resonant cavity is given by

s

ss

EP

η2

2

= (s=f or b), (2.12)

where ηs is the intrinsic impedance of the detector material, which will be defined in the

next section.

The light power absorbed in the active layer (Pl) can be obtained from the

incident power Pi:

iL

212211L

LL

Lsfl

PeRRΨΨLβLβeRR

eeRR

ePPP

22

22

2

22121

21

))(2cos(21)1)(1)(1(

)1)((

α−α−

α−α−

α−

++++−−+−

=

−+=

(2.13)

One of the desired features for RCE photodetectors is high quantum efficiency.

Under the assumption that all the photogenerated carriers contribute to the detector

current, quantum efficiency (η) is defined as the ratio of absorbed power to incident

optical power. The derivation of the quantum efficiency for the photodetectors is based

on the structure shown Fig. 2.2, which can be written as [103]:

( )

++++−+

×

−−=

α−α−

α−

α−

22

2

2

22121

2

1

))(2cos(211

)1)(1(

L212211

L

L

L

eRRΨΨLβLβeRReR

eRη

, (2.14)

From this formula, quantum efficiency is maximized due to high reflection from

the DBR and when the condition 1))(2cos( 2211 =+++ 21 ΨΨLL ββ is satisfied.

43

2.3.2 Formulation of the reflectivity of the two mirrors

A simplified transmission model is applied to calculate reflection coefficients of

two mirrors [100]. The impedance calculated begins at the substrate and ends at the top of

the bottom mirror. Every semiconductor layer is considered to be a transmission line

segment, whose characteristic impedance is given as [100]:

"' εεµη

ji −= , (2.15)

where ε´ and ε˝ are the real and imaginary part of the dielectric constant, and µ is the

material’s permeability. For non-absorbing layer, "' εε >> , ηi can be written as 'εµη =i

and also the propagation constant can be simplified for every non-absorbing layer as

'µεωβ = . Here, ω is the operation frequency, which is related to the incident light. An

equivalent expression for β is given as: n/

2

0λπβ = (λ0 is the wavelength of the incident

light in the vacuum and n is the refractive index for the material).

The substrate impedance is first computed by using Eq. (2.15). The equivalent

input impedance for every layer with its thickness and characteristic impedance is

calculated from [101]:

)tan()tanh(

10

010

iiii

iiiiii l

lγηηγηηηη

−

−

++

= , i=1 to 2N (2.16)

where N is the total number of the contrasting pairs in the quarter mirror stacks,

ii

i iβαγ +=2

, αi is the absorption coefficient of ith layer and βi is the propagation

44

constant of the ith layer, until the top of the bottom mirror is reached. The overall

reflection coefficient can then be evaluated as [101]:

22

2

22

jΨ

absN

absN eR −=+−

=ηηηηΓ (2.17)

where η2N is the input impedance at the interface between the active layer and the top of

the bottom mirror; ηabs is the characteristic impedance of the absorption layer, which can

be found using the same method as used for the substrate’s characteristic impedance. The

reflection coefficient for the top mirror can be acquired in the same manner. The only

difference from Γ2 is to replace η2N with ηair and replace ηabs with ηbarrier. ηair is the

characteristic impedance of air and ηbarrier is the characteristic impedance of the barrier

enhancement layer. The thickness of the barrier enhancement layer and the absorption

layer are limited by satisfying the optimization condition requirement of the quantum

efficiency ( 1))(2cos( 2211 =+++ 21 ΨΨLL ββ ).

2.3.3 Numerical calculation of RCE quantum efficiency

Since the propagation constant β has a wavelength dependence, quantum

efficiency, η, is a periodic function of the inverse wavelength while the thickness of the

barrier enhancement layer and absorption layer are fixed. This can be seen in Fig. 2.3,

which illustrates the calculated wavelength dependency of η. The simulation results are

based on the structure shown in Fig. 2.2. The three curves correspond to the cases of

R1=0.9, 0.3, and 0.05 while L1 = 550Å, L2 = 1175Å, R2 = 0.9, and αL2 = 0.11 are fixed.

The simulation results shown in Fig. 2.3 and Fig. 2.4 do not include the non-linear

dispersion effects, which mean that the refractive index of the material does not change

45

within the whole spectrum range. The refractive index of the barrier enhancement layer

Al0.24Ga0.76As is value at a λ of 0.83 µm while GaAs’s refractive index at 0.83 µm is that

of the absorption layer.

0.4 0.6 0.8 1.0 1.2 1.40.0

0.1

0.2

0.3

0.4

0.5

0.6αL2=0.11, R2=0.9

R1=0.9

R1=0.3

R1=0.05

FSRQ

uant

um E

ffic

ienc

y

Wavelength (µm)

Figure 2. 3 Wavelength dependence of η for RCE detectors having various top mirror reflectivities for fixed L1=550Å, L2=1175 Å, R2=0.9, and αL2=0.1.

It’s observed that η is enhanced periodically at the resonant wavelengths which

occur when π=+++ mΨΨLβLβ 212211 2)(2 (m=1, 2…). The spacing of the cavity

modes is defined as the free spectral range (FSR), i.e., resonant wavelengths and resonant

frequencies, which can be seen in Fig. 2.3 and Fig. 2.4 respectively.

46

0.4 0.6 0.8 1.0 1.2 1.40.0

0.1

0.2

0.3

0.4

0.5

0.6αL2=0.11, R2=0.9

R1=0.9

R1=0.3

R1=0.05

FSR

Qua

ntum

Effi

cien

cy

Wavelength (µm)

Figure 2. 4 Frequency dependence of η for RCE detectors having various top mirror reflectivities for fixed L1=550Å, L2=1175 Å, R2=0.9, and αL2=0.1.

For the photodetector described as the above structure, the FSR is around 330 nm

between the resonant wavelength at 0.83 µm and its adjacent resonant wavelength at the

high energy level side, and also the FSR is about 240 THz between two adjacent resonant

frequencies in Fig. 2.3 and Fig. 2.4 respectively. For a well-designed photodetector, the

active region should be the only place to absorb the incident light. In the above

photodetector structure, the band gap of the absorption material is the smallest. Thus, the

spacing of the cavity modes at the low energy side to the resonant wavelength at 0.83 µm

does not need to be considered, while the resonant wavelength adjacent to 0.83 µm on the

other side is around 0.5 µm, which is larger than the band gap of the barrier enhancement

layer. Therefore, the absorption in the Al0.24Ga0.76As material is decreased by using the

resonant cavity technique if the incident photon energy is smaller than the edge of the

bandgap of Al0.24Ga0.76As.

47

2.3.4 Standing wave effect

The peak η at the resonant wavelengths can be derived by imposing the resonant

condition in Eq. 2.14:

( )

−+×−−= α−

α−α−

221

21

)1(1)1)(1(

2

22

L

LL

eRReReRη (2.18)

In the limit of the a thin active layer αL2 << 1, (2.18) reduces to

( )

α−−α−+

α−≈ 2221

2221

))1(1()1(1

)1(LRR

LRLRη (2.19)

In the simulation results of the previous section, the spatial distribution of the

optical field inside the cavity was neglected. A spatial distribution arises from the

standing wave formed by the two counter propagating waves. It follows that η, which was

derived from the power absorbed in the active region, is a function of the placement of

the active region in the optical field. This is called the standing wave effect (SWE). When

detectors with thick active layers which span several periods of the standing wave are

considered, the standing wave effect can be neglected. For very thin active layers, which

are necessary for strained layer absorbers, the SWE must be considered.

The SWE is conveniently included in the formulation of η as an effective

absorption coefficient, i.e., αα ×= SWEeff , which is either enhanced or decreased by the

placement of the active region. The effective absorption coefficient αeff is the normalized

integral of the product α and the field intensity across the absorption region. Using a

perturbation analysis of Maxwell’s equations, including the loss factors and assuming

48

uniformity along the transverse direction, the effective absorption coefficient can be

expressed as [102]:

dzzE

dzzEzLLL

eff 22/

0

2

02

),(/2

),()(/121

∫

∫λ

+

λλ

λα

=α , (2.20)

where n

0λλ = , E(z, λ) is the total electrical field in the cavity at a given wavelength and

the denominator is the average of the standing wave. Taking α to be negligible outside of

the active region and constant within, we arrive at

dzzE

dzzEL

SWE

LL

Leff22/

0

2

2

)(/2

)(/121

1

∫

∫λ

+

λ

=α

α= (2.21)

The forward (Ef) and backward (Eb) components of the standing wave are given

by Eq. (2.10) and Eq. (2.11). The total electric field E and intensity 2E are :

))((21

21)()0( LLzjb

zjf eLLEeEE +−ββ− ++= (2.22)

and

)()(Re2)()0( *221

22 zEzELLEEE bfbf +++= (2.23)

Substituting Eq. (2.10) and Eq. (2.11) into Eq. (2.23) and assuming α=0, which is

reasonable for a thin active layer which absorbs a small fraction of total power density:

49

[ ][ ] 22122

2)2(21

12

)(2cos21

1

)1(

in2

ΨΨβLj

EΨzLLβRR

eRR

RE

21

+−+++×

−

−=

++ (2.24)

Substituting Eq. (2.24) into Eq. (2.21), we obtain the dependence of the SWE on

the cavity parameters [103]:

[ ])cos(sin)1(

21

2

2222

2ΨβLβL

RβLR

SWE ++

+= (2.25)

0.4 0.6 0.8 1.0 1.2 1.40.8

0.9

1.0

1.1

1.2 (a)

SWE

Wavelength (µm)200 300 400 500 600 700 800 900 1000

0.8

0.9

1.0

1.1

1.2 (b)

SW

E

Frequency (THz)

Figure 2. 5 SWE as a function of wavelength for four different active layer thicknesses: L2a=1175 Å (solid), L2b=2306 Å (dash), L2c=3438 Å (dot), L2d=4569 Å (dash dot) for a cavity with R2=1, ψ2=-π, and the material refractive index will not change with the wavelength. (a) in wavelength spectrum; (b) in frequency spectrum.

Figure 2.5 indicates the wavelength dependence of the SWE for various active

layer thickness L2. As shown in the figure, for a very thin active layer structure, the SWE

is more prominent. Knowledge and control of the phase behavior is particularly important

50

for proper positioning of very thin absorbing layers in high η photodetectors. Also, Fig.

2.5 shows that the SWE becomes more pronounced as the photon energy of the incident

light decreases. Since the SWE is larger than one at the low energy side to the resonant

wavelength while smaller than one at the other side as shown in Figure 2.5, the

absorption coefficient is larger than that without considering the SWE at the long

wavelength side the resonant wavelength while smaller than that at the other side when

the absorption coefficients are modified by Eq. (2.20).

2.4 Formulation of Reflection Coefficient of Mirrors

In this section, formulation of reflectivity of the mirrors will be expressed from

the transmission line analogue and the multiple reflection view point, which is the

theoretical basis for simulating the experimental data of the reflectivity spectrum of the

top mirror in Chapter 5. The transmission line analogue is used for calculating the

effective reflection coefficient of the bottom mirror, while the multiple reflection effect

has been included in calculating the reflection coefficient from the top mirror since light

has been multiply reflected between the two mirrors due to the resonant cavity.

2.4.1 Reflection coefficient calculated from transmission line analogue

When a guided wave traveling along a transmission line encounters an impedance

discontinuity, such as that shown in Fig. 2.6 (a), at the boundary between two lines with

different characteristic impedances, that incident wave is partly reflected back toward the

source and partly transmitted across the boundary into the second line. A similar process

51

applies to a uniform plane wave propagating in an unbounded medium when it

encounters a boundary. In fact, the situation depicted in Fig. 2.6 (b) is exactly analogous

to the transmission line configuration of Fig. 2.6 (a). The boundary conditions governing

the relationships between the electric and magnetic fields of the incident, reflected, and

transmitted waves in Fig. 2.6 (b) are similar to those for the voltages and currents of the

corresponding waves on the transmission line.

Incident wave

Reflected wave

Z01

Transmission line 1 Transmission line 2

Transmitted Wave

Z02

z=0

(a) Boundary between transmission line

Incident plane wave

Reflected plane wave

Transmitted plane Wave

z=0

(b) Boundary between different media

Medium 1 η1 Medium 2 η2

Figure 2. 6 Discontinuity between two different transmission lines is analogues to that between two dissimilar media.

The input impedance of an infinitely long line is equal to its characteristic

impedance. Hence, at z=0, the voltage reflection coefficient (looking toward the

boundary from the voltage point of the first line) is

52

0102

0102ZZZZ

+−

=Γ (2.26).

There is a one-to-one correspondence between the transmission line parameters

( 0,,~,~ ZIV β ) and the plane wave parameters ( ηβ ,,~,~ HE ). This correspondence allows us

to use the transmission line techniques to solve the plane wave propagation problems.

The equivalent electric circuit for the structure shown in Fig. 2.2 can be drawn in

the following picture (Fig. 2.7).

ηL

l1 = λ0/4n1

l2 = λ0/4n2

N pairs quarter wave stack

L2

L1

Absorption layer

Barrier enhancement

layer

air

Γ

Figure 2. 7 Equivalent electric circuit for photodetector shown in Fig. 2.2.

The substrate impedance is first computed by using Eq.(2.15), which corresponds

to the load impedance ηL in Fig. 2.7. Each semiconductor layer can be seen as a

53

transmission line in accordance to its thickness li and characteristic impedance ηi

calculated by using Eq. (2.15). The impedance is transformed for each layer by Eq. (2.16)

until the top of the bottom mirror is reached. Once the input impedance (ηin) at the top of

the bottom mirror is known, the overall complex reflection coefficient from the bottom

mirror can be evaluated as:

absin

absinηηηηΓ

+−

= (2.27).

Reflectivity calculation is straight forward since it is the square of the magnitude

of the reflection coefficient.

2.4.2 Multiple reflection viewpoint

Since the incident light experiences multiple reflections between the top and

bottom mirrors within the resonant cavity shown in Fig. 2.2, from a multiple reflection

viewpoint, the overall or total reflection coefficient of a wave incident on this RCE

photodetector can be computed using the following derivation. There is an assumption

that the partial reflection at the interface between the barrier enhancement layer and the

absorption layer can be neglected due to the smaller characteristic difference between

these two materials.

Figure 2.8 shows the equivalent electric circuit of the RCE photodetector with

reflection and transmission coefficients defined as follows:

Γ = overall, or total, reflection coefficient of a wave incident on the RCE

photodetector.

54

Γ1 = partial reflection coefficient of a wave incident on a load ηair, from the

ηbarrier line.

Γ1´ = partial reflection coefficient of a wave incident on a load ηbarrier, from the

ηair line.

Γ2 = partial reflection coefficient of a wave incident on a load η2N, from the ηabs

line.

τ1 = partial transmission coefficient of a wave from ηbarrier line to ηair line.

τ1´ = partial transmission coefficient of a wave from ηair line to ηbarrier line.

Here η2N is the input impedance at the top surface of the bottom mirror, which is

the equivalent load for a wave incident on this interface.

These coefficients can then be expressed as

airbarrier

airbarrierηηηηΓ

+−

='1 (2.28 a)

'11 Γ

ηηηηΓ −=

+−

=barrierair

barrierair (2.28 b)

absN

absNηηηηΓ

+−

=2

22 (2.28 c)

airbarrier

barrierηη

ηΓτ+

=+=2

1 '1

'1 (2.28 d)

airbarrier

airηη

ηΓτ+

=+=2

1 11 (2.28 e)

Since each round-trip path forward and back through the resonant cavity results in

a )(2 2211 LL ββ +− phase shift and a 2Le α− magnitude decrease, the total reflection

coefficient can be expressed as

55

1)(2

2

)(22

1'

1'

1

1

11

)(221

'1

'1

2)(2

1)(2

21'

1

)(221

'1

'1

22211

22211

22211

2221122211

22211

1

)()(

...

ΓΓΓττΓ

ΓΓττΓ

ΓΓΓττ

ΓττΓΓ

ββ

ββ

ββ

ββββ

ββ

LLLj

LLLji

iiLLLj

LLLjLLLj

LLLj

eeee

ee

eeee

ee

α−+−

α−+−

∞

=

−α−+−

α−+−α−+−

α−+−

−+=

+=

++

+=

∑ . (2.29)

η2N

L2 L1

Absorption layer

Barrier enhancement

layer air

ηabs

ηbarrierηair

Γ1 Γ2

τ1

τ1′

L1+L2

Γ′ 1

1

Γ2

τ1’

Γ1 τ1

Γ1 τ1 Γ2

RCE photodetector

Γ′1

Figure 2. 8 Multiple reflection analysis of the RCE photodetector.

56

2.5 Formulation modified at Oblique Incidence

For normal incidence, the reflection coefficient Γ and transmission coefficient τ

of a boundary between two different media are independent of the polarization of the

incident wave, because the electric and magnetic fields of a normally incident plane wave

are always tangential to the boundary regardless of the wave polarization. This is not the

case for oblique incidence at an angle θi ≠ 0o. In addition, the length of the light path

within each individual layer is different from the thickness of the layer when the light is

not normally incident. In this section, formulae of reflectivities and quantum efficiencies

are modified to be used for oblique incidence, which are then employed to simulate the

quantum efficiency in order to explain the experimental results contained in Chapter 5.

There are two different polarized waves: one with its electric field parallel to the

plane of incidence called parallel polarization, and the other with its electric field

perpendicular to the plane of incidence called perpendicular polarization. The plane of

incidence is defined as the plane containing the normal to the boundary and the direction

of propagation of the incident wave. These two polarization configurations are shown in

Fig. 2.9.

Instead of solving the reflection and transmission problems for the general case of

a wave with an arbitrary polarization, it is more convenient in practice to first decompose

the indicent wave (Ei, Hi) into a perpendicularly polarized component (Eipe, Hi

pe) and a

parallel polarized component (Eipa, Hi

pa), and then after determining the reflected waves

(Erpe, Hr

pe) and (Erpa, Hr

pa) due to the two incident components, the reflected waves can

57

be added together to give the total reflected wave corresponding to the original wave. A

similar process applies to the transmitted wave.

(a) Perpendicular polarization z=0

Z

X

Y θi

θr θt

Epei

Hpei

βi

Eper

Hper

βr

Epet

Hpet

βt

Medium 1 (ε1, µ1)

Medium 2 (ε2, µ2)

(b) Parallel polarization z=0

Z

X

Y θi

θr θt

Epai

Hpai

βi

Epar

Hpar

βr

Epat

Hpat

βt

Medium 1 (ε1, µ1)

Medium 2 (ε2, µ2)

Figure 2. 9 A wave is (a) perpendicularly polarized when its E field is perpendicular to the plane of incidence and (b) parallel polarized when its E field lies in the plane of incidence.

The phase matching condition is known as

tri θβθβθβ sinsinsin 211 == , (2.30)

58

where β1 is the wave number in the first medium, β2 is the wave number in the second

medium, θi is the incident angle, θr is the reflected angle, and θt is the transmitted angle.

The first equality in Eq. (2.30) leads to

ri θθ = (Snell’s law of reflection) (2.31 a)

and the second equality leads to

2

1

2

1

sinsin

nn

i

t ==ββ

θθ

(Snell’s law of refraction) (2.31 b)

The following expressions are for the reflection and transmission coefficients in

the perpendicular polarization case:

t1i2

t1i2ipe

rpe

θθθθ

E

Ecoscoscoscos

ηηηηΓ

+−

==⊥ (2.32 a)

t1i2

i2ipe

tpe

E

Eθηθη

θητcoscos

cos2+

==⊥ (2.32 b)

where θi and θt are defined as the above description, and η1 and η2 have the same

definition as in the previous sections. The Fresnel reflection coefficients for

perpendicular polarization are related by

⊥⊥ += Γτ 1 (2.33)

Equations (2.33) are the expressions for the reflection and transmission coefficients in the

parallel polarization case,

i1t2

i1t2ipa

rpa

θθθθ

E

Ecoscoscoscos

ηηηηΓ

+−

== (2.34 a)

i1t2

i2ipa

tpa

θθθ

E

Ecoscos

cos2ηη

ητ+

== , (2.34 b)

59

The above expressions can be shown to yield the relation

t

iθθ

coscos

)1( Γτ += (2.35).

The thickness of each individual semiconductor layer has to be modified for the

oblique incident case, which can be found by using Eq.(2.36)

22__

_)/(sin1)(sin1cos ji

j

tj

j

tj

jjeff

nθ

L

θ

LLL

−=

−==

θ, (2.36)

where Leff_j is the effective thickness of the jth layer and Lj represents the thickness of the

jth layer; while the θj_t is the transmitted angle in the jth layer and nj is the refractive

index of the jth layer.

When the light is oblique incident on the devices, the partial reflection and

transmission coefficients of a wave in the previous sections at each individual boundary

are replaced with Γ and τ or Γ and τ for perpendicularly polarized wave or parallel

polarized wave, respectively. Also, the thickness of each individual layer has to be

replaced with the effective thickness by using Eq. (2.36).

60

3. A Closed-form Expression to Analyze Electronic Properties in Delta-doped Heterostructures

An important feature of the devices developed here is that delta-doping technique

will be employed in the top AlGaAs layer to produce a confined electron cloud and an

associated transverse electric field, which may result in a reduction of dark current. Also,

the vertical electric field along the growth direction gives the contribution to the

collection of photo-generated carriers. These advantages of the delta modulation doping

will be demonstrated in Chapter 5.

A closed-form model is developed in this chapter to describe the electronic

properties of delta modulation doped heterostructures, particularly the 2DEG sheet

charge density and the electric field distribution in the direction of growth. The model

includes the effects of real-space charge transfer and carrier degeneracy. The electron

transfer and quasi-equilibrium condition in growth direction have been used in order to

express the 2DEG sheet charge density that is only a function of material parameters and

constants. An empirical constant, corresponding to quantized energy states, has been

employed to further simplify this description and to arrive at a closed form expression.

Results from the analytical expressions are shown to agree well with numerical

simulations based on a self-consistent solution of modified Schrödinger and Poisson

equations. In addition to their use in modeling of current conduction in HEMT devices,

we expect that these expressions will serve as versatile tools in the modeling of optical

and spectral effects that occur in the AlGaAs/GaAs heterostructures. The simulation

results and discussions in this chapter help design the delta modulation doped

61

heterostucture part of the devices used for short haul and long haul communications in

Chapter 4 and characterize the electronic properties of those optoelectronics devices.

3.1 Introduction

The successful use of uniformly modulation-doped field-effect transistors (U-

MODFETs) in the design of high-speed devices in optoelectronic applications has been

limited by the occurrence of persistent photoconductivity [63], threshold voltage shift

[64], and collapse of voltage characteristics [65] due largely to effects caused by DX

centers and surface states. Using a delta (δ) doping technique as an alternative choice for

selectively doped heterostructure transistors results in the optimization of its electronic

properties. Experiments show that delta modulation doped MODFET’s provide high

channel electron density, reduced trapping effects, and improved threshold voltage as

well as high breakdown characteristics [55 - 59]. Extensive exploitation of modulation-

doped heterostructure in the novel high speed devices has motivated the development of

theoretical expressions that reveal and help in understanding the underlying device

physics [58, 59, 66 - 71].

Although the advantages of the delta modulation doped devices over the

uniformly modulation doped devices have been shown experimentally, much more

attention has been paid to the latter structure than the former in detailed theoretical

investigations. Specifically, a simplified analytical tool has been used for carrying out

most calculations in terms of sheet carrier density (nso) level in uniformly modulation-

doped heterostructure, which is a closed form expression [69, 72, 73]. Also, it is possible

62

to use the results given by this expression to produce a description of the electric field

profile through the application of Gauss’s Law [74].

Recent experimental results show that strong built-in electric fields produced by

modulation-doped heterostructures aid in the collection photo-generated carriers [54].

Photoreflectance (PR) and electroreflectance (ER) studies of modulation-doped

heterostructures also show that the electric fields change the electric and optical

properties of semiconductor microstructures [104].

The objective of this chapter is to develop a simplified analytical tool for delta

modulation-doped heterostructures, which helps in understanding its electronic behavior

and the underlying device physics, in the form of a closed-form expression. The model

includes the effects of real-space charge transfer and carrier degeneracy. The real-space

electron transfer and quasi-equilibrium condition in growth direction are used as two

identities to describe 2DEG sheet charge density as only a function of material

parameters and constants. An empirical constant corresponding to quantized energy states

has been employed in order to simplify the functions and to arrive at a closed form

description [73]. We calculate sheet charge density variation with delta doping

concentration and electric field profile variation with distance from the interface by using

this method. Also, a comparison between sheet charge density and electric field profile

for different structures is made by using this simplified analytical tool and a much more

complex variational method that is based on simultaneous solution of the Schrödinger

and Poisson equations [105].

63

3.2 Closed-form Expression for Delta Doped Modulation Heterostructures

The conduction band diagram of the delta modulation doped heterostructure is

shown in Fig.3.1. If no parallel conduction occurs in the AlGaAs layers, then the Fermi

level is at or below the bottom of the conduction band in the whole AlGaAs region, i.e.,

Cf EE ≤ for the delta-doped heterostructure. The free electron concentration can be

written using Boltzmann statistics as

)/exp()( kTqVNzn c δ= (3.1)

where Nc is conduction band effective density of states and Vδ is as indicated as in

Fig.3.1.

The space charge density ρ(z) in AlGaAs delta doped region is given by

)]()([)( znzNqz d −= +ρ (3.2)

where

]/)exp[(1)(

kTqVEgN

zNdn

dd

δ

+

++= (3.3)

is the concentration of the ionized donors. Here, Nd is the total donor impurity

concentration in the delta doped region, gn is the degeneracy factor of the donor level, Ed

is the donor activation energy, k is the Boltzmann constant, and T is the lattice

temperature. The difference of energy levels between the conduction band and Fermi

level ( Cf EEqV −=δ ) in the delta-doped region can be assumed to be constant due to its

confinement to a small region, even though a large electric field exists there.

64

GaAs absorption layer

AlGaAs spacer layer

EC

Ef

Z

δ-doping

EAlGaAs(z)

-qVδ

Eo

AlGaAs top layer

EGaAs(z)

Zs

Figure 3. 1 Schematic diagram of conduction band of a modulation doped heterojunction.

The amount of electron transfer across the interface is found by ignoring the

effect of AlGaAs surface states and equating the electrons depleted from AlGaAs delta-

doped region with the electrons accumulated in the triangular potential well of GaAs,

hence

dcd

n

dso Z

kTqV

N

kTqVE

g

Nn

−+

+= )exp(

)exp(1

δ

δ (3.4)

where nso is sheet charge density in the quantum well and Zd is the thickness of delta

doped region. Rearranging this relation produces a quadratic equation in terms of

)/exp( kTqVδ , whose meaningful root is then calculated to yield

65

cn

dd

socncn

d

socn

d

so

Ng

NZn

NgNgZn

NgZn

kTqV

'

'2

''

2

4)exp(

−−

++

+−

=δ (3.5)

where )/exp(' kTEgg dnn = . Using Taylor series expansion and retaining the first two

terms, i.e. assuming qkTV /<<δ , this equation can be simplified to

12

4

'

'2

''

−

−−

++

+−

=cn

dd

socncn

d

socn

d

so

Ng

NZnNgNg

ZnNg

Zn

kTqVδ (3.6)

The assumption leading to Eq. (3.6) implies that the conduction band in AlGaAs

at the point of δ-doping is above the Fermi level but by less than a kT. This is a valid

assumption since if it is below Ef, (Vδ >0) then there is large parasitic conduction in

AlGaAs due to a large number of mobile electrons. On the other hand, if

)( Cf EEqV −−=− δ is much greater than kT, it indicates that a small number of dopants

are ionized, hence the number of carriers that are transferred to GaAs is small, or mobile

charge density in GaAs quantum well is low. So, in fact the assumption of Vδ =0,

indicates that about half of the donors are ionized and transferred to GaAs which is a rule

of thumb often used by expitaxial growers to relate delta doping concentration to the

2DEG mobile carrier density.

Equation (3.6) establishes a relationship between Vδ and nso; a second identity can

be drawn from the energy band diagram of Fig.3.1 given that the Fermi level is constant

due to equilibrium in Z-direction

0)( =−+∆−+− δ ofCsAlGaAs EEEZqEqV (3.7)

66

where EAlGaAs is the electric field in the spacer region, Zs is the thickness of the spacer

layer, ∆EC is the magnitude of the conduction band discontinuity and Eo is the conduction

band at the interface in the narrow gap material, taken as a point of reference for energy.

The second term in this equation is the potential change in the spacer region.

The electric field value in the spacer region can be readily obtained from sheet

carrier density level using Gauss’s law and continuity of displacement vector as

AlGaAs

soAlGaAs

qnE

ε= , (3.8)

where AlGaAsε is the complex dielectric permittivity of AlGaAs material.

The last term in Eq.(3.7) can also be derived in terms of GaAs sheet charge

density nso in the form ))(ln(/ soof nfqkTEE ×=− [69, 72], but this exact formulation

still requires empirical constants corresponding to the 1st and 2nd quantized states.

Instead a linear approximation is often employed which offers great accuracy for

depletion type devices, (i.e., large sheet charge density) and lends itself to mathematical

manipulating [73]

qE

bnq

EE Foso

of ∆+=

−, (3.9)

Here, b and ∆EFo are fitting parameters that are found by simple optimization methods. In

fact, ∆EFo is 0 eV at 300°K and 0.025 eV at 77K and can be ignored.

Substituting Eq.(3.6), Eq.(3.8), and Eq.(3.9) in Eq.(3.7) results in a quadratic

equation in terms of nso which can be solved to yield

AACBBnso 2

42 −+−= (3.10)

where

67

+

++=

AlGaAs

s

dcAlGaAs

s qZb

ZNqkTqZ

bAεε 2

/2 ,

+

∆−∆+

+

+

ε+=

kTE

g

qkTZNqkT

qEEkT

kTE

g

qkTZNqkTqZ

bB

dn

dc

CFo

dn

dcAlGaAs

s

exp

/2

/

exp2

/2

/2

,

and

2

2

)/(exp

exp

/

qkTN

kTE

g

NkTE

g

qkTq

EEkT

qEEkT

C

cd

n

d

dn

CFo

CFo

−

∆−∆++

∆−∆+=

Equation (3.10) is in terms of material parameters and constants. The only fitting

parameter is the constant b which is obtained by simple optimization methods to be

0.090, 0.095 and 0.100x10-16 Vm2 for, respectively, spacer layer thicknesses of Zs = 50,

70, and 100 Å.

An important advantage of having a closed form relation for sheet charge density

is that other structure characteristics, such as the electric field in the direction of growth

may also be obtained, as discussed next.

68

3.3 Closed-form Model of Electric Field and Potential

The electric field strength in the GaAs side of the heterointerface is given by

GaAs

soGaAs

qnEzE

ε=== int)0( (3.11)

This value becomes a boundary condition for determining the entire electric field

profile inside the GaAs layer. Derivation of the electric field is significantly simplified by

the band bending analysis of 2SiOSi − interfaces, where similar inversion conditions to

those in AlGaAs/GaAs heterostructures have produced a model of the potential profile of

the form [74].

+=

kTzqE

qkTnzU soGaAs 2

1ln2),( int (3.12)

From this analytical conduction band model, the electric field profile is obtained

directly from Poisson’s equation

zqEkTEkT

zUnzE sGaAs

int

int0 2

2),(

+×

=∂∂= (3.13)

The electric field profile of Eq.(3.13) is a function of the spatial position Z and of

the sheet carrier density in the form of the interface field strength.

Usefulness of expressions Eq.(3.10), Eq.(3.12) and Eq.(3.13) is evident in

describing the sheet charge density, potential and electric field variation in the direction

of growth, their accuracy, however, needs to be established in comparison with other

modeling techniques. The choice of numerical simulation techniques is between

commercial packages or a solution of Schrödinger and Poisson equations. The latter in its

69

brute force form is very computationally intensive. In what follows we describe a

numerical model based on self-consistent solution of a modified Schrödinger and Poisson

equations and then compare numerical results with our closed form analytical description.

3.4 Numerical Model Based on Schrödinger and Poisson Equations

A more rigorous requirement for modeling heterojunctions is incorporation of

quantization effects and solution of the wave function in the quantum well of the narrow

bandgap material. The most accurate method is to use a full numerical model that may

solve in a self-consistent manner the Schrödinger and Poisson equations [106, 107]. An

alternative approach to the full numerical calculation is the use of variational techniques

[108], which can then be incorporated into more complicated models. In this section we

provide a modified self-consistent solution of Schrödinger and Poisson equations to

verify the closed-form analytical description developed above.

This method starts by assuming a form for Eigen functions. Then, applying

boundary conditions on this wave function and its derivative, as well as its ortho-

normalization, reduces the number of the unknown coefficients. The program iteratively

and self consistently solves the Poisson equation with this form of the wave function in

Schrödinger equation to determine the remaining parameters.

The potential well created in the AlGaAs/GaAs interface is relatively narrow

[106], [109], therefore, it is sufficient only to consider the first two bound states. For the

ground and the first excited energy levels, a convenient form of the wave function that

70

captures both spatial confinement and exponential decay characteristics can be written

[110], for GaAs side (z>0) as:

)2

exp()()( 121111

zXCzXXCz −+=Ψ (3.14)

)2

exp()()( 2265422

zXzCzCCXz −++=Ψ (3.15)

And for AlGaAs side (z<0):

)2

exp()( 3331

zXXCz =Ψ

(3.16)

)2

exp()( 4472

zXXCz =Ψ (3.17)

where C1-7 and X1-4 are 11 parameters that depend on the structure and are determined as

follows.

The wave functions described by Eq.(3.14) – Eq.(3.17) and their derivatives

should be continuous at the interface. This, in addition to orthonormality conditions for

Ψ1(z) and Ψ2(z) are used to reduce the number of variation parameters from 11 to 4,

which only include X1-4.

Further constraints are set on the Eigen values and Eigen functions by noting that

the lower the total energy of the system is, the more stable it is. This is achieved by

minimizing

dzzHzE iii )()( ΨΨ= ∫∞

∞− (3.18)

where H is the Hamiltonian operator and Ei is the ith energy level with respect to the

Fermi level.

Electric potential V(z) is obtained from the Poisson equation:

71

[ ]222

2112

2)()()()()( zznzznpNq

zzV

aGaAs

ΨΨ −−+−ε

−=∂

∂ − (3.19)

where

+=

kTqE

Nzn iDi exp1ln)( 2 i=1,2 (3.20)

and 2*2 / hπkTmN D = is the 2D density of states. Poisson equations in other regions are

the same as the conventional description without quantum effects.

An iterative solution of the Schrödinger equation with this particular form of the

wave function, and Poisson equation with the same potential allows a self-consistent

description. The calculation program is based on a shooting method described in [105].

As a result the static potential, electric field, and wave functions as well as electron

distribution are determined.

3.5 Calculation Scheme for Numerical Model Based on Schrödinger and Poisson Equations

Figure 3.2 shows the calculation scheme used for the modified self-consistent

solution based on Schrödinger and Poisson equations.

The calculation starts at the GaAs buffer side. Since it is under the equilibrium

condition, the static potential V and the electric field E are approaching zero. The static

potential is fixed at almost zero and the electric field E is the free parameter at the

starting point. Then, Runge-Kutta method is used to solve the second order differential

equations, which are the normal Poission equations in all the regions except the triangular

72

well, where Schrödinger equations are used to calculate the two dimensional electron

densities.

Initialization

Set initial E at the GaAs buffer layer

Calculations into the surface

Minimization of <E1>

Calculation of n1

Minimization of <E2>

Calculation of n2

<E1>+<E2>converge ?

Desired V at the AlGaAs surface ?

Use updated X1-4 parameters

No

Yes

No

Stop

Modify shooting Eat the GaAs buffer

layer

Figure 3. 2 Flow chart diagram of computer program. E is electric filed, E1 and E2 are two energy level, n1 and n2 are 2DEG concentration at E1 and E2, respectively, V is static potential.

73

A downhill simplex method in multidimensions [111] is used to minimize the

energy level, thus to achieve the four reasonable parameters in the two wave functions.

The downhill simplex method is due to Nelder and Mead [112]. The method requires

only function evaluations, not derivations. It is not very efficient in terms of the number

of function evaluations that it requires. However, the downhill simplex method may

frequently be the best method to use if the figure of merit is “get something working

quickly” for a problem whose computational burden is small.

If the static potential V at the AlGaAs surface is the desired value, the program

will stop. Otherwise, the shooting method will find the adjustment of the free parameters

at the starting point that zeros the discrepancies at the other AlGaAs surface.

3.6 Results and Discussion

The AlGaAs/GaAs heterostructure used in the simulations is illustrated in Fig.

3.3. The structure consists of unintentionally doped (n-type 8x1014 cm-3) top

Al0.24Ga0.76As layer, which is used to increase Schottky barrier and to lower the leakage

current, a 20Å delta modulation doped n+-Al0.24Ga0.76As layer, and an undoped AlGaAs

spacer layer followed by unintentionally doped (p-type 1014 cm-3) GaAs layer. Thus, the

delta-doped layer is placed between the unintentionally doped Al0.24Ga0.76As layer and

Al0.24Ga0.76As spacer layers.

74

p- 1014cm-3 background doped GaAs

50~100 Å undoped Al0.24Ga0.76As spacer

δ-doped layer Zd=20Å

500 Å n-(6~8*1014cm-3) Al0.24Ga0.76As barrier

Figure 3. 3 Schematic diagram of delta-doped AlGaAs/GaAs heterostructure.

Figure 3.4 demonstrates the effect of the approximations performed in order to

derive a closed form formula for 2DEG sheet carrier density nso. Two plots are compared

for three spacer layer thicknesses; in one Eq.(3.5), which is an exponential function, is

iteratively solved with Eq.(3.7) while in the second case it is linearized to yield Eq.(3.6)

which then leads to the closed form Eq.(3.10). It is observed that the two techniques yield

similar results especially when delta doping concentration is beyond 1013 cm-2 and when

spacer layer is thin, i.e., when the 2DEG density is high. However, for smaller values of

doping, replacing )/exp( kTqVδ with kTqV /1 δ+ is not a very good approximation. This

indicates that Eq.(3.10) is most valid when the conduction band of the delta doped region

is above but in the vicinity of the Fermi level; a condition that is almost always met for

depletion type devices.

75

4.0x1012 8.0x1012 1.2x1013 1.6x1013 2.0x10138.0x1011

1.0x1012

1.2x1012

1.4x1012

1.6x1012

1.8x1012

100 Å

70 Å

50 Å

without using equation (3.6) approximationclosed-form expression

Shee

t Cha

rge

Den

sity

(cm-2

)

Delta Doping Concentration (cm-2)

Figure 3. 4 Simulation of nso against AlGaAs delta doping concentration at 300K for various spacer layer thickness.

In order to check the accuracy of the closed-form expression, it is compared in

Fig. 3.5 with the numerical model based on modified Schrödinger and Poisson equations

for various spacer layer thicknesses. Results of iterative solutions of Eq.(3.5) and Eq.(3.7)

are also shown in that figure. It is observed that the closed-form expression provides a

description that for a populated triangular well closely matches the much more involved

numerical method based on solution of Schrödinger and Poisson equations. It needs to be

repeated that the closed form expression requires one fitting parameter that has to be

determined for each spacer layer thickness, the values of which for 50, 70 and 100 Å

thicknesses were given earlier.

76

4.0x1012 8.0x1012 1.2x1013 1.6x1013 2.0x10138.0x1011

1.0x1012

1.2x1012

1.4x1012

1.6x1012

1.8x1012

50 Å

70 Å

100 Å

without using equation (3.6) approximationmodified Schrodinger and Poission model

closed-form expression

Shee

t Cha

rge

Den

sity

(cm-2)

Delta Doping Concentration (cm-2)

Figure 3. 5 Simulation of nso against AlGaAs delta doping concentration at 300K for various spacer layer thickness. Also shown are numerical results of analytical expressions for nso.

In addition to the sheet charge density distribution, the electric field profile in the

narrowband material can also be analytically derived as given in Eq.(3.13). That

expression, with the same linearization factor used for Fig.3.5, is plotted in comparison to

the field derived from numerical solution of Schrödinger and Poisson equations in

Fig.3.6. The volume delta doping concentration is 5x1019 cm-3 and the thickness of the

donor plane is 20 Å, which corresponds to an areal doping concentration of 1013 cm-2. It

is seen that the electric field strength at the heterointerface is closely modeled by the

closed-form expression. Also, away from the interface when the field reaches values that

77

are mainly due to background doping, the analytical and numerical solutions are

identical. However, discrepancy exists between analytical and numerical values in the

vicinity of the interface and up to about 60 Å toward the substrate. This discrepancy is

partly due to ignoring background doping concentration, or bulk charges, when relating

the field to the charge by Gauss’s law in Eq.(3.11). Nevertheless, it is seen from this

comparison that the analytical expression compares well with much more involved

numerical modeling methods.

10-1 100 101 102 103 1040.0

5.0x104

1.0x105

1.5x105

2.0x105

2.5x105

100 Å

70 Å

Distance from the interface (Å)

50 Å

modified Schrodinger and Poission model

closed-form expression

Ele

ctri

c F

ield

(V

/cm

)

Figure 3. 6 Comparison of electric field strength profile by using Eq. (3.13) and modified Shrödinger and Poisson model 300K for various spacer layer thickness.

78

3.7 Conclusions

The benefits of using delta modulation doped AlGaAs/GaAs heterostructure in the

design of devices is mainly derived from the ability to remove the limitation for the

uniformly modulation doped heterostructure, such as the occurrence of persistent

photoconductivity, threshold voltage shift, and collapse of voltage characteristics, to

produce high performance systems. Novel HEMT and other optoelectronic devices use

delta doped heterostructures to garner the benefits in sensitivity, speed, and efficiency

that arise from the presence of channel confinement and a strong electric field in the

absorption layer. For the purpose of studying these effects, a closed-form analytical

expression for describing sheet charge density in the delta modulation doped

heterostructure has been developed to help the design and analyze the physical

mechanism underlying the device behavior. This expression was shown to follow closely

the behavior of the numerical simulations based on much more involved methods using a

self-consistent solution of Schrödinger and Poisson equations. Versatility of the

developed analytical expression was shown by deriving the electric field profile and

showing that outside a region of about 50Å it matched closely with numerical simulation

results. In addition to their use in modeling of current conduction in HEMT devices, we

expect that these expressions would serve as versatile tools in the modeling of optical and

spectral effects that occur in the AlGaAs/GaAs heterostructures.

79

4. III-V Material based Doped HMSM Photodetector Design with Resonant Cavity for Optical Communications

III-V material based resonant-cavity-enhanced, heterostructure metal-

semiconductor-metal photodetector designs are presented in this chapter. One is GaAs-

based design for short haul optical communication; the other is InP based design for long

haul optical communication. The GaAs based photodetector utilizes a Al0.24Ga0.76As/

Al0.9Ga0.1As distributed Bragg reflector (DBR) operating around 0.85 µm; while the InP

based photodetector employs a In0.527Al0.144Ga0.329As/ InP (DBR) operating around 1.55

µm. The simulation results show clear peaks at 0.85 µm with a 30 nm full width at half

maximum (FWHM) and 1.55 µm with a 0.1 µm FWHM for GaAs based and InP based

photodetectors, respectively. At the resonance wavelength, a several-fold and a 3.5 fold

increase can be achieved in quantum efficiency compared to a detector of the same

absorption depth in GaAs and InP based designs respectively. The top reflector is a delta

modulation doped wide band gap material that also acts as the barrier enhancement layer

thus providing very low dark current values. Based on the simulation results and

discussions of the optical and electrical properties of the device, an optimization

including wavelength selectivity, optical sensitivity, quantum efficiency, and dynamic

speed will be considered during the design. Combination of low dark current, fast

response, wavelength selectivity, and compatibility with high electron mobility

transistors makes these devices especially suitable for optical communications purposes.

The characteristic performance of GaAs based devices is discussed in the next chapter.

80

4.1 Introduction

Vertical cavity surface emitting lasers (VCSEL) emitting at 850 nm [113] have

been a preferred source for high-speed short-haul communication systems. These

VCSELs are particularly suitable for local area networks (LAN) using multimode optical

fibers (MMF) with typical core diameters of 50 and 62.5 µm. The circular output beam of

the VCSELs allows for easy coupling of light into the MMF. It is also desirable to have

photodetectors with large active windows compatible with MMF for low cost coupling of

light at the receiving end. Furthermore, high sensitivity and high bandwidth are also

necessary attributes for photodetectors used in optical communication applications. As

VCSELs with modulation rates approaching 10 Gb/s become commercially available

[114], compatible high speed performance is required from photodetectors.

The two major speed-limiting factors in vertically illuminated photodiodes are the

depletion capacitance and the transit time [3]. The capacitance limit can be alleviated

either by employing smaller device areas or by increasing the depletion width, thereby

decreasing the capacitance per unit area. However, an increased depletion width

consequently increases the transit time.

Utilization of a thin absorption layer at an optimized position within the depletion

region can further improve the transit-time-limited bandwidth of conventional

photodiodes. The reduction in quantum efficiency resulting from a thin absorption layer

can be compensated for by using resonant cavity enhanced (RCE) detection. In addition

to their important application in vertical cavity surface emitting lasers (VCSEL’s),

resonant cavities (RC’s) have been exploited in the design of vertical photodetectors,

81

such as p-i-n heterojunction photodiodes, Schottky barrier internal emission photodiodes,

and quantum well infrared photodetectors [80 - 82]. Resonant-cavity-enhanced (RCE)

photodetectors have attracted attention in the past few years due to their potential in

solving the trade off between high quantum efficiency and high speed while, at the same

time, offering narrow spectral bandwidth detection useful in wavelength-division

multiplexing (WDM) applications [25].

On the other hand, the growing interest in mobile communication by wireless

links to the data highway has led to the concept of fiber-fed transceiver cells utilizing

microwave photonics. Millimeter-wave fiber-radio systems have attracted special interest

[115]. As a high-speed optical receiver for these systems, monolithic receiver

optoelectronic integrated circuits (OEICs) are attractive due to their potential for high-

speed operation, compactness, and cost reduction. The trend towards monolithic OEIC

motivates appreciable research activity directed towards the employment of planar

photodetectors, which can be easily fabricated and are compatible with the FET process.

Planar metal-semiconductor-metal photodetectors (MSM-PD’s) are good candidates for

such OEIC receivers [16, 17]. The FET technology itself is strongly affected by progress

in heterojunction-based devices that take advantage of the reduced dimensionality regime

of conduction; the high electron mobility transistor (HEMT) being a prime example. This

has motivated the development of heterojunction based photodetectors that enjoy better

conduction while being compatible with HEMT technology [16]. In particular, we have

previously proposed AlGaAs/GaAs heterostructure metal-semiconductor-metal

photodetectors (HMSM-PD’s) that show much less dark current than conventional MSM

82

due to both the two dimensional electron gas (2DEG) and the barrier enhancement effect

due to the wide-gap material [52 - 54].

A common problem with planar, as well as vertical, photodetectors is the trade-off

between speed and quantum efficiency; in order to achieve a fast response from

photodetectors, the depleted absorption region needs to be small for reduced path length,

but it results in a decreased responsivity due to small absorption depth. Resonant cavity

technique offers the possibility to balance such conflict between fast speed and sensitivity

[75]. Also, the main drawback of MSM-PD’s is their low responsivity due to the metal

showing effect. Resonant-cavity photodetector (RCE-PDs) have been demonstrated to be

an attractive design to achieve high quantum efficiency while using a thin absorbing layer

[116, 117].

Schottky barrier height and band-edge discontinuities play an important role in

the behavior of heterojunction devices by strongly affecting current transport [52, 53,

118, 119]. Several techniques have been proposed to modulate the Schottky barrier

height, heterojunction barrier height and band-edge discontinuities including: tuning of

the conduction and valence-band barrier heights at an abrupt intrinsic semiconductor-

semiconductor heterojunction via incorporation of a doping interface dipole [120];

controlling the effective Schottky barrier height over a wide range using highly doped

surface layers [121]; increasing the barrier height due to energy quantization of confined

electrons [122]; and increasing Schottky contact through the electron-electron cloud

effect in the modulation-doped heterostructures [54].

The last effect is particularly relevant in the present work. The electron cloud that

is formed in the narrow gap material of a heterojunction exerts a repulsive force on the

83

electrons that are emitted from the metal to the wide gap material, thus decreasing the

dark current. It also influences absorption of the optically generated carriers though a

field-induced change in the index of refraction, a change similar to the Franz-Keldysh

effect [123].

Two different techniques of uniform doping or delta doping of the wide-gap

material have been employed in order to form such an electron cloud in modulation

doped field-effect transistors (MODFET). Delta doping is a better candidate than

uniformly doping in the modulation doped heterojunction devices due to the optimization

of its electronic properties as mentioned in Chapter 3.

A transmission line model has been employed to design the resonant cavity and

the distributed Bragg reflector (DBR) that forms the bottom mirror, which exposes how

the parameters are calculated to optimize the quantum efficiency of the overall structure

[101]. Also, a variational method and a newly developed closed-form expression as

described in Chapter 3 are used to calculate the electric field profile [105,124] in the

device.

4.2 Material Selection

The development of heterostructure science and technology is largely influenced

by the availability of suitable substrates and the need from industrial applications. Among

III-V compounds, the ternary (GaAl)As system lattice-matched to GaAs substrated and

quaternary (GaIn)(AsP) and (Al,Ga,In)As systems lattice-matched to InP substrate have

been extensively studied, the former for short haul fiber optic communications and the

84

latter for long haul fiber optic communications for reasons enumerated in Chapter 1 and

Chapter 2.

4.2.1 III-V material parameters’ calculation

The process involved in making a ternary III-V material is much easier and also

cheaper than that of a quaternary material. InAs and AlAs are the materials to be

considered to make a ternary material with GaAs. AlAs is the best choice due to its larger

bandgap (Table 4.1), which can make a new wider bandgap ternary material, thus

enhancing the Schottky barrier between metal and GaAs.

The quaternary (GaIn)(AsP) and (Al,Ga,In)As systems lattice-matched to InP

substrate have been employed for long haul fiber optic communications. The absorption

materials, the barrier enhancement layer material, quarter wave stack pair materials are

selected based on this quaternary (GaIn)(AsP) and (Al,Ga,In)As systems.

Table 4. 1 Lattice constant, gap energy, and electron affinity for a selected number of III-V binary compounds [125] [126].

Compound Lattice Constant (Å)

Gap (eV) Energy at 300 K Electron affinity (eV)

AlP 5.451 2.45 Eχ AlAs 5.6605 2.163 Eχ (3.5) [125] AlSb 6.1355 1.58 Eχ 3.64 GaP 5.45117 2.261 Eχ 4.0 GaAs 5.65325 1.424 EΓ 4.05 (4.07) [126] GaSb 6.09593 0.726 EΓ 4.03 (4.06) [126] InP 5.86875 1.351 EΓ 4.4 InAs 6.0585 0.360 EΓ 4.54 (4.90) [126] InSb 6.47937 0.172 EΓ 4.59 (4.59) [126]

85

4.2.1.1 Ternary (GaAl)As system

The material must be lattice matched to the GaAs substrate. Assuming a linear

dependence of lattice constant a on composition, the lattice-matching condition is

321 )1( axaxa =+− (4.1)

where a1 is the lattice constant for GaAs, a2 is that of AlAs, and x is the percentage of Al

composition. And a3 is that of new ternary material AlxGa1-xAs.

If we again assume a linear relation between the energy gap, the energy gap of the

ternary is given by

321 )1( ExExE =+− (4.2)

where E1 is the energy gap for GaAs, E2 is the energy gap for AlAs, and the definition of

x is Al mole fraction. And E3 is the energy gap for new ternary material AlxGa1-xAs.

While GaAs is a direct-gap semiconductor, AlAs is an indirect gap

semiconductor. In AlxGa1-xAs the transition from direct to indirect gap occurs at x=0.45

with )()( 6 gg EEE Γ−Γ= varying as

xEg 247.1424.1 += (4.3)

in the direct gap region and with )()( 6 gg EXEE Γ−= varying as

2)45.0(147.1985.1 −+= xEg (4.4)

in the indirect gap region. Therefore, a gap discontinuity exists at the AlxGa1-xAs and

GaAs interface. There are two different methods to calculate the band gap discontinuity,

which can be computed by using the following explanation.

86

One physical quantity commonly used in constructing the energy band diagram at

a semiconductor-metal interface is electron affinity χe. For AlxGa1-xAs, the quantity

varies with composition as

xe 06.107.4 −=χ (4.5)

in the direct gap region (x < 0.45), and as

xe 14.064.3 −=χ (4.6)

in the indirect gap region (0.45 <x <1.0). Figure 4.1 shows conduction band edge EC in

GaAs and AlxGa1-xAs relative to vacuum level. A conduction band discontinuity ∆EC can

be expected to behave according to the following expression:

xEC 06.121 =χ−χ=∆ (4.7)

where x is less than 0.45. The results on capacitance-voltage C-V and current density-

voltage J-V measurements in heterojunction, however, yield the following empirical

relation [127-129]:

gC EE ∆=∆ 60.0

(4.8)

Another relevant property is the dielectric constant εAlGaAs which for AlxGa1-xAs is

given by

0)0.31.13( εε xAlGaAs −=

(4.9)

87

χ1 χ2

Vaccum level

Ec2

Ec1

∆Ec

Figure 4. 1 Energy band diagrams showing existence of a conduction-band-edge discontinuity at interface between semiconductors with different values of electron affinity.

Table 4.2 lists parameters of the AlxGa1-xAs ternary materials, which have been

calculated by using the above formulae (4.1-4.9). The linear dependence on the

composition has been used in most cases Eq.(4.1) and (4.2). The refractive index is the

square root of relative dielectric constant.

Table 4. 2 AlxGa1-xAs material information.

Compound Lattice Constant (Å)

Gap (eV)

Gap (µm)

∆EC (eV) Eq 4.8

Affinity (eV)

∆EC (eV) Eq 4.7

Dielectric constant (0.83 µm)

λ/(4n) at 0.83 µm

(nm) GaAs 5.6533 1.424 0.871 0.000 4.07 0.000 13.455 56.57 AlAs 5.661 2.168 0.572 0.496 3.5 0.570 9.053 68.97

Al0.24Ga0.76As 5.6551 1.7233 0.720 0.200 3.816 0.254 12.127 59.59 Al0.2Ga0.8As 5.6548 1.6734 0.741 0.166 3.858 0.212 12.337 59.08

Al0.15Ga0.85As 5.6545 1.6111 0.770 0.125 3.911 0.159 12.636 58.37 Al0.9Ga0.1As 5.6602 2.1283 0.583 0.470 3.514 0.556 9.419 67.61

Al0.35Ga0.65As 5.6560 1.8605 0.667 0.291 3.699 0.371 11.609 60.90

88

4.2.1.2 Quaternary (GaIn)(AsP) and (Al,Ga,In)As systems

Table 4.3 shows the material parameters of the quaternary (GaIn)(AsP) and

(Al,Ga,In)As systems lattice-matched to InP substrate.

Table 4. 3 Material parameters of quaternary (GaIn)(AsP) and (Al,Ga,In)As systems.

Compound Lattice Constant (Å)

Gap (eV)

Barrier (eV)

Dielectric constant (1.55 µm)

Refractive Index

(1.55 µm) λ/(4n) at 1.55 µm (nm)

AlAs 5.660 2.153 0.841 8.237 2.870 135.016 GaAs 5.653 1.420 0.401 11.364 3.371 114.949 InP 5.869 1.350 0.359 10.037 3.168 122.312

InAs 6.058 0.360 -0.235 12.388 3.520 110.095 GaP 5.451 2.740 1.193 9.322 3.053 126.916

In0.53Ga0.47As 5.868 0.752 0.000 12.469 3.531 109.738 In0.52Al0.48As 5.867 1.457 0.423 10.243 3.200 121.075

(In0.53Ga0.47As)0.5 (In0.52Al0.48As)0.5 5.868 1.055 0.182 11.156 3.340 116.014 (In0.53Ga0.47As)0.6 (In0.52Al0.48As)0.4 5.868 0.988 0.142 11.395 3.376 114.791 (In0.53Ga0.47As)0.7 (In0.52Al0.48As)0.3 5.868 0.925 0.104 11.693 3.420 113.318 (In0.53Ga0.47As)0.44

(InP)0.56 5.868 1.038 0.172 10.659 3.265 118.690

To calculate the energy band gap of the ternary and quaternary materials, data

from Science and Technology has been used as a reference [130]. Based on the

information given in this reference, energy band gaps of the ternary materials in the

above table have been calculated by using the following formula:

2g xxE 0.436+0.629+0.36As)Ga(In xx-1 = (4.10)

and

2g x+xE 0.741.91+0.37As)Al(In xx-1 = (4.11)

respectively; x is the mole fraction of the Ga in InGaAs and the Al in InAlAs ternary

materials.

89

The energy band gap of the (In0.53Ga0.47As)1-z(In0.52Al0.48As)z quaternary materials

is calculated from

2g zzE 0.20+0.49+0.76)As)Ga(InAs)Al((In z-10.470.53z0.480.52 = (4.12),

where z is the mole fraction of (In0.52Al0.48As) in (In0.53Ga0.47As)1-z(In0.52Al0.48As)z.

Another quaternary material of importance, (In0.53Ga0.47As)z(InP)1-z, lattice-

matches to the InP substrate, and the formula to calculate its energy band gap is

2g z+zE 0.1490.775-1.35)(InP)As)Ga((In z-1z0.470.53 = (4.13)

where z is the composition of (In0.53Ga0.47As) in (In0.53Ga0.47As)z(InP)1-z.

4.2.2 Absorption layer

4.2.2.1 Absorption materials for 800-900 nm optical window

For fiber optic communication operating in the 800-900 nm optical window,

GaAs and Si are the best candidates for the active region material, which can be seen in

Fig. 1.10. Table 4.4 summarizes the relevant optical and electrical characteristics of GaAs

and Si [131].

Table 4. 4 Optical and electrical characteristics of GaAs and Si.

Material Si GaAs Mobility (cm2/(V.s)) 1350 8600

Energy band gap (eV) 1.12 (indirect) 1.42 (1.35) (direct) Interface state density (cm-2) <1010 >1012

Passivation Layer MOS / Processing Mature and low cost Not so mature and high cost

90

It can be seen from the above table, as a natural microelectronic material, Si

integrated circuit processing is much more mature than that of GaAs. When used for

making optoelectronic device, however its importance has been limited by speed, due to

low mobility, and quantum efficiency, due to its indirect bandgap. GaAs as another

standard integrated circuit processing material plays an important role in fiber optic

communication. Therefore, GaAs is used as the active region material in the following

design.

4.2.2.2 Absorption materials for 1550 nm optical window

For fiber optic communication operating in the 1550 nm optical window, InGaAs

and Ge are the best candidates for the active region material, which can be seen in Fig.

1.10. The former is III-V material and the latter is IV material.

Table 4. 5 Optical and electrical characteristics of In0.53Ga0.47As and Ge

Material Ge In0.53Ga0.47As Electron Mobility (cm2/(V.s))

3900 13800 (LPE) 11200 (MOCVD)

Hole Mobility (cm2/(V.s)) 800 Energy band gap (eV) 0.664 (indirect) /

0.805 (direct) 0.75

While Ge photodiodes were the components of choice for the earlier fiber

transmission at 1.3 µm, their degraded performance at 1.55 µm and the development of

InP-based optoelectronic technology have lead In0.53Ga0.47As photodiodes to be the best

choice for meeting most demands of long haul communications (long wavelength

91

transmission). Table 4.5 compares the optical and electrical characteristics of

In0.53Ga0.47As and Ge.

As can be seen from the table, the electron mobility of In0.53Ga0.47As is almost

three times of that of Ge. In the manufacture of optoelectronic devices, Ge’s importance

has been limited by low speed due to this low mobility. Also, time-division-multiplexed

(TDM) optical transmission systems have been demonstrated at 40 Gb/s [132]. InP-based

heterostructures have traditionally been utilized for the fabrication of photodetectors and

integrated optoelectronic circuits (OEICs) operating at long wavelengths (1.55 µm) for

optical fiber applications due to speed requirement. The In0.53Ga0.47As epi-layer absorbs

photons in the regime of 1.0~1.6µm wavelength (Fig. 1.10) and also has a high electron

mobility (~12,000cm2V-1S-1 at 300K) and high saturation velocity (~2.5x107cm/s) (Fig.

4.12), which make lattice-matched growth of In0.53Ga0.47As on an InP substrate of great

promise for the absorption region in a photodetector and for the active channel in

electronic devices used in wavelength 1.55µm and 1.3µm fiber bands in long haul

communications [20, 34 - 40]. Therefore, In0.53Ga0.47As was selected as the active region

material in the following design.

4.2.3 Barrier enhancement layer

4.2.3.1 Barrier enhancement layer for GaAs based photodetectors

The barrier enhancement layer is the top layer of the entire structure. The top

mirror is the interface between the barrier enhancement layer and air, which should

reduce reflection from air and recirculate photons reflected by the bottom mirror.

92

Heterojunction based photodetectors enjoy better conduction due to a reduced

dimensionality region. For this reason, it is advantageous to choose a material that creates

a heterojunction with GaAs.

There are four requirements for the barrier enhancement layer material. First, it

should enhance the Schottky barrier between metal and GaAs; second, the bandgap

discontinuity should be large enough to confine a two dimensional electron gas in the

triangular well; third, the material must lattice match with GaAs, which removes the

stress affecting the quality factor of the device; the last consideration is that the refractive

index difference between this layer material and the air has to be reasonable in order to

create a good resonant cavity.

A 55 nm Al0.24Ga0.76As layer has been used which offers the following electronic

properties. First, this layer lattice-matches to the absorption layer, with reduced DX-

center defect levels due to low Al mole fraction, while providing surface stability.

Second, it enhances the Schottky barrier between metal and GaAs due to its larger

bandgap. Third, this layer is delta-doped to produce a 2DEG that is confined to the

vicinity of the heterojunction by the conduction band discontinuity of about 0.3 eV.

The last is the most important feature of this device. The confined electronic

states of the quantum well at the interface as well as the electron cloud of the 2DEG have

been shown to further enhance the barrier height and reduce the dark current, and thus the

noise of these detectors [133]. This electron cloud is confined by a vertical electric field

that has also been shown to aid in transport of photoelectrons [54]. Finally, modulation

doping of this layer makes the growth compatible with HEMT. This top AlGaAs layer is

delta doped, rather than uniformly, in order to take advantage of high channel electron

93

density, reduced trapping effects, and improved threshold voltage as well as high

breakdown characteristics [55-59]. The lattice mismatch for Al0.24Ga0.76As to the GaAs

substrate is 0.032%.

4.2.3.2 Barrier enhancement layer for InP based photodetectors

Four requirements for the barrier enhancement layer material should be the same

as the described in the previous section. Table 4.6 lists the performance of the barrier

enhancement layer structure above the In0.53Ga0.47As active layer based on current

background. However, low Schottky barrier height (~0.2eV) on n- In0.53Ga0.47As causes

excess leakage current when the contacts are formed directly with the material [85],

preventing it from being further developed. Experimental results show that a lattice-

matched material In0.52Al0.48As may serve as a barrier enhancement layer on the top of

In0.53Ga0.47As to limit the leakage current to an acceptable value [86 - 88]. There are

several research groups concentrating on such Schottky barrier photodiodes [134 - 136].

Table 4. 6 Performance of barrier enhancement layer structure above In0.53Ga0.47As active layer [85, 47, 134-136].

Barrier enhancement layer Dark current Barrier height In0.52Al0.48As < 1 pA/µm2 at 5V,

< 25 pA/µm2 at 15V, < 300 pA/µm2 at 30V

Al / In0.52Al0.48As: 0.8 eV Au / In0.52Al0.48As: 0.82 eV

InGaP 1.6pA/µm2 at 10V P+-In0.53Ga0.47As < 0.1 ~ 1 nA/µm2 at 5V

P+-InP < 0.1 ~ 1 nA/µm2 at 10V

A 55 nm In0.52Al0.48As has been employed due to the following electronic

properties. First, this layer lattice-matches to the absorption layer. Second, it enhances the

94

Schottky barrier between metal and In0.53Ga0.47As to limit the dark current to an

acceptable level. Third, this layer is delta-doped to produce a 2DEG that is confined to

the vicinity of the heterojunction by a conduction band discontinuity of about 0.42 eV.

The lattice mismatch for In0.53Ga0.47As to the InP substrate is less than 0.017%.

4.2.4 Distributed Bragg reflector

4.2.4.1 DBR for GaAs based photodetectors

A distributed Bragg reflector is composed of number of pairs of quarter wave

stacks, which form the bottom mirror of a Fabry-Perot resonant cavity.

From Eq.(2.14), the larger the reflection coefficient of the bottom mirror, R2, is,

the larger is the quantum efficiency, which is demonstrated by simulation results in the

next section. A large reflectivity of the bottom mirror is a necessary condition for good

device performance. Equation (2.17) shows a large difference in characteristic impedance

results in a large reflection coefficient, and therefore a large reflectivity. Equations (2.14)

to (2.17) are used to compute the reflectivity for the light incident at the top of the bottom

mirror. A pair of materials having large refractive contrast is the best choice to form the

DBR; having a highly reflective bottom mirror while needing less pairs, decreases costs

of the device.

There are two further requirements for the materials. First, material with a band

gap larger than the energy of the incident light has priority. If this is the case, the DBR

material will not absorb the incident light, which means that no carriers are generated

below the GaAs absorption region. This situation results in a short light path existing

95

within the structure. Therefore, the performance of the time response of the device is

improved.

Second, lattice-matched materials help prevent imperfections that might result

from bonding process from affecting the quality-factor of the microcavity.

Based on the material parameters shown in Table 4.2, Al0.24Ga0.76As and

Al0.9Ga0.1As are suitable pairs to construct this DBR- mirror. The lattice mismatch for

Al0.24Ga0.76As and Al0.9Ga0.1As to the GaAs substrate is 0.032% and 0.122% respectively.

4.2.4.2 DBR for InP based photodetectors

The material for the DBR on the InP substructure must satisfy the same three

requirements. First, a pair of materials having large refractive contrast is the best choice

to form a DBR, which results in a low cost device to achieve the same functionality.

Second, the material with a band gap larger than the energy of the incident light has

priority to be selected, which helps decrease the length of the light path, and produce a

faster device. Third, material must lattice-match to the substrate preventing imperfections

in the bonding process from affecting the quality-factor of the microcavity.

Based on the material parameters shown in Table 4.3, In0.527Al0.144Ga0.329As and

InP are such suitable pairs. The lattice mismatch for In0.527Al0.144Ga0.329As to the InP

substrate is 0.01%.

96

4.3 Selection of Structure Parameters

The thickness of the barrier enhancement layer and the absorption layer, in turn,

are determined by satisfying the optimization condition of the quantum efficiency

1))(2cos( 212211 =Ψ+Ψ++ LL ββ .

For the DBR reflector, the thickness of each individual layer in the stacks is one

quarter of the effective wavelength of the incident light, which can be expressed as (λ0/n).

Here λ0 is the incident light wavelength in a vacuum and n is the refractive index of the

material at the resonant frequency.

This section will be arranged as follows: first, the growth technique will be

described; then, the dispersion relation used in the theoretical simulation will be

discussed; the number of the quarter wave stack pairs will be decided and the thickness of

the absorption layer will be determined from the simulation results; finally, from the

simulation results and discussion of the electric field profile along growth direction, the

thickness of the spacer layer will be selected, thus the thickness of the barrier

enhancement layer will be determined based on the resonant requirement

1))(2cos( 212211 =Ψ+Ψ++ LL ββ .

4.3.1 The grown RCE heterojunction MSM

The schematic cross-sections of the grown RCE heterojunction MSM of GaAs

based and InP based photodetectors are shown in Fig.4.2 and Fig.4.3 respectively.

97

4.3.1.1 GaAs based photodetector structures

Figure 4.2 shows the schematic cross-section of GaAs based photodetectors with

RCE heterojunction MSM.

GaAs Substrate

200nm GaAs Buffer

DBR quarter wave stacks

117.5nm undoped GaAs absorption layer

Si δ-doping 5x1012 cm-2

light

5 nm nid Al0.24Ga0.76As Spacer

(λ0/4n) undoped Al0.9Ga0.1As (67.6nm)

(λ0/4n) undoped Al0.24Ga0.76As (59.6nm)

50 nm nid Al0.24Ga0.76As Barrier

Figure 4. 2 Device structure of GaAs based resonant-cavity-enhanced HMSM photodetector.

The layer structure was grown by solid-source molecular beam epitaxy on a semi-

insulating GaAs substrate. Twenty-periods of the Al0.24Ga0.76As/Al0.9Ga0.1As DBR were

grown on a 200 nm GaAs buffer layer. The thickness of the top barrier enhancement

layer is 50 nm and the spacer layer is 5 nm, which separates the ionized donors and the

electrons and removes the scattering effects in the 2DEG, thus increasing transport speed.

A Si delta doping layer with sheet density of 5 x 1012cm-2 was grown between the barrier

98

enhancement and spacer layers due to its previously mentioned advantages [55 - 59]. The

bottom mirror was designed for high reflectance at a 830 nm center wavelength. The

thickness of the quarter-wave pair is one half of the effective wavelength, and therefore

the thickness of each layer is one quarter of the effective wavelength (λ0/n).

4.3.1.2 InP based photodetector structures

InP Substrate

25nm InP:Fe Buffer

(λ/4n) In0.527Al0.144Ga0.329As (113.3nm)

(λ/4n) Undoped InP (122.3nm) 20 periods

385.8 nm undoped In0.53Ga0.47As absorption layer

5 nm undoped In0.52Al0.48As spacer

Si δ-doping 1013cm-2 50 nm n-(6~8*1014cm-3) In0.52Al0.48As barrier

40 nm n+(1.5*10^18 cm-3) GaAs cap

Figure 4. 3 In0.52Al0.48As/In0.53Ga0.47As/InP HMSM RCE-PD schematic diagram.

The In0.52Al0.48As/In0.53Ga0.47As/InP HMSM RCE-PD is illustrated in Fig.4.3. The

layer structure was also grown by solid-source molecular beam epitaxy on a semi-

insulating InP substrate. Fifteen-periods of the In0.53Ga0.47As/InP DBR were grown on a

25 nm InP buffer layer. The thickness of the top barrier enhancement layer is 50 nm and

99

the spacer layer is 5 nm. A Si delta doping layer with sheet density of 1013cm-2 was

grown between the barrier enhancement and spacer layers due to its previously

mentioned advantages. The bottom mirror was designed for high reflectance at a 1550 nm

center wavelength. The thickness of each individual layer in the quarter-wave pair is one

quarter of the effective wavelength. The thickness of the active layer has to satisfy the

optimization of quantum efficiency.

4.3.2 Dispersion relation expression

Material dispersion effects have to be considered in optimization of quantum

efficiency. This section describes the disperstion relation expression of the ralted material

systems.

4.3.2.1 Dispersion relation in ternary (GaAl)As system

The dispersion relation is a result of two factors. One is due to material dispersion

properties [125]. The other is that light with a wavelength that does not match the

thickness of the DBR is incident on the device.

The fundamental optical excitation spectrum of a material can be described in

terms of a frequency-dependent complex dielectric constant ε(ω):

)()()( 21 ωεωεωε i+=

(4.14)

The dielectric constant has well-known integral dispersion relations between the

real and imaginary parts of the function ε(ω) dependent on the frequency ω [Kramers-

Kronig relations] [123]:

100

'

022'

'2

'

1)(

)(2)( ωωωωεωωε d∫

∞

−π+1=

(4.15)

'

022'

'1

2)(

)(2)( ωωω

ωωεωε d∫∞

−π−=

(4.16)

A model of the dielectric constant of semiconductors based on simplified models

of the interband transitions will be employed [137]. The lowest-direct gaps in the zinc-

blende type semiconductors occur in the center of the Brillouin zone, where is has four-

fold (counting the two spin states) E0 and two-fold E0+∆0 gaps. The real part of ε(ω) in

the zinc-blende material below the band edge can, thus, be written as [137]

002/3

00001 )()]/([21)()( BfEEfA +++= χ∆χωε

(4.17)

with

])1()1(2[)( 2/12/12 χχχχ −−+−= −f

(4.18),

0/ Eωχ h=

(4.19),

and

)/( 000 ∆ωχ += Eh

(4.20).

The constants A0 and B0 as a function of composition x, as determined by least-

square fitting Eq.(4.17) with the experimental data, are found to be [125]:

xxA 0.193.6)(0 +=

(4.21)

xxB 2.104.9)(0 −=

(4.22)

Table 4.7 [138-140] shows the electric band parameters for GaAs, AlAs, and

AlxGa1-xAs, which are used to achieve the dispersion relation expression.

101

Table 4. 7 Electronic parameters for GaAs, AlAs, and AlxGa1-xAs.

Parameter GaAs AlAs AlxGa1-xAs Band-gap energy

Egα (eV)

1.424 (EgX) 2.168 (Eg

X) 1.424+1.247x (0<x<0.45)

1.900+0.125x+0.143x2 (4.5<x<1)

Critical-point energy (eV) E0

E0+∆0

1.425 1.765

3.02 3.32

1.425+1.155x+0.37x2 1.765+1.115x+0.37x2

4.3.2.2 Dispersion relation of quaternary (GaIn)(AsP), (Al,Ga,In)As system

The (GaIn)(AsP) quaternary system has generated much interest recently because

it can be grown epitaxially on InP without lattice mismatch over a wide range of

compositions. The real part of ε(ω) of the material in this system still can be written as

Eq.(4.17-4.20) [141]. Table 4.8 shows the parameters used in the calculation of ε1(ω).

Table 4. 8 Parameters used in the calculation of ε1(ω).

Material E0 E0+∆ A0 B0 InP 1.35 1.45 8.40 6.60 GaP 2.74 2.84 22.25 0.90

GaAs 1.42 1.76 9.29 7.86 InAs 0.36 0.79 4.36 10.52

A0 and B0 are given by the following two equations in (In0.53Ga0.47As)z(InP)1-z:

zzA 40.340.8)(0 −=

(4.23 a)

and

zzB 40.360.6)(0 +=

(4.23 b).

The dielectric constant ε1(ω) of In1-xGaxAszP1-z can then be specified in terms of z

alone. The definition of z is the composition of (In0.53Ga0.47As) in (In0.53Ga0.47As)z(InP)1-z.

102

The refractive index dispersion of the (Al,Ga,In)As quaternary systems for

various (Al,In)As mole fractions can be calculated as described in the following. The

index of dispersion of the (Al,Ga,In)As quaternary for various (Al,In)As mole fractions,

z, i.e., (In0.53Ga0.47As)1-z(In0.52Al0.48As)z is known from the previous waveguide

measurements [142]. By fitting the data to a first-order Sellmeier equation of the form

21

2

21

12

CλλBA)n(

−+=λ (4.24),

the empirical A1, B1, and C1 coefficients as a function of In0.52Al0.48As mole fraction z can

be obtained

z(z)A1 012.1689.9 −= (4.25 a),

z(z)B1 376.0590.1 −= (4.25 b),

and

21 4.3300.7024.1102)(C zzz +−= (4.25 c).

where 0.3 < z <1.0 [143].

A linear interpolation has been employed to calculate the rest of the lattice

constants, energy band gaps, and some other electronic and optical parameters of the

materials in the same manner as depicted in previous sections.

4.3.3 Reflectivity from the bottom mirror

The simulations are based on the simplified resonant-cavity-enhanced

heterojunction photodetector shown in Fig.2.2. The materials shown in Fig. 4.2 and Fig.

4.3 are employed to fill each layer in Fig.2.2 for GaAs based and InP based

photodetectors correspondingly.

103

Figure 4.4 and Fig. 4.5 show the calculated reflection coefficients of a wave

incident on the top of the DBR reflector for GaAs based and InP based photodetectors

respectively, which include the materials dispersion effects as mentioned in the above

section.

4.3.3.1 Reflectivity from the bottom mirror in GaAs based PD

Figure 4.4 shows how the reflection coefficient changes with wavelength. Since

the energy band gap of Al0.24Ga0.76As and Al0.9Ga0.1As are both larger than the incident

photon’s energy considered, the absorption effect is neglected here.

720 760 800 840 880 920 9600.0

0.2

0.4

0.6

0.8

1.0N=30N=20

N=15

N=10

Ref

lect

ivit

ies

of t

he b

otto

m m

irro

r

Wavelength (nm)

Figure 4. 4 Reflectivity of bottom mirror vs wavelength for different numbers of quarter wave pairs. N is the number of quarter wave pairs. +: N=10; ×: N=15; • : N=20; ∗ : N=30. (GaAs based PD)

104

N is the total number of the contrasting pairs in the quarter mirror stacks. The

more quarter mirror stacks, the higher the reflectivity of the Bragg mirror. Also, the more

quarter mirror stacks, the sharper the curve, which means with high reflectivity of the

bottom mirror, a high spectral resolution can be achieved for the corresponding receiver.

This kind of feature makes it behave like a filter, which can help it to serve as a

wavelength selected receiver in the WDM (wavelength division multiplexing) systems.

FWHM (full width at half maximum) of these four curves are approximately 95nm,

82nm, 77nm, and 71nm and also the peak value of the reflectivities of these four different

structures are 0.7259, 0.9136, 0.9748 and 0.9980 at 830 nm respectively while N equals

to 10, 15, 20 and 30. For N=20, the reflectivity of the bottom mirror almost reaches unity

and also the bandwidth at 90% of its peak value is 57 nm, which is only 3 nm different

from the ideal case. Thus, 20 quarter wave pairs were selected in the design for the

distributed Bragg reflector.

4.3.3.2 Reflectivity from the bottom mirror in InP based PD

Figure 4.5 shows the reflection coefficient′s dependence on wavelength. There are

two factors that produce such a curve. One is from material dispersion properties. The

second is that the thickness of all these layers does not match the wavelength of the

incident light when it varies from 1.55µm. Since the energy band gap of

In0.527Al0.144Ga0.329As and InP are both larger than the incident photon energy considered,

the absorption effect is neglected here. N is the total number of the contrasting pairs in

the quarter mirror stack. The more quarter mirror pairs, the higher the reflectivity of the

105

Bragg mirror. Also, the more quarter mirror pairs, the sharper the curve, meaning high

reflectivity of the bottom mirror creates a high resolution in the corresponding receiver.

This type of feature creates filter-like behavior, which allows it to serve as a wavelength

selective receiver in the WDM (wavelength division multiplexing) systems. Except

N=10, FWHM (full width at half maximum) of the other three curves is approximately

equal to 0.1µm.

1.4 1.5 1.6 1.70.0

0.2

0.4

0.6

0.8

1.0

N=15

N=20

N=30

N=10

Ref

lect

ivit

y of

th

e b

otto

m m

irro

r

wavelength (um)

Figure 4. 5 Reflectivity of bottom mirror vs wavelength for different numbers of quarter wave pairs. N is the number of quarter wave pairs. +: N=10; • : N=15; ×: N=20; ∗ : N=30. (InP based PD)

106

4.3.4 Quantum efficiency

4.3.4.1 Quantum efficiency in GaAs based PD

Figure 4.6 shows how the quantum efficiency of the whole structure is dependent

on wavelength for the different thicknesses of the absorption layer.

760 800 840 880 9200.0

0.2

0.4

0.6

0.8

1.0m=4

m=3

m=1

m=2

Qua

ntum

Eff

icie

ncy

Wavelength (nm)

Figure 4. 6 Quantum efficiency of entire structure vs wavelength for different thickness of absorption layer (number of quarter wave pairs is fixed as N=20). m represents thickness of GaAs absorption layer. • : m=1; +: m=2; ×: m=3; ∗ : m=4. (GaAs based PD)

In this figure, the number of the quarter wave pairs is fixed at 20. Different m

values correspond to different thicknesses of the absorption layer, which represents the

thickness of the GaAs layer: 117.5 nm, 230.6 nm, 343.8 nm, and 456.9 nm for an m of 1

to 4 respectively. Their relation is decided by the formula

107

πββ mLL 2)(2 212211 =Ψ+Ψ++ . The thicker the absorption layer is, the larger the peak

value is. However, a thick absorption layer will increase transit time of the optically

generated carriers. Thus, a tradeoff between response and quantum efficiency has to be

considered. This figure also suggests that m only changes the peak value and does not

affect the shape of the curves. The peak quantum efficiencies of these four structures are

54.2%, 79.1%, 91.0%, and 96.2% respectively. There is no significant difference between

the FWHM of these different curves, which is around 28 nm for each. When m is larger

than 3, i.e., the thickness of absorption layer is greater than 340.8 nm, the benefits of

increasing the thickness of the absorption layer become significantly reduced.

4.3.4.2 Quantum efficiency in InP based PD

Figure 4.7 shows how the quantum efficiency of the whole structure changes with

wavelength for different thickness of the absorption layer. The number of the quarter

wave pairs is fixed at 15.

Different m values correspond to different thicknesses of the absorption layer.

Their relation is decided by the formula πββ mLL 2)(2 212211 =Ψ+Ψ++ . The thicker the

absorption layer, the higher the peak value. However, a thick absorption layer creates a

lower time response by producing long path for electrons to travel to the triangular well.

A tradeoff between fast response and high quantum efficiency has to be considered here.

It is shown in this figure that m only changes the peak value and does not affect the shape

of the curves. There is no difference between the FWHM of these different curves. When

m is larger than 3 (the thickness of the absorption layer is greater than 600nm), the

benefits from increasing the thickness of the absorption layer decrease significantly.

108

1.4 1.5 1.6 1.70.0

0.2

0.4

0.6

0.8

1.0

m=4

m=2

m=3

m=1Qua

ntum

Eff

icie

ncy

Wavelength (um)

Figure 4. 7 Quantum efficiency of entire structure vs wavelength for different thickness of absorption layer (number of quarter wave pairs is fixed as N=15). m represents thickness of InGaAs absorption layer. +: m=1; • : m=2; ×: m=3; ∗ : m=4. (InP based PD)

4.3.5 Sheet charge density

In order to understand the tradeoff between the response time and quantum

efficiency, the electronic properties, primarily the sheet charge density in the triangular

well and the electric field profile have to be examined in this type of structure. A closed-

form expression developed by our group and a modified self-consistent method has been

employed to simulate the devices referred to in this thesis. The number shown in Fig.4.8

represents the thickness of the spacer layer between the delta-doped layer and

AlGaAs/GaAs interface. It was observed that for the same doping concentration in the

109

delta doped plane, the thinner the spacer layer, the larger the sheet carrier density in the

triangular well on GaAs side. The thickness of the spacer in our device is 5 nm and

doping concentration is 5 x 1012 cm-2, which means the sheet carrier density in the well is

around 1.4x1012 cm-2 and 1.5x1012 cm-2 from two different simulation methods.

4.0x1012 8.0x1012 1.2x1013 1.6x1013 2.0x10138.0x1011

1.0x1012

1.2x1012

1.4x1012

1.6x1012

1.8x1012

100 Å

70 Å

50 Å

modified Schrodinger and Poission modelclosed-form expression

Shee

t Cha

rge

Den

sity

(cm

-2)

Delta Doping Concentration (cm-2)

Figure 4. 8 Simulation of nso against AlGaAs delta doping concentration at 300K for various thickness of spacer layer. (GaAs based PD)

110

4.3.6 Electric field

4.3.6.1 Electric field profile in GaAs based PD

10-1 100 101 102 103 1040.0

5.0x104

1.0x105

1.5x105

2.0x105

100 Å

70 Å

50 Å

Distance from the interface (Å)

modified Schroinger and Poisson model

closed-form expression

E

lect

ric

Fie

ld (

V/c

m)

Figure 4. 9 Comparison of electric field strength profile by using closed-form expression and modified Schrödinger and Poisson model 300K for various spacer layer thickness (GaAs based PD)

Knowing the electric field distribution in the device is the best way to

comprehend the transport behavior of the photogenerated carriers. Figure 4.9 shows the

electric field profile in the absorption region away from the heterointerface, which is

implemented using the closed-form analytical model equation and the modified self-

consistent solution of Schrödinger and Poisson equations.

111

Figure 4. 10 Drift velocity in GaAs material [144].

From Fig. 4.9, the electric field strength at the interface is around 2.0 x 105 V/cm,

1.7 x 105 V/cm, and 1.4 x 105 V/cm while the thickness of the spacer layer is 5 nm, 7 nm

and 10 nm respectively for a doping concentration of 5 x 1012 cm-2. This electric field

remains relatively constant in the quantum well and drops to about 4.7 x 104 V/cm, 4.4 x

104 V/cm, and 4.1 x 104 V/cm at 100 Å away from the interface for each case, which is

the critical value for both electrons and holes to reach saturation velocity [144]. Each

curve reaches a constant value of 7 x 103 V/cm at around one thousand Å away from the

Al0.24Ga0.76As/GaAs interface. The electrons have reached their saturation velocity while

the electric field is larger than 7 x 103 V/cm based on the information from Fig.4.10. This

indicates that the whole absorption region experiences a vertical field that is very strong

close to the surface, where exponentially larger numbers of optical carriers are produced.

112

4.3.6.2 Electric field profile in InP based PD

Figure 4.11 shows the electric field profile in the absorption region away from the

heterointerface by using two different theoretical methods. Simulation results are created

from the closed-form analytical model equation and the modified self-consistent solution

of Schrödinger and Poisson equations. The electric field strength at the heterointerface is

closely modeled by the closed-form expression, however, near interface values are

slightly lower than expected and also the curve calculated based on the modified self-

consistent solution of Schrödinger and Poisson equations is flatter than the other within

100Å of the interface. The fitting parameter b can be reoptimized for the closed-form

expression to achieve a closer electric field strength value near the interface to the

modified self-consistent solution of Schrödinger and Poisson equations. The flatter curve

for the modified self-consistent solution of Schrödinger and Poisson equations within

100Å is due to the assumption in this simulation that triangular quantum well width is

around 100Å. Thus, the electric field strength is a flat line within that region.

Nevertheless, it is seen from this comparison that the analytic expression compares well

with much more involved modeling methods.

113

10-2 10-1 100 101 102 1030.0

1.0x105

2.0x105

3.0x105

4.0x105

Ele

ctri

c fi

eld

(V/c

m)

Distance from the interface (0.1nm)

Figure 4. 11 The electric field strength profile by using closed-form expression and modified Schrödinger and Poisson model 300K. (InP based PD)

From Fig. 4.11, the electric field strength at the interface is around 3.8x105V/cm,

and within the triangular quantum well (100Å), the electric field values are still above

5x104V/cm, which is the critical value for both holes and electrons to reach saturation

velocity as shown in Fig. 4.12. According to the simulation data, while the thickness of

the absorption layer is beyond 1700Å, which is thicker than the thickness when m=1, the

electric field is below 4x103V/cm. Field-dependent drift velocity of electrons decreases

rapidly and field-dependent drift velocity of holes is less than 1% of the saturation

velocity of electrons when the electric field is below 4x103V/cm. For the photo response

spectrum, a long tail is explained as the slow motion of holes. When m=1, the internal

quantum efficiency of the peak value is around 40%, which is tolerable in our case. To be

114

conservative, m=2 is our choice, which means that the thickness of the absorption layer is

around 385.8 nm.

Figure 4. 12 Drift velocity of electrons and holes in In0.53Ga0.47As [145]

4.4 Conclusions

An AlGaAs/GaAs based RCE, HMSM PD with an Al0.24Ga0.76As/Al0.9Ga0.1As

DBR operating around 830 nm and an InAlAs/InGaAs based RCE, HMSM PD with an

In0.527Al0.144Ga0.329As/InP DBR operating around 1550 nm was designed. Delta doping is

employed in the top wide band gap materials to produce a confined electron cloud and an

associated transverse electric field. The effect of doping will be investigated by current-

voltage and temporal response measurements of doped and undoped devices in the

following chapter. The design process requires considering the speed, quantum efficiency

and sensitivity of the device. These favorable performance characteristics combined with

115

the growth substrate and compatibility of the growth structure with high electron mobility

transistors, makes GaAs based and InP based delta doped device excellent candidates for

short haul (local area) and long haul high speed telecommunication applications

respectively.

Based on the analysis in Section 4.3, the top view and the schematic cross-section

of GaAs based PD is shown in Fig. 4.13. The layer structure was grown by solid-source

molecular beam epitaxy on a semi-insulating GaAs substrate. Twenty-periods of a

Al0.24Ga0.76As/Al0.9Ga0.1As DBR were grown on a 200 nm GaAs buffer layer. The

thickness of the top barrier enhancement layer is 50 nm and the spacer layer is 5 nm,

which separates the ionized donors and the electrons and removes the scattering effects in

the 2DEG, thus increasing transport speed. A Si delta doped layer with sheet density of

5x1012cm-2 was grown between the barrier enhancement and spacer layers due its

previously mentioned advantages using uniform doping [56 - 60]. The bottom mirror was

designed for high reflectance at a 830 nm center wavelength. The thickness of the

quarter-wave pair is one half of the effective wavelength (λ0/n). The device area was 40 x

40 µm2 with a typical interdigital pattern using finger width of 1 µm or 2 µm and distance

of 2 or 4 µm.

116

Metal Semiconductor Metal

GaAs Substrate

200nm GaAs Buffer

DBR quarter wave stacks

117.5nm undoped GaAs absorption layer

Si δ-doping 5x1012 cm-2

light

5 nm nid Al0.24Ga0.76As Spacer

(λ0/4n) undoped Al0.9Ga0.1As (67.6nm)

(λ0/4n) undoped Al0.24Ga0.76As (59.6nm)

50 nm nid Al0.24Ga0.76As Barrier

40µm

40µm

gap

finger

Figure 4. 13 Top view and schematic cross-section of GaAs based PD.

The schematic cross-section of InP based PD is shown in Fig. 4.14. The layer

structure was grown by solid-source molecular beam epitaxy on a semi-insulating InP

substrate. Fifteen-periods of a In0.527Al0.144Ga0.329As/InP DBR were grown on a 25 nm

InP buffer layer. The thickness of the top barrier enhancement layer is 50 nm and the

spacer layer is 5 nm. A Si delta doped layer with sheet density of 1013cm-2 was grown

117

between the barrier enhancement and spacer layers. The bottom mirror was designed for

high reflectance at a 1550 nm center wavelength. The thickness of the quarter-wave pair

is one half of the effective wavelength (λ0/n). The device area was 40 x 40 µm2 with a

typical interdigital pattern using finger width of 1 µm or 2 µm and distance of 2 or 4 µm.

InP Substrate

25nm InP:Fe Buffer

15 periods

light

Schottky Schottky

Si δ-doping 13 2

(λ/4n) In0.527Al0.144Ga0.329As (113.3nm)

(λ/4n) Undoped InP (122.3nm)

385.8.nm undoped In0.53Ga0.47As absorption layer

5 nm undoped In0.52Al0.48As spacer

50 nm n-

(6~8*1014cm-3) In0.52Al0.48As

barrier

Figure 4. 14 InP based PD diagram.

118

5. Performance Characteristics of AlGaAs/GaAs Delta Doped HMSM Photodetector with Resonant Cavity for Short Haul

Communications

Design considerations for an AlGaAs/GaAs based resonant-cavity-enhanced

(RCE), heterostructure metal-semiconductor-metal (HMSM) photodetector with a

Al0.24Ga0.76As/Al0.9Ga0.1As distributed Bragg reflector was presented in Chapter 4. In this

chapter, we present the experimental results. In the first section, the photocurrent

spectrum is presented, which shows a clear peak around 850 nm with full width at half

maximum (FWHM) equal to around 30 nm. The device shows a 0.08 A/W average

photoresponsivity with a 9.2 fA/µm2 dark current. Time response measurements using

femtosecond pulses show rise time, fall time and FWHM of 10.6 ps, 9 ps, and 18.4 ps,

respectively, giving a 3-dB bandwidth of about 33-GHz for this device. Capacitance

voltage measurements indicate a very low capacitance value, which is below 30 fF.

In the second section, we investigate the effect of delta doping is employed in the

top AlGaAs layer. This technique produces a confined electron cloud and an associated

transverse electric field. The effect of doping is studied by comparing current-voltage and

temporal response measurements of doped and undoped devices. All figures of merit

show improvement for doped devices. An important feature of the delta doped device is

an improvement in the optical response; its dc photocurrent increases by a factor of 1.6

while the dark current reduces by about a factor of 7.8 under 4V bias, resulting in a factor

of 12.5 increase in the dynamic range. Current voltage measurements under different

temperatures demonstrate that the doped devices have larger activation energy and a

lower capacitance value at low bias range compared with the undoped device. There is

119

about a 7 GHz expansion of the 3dB bandwidth under 5V bias for the delta-doped device.

A number of devices with different geometry have been measured to illustrate the aiding

field mechanism.

In the third section, further comparison between the delta-doped and undoped

device are discussed, which includes structures from transmitted electron microscope

(TEM) pictures and the reflectivity for the light incident on the top surface of the devices

from the reflectivity spectrum. The structures parameters are based on the TEM figure.

The simulation results of the reflectivity based on the Chapter 2 analysis have been

completed, including the standing wave effect which means that the quantum efficiency

is a function of the placement of the active region in the optical field.

Based on the wide range of experimental data, the favorable performance

characteristics, combined with its substrate and compatibility with high electron mobility

transistors, makes the doped device, for receivers used in the 850 nm wavelength fiber

band, of importance to short haul communications.

5.1 Wavelength Selectivity, High Sensitivity, and High Speed

As shown in Fig.4.13, a twenty period Al0.24Ga0.76As/Al0.9Ga0.1As DBR grown on

a 200 nm GaAs buffer layer, a top barrier enhancement layer of 50 nm, a spacer layer of

5 nm, and a Si delta (δ) doped layer with sheet density of 5 x 1012cm-2 grown between the

barrier enhancement and spacer layers are the primary components of our device. The

device area was 40 x 40 µm2 with a typical interdigital pattern shown in Fig. 1.7 with

finger width of 1 µm or 2 µm and distance between fingers of 2 or 4 µm.

120

5.1.1 Wavelength selectivity

750 800 850 900 9500.0

0.1

0.2

0.3

0.4

0.5

0.6

deviate from normal incident 45o

normal incident

Qu

antu

m E

ffic

ien

cy

Wavelength (nm)

Figure 5. 1 Simulation results for quantum efficiency of layered structure as a function of wavelength for two different incident angles.

Figure 5.1 shows the simulation results of the quantum efficiencies as a function

of wavelength at two different angles of incidence for our devices. Compared to a device

without a resonant cavity, a seven-fold enhancement is achieved in quantum efficiency

with a 1 µm-1 absorption coefficient. The peak of quantum efficiency varies with angle of

incidence due to a difference in optical path length. The calculated full width at half

maximum (FWHM) is around 30 nm. This value can be reduced to less than 10 nm if the

121

reflectance of the top mirror is larger than 0.9, however that would require a much thicker

layered structure to compensate for the quantum efficiency.

Figure 5.2 shows the experimental photocurrent spectral response of the RCE-

HMSM photodetector with a 2 µm finger width and a 4 µm gap width. A monochrometer

with 0.15 nm resolution was used to select the excitation wavelength from a chopped

tungsten light source. The signal was measured by a lock-in amplifier. The spectral

response was measured under 10V reverse bias.

700 750 800 850 900 950 10000.0

2.0x10-13

4.0x10-13

6.0x10-13

8.0x10-13

1.0x10-12

1.2x10-12

1.4x10-12

Pho

tocu

rren

t (a.

u.)

Wavelength (nm)

Figure 5. 2 Photocurrent spectral response of resonant-cavity-enhanced HMSM photodetector measured at 10V reverse bias. (Data courtesy of IME-CNR, Lecce, Italy)

The resonant peak value is around 850 nm due to the angle of incidence of the

single mode fiber optic line, in accordance with Fig. 5.1. The FWHM value is seen to be

122

in good agreement with the simulation results of Fig. 5.1. The shape of the photocurrent

response, however, is asymmetric. This is due to the fundamental absorption edge of

GaAs, which is around 870 nm and limits low energy absorption. Also, Fig. 5.2 is not

normalized to photon flux, which would make it more comparable with Fig. 5.1. Finally,

the dependence of the absorption coefficient on wavelength is not included in this

simulation. A large increase in the photocurrent is observed around 710 nm, due to

absorption in Al0.24Ga0.76As layers.

5.1.2 Sensitivity, light response

One of the common problems in measuring light intensity is that signals from

most photodetectors are non-linear. Figure 5.3 shows the photoresponse of our

photodetector with a 2 µm finger width and a 4 µm gap width at 20V reverse bias, at

different incident light power. Current of the photodetector is measured at the same

distance from the laser. The intensity of the light incident on the photodetector is given in

terms of light power. A linear relation is obtained as shown in Fig.5.3.

If one linear curve is employed to fit the experimental data, the photoresponse can

be written as

reinreRe BPAI += (5.1)

where Are and Bre are the two fitting parameters, Pin is the incident power, and Ire is the

photocurrent at different incident power. Thus, parameter Are is the responsivity and can

be extracted from experimental data presented in Fig. 5.1, to be 0.081 A/W with a 0.002

A/W deviation. Parameter Bre is equal to 1.2 x 10-6 A with a 9 x 10-7 A deviation. With a

0.081 A/W responsivity, the corresponding thickness of the active layer without resonant

123

cavity can be calculated to be around 1.2 µm. This calculation is based on the assumption

of a 0.25 µm-1 absorption coefficient at 850 nm, according to Fig. 1.10 and a reflectivity

of 0.3 from the top layer. While in our device, the thickness of the absorption layer is

about 0.12 µm, which is noly one tenth of the thickness of the conventional device. The

device shows a nine fold photoresponse increase over the conventional device. While in

the simulation results using Eq.(2.14), the resonant caivity only gives around eight-factor

increase in the quantum efficiency at the resonant wavelength with a 0.25 µm-1

absorption coefficient. Besides the resonant cavity technique, maybe the other

contributions may need to be considered in characterizing the performance of the delta

doped HMSM RCE photodetecotrs. Another possibility is that the absorption coefficient

is underestimated. Even with the assumption of a 0.5 µm-1 absorption coefficient at 850

nm, the experimental data shows that the device still demonstrates a 4.4 fold

photoresponse increase over the conventional device, lower than the 7.5 factor increase in

the quantum efficiency obtained from the simulation results.

It can be seen in the above figure that the curve may be better fit by using two

linear parts. The first is in the lower incident power range, below 0.1 mW. The other is in

the comparatively higher incident power, greater than 0.1 mW. Then it can be observed

that in the lower incident power range, the photo response is around 0.19 A/W; while in

the other range, the photo response is slightly lower, around 75 mA/W. A lower

responsivity at an incident power larger than 0.1 mW may be explained by considering

that this device gradually reaches the saturation photoresponse under such incident power

intensity.

124

Finally, the dark current of the device is also calculated from Fig. 5.3 to be around

15 picoamps at this bias, which normalizes to the very low value of 9.2 femtoamps/ µm2.

This is one of the lowest dark currents reported in the literature.

1.0x10-7 1.0x10-6 1.0x10-5 1.0x10-4 1.0x10-3 1.0x10-21.0x10-8

1.0x10-7

1.0x10-6

1.0x10-5

1.0x10-4

1.0x10-3

20V

Pho

to c

urre

nt (A

)

Incident Optical Power (W)

Figure 5. 3 Photoresponse of resonant-cavity-enhanced HMSM photodetector measured at 20V reverse bias at different incident light power. (Data courtesy of IME-CNR, Lecce, Italy)

5.1.3 High speed (time domain)

The high-speed time response measurement setup is shown in Fig.5.4. A mode-

locked Ti: Sapphire laser, pumped by an Ar-ion laser, was used to excite picosecond

pulses in the device. The laser provided ~ 100fs wide optical pulses with 740 ~ 1000 nm

wavelength and 76 MHz repetition rate. The excitation beam was intensity modulated by

125

an attenuator and focused by a microscope objective to a 10-µm-diameter spot on the

active region of the device. During the measurements, the device was biased through the

bias-tee using a voltage source. The device was measured by a 50 GHz sampling

oscilloscope. The time response measurement was done by Dr. Marc Currie at the Naval

Research Laboratory in Washington DC.

Figure 5. 4 Schematic of high-speed time response measurements setup.

Figure 5.5 shows the temporal response of a photodetector with 1 µm fingers and

4 µm spacing between fingers, measured at 5 V bias with a 0.1 mW incident power. As

seen in the Fig. 5.5, FWHM of the time response is 10.6 ps, its rise time is 9 ps, and fall

time is 18.4 ps. The incident power is 0.1 mW, half of which shines on the photodetector.

From the above figure, the magnitude of the peak value is 0.14 V, which results in a 2.8

kV/W peak value normalized to the incident power.

126

0 10 20 30 40 50 600.85

0.90

0.95

1.00

5V

Vol

tage

(V

)

Time (psec)

Figure 5. 5 Temporal response of photodetector with 1 µm finger and 4 µm gap with a 0.1 mW incident power at 5V reverse bias.

5.1.4 High speed (frequency domain)

If the highest frequency contained in an analog signal V(t) is Fmax = B, the

sampling rate FN = 2B = 2Fmax is called the Nyquist rate [146]. A sample remedy that

avoids this potentially troublesome situation is to sample the analog signal at a rate higher

than the Nyquist rate.

The sampling time period in Fig. 5.6 is 0.1 ps, while the entire acquisition time is

51.2 ps. Therefore, the sampling rate is 104 GHz, which is large enough here even if the

highest frequency contained in an analog signal V(t) is larger than 1000 GHz. Since the

acquisition time is 51.2 ps, some generated carriers whose collection time is beyond that

are not counted. Based on Fig. 4.10, if carrier behavior of holes is neglected since the

127

electrons dominate the transport behavior, the acquisition time period is sufficiently long.

This can be demonstrated from Fig. 4.9. The electric field curve reaches a constant value

of 7 x 103 V/cm at the interface between the GaAs absorption region and the Bragg

layers, which indicates that the electrons reach the saturation velocity within the whole

absorption region. A Fourier transform is performed on the experimental data in Fig. 5.5

and shown in Fig 5.6. The transformed data reveals a 3 dB (photocurrent) bandwidth of

33 GHz.

1 100.1

0.2

0.3

0.4

0.50.60.70.80.9

1

5V

3dB:33GHz

Freq

uenc

y re

spon

se

Frequency (GHz)

Figure 5. 6 Calculated frequency response from Fig. 5.5.

128

5.1.5 Long trace of time response

To better understand the transport mechanism of the device, carrier behavior of

holes must be considered. From the drift velocity changing with the electric field shown

in Fig.4.10, it indicates that the drift velocity of the holes reaches 2 x 106 cm/s when the

electric field is 1.25 V/µm. For a photodetector with a 1 µm finger and 4 µm spacing

between fingers under 5 V bais, the average lateral electric field in the GaAs region is

around 1.25 V/µm. The transit time for the photogenerated holes carriers to be collected

at the cathode contact traveling from the anode is about 200 ps. The acquisition time

should be at least longer than 200 ps to get all the information for the transport behavior

of the photogenerated holes.

Figure 5.7 shows the long trace temporal response of a photodetector with a 1 µm

finger and 4 µm spacing between fingers, measured at 5 V bias with the same incident

power as for the short trace time response measurement shown in Fig.5.5. The sampling

time period in Fig. 5.7 is 2 ps, while the entire acquisition time is 1024 ps. Therefore, the

sampling rate is 500 GHz. Since the acquisition time is 1024 ps, the characteristics of the

device depend on the transport behavior of both photogenerated holes and electrons. The

insert picture shown in Fig.5.7 is a Fourier transform performed on the experimental data.

The transformed data reveals a 3 dB (photocurrent) bandwidth of 1.65 GHz. Therefore,

the effect of holes will eventually limit the bit rates during data transmission.

Experimental data in Fig 5.7 do not represent the best performance of our device,

which are only employed for the comparison with a short trace shown in Fig. 5.5. In

Section 5.2.6, we present that the best performance of the device can be achieved by

129

changing the operation condition such as the bias and the input power and optimizing

geometry of the device.

0 200 400 600 800 10000.90

0.95

1.00

5V

Vol

tage

(V)

Time (p sec)

0.1 1 100.1

0.2

0.3

0.4

0.50.60.70.80.9

1

Fre

quen

cy R

espo

nse

Frequency (GHz)

Figure 5. 7 Long trace time response with 1 µm finger and 4 µm gap with a 0.1 mW incident power at 5V reverse bias.

5.1.6 Capacitance measurement

The capacitance measurements have been performed at 1 MHz frequency and 30

mV amplitude of the oscillating voltage with a reverse bias voltage on the devices by

using a precision LCR meter. Figure 5.8 shows the capacitance-voltage curves of the

delta modulation doped devices with different geometries under dark. The symbols, , ,

130

, and , represent the experimental data of the devices with a 1 µm finger width and a

2 µm gap, a 1 µm finger width and a 4 µm gap, a 2 µm finger width and a 4 µm gap, and

a 2 µm finger width and a 4 µm gap respectively.

0 2 4 6 8 10 12 14 161.4x10-14

1.6x10-14

1.8x10-14

2.0x10-14

2.2x10-14

2.4x10-14

2.6x10-14

W1G2 W1G4 W2G4 W2G2

Dar

k C

apac

itan

ce (F

)

Bias (V)

Figure 5. 8 C-V curves for four different interdigital structures of delta doped devices. (Data courtesy of IME-CNR, Lecce, Italy).

The figure indicates that the capacitance values are independent of the applied

voltage for all the devices. Also, the maximum capacitance value in this figure is around

26 fF, which shows a 1.3 ps maximum RC (resistor-capacitor) time constant for those

devices with a 50 Ω resistor in the circuit. Compared with the experimental data shown in

the above temporal response figures, it demonstrates that the performance of these

devices is not limited by an RC time constant.

131

5.2 Improvement of MSM Photodetector using Delta-doped AlGaAs/GaAs Heterostructure

A heterostructure metal-semiconductor-metal (HMSM) photodetector combining

low dark current, fast response, high sensitivity and wavelength selectivity, due to its

resonant-cavity-enhanced (RCE) structure, has been presented in the above section. To

further improve the characteristics of such a photodetector, the underlying current

conduction mechanisms have to be investigated. Schottky barrier height and band-edge

discontinuities play an important role in the behavior of heterojunction devices by

strongly affecting current transport [52, 118, 119]. Several techniques have been

proposed to modulate Schottky barrier height, heterojunction barrier height and band-

edge discontinuities including: tuning of the conduction and valence-band barrier heights

at an abrupt intrinsic semiconductor-semiconductor heterojunction via incorporation of a

doping interface dipole [120]; controlling the effective Schottky barrier height over a

wide range using highly doped surface layers [121]; increasing the barrier height due to

energy quantization of confined electrons [122]; and increasing Schottky barrier through

the electron-electron cloud effects in the modulation-doped heterostructures [54].

5.2.1 Band bending profile

To further improve the characteristics of such a photodetector, the underlying

current conduction mechanisms have to be investigated. Since Schottky barrier height

and band-edge discontinuities strongly affect current transport in heterojunction devices,

[54, 65, 122] two different groups of devices are employed to characterize its underlying

132

mechanism. Figure 5.9 shows a quasi two-dimensional sketch of the potential profile

along the growth direction for the delta-doped (right) and undoped (left) devices under

thermal equilibrium. The figure, although only qualitative, shows band bending due to

delta doping of AlGaAs; it is noteworthy that current transport is in the lateral direction

and the absorption region is shown only up to the non-absorbing Bragg layers. There is

no band bending in the undoped devices since the semiconductor material is

unintentionally doped, while the band bending profile of the doped device is due to its

delta-doped plane. Simulation results based on self-consistent solution of Poisson and

Schrödinger equations show that sheet charge density is around 1.4 x 1012 cm-2, Fermi

level is below the bottom of the conduction band in the entire AlGaAs region, and the

electric field is about 2.1 x 105 V/cm at the heterojunction interface on the GaAs side.

This electric field remains relatively constant in the quantum well and drops to about 4.7x

104 V/cm at 100 Å from the interface, reaching a constant value of 7 x 103 V/cm at the

interface with the Bragg layers (refer Fig. 4.9). This indicates that the whole absorption

region experiences a vertical field that is very strong close to the surface, where

exponentially larger numbers of optical carriers are produced. These values are calculated

for thermal equilibrium as sketched in Fig. 5.9, application of bias, however, would

modify the electric field and electrostatic potential profile due to the effect of the

Schottky contact. Nevertheless, in the vicinity of the anode we can expect similar values

indicating the aiding effect of the field on photoelectron transport.

133

anode

AlGaAs

GaAs Ec

Ef

Ev

cathode∆Ec

∆Ev

φp2

φn1

(a)

cathode anode

GaAs

AlGaAs

EfEc

Ev

φp2

φn1

∆Ec

∆Ev VD2

(b)

Figure 5. 9 Schematic diagram of energy band of devices: (a) undoped device; (b) doped device.

5.2.2 Current-voltage comparison

5.2.2.1 Experimental data

Figure 5.10 compares the I-V curves of the dark current and photocurrent for

doped and undoped devices with finger widths of 2 µm and distance between fingers of 4

µm. It is observed that the dark current of the delta-doped device is lower by about a

factor of 8 compared to the undoped device. An important feature of the delta doped

device is its improvement of the optical response; its dc photocurrent increases by a

factor of 1.6 while the dark current reduces by about a factor of 7.8 under 4V bias,

resulting in a factor of 12.5 increase in the dynamic range. Responsivity values measured

134

at various light intensities showed an average improvement of a factor of 1.5 while dark

current normalizes to a very low value of 9.2 femtoamps/ µm2.

0 4 8 12 16 201x10-13

1x10-12

1x10-11

1x10-10

1x10-9

1x10-8

1x10-7

1x10-6

Dark Current

12.6µW

C

urre

nt (A

)

Voltage (V)

Figure 5. 10 Comparison of I-V of undoped and δ-doped devices. ο: undoped device; • : doped device (Data courtesy of IME-CNR, Lecce, Italy).

5.2.2.2 Thermionic emission theory

The reverse current density Jn1 for the cathode contact is given by [147]

)1(

)1(121

1211

)(

)(2*1

Vns

Vnn

eeJ

eeeTAJnn

nnn

βφφβ

βφφββφ

−∆−∆

−∆−∆−

−=

−= (5.2)

where An∗ is the effective Richardson constant for electrons, T is the temperature,

kTq /=β , ∆φn1 is the image-force-induced lowering of the Schottky barrier height, the

135

quantity ∆φn2 models the barrier enhancement that results from the repulsive effect of the

mobile 2DEG on the electrons that are thermionically emitted from the cathode [133],

and V1 is the bias value dropped at the cathode.

GaAs absorption layer

AlGaAs

Ec

Ef

δ-doping

Ec

Ef

cathode

Ev

Ev φp2

φn1

∆Ec

∆Ev

φn1

anode

φp2

∆Ec

∆Ev VD2

(a)

(b)

Figure 5. 11 Potential profile at zero bias of undoped and δ-doped devices. (a): undoped device; (b): doped device.

Figure 5.11 shows the potential profile for two different devices at zero bias.

Equation 5.2 gives the reverse current density Jn1, which is the electron current in the

device. The hole current originates from thermionic emission of holes from the anode

contact. As shown in Fig. 5.11, the effective barrier for holes at the anode contact is given

by )( 222 VVDp −+φ , and V2 is the bias value dropped at the anode, which is forward

biased. Those emitted holes which diffuse from x2 to x1 constitute the hole current.

136

Ec

Ev

φn1

∆Ec

∆Ev

φn1

φp2

(a)

(b)

V

φp2

VD2-V2 Ev

GaAs absorption layer

δ-doping AlGaAs

cathode

∆Ec

Ec

∆Ev

anode

V2 V1

x1 x2

Figure 5. 12 Potential profile at V=V1+V2 bias of undoped and δ-doped devices. (a): undoped device; (b): doped device.

In the neutral region (x1 >x > x2) the steady state continuity equation for holes is

given by

002

2

=−

−∂∂

pp

n

Dpp

xp

τ (5.3)

where pn0 is the equilibrium hole density, Dp is the diffusion coefficient, and τp is the

lifetime.

The solution of Eq.(5.3) is simply

pp LxLxn BeAepp //

0−+=− (5.4)

137

where Lp is the diffusion constant, which equals ppD τ . The boundary conditions are

(1) at x = x1, )/(0

1 kTqVn epp −= , and (2) at x = x2,

)(2*2

222 VVpp

DpeTAJ −+φ−= β (5.5)

where Ap* is the effective Richardson constant for holes. The arbitrary constants A and B

in Eq.(5.4) can be determined from the boundary conditions. The hole current density Jp1

is then given by the gradient at x1 and the condition that Jp1 =0 at thermal equilibrium

condition (i.e., V = 0):

)]1(]/)cosh[(

)1()/)tanh((

[

22

1

1

12

120

1

−−

+

−−

=

=

−

−

V

p

Vps

V

p

pnp

xpp

eLxx

eJ

eL

LxxpqD

dxdpqDJ

Dβ

β

β (5.6).

where (x2-x1) is the undepeleted region in the GaAs channel.

Based on the above derivation, the contributions of electron and hole current to

the total current under small bias is [147]:

)]1(]/)cosh[(

)1()/)tanh((

[

)1(

22

1

121

12

120

)(

11

−−

+

−−

+

−=

+=

−

−

−φ∆−φ∆

V

p

Vps

V

p

pnp

Vns

pn

eLxx

eJ

eL

LxxpqDeeJ

JJJ

D

nn

ββ

β

ββ

(5.7)

where 12* neTAJ nnsφ−= β and 22* peTAJ pps

φ−= β . φn1, φp2, and VD2 are defined as

shown in Fig. 5.9, Fig. 5.11, and Fig. 5.12. The second term in Eq.(5.7) is much smaller

than the first for both devices, and can be neglected. Further, for better modeling, scaling

138

terms should be added to either the first or the last term which reflect majority carrier

concentration values. The following section is a discussion based on the description in

this section about the experimental data of I-V comparison shown in Fig.5.10.

5.2.2.3 Discussions

Image-force lowering of the barrier due to band bending and ionized donors in

AlGaAs should increase the thermionic emission of the δ-doped device in comparison to

the undoped device; however, we observe an opposite effect under low biases in Fig.

5.10. This is due to increase of the barrier by the exerted force of the mobile electron

cloud, depicted by ∆φn2, as well as band bending at the anode that adds to the hole

barrier, i.e., due to VD2 in Eq.(5.7). With increasing bias, the electron cloud of the

triangular well under the cathode side is depleted and the extra barrier for the holes in the

anode side becomes smaller due to forward bias, leading to an increase of current. In fact,

with increasing bias, the electron cloud under the cathode is further depleted, and the

image-force-induced lowering of the Schottky barrier causes more current to flow in the

delta doped sample, while in the undoped one, the cathode barrier is not lowered as in the

doped device. A potential distribution in 2 DEG based on the conformal mapping

technique will be employed to help to illuminate the difference of the dark current

between the undoped and doped device in the following section.

139

5.2.2.4 Potential distribution in 2DEG

The distribution of the electric potential in a 2DEG system can be derived by

using a conformal mapping technique. The x axis is shown in Fig. 5.13 is the plane of a

complex argument iyxz += in the direction perpendicular to the surface of the 2D gas

in the plane of the p-type contact boundary. The y axis is in the plane containing the 2D

gas as shown in Fig. 5.13. The real part of the gradient of the complex potential dzdV /

on the axis is equal to zero because the plane of the p+ contact is an equipotential surface.

The imaginary part of the gradient is equal to zero for y > ddep because half-plane of the

2D electron gas is an equipotential surface. Finally, the real part of this function is equal

to GaAs

sqnε2

where εGaAs is the dielectric permittivity of the semiconductor and ns is the

2DEG sheet charge density. This function has opposite signs at the two sides of the cut

made between the singular points depidz = and depidz −= . Hence, the discontinuity of

the electric induction vector is equal to qNs and dzdV / is an even function. Therefore, it

is sufficient to solve the problem for the y ≥ 0, x > 0 quadrant. The conformal

transformation 2)(depdzw = converts this quadrant into the half-plane Im w > 0. Then the

problem reduces to the solution of the Laplace equation for dwdV / whose real part is

equal to zero for w > 0 and w < -1 and whose imaginary part is equal to

])(4/[ 2/1wdqn GaAsdeps −ε for 0 > w >-1. Using a standard procedure, the gradient of the

complex potential is obtained as follows:

depdep

depdep

GaAs

s

ddz

ddzqnidzdV

−+

++πε

−=2/122

2/122

)(

)(ln

2/ (5.8)

140

Choosing the potential of the p contact as a reference point and integrating

Eq.(5.8) with respect to z, the complex function of the potential can be obtained as:

])(

)(ln

)(

)(ln[

2 2/122

2/122

2/122

2/122

zdz

zdzd

ddz

ddzz

qniV

dep

depdep

depdep

depdep

GaAs

s

−+

+++

−+

++πε

−= (5.9)

+ + + + +

z

y

x

p+ drain

depletion region

2D electron gas

R

w

Figure 5. 13 Simplified model of 2D electron gas p-type semiconductor junction.

From Eq.(5.9), the potential distribution along the positively charged depletion

layer can be achieved

)]/(sin2)(

)(ln[

2)( 1

2/122

2/122

depdepdepdep

depdep

GaAs

s dydydd

dydy

qnyV −+

−−

+−πε

= (5.10)

Hence, the potential V at y = ddep is given by

141

GaAs

depsdqnV

ε=

2 (5.11)

It is noteworthy that for a two 2DEG the relation between bias and depletion

region is calculated from GaAs

depsdqnV

ε=

2 [148], which gives a value of over 10 V,

consistent with the above argument.

5.2.3 Comparison of current voltage at different temperature

Current-voltage measurements for GaAs based HMSM RCE-PDs have been

carried out in the cryostat as a function of the temperature from 360 K to 280 K. Figure

5.14 shows the experimental data of I-V changing with temperature for the undoped

device and the doped device respectively. Both types of devices have the same geometry

with finger widths of 2 µm and distance between fingers of 4 µm. The empty symbols

represent the experimental data of the undoped devices while the solid symbols stand for

those of the doped devices.

For all temperatures, the behavior is quite similar. The undoped devices show an

almost exponential increase at low voltage, followed by a ‘quasi-saturation’. The doped

devices indicate lower currents under low bias compared with the undoped devices.

The measurement results in Fig. 5.14 agree with what have been observed in Fig.

5.10, which further demonstrate that the aiding field and band bending associated with

the delta modulation doped heterostructure improve the performance of GaAs based

HMSM RCE photodetectors.

142

0 2 4 6 8 10 12 141x10-15

1x10-14

1x10-13

1x10-12

1x10-11

1x10-10

360 K 350 K 340 K 330 K 320 K 310 K 300 K 290 K 280 K

Cur

rent

(A

)

Bias (V)

0 2 4 6 8 10 12 141x10-15

1x10-14

1x10-13

1x10-12

1x10-11

1x10-10

360 K 350 K 340 K 330 K 320 K 310 K 300 K Tamb

Cur

rent

(A)

Bias (V)

(a)

(b)

Figure 5. 14 Current-voltage measurement under different temperature for GaAs based devices. empty symbols: undoped device; solid symbols: doped device. (Data courtesy of IME-CNR, Lecce, Italy).

Figure 5.15 shows the derivative currents with respect to 1/kT in log scale under

5V, 10V, and 15V bias respectively. Part (a) and (b) in Fig.5.15 are for the experimental

143

data of the undoped and doped devices correspondingly. All curves indicate linear

behavior except the points measured under the low temperature in the doped device. With

a linear curve to be employed to fit those experimental data, the activation energies have

been deduced. The activation energys are 0.50eV, 0.42eV, and 0.34eV for the undoped

device and 0.686eV, 0.65eV, and 0.60eV for the doped device under 5V, 10V, and 15V

bias respectively. It can be observed that under the same bias, the doped device has larger

activation energy compared to the undoped device. With increasing bias, the activation

energy decreases in both devices, which also means the dark current increases with

increasing bias.

32 34 36 38 40 42-28

-26

-24

-22

-20 Ea=-0.34 eV at 15 V Ea=-0.42 eV at 10 V Ea=-0.50 eV at 5 V

ln (c

urre

nt)

1/kT (eV-1)

32 34 36 38 40 42

-28

-26

-24

-22 Ea=-0.60 eV at 15 V Ea=-0.65 eV at 10 V Ea=-0.686 eV at 5 V

ln (c

urre

nt)

1/kT (eV-1)

(a) (b)

Figure 5. 15 Ln(I) vs 1/kT at 5V, 10V, and 15V for GaAs based. empty symbols: undoped device; solid symbols: doped device. (Data courtesy of IME-CNR, Lecce, Italy).

144

5.2.4 Comparison of capacitance- voltage measurements

The capacitance-voltage curves of samples with different geometries under dark

conditions are reported in Fig. 5.16. Part (a) and (b) in Fig.5.16 represents the

experimental data of the undoped and doped devices correspondingly. The symbols here

have the same meaning as in Fig.5.8.

The most obvious difference in the characteristics between these two types of

devices is that doped samples show capacitance values independent of the applied

voltage, while the undoped samples indicate higher capacitance values at low bias

compared to the doped samples having the same geometry. It is observed that the

capacitance values of the undoped devices are almost one order of magnitude greater

with a low applied voltage than with a high bias. For the undoped devices, the

capacitance maitains a constant value up to almost 2V, and then it jumps to a low value at

this critical voltage. The behavior of the undoped devices is the same as what was

observed in Fig. 5.10.

The capacitance of the interdigital structure can be calculated from Eq.(5.12)

[145]:

))1/()1(2log()(2 κ−κ++πε

≈GW

AC GaAs (5.12)

where εGaAs is the GaAs permittivity, A is the interdigited area, and

2/14 )))(4/(tan1( GWW +−= πκ is a dimensionless quantity. W and G represent the

finger width and the distance between the fingers. Table 5.1 lists the measured

capacitance compared with the theoretical capacitance. It shows that at high applied

voltages, the experimental results agree well with calculated values.

145

0 2 4 6 8 10 12 14 160

4x10-14

8x10-14

1x10-13

2x10-13

W1G2 W1G4 W2G4

Da

rk C

apac

itanc

e (F)

Bias (V)

0 2 4 6 8 10 12 14 161.4x10-14

1.6x10-14

1.8x10-14

2.0x10-14

2.2x10-14

2.4x10-14

2.6x10-14

W1G2 W1G4 W2G4 W2G2

Dark

Cap

acita

nce (

F)

Bias (V)

(a) (b)

Figure 5. 16 C-V curves GaAs based.photodetectors, empty symbols: undoped device; solid symbols: doped device. (Data courtesy of IME-CNR, Lecce, Italy).

Table 5. 1 Measured and theoretical capacitance values.

Geometry undoped device (fF)

δ doped device (fF)

calculated values (fF)

W1G2 24.4 26 26.2 W1G4 11.5 16.5 12.4 W2G2 - 21.5 25.2 W2G4 14.4 16 13.0

5.2.5 Time response comparison

An important feature of the δ-doped device is its improvement in the optical

response as partially observed in Fig. 5.10. Its dc photocurrent increases by a factor of 1.6

while the dark current reduces by about a factor of 7.8 under 4V bias, resulting in a factor

of 12.5 increase in the dynamic range. Responsivity values measured at various light

146

intensities show an average improvement of a factor of 1.5 while dark current normalizes

to a very low value of 9.2 femtoamps/ µm2 of device area.

0 10 20 30 40 50 600.80

0.85

0.90

0.95

1.00

5V

Vol

tage

(V)

Time (psec)

1 100.1

1

Frequency (GHz)

Fre

quen

cy R

espo

nse

Figure 5. 17 Comparison of temporal response of undoped and doped devices under a bias of 5V; insert shows comparison of their calculated frequency response. ο: undoped device; • : doped device.

Figure 5.17 shows the temporal response of a photodetector with a 1 µm finger

and 4 µm spacing between fingers, measured by a 50 GHz sampling scope at 5 V bias. As

seen in the figure, FWHM of the time response is 10.6 ps (11.0 ps), its rise time is 9.0 ps

(8.7 ps), and 18.4 ps (19.4 ps) for the doped (undoped) device. Fourier transform of the

data is shown in the inset of the figure and has a 3 dB (photocurrent) bandwidth of 33

GHz and 26 GHz for the doped device and the undoped devices, respectively. The figure

147

also shows an increase of peak response, for the same incident light intensity, by almost a

factor of 4. A large number of devices were measured, showing consistent improvement

in figures of merit for the delta doped device.

Time response data verifies that both collection and transport are affected by the

delta doping. This is explained by examining the schematic energy band diagram of Fig.

5.9, noting that photo-carriers move lateral to growth layers and the energy band will be

modified and tilted from cathode to anode as a result of the applies bias. The potential

profile for the delta-doped device is such that the photoelectrons that are absorbed in

GaAs have adequate potential energy, due to vertical band bending, to overcome the

conduction band discontinuity. The band bending in the cathode side would hinder hole

collection, but the reverse-bias of the Schottky cathode would tend to deplete the 2DEG

and hence reduce this bending to make it similar to an undoped device. The vertical field

also aids transport of photo-electrons by adding to their velocity in the direction of

collection, towards the surface and contacts. Holes, on the other hand, are pushed away

from the surface causing broadening of the transit time, however, this long tail of

response is controlled by the fact that transit distance in GaAs is limited by the Bragg

layers.

5.2.6 Discussion of time response

The previous three sections discussed that delta doping in the wide band gap

material affect both collection and transport behavior of the photogenerated carriers. In

this section, more detailed experimental data with different geometry size are presented

148

to clarify the aiding field and band bending effects in helping the collection and transport

of the carriers.

5.2.6.1 Comparison of temporal response (short trace)

Figure 5.18 shows the comparison of temporal response of photodetectors with a

1~2 µm finger and 2~4 µm spacing between fingers, measured by a 50 GHz sampling

scope at 5, 10, and 20 V bias respectively. W1G2, W2G2, W1G4, and W2G4 devices

represent a device with 1 µm finger and 2 µm spacing, 2 µm finger and 2 µm spacing, 1

µm finger and 4 µm spacing, and 2 µm finger and 4 µm spacing in the following

description respectively.

The experimental setup is the same as described in Section 5.1.3. The wavelength

of the incident light is tuned at 850 nm, the resonant wavelength. The sampling period is

0.1 ps, while the acquisition time is 51.2 ps for the entire group of data, which is defined

as the short trace data. As elucidated in Section 5.1.3, Section 5.1.4, and Section 5.1.5,

the behavior of the photogenerated electron carriers dominates the characteristic of

transport and collection of carriers.

In Fig. 5.18, the incident power is 0.1 mW, half of which shined on the

photodetectors. Four groups of devices have been measured at different biases for the

analysis. Part (a) and (b) are the comparisons of peak amplitude normalized to the

incident power among the photodetectors with different geometries, which can be

achieved from the temporal response spectrum directly. In part (a) and (b), horizontal

axis indicates the different biases, while vertical axis represents the normalized peak

amplitudes. Part (c) and (d) are the comparisons of 3dB bandwidth, which can be

149

achieved by performing a Fourier transform on the experimental data of temporal

response. The horizontal axis has the same meaning as in part (a) and (b), but the vertical

axis indicates the 3dB bandwidth of the devices.

4 8 12 16 20

1

2

3

4

5

W2G2

W1G2

Peak

Am

plitu

de (V

/mW

)

Voltage (V)

4 8 12 16 2020

30

40

50

W2G2

W1G2

3dB

(GH

z)

Voltage (V)

4 8 12 16 200

1

2

3

4

5

W1G4

W2G4

Peak

Am

plitu

de (V

/mW

)

Voltage (V)

4 8 12 16 20

20

30

40

W1G4

W2G4

3dB

(GHz

)

Voltage (V)

(a) (b)

(c) (d)

Figure 5. 18 Comparison of temporal response (short trace) at the different bias. Empty symbols: undoped devices; solid symbols: doped devices. and : W1G2; and : W2G2; ∆ and : W1G4; and : W2G4.

150

The solid symbols represent the doped devices while the empty symbols indicate

the undoped devices. Part (a) and (c) show the data of the devices with a 2 µm spacing

between fingers, where and stand for the data of the devices with a 1µm finger width,

and and represent the data of the devices with a 2µm finger width. Part (b) and part

(d) show the data of the devices with a 4 µm spacing between fingers, where ∆ and

signify the data of the devices with a 1µm finger width, and and indicate the data of

the devices with a 2µm finger width.

Part (a) and (b) show that the normalized peak amplitudes of the doped devices

are larger than those of the undoped devices with the same geometry and size under the

same voltage bias. Part (a) shows that with increasing bias, there is almost a linear

increase in the normalized peak amplitude for the doped groups; while in the undoped

groups, there is a faster increase from 5 volts to 10 volts than from 10 volts to 20 volts.

Also, it has been observed that although W1G2 and W2G2 devices have the same

spacing distance between the fingers, the former have larger normalized peak amplitudes

than the latter.

The advantage of the normalized peak amplitude of the doped devices over the

undoped devices can be explained the same as our previous arguments that the band

bending and aiding field in the vertical direction help the collection and transport of the

photogenerated electrons.

There are two reasons explaining the normalized peak amplitude increase with

increasing bias. One is that the average drift velocity of photogenerated electrons

increases with increasing bias. The other is that more photogenerated holes have been

collected within 51.2 ps acquisition time since the drift velocity of the holes increases

151

with increasing bias. In the undoped devices, since a portion of the applied voltage drops

over the anode to help the photogenerated electrons overcoming the conduction band

discontinuity, two mentioned reasons cause an increase of normalized peak amplitude in

the low bias range while the second one dominates after 10 volts bias, which results in a

faster increase in the low bias than in the high bias.

Although the conduction band discontinuity exists in the doped devices, the band

bending in the potential distribution along the growth direction as shown in Fig.5.9 helps

to collect the photogenerated electron carriers in the anode contact, which means that no

voltage needs to drop on the electrodes to collect the electrons. As indicated in part (a) of

Fig.5.18, there is almost a linear increase in the normalized peak amplitude for the doped

devices. The W1G2 group has larger normalized peak amplitudes than the W2G2 group

due to the larger active region in the former devices.

Part (c) of Fig.5.18 shows that the 3dB bandwidth comparison of the W1G2 and

the W2G2 groups by performing a Fourier transform on the experimental data of the

temporal response. In the W1G2 group, as indicated in Fig.5.18, 3dB bandwidths of the

doped device are larger than those of the undoped device at three different applied

voltages. It is also observed that in the W1G2 group, with increasing bias, the 3dB

bandwidth of the undoped device shows an increase from 5V to 10V while a decrease

from 10V to 20V. However, the trend of the 3dB bandwidth changing with bias is

completely different in the doped device from the undoped device of the W1G2 group. In

the doped device of the W1G2 group, the 3dB bandwidth decreases from 5V to 10V at

first, then increases from 10V to 20V.

152

The advantage of the 3dB bandwidth of the doped devices over the undoped

devices can be explained by the fact that the aiding field in the vertical direction

accelerates the transport behavior of photogenerated electrons.

In the undoped device of the W1G2 group, as explained for the normalized peak

amplitude changing with bias, some portion of the applied voltage drops on the anode to

collect the photogenerated electrons, even when the applied voltage is larger than 5 volts,

the average drift velocity of photogenerated electrons should not reach the saturation

velocity. With increasing bias between 5V to 10V, the average drift velocity of

photogenerated electrons continues to increase, which results in an increase of the 3dB

bandwidth. The decrease in the 3dB bandwidth of the undoped device in the W1G2 group

with changing a bias from 10V to 20V can be explained by the following. When the bias

is larger than 10V, the average drift velocity of the electrons reaches the saturation

velocity and more photogenerated holes contribute to the photocurrent within 51.2 ps

acquisition time with increasing bias. Therefore, although there is an increase of the

normalized peak amplitude of undoped device in the W1G2 group with increasing bias

between 10V to 20V, the collection of more holes results in a decrease in the 3dB

bandwidth due to the slower transport behavior of these holes compared to electrons as

shown in Fig.4.10.

While in the doped device of the W1G2 group, since no voltage drops on the

anode to collect electrons, the average drift velocity of electrons reaches the saturation

velocity at 5V. Thus, the decreasing 3dB bandwidth with increasing bias between 5V to

10V can be explained the same way as a decrease in the undoped device with an applied

153

voltage varying from 10V to 20V. The increase between 10V to 20V is due to the

increase of the average drift velocity of holes with increasing bias.

As for the 3dB bandwidth of W2G2 group in part (c) of Fig.5.18, it is observed

that the undoped device has the same trend in 3dB bandwidth with applied voltage as the

undoped device of the W1G2 group; while the doped device has a faster increase in 3dB

bandwidth with a bias between 10V to 20V than from 5V to 10V.

The possible reason is that the critical bias voltage to alter the trend of 3dB

bandwidth changing with applied voltage may be smaller than 5V due to the wide finger

effect, which modifies the electric field distribution from that in the devices of the W1G2

group. Thus, the undoped device has a larger 3dB bandwidth than the doped device in

W2G2 group at 5V and 10V bias.

The explanation for the difference of the peak amplitude in part (b) and 3dB

bandwidth in part (d) of Fig.5.18 between the undoped devices and the doped devices

follows the above description for the W1G2 and W2G2 groups. There is a 2.5 factor

increase in the peak amplitude of the doped device with a 2 µm finger and 4 µm spacing

at 20V bias, which agrees with the results in the current voltage measurements shown in

Fig.5.10. The highest 3dB bandwidth is 45.2 GHz for a W1G2 doped device at a bias of

5V.

5.2.6.2 Comparison of temporal response (long trace)

The only difference for Fig.5.19 from Fig.5.18 is the sampling period and the

entire acquisition time. The sampling periode is 2 ps and the acquisition time is 1024 ps.

The transport and collection behavior of the photogenerated electrons does not dominate

154

here, while the transport behaviors of both electrons and holes carriers have to be

considered in analyzing the characteristic performance of the devices.

4 8 12 16 200

1

2

3

W2G2

W1G2

Peak

Val

ue (V

/mW

)

Voltage (V)

4 8 12 16 200

2

4

6

8

W2G2

W1G2

3dB

(GH

z)

Voltage (V)

4 8 12 16 200

1

2

3

4

W1G4

W2G4

Peak

Am

plitu

de (V

/mW

)Voltage (V)

4 8 12 16 200

4

8

W1G4

W2G4

3dB

(GH

z)

Voltage (V)

(a) (b)

(c) (d)

Figure 5. 19 Comparison of temporal response (long trace) at the different bias. Empty symbols: undoped devices; solid symbols: doped devices. and : W1G2; and : W2G2; ∆ and : W1G4; and : W2G4.

155

Figure 5.19 is much simpler than Fig.5.18. In part (a) and (b) of Fig.5.19, it is

observed that the normalized peak amplitudes of the doped devices are larger than those

of the undoped devices with the same geometry and size under the same voltage bias.

Also, it shows that with increasing bias, there is an almost linear increase in the

normalized peak amplitude for the undoped groups; as for the doped groups, the W1G2

and W2G2 devices have a faster increase from 5 volts to 10 volts than from 10 volts to 20

volts, while the W1G4 and W2G4 devices show saturation in the normalized peak

amplitude after 10 volts. The W1G2 and W1G4 devices have larger normalized peaks

amplitude than the W2G2 and W2G4 devices in part (a) and (b) correspondingly.

In part (c) and (d) of Fig.5.19, it is shown that the 3dB bandwidths of the doped

devices are larger than those of the undoped devices. Also, it consistently indicates that

the 3dB bandwidths of all devices increase with increasing bias monotonically.

The increase of the normalized peak amplitude in the doped devices over the

undoped devices follows the same explanation as the aiding field effects in the vertical

direction of the doped devices. Since the acquisition time is 1024 ps, a comparative

amount of holes contribute to the photocurrent even at a low bias. The transport behavior

of holes dominates the changes in temporal response with increasing bias due to their

slower behavior compared to the electrons. With increasing bias, the average drift

velocity of holes increases. Therefore, there is an increase in the normalized peak

amplitude. Since no voltage drops on the anode to collect photogenerated electrons in the

doped devices, there is a slower increase from 10V to 20V than from 5V to 10V in the

normalized peak amplitude of the W1G2 and W2G2 groups and the normalized peak

amplitude of the W1G4 and W2G4 groups reach the saturation status. The larger

156

normalized peak amplitude in the W1G2 and W1G4 groups than in the W2G2 and W2G4

groups is due to the larger active region.

As mentioned in the above paragraph, the transport behavior of holes dominates

the changes in temporal response for a large acquisition time. The increase of the average

drift velocity of the photogenerated holes result in a decrease of average collection time

of carriers. In part (c) and (d) of Fig.5.19, 3dB bandwidth increases with increasing bias

monotonically consistent in all devices. The highest 3dB bandwidth among long trances

is 6.2 GHz for the doped device in the W1G4 group at 20 volts.

From discussion in Sections 5.2.6.1 and 5.2.6.2, it is shown that the characteristic

performance of the devices can be optimized by choosing suitable geometry and proper

operation bias. Also, in the other experimental data of temporal response, we observed

that it is obvious that the power of the incident light affects the transport behavior of the

photogenerated carriers. More detailed analysis depends on simulation results from ISE

commercial software and a description of the dynamic behavior of the photogenerated

carriers based on Ramo’s theory to be done in future work.

5.3 Further Comparison of Undoped and Delta-doped Devices

We continue our device characterization by investigating the structural difference

between the undoped and δ doped devices, which may be responsible for the differences

in the optical and electronic properties in the two different types of samples.

157

5.3.1 TEM (transmitted electron microscopy) structure

In Fig. 5.20, particularly in its Bragg reflector region, the undoped device is

structurally better than the doped device, in terms of presence of defects and interface

quality. The doped device shows faults propagating through the layers of the

Al0.9Ga0.1As/Al0.24Ga0.76As super lattice. In the undoped sample as shown in Fig. 5.20(a),

the thickness of Al0.9Ga0.1As is 67 ± 1 nm and the thickness of Al0.24Ga0.76As is 61 ± 1

nm; while in the doped sample as shown in part (b), the thickness of Al0.9Ga0.1As is 67 ±

2 nm and the thickness of Al0.24Ga0.76As is 60 ± 2 nm.

100 nm100 nm

Al0.9 GaAsAl0.24 GaAs

100 nm100 nm100 nm

(a) (b)

Figure 5. 20 TEM picture for DBR layer. (a) undoped device, Al0.9Ga0.1As: (67±1) nm, Al0.24Ga0.76As: (61±1) nm. (b) doped device, Al0.9Ga0.1As: (67±2) nm, Al0.24Ga0.76As: (60±2)nm (Data courtesy of IME-CNR, Lecce, Italy).

The interfaces of the doped samples are much broader than in the undoped device,

as shown by the comparison of the contrast line scan profiles obtained from both

158

samples. Figure 5.21 indicates the comparison of the contrast line scan profiles. In

particular, it is worth noting that, even in the case of the doped device, the Al0.9Ga0.1As /

Al0.24Ga0.76As interface is sharper than the Al0.24Ga0.76As /Al0.9Ga0.1As interface, as

clearly evidenced by the linear fit interpolations of the contrast line scan profile.

1

2

3 54

6 7

8 9

1 0

A l0 .9 G a A s / A l0 .2 4 G a A sin t e r fa c e

A l0 .2 4 G a A s /A l 0 .9 G a A s in t e r fa c e

(a)

(b)

Figure 5. 21 Comparison of contrast line scan profiles (a) undoped device, (b) doped device (Data courtesy of IME-CNR, Lecce, Italy).

In Fig. 5.21 (b), the odd numbers represent the Al0.9Ga0.1As /Al0.24Ga0.76As

interfaces while the even numbers represent the Al0.24Ga0.76As /Al0.9Ga0.1As interfaces.

Those interfaces are called interfacial layers. For the simulation in the next section, each

159

interfacial layer has been divided into ten layers. Those ten layers have the same

thickness and the Al mole fraction decreases from 0.9 to 0.24 for the Al0.9Ga0.1As

/Al0.24Ga0.76As interfaces. While for the Al0.24Ga0.76As /Al0.9Ga0.1As interfaces, Al

composition increases from 0.24 to 0.9.

The undoped sample has a clear interface, which is indicated in Fig 5.21 (a).

There is only one layer used to be interfacial layer, where Al mole fraction is the average

of Al0.9Ga0.1As and Al0.24Ga0.76. The thickness of this interfacial layer is 1nm.

5.3.2 Comparison of the reflectivities between two devices

Reflectivity measurements have been done by using an integrating sphere. First, a

“reference” has been measured, which is a completely reflective surface. Then, the

reflected signal was measured, which is the summation of the reflected and diffused

signal. Fig. 5.22 shows the comparison of the measured reflectivity spectrum between the

doped device and the undoped device. The solid dots represent the reflectivity for the

light incident on the doped device while the empty dots represent the reflectivity for the

light incident on the undoped device.

As shown in Fig. 5.22, the plot shows a broad band in reflectivity. For the doped

device, FWHM of the curve is around 60 nm, while for the undoped device, FWHM of

the curve is about 64 nm, which is in agreement with the simulation results in Fig. 4.4.

The FWHM of the reflectivity is 71 nm for light normally incident on the DBR. Also, the

spectrum shows a resonant peak value of 835 nm for the doped device and 849 nm for the

undoped device respectively. In the design, a resonant peak value of 830 nm for light

normally incident on the device was targeted.

160

Another difference between the simulation results in Fig 4.4 and the experimental

data in Fig. 5.22 is that Fig 4.4 shows the reflectivity spectrum for light normally incident

on the bottom mirror with a 830 nm resonant peak while Fig. 5.22 indicates the

reflectivity spectrum for the light incident on the top surface of the entire growth

structure. Fig. 5.23 shows the different interfaces for the light to be reflected, where part

(a) is the structure for the light incident on the bottom mirror which is used to simulate

the reflectivity spectrum as shown in Fig 4.4 while part (b) is the structure for the light

incident on the top layer of the whole growth structure which is used to measure the

reflectivity spectrum as shown in Fig. 5.22.

700 800 900 100040

60

80

100

120

140

160

180

Ref

lect

ivit

y (a

.u.)

Wavelength (nm)

Figure 5. 22 Comparison of reflectivity spectrum between undoped device and doped device. ο: undoped device; • : doped device (Data courtesy of IME-CNR, Lecce, Italy).

161

The simulation results for the reflectivity spectrum from the whole growth

structure are discussed in the next section. And growth structures for the simulation are

employed based on the TEM experimental data. The structural information has been

given in the previous section.

GaAs Substrate

25nm GaAs Buffer

(λ/4n) Al0.9Ga0.1As (67.6nm)

(λ/4n) Undoped Al0.24Ga0.76As (59.6nm)

20 periods quarter wave stack

GaAs Substrate

25nm GaAs Buffer

(λ/4n) Al0.9Ga0.1As (67.6nm)

(λ/4n) Undoped Al0.24Ga0.76As (59.6nm)

20 periods quarter wave stack

117.5nm undoped GaAs absorption

layer

5 nm undoped Al0.24Ga0.76As spacer

5*1012cm-2

Si δ-doping

50 nm n-(6~8*1014cm-3) Al0.24Ga0.76As barrier enhancement layer

30 nm n+(1.5*1018 cm-3) GaAs cap

(a) (b)

Figure 5. 23 Interfaces for light to be reflected. (a) bottom mirror, (b) top mirror.

5.3.3 Simulation results of the reflectivity spectrum

There are two factors resulting in the resonant wavelength differences between

the simulation and actual data. One is a variation in the actual layer thickness from the

value used in simulation. The second is the angle of incidence of light on the device. In

162

the simulation, the incident light was assumed to be exactly normal to the device, while

in testing, there was probably a slight variation in this angle.

700 800 900 100020

40

60

80

100

120

140

160

180

Refle

ctivit

y

Wavelength (nm)

700 800 900 100020

40

60

80

100

120

140

160

180

Refle

ctivit

y

Wavelength (nm)

(a) (b)

Figure 5. 24 Comparison of reflectivity spectrum between undoped device and doped device. (a) undoped device, solid line: experimental data, dashed line: simulation results; (b) doped device, solid line: experimental data, dashed line: simulation results.

The simulations of the reflectivity of the entire growth structure have been

calculated based on the formula in Section 4.3.

In the simulation results shown in Fig. 5.24, the structures employed are based on

the description in Section 5.3.1; dispersion effects coming from material have been

calculated based on the formula in Section 4.3.2; and absorption coefficients changing

with the wavelength have also been included based on Fig. 1.10.

The simulation results show that the difference in the thickness of the quarter

wave stack layers between the undoped and doped device affects the position of the

163

resonant peak value in the reflectivity spectrum, while the interface quality affects the

shape of the curve, especially near the resonant wavelength.

We must also account for the magnitude difference of the resonant peaks. The

reflectivity in the experimental data is a relative value, which is not normalized. The

simulation result however is normalized reflectivity. The figure shows that the

normalized reflectivity of the simulation results simply multiply 180. Another possible

factor resulting in a difference between the experimental data and simulation results is a

change in the optical properties of the material due to the thin layer effect.

5.3.4 Comparison of the internal quantum efficiency

Figure 5.25 shows the simulation results of the quantum efficiency. The structures

used for the simulation are exactly the same as in the above simulation. Part (a) is for the

light perpendicularly incident on the devices, which is the same for the time response

measurement as in Fig. 5.17; while in part (b), the incident angle for the simulation is

about 50o, which is the same for current-voltage measurement shown in Fig. 5.10. The

structures, the dispersion effects coming from the materials, and the absorption

coefficients changing with wavelength are the same as those used for the simulation of

the reflectivity spectrum in the previous section. The only difference is that there is not a

cap layer in the simulation of the quantum efficiency. Incidentally, the cap layer in the

growth structure will be used for high electron mobility transistor (HEMT) device design.

164

650 700 750 800 850 900 950 1000 10500.0

0.1

0.2

Quan

tum

effici

ency

(a.u.

)

Wavelength (nm)

650 700 750 800 850 900 950 1000 10500.0

0.1

0.2

Quan

tum

effici

ency

(a.u.

)

Wavelength (nm)

(a) (b)

Figure 5. 25 Comparison of simulation results of quantum efficiency between undoped device and doped device. ο: undoped device; • : doped device. (a) incident angle is 0o; (b) incident angle is 50o.

There is an obvious difference between Fig. 5.25 and Fig. 4.6. The quantum

efficiency shows asymmetric behavior on both sides of the resonant wavelength. The

simulation results in Fig. 4.6 do not include the effects originating from the absorption

coefficient’s dependence on wavelength. The absorption coefficient is assumed to be 1

µm-1 within the entire spectrum region, however Fig. 1.10 indicates a large difference

within different spectrum regions of the absorption coefficient. Figure 1.10 shows no

absorption when the wavelength of the incident light is larger than approximately 900

nm. GaAs has stronger absorption ability in the high energy region, resulting in an

asymmetric curve as shown in Fig. 5.25. Since the absorption coefficient at the resonant

wavelength is around 0.3 µm-1, smaller than 1 µm-1 used in the simulation of Fig. 4.6, the

quantum efficiency is lower in the figure at the resonant wavelength.

165

Figure 5.25 shows that the magnitude of the peak value at the resonant

wavelength of the doped device is slightly larger than that of the undoped device in part

(a) while about two times larger in part (b). FWHM of the doped device is around 17.0

nm, while in the undoped device it is around 20.2 nm in part (b). For light normally

incident on the devices, the FWHM in both devices is 25.6 nm, slightly smaller than that

in the selectivity spectrum, which can also be explained when we consider that absorption

effects in the wide gap material have not been included in the simulation.

For light almost perpendicularly incident on the devices at 850 nm as shown in

part (a), the quantum efficiency of the doped devices is 14.3% while in the undoped

device, it is 12.2%. Therefore, a four times magnitude difference in the time response

measurement in Fig. 5.17 can not be explained only from the difference of the growth

structure. When the devices are illuminated at an angle around 50o away from the normal

incident at 850 nm, the quantum efficiency of the doped devices is about two times of

that of the undoped devices. This result also can not account for the greater than one

order of magnitude difference in the current voltage measurement under low bias.

The above description further supports our explanation for the increase in

responsivity and speed of response. It is attributable to the vertical electric field and

potential profile in the direction of growth due to delta modulation doping.

5.4 Conclusions

An AlGaAs/GaAs based resonant-cavity-enhanced, heterostructure metal-

semiconductor-metal photodetector with a Al0.24Ga0.76As/Al0.9Ga0.1As distributed Bragg

166

reflector operating around 850 nm was fabricated and tested. Delta doping is employed in

the top AlGaAs layer to produce a confined electron cloud and an associated transverse

electric field. The effect of doping is investigated by current-voltage and temporal

response measurements of doped and undoped devices. We observe concurrent

improvement in dark current under low biases, in DC photoresponse, and in time and

frequency response. We suggest that the mechanism responsible for reduction of dark

current is the enhancement of the cathode metal-semiconductor barrier due to the effect

of the confined electron cloud, as well as band bending in the wide gap material at the

anode that reduces hole current flow. Time response data consistently shows

improvement of peak response, fall time and FWHM for the doped device. The increase

in responsivity and speed of response is attributed to the vertical electric field and

potential profile in the direction of growth due to delta modulation doping. In Section 5.3,

the growth structures from TEM pictures have been employed to simulate the internal

quantum efficiency, which further demonstrates that the vertical electric field and

potential profile in the direction of growth due to delta modulation doping is responsible

for the improvements observed.

These favorable performance characteristics combined with the substrate and

compatibility of the structure with high electron mobility transistors, makes the delta

doped device an excellent candidate for short haul (local area) high speed

telecommunication applications.

167

6. Contributions and Future Directions

6.1 General

First, we conclude by emphasizing the main contributions of this thesis in this

chapter. Second, future work that will continue the development and analysis of GaAs

and InP based photodetectors is discussed. In theoretical analysis parts, ISE-TCAD

commercial simulation tool will be employed to achieve the electric field profile in the

devices and Ramo’s theory will be used to depict the dynamic behavior of the devices.

For the experimental portion, transmission lines have been designed for high speed

measurement to remove the limitations of the test systems. An electro-optical test will be

used for the time response test in the future. Besides this work, the growth structure can

be designed for HEMT devices. The last part of the future work lists the different device

designs for HEMT.

6.2 Contributions

In this dissertation we developed a closed-form model to describe the electronic

properties of delta modulation doped heterostructures, particularly the 2DEG sheet

charge density and the electric field distribution in the direction of growth. The model

includes the effects of real-space charge transfer and carrier degeneracy. The electron

transfer and quasi-equilibrium condition in the growth direction have been used in order

168

to express the 2DEG sheet charge density as a function of only material parameters and

constants. An empirical constant, corresponding to quantized energy states, has been

employed to further simplify this description and to arrive at a closed form expression.

Results from the analytical expressions are compared with numerical simulations based

on a self-consistent solution of modified Schrödinger and Poisson equations.

We designed two III-V material based HMSM photodetectors with RCE and delta

doping in the wide bandgap material in this dissertation, where HMSM is compatible

with monolithic OEIC technology, RCE solves the trade-off between fast speed and high

quantum efficiency while, at the same time, offering narrow spectral bandwidth detection

useful in wavelength-division multiplexing (WDM) applications, and the delta doping

plane in the wide band material modulates the Schottky barrier height to further reduce

dark current. The GaAs-based design is for short haul optical communication; while the

InP based design is for long haul optical communication. The GaAs based photodetector

utilizes a Al0.24Ga0.76As/ Al0.9Ga0.1As distributed Bragg reflector (DBR) operating around

0.85 µm; while the InP based photodetector employs a In0.527Al0.144Ga0.329As/ InP (DBR)

operating around 1.55 µm.

A transmission line model is employed to design the resonant cavity and the

distributed Bragg reflector (DBR) while a closed-form model is used to optimize the

electronic properties of delta modulation doped heterostructures, particularly the 2DEG

sheet charge density and the electric field distribution in the direction of growth. The

simulation results show clear peaks at 0.85 µm with a 30 nm full width at half maximum

(FWHM) and 1.55 µm with a 0.1 µm FWHM for GaAs based and InP based

photodetectors, respectively. Also, the simulation results show that the GaAs and InP

169

based photodetectors have a seven-fold and a 3.5 fold increase in quantum efficiency at

the resonance wavelength compared to a detector of the same absorption depth

respectively. Based on the simulation results and discussions of the optical and electrical

properties of the device, an optimization including wavelength selectivity, optical

sensitivity, quantum efficiency, and dynamic speed are considered in the design.

The HMSM RCE GaAs-based photodetectors have been fabricated, characterized

and analyzed. The photocurrent spectrum shows a clear peak at this wavelength with full

width at half maximum (FWHM) of around 30 nm. Photo response shows 0.08 A/W

average photo responsivity, which means the device has a 4.4 fold photoresponse

increase over the conventional device with an assumption of 0.5 µm-1 absorption

coefficient at 850 nm. The top reflector is a delta modulation doped Al0.24Ga0.76As layer

that also acts as the barrier enhancement layer producing a low dark current of 9.2

fA/µm2. The breakdown voltage is above 20 V. Time response measurements show rise

time, fall time and FWHM of 9 ps, 18.4 ps, and 10.6 ps, respectively, giving a 3dB

bandwidth of about 33-GHz. Capacitance-voltage measurements indicate a less than 30

fF capacitance value.

Delta doping of the top AlGaAs layer produces a confined electron cloud and an

associated electric field. The delta doped device shows a factor of 7.8 reduction in dark

current and a factor of 1.6 increase in DC photocurrent with a 4 volts bias, and about 7

GHz expansion of the 3dB bandwidth under 5V bias compared to an undoped device. We

propose that the mechanism responsible for the reduction of dark current is enhancement

of the cathode metal-semiconductor barrier due to the confined electron cloud, as well as

band bending in the anode that reduces hole current flow. The increase in responsivity

170

and speed of response is attributed to the vertical electric field and potential profile in the

direction of growth.

6.3 Future Work

6.3.1 ISE-TCAD simulation

In previous work of our group, ISE-TCAD commercial simulation software

results show that there is a strong electric field in thin Al0.24Ga0.76As layer. Al0.24Ga0.76As

wide gap material does not contribute to the dark current in the typical device structure

shown as Fig. 6.1.

Moreover, due to its energy gap value, this layer is transparent to radiation of

wavelength greater than 710 nm. The underlying GaAs is responsible for the absorption

and current flow.

In the narrow band gap material GaAs, the vertical component of the electric field

depends on the doping of the AlGaAs layer, in the sense that it increases as the doping

concentration level increases in AlGaAs. This aiding field pushes the photogenerated

electrons toward the AlGaAs/GaAs interface. While falling in the triangular well, the

electrons will drift towards the anode due to the applied horizontal field.

For the HMSM RCE-PD devices, the current-voltage characteristics under light

have been measured for both the undoped and the doped devices. From the comparison of

the experimental data, the above description can be employed to explain the different

characteristics between these two devices. Therefore, it is necessary to calculate the

171

electric-field profiles in these two different types of devices under different experimental

conditions.

GaAs Substrate

GaAs 5000Å 2DEG

AlGaAs spacer 100Å

Light

n-AlGaAs 500Å

Schottky Schottky

Figure 6. 1 HMSM typical device structure.

The commercial software- ISE-TCAD is a multidimensional, electrothermal,

mixed mode device and circuit simulator for one-, two-, and three-dimensional

semiconductor devices. This software should be used to construct a two-dimensional

electric field profile for modeling the dynamic behavior of the device.

172

6.3.2 Dynamic behavior

Interdigital MSM Schottky contact diodes fabricated on GaAs or InP are

attractive photodetectors for multigigabit optical communication systems. The most

appealing features for the application of MSM photodetectors as the front end of

integrated high frequency optoelectronic receivers are their fast response, high sensitivity,

and low dark current. The response is determined by carrier transit times and resistor-

capacitor (RC) charging times of the external circuit. The response of small area detectors

is then dominated by carrier transit times which in principle can be minimized by

choosing a small distance between the Schottky contacts. Such a geometry permits rapid

carrier collection after photoexcitatoin.

To optimize the design of MSM detectors of a required bandwidth, it is necessary

to identify the factors limiting their performance and to investigate the variation of their

properties. A numerical simulator based on a finite difference numerical method and on

Monte Carlo procedure should be employed to describe the dynamic behavior. The

following paragraph is a brief description of the principles of the method.

When a photon interacts within the semiconductor, it produces a certain number

of hole-electron pairs. If an electric field is applied, the photo-produced charges drift

toward their respective electrodes. The single carrier motion induces a current signal on

the external read-out circuit, which can be evaluated by Ramo’s theorem [149, 150]:

wEetirr

•ν=)(

(6.1)

where i(t) is the instantaneous current received by the given electrode due to a single

carrier motion, e is the electrode charge, v is the carrier velocity, which is a function of

the drift field, and Ew is the so-called “weighing field”. The weighing field Ew(x,z) is

173

calculated by grounding all the electrodes with the exception of the investigated anode,

which is raised to unit potential.

Schottky Schottky Schottky

V 0 0

Z

X

Figure 6. 2 Cross section of simulated device: X is carrier transport direction, Z is growth direction; device is biased at V volts.

A different finite method has been adopted to calculate Ew and the other physical

quantities of interest. The model is two-dimensional: the Laplace equation is solved in an

x-z section of the detector over a numerical grid with a constant mesh, finite difference

iterative method. Figure 6.2 shows a cross section of the simulated device. There is an

assumption that the active region of a SI GaAs or SI InGaAs reverse biased detector is

almost neutral so the Laplace equation can be used to solve the electrostatic problem. In

this way, the potential V(x,z) and the electric field E(x,z) distributions are found. The hole

174

and electron drift velocity is calculated from the electric field using parameterization of

the experimental data [144, 145]. This work is presently continuing in our research group.

6.3.3 Electro-Optic measurement of microwave circuits

It has been mentioned in Chapter 5 that the measurement systems may have

prevented us from drawing conclusions about the intrinsic photoresponse speed. A

technique which utilizes short-pulse lasers and electro-optic materials for measuring

electrical transients has extremely high temporal resolution, which is less than 300

femtoseconds. A sample structure optimized for electro-optical (EO) sampling

measurements has been designed that will be explained below.

EO sampling mechanism will be explored. Electro-optic sampling uses the

principle of an electric field induced birefringence in crystals such as lithium tantalate.

Introduction of the lithium tantalate into an electric field, such as that radiated above a

circuit, results in a linear change in the refractive index ellipsoid for a given direction

through the crystal. Measurement of the refractive index change is achieved by detecting

the polarization rotation induced in an optical beam passing through the crystal. The

extent of polarization rotation gives a direct measurement of the electric field strength.

Figure 6.3 shows the electro-optic sampling system schematic. A commercial Ti:

sapphire laser will be used to excite picosecond pulse in the microbridge and electro-

optically measure the signal propagating on the coplanar waveguide (CPW) line or

coplanar strip (CPS) line.

175

Figure 6. 3 Electro-optic sampling system schematic [151].

The laser provids ~ 100fs wide optical pulses (76 MHz repetition rate), which are

split into two paths. The first (excitation) beam is frequency doubled in a nonlinear

crystal, intensity modulated, and focused by a microscope objective to a 10 µm diameter

spot on MSM. The second (sampling) beam traveles through a computer-controlled delay

line and is focused on a ~10 µm diameter spot at the gap between the center and ground

CPS or CPW line, only ~20 µm from MSM where it is generated. The sampling beam is

reflected by a dielectric infrared coating on the bottom face of the LiTaO3 crystal and

directed to an analyzer. The electric field of the measured pulse, which is parallel to the

LiTaO3 optical axis, induces extra birefringence into an intensity change that is detected

176

at the modulation frequency by a lock-in amplifier, resulting in a time-domain mapping

of the electric field at the sampling point. Figrue 6.4 is the experimental setup for the

Electro-optic measurement.

Figure 6. 4 External electro-optic sampling scheme[151].

6.3.4 HEMT design

We designed a new cluster of devices with active area of 40x40 µm2, employing

the same planar interdigital structure. Arrays of devices were produced with metal finger

width varying between 1-2 microns in steps of 1 micron, and inter-finger spacing varying

between 2-4 microns.

177

The design criteria are to investigate other alternative designs that are compatible

with the same wafer structure; i.e., still holds compatibility to HEMT and MESFET

amplifiers.

The fabrications of the following group of new devices are in progress:

HMSM (Sh-Sh): Schottky contact on both sides of the barrier enhancement layer.

HMSM (Oh-Sh): Ohmic contact on one side of the barrier enhancement layer, and

Schottky contact on the other side of the barrier enhancement layer.

HMSM (Sl-Sl): Schottky contact on both sides of the 2DEG.

HMSM (Oh-Sl): Ohmic contact on one side of the barrier enhancement layer, and

Schottky contact on the other side of the 2DEG.

HEMT with Ohmic contacts.

Figure 6.5 shows the series of GaAs based heterostructure RCE devices, while

Fig. 6.6 indicates InP based heterostructure RCE devices.

178

HMSM (Sh-Sh): Schottky contact on

both sides of the barrier enhancement

layer.

HMSM (Oh-Sh): Ohmic contact on

one side of the barrier enhancement layer, and Schottky contact on the other side of the barrier enhancement layer

GaAs Substrate

25nm GaAs Buffer

(λ/4n) Al0.9Ga0.1As (676 Å)

(λ/4n) Undoped Al0.24Ga0.76As (596 Å) 20 periods

Si δ-doping 5 x 1012cm-2

GaAs 1175Å 2DEG

Al0.24Ga0.76As 50Å

500Å Al0.24Ga0.76As n-(6~8*1014cm-3) barrier enhancement layer

Schottky Schottky

GaAs Substrate

25nm GaAs Buffer

(λ/4n) Al0.9Ga0.1As (676 Å)

(λ/4n) Undoped Al0.24Ga0.76As (596 Å) 20 periods

GaAs 1175Å 2DEG

Al0.24Ga0.76As 50Å

Schottky Ohmic

500Å Al0.24Ga0.76As n-(6~8*1014cm-3) barrier enhancement layer

Si δ-doping 5 x 1012cm-2

179

HMSM (Sl-Sl): Schottky contact on both sides of

the 2DEG.

HMSM (Oh-Sl): Ohmic contact on

one side of the barrier enhancement layer, and Schottky contact on the other side of the 2DEG

GaAs Substrate

25nm GaAs Buffer

(λ /4n) Al0.9Ga0.1As (676 Å)

(λ /4n) Undoped Al0.24Ga0.76As (596 Å) 20 periods

GaAs 1175Å 2DEG

Al0.24Ga0.76As 50Å

Schottky Si δ-doping 5 x 1012cm-2

Schottky

500Å Al0.24Ga0.76As

layer

GaAs Substrate

25nm GaAs Buffer

(λ/4n) Al0.9Ga0.1As (676 Å)

(λ/4n) Undoped Al0.24Ga0.76As (596 Å) 20 periods

GaAs 1175Å 2DEG

Al0.24Ga0.76As 50Å

Schottky Si δ-doping 5 x 1012cm-2

Ohmic

500Å Al0.24Ga0.76As n-(6~8*1014cm-3) barrier enhancement

layer

180

HEMT with Ohmic contacts

GaAs Substrate

25nm GaAs Buffer

(λ /4n) Al0.9Ga0.1As (676 Å)

(λ/4n) Undoped Al0.24Ga0.76As (596 Å) 20 periods

GaAs 1175Å 2DEG

Al0.24Ga0.76As 50Å

Si δ-doping 5 x 1012cm-2

Ohmic

Schottky

Ohmic

500Å Al0.24Ga0.76As n-(6~8*1014cm-3) barrier enhancement layer

Source Drain

Gate

Figure 6. 5 Series of GaAs based heterostructure RCE devices.

181

HMSM (Sh-Sh): Schottky contact on

both sides of the barrier enhancement

layer

HMSM (Oh-Sh): Ohmic contact on

one side of the barrier enhancement layer, and Schottky contact on the other side of the barrier enhancement layer

InP Substrate

25nm InP Buffer

(λ/4n) In0.527Al0.144Ga0.329As (1133 Å)

(λ/4n) Undoped InP (1223 Å) 15 periods

Si δ-doping 1 x 1013cm-2

In0.53Ga0.47As 3858Å 2DEG

In0.52Al0.48As 50Å

500Å In0.52Al0.48As n-(6~8*1014cm-3) barrier enhancement layer

Schottky Schottky

InP Substrate

25nm InP Buffer

(λ/4n) In0.527Al0.144Ga0.329As (1133 Å)

(λ/4n) Undoped InP (1223 Å)

15 periods

In0.53Ga0.47As 3858Å 2DEG

In0.52Al0.48As 50Å

Si δ-doping 1 x 1013cm-2

Schottky Ohmic

500Å In0.52Al0.48As n-(6~8*1014cm-3) barrier enhancement layer

182

HMSM (Sl-Sl): Schottky contact on both sides of

the 2DEG

HMSM (Oh-Sl): Ohmic contact on one

side of the barrier enhancement layer,

and Schottky contact on the other side of

the 2DEG

InP Substrate

25nm InP Buffer

(λ /4n) In0.527Al0.144Ga0.329As (1133 Å)

(λ/4n) Undoped InP (1223 Å)

15 periods

In0.53Ga0.47As 3858Å 2DEG

In0.52Al0.48As 50Å

Schottky Si δ-doping 1013cm-2

Schottky

500Å In0.52Al0.48As

InP Substrate

25nm InP Buffer

(λ/4n) In0.527Al0.144Ga0.329As (1133 Å)

(λ/4n) Undoped InP (1223 Å)

15 periods

In0.53Ga0.47As 3858Å 2DEG

In0.52Al0.48As 50Å

Schottky Si δ-doping 1013cm-2

Ohmic

500Å In0.52Al0.48As

183

HEMT with Ohmic contacts

InP Substrate

25nm InP Buffer

(λ /4n) In0.527Al0.144Ga0.329As (1133 Å)

(λ /4n) Undoped InP (1223 Å)

15 periods

In0.53Ga0.47As 3858Å 2DEG

In0.52Al0.48As 50Å

Si δ-doping 1013cm-2

Ohmic

Schottky

Ohmic

500Å In0.52Al0.48As n-(6~8*1014cm-3) barrier enhancement layer

Source Drain

Gate

Figure 6. 6 Series of InP based heterostructure REC devices.

184

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197

Appendix A: Transmission line design

A1 Requirements of Geometry of Structure

Wave traveling time along the transmission line should be much shorter than the

repetition time and longer than the FWHM of the device. Here, the traveling time, t, is

defined as the window size for the reflection free time, thus eliminating from waveforms

the artifacts that may be caused by reflections at the end of the transmission line.

Parameter t can be expressed by

gVlt 2=

(A.1)

Here, l is the length of the transmission line and Vg is the group velocity of the

microwave signal and Vg is defined by

reg

cVε

=

(A.2)

εre is the effective relative dielectric constant considering quasi-TEM mode.

Since the FWHM of all of our devices is less than 13 ps using oscilloscope

measurement, the reflection free window is designed around 40 ps.

The width of the transmission line must be determined by impedance matching.

The characteristic impedance of the coaxial line is 50Ω. If the characteristic impedance of

the transmission line is designed to 50Ω, which means it is matched to that of the coaxial

line, it will reduce the reflection effect.

198

A2 Formula for Calculation

signal

ground

2a=5µm 2b=96µm

Photodetector

l=2.25mm

45.5µm

45.5µm

l=2.25mm

Figure A. 1. Coplanar stripe transmission line scheme with a 50 µm pitch.

The definition of the pitch for CPS is given by

)(2 abapitch −+×=

(A.3)

where 2a is the width of the space between the metal, 2b is the width between the edges

of the two metals, which will be seen in Fig. A.1.

And the definition of the pitch for CPW is given by

2bcbpitch −+=

(A.4)

where 2a is the width of the signal line, 2b and 2c are shown in the CPW schematic (Fig.

A.2).

199

signal

ground

2b=200µm

Photodetector

l=2.25mm

500µm

l=2.25mm

2a=84µm

ground500µm

58µm

58µm

2c=1200µm

Figure A. 2. Coplanar waveguide transmission line scheme with a 350 µm pitch.

The equations (A.5-A.8) will be employed to achieve optimized structures for the

electro-optic sampling measurement [1].

2' 1 kk −= (A.5)

)]1/()1(2ln[)()(

''' kkkKkK

−+×= π for 0 ≤ k ≤ 0.707 (A.6 a)

)]1/()1(2ln[1)()(

' kkkKkK −+×=

πfor 0.707 ≤ k ≤ 1 (A.6 b)

200

The formula for calculating the characteristic impedance of CPS are given by Eq.

(A.7)

bak =1 (A.7 a)

)2/sinh()2/sinh(

2 hbhak

ππ= (A.7 b)

)()(

)()(

211

1

1'

2'

2

kKkK

kKkKr

re−+= εε (A.7 c)

)()(120

1'

10 kK

kKZre

cs επ= (A.7 d)

where h is the thickness of the substrate. The equations (A.7) are used in the symmetric

CPS with finite dielectric thickness.

The formula for calculating the characteristics impedance of CPW are given by

22

22

3 /1/1cacb

bak

−−= (A.8 a)

)2/(sinh/)2/(sinh1)2/(sinh/)2/(sinh1

)2/sinh()2/sinh(

22

22

4 hchahchb

hbhak

ππππ

ππ

−−= (A.8 b)

)()(

)()(

211

3

3'

4'

4

kKkK

kKkKr

re−+= εε (A.8 c)

)()(30

3

3'

0 kKkK

Zre

cp επ= (A.8 d)

where h is the thickness of the substrate. And Eq. (A.8) is used in the symmetric CPW

with finite dielectric thickness and finite width ground planes.

201

A3 Simulation Results

0.01 0.1 0.720

40

60

80

100

120

140

20

40

60

80

100

120

140C

hara

cter

istic

impe

danc

e (Ω

)

Ratio a/b

Pitc

h (µ

m)

Figure A. 3. Simulation results for CPS with a pitch of 50 µm.

The probe size limits CPS with a pitch 50 or 100 µm, CPW with a pitch of 350

µm. The thickness of the substrate is assumed to 600 µm in the following design. Figure

A.3 shows the simulation results if the pitch is equal to 50 µm.

From Figure A.3, it can be seen when a/b ratio equals 0.052, Z0cs equals 50 Ω and

pitch equals 50 µm. By using the formula (A.7), the values of 2a=5 µm, 2b = 96 µm, and

εre = 7.09 are shown in Fig. A.1. Thus, the group velocity is given by Eq. (A.2). Here Vg

is equal to 1.13∗ 108 m/s. If the window size is 40 ps, the length of the transmission line is

202

equal to mmtV

l g 25.22

=×

= . Figure A.4 shows the simulation results for the pitch of 100

µm.

0.01 0.1 0.720

40

60

80

100

120

140

160

20

40

60

80

100

120

140

160

Pitc

h (µ

m)

Cha

ract

erist

ic im

peda

nce

(Ω)

ratio of a/b

Figure A. 4. Simulation results for CPS with a pitch of 100 µm.

From Figure A.4, it can be seen when a/b ratio equals 0.053, Z0cs equals 51.5 Ω

and pitch equals 100 µm. By using the formula (A.7), the values of 2a=10 µm, 2b = 190

µm, and εre = 7.08 are shown in Fig. A.5. Thus, the group velocity is given by Eq.(A.2).

Here Vg is equal to 1.13∗ 108 m/s. If the window size is 40 ps, the length of the

transmission line is equal to mmtV

l g 25.22

=×

= . Figure A.6 shows the simulation results

for CPW with a 350 µm pitch.

203

signal

ground

2a=10 µm2b=190µm

Photodetector

l=2.25mm

90µm

90µm

l=2.25mm

Figure A. 5. Coplanar strip transmission line scheme with a 100 µm pitch.

0.01 0.1 0.720

40

60

80

100

120

140

Ratio a/b

Cha

rate

rist

ic im

peda

nce

(Ω)

Figure A. 6. Simulation results for CPW with a pitch of 350 µm.

204

From Figure A.6, it can be seen that when a/b ratio equals 0.42, Z0cs equals 50 Ω

and pitch equals 350 µm. By using formula (A.8), the values of 2a=84 µm, 2b = 200 µm,

and εre = 7.08 are shown in Fig. A.2. Thus, the group velocity is given by Eq. (A.2). Here

Vg is equal to 1.13∗ 108 m/s. If the window size is 40 ps, the length of the transmission

line is equal to mmmtV

l g 25.21025.22

3 =×=×

= − .

Reference:

1. K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, “Microstrip Lines and Slotlines,” Artech House, 2nd Edition, 1996.

205

VITA

Xiying Chen was born in Tongling, P. R. China in February 1972. She received her

Bachelor of Science majoring in applied physics from the department of Physics II of

Fudan University in June of 1993 and Master of Science majoring in condensed matter

physics from the department of Physics of Fudan University in June of 1996. From 1996

to 1997, she was a process metrology engineer and then became a failure analysis

engineer at Huahong microelectronic company in Shanghai of China. She then worked

for Huahong – NEC electronic company in Shanghai of China from 1997 to1998 as a

product engineer who handled process integration and quality control for a 0.35 µm 8

inch DRAM product line. From September 1998, while a graduate student at Drexel

University, she was involved in several research activities, which included InGaAs/InP

designs for optoelectronic devices used in long haul communications, AlGaAs/GaAs

designs for optoelectronic devices used in short haul communications, theoretical

derivation of a closed-form expression to analyze electronic properties in δ-doped

heterostructures, optical and electronic buffer in optical communications, AlGaAs/GaAs

heterodimensional device designs, and monolithic laser driver for OC768. Her main

research interest was to design new optical receivers for optical communications. During

her graduate studies at Drexel University, she designed two novel photodetectors, a GaAs

based photodetector for short haul communication, and an InP based photodetectors for

long haul communication. Her research activities have been published in several

prestigious technical journals: J. Applied Physics, Applied Physics Letters, J. Crystal

Growth, J. Vaccum Science & Technology B, Surface and Interface Analysis, Acta

Physics Sinica, and Chinese J. Semiconductor. She has published fourteen journal papers,

nine conference papers, and holds two patents. Currently, she has submitted three journal

papers. She was awarded the 2nd best student paper in 2001 and the 1st best student paper

in 2002 at IEEE Sarnoff Symposium on Advances in Wired and Wireless

Communications, New Jersey. She has received Allen Rothwarf Outstanding Graduate

Student Award from Drexel University in 2001. In 1993, she achieved the Honored

Graduate by Higher Education Bureau of Shanghai. Ms. Chen is a student member of

IEEE.