Novel Heterostructure Metal-Semiconductor-Metal

Transcription

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
4.4
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
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
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-bandedge 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
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
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 selfconsistent 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.
1.1
Introduction
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
C ci = BW × log
2 (1
+ SNR ) ,
(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 lightemitting 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.
Transmitter
Electrical
input
signal
Drive
circuit
Light
source
Fiber
flylead Connector
Optical
splice
Optical
fiber
Optical
coupler
Repeater
Optical
receiver
Electronics
Optical
transmitter
Receiver
Optical
Amplifier
Electrical signal
Signal
restorer
Photodetector
Electricl
signal
out
Amplifier
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.
Bias voltage
Photodiode
R
Figure 1. 2
amplifier.
AMP
L
Block diagram of an optical receiver, consisting of a photodetector and an
Photo-diode
(Ideal)
Rs
RD
Ls
CD
Ra
Equivalent photodiode circuit
Figure 1. 3
Output
Optical receiver equivalent circuit.
Ca
AMP
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 electronhole 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 edgeilluminated 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
+
+
P
N
n
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.
Antireflection
coating
Metal contact
Metal contact
Metal contact
p
Metal
contact
P
p
i
i
n
i
n+
n
Metal contact
Metal contact
(a)
(b)
Metal
contact
n
Metal contact
Antireflection
coating
(c)
Figure 1. 5
p-i-n photodiode: (a) front-illuminated PD; (b) fear-illuminated PD; (c) edgeilluminated 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
G =
I
I
(1.2)
p
p+
i
p
n+
Electric 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].
p-i-n
p-i-n
Si
0.4-1.1
0.4-0.45
75-90
Material
Ge
0.8-1.8
0.8-0.87
50-55
InGaAs
1.0-1.7
0.5-0.95
60-70
V
APD
p-i-n
APD
p-i-n
APD
p-i-n
APD
p-i-n
1-10
0.1-1
0.125-1.4
0.01
50-100
50-200
50-500
50-500
0-0.0015
1.5
6-10
10-40
1-20
1-5
0.0025-40
1.5-3.5
0.1555-53
2.5-4
5-6
-
APD
APD
200-250
0.02-0.05
20-40
0.7-1.0
20-30
0.5-0.7
Parameter
Wavelength
Responsivity
Quantum
Efficiency
APD gain
Dark Current
Symbol
λ
R
η
Unit
nm
A/W
%
Type
M
Id
nA
Bandwidth
BW
GHz
Bit rate
BR
Gbit/s
Reverse
voltage
V
k-factor
1.4
kA
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.
ARC
p+
contact
n-
n+
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.
ARC
n
contact
n+
p π
p-(π)
p+
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 multiGigabyte/s levels is rapidly becoming very attractive [12 - 15].
pin
HBT
pin
FET
FET
pin
substrate
(a)
substrate
(b)
substrate
(c)
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].
B
n
p+
E
p
n
n+
n+
S.I.
S.I.
Photodiode
bipolar transistor
S
G
D
n or p
S.I.
M.S.M. diode
C
n+
n
buffer n-, pS.I.
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
6, 20-26].
Comparison of characteristics of Si and GaAs photodiodes for 0.85 µm [5,
Parameter
Wavelength
Responsivity
Symbol Unit
nm
λ
R
A/W
Quantum
Efficiency
η
Dark Current
Bandwidth
%
Id
nA
BW
GHz
Bit rate
BR
Gbit/s
Reverse voltage
V
V
Type
p-i-n
MSM
p-i-n
MSM
p-i-n
MSM
p-i-n
MSM
p-i-n
MSM
p-i-n
MSM
Si
0.4-1.1
0.4-0.45
Material
GaAs
0.6-0.9
0.35-0.45
75-90
100
1-10
< 1nA
0.125-1.4
> 10GHz
0.01
> 2.5 Gbits/s
50-100
18
1.4.3
For the 1.3 µm optical transmission window, both single mode fiber and multimode 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
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 dispersionshifted 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 highquality 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.
hν
n+ Ge
92% Ge
76% Ge
Uniform n+ Ge cap
layer, 550oC, 30mT
Relaxed graded buffer 10% Ge
µm-1 750oC, 250 mT
µm-1 750oC, 250 mT
50% Ge
CMP
µm-1 750oC, 250 mT
(001) Si substrate offcut 6o to
in-plane <110>
Figure 1. 15
1.4.4.2
Ge photodiode on SiGe/Si [34].
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].
p+
nn
n+
Figure 1. 16
InGaAsP
InGaAs
InGaAsP
InP
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 IIIV 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
Gate
narrow band
gap material
wide band
gap material
SI Substrate
2DEG
HEMT
Figure 1. 17
1.5
MESFET
Fundamental device structure of III-V MESFET and heterostructure HEMT.
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 highspeed, 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
Year
Medium
Voice
channels
Progress in trans-Atlantic-transmission (TAT) capacity.
1956
1963
1970
1976
1988
Coaxial Coaxial Coaxial Coaxial Fiber
(1.3 µm)
84
128
720
4000
40,000
1997
Fiber
(1.55 µm)
60,000
(5Gbit/s)
2001
Fiber
(1.55 µm)
≈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 highspeed, 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. Offresonant 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).
Mirror 1
Mirror 2
E3
E2
E1=r1r2e-jΨE0
E1
E0
+
E
r1r2e-jΨ
E0
t 1 r1
d
r2 t 2
z=0
(a)
Figure 2. 1
(b)
Two-mirror planar resonator (Fabry-Perot Mirror).
Resonator modes are the standing waves. A monochromatic wave of frequency f
has a wavefunction,
37
r
r
E (r , t ) = E (r ) exp( j 2π f t )
(2.1)
which represents the transverse component of the electric field. The complex amplitude
r
E (r ) should satisfy the Helmholtz equation,
r
r
∇ 2 E (r ) + β 2 E (r ) = 0
(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
r
appropriate boundary conditions, which require that E (r ) equals zero at z=0 and z=d
plane. This restricts β to the values β m =
limited to the discrete values f m = m
up
2d
mπ
, which also means that the frequency f is
d
. Thus, the adjacent resonance frequencies are
separated by a constant frequency difference f m+1 − f m =
up
2d
.
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
Ψ = 2β d =
4π f d 4π d
=
,
up
λ
(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
Ei +1 = r1 r2 e − jΨ Ei
(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 h = r1r2 e − jΨ .
The net result is the superposition of an infinite number of waves
E = E0 + E1 + E 2 + ....
∞
∞
i =0
i =0
= ∑ Ei = ∑ E 0 h i =
.
E0
E0
=
1 − h 1 − r1 r2 e − jΨ
(2.5)
Therefore, the wave intensity in the resonator is found to be
I= E
=
=
2
=
2
E0
1 − r1r2 e − jΨ
2
E0
(2.6)
1 − R1 e − jΨ 1 R2 e − jΨ 2 e − jΨ
I0
1 + R1 R2 − 2 R1 R2 cos(Ψ +Ψ 1 +Ψ 2 )
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 I 0 = E0
of the initial wave, and F =
can
be
maximized
π( R1 R2 )1 / 2
1 − R1 R2
when
2
is the intensity
is the finesse of the resonator. The intensity, I,
cos(Ψ + Ψ 1 + Ψ 2 )
equals
unity,
which
requires Ψ + Ψ 1 + Ψ 2 = 2mπ . If F is large, which requires that the mirrors have large
reflectivities, then I has sharp peaks centered at the values Ψ + Ψ 1 + Ψ 2 = 2mπ .
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 exp(−2α d ) , 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
I=
=
2
E0
1 − e −αd R1 e − jΨ 1 R2 e − jΨ 2 e − jΨ
1 + R1 R2 e
− 2 αd
(2.7)
I0
− 2 R1 R2 e −αd cos(Ψ + Ψ 1 + Ψ 2 )
Also, the finesse F can be expressed as a function of the effective loss coefficient
αr
F=
π exp(−α r d / 2)
,
1 − exp(−α r d )
(2.8)
where αr can be calculated from the formula
αr = α +
1
1
ln(
).
2d
R1 R2
(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
Z=0
Ei
Barrier
Ef enhancement
layer
Eb
absorption
layer
√R1e-jΨ1
t1
L1
L2
√R2e-jΨ2
DBR reflector
Figure 2. 2
Schematic
photodetector.
diagram
of
resonant-cavity-enhanced
heterojunction
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:
E f = t1 Ein + e −αL2 R1 e − jΨ 1 R2 e − jΨ 2 e − jΨ E f
= t1 Ein + e −αL2 R1 e − jΨ 1 R2 e − jΨ 2 e − j ( 2β1L1 + 2β2 L2 ) E f
= t1 Ein + e
⇒ Ef =
−αL2
1− e
R1 e
−αL2
− jΨ 1
R1 e
R2 e
t1
− jΨ 1
− jΨ 2
e
− j (2
2π
2π
L1 + 2 L2 )
λ1
λ2
R 2 e − jΨ 2 e − jΨ
Ein
Ef
(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:
Eb = e −αL2 / 2 R2 e − jΨ 2 e − jΨ / 2 E f
(2.11)
= e −αL2 / 2 R2 e − jΨ 2 e − j ( β1L1 + β2 L2 ) E f
The optical power inside the resonant cavity is given by
Ps =
Es
2
2η s
(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:
Pl = ( Pf + Ps )(1 − e −αL2 )
=
(1 − R1 )(1 + R2 e −αL2 )(1 − e −αL2 )
1 − 2 R1 R2 e −αL2 cos(2( β1 L1 + β 2 L2 ) + Ψ 1 + Ψ 2 ) + R1 R2 e −2αL2
Pi
(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]:
η = (1 − R1 )(1 − e −αL2 )
(
)

1 + R2 e −αL2
×
− αL
− 2αL2
1 − 2 R1 R2 e 2 cos(2( β1 L1 + β 2 L2 ) + Ψ 1 + Ψ 2 ) + R1 R2 e
 , (2.14)


From this formula, quantum efficiency is maximized due to high reflection from
the DBR and when the condition cos(2( β1 L1 + β 2 L2 ) + Ψ 1 + Ψ 2 ) = 1 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]:
ηi =
µ
ε − jε "
'
,
(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, ε ' >> ε " , ηi can be written as ηi =
µ
ε'
and also the propagation constant can be simplified for every non-absorbing layer as
β = ω µε ' . Here, ω is the operation frequency, which is related to the incident light. An
equivalent expression for β is given as: β =
2π
(λ0 is the wavelength of the incident
λ0 / n
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]:
η i = η 0i
η i −1 + η 0i tanh(γ i li )
, i=1 to 2N
η 0i + η i −1 tan(γ i li )
(2.16)
where N is the total number of the contrasting pairs in the quarter mirror stacks,
γi =
αi
2
+ iβ i , 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]:
Γ2 =
η 2 N − η abs
= R2 e − jΨ 2
η 2 N + η abs
(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 ( cos(2( β1 L1 + β 2 L2 ) + Ψ 1 + Ψ 2 ) = 1 ).
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.
0.6
0.5
Quantum Efficiency
αL2=0.11, R2=0.9
FSR
0.4
0.3
0.2
R1=0.05
0.1
R1=0.3
0.0
R1=0.9
0.4
0.6
0.8
1.0
1.2
1.4
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 2( β1 L1 + β 2 L2 ) + Ψ 1 + Ψ 2 = 2mπ (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
0.6
0.5
Quantum Efficiency
αL2=0.11, R2=0.9
FSR
0.4
0.3
0.2
R1=0.05
0.1
R1=0.3
0.0
R1=0.9
0.4
0.6
0.8
1.0
1.2
1.4
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:
(
)
 1 + R e −αL2

2
η = (1 − R1 )(1 − e −αL2 ) × 

− αL
 (1 − R1 R2 e 2 ) 2 
(2.18)
In the limit of the a thin active layer αL2 << 1, (2.18) reduces to
 (1 + R (1 − αL ) ) 
2
2
η ≈ (1 − R1 )αL2 

 (1 − R1 R2 (1 − αL2 )) 2 
(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., α eff = SWE × α , 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]:
2
L1 + L2
∫ α( z ) E ( z , λ)
1 / L2
dz
0
α eff =
2/λ
,
2
λ/2
∫ E ( z , λ)
(2.20)
dz
0
where λ =
λ0
n
, 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
L1 + L2
SWE =
α eff
α
1 / L2
2
∫ E( z)
dz
L1
=
2/λ
λ/2
∫ E ( z)
(2.21)
2
dz
0
The forward (Ef) and backward (Eb) components of the standing wave are given
2
by Eq. (2.10) and Eq. (2.11). The total electric field E and intensity E are :
E = E f (0)e − jβz + Eb ( L1 + L2 )e jβ( z −( L1 + L2 ))
(2.22)
and
2
2
2
{
*
}
E = E f (0) + Eb ( L1 + L2 ) + 2 Re E f ( z ) Eb ( z )
(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
E
2

(1 − R1 )

=
 1 − R1 R2 e j ( 2 βL +Ψ 1 +Ψ 2 )

[


2


(2.24)
]
× 1 + R2 + 2 R2 cos[2 β ( L1 + L 2 − z ) + Ψ 2 ] Ein
2
Substituting Eq. (2.24) into Eq. (2.21), we obtain the dependence of the SWE on
the cavity parameters [103]:
SWE = 1 +
2 R2
βL2 (1 + R2 )
[sin βL2 cos( βL2 + Ψ 2 )]
(a)
1.2
1.1
SWE
SWE
(b)
1.2
1.1
1.0
0.9
0.8
(2.25)
1.0
0.9
0.4
0.6
0.8
1.0
Wavelength (µm)
1.2
1.4
0.8
200 300 400 500
600 700 800 900 1000
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.
Transmission line 1
Z01
z=0
Transmission line 2
Incident wave
Transmitted Wave
Z02
Reflected wave
(a) Boundary between transmission line
z=0
Incident plane wave
Transmitted plane Wave
Reflected plane wave
Medium 1 η1
Medium 2 η2
(b) Boundary between different media
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
Γ =
Z 02 − Z 01
Z 02 + Z 01
(2.26).
There is a one-to-one correspondence between the transmission line parameters
~ ~
~ ~
( V , I , β , Z 0 ) and the plane wave parameters ( E , H , β ,η ). 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).
l1 = λ0/4n1
L2
Absorption
layer
air
L1
Barrier
enhancement
layer
Figure 2. 7
Γ
ηL
l2 = λ0/4n2
N pairs quarter wave stack
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:
Γ =
η in − η abs
η in + η abs
(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
Γ 1' =
η barrier − η air
η barrier + η air
(2.28 a)
Γ1 =
η air − η barrier
= −Γ 1'
η air + η barrier
(2.28 b)
Γ2 =
η 2 N − η abs
η 2 N + η abs
(2.28 c)
τ 1' = 1 + Γ 1 ' =
τ1 = 1 + Γ 1 =
2η barrier
η barrier + η air
2η air
η barrier + η air
(2.28 d)
(2.28 e)
Since each round-trip path forward and back through the resonant cavity results in
a − 2( β 1 L1 + β 2 L2 ) phase shift and a e −αL2 magnitude decrease, the total reflection
coefficient can be expressed as
55
Γ = Γ 1' + τ 1'τ 1Γ 2 e − j 2( β1L1 + β 2 L2 ) e −αL2
+ τ 1'τ 1Γ 2 e − j 2( β1L1 + β 2 L2 ) e −αL2 Γ 1e − j 2( β1L1 + β 2 L2 ) e −αL2 Γ 2 + ...
∞
= Γ 1' + τ 1'τ 1 ∑ (Γ 2 e − j 2( β1L1 + β 2 L2 ) e −αL2 ) i (Γ 1 ) i −1
.
i =1
'
'
= Γ 1 + τ1 τ1
Γ 2 e − j 2( β1L1 + β 2 L2 ) e −αL2
1 − Γ 2 e − j 2( β1L1 + β 2 L2 ) e −αL2 Γ 1
RCE
photodetector
τ1
ηbarrier
ηair
ηabs
Barrier
enhancement
layer
air
τ1′
Γ′1
η2N
Absorption
layer
L1
L2
Γ1
Γ2
L1+L2
1
Γ′1
Figure 2. 8
τ1’
τ1
Γ1
Γ2
τ1
Γ1
Γ2
Multiple reflection analysis of the RCE photodetector.
(2.29)
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, Hipe) and a
parallel polarized component (Eipa, Hipa), and then after determining the reflected waves
(Erpe, Hrpe) and (Erpa, Hrpa) 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.
X
βr
Hper
θr
Z
Y
βi
Epei
Hpet
θt
θi
Medium 1
( ε1 , µ 1 )
βt
Epet
Eper
Hpe
Medium 2
( ε2 , µ 2 )
i
z=0
(a) Perpendicular polarization
X
βr
Epa
r
Epat
Hpar
θr
θi
Medium 1
( ε1 , µ 1 )
θt
Hpa
Hpat
Y
βi
Epai
βt
Z
Medium 2
( ε2 , µ 2 )
i
z=0
(b) Parallel polarization
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
β1 sin θ i = β1 sin θ r = β 2 sin θ t ,
(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
θ i = θ r (Snell’s law of reflection)
(2.31 a)
and the second equality leads to
sin θ t β1 n1
=
=
(Snell’s law of refraction)
sin θ i β 2 n 2
(2.31 b)
The following expressions are for the reflection and transmission coefficients in
the perpendicular polarization case:
Γ⊥ =
τ⊥ =
E rpe
E ipe
E tpe
E ipe
=
=
η 2 cos θi − η 1 cos θt
η 2 cos θi + η 1 cos θt
2η 2 cos θ i
η 2 cos θ i + η 1 cos θ t
(2.32 a)
(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
τ ⊥ = 1+ Γ ⊥
(2.33)
Equations (2.33) are the expressions for the reflection and transmission coefficients in the
parallel polarization case,
Γ =
τ
=
E rpa
E ipa
E tpa
E ipa
=
η 2 cos θt − η 1 cos θi
η 2 cos θt + η 1 cos θi
(2.34 a)
=
2η 2 cos θi
,
η 2 cos θt + η 1 cos θi
(2.34 b)
59
The above expressions can be shown to yield the relation
τ
= (1 + Γ )
cos θi
cos θt
(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)
Leff _ j =
Lj
cos θ j _ t
=
Lj
1 − (sin θ j _ t ) 2
=
Lj
1 − (sin θ i / n j ) 2
,
(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 modulationdoped 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 modulationdoped 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.,
E f ≤ EC for the delta-doped heterostructure. The free electron concentration can be
written using Boltzmann statistics as
n( z ) = N c exp(qVδ / kT )
(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
ρ ( z ) = q[ N d + ( z ) − n( z )]
(3.2)
where
N d + ( z) =
Nd
1 + g n exp[( E d + qVδ ) / kT ]
(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 ( qVδ = E f − EC ) 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
EC
EGaAs(z)
EAlGaAs(z)
-qVδ
Ef
Z
Eo
δ-doping
AlGaAs spacer layer
AlGaAs top layer
GaAs absorption layer
Zs
Figure 3. 1
Schematic
heterojunction.
diagram
of
conduction
band
of
a
modulation
doped
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 deltadoped region with the electrons accumulated in the triangular potential well of GaAs,
hence
n so


Nd
qV
=
− N c exp( δ
kT
1 + g exp( E d + qVδ )
n
kT



) Z d


(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(qVδ / kT ) , whose meaningful root is then calculated to yield
65
exp(
qVδ
)=
kT
n

−  so g n' + N c  +
 Zd

2
 n so '

n


g n + N c  − 4 g n' N c  so − N d 
 Zd

 Zd

(3.5)
'
2g n N c
where g n' = g n exp( E d / kT ) . Using Taylor series expansion and retaining the first two
terms, i.e. assuming Vδ << kT / q , this equation can be simplified to
qVδ
kT
=
n

−  so g n' + N c  +
 Zd

2
 nso '

n


g n + N c  − 4 g n' N c  so − N d 
 Zd

 Zd

− 1 (3.6)
'
2 gn Nc
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
− qVδ = −( E f − EC ) 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
− qVδ + qE AlGaAs Z s − ∆EC + ( E f − Eo ) = 0
(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
E AlGaAs =
qn so
ε AlGaAs
,
(3.8)
where ε AlGaAs 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 E f − Eo = kT / q × ln( f (n so )) [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]
E f − Eo
q
= bn so +
∆E Fo
,
q
(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
nso =
where
− B + B 2 − 4 AC
2A
(3.10)
67

qZ s
kT / q
A =  b +
+2
ε AlGaAs
2N c Z d


qZ s
 b +
ε AlGaAs


 ,




qZ s
kT + ∆E Fo − ∆EC
kT / q  
kT / q

+
B = 2 b +
+
ε AlGaAs 2 N c Z d  
q
E 

 2 g n exp d 
 kT 

kT / q
kT / q
+
2N c Z d
E 
g n exp d 
 kT 





,
and
2
 kT + ∆E Fo − ∆EC 

C = 
q


 kT + ∆E Fo − ∆EC 
kT / q

+ 
q

 g exp E d 
n
 kT 
Nd
−
(kT / q ) 2
E 
g n exp d  N c
 kT 
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
EGaAs ( z = 0) = Eint =
qn so
ε GaAs
(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 Si − SiO 2 interfaces, where similar inversion conditions to
those in AlGaAs/GaAs heterostructures have produced a model of the potential profile of
the form [74].
U GaAs ( z , n so ) =
2kT  qEint z 
ln1 +

2kT 
q

(3.12)
From this analytical conduction band model, the electric field profile is obtained
directly from Poisson’s equation
EGaAs ( z , n s 0 ) =
2kT × Eint
∂U
=
∂z 2kT + qEint z
(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 orthonormalization, 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:
Ψ 1 ( z ) = C1 X 1 ( X 1 z + C 2 ) exp(−
X1z
)
2
Ψ 2 ( z ) = X 2 (C 4 + C5 z + C 6 z 2 ) exp(−
(3.14)
X2z
)
2
(3.15)
And for AlGaAs side (z<0):
Ψ 1 ( z ) = C 3 X 3 exp(
X3z
)
2
(3.16)
Ψ 2 ( z ) = C 7 X 4 exp(
X4z
)
2
(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
Ei =
∞
∫ Ψi ( z ) H Ψi ( z )dz
(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
∂ 2V ( z )
∂z
2
=−
q
ε GaAs
[− N
a
−
2
+ p − n1 ( z )Ψ 1 ( z ) − n2 ( z )Ψ 2 ( z )
2
]
(3.19)
where

 qE
ni ( z ) = N 2 D ln 1 + exp i
 kT


 i=1,2

(3.20)
and N 2 D = m*kT / πh 2 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>
Use updated
X1-4 parameters
Calculation of n1
Minimization of <E2>
Calculation of n2
No
Modify shooting E
at the GaAs buffer
layer
<E1>+<E2>
converge ?
Yes
Desired V at the
AlGaAs surface ?
No
Stop
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
500 Å n-(6~8*1014cm-3)
Al0.24Ga0.76As barrier
δ-doped layer
Zd=20Å
50~100 Å undoped Al0.24Ga0.76As
spacer
p- 1014cm-3 background doped GaAs
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(qVδ / kT ) with 1 + qVδ / kT 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
12
-2
Sheet Charge Density (cm)
1.8x10
closed-form expression
without using equation (3.6) approximation
12
1.6x10
50 Å
12
1.4x10
70 Å
12
1.2x10
12
100 Å
1.0x10
11
8.0x10
12
4.0x10
12
8.0x10
13
1.2x10
13
1.6x10
13
2.0x10
-2
Delta Doping Concentration (cm )
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
12
-2
Sheet Charge Density (cm)
1.8x10
12
1.6x10
modified Schrodinger and Poission model
without using equation (3.6) approximation
50 Å
12
1.4x10
70 Å
12
1.2x10
100 Å
12
1.0x10
11
8.0x10
12
4.0x10
12
8.0x10
13
1.2x10
13
1.6x10
13
2.0x10
-2
Figure 3. 5
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
E lectric Field (V /cm )
numerical modeling methods.
2.5x10
5
2.0x10
5
1.5x10
5
50 Å
70 Å
100 Å
1.0x10
5
5.0x10
4
0.0
-1
10
0
1
2
3
10
10
10
10
Distance from the interface (Å)
10
4
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 GaAsbased 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 highspeed 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 semiconductorsemiconductor 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)
AlP
5.451
AlAs
5.6605
AlSb
6.1355
GaP
5.45117
GaAs
5.65325
GaSb
6.09593
InP
5.86875
InAs
6.0585
InSb
6.47937
Gap (eV)
Energy at 300 K
2.45
2.163
1.58
2.261
1.424
0.726
1.351
0.360
0.172
Eχ
Eχ
Eχ
Eχ
EΓ
EΓ
EΓ
EΓ
EΓ
Electron affinity
(eV)
(3.5) [125]
3.64
4.0
4.05 (4.07) [126]
4.03 (4.06) [126]
4.4
4.54 (4.90) [126]
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
a1 (1 − x) + a 2 x = a3
(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
E1 (1 − x) + E 2 x = E3
(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 E g = E (Γ6 ) − E (Γg ) varying as
E g = 1.424 + 1.247 x
(4.3)
in the direct gap region and with E g = E ( X 6 ) − E (Γg ) varying as
E g = 1.985 + 1.147( x − 0.45) 2
(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
χ e = 4.07 − 1.06 x
(4.5)
in the direct gap region (x < 0.45), and as
χ e = 3.64 − 0.14 x
(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:
∆EC = χ1 − χ 2 = 1.06 x
(4.7)
where x is less than 0.45. The results on capacitance-voltage C-V and current densityvoltage J-V measurements in heterojunction, however, yield the following empirical
relation [127-129]:
∆EC = 0.60∆E g
(4.8)
Another relevant property is the dielectric constant εAlGaAs which for AlxGa1-xAs is
given by
ε AlGaAs = (13.1 − 3.0 x)ε 0
(4.9)
87
Vaccum level
χ2
χ1
Ec2
∆Ec
Ec1
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
Compound
GaAs
AlAs
Al0.24Ga0.76As
Al0.2Ga0.8As
Al0.15Ga0.85As
Al0.9Ga0.1As
Al0.35Ga0.65As
AlxGa1-xAs material information.
Lattice
Constant
(Å)
5.6533
5.661
5.6551
5.6548
5.6545
5.6602
5.6560
Gap
(eV)
1.424
2.168
1.7233
1.6734
1.6111
2.1283
1.8605
Gap
(µm)
0.871
0.572
0.720
0.741
0.770
0.583
0.667
∆EC
(eV)
Eq 4.8
0.000
0.496
0.200
0.166
0.125
0.470
0.291
Affinity
(eV)
4.07
3.5
3.816
3.858
3.911
3.514
3.699
∆EC
(eV)
Eq 4.7
0.000
0.570
0.254
0.212
0.159
0.556
0.371
Dielectric
constant
(0.83 µm)
13.455
9.053
12.127
12.337
12.636
9.419
11.609
λ/(4n) at
0.83 µm
(nm)
56.57
68.97
59.59
59.08
58.37
67.61
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
AlAs
GaAs
InP
InAs
GaP
In0.53Ga0.47As
In0.52Al0.48As
(In0.53Ga0.47As)0.5
(In0.52Al0.48As)0.5
(In0.53Ga0.47As)0.6
(In0.52Al0.48As)0.4
(In0.53Ga0.47As)0.7
(In0.52Al0.48As)0.3
(In0.53Ga0.47As)0.44
(InP)0.56
Lattice
Constant
(Å)
5.660
5.653
5.869
6.058
5.451
5.868
5.867
Gap
(eV)
Barrier
(eV)
2.153
1.420
1.350
0.360
2.740
0.752
1.457
0.841
0.401
0.359
-0.235
1.193
0.000
0.423
Dielectric
constant
(1.55 µm)
8.237
11.364
10.037
12.388
9.322
12.469
10.243
5.868
1.055
0.182
11.156
3.340
116.014
5.868
0.988
0.142
11.395
3.376
114.791
5.868
0.925
0.104
11.693
3.420
113.318
5.868
1.038
0.172
10.659
3.265
118.690
Refractive
Index
(1.55 µm)
2.870
3.371
3.168
3.520
3.053
3.531
3.200
λ/(4n) at 1.55
µm (nm)
135.016
114.949
122.312
110.095
126.916
109.738
121.075
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:
E g (In1-x Ga x As) = 0.36 + 0.629 x + 0.436 x 2
(4.10)
E g (In1-x Al x As) = 0.37 + 1.91x + 0.74 x 2
(4.11)
and
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
E g ((In 0.52 Al 0.48 As) z (In 0.53 Ga 0.47 As)1-z ) = 0.76 + 0.49 z + 0.20 z 2
(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, latticematches to the InP substrate, and the formula to calculate its energy band gap is
E g ((In 0.53 Ga 0.47 As) z (InP)1-z ) = 1.35 - 0.775 z + 0.149 z 2
(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
Mobility (cm2/(V.s))
Energy band gap (eV)
Interface state density (cm-2)
Passivation Layer
Processing
Si
1350
1.12 (indirect)
<1010
MOS
Mature and low cost
GaAs
8600
1.42 (1.35) (direct)
>1012
/
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
Electron Mobility
(cm2/(V.s))
Hole Mobility (cm2/(V.s))
Energy band gap (eV)
Ge
3900
800
0.664 (indirect) /
0.805 (direct)
In0.53Ga0.47As
13800 (LPE)
11200 (MOCVD)
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 DXcenter 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 latticematched 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
In0.52Al0.48As
InGaP
P+-In0.53Ga0.47As
P+-InP
Dark current
< 1 pA/µm2 at 5V,
< 25 pA/µm2 at 15V,
< 300 pA/µm2 at 30V
1.6pA/µm2 at 10V
< 0.1 ~ 1 nA/µm2 at 5V
< 0.1 ~ 1 nA/µm2 at 10V
Barrier height
Al / In0.52Al0.48As: 0.8 eV
Au / In0.52Al0.48As: 0.82 eV
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
cos(2( β1 L1 + β 2 L2 ) + Ψ1 + Ψ2 ) = 1 .
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
cos(2( β1 L1 + β 2 L2 ) + Ψ1 + Ψ2 ) = 1 .
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.
light
50 nm nid Al0.24Ga0.76As Barrier
5 nm nid Al0.24Ga0.76As Spacer
117.5nm undoped
(λ0/4n) undoped Al0.24Ga0.76As (59.6nm)
Si δ-doping
5x1012 cm-2
DBR quarter
wave stacks
200nm GaAs Buffer
GaAs Substrate
Device structure of GaAs based resonant-cavity-enhanced HMSM
photodetector.
Figure 4. 2
The layer structure was grown by solid-source molecular beam epitaxy on a semiinsulating 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
40 nm n+(1.5*10^18 cm-3) GaAs cap
50 nm n-(6~8*1014cm-3) In0.52Al0.48As barrier
5 nm undoped In0.52Al0.48As spacer
Si δ-doping
1013cm-2
385.8 nm undoped In0.53Ga0.47As absorption layer
(λ/4n) Undoped InP (122.3nm)
20 periods
(λ/4n) In0.527Al0.144Ga0.329As (113.3nm)
25nm InP:Fe Buffer
InP Substrate
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 semiinsulating 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):
ε (ω ) = ε 1 (ω ) + iε 2 (ω )
(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 [KramersKronig relations] [123]:
100
ε 1 (ω ) = 1 +
ε 2 (ω ) = −
∞
2 ω 'ε 2 (ω ' )
dω '
∫
'
2
2
π 0 (ω ) − ω
(4.15)
∞
2 ωε 1 (ω ' )
dω '
∫
'
2
2
π 0 (ω ) − ω
(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 zincblende type semiconductors occur in the center of the Brillouin zone, where is has fourfold (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]
1
2
ε 1 (ω ) = A0 { f ( χ ) + [ E0 /( E0 + ∆0 )]3 / 2 f ( χ 0 )} + B0
(4.17)
f ( χ ) = χ −2 [2 − (1 + χ )1 / 2 − (1 − χ )1 / 2 ]
(4.18),
χ = hω / E0
(4.19),
χ 0 = hω /( E0 + ∆0 )
(4.20).
with
and
The constants A0 and B0 as a function of composition x, as determined by leastsquare fitting Eq.(4.17) with the experimental data, are found to be [125]:
A0 ( x) = 6.3 + 19.0 x
(4.21)
B0 ( x) = 9.4 − 10.2 x
(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
Band-gap energy
Egα (eV)
GaAs
1.424 (EgX)
Critical-point energy
(eV)
1.425
E0
1.765
E0+∆0
4.3.2.2
AlAs
2.168 (EgX)
AlxGa1-xAs
1.424+1.247x
(0<x<0.45)
1.900+0.125x+0.143x2
(4.5<x<1)
3.02
3.32
1.425+1.155x+0.37x2
1.765+1.115x+0.37x2
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
Material
InP
GaP
GaAs
InAs
Parameters used in the calculation of ε1(ω).
E0
1.35
2.74
1.42
0.36
E0+∆
1.45
2.84
1.76
0.79
A0
8.40
22.25
9.29
4.36
B0
6.60
0.90
7.86
10.52
A0 and B0 are given by the following two equations in (In0.53Ga0.47As)z(InP)1-z:
A0 ( z ) = 8.40 − 3.40 z
(4.23 a)
B0 ( z ) = 6.60 + 3.40 z
(4.23 b).
and
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
n( λ ) 2 = A1 +
B1 λ 2
λ 2 − C1
2
(4.24),
the empirical A1, B1, and C1 coefficients as a function of In0.52Al0.48As mole fraction z can
be obtained
A1 (z) = 9.689 − 1.012 z
(4.25 a),
B1 (z) = 1.590 − 0.376 z
(4.25 b),
C1 ( z ) = 1102.4 − 702.0 z + 330.4 z 2
(4.25 c).
and
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
R eflectivities of the bottom m irror
photon’s energy considered, the absorption effect is neglected here.
1.0
N=30
N=20
0.8
N=15
N=10
0.6
0.4
0.2
0.0
720
760
800
840
880
920
960
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
R eflectiv ity of th e b ottom m irro r
equal to 0.1µm.
1.0
N=30
0.8
N=20
0.6
N=15
0.4
N=10
0.2
0.0
1.4
1.5
1.6
1.7
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.
1.0
m=4
m=3
Quantum Efficiency
0.8
0.6
m=2
m=1
0.4
0.2
0.0
760
800
840
880
920
Wavelength (nm)
Figure 4. 6
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
2( β1L1 + β 2L2 ) + Ψ1 + Ψ2 = 2mπ . 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 2( β1L1 + β 2L2 ) + Ψ1 + Ψ2 = 2mπ . 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
1.0
m=4
Quantum Efficiency
0.8
m=3
0.6
m=2
0.4
m=1
0.2
0.0
1.4
1.5
1.6
1.7
Wavelength (um)
Figure 4. 7
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 closedform 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.
12
Sheet Charge Density (cm-2)
1.8x10
12
1.6x10
50 Å
12
1.4x10
70 Å
12
1.2x10
100 Å
12
1.0x10
11
8.0x10
12
4.0x10
12
8.0x10
13
1.2x10
13
1.6x10
13
2.0x10
-2
Figure 4. 8
various thickness of spacer layer. (GaAs based PD)
110
4.3.6
Electric field
Electric Field (V/cm )
4.3.6.1
Electric field profile in GaAs based PD
2.0x10
5
1.5x10
5
50 Å
modified Schroinger
and Poisson model
70 Å
100 Å
1.0x10
5
5.0x10
4
0.0
-1
10
0
1
2
3
10
10
10
10
Distance from the interface (Å)
4
10
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 selfconsistent 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 selfconsistent 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.
E lectric field (V /cm )
113
4.0x10
5
3.0x10
5
2.0x10
5
1.0x10
5
0.0
-2
10
10
-1
10
0
10
1
10
2
10
3
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
4.4
Drift velocity of electrons and holes in In0.53Ga0.47As [145]
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 currentvoltage 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
40µm
finger
40µm
gap
Metal
Semiconductor
Metal
light
50 nm nid Al0.24Ga0.76As Barrier
5 nm nid Al0.24Ga0.76As Spacer
117.5nm undoped
Si δ-doping
5x1012 cm-2
DBR quarter
wave stacks
200nm GaAs Buffer
GaAs Substrate
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.
light
Schottky
Schottky
50 nm n(6~8*1014cm-3)
In0.52Al0.48As
barrier
Si δ-doping
13
2
5 nm undoped In0.52Al0.48As spacer
385.8.nm undoped In0.53Ga0.47As absorption layer
(λ/4n) Undoped InP (122.3nm)
(λ/4n) In0.527Al0.144Ga0.329As (113.3nm)
25nm InP:Fe Buffer
InP Substrate
Figure 4. 14
InP based PD diagram.
15 periods
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
Q u a ntum E ffic ien cy
0.6
0.5
0.4
0.3
deviate from normal incident 45
o
normal incident
0.2
0.1
0.0
750
800
850
900
950
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 RCEHMSM 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.
-12
1.4x10
Photocurrent (a. u.)
-12
1.2x10
-12
1.0x10
-13
8.0x10
-13
6.0x10
-13
4.0x10
-13
2.0x10
0.0
700
750
800
850
900
950
1000
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
I Re = Are Pin + Bre
(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.
-3
1.0x10
20V
-4
Photo current (A)
1.0x10
-5
1.0x10
-6
1.0x10
-7
1.0x10
-8
1.0x10
-7
1.0x10
-6
1.0x10
-5
1.0x10
-4
1.0x10
-3
1.0x10
-2
1.0x10
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 modelocked 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
1.00
V oltag e (V )
5V
0.95
0.90
0.85
0
10
20
30
40
50
60
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
Frequency response
33 GHz.
1
0.9
0.8
0.7
0.6
0.5
5V
0.4
3dB:33GHz
0.3
0.2
0.1
1
10
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.
1.00
Frequency Response
Voltage(V)
5V
0.95
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.1
1
10
Frequency (GHz)
0.90
0
200
400
600
800
1000
Time (p sec)
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
Dark Capacitance (F)
a 2 µm finger width and a 4 µm gap respectively.
2.6x10
-14
2.4x10
-14
2.2x10
-14
2.0x10
-14
1.8x10
-14
1.6x10
-14
1.4x10
-14
W1G2
W1G4
W2G4
W2G2
0
2
4
6
8
10
12
14
16
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 bandedge 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
AlGaAs
AlGaAs
∆Ec
φn1
GaAs
cathode
φn1 cathode
anode
Ec
φp2
Ef
∆Ec Ec
Ef
φp2
GaAs
∆Ev
Ev
Ev
(a)
anode
VD2
∆Ev
(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.
-6
1x10
12.6µW
-7
1x10
-8
Current (A)
1x10
-9
1x10
-10
1x10
-11
1x10
Dark Current
-12
1x10
-13
1x10
0
4
8
12
16
20
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]
J n1 = An *T 2 e − βφn1 e β ( ∆φn1 −∆φn 2 ) (1 − e − βV1 )
= J ns e β ( ∆φn1 −∆φn 2 ) (1 − e − βV1 )
(5.2)
where An∗ is the effective Richardson constant for electrons, T is the temperature,
β = q / kT , ∆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.
Ec
φn1
∆Ec
Ef
Ev
φp2
∆Ev
(a)
Ec
φn1
∆Ec
Ef
∆Ev
δ-doping
cathode
Ev
φp2
VD2
(b)
AlGaAs
GaAs absorption
layer
anode
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 (φ p 2 + V D 2 − V2 ) , 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
Ec
φn1
V
(a)
Ev
φn1
V1
∆Ev
φp2
∆Ec
Ec
∆Ev
x2
x1
V2
Ev
δ-doping
φp2
(b)
VD2-V2
AlGaAs
GaAs absorption
layer
cathode
anode
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
∂ 2 p p − pn0
−
=0
D pτ p
∂x 2
(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
p − p n 0 = Ae
x / Lp
+ Be
− x / Lp
(5.4)
137
where Lp is the diffusion constant, which equals
D pτ p . The boundary conditions are
(1) at x = x1, p = p n0 e ( − qV1 / kT ) , and (2) at x = x2,
J p 2 = A p *T 2 e
− β ( φ p 2 +VD 2 −V2 )
(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):
J p1 = qD p
=[
+
dp
dx
x1
qD p p n 0 tanh(( x 2 − x1 ) / L p )
Lp
J ps e − βVD 2
cosh[( x 2 − x1 ) / L p ]
(1 − e − βV1 )
(5.6).
(e βV2 − 1)]
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]:
J = J n1 + J p1
= J ns e β ( ∆φn1 −∆φn 2 ) (1 − e − βV1 )
+[
+
qD p p n 0 tanh(( x 2 − x1 ) / L p )
Lp
J ps e − βVD 2
cosh[( x 2 − x1 ) / L p ]
(1 − e − βV1 )
(5.7)
(e βV2 − 1)]
where J ns = An *T 2 e − βφn1 and J ps = A p *T 2 e
− βφ p 2
. 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 z = x + iy 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 dV / dz
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
qn s
where εGaAs is the dielectric permittivity of the semiconductor and ns is the
2ε GaAs
2DEG sheet charge density. This function has opposite signs at the two sides of the cut
made between the singular points z = id dep and z = −id dep . Hence, the discontinuity of
the electric induction vector is equal to qNs and dV / dz is an even function. Therefore, it
is sufficient to solve the problem for the y ≥ 0, x > 0 quadrant. The conformal
transformation w = (
z
d dep
) 2 converts this quadrant into the half-plane Im w > 0. Then the
problem reduces to the solution of the Laplace equation for dV / dw whose real part is
equal to zero for w > 0 and w < -1 and whose imaginary part is equal to
qn s d dep /[4ε GaAs (− w)1 / 2 ] for 0 > w >-1. Using a standard procedure, the gradient of the
complex potential is obtained as follows:
( z 2 + d dep 2 )1 / 2 + d dep
qn s
dV / dz = −i
ln
2πε GaAs ( z 2 + d dep 2 )1 / 2 − d dep
(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:
( z 2 + d dep 2 )1 / 2 + d dep
( z 2 + d dep 2 )1 / 2 + z
qn s
V = −i
+ d dep ln
[ z ln
] (5.9)
2πε GaAs
( z 2 + d dep 2 )1 / 2 − d dep
( z 2 + d dep 2 )1 / 2 − z
w
x
depletion
region
p+ drain
y
2D electron gas
+++++
z
Figure 5. 13
R
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
(d dep 2 − y 2 )1 / 2 + d dep
qn s
V ( y) =
[ y ln
+ 2d dep sin −1 ( y / d dep )]
2
2 1/ 2
2πε GaAs
d dep − (d dep − y )
Hence, the potential V at y = ddep is given by
(5.10)
141
V =
qn s d dep
(5.11)
2ε GaAs
It is noteworthy that for a two 2DEG the relation between bias and depletion
region is calculated from V =
qn s d dep
2ε GaAs
[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.
C urrent (A )
142
1x10
-10
1x10
-11
1x10
-12
1x10
-13
1x10
-14
1x10
-15
360
350
340
330
320
310
300
290
280
0
2
4
6
8
10
12
K
K
K
K
K
K
K
K
K
14
Bias (V)
Current (A)
(a)
1x10
-10
1x10
-11
1x10
-12
1x10
-13
1x10
-14
1x10
-15
360 K
350 K
340 K
330 K
320 K
310 K
300 K
Tamb
0
2
4
6
8
10
12
14
Bias (V)
(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.
-20
-22
Ea=-0.34 eV at 15 V
Ea=-0.42 eV at 10 V
Ea=-0.50 eV at 5 V
-24
ln (current)
ln (current)
-22
Ea=-0.60 eV at 15 V
Ea=-0.65 eV at 10 V
Ea=-0.686 eV at 5 V
-24
-26
-26
-28
-28
32
34
36
38
-1
1/kT (eV )
(a)
40
42
32
34
36
38
40
42
-1
1/kT (eV )
(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]:
C≈
where
πε GaAs A
(5.12)
2(W + G ) log(2(1 + κ ) /(1 − κ ))
εGaAs
is
the
GaAs
permittivity,
A
is
the
interdigited
area,
and
κ = (1 − tan 4 (πW / 4(W + G )))1 / 2 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
-13
2x10
-14
2.6x10
W1G2
W1G4
W2G4
-13
1x10
W1G2
W1G4
W2G4
W2G2
-14
2.4x10
-14
-14
8x10
-14
4x10
0
0
2.2x10
-14
2.0x10
-14
1.8x10
-14
1.6x10
-14
2
4
6
8
10
12
14
16
1.4x10
0
2
4
6
8
Bias (V)
Bias (V)
(a)
(b)
10
12
14
16
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
Geometry
W1G2
W1G4
W2G2
W2G4
5.2.5
Measured and theoretical capacitance values.
undoped device
(fF)
24.4
11.5
14.4
δ doped device
(fF)
26
16.5
21.5
16
calculated values
(fF)
26.2
12.4
25.2
13.0
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.
1.00
5V
1
0.90
Frequency Response
Voltage (V)
0.95
0.85
0.1
1
10
Frequency (GHz)
0.80
0
10
20
30
40
50
60
Time (psec)
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.
5
5
4
W2G2
3
2
1
4
8
12
16
4
Peak Amplitude (V/mW)
W1G2
W1G4
3
W2G4
2
1
0
20
4
8
12
Voltage (V)
16
20
Voltage (V)
(a)
(b)
50
40
W1G2
W1G4
W2G2
30
3dB (GHz)
3dB (GHz)
40
30
20
20
4
8
12
Voltage (V)
(c)
16
20
W2G4
4
8
12
16
20
Voltage (V)
(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.
W2G2
2
1
0
4
W1G2
4
8
12
16
Peak Value (V/mW)
3
3
W2G4
2
1
0
20
W1G4
4
8
Voltage (V)
(a)
16
20
(b)
8
8
6
W1G4
W1G2
3dB (GHz)
3dB (GHz)
12
Voltage (V)
4
W2G2
4
W2G4
2
0
0
4
8
12
Voltage (V)
(c)
16
20
4
8
12
16
20
Voltage (V)
(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.
As
Ga
Al 0.9
s
aA
4G
Al 0.2
100 nm
100 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.
(a)
1
A l 0 . 9 G a A s / A l 0 .2 4 G a A s
in 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
2
3
(b)
4
5
6
7
8
9
10
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.
180
R eflectivity (a.u.)
160
140
120
100
80
60
40
700
800
900
1000
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.
30 nm n+(1.5*1018 cm-3) GaAs cap
50 nm n-(6~8*1014cm-3) Al0.24Ga0.76As
barrier enhancement layer
5 nm undoped Al0.24Ga0.76As spacer
(λ/4n) Undoped Al0.24Ga0.76As
(59.6nm)
(λ/4n) Al0.9Ga0.1As (67.6nm)
20
periods
quarter
wave
stack
117.5nm undoped GaAs absorption
layer
(λ/4n) Undoped Al0.24Ga0.76As
(59.6nm)
(λ/4n) Al0.9Ga0.1As (67.6nm)
25nm GaAs Buffer
25nm GaAs Buffer
GaAs Substrate
GaAs Substrate
(a)
Figure 5. 23
5*1012cm-2
Si δdoping
20
periods
quarter
wave
stack
(b)
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.
180
180
160
160
(a)
140
120
Reflectivity
Reflectivity
120
100
80
100
80
60
60
40
40
20
(b)
140
700
800
900
1000
20
700
Wavelength(nm)
800
900
1000
Wavelength(nm)
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
0.2
Quantumefficiency (a.u.)
Quantumefficiency (a.u.)
0.2
0.1
0.1
0.0
650 700 750 800 850 900 950 1000 1050
0.0
650 700 750 800 850 900 950 1000 1050
Wavelength(nm)
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.
Light
Schottky
Schottky
n-AlGaAs 500Å
AlGaAs spacer 100Å
GaAs 5000Å
2DEG
GaAs Substrate
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 resistorcapacitor (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]:
r r
i (t ) = eν • E w
(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.
Z
X
Schottky
Schottky
Schottky
0
V
0
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 electrooptically 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
Schottky
Schottky
500Å Al0.24Ga0.76As
n-(6~8*1014cm-3) barrier enhancement layer
Si δ-doping
5 x 1012cm-2
Al0.24Ga0.76As 50Å
GaAs 1175Å
2DEG
(λ/4n) Undoped Al0.24Ga0.76As (596 Å)
20
periods
HMSM (Sh-Sh):
Schottky contact on
both sides of the
barrier enhancement
layer.
(λ/4n) Al0.9Ga0.1As (676 Å)
25nm GaAs Buffer
GaAs Substrate
Ohmic
Schottky
500Å Al0.24Ga0.76As
Si δ-doping
5 x 1012cm-2
Al0.24Ga0.76As 50Å
GaAs 1175Å
2DEG
(λ/4n) Al0.9Ga0.1As (676 Å)
25nm GaAs Buffer
GaAs Substrate
20
periods
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
179
500Å
Schottky
Al 0.24Ga 0.76As
layer
Schottky
Si δ-doping
5 x 10 12cm -2
Al0.24Ga 0.76 As 50Å
GaAs 1175Å
2DEG
(λ/4n) Undoped Al 0.24Ga 0.76As (596 Å)
20
periods
(λ/4n) Al0.9Ga 0.1As (676 Å)
25nm GaAs Buffer
HMSM (Sl-Sl):
Schottky contact
on both sides of
the 2DEG.
GaAs Substrate
Ohmic
500Å Al0.24Ga0.76As
n-(6~8*1014cm-3) barrier enhancement
layer
Schottky
Si δ-doping
5 x 1012cm-2
Al0.24Ga0.76As 50Å
GaAs 1175Å
2DEG
(λ/4n) Al0.9Ga0.1As (676 Å)
25nm GaAs Buffer
GaAs Substrate
20
periods
HMSM (Oh-Sl):
Ohmic contact on
one side of the
barrier enhancement
layer, and Schottky
side of the 2DEG
180
Source
Drain
Gate
Ohmic
Ohmic
Schottky
500Å Al0.24Ga0.76 As
n-(6~8*1014 cm-3) barrier enhancement layer
Si δ-doping
5 x 1012cm-2
Al0.24Ga0.76 As 50Å
GaAs 1175Å
2DEG
20
periods
HEMT with
Ohmic contacts
(λ/4n) Al0.9Ga0.1As (676 Å)
25nm GaAs Buffer
GaAs Substrate
Figure 6. 5
Series of GaAs based heterostructure RCE devices.
181
Schottky
Schottky
500Å In0.52Al0.48As
Si δ-doping
1 x 1013cm-2
In0.52Al0.48As 50Å
In0.53Ga0.47As 3858Å
2DEG
(λ/4n) Undoped InP (1223 Å)
15
periods
HMSM (Sh-Sh):
Schottky contact on
both sides of the
barrier enhancement
layer
(λ/4n) In0.527Al0.144Ga0.329As (1133 Å)
25nm InP Buffer
InP Substrate
Ohmic
Schottky
500Å In0.52Al0.48As
Si δ-doping
1 x 1013cm-2
In0.52Al0.48As 50Å
In0.53Ga0.47As 3858Å
2DEG
(λ/4n) In0.527Al0.144Ga0.329As (1133 Å)
25nm InP Buffer
InP Substrate
15
periods
HMSM (Oh-Sh):
Ohmic contact on
one side of the
barrier enhancement
layer, and Schottky
side of the barrier
enhancement layer
182
500Å
In0.52 Al0.48 As
Schottky
Schottky
Si δ-doping
1013cm-2
In0.52 Al0.48 As 50Å
In0.53Ga0.47As 3858Å
2DEG
15
periods
HMSM (Sl-Sl):
Schottky contact
on both sides of
the 2DEG
(λ/4n) In0.527 Al 0.144Ga0.329As (1133 Å)
25nm InP Buffer
InP Substrate
Ohmic
500Å In0.52Al0.48As
Schottky
In0.52Al0.48 As 50Å
In0.53Ga0.47As 3858Å
2DEG
(λ/4n) In0.527Al0.144Ga0.329As (1133 Å)
25nm InP Buffer
InP Substrate
Si δ-doping
1013cm-2
15
periods
HMSM (Oh-Sl):
Ohmic contact on one
side of the barrier
enhancement layer,
and Schottky contact
on the other side of
the 2DEG
183
Source
Ohmic
Drain
Gate
Ohmic
Schottky
500Å In0.52 Al0.48 As
n-(6~8*1014 cm -3) barrier enhancement layer
Si δ-doping
1013cm-2
HEMT with
Ohmic contacts
In0.52 Al0.48 As 50Å
In0.53Ga0.47As 3858Å
2DEG
15
periods
(λ/4n) In0.527 Al 0.144Ga0.329As (1133 Å)
25nm InP Buffer
InP Substrate
Figure 6. 6
Series of InP based heterostructure REC devices.
184
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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
t=
2l
Vg
(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
Vg =
c
ε re
(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
Photodetector
l=2.25mm
l=2.25mm
45.5µm
2b=96µm
2a=5µm
45.5µm
Figure A. 1.
signal
ground
Coplanar stripe transmission line scheme with a 50 µm pitch.
The definition of the pitch for CPS is given by
pitch = 2 × a + (b − a)
(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
pitch = b +
c−b
2
(A.4)
where 2a is the width of the signal line, 2b and 2c are shown in the CPW schematic (Fig.
A.2).
199
ground
500µm
Photodetector
58µm
l=2.25mm
2c=1200µm 2b=200µm
l=2.25mm
signal
2a=84µm
58µm
500µm
Figure A. 2.
ground
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].
k' = 1− k2
(A.5)
π
K (k )
for 0 ≤ k ≤ 0.707
=
'
K (k ) ln[2 × (1 + k ' ) /(1 − k ' )]
(A.6 a)
K (k ) 1
= ln[2 × (1 + k ) /(1 − k )] for 0.707 ≤ k ≤ 1
K ' (k ) π
(A.6 b)
200
The formula for calculating the characteristic impedance of CPS are given by Eq.
(A.7)
k1 =
a
b
(A.7 a)
k2 =
sinh(πa / 2h)
sinh(πb / 2h)
(A.7 b)
ε re = 1 +
Z 0cs =
ε r − 1 K (k2 ) K ' (k1 )
2
K ' (k2 ) K (k1 )
120π K (k1 )
ε re K ' (k1 )
(A.7 c)
(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
k3 =
a 1 − b2 / c2
b 1 − a2 / c2
(A.8 a)
k4 =
sinh(πa / 2h) 1 − sinh 2 (πb / 2h) / sinh 2 (πc / 2h)
sinh(πb / 2h) 1 − sinh 2 (πa / 2h) / sinh 2 (πc / 2h)
(A.8 b)
ε re = 1 +
Z 0cp
ε r − 1 K ( k 4 ) K ' ( k3 )
2
K ' ( k 4 ) K ( k3 )
30π K ' (k 3 )
=
ε re K (k 3 )
(A.8 c)
(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
140
140
120
120
100
100
80
80
60
60
40
40
20
0.01
0.1
Pitch (µm)
Simulation Results
Characteristic impedance (Ω)
A3
20
0.7
Ratio a/b
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 l =
Vg × t
2
= 2.25mm . Figure A.4 shows the simulation results for the pitch of 100
160
160
140
140
120
120
100
100
80
80
60
60
40
40
20
0.01
0.1
Pitch (µm)
Characteristic impedance (Ω)
µm.
20
0.7
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 l =
for CPW with a 350 µm pitch.
Vg × t
2
= 2.25mm . Figure A.6 shows the simulation results
203
Photodetector
l=2.25mm
l=2.25mm
90µm
2b=190µm
2a=10 µm
90µm
Figure A. 5.
Charateristic impedance (Ω)
ground
Coplanar strip transmission line scheme with a 100 µm pitch.
140
120
100
80
60
40
20
0.01
0.1
0.7
Ratio a/b
Figure A. 6.
signal
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 l =
Vg × t
2
= 2.25 × 10− 3 m = 2.25mm .
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.

Novel Heterostructure Metal-Semiconductor-Metal

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